Production and processing of graphene and related materials

The concept of solution based bottom-up synthesis relies on the preparation of large polycyclic aromatic hydrocarbons (PAHs), often referred to as nanographenes [22, 23] The reaction is based on the intramolecular oxidative cyclodehydrogenation of corresponding oligophenylene precursors and was extended from defined molecules to polymers, i.e. from PAHs to GNRs [23]. Since then, the synthesis of GNRs through intramolecular cyclodehydrogenation of polyphenylene polymers was achieved, through AA-, AB- and A2B2-type polymerizations as summarized in Refs. [24–27].

The most critical issue in the solution-synthesis is to achieve high (>600 000 g mol⁻¹ on average by Diels Alder (DA) polymerization) molecular weight of the precursor polymer. While the width of GNRs is determined by the monomer dimensions, the molecular weight is directly proportional to the number of repeating units, therefore proportional to the length of the resulting GNR after the cyclodehydrogenation -graphitization- step. E.g. DA polymerization provides a molecular weight  >600 000, on average corresponding to a length of 600 nm [23].

Figure I.1 provides an overview of the polymerization routes explained in what follows along with the relevant references.

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A2B2-Polymerization requires two monomers with complementary functional groups A and B (see figure I.1). These can be A  =  Cl, Br, I, Otf (Trifluoromethanesulfonate) in combination with B being a boronic acid or boronic acid ester. In this case, the underlying carbon-carbon bond formation is based on the Suzuki-reaction. In contrast, if A is a diene and B a dienophile, it belongs to the reaction class of a Diels-Alder reaction. The most prominent combination for a Diels-Alder reaction to form PAHs is the combination of a cyclopentadienone and a substituted acetylene [28, 29]. The benefit of this inverse electron demand- Diels-Alder reaction is the tandem cycloaddition and carbon-monoxide-extrusion reaction. Therefore, both reaction classes require different protocols. In all cases, the polymerization follows a step-growth mechanism and is defined by Carother's equation [30]. In this case, the functionalized monomers first react into monomers, dimers, trimer, oligomers and finally high molecular weight polymers. The stoichiometry of both monomers is of fundamental importance to achieve a high degree of polymerization and thus molecular weight. From our experience, a small deviation imbalance in stoichiometry or impurity of at least one monomer of even 2% will not allow high molecular weight polymer formation. To ensure exact stoichiometry, the purity of monomers as well as dryness is a critical issue. A balance used to weight the monomers must require an accuracy of 0.1 mg. In a theoretical example, an impurity of 2% at a degree of polymerization of 98%, will cut molecular weight to half [30].

A Suzuki reaction is a palladium catalyzed reaction. The active catalyst is a Pd(0) species which is oxygen sensitive. This protocol requires the preparation of the reaction under inert condition. To exclude oxygen from the reaction, both monomers and a base (potassium carbonate) are usually evacuated in a Schlenk-type glassware. Afterwards, the solvents (a combination of toluene, ethanol and water, typically 3:1:1), is bubbled with Ar for at least 20 min when a total volume of solvent is in the range of 100–200 ml. It is recommended to apply high (~1200 rpm) stirring during bubbling to ensure a complete saturation of the solvent mixture with Ar. After the reaction apparatus is in contact with the preheated oil bath, the catalyst (Pd(PPh₃)₄) is added under Ar. During the reaction, no oxygen should enter the reaction chamber. In addition, it is recommended to cover the reaction chamber with Al foil to protect it from light. To track the reaction, samples can be taken in different intervals of 15 min to several hours, always under Ar protection. These (0.1 ml) can be quenched by adding a drop of water and extracted with an organic solvent such as dichloromethane or chloroform and are required for tracking the molecular weight increase by mass spectrometry [31]. Matrix-assisted laser desorption/ionization-time of flight (MALDI-TOF) [31] using tetracyanoquinodimethane (TCNQ) as matrix is suitable for GNRs.

With prolonged reaction time in the order of hours to days, the molecular weight of the resulting polymer will increase. However, the solubility of the formed polymer will decrease. Before the polymer precipitates out of the solution, the residual terminal functional groups (halogen or boronic acid) must be 'end-capped', to avoid undesired atoms at the terminal positions of the GNR. The 'end-capping' must be performed before precipitation of the polymer to ensure conversion of unreacted functional groups. This is achieved by adding a suitable end-capper, e.g. bromo-benzene followed by adding an excess of phenylboronic acid in the respective solvent. The reaction is continued for several hours (at least one) to ensure the full conversion of the terminal functional groups. Afterwards, the reaction is quenched by the addition of water. After extraction and precipitation into typically methanol, the crude polymer can be characterized by mass spectrometry (MS) and analytical site exclusion chromatography (SEC) using polystrene or Poly(p-phenylene) as internal standard, although the molecular weight values derived from SEC analyses are only rough estimations and the absolute molecular weights may be obtained by laser light scattering experiments [32].

Nevertheless, the SEC data are useful for qualitative comparison of the molecular weights of different polymer samples and a crucial indicator for the resulting GNR's length. At this stage, it is recommended to narrow the broad molecular weight distribution by gel permeation chromatography or centrifugation into fractions of a lower polydispersity index (<1.5). UV–vis absorption spectroscopy can also provide a qualitative analysis of the polymer length since the wavelength of maximum absorption will red-shift with extension of conjugation length.

In contrast to the Suzuki and Yamamoto reaction, the Diels Alder reaction does not require a metal catalyst and can be performed only by the thermal treatment of both monomers [32].This is typically conducted in in either in diphenylether as solvent (reflux, 20–28) or in the pure melt of monomer at T ~ 260 °C–270 °C during 5 h. However, the constant solubility of the propagating chain must be ensured similar to the Suzuki polymerization.

AA-type Yamamoto polymerization (see figure I.1) is unrestricted by the stoichiometry problem and is thus easier to handle than A2B2-type polymerization methods [33, 34]. Furthermore, it is a highly efficient even in sterically demanding systems [35, 36] which can improve the molecular weights (M_W  =  52 000 g mol⁻¹, M_n  =  44 000 g mol⁻¹) of the resulting polyphenylene precursors over the ones obtained by the Suzuki reaction.

The catalytic Ni(0) is not as stable as the Pd(0) derivative. Therefore, for the preparation of the reaction mixture (Ni(COD)₂, COD, bipy in THF), precaution in avoiding both oxygen and light must be taken. As a general rule the active catalyst system is deep purple. We observe that it will quickly turn dark in contact with traces of oxygen.

Another effective way to overcome the issues of A2B2-type polymerisations and the labile Ni(0) catalysts is to take advantage of AB-type reactions. AB-polymerizations for the solution synthesis of GNRs are established for Diels-Alder and Suzuki protocols (see figure I.1). Theyovercome the issue of stoichiometry and result in precursor polymers with high molecular weight.

The cyclodehydrogenation of precursor polymers usually follows a similar protocol. The Scholl-reaction, an oxidative cyclodehydrogenation using Iron(III)chloride as both oxidant and Lewis acid is the most used. The handling of the reaction is similar for a broad variety of GNRs (see figure I.1).

In a typical procedure, the precursor polymer is dissolved in unstabilized dichloromethane (DCM), which is saturated with Ar by bubbling for 15 min. It is recommended to apply a continuous DCM saturated Ar stream through the reaction chamber. As a starting point for novel systems, usually six FeCl₃ per hydrogen to be removed are recommended as oxidant. The FeCl₃ oxidant is added as suspension (~100 mg per ml) in nitromethane.

Samples can be taken in sequential time frames of 15 min to days and analyzed after quenching of methanol. Due to the decreased solubility of the planarized GNR compared to precursor polymers, it is recommended to use MALDI-TOF MS, as well as absorption and Fourier transform infrared spectroscopy (FTIR) for both qualitative and quantitative verification of the degree of cyclodehydrogenation. One of the most dominant side reactions is the formation of chlorinated species. The amount of chlorination can be controlled by the amount of FeCl₃ equivalents (6–12), as well as the reaction time, from minutes to days. We conduct the reaction generally at RT.

On-surface bottom-up use of specifically designed molecular precursor monomers that carry the full structural information of the final GNR together with leaving groups that can be activated on the surface, so that the target structure is built by establishing covalent bonds between activated sites of adjacent precursor monomers. By this approach, selective growth of a single type of GNR is possible [21], and depends solely on the choice of the precursor monomer and an activation protocol that triggers the surface-assisted reaction steps under optimized conditions. Advances in GNR fabrication and characterization are described in Ref. [37].

The bottom-up synthesis of GNRs on surfaces critically depends on the atomic perfection of the used precursor monomers as well as control over the surface-assisted synthesis steps [21]. In the case of 1d target structures (such as for the case of GNRs) this is even more pronounced, since any defect changes the electronic properties or may act as a growth stopper. It is therefore crucial to start with ultrapure precursor monomer samples so that undesired coupling configurations arising from contaminations are minimized. We find that purity judged from nuclear magnetic resonance (NMR) spectroscopy is not sufficient in order to guarantee the lowest defect density and maximum GNR length, so that precursor monomer samples need to be further purified with up to eight recrystallization steps. Similarly important is the preparation of 'clean' growth substrates: Au(1 1 1) single crystals were used or Au thin films on mica [1725]. The subsequent surface-assisted synthesis steps are schematically depicted in figure I.2.

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All steps are accomplished at a pressure below 2 · 10⁻⁹ mbar while heating the sample to a specific T. In the first step, precursor monomers are deposited on a clean substrate held at T₀. Quartz crucibles that are resistively heated up to the T needed are used for maintaining a precursor monomer flux of 0.1 nm per minute at the sample position, as determined with a quartz microbalance. The sample temperature is then raised to T₁ for the halogen cleavage (activation) and to T₂ for the polymerization of the activated precursors. Finally, GNRs are formed by triggering cyclodehydrogenation of the polymers by heating the growth substrate to T₃ [37]. While each of these steps is crucial for GNR synthesis, not all of the intermediate products are easily accessible for structural characterization. E.g. monomer activation at T₁ ideally leads to doubly activated precursor monomers (biradicals) that coexist with the cleaved halogens at the surface. Practically, however, this phase is often not accessible because the activated species frequently undergo polymerization directly at these T [21].

This implies that the activation barrier related to diffusion and covalent bond formation between the biradical species is smaller or equal to the energy barrier for halogen bond cleavage [38]. Deposition, activation, and polymerization steps can be combined into a single step by depositing precursor monomers directly at the polymerization temperature T₂  =  450 K. The time for this combined step is the deposition time (1–10 min, depending on target GNR coverage) plus 15 min holding time [37]. This step is followed by the cyclodehydrogenation step, which is triggered by increasing the temperature to T₃  =  630 K and holding it for 15 min. It is crucial not to exceed this T in order to avoid further activation of the formed GNRs. For higher T₃  ≈  660 K covalent crosslinking of GNRs was found [39], as well as the formation of GNRs of multiple widths related to partial edge dehydrogenation of GNRs, which triggers GNR fusion (cross-dehydrogenative coupling) to form seamless higher-order GNRs [39]. After cyclodehydrogenation, the sample is cooled to RT and either transferred to a connected scanning tunneling microscope for in situ characterization (see section IX.1) or directly taken out of the UHV chamber for characterization and/or further processing under ambient conditions.

The above mentioned parameters are valid for the growth of GNRs on Au(1 1 1), for which the highest quality is achieved for all reported GNR types [1726]. GNR synthesis under less stringent conditions was also reported [40]. Using a CVD setup, the synthesis of Chevron GNRs [41] and 9-AGNRs [42] were achieved.

An overview on published GNR structures is given in figure I.3. The most frequently used halogen atom is Br. The two main reasons for using Br is its better synthetic accessibility for most of the precursor monomers (as compared to I) and lower reactivity with the growth substrates (as compared to Cl [43]).

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Depending on the choice of the precursor monomer, the selective synthesis of AGNRs with different width and bandgap was achieved [21, 44, 48, 49]. On-surface synthesis of ZGNRs was demonstrated for 6-ZGNRs using a methyl-based monomer design [57]. Chiral GNRs with a controlled sequence of armchair and zigzag segments along the GNR edge were made based on halogen-substitution of bianthryl [58]. GNRs with a controlled width-modulation along the axis, the so-called Chevron GNRs, were synthesized based on dibromo-substituted 1,2,3,4-tetraphenyltriphenylene [21]. This monomer design in particular, is well accessible for substitutional doping [54, 55, 1727]. Since chemical doping is achieved at the level of monomer synthesis, a fully controlled level of doping and periodic arrangement of the doping sites is reached in the final GNR. Chevron GNRs were fabricated with a number of nitrogen-substitution patterns [54–56]. For 7-AGNRs, substitutional boron-doping was achieved allowing to controllably modify the electronic properties [51, 52]. The combination of different precursors during the polymerization step gives access to different GNR heterostructures with additional opportunities, making specific electronic properties at the interfaces of dissimilar GNR segments available [48, 59–62]. Width-modulated GNRs were prepared, allowing to achieve distinct topological quantum phases [63, 64].

The main method applied for developing new bottom-up synthesized GNR structures is in situ scanning tunneling microscopy (STM, see section IX.1). It allows accessing the growth at the surface-related synthesis steps by interrupting the growth protocol (figure I.2) after a specific step and, subsequently, transferring the substrate to a connected STM chamber. Beside coverage determination, STM was used for the determination of polymer length after the polymerization step as well as for the determination of possible undesired coupling motifs that can occur by either not entirely purified precursor monomer batches or a not fully selective monomer design, which potentially allows for covalent coupling configurations that are not compatible with the envisaged final GNR structure. With the exception of 5-AGNRs, polymerization of the activated precursor monomers yields structures where not all molecular subunits are planar with respect to the substrate surface [21, 48]. The related apparent height imaged by STM is for all monomers above 0.25 nm, higher than the apparent height of the final GNR structure (~0.19 nm). Using this sensitivity, STM allows for a direct access to the onset T of the cyclodehydrogenation step by identifying polymer segments, where lowered apparent height indicates the related planarization of the polymer to the final GNR. For the investigation of individual GNRs, T below ~25 K are needed to suppress their mobility on the surface (figure I.4).

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An even higher resolution is achieved by using non-contact atomic force microscopy (nc-AFM) where the tip apex can be decorated with specific molecules or atoms to yield unprecedented insight into the chemical structure of the synthesized carbon nanostructures [66]. Tungsten tips attached to a tuning fork sensor [67] have been used in a low-T STM (ScientaOmicron) functionalized with CO molecules by dosing CO onto the surface and a controlled pick-up procedure [68]. By recording the frequency shift image at constant height (figure I.4(b)), the chemical structure of GNRs can be visualized with a resolution that is going down to individual chemical bonds. The sensitivity is high enough to resolve, e.g. additionally attached hydrogens at ZGNR edges (H₂- instead of H-termination) [57]. With this unique structural sensitivity, nc-AFM is complementary to STM (see section IX.1), which is only indirectly sensitive to the atomic composition by recording an apparent structure defined by the local density of states near the Fermi level. The constant-height imaging mode, however, can only be applied to the flat final GNR structures [48]. Non-planar structures, such as the used precursor monomers and the polymer intermediates, are hardly accessible by nc-AFM due to the related 'constant height' imaging mode [66].

The main ex situ characterization tool applied to GNRs is Raman spectroscopy (see section IX.2/Raman) [1714]. Owing to their atomically defined structure, GNRs present well defined Raman peaks (figure I.4(c)). The main peaks are the G and D modes with overtones and the width-dependent radial-breathing-like mode (RBLM) (~396 cm⁻¹ for 7-AGNRs) [40]. The D peak is intrinsic for GNRs due to the presence of edges [1715]. For laser energies ranging from 457 to 633 nm, between 1–2 mW power were used (higher power can result in thermal effects at ambient conditions [1725]). For laser energies in the infrared range (785 nm) a max of 10 mW is used [1725]. It is important to select the photon energy of the laser source close to the GNR bandgap to be in resonance [48]. For 7-AGNRs with an optical band gap of 1.9 eV [69], Raman spectra were recorded using a green laser (532 nm, 2.33 eV). For 9-AGNRs with an optical band gap of 1.1 eV [70], Raman spectra were recorded with an infrared laser line (785 nm, 1.55 eV). Exchanging the two laser lines for both examples leads to a loss of resonance conditions and the width-characteristic RBLM mode cannot be resolved anymore [1725].

The on-surface synthesis of GNRs relies on the catalytic action of the metallic growth substrate, and therefore requires their transfer onto dielectric substrates for further characterization of their electronic or optical properties. Similarly, in order to explore GNRs as active materials in electronic or optoelectronic devices, their transfer to dielectric substrates is required. The potential of GNR-based devices was demonstrated by the realization of GNR-based field effect transistors (FETs) with an on current of 1 µA and on/off ratio of 10⁵ [71, 72]. Furthermore, devices using CVD-GNRs as active material were reported with high on/off ratio and high photoresponsivity of 5  ×  10⁵ A W⁻¹ [41, 42]. Transfer was achieved using a sacrificial PMMA layer deposited onto the as-grown GNRs [72], stripped off after GNR transfer to the target substrate. A transfer method was developed allowing for the transfer of GNRs without PMMA, which avoids possible contamination problems related to PMMA residues [40, 55]. This relies on is delamination of Mica from a Mica/Au/GNR stack in an hydrochloric acid, from which the remaining Au/GNR stack is picked up with the target substrate. In a last step, the Au layer is then dissolved leaving a clean GNR film (without Au or iodine residues) on the target substrate. To do so, the Mica/GNR/Au stack was placed on concentrated (38%) hydrochloric acid (HCl) with the Au/GNR film facing up. After 15–20 min the mica detaches from Au. Once the mica is detached, the acid is removed from the container. In order to prevent sticking of the Au film at the container walls, it is important to not remove the acid completely in one step. After initially removing ¾ of the acid, water is added and the liquid removed in five iterative steps. In the last dilution step, the container is kept full of water for the pickup of the Au film with the target substrate. It is important that the target substrate is free of any impurities.

With the help of tweezers, the target substrate is approached (facing down) and pressed against the floating Au/GNR film until they stick together. The merged Au/GNR/substrate stack is then pulled out of the water. At this stage, the Au film is usually not completely flat on the substrate. In order to increase the contact between Au film and substrate, 1–2 drops of pure ethanol are added and dried under ambient conditions. Once dried, the Au/GNR/substrate stack is further heated on a hot plate (100 °C, 10 min). This two-step process results in a flattening of the Au film on top of the target substrate. The Au film was then removed by adding 1–2 drops of Au etchant (KI/I₂, no dilution) on top of the Au film and waiting until the Au film was completely etched away (around 5 min). Finally, to clean the GNRs/substrate, this was soaked in water (5–10 min), rinsed with 20–30 ml of acetone/ethanol and water and finally dried under N₂ flux [1725].

Using this method, 5-AGNRs, 7-AGNRs, 9-AGNRs and Chevron GNRs were transferred to SiO₂, CaF₂, Al₂O₃, glass slides and TEM grids (lacey carbon supported graphene, TedPella.com). The main characterization tool used to prove that the structure of the GNRs remains intact upon transfer was Raman spectroscopy. An example of Raman spectra taken before and after transfer of 7-AGNRs is in figure I.4(c)). All the characteristic 7-AGNR modes are present in the spectrum taken after transfer. Most importantly, the RBLM at 397 cm⁻¹ remains equally intense and does not show significant broadening.

Molecular self-assembly of aromatic molecules can be performed from solvents [73, 83] or by vapor phase deposition [84, 85]. For the self-assembly on coinage metal substrates such as Cu, Ag or Au, typically thiol functional groups are employed providing a covalent binding of the molecules to the substrate [86]. The solvent-based self-assembly of 1,1'-biphenyl-4-thiol (BPT, (1a), in figure I.5(b)), an aromatic precursor used for the production of SLG [74, 79] on Au substrates, can be conducted by immersing the substrate into a solution of BPT in dimethylformamide (DMF) [85]. Alternatively, a BPT SAM can be prepared by vapor deposition, i.e. exposure of sputter-clean Au substrates to BPT vapor [85]. Both methods allow the formation of BPT SAMs with comparable structural quality, although the solvent-based preparation typically results in a slightly higher (~5%) packing density of the formed SAMs. In case of the self-assembly from solvents the solvent/molecule interactions play an important role [86], and the packing density of the formed SAMs can be tuned by adjusting the solvent polarity and concentration of the precursor molecules [73]. In comparison to solvent-based self-assembly, self-assembly by vapor deposition requires high vacuum equipment, but SAM formation is achieved in a significantly shorter time (~1 h compared to 3 days [74, 84, 85]. For practical reasons, these different aspects have to be considered when designing the experiment. Furthermore, vacuum vapor deposition is preferred over solution deposition in the case of the formation of thiol-based SAMs on oxidative metal substrates (e.g. Cu or Ni), as the metal oxidation which hinders the self-assembly is avoided [84, 86].

Electron irradiation of aromatic SAMs results in lateral crosslinking of the constituting molecules and formation of CNMs [73, 82, 87]. The mechanisms of this process are discussed in Refs. [82] and [88]. Here, we summarize essential features of this process [89–91]. In aliphatic SAMs, electron irradiation results in significant (up to 80%–90%) molecular decomposition and desorption [92, 93]. In contrast, in aromatic SAMs the same treatment a thin carbon layer is formed. To induce the crosslinking in aromatic SAMs with low-energy electrons (50–100 eV), typically doses of ~50 mC cm⁻², corresponding to ~750 electrons per molecule, are used. Because of electron irradiation, C–H cleavage takes place [90], which is the predominant process leading to crosslinking between adjacent aromatic rings. As suggested by UV photoelectron spectroscopy, quantum chemical and molecular dynamics calculations of BPT SAMs on gold, the formation of single- and double-links (C–C bonds) between phenyl rings of the molecules is expected during crosslinking [82]. This is supported by UV–vis spectroscopy of the formed CNMs [76]. Molecular dynamic calculations suggest [91] that a partial dissociation of the aromatic rings can take place and play a role in the formation of a carbon network. Such a mechanism would be in agreement with partial desorption of carbon in purely aromatic SAMs as observed by XPS. The XPS data also show that the irradiation and the subsequent molecular reorganization also affects the S-Au bonds. These structural changes at the molecule/substrate interface are in agreement with the LEED and STM results showing a loss of the long range (>5 nm) order in the SAMs upon electron irradiation [74].

Complete crosslinking of aromatic SAMs can be also achieved via He⁺ ion irradiation [94] with exposure dose ~1 mC cm⁻², ~60 times smaller than the corresponding electron irradiation dose [82]. Most likely, this effect is due to the energy distribution of secondary electrons that have a maximum at energies below 50 eV, which results in a more efficient dissociative electron attachment (DEA) process. Crosslinking can also be achieved employing UV/EUV [83] and higher energy electrons (few keV) [95].

After electron irradiation of the aromatic SAMs, the CNMs can be separated from the original substrates and transferred using PMMA assisted transfer onto new solid or perforated substrates (e.g. grids, see section VI) [78], where they form large free-standing areas (up to 0.3 mm²). Figure I.6 shows helium ion microscope (HIM) images of free-standing CNMs from different types of aromatic molecular precursors [73]. These images show unbroken membranes, which demonstrate mechanically stable CNMs. CNMs with large free-standing areas up to ~0.3 mm² can be obtained in this way. Since the thickness of CNMs is determined by the size of the precursor molecules and their packing in the SAMs, it can be tailored by varying these parameters enabling nanomembrane engineering. Figures I.6(a)–(c) show examples of CNMs where the thinnest nanomembrane has a thickness ~0.6 nm, while the thickest CNM is ~2.2 nm. Different CNMs have been fabricated and were investigated by HIM [73]. A relation between size and shape of precursor molecules, degree of order in its SAMs and the appearance of the CNM has been established [73]. If the molecule form a densely packed SAM (1(a)–(c), 2(a)–(c) and (e) in figure I.6(b)), the corresponding CNM is homogeneous and free of holes above 1.5 nm diameter. Figure I.6(d) shows a HIM image of such a CNM made from terphenylthiol (1c). Conversely, CNMs made from large molecules, i.e. hexabenzocoronenes (HBC, 3(b) and (c) in figure I.6(b)) or S,S'-(3',4',5',6'-tetraphenyl-[1,1':2',1''-terphenyl]-4,4''-diyl) diethanethioate (HPB, 3a in figure I.6(b)), form less ordered SAMs and exhibit pores, as presented in figures I.6(e) and (f). Here the dark spots are pores with diameters of 2–10 nm. Note that these pores have a narrow size distribution (see histogram insets). In case of the HBC precursor, the mean size of the nanopores is ~6 nm with surface density ~9.1  ×  10¹⁴ pores m⁻² The more compact HPB precursor shows a size ~2.4 nm with a surface density `1.3  ×  10¹⁵ pores m⁻². The formation of nanopores in these CNMs can be attributed to the large lateral dimensions of HBC and HPB molecules in comparison to smaller molecular precursors (see figure I.6(b)) and, in the case of HBCs, to the tendency of the disk like molecules to intermolecular stacking, which reduces the ordering in the respective SAMs. The average pore diameter correlates with the SAM thickness and decreases from 6.4 to 3.0 nm when the thickness increases from 1 to 2 nm [73].

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I.2.3.1. Formation of nanocrystalline graphene/GRMs

CNMs are stable up to to 800 K [83], which enables their conversion into graphene/GRMs via pyrolysis in vacuum or inert atmosphere [73, 78]. The crystallinity of the produced GRM can be tuned by the annealing conditions, i.e. T and substrate material. The formation of nanocrystalline sheets by annealing of free-standing CNMs [78] on TEM grids (figure I.7(a)) was reported on Au, on [79] or SiO₂[76, 77]. Although S is initially present in the CNMs both, XPS (of supported sheets) and scanning Auger microscopy (of suspended sheets), indicate that after annealing above 800 K all sheets consist only of carbon [78, 82]. At this T, the structural transformation of CNMs sets in, evident from appearance of the characteristic D-, G- and 2D peaks in the Raman spectra [96] [77–79]. This can also be visualized by HRTEM [73, 79]. As shown in figure I.7(b), after annealing of a BPT CNM (chemical formula (1a) in figure I.5(b)), most of the sheet area (~70%) is SLG recognized by the hexagonal arrangement of carbon atoms. Randomly oriented nanocrystalline graphene domains are connected with each other via heptagon-pentagon grain boundaries [97] (see inset to figure I.7(b)); a small fraction (~20%) of the sheet consists of bilayer graphene (BLG) as indicated by the Moiré pattern [98] and some of the area (~10%) shows an amorphous carbon phase [99].

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The conversion of CNMs influences the electrical and optical properties [76, 78, 79]. Figure I.7(c) shows the sheet resistivity of BPT CNMs as a function of annealing T. The measurements were conducted at RT by different methods after respective annealing steps on both supported and suspended GRM [78, 79]. The non-annealed CNMs do not show lateral conductivity. Electrical conductivity is first detected after annealing at ~800 K. After annealing a ~1200 K the conductivity increases by six orders of magnitude approaching ~10 kOhm sq⁻¹. To characterize the influence of this transformation on electrical transport, the T dependencies of the electrical conductivity, σ(T), and the electric field effect were studied in Hall-bar devices [79]. Samples with lower annealing T (900, 950 and 1050 K), (1–3) in figure I.7(d), have insulating behavior with a positive curvature in T. Their T dependence can be described by $\newcommand{\e}{{\rm e}} \sigma \left( T \right)\propto \exp \left[ -{{\left( \frac{{{T}_{0}}}{T} \right)}^{\frac{1}{3}}} \right]$, representing the Mott law [79], characteristic of thermally activated variable range hopping in a 2d system with weak Coulomb interactions [79]. For the sample with the highest degree of transformation, (5) in figure I.7(d), σ(T) shows a negative curvature with σ(T) $\propto$ T^1/2, i.e. a semi-metallic state. Since the conductivity of nanocrystalline carbon in the insulating regime strongly depends on the density of states, a large ambipolar electric field effect is observed. The electron mobility in the resulting nanocrystalline carbon film~50 cm² V⁻¹ s⁻¹ at RT [79]. The evolution of the transport characteristics upon conversion of CNMs into nanocrystalline carbon is reminiscent of that observed upon the thermal reduction of graphene oxide (GO) into reduced graphene oxide (RGO) [100, 101]. In both cases the final material presents an interconnected network of graphen nanocrystallites. However, in case of the RGO, a residual amount of oxygen containing groups is present [102], whereas nanocrystalline GRM sheets obtained by the conversion BPT CNMs consist only of carbon [73, 78, 79].

The thickness of the formed nanocrystalline sheets depends on the structure of precursor molecules, their ability to form SAMs and to be crosslinked into CNMs. Thus, by varying precursors (see figure I.5(b)), the thickness of the formed nanocrystalline sheets can be tuned by a factor ~3 [73]. The resistivity correlates with the thickness of the sheets, with lower resistivity for thicker sheets [73, 76]. An interesting opportunity is opened by using N- or boron-containing precursors, as in this case, GRM sheets doped by these elements can be expected, which are of interest for applications in catalysis [103] or energy storage [104].

Employing the conversion of CNMs into GRM by performing pyrolysis on catalytically active substrates like copper, graphene layers with high crystallinity and, therefore, high mobility above 2000 cm² V⁻¹ s⁻¹ can be attained [74]. As a model system, the conversion of BPT SAMs is presented (see chemical formula (1a) in figure I.5(b)) into graphene on copper foils. The Raman spectroscopy data (see figure I.8(a)) show an evolution of the characteristic D, G and 2D Raman peaks as a function of T (see section IX.2/Raman for an introduction to the technique). The conversion of a CNM into graphene with T is clearly observed. For the highest annealing T (830 °C), the same features as known for single-layer graphene prepared by mechanical exfoliation (G peak at 1587 cm⁻¹ and a narrow Lorentzian 2D peak at 2680 cm⁻¹ (FWHM  =  24 cm⁻¹) [105] are observed after the conversion. The grown sheets were transferred onto grids and onto oxidized highly doped Si-wafers and were characterized by HRTEM and by electric transport [74]. The HRTEM and selected area diffraction (SEAD) data confirm formation of SLG [106], figures I.8(b) and (c). The dark-field TEM imaging shows that the formed sheets consist of graphene single crystals with lateral dimensions up to 1–2 µm [74].

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Electric transport properties of the synthesized graphene films were studied by four-point measurements in the Hall bar geometry (see inset in figures I.8(d) and (e)) [74]. Figure I.8(d) presents the observed ambipolar nature as measured in a FET device. The RT charge carrier mobility, µ, extracted from the data at a hole-concentration of 1  ×  10¹² cm⁻², is ~1600 cm² V⁻¹ s⁻¹. µ values at lower charge carrier concentrations are ~2300 cm² V⁻¹ s⁻¹. Further characterization of the transport properties (see section IX.3) at low T (T  =  0.3 K) in a magnetic field of 15 T demonstrates that by varying the charge density with the back-gate voltage, Shubnikov–de Haas oscillations and resistivity plateaus of the quantum Hall effect specific for SLG are observed [107]. These results confirm the electronic quality of the grown sheets, l making them attractive for electronic applications.

Since only the electron-beam irradiated areas of SAMs undergo conversion into graphen, both large-area up to 10 cm² and more graphene sheets and carbon films of various architectures (e.g. nano-ribbon, dot, anti-dot patterns) can be fabricated from SAMs by employing either defocused electron flood exposures [74, 78] or exposures by focused electron beams [75]. Because only electron-irradiated (crosslinked) regions of aromatic SAMs are converted into grapheneupon annealing, whereas non-irradiated (pristine) SAMs desorb from the surface [83], the suggested approach provides an opportunity to directly grow graphene patterns by area-selective electron irradiation [80], figure I.9(a). Therewith, at least four technological steps (spin-coating of photoresist, developing of photoresist, reactive ion etching, stripping of photoresist) employed in the conventional microfabrication of graphene electronic devices are omitted. Figure I.9(b) shows a graphene pattern grown on Cu at 800 °C after a BPT SAM is locally crosslinked by a primary electron beam of 3 keV and doses ranging from 75 mC cm⁻² to 125 mC cm⁻². The transfer of this structure onto a 300 nm SiO₂/Si substrate is presented in figure I.9(c). By comparing the distances between the single structure elements in figure I.9(b) (on Cu) and 9(c) (on SiO₂/Si), the structural integrity is conserved during transfer. Only a few elements show folding defects or missing parts. In this case, the local adhesion to the substrate is too weak to withstand the forces occurring during the removal of the transfer medium in solvent [80]. More advanced transfer techniques, like electrochemical delamination [108] or a clean-lifting transfer [109] may be applied to avoid or minimize the creation of defects (see section VI). The minimum size of the features in the grown pattern correspond to ~1 µm. The lateral resolution is defined in principle by the resolution of electron-beam lithography, ~7 nm for SAMs [110]. Another interesting opportunity is given by the fact that molecular self-assembly can be conducted on non-planar surfaces, thus it is also feasible to apply the developed methodology to create graphene structures on any 3d shape.

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Graphite consists of stacked graphene layers bonded by van der Waals (vdW) forces [120]. Carbon atoms are hexagonally arranged and SLGs are parallel to each other. Graphite has two main allotropic forms, hexagonal [121] (figure II.1(a)) and rhombohedral [122] (figure II.1(b)). In both cases the carbon hybridization is sp², the C–C distance in the basal plane is 0.1417 nm, and the distance between the layers is 0.3320 nm. The hexagonal form is the most stable, with layers stacked in an ABAB sequence (unit cell constants: a  =  0.2456 nm, c  =  0.6708 nm) [121]. In Rhombohedral graphite the sequence of the layers is ABCABC (unit cell constants: a  =  0.2566 nm, c  =  0.100 62 nm) [122].

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Graphite can be natural or synthetic. The latter can be obtained by subjecting nongraphitic carbons as pitches and cokes to high temperatures (1700 °C–2700 °C) in inert atmosphere or vacuum [123–125].This is the case of graphitizable carbons, i.e. non-graphitic carbons which, upon thermal treatment, convert into graphitic carbon, [126]. The degree of graphitization, the amount of disordered phase converted in their graphitic counterpart, can be further increased by performing thermal treatment under high pressure (100–1000 MPa) [127]. Graphitic materials can also be obtained by CVD of hydrocarbons, such as methane [128] or ethane [129] at T ~ 1200 °C or by catalytic (c-CVD) and these synthetic methods are reviewed in section V.

Graphene can be obtained by exfoliation of graphite [130]. The presence of defects in the layers leads to graphene with lower conductivity [120, 131–134]. Graphite with large crystal size allows one to obtain bigger flakes [132]. The crystal boundaries of the starting graphite have an impact on the amount and type of oxygen functional groups introduced in the oxidation reaction resulting in GO [132], influencing also the sonication time required to overcome the vdW interactions [133], as well as the chemical structure of the RGO obtained after thermal [135] or chemical reduction [135]. The microstructure of graphite can be distinguished by polarized light microscopy [120], where the different crystalline domains are defined by the interference colours (figure II.2(a). Figure II.2(b) shows anSEM image of graphite in which these features cannot be observed. The distribution of crystal size also influences the polydispersion in lateral size of the obtained GO/RGO material, limiting the maximum lateral size. The final average size of graphene is usually much smaller than the initial crystal size in graphite, and is mainly dictated by the mechanical process of exfoliation at the meso- and nano-scale [136, 137].

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GO/RGO has been prepared from different natural graphites [138]: flaky, (natural graphite of finely powdered crystalline graphite with grain size smaller than 250 µm), lumpy (crystalline graphite with a walnut to a pea size), and amorphous (exhibiting only short range order) [139, 140]. Lower crystallinity of the parent material (lumpy  >  natural  >  amorphous) leads to higher defects, smaller GO sheets' size and higher surface areas (figure II.3). Natural graphites can contain silicates and other particles that can contaminate the final GRM, as detected by thermogravimetric (TGA) measurements [141].

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Smaller particle size will result in higher content of oxygen functional groups in GO, because of easier diffusion of reagents during oxidation. This influences the final electrical and thermal properties [142, 143]. Graphite with particle sizes  >200 µm are adequate for the production of GRM to be used in thermoset composites by infusion [144]. Particle size  >600 µm are ideal for conductive thermoset composites [145].

The discrete particle size of graphite, as observed in SEM, is different than the particle size determined by other techniques such as laser diffraction, optical microscopy or granulometry. Laser diffraction or granulometry increase the measured particle size of graphite due to the agglomeration of discrete crystals. SEM can distinguish between different or discrete crystals and allows the measurement of particle size with more accuracy. In the case of optical microscopy, it is more difficult to separate particle sizes.

Expanded graphite is a graphite-derived material formed by a two-step oxidation-reduction process that retains the long-range-ordered layered structure of graphite, yielding a large interlayer distance. It can be used for the preparation of GRM by liquid methods [147]. Typical expanded graphites used for the preparation of graphene flakes have a medium diameter D50, i.e. the value of the particle diameter at 50% in the cumulative distribution of particle size diameters, from 15 to 50 µm.

Non-graphitic carbons were also proposed [148, 149] as precursors for the synthesis of GRM by top-down techniques. e.g. petroleum and coal-tar pitches pass through a liquid or liquid-crystalline phase when subjected to heat treatment in inert atmosphere [150]. These materials are graphitizing and develop a graphitic microstructure upon heating to 3000 °C [151]. When these precursors are carbonized at lower temperatures (1000 °C), they become cokes. A coke is a solid carbonaceous material derived from distillation of low-ash, low-sulphur bituminous coal, or derived from oil refinery coke units or other cracking processes [152]. It has a partially organized lamellar structure resulting from the parallel stacking of layers of sp²-hybridized carbon atoms. Therefore, Refs. [148, 149] suggested that these could be used for the preparation of graphene flakes. Since high T (up to 2500 °C–3000 °C) are required to obtain synthetic graphites, the direct use of cokes as precursors reduces the environmental impact of the whole process. Moreover, the broad range of microstructures and chemical compositions of cokes (as determined by the carbon source and the carbonization conditions) makes them a suitable starting material for the synthesis of graphene or GO with targeted structures and compositions.

Due to the different microstructure and chemical composition of cokes and graphites, the conditions for the synthesis of GRM should also be adjusted. Thus, compared to graphites, cokes require larger amounts of reactants during their oxidation by the Hummers' method. Otherwise, its exfoliation into GO would have a much lower yield [148]. When cokes and graphites were exfoliated in NMP, flakes from coke had a larger number of defects and smaller lateral size (~400 nm) than those from graphite (~1 µm) [148]. Similarly, as the crystallinity of cokes increases, its subsequent exfoliation yields flakes with larger lateral size and in higher yield [149].

CNTs or nanofibres (CNFs), have also been explored as alternative precursors to produce graphene sheets and GNRs in liquid media [17, 116, 117]. Twisted ribbon-shaped carbon nanofibers are helical carbon nanofibers comprising 5–6 stacked graphene layers [117, 153–155]. Two approaches have been proposed for the production of graphene flakes and sheets from these [153, 154]. The first is based on a mechano-chemical method, through melamine intercalation during ball milling in different solvents such as isopropanol, THF or DMF. Ref. [153] produced graphene suspensions in low boiling point solvents such as 2-propanol (~83 °C) and THF (66 °C) by a scalable method [153]. Ref. [154] obtained GO/RGO flakes^® using the Hummers' method [156] and different reduction techniques [154, 157, 158].

GNRs have been produced from CNTs as the starting material by solution-based oxidative processes [17, 117]. CNTs suspended in concentrated H₂SO₄ were oxidized by adding KMnO₄ (500 wt%with respect to CNTs) at T  <  70 °C [17].The resulting GNRs have straight edges and are dispersible in water and other polar solvents due to the presence of oxygen moieties. Unzipping single-wall carbon nanotubes (SWNTs) [17] gives GNRs, but these are difficult to disentangle. Multi-wall carbon nanotubes (MWNTs) led to less entangled GNRs [17], that can be separated to single layers after sonication. Carbonyls, carboxyls and hydroxyl groups present in the GNRs can be reduced by treatment with aqueous hydrazine (N₂H₄·H₂O) after dispersing them in aqueous sodium dodecyl sulphate in order to prevent their re-aggregation. CNT unzipping by intercalation of lithium and ammonia and subsequent exfoliation was also reported [116]. However, this procedure yields a mixture of multilayer GNRs, partially open MWNTs, and flakes, contrary to oxidation with KMnO₄, which allows a nearly 100% yield of GNRs with no presence of partially open MWNTs [117].

II.2.1.1. Solvents and detergents

II.2.1.2. Molecule-assisted LPE

II.2.2.1. General considerations

II.2.2.2. Sonication

II.2.2.3. Shear exfoliation

II.2.2.4. Microfluidization

Microfluidization is a homogenization method that applies high pressure (up to 207 MPa) [247] to a fluid forcing it to pass through a microchannel, figure II.5. The key advantage over other LPE methods is that high shear rates ($\dot{\gamma }$  >  10⁶s⁻¹ [248, 249]) can be applied to the whole fluid volume [249], not just locally. Microfluidization was used for the production of polymer nanosuspensions [247], in pharmaceutical applications to produce liposome nanoparticles with diameters smaller than 80 nm to be used in eye drops for drug delivery to the posterior segment tissues of the eye [250], or to produce aspirin nanoemulsions [251], as well as in food applications for oil-in-water nanoemulsions [252]. Microfluidization was also used for the de-agglomeration and dispersion of CNTs [253].

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The main step of this process involves placing the graphite/solvent mixture into an inlet reservoir. An intensification pump, driven by electro-hydraulics, provides two motions, suction and compression, drawing a portion of sample into the processor through a one-way valve, and then pushing this sample fraction past the pressure gauge and through sub-millimetre sized channels within a diamond interaction chamber, where graphite exfoliation takes place [178].

Interaction chambers are typically based on two geometries, Y- and Z type. The Z-type chamber is preferred for graphite exfoliation, since the geometry consists of sharp turns and a narrow rectangular cross-section for optimal shear. The chamber G10Z is ~87 µm in diameter. The motion of the intensification pump creates mixing within these micro channels, generating pressures  >  30 000 psi (~2100 bar). The fluid dynamics of the process can be turbulent or laminar as defined by the Reynolds number, dependent on the kinematic viscosity and density of the solvent used [178].

Below are two typical recipes for the production of graphitic flakes without centrifugation (Method 1), or FLGs following centrifugation (Method 2). Due to the dimensions of the interaction chamber, microfluidic processing of large (>100 µm) graphite flakes may block the microfluidic channel. Instead, smaller powder sizes are advisable (typically, the particle diameter corresponding to 90% cumulative (from 0 to 100%) of the undersize particle size distribution (D90), less than 30 µm).

II.2.2.4.1. Method 1: production of multi-layered flakes

This method [178] refers to the production of high yield (100 wt.%), high concentration (up to 100 g l⁻¹) graphene-based inks that are not centrifuged. Graphite powders (natural or synthetic, particle size  <30 µm) are mixed at a concentration up to 100 g l⁻¹ with SDC at a concentration 9 g l⁻¹ in water in typical batch sizes of 250–500 ml. The material is collected in a beaker and placed back in to the inlet reservoir to cycle automatically for the desired length of time depending on the number of process cycles, n (where n is typically  <70). The final product is collected. Sodium carboxymethylcellulose (NaCMC) (10 g l⁻¹) is added whilst stirring to adjust the viscosity to the required value. NaCMC is slowly added until fully dissolved in order to avoid the formation of clumps. Clumps that are formed should be ground with a spatula and the ink left to stir overnight.

Figure II.6 shows SEM images of the coatings comprising the starting graphite (figure II.6(a)), after 5 (figure II.6(b)) and 100 cycles (figure II.6(c)). Flake size reduction and platelet-like morphology is observed after microfluidic processing.

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Since these inks are not further processed by centrifugation, Y_W (yield by weight) is 100 wt.%. 4 wt% of the exfoliated material consists of FLGs (<4 nm thick) that can be isolated using Method 2 below, and 96 wt% are flakes in the 4 to 70 nm thickness range. The stabilized dispersion can be used for blade coating and screen printing. Figure II.7 plots the sheet resistance (Rs) and thickness of blade coated films as a function of process cycles at a flake loading of 80 g l⁻¹ (73 wt.%), highlighting that exfoliated materials produce thinner films with lower R_s. The bulk conductivity of films increases with loading with a plateau above 80 wt.%, and the critical thickness at which bulk conductivity is reached is less when loading is higher. After annealing (300 °C–40 min), R_s reaches 2 Ω □⁻¹ at 25 µm (conductivity, σ  =  2  ×  10⁴ S m⁻¹), suitable for electrodes in devices such as OPVs [254, 255], organic thin-film transistors (OTFTs) [256] or radio-frequency identification (RF-IDs) [257]. The inks can then be deposited on glass and poly(ethylene terephthalate) PET flexible substrates using blade coating and screen printing to demonstrate the viability for these applications (OPVs, OTFTs, RF-IDs). Screen printing is discussed in section III.

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II.2.2.4.2. Method 2: production of FLGs

Below we show that FLG can be obtained by adding an additional centrifugation step. Graphite powders (natural or synthetic) with D90  <  30 µm are mixed at a concentration 12 g l⁻¹ with SDC at a concentration ~0.5 g l⁻¹ in water and microfluidized for n typically  <100). Following processing, samples are centrifuged typically at 10 000 rpm (17 000 g) for one hour. Films obtained by vacuum filtration of the FLG ink have R_s ~ 4.5 kΩ □⁻¹ at 90 nm thickness, significantly better than the equivalent sonication produced graphene films that have R_s ~ 8.9 kΩ □⁻¹ at 160 nm. The effects of processing cycles, pressure, surfactant concentration, centrifugation speed and graphite loading on graphene concentration are shown in figures II.8(a)–(f) AFM indicates that the exfoliated material consists of FLG, with ~18% SLG (figure II.9).

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II.2.2.5. Ball milling

Ball milling can produce FLG at low-cost and under environmentally friendly conditions. It does not require solvents, avoiding the use of toxic organics, while increasing efficiency in terms of time and energy.

Two effects take place in ball milling [163]: the shear force, that promotes the synthesis of large-sized flakes, of the order of the starting graphite planes, and the vertical impacts applied by the balls during the rolling actions, which tend to deteriorate the flakes and must then be minimized in order to reduce the number of defects. Ref. [258] reported changes of graphite, during milling processes, through a nanocrystalline phase prior to amorphization. To avoid this and favour the shear force process, the use of solid exfoliating agents is recommended.

Exfoliating agents, including triazine derivatives, can be used to form multipoint interactions with the exfoliated flakes. Amounts around few grams of graphite and exfoliating agents, such as melamine (2,4,6-triamine-1,3,5-triazine), can be used to prepare FLGs, which can subsequently be dispersed in organic solvents, such as DMF or in aqueous media [179]. The lateral size of the resulting flakes can be modulated depending on the ball-milling conditions (atmosphere, revolutions, and time of treatment). Different triazine derivatives were tested, in relation to their ability to exfoliate graphite, not only experimentally but also by computational studies, which evidenced that melamine is a good option to favour exfoliation [259]. Melamine not only has an aromatic nucleus that can interact with the graphene π-system [259], but can also form an extended network on its surface, owing to the presence of hydrogen bonds (figure II.10). Melamine can then be washed away using hot water, leaving high quality graphene suspensions, with very small Raman D peak.

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In a typical experiment, 7.5 mg of graphite and 22.5 mg of melamine are ball-milled at 100 rpm for 30 min, under air atmosphere, in a stainless steel grinding jar containing ten stainless steel balls of 1 cm of diameter. The resulting solid mixture is dispersed in 20 ml of solvent, obtaining black suspensions. Filtration can remove melamine from the suspensions, giving rise to FLG dispersions in different solvents. If DMF is used as a solvent, colloidally stable dispersions are obtained with no precipitate observed. If water is used as a solvent, a concentration gradient appears, and some precipitation takes place after stabilization of the dispersion, at room temperature, for 5 days.

When preparing dispersions in water, melamine can also be eliminated by dialysis, which is highly recommended, mainly because this technique allows keeping the flakes always in dispersion [213]. It is advisable to hand-shake the dialysis sack and to apply a pulse of mild (bath sonication for no more than 1 min) if any precipitate appears in the black dispersion during dialysis. Once melamine is removed, the black dispersion is kept in the stabilization container at room temperature for 5 days, in order to obtain a concentration gradient. The liquid fraction with stable sheets in suspension needs to be carefully extracted, avoiding the meniscus and the precipitate, in which non-exfoliated graphite remains. The obtained aqueous dispersions, with concentration ~0.1 g l⁻¹, are stable at RT for a few weeks. According to elemental analysis, these dispersions contain an amount of melamine lower than 1 ppm, which is considered non toxic [260].

Characterization of the FLG shows a low number of defects, with Raman ~0.2–0.6, confirming that no oxidation occurs during the preparation [179]. In [261], ab initio calculations on graphene-melamine-water systems have been performed focusing on how small amounts of melamine molecules tune the adsorption of few water layers on SLG. These reveal that melamine acts as a non-covalent anchor, keeping some water molecules near SLG, providing a quantitative estimation of the non-covalent interactions (dispersion and hydrogen-bonding), which provide the required driving force to stabilize the SLG-water systems.

A further advantage is that the aqueous suspensions can be lyophilized after having been frozen [262]. A very soft and low-density black powder, consisting of FLGs, is produced this way. This solid can be safely stored and shipped, being easily dispersed in water, culture media or other solvents, using mild sonication combined with shaking with no change in its structure (figure II.11). The mass yield of the entire process, starting from graphite, is ~30%.

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In [179], powders were characterized with elemental analysis (EA), TGA, XPS, TEM and Raman spectroscopy. EA resulted in average values ~94.3 wt%C, 0.4 wt%H, 0.4 wt%N and 4.9 wt%O [1728]. TGA showed a weight loss [1728], in agreement with EA, confirming the non-oxidative nature of the milling treatment. This feature was also corroborated by XPS [179], as deconvoluted plots confirmed the presence of small amounts of oxygenated groups, from the C 1s and O 1s core level spectra and traces of melamine. XPS spectra (figure II.12) indicate that 15 min ultrasonication does not add a significant number of defects. TEM was used to determine the lateral flake sizes [1729], concluding that FLG have a wide size distribution ~200–2000 nm.

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There is an increasing interest in the use of GRMs in biological applications. Dispersions in water and culture media allow the preparation of hydrogels for drug delivery [259], the study of synaptic functions in culture brain cells [263, 264] as well as environmental toxicity studies [262].

The addition of small amounts of solvent during milling was reported to improve exfoliation [153]. Solvent drop grinding was shown to be an effective technique to accelerate mechanochemical reactions [265]. The addition of catalytic amounts of a liquid phase facilitates molecular mobility, inducing reactivity in normally inactive systems. Therefore, wet milling conditions have been probed, and ball milling exfoliation of carbon nanofibers was reported [153]. Melamine was used as the exfoliating agent: 0.5 ml of solvent was added to 30 mg of nanofibres/melamine mixture. The Hansen solubility parameters of each material were studied in order to discriminate SLG from the rest of materials (FLG, poorly exfoliated carbon fibres and melamine) after the milling treatment. This allows one to select a suitable solvent to disperse mainly SLGs [153]. The quality of exfoliation was studied by Raman spectroscopy. Although there is a compromise between exfoliation quality and graphene concentration, these wet conditions follow the same trend established by the Hansen solubility parameters, permitting SLG dispersion [153].

To achieve larger particle sizes (in the range of microns), mechanical exfoliation by ball milling or high-shear mixing can be combined with chemical intercalation. Intercalating Li and ammonium-based ions (such as tetraethylammonium-Et₄N⁺- ions) between layers weakens the van der Waal forces [266]. Ball milling supplies shear forces high enough to exfoliate the intercalated compounds. Using ionic liquid (IL) or ammonium based deep eutectic solvents as the milling liquid accelerates the kinetics of the intercalation because it increases the activity of ammonium ions [266]. Deep eutectic solvents are green solvents having the advantages of non-flammability [267], high thermal stability (>150 °C) [267], wide liquid phase range (usually over a range of 200 °C–500 °C) [268], negligible vapour pressure (<10 Pa at RT) [269] and easy recycling [270]. These properties eliminate the safety problems associated with typical organic solvents. An eutectic mixture of urea and choline chloride (2:1) can be produced by stirring the two components until clear liquid is formed. The liquid can be then charged into the grinding chamber with 2 g graphite, 4 g battery grade Li chips, and yttria stabilized zirconia milling media. The ball milling runs under a flow of N₂ gas inside a glovebox. It is better to pause the grinding process for 30 min every 2 h to allow the system to cool. To recover the exfoliation product, the samples are then washed with DMSO, and centrifuged at 1500 rpm to remove thick flakes. The milling speed should be controlled to below 500 rpm to avoid extensive heating and to minimize defects in the produced flakes.

GO has a number of properties that are advantageous for applications. Due to its oxygenated surface, it can undergo complete exfoliation in water [271–275], yielding colloidal suspensions of individual sheets [273, 276, 277], that can be further functionalized, deoxygenated or dispersed in polymeric matrixes to give new multifunctional materials and composites [276]. This, combined with chemical tailoring [216, 217, 278] and biofunctionalization [279–283] makes GO a promising candidate for biomedical applications where water compatibility is crucial, e.g. in tissue engineering, drug delivery, cancer treatment and biosensing [281–289]. Unlike liquid-exfoliated LMs, GO is typically one layer thick [276]. This high surface to volume ratio and the mechanical strength lends itself to using GO as electrode material in energy storage and conversion [290, 291] or as filtration membrane for gas and ion separation [292, 293]. In addition, GO has some unique features. For example, unlike other LMs, it is amphiphilic, due to the non-uniform distribution of the various oxygen functional groups and can self-assemble into a range of nanostructures with different morphology at interfaces [294]. When increasing the concentration in dispersion, GO undergoes a phase transition from colloidal isotropic to nematic liquid crystalline phase, where the GO sheets are oriented in parallel [295]. The liquid crystalline phase leads to an enhanced alignment of GO sheets in those assembled structures, offering improved mechanical and electrical/thermal properties, compared to the random-oriented configuration of GOs which is important for electrochemical applications and opens up possible applications of GO in optical switches and photonic crystals [295].

GO can be prepared by oxidation of graphite using highly oxidant reactants such as H₂SO₄, KMnO₄, H₂O₂ [156, 157]. The preparation method strongly influences the surface chemistry and related chemo-physical properties, ultimately affecting its functionalities. In 1859, Brodie first reported the synthesis of GO by adding potassium chlorate (KClO₃) to a slurry of graphite in fuming nitric acid (HNO₃) in a single portion [296]. In 1898, Staudenmaier improved Brodie's method by replacing ~two thirds of fuming HNO₃ with concentrated H₂SO₄ and by adding KClO₃ in multiple portions during the reaction, rather than in a single portion. Such modification had the same oxidation efficiency of reiterative Brodie oxidations (achieving high oxygen contents, up to C:O  =  2:1) but in a single synthetic step. However, the Brodie and Staudenmaier method was not widely used because of the potential risk of explosions [297]. In 1958 Hummers and Offeman proposed a safer approach, currently widely adopted and known as Hummer's method [156], consisting of the replacement of KClO₃ by KMnO₄ and NaNO₃ in concentrated H₂SO₄. Ref. [298] reported that excluding NaNO₃, increasing KMnO₄ and a mixture of H₂SO₄/H₃PO₄ can improve the oxidation process. In these conditions the reaction is not exothermic and no toxic gas is produced.

The method proposed in Refs. [272, 298] allows one to prepare highly soluble (>4 g l⁻¹) water-soluble GO for studying the biological and toxicology effects on living cells [235, 286, 287]. In this way, GO sheets could be prepared with constant surface chemistry, but varying lateral size, spanning from 100 µm down to less than 100 nm [235]. The lateral size of the GO flakes after a typical oxidation can be tuned by sonicating the starting solutions for different times, from 0 to 100 h, in milliQ water (for a systematic study of GO size versus sonication time see Ref. [136]). GO can also be prepared by the Hummer's method directly on SiC wafers from graphene on SiC, with the property that the GO layers remain on the substrate for further surface studies and electronic devices production [299–301].

It is still not clear which are the most relevant factors regulating the interactions between GO and biological molecules, tissue structures and organisms. Numerous studies [235, 286, 287, 302] have shown that GO chemical purity, chemo-physical parameters and morphological properties can play a crucial role on cells viability and functionalities [302].

Taking advantage of the size tunability and high solubility of GO, the effect of the lateral size of GO in different biological systems was investigated for human and murine phagocytic cells [235], human intestinal cells [286], human lung and colon carcinoma cells [303], different enzymes of human [287] or bacterial [304] origin, gelatine membranes and fibres of animal origin [305].

In Ref. [235], three GO solutions, sonicated for 0, 2 and 26 h (with average lateral size ~1.3, 0.27 and 0.13 µm) were mixed with human monocyte macrophages (hMDM) and murine intraperitoneal macrophages (mIPM), revealing that the flake size has significant impact on different cellular parameters (i.e. cells viability, reactive oxygen species (ROS) generation and cellular activation, figure II.13). Ref. [235] reported a strong interaction (>90% internalization) with the cellular membrane, leading to the sliding of flakes under the membrane layer. GO samples could be internalized by both human and murine macrophages in a size-dependent manner. The more the lateral dimensions of GO were reduced, the higher were the cellular internalization and the effects on cellular functionality [235]. Flakes with the smallest lateral dimensions (<300 nm) were better internalized by primary macrophages. A 'mask effect' was observed due to the 2d shape of GO, with a preferential parallel orientation of the GO sheets onto to the cellular surface.

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An efficient an green electrochemical oxidation of graphite to GO was reported [306]. Compared to traditional GO synthesis, the process bears the advantage that it is scalable, fast (<30 min opposed to hundreds of hours) and the risk of explosions is minimized. While electrochemical exfoliation has been developed to synthesize GRM with minimal oxidation (see section II.5), it has previously not been used to prepare GO. The electrochemical GO production can be achieved in two sequential steps starting using flexible graphite paper as anode and Pt as a cathode. In the first step (typically 20 min), a stage-I GIC is formed in concentrated H₂SO₄. In the second step, diluted (50 wt%) H₂SO₄ is used as electrolyte and the GIC as anode. Within seconds, the intercalation compound is oxidized and exfoliated. The dispersion produced is then filtered and washed to remove sulfuric acid and then redispersed by bath sonication if desired. Due to the lower acid concentration in the exfoliation step compared to the traditional Hummer's method, the dispersion is less viscous facilitating the filtration and washing step. Importantly, the process can be designed in such a way that a continuous oxidation and exfoliation is achieved and the degree of oxidation is readily tuneable by the concentration of sulfuric acid. The most critical step is the choice if starting material, as neither graphite powders, not flakes or rods are suitable.

There is a growing and active investigation into the preparation and use of RGO due to its good electrical conductivity properties (from 10⁻⁵ S cm⁻¹ to 1000 S cm⁻¹, [307]), and increase in mechanical reinforcement of polymeric matrixes [308]. E.g., 0.2% RGO can improve from 25% to 50% the mechanical properties of epoxy matrix composites[309]. Whereas thermal, chemical and thermochemical reduction of graphene and GO are customizable and versatile methods for preparing different types of RGO, they show several problems that hamper the synthesis of defect–free SLG. Among them, there are difficulties in complete removal of functional groups and the restitution of morphological characteristics of the material prior to the oxidation and sonication processes. RGO is highly polydisperse [307] in the lateral size, from less than 1 µm to more than 100 µm, due to the distribution of crystal size in the starting natural or synthetic graphites, and also due to the scissor effect that breaks the graphenic planes during the oxidation and/or the sonication processes [310]. However, the RGO thickness is controlled by the exfoliation of GO [311] and, depending on the preparation method and conditions, 1L can be obtained [312]. One of the first isolation of graphene was realized by reduction of GO by hydrazine in 1962 [273, 274].

There are several key characteristics of RGO that should be considered and evaluated to obtain optimum performance for a particular application: average lateral size, thickness, C/O ratio, the quantification of other heteroatoms, and surface area. Lateral sizes  >5–10 µm are not suitable for fiber reinforced composites by vacuum assisted liquid resin infusion, LRI, or resin transfer moulding (RTM), due to the difficult filtration of the RGO flakes by the fabrics during the processing [313]. Lateral sizes  >30 µm produce low percolation threshold composites, as compared with medium (<20 µm) and small (<5 µm) ones, due to size of overlapped areas and the higher number of contacts between particles [314].

Thickness is also a key factor for the performance of RGO in applications. In photocatalytic applications of RGO-TiO₂ the highest photocatalytic activity was observed with the SLG composites, and it decreased with N; this effect is attributed to higher charge carrier mobility and improved prevention of electron–hole pairs recombination [315]. Better results were obtained by co-exfoliation of graphite and TiO₂ [1716]. In some composites, this effect is also observed [143], however, in most of the applications in composites, SLG is not needed.

The C/O ratio and the quantification of other heteroatoms are important factors to determine the range of applications suitable for RGO. RGO with high (10%) to medium or low (1%) content of O is not suitable for thermal conductive properties, and a decrease to the oxygen content to lower than 0.5%w and distances between defects  >15 nm are needed [141]. Also, the sp²/sp³ ratio is relevant for energy applications [309], catalysis [316] and gas absorption [317]. In many applications, such as mechanical reinforcement of polymers, increase dispersion in composites or fire retardancy [318] and for further covalent functionalization, GO with 15%–25% O concentration is needed and ~8%–4% O are recomended.

Surface area is another of the key characteristics. The Brunauer–Emmett–Teller (BET) theory serves as the basis for an important analysis technique for the measurement of the specific surface area of materials. We will refer to those experimental methods as BET specific surface area, SBET, measurements. SBET is related to N and is a key factor enabling a material for energy applications. N can be estimated by dividing the maximum surface area of SLG, 2630 m² g⁻¹ by the specific surface determined experimentally by BET 2630/SBET, [319]. According to Ref. [320], RGO with SBET ~600–700 m² g⁻¹ are mostly SLG.

The density of RGOis another key parameter. GRMs with high SBET values produced by thermochemical reduction exhibit low densities, even lower than 4 g l⁻¹ [311]. For some applications a compaction of the RGO for further processing is needed [321].

Many strategies exist for the chemical, thermal and thermochemical reduction of GO, which strongly depend on the process and conditions selected for the reduction process, and the final performance required. Toxic hydrazine, sodium borohydride, hydroquinone have been used [322], as well as 'green reducers' such as organic acids [323], alcohols [324] and local high T reduction [300]. Biochemical molecules [325], amino acids [325], natural extracts [325] or metals [326], and several approaches other have been proposed [327].

Hydroiodic acid, often in combination with other acids, has been suggested as potent and versatile reducing agent [328]. GO reduction can be carried out at low T either in solution or for GO films and papers, in the gas phase [328]. GO self-assembled on the air/water interface can also be efficiently reduced by hydroiodic acid [329]. When using hydroiodic acid on GO films, it was found that the strength and ductility of the film was improved [157]. Compared to other methods of thermal reduction, such as reduction with hydrazine or vitamin C, it was found that hydroiodic acid reduces the GO without causing additional damage to the lattice [328].

Based on reproducibility, post-processability and ease up-scaling, alcohols are ideally suited for chemical reduction [324]. GO is first dispersed in the selected alcohol. Concentrations of GO ~5–20 g l⁻¹ should be used because, before the reflux of GO in alcohol, ultrasonication (of a batch or in a continuous system) is needed for the exfoliation from graphite oxide to and an increase of viscosity should be avoided. The higher the GO lateral size, the lower GO concentration should to be used, due to the lower stability of the GO in the suspension. The main disadvantage of this process is the high volume of alcohols needed. E.g., to process 100 g of GO, a 20 l vessel is needed. However, alcohols can be recycled by column distillation with recycling yields  >95%. Critical parameters are the selection of the alcohol and the time under reflux. By using x-ray diffraction, the reduction can be monitored based in the decrease of the intensity of the (0 0 1) peak of GO and the presence of (0 0 2) peak of RGO [330].

The electrical conductivity of RGO is also dependent on the chemical reduction process [307]. A Longer reflux time in isopropyl alcohol (IPA) produces higher conductivity. However, after 15 h no significant improvements are observed, see figure II.14.

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After this reduction step, filtration of RGO at RT is required. This is easy to perform, due to the powdery aspect of the material. This can be air-dried or oven dried at less than 100 °C for 12 h. It is important to control the drying process to prevent contaminations, avoid thermal expansion and decrease density for further processing. High pressure and hydrothermal methods are more complex [331, 332], but efficient reduction of GO can be achieved, obtaining lower O concentration compared with traditional chemical reductors, such as hydrazine [332].

The products obtained from chemical reduction of exfoliated GO [307] have usually poor, <100 S cm⁻¹, electrical properties due to the high O concentration (>10%) and the presence of structural defects [157, 158, 333].

RGO can be prepared by thermochemical methods as an alternative route for reduction of GO [311], where restoring the sp² SLG structure is additionally achieved by thermal annealing [276]. Besides O removal by reduction, enhancing the graphitization by repairing the C–C sp² π-bond network at defect regions during the reduction process [311] can further improve the electrical properties of exfoliated RGO, for electrical, thermal, and self-sensing applications.

For the preparation of RGO with  <1% O, several strategies can be used, such as  >1800 °C annealing T, long processing times (>60 min at 1500 °C), reducing atmospheres, such as H₂, alcohols, hydrocarbons, etc. Thermochemical reduction can be done at medium 800 °C or high T (>1200 °C), depending on the final requirements. The choice of the working atmosphere has an impact on the final RGO characteristic, particularly on its O content. Thermal reduction can be done in vacuum [334] or inert atmosphere [311] in a reducing H₂ environment [335] and using carbon donor molecules. Alcohols are very effective in the reduction of GO and the partial restoration of the graphitic structure due to their carbon donor characteristics. Other carbon donor molecules or a combination of hydrocarbons [336] are alternatives for the production RGO with O content  <2% O at moderate T  <  800 °C.

In thermochemical reduction, the working atmosphere comprises a gas carrier, which in most cases is an inert gas such as N₂ or Ar, and the carbon donor/source molecule or combination of molecules. Ar is preferred as gas carrier over N₂, due to the potential doping of with N RGO during the reduction process. For the restoration atmosphere, it is crucial to control the carbon donor and also the kinetics of the pyrolytic decomposition of the active gas. Carbon molecules result in the decomposition and formation of other non-graphene species and non-desired aromatic molecules [337]. Thus a low concentration, usually  <5% is recommended. Significant improvement of the reduction process when compared to the material obtained in H₂ was reported [338].The use of carbon donor atmospheres is the most cost-efficient to obtain highly reduced GO, with O concentration from 0.25% to 1%.

The reduction T determines the kinetics of the thermal decomposition (from 300 to 2000 °C), but a low cost- efficient reduction must be pursued in an industrial enviroment and the time and T of the process should be the lowest possible. Efficient processes at low T have been reported in [339], obtaining graphene for Li batteries at a low T ~ 300 °C in 5 min.

Graphene flakes can be used as building blocks for the preparation of 3d low density structures, such as sponges, foams, hydro- or aerogels [340–346]. These materials exhibit a highly open structure, with interconnected hierarchical pores that enhance the accessibility to the whole surface of the material and improve ion diffusion. The assembly of the graphene sheets into macrostructures can also improve the mechanical properties, while retaining other properties associated to individual graphene layers [340, 341]. GO can be used for the preparation of composites with tailored macroporous structure through the assembly of GO sheets with different templates. After template removal, complex GO-based materials with hierarchical porosities can be prepared [347]. The combination of processing at RT and a subsequent treatment at moderate T allows the preparation of highly conductive bare carbonaceous electrodes [348] and composites, which may serve as self–standing electrodes for Li ion batteries [347].

Ice–templating [349] is a useful technique for the preparation of macroporous reduced graphene oxide-based aerogels (ARGO). Ice–templating involves the freezing of a GO suspension, then subsequently freeze-dried to sublime the ice crystals formed within the structure. This process is useful for the preparation of a variety of a homogeneous nanostructured composites, with application in energy storage, catalysis, sensing or separation [350], it offers a better control on the porosity of the resultant materials. The modification of parameters such as T or immersion rate, impacts the textural properties of the resultant material. Ice-templating also allows gives structures with hierarchical porosity, which can favor the transport and diffusion of molecules to the whole surface of the material, highly desired in adsorption processes for separation and purification purposes and catalytic applications, not only of soluble pollutants in waste waters, but also for immiscible substances in biphasic systems [1730]. In energy storage applications, ARGO was proposed as electrodes for supercapacitors, Li-ion, Na-ion or metal-air batteries [341].

Ice-templated ARGO have been investigated as self-standing electrodes for energy storage devices [351]. These structures can be assembled into the electrochemical cells without the need of binders, which do not contribute to the capacity of the electrode, but can decrease its conductivity and block the access of the electrolyte ions to the surface of the active materials. As anodes for Li ion batteries (LIBs), sp² graphene not only improves the electrodes electronic conductivity, thus enhancing the power of the device, but it can also buffer the volume changes undergone by some active species used as high energy anodes for LIBs, during alloying with Li [352].

The processing of these materials as self-standing composites provides additional value to the electrodes since they can be directly mounted into flexible portable electronics [353].

ARGO composites can be prepared following the route schematized in figure II.15. First, an homogeneous suspension of GO, alone or in the presence of a certain precursor of the desired particles, is prepared. Second, the suspension is rapidly frozen by its immersion in liquid nitrogen. Then it is freeze-dried to remove the ice-crystals formed upon freezing, leaving the macroporous structured in the GO-based monoliths. Finally, samples are partially reduced by a thermal treatment conducted under inert atmosphere, yielding a macroporous carbonaceous network in which RGO sheets are decorated with crystalline particles.

The microstructure and porosity of the resultant aerogels can be tuned by changing rate and T of freezing. Fast freezing does not allow graphene layers to self-arrange with the ice crystals front, giving rise to materials containing macropores randomly distributed within the structure [354].

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Figure II.16 shows photographs of different aerogels obtained by ice templating. In these cases, GO suspensions obtained by the sonication of graphite oxide by the Hummer's method were used [120]. For the synthesis of Sn-based ARGO composites an aqueous suspension was used, but in the case of Si-ARGO, the GO and the SiNPs were initially dispersed in ethanol. Homogeneous GO suspensions in the presence of the precursor are in this way obtained [352, 355]. Then, the suspension is frozen in liquid nitrogen, and subsequently freeze-dried to sublime the ice-crystals, leaving the macroporous structured monoliths. Finally, the samples undergo thermal treatment under inert atmosphere to reduce GO and to form the desired crystalline phase.

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For the preparation of the GO suspension in ethanol ~5 g l⁻¹, an aqueous suspension of GO is washed several times with dry ethanol. The suspension is then sonicated and centrifuged to remove aggregates in the sediment. When mixing Si NPs and GO, the use of ethanol is justified, since Si-RGO composites generally need pre-oxidation of the Si NPs or ultrasonication, in order to improve their dispersibility in polar media, to be homogeneously mixed with GO [356, 357]. A highly homogeneous, see figure II.17, and stable dispersion of non-oxidized Si NPs was achieved in this way [355].

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Si-GO composites were prepared by mixing Si nanoparticles with the GO suspension in ethanol under inert atmosphere, then, solvent was reduced to 10% to be subsequently frozen and freeze-dried, to be then thermally reduced at 1000 ºC under dynamic Ar/H2 (95:5) atmosphere. The resulting material has large macropores in a highly open porous structure formed by graphitic flakes homogeneously decorated with Si NPs (~50 nm diameter), figure II.17(d).

This procedure also allows the in situ deposition of the particles on the surface of the graphene flakes. Sn and SnO₂-ArGO, were prepared by dissolving SnSO₄ in the GO suspension and the the pH was increased to 9 using NH₃ solution. Then, the suspension was freeze dried to obtain macroporous Sn(OH)₄–GO composites [352].

GO-based aerogels were thermally reduced under a dynamic argon flow to increase their electrical conductivity. Heating the samples under a dynamic argon flow, Sn-ARGO (figure II.17(b)) at 800 °C and SnO₂-ARGO (figure II.17(c)) at 650 °C were obtained [352]. Figure II.17 shows a highly porous material formed by RGO flakes which contain large macroporous randomly distributed along the structure. In both samples, the Sn sub-micrometer particles showed a homogeneous distribution on the graphene sheets and a narrow particle size distribution, higher in the case of the metallic Sn particles (~750 nm diameter) than SnO₂ particles (~250 nm diameter), ascribed to the carbothermal reduction, melting and re-crystallization of Sn particles [358] over 650 °C.

These aerogels have been processed as self-standing electrodes, without any binder nor metallic support, showing promising results as anodes in LIBs[347]. In the case of the SnO₂-ARGO composites, reversible capacity of 1010 mAh ${\rm g}_{{\rm electrode}}^{-{\rm 1}}$ was measured at 0.05 A g⁻¹ and 470 mAh ${\rm g}_{{\rm electrode}}^{-{\rm 1}}$ at 2 A g⁻¹, with reasonable Coulombic efficiencies (>98%) and stability after 150 charge–discharge cycles [355]. Si-ARGO electrodes showed reversible specific capacities ~700 mAh ${\rm g}_{{\rm electrode}}^{-{\rm 1}}$ with associated Coulombic efficiencies  >99% within 2–0.05 V. These electrodes also showed a good stability during 100 charge–discharge cycles [355]. This indicates that ARGO can accommodate volume changes of Si particles and, at the same time, improve the conductivity of the electrode without additives. Due to their high electronic conductivities and light weight, graphene aerogels are good candidates as support in the preparation of electrodes for next-generation Li batteries such as Metal-air batteries or Li-S batteries [359] or Li ion capacitors [360].

Membranes can be fabricated, e.g. by vacuum filtration, even though other deposition techniques can be used [1731]. GO membranes have gas and ion filtration properties [293] making GO an interesting material for water purification and desalination. Ref. [361] reported that GO based membranes are permeable to water, but hold back most other liquid and gases. Research in this area has been expanding with a range of review papers [293, 362–365]. A brief overview will be given here.

GO-based membranes are both selective and highly permeable to water, chemically and physically stable. However, fouling and biocompatibility still need to be addressed [362]. GO/FLG hybrid membranes were reported improved chemical resistance towards chlorine, and enhanced NaCl rejection (up to 85%) [366].

These GO material membranes can be described as an interlayer nanocapillary network, due to the connected interlayer spaces [365]. This network, together with the gaps between edges of non-interlocked neighboring GO sheets, and the cracks or holes of the GO sheet, provide passage for molecules or ions to permeate through the GO membrane in aqueous solutions so that effective separation of different molecules and ions can be achieved depending on the network morphology, degree of GO oxidation, lateral size, stacking in combination with size and chemical nature of molecules and ions. Molecules or ions with smaller hydrated radius, less charge and weaker interaction with GO sheets permeate through the GO membrane more easily than larger ones, driven by the high capillary-like pressure [365, 1731]. The separation performance at high water flux and rejection rates can be tuned by adjusting the GO sheet size, the thickness of the GO membrane, water pH, and the GO membrane structure as summarized in Ref. [365].

The key aspect of these type of membranes is the self-assembly of the flakes into well-ordered macroscopic laminates unlike in GRM-polymer composites, where the flakes are less ordered and less densely packed [363]. The flakes arrangement in the membrane is thus an important parameter influencing separation performance. This not only depends on the characteristics of the flakes themselves (size/thickness, degree of oxidation), but also on the deposition technique [367]. Highly ordered, interlocked GO flakes were obtained by building membranes by spin-coating a GO dispersion in a layer by layer fashion. These interlocked membranes showed better CO₂/nitrogen selectivity than less ordered ones [363, 364]. For a more detailed discussion on transport mechanisms see Refs. [363, 364].

The intercalation of graphite with sulfuric acid can be exploited for the production of GO. Graphite can also be intercalated by a number of other species to yield GIC [160]. The fabrication of donor-GIC after intercalation with, e.g. alkali metals, has gained increasing importance. Refs. [368–374] reported that such acceptor-GICs are very suitable precursors for covalent functionalization of graphene (see section VIII.1).

In typical covalent functionalization sequences, the negatively charged SLG first act as reductants for electrophiles (for example alkylhalide) [368], which are subsequently attacked by the intermediately generated organic radicals or H-atoms, yielding covalently modified graphene. This wet-chemical functionalization is facilitated by the fact that, due to Coulomb repulsion, the negatively charged graphenide [373] layers within the solid GICs can be dispersed in suitable organic solvents (see Ref [373] for more details).

One fundamental question is if whether all negative charges of the graphenide intermediates can be controlled or even completely removed in such redox reactions [376]. Only complete oxidation is expected to avoid reactions with moisture and O during workup [375], leading to side products with undesired and additional O and H functionalities. More importantly, the controlled removal of all negative charges from the solvent exfoliated graphenide intermediates with a suitable oxidation reagent allows for the bulk production of defect-free graphene. Ref. [375] reported that the treatment of K intercalated graphite with benzonitrile (PhCN) leads to discharging, i.e. taking away of the electrons from charged layers, of the individual graphenide sheets upon the formation of the colored radical anion PhCN.-, figure II.18, which can be used to monitor the accompanying exhaustive and Coulomb force-driven migration of K counterions from GICs into the surrounding benzonitrile phase. The suppression of reactions of dispersed graphenides with moisture and air takes place when no treatment with benzonitrile is provided, resulting in graphene. This represents a mild, scalable, and inexpensive method for wet-chemical graphene production. This reductive graphite exfoliation approach can be extended to water as solvent [377].

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LMs, such as TMDs, can be reductively exfoliated via intercalation compounds [159]. Typically, MoS₂ is intercalated with n-Butyllithium (n-BuLi) in an inert solvent such as hexane [378]. In contrast to graphite, intercalated MoS₂ does not react with water [378] so that this can be used for subsequent exfoliation.

Water is added to the reaction mixture to destroy excess BuLi. At the same time, gas formation occurs, which acts as driving force to expand MoS₂ and individualize the layers. After further washing and centrifugation-based purification, a colloidally stable MoS₂ dispersion in water can be obtained with negatively charged, predominantly 1L flakes (70%–90%). As a result of the negative charges, a phase transformation from the semiconducting 2H-MoS₂ polytype to the metallic 1T polytype is observed. Such negatively charged MoS₂ can be used as precursor for subsequent covalent functionalisation using electrophiles [379, 380]. Another approach, based on chlorosulfonic acid assisted exfoliation was developed, allowing to keep the original semiconducting properties of 2H-TMD (as MoS₂ and WS₂) [381, 1412, 1413, 1732, 1733].

This intercalation chemistry was explored in the 80s [159], but the interest was not in producing exfoliated flakes in a liquid dispersion. Ref. [379] studied the impact of intercalation conditions on the final product of chemically exfoliated MoS₂. In a typical exfoliation of MoS₂ with n-BuLi, the n-BuLi is used in ~10-fold excess. These reaction conditions can lead to the introduction of defects, as exemplified by a significant mass loss in TGA under inert conditions (figure II.19(a)). No specific mass fragments can be assigned to this weight loss, suggesting it is not the result of a well-defined surface derivatization [379]. The major mass fragment observed has a mass over charge (m/z) ~18 and was assigned to -OH groups, figure II.19(a). This disruption of the structure is not observed when MoS₂ is used in excess over n-BuLi. The work-up is more tedious, with less material obtained as individualized flakes. After centrifugation, flakes with similar lateral dimensions and thickness distribution are produced (figure II.19(b)) suggesting that there is scope to optimize chemical exfoliation with respect to yield of 1L MoS₂.

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H₂SO₄ can be used to prepare GICs as the ionic diameter of sulfate ion (0.46 nm) is close to the interlayer spacing of graphite (0.33 nm), which is the prerequisite for efficient intercalation. Efficiency here relates to the degree of exfoliation, a higher ratio of MLG is considered more efficient than thicker flakes. In this way efficiency is related to the average thickness of the exfoliated platelets: the lower the thickness, the higher the efficiency. Dilute H₂SO₄ aqueous solutions were used [384, 385] to encourage graphite exfoliation because it is less corrosive. Ref. [385] immersed a graphite anode together with a counter electrode (Pt foil) into 0.1 M H₂SO₄The exfoliation started when a potential of 10 V was applied. This gave 80% 1-3LG with high exfoliation yield (60%) and high C/O ratio (12.3). Under electric current, the oxidation effect on graphene is strong, owing to the interplay between proton (H⁺) and sulfate ion at low pH. The oxidation effect is defined as the oxygen content in the exfoliated materials, which usually results from the attack of oxygen-containing radicals by water splitting [386]. Water electrolysis generates oxidative radicals (HO· and O·), which contains a collection of sulfate salts (e.g. sodium sulfate, ammonium sulfate, etc) instead of H₂SO₄ [387]. By doing so, Ref. [387] reported  >85% of 1-3LG with dimensions up to 40 µm and C/O ~ 17.2, implying a low level of O functionalization. Another strategy to suppress oxidation is to remove radicals from water splitting [388]. A series of scavengers have been investigated. Ref. [388] reported 2,2,6,6-Tetramethyl-1-piperidinyloxy (TEMPO) to be the most effective, reaching C/O ~ 25.3, average sizes ~5–10 µm and hole mobility up to 405 cm² V⁻¹ s⁻¹. Electrochemical exfoliation can produce not only graphene but also highly oxidized GO [306]. E.g., a two-step anodic oxidation in concentrated (98 wt%) and diluted (50 wt%) H sulfuric acid enables the synthesis of GO with C/O  <  2 and high yield (95%) of 1L similar to those achieved by traditional Hummer's methods.

There are still several challenges: (1) the exfoliation only occurs at a single electrode (anode or cathode), limiting the production rate; (2) insufficient intercalation results in polydisperse flakes (with varying N), which requires additional separate procedures; (3) flakes trend to restack in solution, due to strong in-plane interaction when the stabilizers are absent, which needs careful selection of suitable electrolytes.

Another strategy to minimize O content is to use cathodic intercalation and O-free electrolytes [389]. The intercalation of small cations with graphite from organic solvents is the principle of many energy storage devices [389–393]. Graphene can be prepared by electrochemical intercalation of Li⁺ within the graphite interlayer space, followed by dissociation of the resultant intercalating compound using prolonged sonication. Ref. [394] tried to reduce the sonication time by intercalating graphite with Li, followed by a second intercalation of large tetra-n-butylammonium ions. In both cases, the strong decomposition reaction of the solvent cations hindered the formation of LiC₆ and/or ammonia GICs. Therefore, another sonication step was need to completely detach the graphene flakes.

Graphite can be fully exfoliated via an electrochemical process in organic solvents without the need of sonication or an inert atmosphere, by using DMSO saturated with Li and small alkylammonium ions (triethylammonium, Et₃NH⁺) [395]. An electrochemical program is used to apply a controlled cathodic potential on the graphite electrode, enabling the formation of exfoliated powder [266]. In a three-electrode system, a chronoamperometric step of  −1.7 V on Ag/AgCl is applied for 5 min, followed by linear sweep voltammetry at a rate of 10 mV s⁻¹. The potential is then kept at  −5 V for 5 min, to allow intercalation of the electrolyte cations, finally it is swept linearly back to the open-circuit potential to decompose the resultant complex compound. During the first chronoamperometric and the second linear sweep voltammetry steps, solvated carbanion complexes are formed according to reactions II.1-5. The second chronoamperometric step at  −5 V is important to complete the intercalation process. This intercalated compound could decompose cathodically if the potential is held at negative values according to reaction (6) or on the oxidation cycle according to 7. In both cases, dissociation of the intercalated compound is associated with Et₃N gas formation, more likely taking place between the graphene layers, which applies more stress on SLGs and separate them further apart.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle 2{\rm E}{{{\rm t}}_{3}}{\rm N}{{{\rm H}}^{+}}+2{{e}^{-}}={{{\rm H}}_{2}}+2{\rm E}{{{\rm t}}_{3}}{\rm N}\nonumber \end{align} \tag{ II.1 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle n{\rm E}{{{\rm t}}_{3}}{\rm N}+{{e}^{-}}+{\rm C}={{\left( {\rm E}{{{\rm t}}_{3}}{\rm N} \right)}_{n}}{{{\rm C}}^{-}}\nonumber \end{align} \tag{ II.2 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm L}{{{\rm i}}^{+}}+{{e}^{-}}={\rm Li}\nonumber \end{align} \tag{ II.3 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle m{\rm Li}+{{e}^{-}}+{\rm C}={\rm L}{{{\rm i}}_{m}}{{{\rm C}}^{-}}\nonumber \end{align} \tag{ II.4 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle n{\rm E}{{{\rm t}}_{3}}{\rm N}+m{\rm Li}+{{e}^{-}}+{\rm C}={\rm L}{{{\rm i}}_{m}}{{\left( {\rm E}{{{\rm t}}_{3}}{\rm N} \right)}_{n}}{\rm C}\nonumber \end{align} \tag{ II.5 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle & {\rm L}{{{\rm i}}_{m}}{{\left( {\rm E}{{{\rm t}}_{3}}{\rm N} \right)}_{n}}{{{\rm C}}^{-}}+{{e}^{-}}+2{\rm E}{{{\rm t}}_{3}}{\rm N}{{{\rm H}}^{+}} \nonumber \\ & ={\rm C}+m{\rm Li}+\left( n+2 \right){\rm E}{{{\rm t}}_{3}}{\rm N}+{{{\rm H}}_{2}}\nonumber \end{align} \tag{ II.6 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm L}{{{\rm i}}_{m}}{{\left( {\rm E}{{{\rm t}}_{3}}{\rm N} \right)}_{n}}{{{\rm C}}^{-}}={\rm C}+m{\rm Li}+n{\rm E}{{{\rm t}}_{3}}{\rm N}+{{e}^{-}}.\nonumber \end{align} \tag{ II.7 }$$

The intercalation from RT electrolytes is a slow process (diffusion coefficient  <1.2  ×  10⁻¹⁰ cm² s⁻¹) [396] and limited to few µm from the edge of the graphite grain [397]. Attempts to increase chemical activities of Li ions or other cations by using pure ILs or deep eutectic solvents did not overcome the kinetic barriers [398]. Hence, it is important to repeat the exfoliation process for more than one cycle to obtain a yield  >70% the big flakes [389]. Another alternative is to use molten salts at T  >  500 °C as the electrolyte. [399–401] developed for the exfoliation of graphite based on Li intercalation from molten LiCl electrolyte containing water. In a typical experiment, anhydrous LiCl powder, which serves as anode, is charged in a graphite crucible. The cathode is graphite. The cell is heated to ~800 °C, above the melting point of LiCl, and a stream of water is bubbled into the molten bath. Electrolysis is achieved by applying a constant direct current between cathode and anode. After allowing the cell to cool down to RT (Ar gas flow), graphene powder can be recovered from the solidified salt by washing with hot distilled water and vacuum filtering. Finally, the black powder is heated at 1300 °C under inert gas atmosphere containing hydrogen. The process demonstrates commercial viability and a molten salt volume ~10 L can produce ~4.5 kg flakes in a day [400, 402].

Microwave (MW) irradiation is currently employed in many fields of organic synthesis to shorten reaction times, to enhance both reaction yields and product purity, to provide eco-sustainable synthetic methodologies, by replacing or reducing the use of polluting reagents [217]. Graphite can interact with the oscillating electrical field of MW radiation, giving high T gradients and increased reaction rates (e.g. for fast functionalization of GO) [217] as compared to conventional, procedures such as conventional chemical functionalization at RT in solution. Therefore, the T attainable using MW (>80 °C) can be applied to exfoliate graphite [217].

Electrochemistry can be used for a fast (<30 min) and massive (>70%w/w intercalated molecules/graphite) intercalation of suitable molecules, such as perchlorate ions, into graphite [217]. Degradation of these molecules in GICs is then triggered by MW irradiation, creating a gas pressure surge in graphite and yielding exfoliation [217].

Charged perchlorate ions could act as 'Trojan horses', to favour the intercalation of uncharged acetonitrile molecules [348]. These work as nanoscopic foaming agents, and decompose with MW irradiation to generate a pressure surge within graphite, resulting in exfoliation. The process yields soluble, monoatomic (52% SLG), large (72% of the sheets extending beyond 1 µm) GRM sheets characterized and then tested as transparent electrodes [348] and capacitors [348]. These electrodes can also be functionalized with nanoporous layers of inorganic oxides, after the pre-intercalation of electrolyte species (e.g., FeCl₃–nitromethane electrolytes), to obtain, e.g. composite electrodes for LIB [1735].

Electrochemical treatment can be performed starting from HOPG as a working electrode and a Pt wire as a reference electrode. Ions such as sulfates and perchlorates can be efficiently intercalated into graphite, whereas intercalating uncharged molecules is more difficult [131], and can usually be achieved only by several hours sonication, with a lower yield (few%) of both exfoliated material and 1L. The exfoliation process works only if the surface energy of the intercalated organic liquid is similar to that of graphene [131]. The process is limited to high-boiling solvents (T  >  100 °C), such as NMP or DMF. To overcome this challenge, Ref. [348] used perchlorate ions to promote the intercalation of an organic, uncharged molecule (acetonitrile), which was present in high excess, as a solvent. Graphite was intercalated and partially expanded by electrochemical insertion of ClO₄- in acetonitrile by applying a  +  5V for 0.5 h. In this way, negatively charged ClO₄  −  ions intercalated through grain boundaries or defect sites and favoured the penetration of the smaller, uncharged acetonitrile molecules. The fundamental role of ClO₄  −  was demonstrated in a comparison experiment by using acetonitrile alone, for which no intercalation was observed [348]. The amount of molecules intercalated into graphite was high (70% w/w), as estimated from TGA of the intercalated graphite electrode [348].

After electrochemical intercalation, MW irradiation expanded the graphite interlayers through decomposition and gas evolution of acetonitrile to yield a foam-like, multilayered powder [348]. The expansion was fast (~10 s) and yielded an increase in volume of the initial graphite ~600% [348]. The role of acetonitrile in the expansion was demonstrated in a comparison experiment, in which no expansion was observed for graphite treated only in aqueous solutions of HClO₄ or NaClO₄ without acetonitrile [348]. Figure II.20 shows a schematic of the process, and photographs of the material at the different processing stages.

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The exfoliation of LMs usually results in a heterogeneous dispersion of flakes having different morphology, i.e. lateral size and thickness [166]. There are many methods for the selection and processing of flakes [115, 131, 183–185, 424, 425] by means of ultrasonication [115, 131, 174, 183–185, 204, 424–427], shear mixing [176, 177, 238, 428–430], ball milling [179, 431–436], microfluidization [178], and wet-jet milling [437–440]. Centrifugation based size selection methods can be classified into sedimentation based-separation (SBS) and density gradient ultracentrifugation (DGU) [195]. Materials subjected to SBS are sorted on the basis of different sedimentation rates in response to a centrifugal force. Owing to its ease in handling, SBS is the most commonly applied size selection technique for GRMs. Typically, small and thin flakes are separated from larger, thicker counterparts. However, achievable size distributions are still rather broad except for the smallest and thinnest flakes. To tackle this, a number of variations to traditional single step SBS have been developed, such as band sedimentation [185] and liquid cascade centrifugation [186]. Different to SBS, DGU exploits the movement of the dispersed object to the point in the centrifuge tube where the buoyant density of the material matches that of the surrounding liquid. The addition of density gradient media to the mixture is typically required to adjust the density of the liquid to the higher density material [168]. As such, DGU has the potential to separate flakes by thickness, but is more challenging to perform than SBS. In the following sections we will discuss these different strategies, highlighting pros and cons.

The SBS process is widely used to separate materials of different nature and morphology ranging from metallic nanoparticles (MNPs) [441], CNTs [442–445], to GRM flakes [115, 131, 174, 177, 183–185, 204, 238, 424–428, 430]. A theoretical description of the sedimentation process can be found in Ref. [195]. In brief, three forces act on the objects during the centrifugation, which determine their sedimentation rate (see figure III.1(left)): (I) the centrifugal force F_c  =  m_2Dω²r, which is proportional to the mass of flake itself (mGRM), to the square of the angular velocity (ω), and to the distance from the rotational axes (r), (II) the buoyant force F_b  =  −mS 2r, which is linked with the Archimedes' principle, being proportional to the mass of the displaced solvent (mS) times the centrifugal acceleration, and (III) the frictional force F_f  =  −fv, i.e. the force acting on the GRM flakes moving with a sedimentation velocity (ν) in the solvent. F_f is proportional to the friction coefficient (f ) between solvent and the GRM flake. f  depends on both physical parameters of the dispersed flakes, i.e. lateral size and thickness, and physico-chemical properties of the solvent they are dispersed in, i.e. the viscosity (η). Both parameters have a strong influence on the value of f .

Overall, the sedimentation of GRM flakes depends on their mass and frictional coefficient, which is shape dependent [115, 166, 424]. In first approximation, thick and large GRM flakes, having larger mass with respect to small and thin flakes, sediment faster with respect to the latter, since these have smaller mass. This allows to separate GRM flakes with different morphology [166, 424], see figure III.1. However, it is challenging to isolate large and thin flakes. The definition of large/thick and small/thin depends on the material that is used in combination with the centrifugal acceleration and the medium. This will be detailed further down below for a few examples.

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Thus, taking into account the dependence of the physical dimensions of the flakes on the centrifugal acceleration (expressed as relative centrifugal field, RCF, in units of the earth's gravitational field, g), it is possible to exploit SBS to prepare GRM flakes of different morphology. In a typical experiment, a dispersion is centrifuged at a fixed g-for a given time. Supernatant and sediment are then separated. The sediment contains larger and thicker flakes than the supernatant. By changing the centrifugal acceleration and centrifugation time, the flake sizes can be adjusted. E.g. the flakes in the supernatant will be smaller after centrifugation at higher accelerations or longer times. Any centrifuge (benchtop or ultracentrifuge) with either fixed angle rotor or swinging bucket rotors can be used.

Even though it is not required that the centrifugation is run for several hours until an equilibrium is reached, i.e. all flakes that will sediment at a given centrifugal acceleration have reached the bottom of the vial, it is recommended not to use centrifugation times shorter than 30 min. When centrifugation times are short, a steeper size/thickness gradient is formed in the vial. As a result, the size and thickness distributions in supernatant and sediment will depend on how the sample is decanted, leading to poor reproducibility. Centrifugation times ~1–3 h are recommended and lead to reproducible results. This also depends on the rotor and vial size, hence the distance the flakes need to travel to reach the bottom [246]. Often sediments are then discarded and supernatants collected for analysis and/or further processing. However this makes it a wasteful process.

With SBS, it has been possible to prepare samples having lateral sizes ranging from few nm to a few µm, both for FLG [131, 176, 184, 424–427, 446, 447] and other LMs [174, 185, 244, 425, 448, 449]. In terms of thickness, dispersions with SLG content up to ~60% were demonstrated in an SDC based aqueous dispersion [446], while ~33% SLG was reported for dispersion in NMP [447]. Such 1L-rich dispersions from SBS also contain predominantly laterally very small (<50 nm) flakes [446, 447]. Apart from the difference in percentage of SLG, the flakes processed in water-surfactant dispersions are, on average, also smaller (~200 nm) [184, 427, 446] with respect to NMP (~1 µm) [131, 447]. This difference is related to the difference in the viscosity of the solvents. When comparing the most widely used solvents (NMP and water where, with the addition of surfactant, the viscosity decreases) the viscosity of NMP (1.7 mPa s) [450] is significantly higher than water (~1 mPa s) [451]. A higher solvent viscosity increases the frictional force [195], reducing the sedimentation velocity [195]. Therefore, when using similar centrifugation conditions (centrifugation time and centrifugal acceleration), the flakes retained in the supernatant will be larger/thicker in higher viscosity solvents.

SBS also suffers from the further disadvantage that all flakes(also small  <  50 nm) remain in the supernatant when operating at the low centrifugal acceleration (<1000 g) used to isolate large (µm) flakes. Hence, dispersions containing larger flakes on average are significantly more polydisperse and show broad size (20-few µm) and thickness (1–20 layers) distributions. This can be partially overcome by a band sedimentation approach, where the dispersion is placed on top of a solvent race layer (without flakes) prior to centrifugation [185]. E.g. a dispersion containing flakes in an aqueous surfactant can be onto a race layer of deuterated water containing the same surfactant [185]. During centrifugation, the flakes spread throughout the vial according to their sedimentation rate, related to their size. The centrifugation is stopped before the dispersion constituents reach the bottom of the vial, allowing for a collection of various fractions in one run. Smaller/thinner flakes remain closer to the top and are thus efficiently isolated from larger/thicker ones, closer to the bottom. This was demonstrated for MoS₂ [185]. In this case, centrifugation at 1500 g for 10 min yielded various fractions ranging from mean lateral sizes of 350 nm and arithmetic mean N~15 in fractions close to the bottom, to 40 nm and 2L in fractions extracted from the top of the vial. Compared to traditional homogeneous SBS, the distribution histograms were narrower, i.e. the standard distribution was reduced by ~2 [185].

Even though this approach can be advantageous when various fractions with narrower thickness distributions than SBS are required, it suffers from a few disadvantages. First, the material quantity that can be processed in a single step is lower because it is beneficial to keep the sample layer thin, so that most of the volume in the cuvette is taken up by the race layer. Second, the final size-selected sample is diluted during the process, making high concentrations inaccessible. Third, a swinging-bucket rotor is required, as a fixed-angle rotor will not lead to such a defined movement of flakes through the race layer. Therefore, liquid cascade centrifugation (LC) has been suggested as versatile alternative to the above mentioned single step SBS.

LCC is versatile and can be carried out using benchtop centrifuges [186]. This is a multi-step procedure, whereby various cascades can be designed according to the desired outcome. To demonstrate this process, a general cascade is portrayed in figure III.2. It involves multiple centrifugation steps, each with a higher centrifugal acceleration [186]. After each step the sediment is retained and the supernatant is then used in the proceeding stage. As a result, each sediment contains flakes in a given size range, 'trapped' between two centrifugation stages with different speeds. Similar to band sedimentation, small/thin flakes are removed from dispersions with predominantly larger/thicker flakes. As with traditional SBS, the lateral dimensions and N obtained depend on the design of the cascade (centrifugal accelerations), starting material and solvent. A few examples of lateral sizes and thicknesses are summarised in table III.1.

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Critical to LCC, the resulting sediment can be redispersed by mild agitation (shaking, or  <5 min bath sonication) in the respective medium, enabling one to reach any desired flake concentration, as well as modification of the concentration of additives (such as polymers or surfactants). Virtually no material is wasted in LCC, resulting in the collection of larger masses of size-selected flakes from a single dispersion compared to homogeneous SBS, where the sediments are discarded. The procedure was thus found to be ideal to study size effects in applications [452]. It was applied to WS₂ and MoS₂ [186, 245, 452, 453] as Ni(OH)₂ [240], GaS [188], BP [190] and FLG [176, 236] in solvents [176, 188, 190] as well as aqueous surfactant [177, 186, 236, 240, 452] or polymer systems [453]. Due to its versatility and the large accessible quantities, other reports adopted the procedure [454, 455]. Typical mean lateral sizes and N are given in table III.1 for a range of materials.

From this table it is clear, that the outcome of the size selection depends on the centrifugal accelerations, the density of the material and medium. A deeper understanding and systematic analysis will enable the prediction of the outcome of the size selection. In any case, to achieve efficient size selection, it is critical to remove the supernatant from the sediment as completely as possible. This also means that for this procedure to work, the centrifugation time has to be long enough to allow the majority of the flakes to sediment to the bottom of the vial. This does not require centrifugation to equilibrium (unlike DGU). One can obtain a good separation of supernatant and pellet-like sediment after 2 h of centrifugation, when the filling height of the dispersion in the vial is  <10 cm. Centrifugation times should be extended if greater filling heights are used [246].

The chosen size-selection cascade can be modified readily to suit a desired outcome. While this specific procedure yields flakes sizes and thicknesses over a broad size range in the different fractions, if only specific sizes are targeted, some centrifugation steps can be skipped. E.g. if medium-sized flakes are desired, the sample can be centrifuged at only two different centrifugal accelerations and the sediment redispersed. In first approximation, flake size selection occurs by mass in such a standard cascade, still making it difficult to select large (µm), thin (1–3 L) flakes like in homogeneous SBS. However, a design of secondary cascades [186] involving a combination of long (14 h), low-speed centrifugations (~1/5 of the lower g-boundary of the initial trapping) to remove thicker material and short (60 min), high-speed centrifugations (above the higher g-boundary of the initial trapping) to remove very small (10–20 nm) flakes has shown potential to overcome this limitation yielding a ~75% 1L (mean N ~1.3) with an average lateral size ~40 nm in the case of WS₂ [186].

III.1.3.1. Density gradient centrifugation

The control of the ink rheology is key to ensure consistency and reproducibility. This is usually achieved by studying flow and deformation of the materials under external perturbation [485]. The complex structure of the ink determines a rheological behavior which is typical of non-Newtonian flow [486]. Thus, there is a non-linear relation between shear rate $\boldsymbol{\dot{\gamma }}$ shear stress (τ), and apparent viscosity η (η_app  =  σ$\boldsymbol{\dot{\gamma }}$) which depend on $\boldsymbol{\dot{\gamma }}$ (or τ). This behavior is different from Newtonian liquids, where η  =  σ$\boldsymbol{\dot{\gamma }}$ [487]. The shear rate determines the η behavior of inks and, thus, their range of application. Depending on their flow behavior, there are different classifications for non-Newtonian inks [488]: dilatant where η_app increases with increasing $\boldsymbol{\dot{\gamma }}$[488], pseudoplastic, where η_app decreases with increasing $\boldsymbol{\dot{\gamma }}$ [488], and thixotropic, where η_app decreases with time under a constant deformation and will start to rebuild once the shear force η_app is removed [488], figure III.3. The ink rheology is strongly influenced by the GRM volume fraction, φ, with their shape and spatial arrangement [489], GRM flakes dispersed in a liquid affect its flow field resulting in an increase in energy dissipation due to fluid-flake and/or flake-flake interactions [489, 490]. These interactions increase with φ, restricting the flakes diffusion into small 'domains', formed by the nearest neighbors and η diverges. However, a theoretical model to predict η of fluids with dispersed GRMs does not exist yet. Such model is not even available for NPs in general, although a significant research effort has been carried out [491–493].

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We now discuss the main ink requirements and the state of the art of the formulation for the of GRM-based inks for the main deposition/printing techniques.

Coating approaches, such as drop and spin coating, do not require a structured ink formulation, and, usually, the as-prepared dispersion can be directly deposited onto the target substrates. On the contrary, although the ink for spray coating deposition does not require a high viscosity, the aerosol formation and the subsequent drying process need the control of several processing parameters [494] such as viscosity [495], flow rate [496], and the distance substrate/spray-nozzle [497]. The nature of the solvent, which determines its evaporation rate at the substrate surface [496], is also a critical point for a uniform deposition. The solvent vapor pressure is crucial. Solvents having low vapor pressure, such as NMP (0.5mm Hg @25 °C), one of the most common for LPE of graphite [164], promote long crystal formation time [496]. This allows a consistent structural arrangement prior to the transition to the solid phase of the deposited feature [496]. On the contrary, high vapor pressure solvents, such as, e.g. isopropyl alcohol (IPA, 33mm Hg @25 °C) and toluene (24 mm Hg @25 °C), promote faster solvent evaporation [1741]. This subsequently reduces the ability of the flakes to organize in a ordered manner. The consequence will be a decrease of the final device performance, such as, e.g. a reduction of the charge carriers mobility in FETs [496]. Other sources of instability for the coating are linked with the geometry of the spray coating system, i.e. small nozzle size, or the jetting pressure, i.e. low pressures reduce the flow rate, which produce scattered droplets on the substrate and eventually a non-uniform coating [496]. A continuous coating is obtained by high deposition rates [145, 496]. The uniformity of the coating is also determined by the appropriate substrate/nozzle distance [497]. If this too short, the ink previously deposited onto the substrate can be blown away by the incoming flow. If it is large, the solvent can evaporate during the flight time, i.e. before the droplets reach the substrate.

The formulation of the ink for an inkjet process requires the control and tuning of various liquid properties such as ρ, η, and γ [498], which are then summarized in the following dimensionless figures of merit (FOM): the Reynolds (N_Re) and Weber (N_We) [499, 500] and the inverse of the Ohnesorge number, Z (1/N_Oh) [500]. The Z number is independent on the drop velocity (m · s⁻¹) and it is the most used FOM for inkjet printing [501–507]. Different Z values have been proposed, ranging from 1 to 91 with different functional materials [501–507].

Other parameters for the ink formulation have to be considered, such as, e.g. the physical dimensions of the flakes dispersed in the ink, that can agglomerate and clogg the print-head. Usually, it is required that flakes have lateral sizes smaller than ~1/50 of the nozzle diameter [508] (typically ~100 µm [509]). Other parameters to be optimized for the printing/deposition process are wetting and adhesion [510] to the substrate, as well as the distance between nozzle and substrate (typically 1–3 mm) [511].

An even more structured inkis needed for flexography and gravure printing. Although both require a high viscosity ink, there are several differences [166]. In flexography, there is a plate with a raised surface that spreads the ink onto the target substrate. Gravure is an intaglio process, where the ink is first transferred onto an image carrier and then printed on the target substrate. As summarised in table III.2 and Ref. [166], gravure printing is usually faster (~1000 m min⁻¹) than flexo (~500 m min⁻¹), with printed stripes thicker (~1 µm in gravure) than in flexography (<1 µm). The viscosity is also different: in flexography this is in the 50–500 mPa · s range, while in gravure it is higher 100–1000 mPa · s.

GRM-based inks for flexography and gravure were formulated [512, 513]. Ref. [512] reported a flexography ink by using CMC as a binder for FLG flakes in a water/isopropanol solution, obtaining a η ~20 mPa · s. The as-formulated ink was printed onto a flexible ITO substrate at 0.4 m s⁻¹, and used as counter electrode for the realization of a flexible dye-sensitized solar cell (DSSC) [512]. A FLG/terpineol ink (η ~0.2–3 Pa · s from the homogeneous dispersion of FLG-ethyl cellulose powder (5–10 wt%) in a mixture of ethanol/terpineol (2.5:1 volume%) was reported in Ref. [513]. For the formulation of high viscosity GRM-based inks, there are several issues to be addressed. First, the solvents used in LPE (e.g. NMP) are toxic and have very low η (<2 mPa · s). The use of alternatives such as volatile alcohols, e.g. ethanol [513] and isopropanol [512], is against the current environmental regulations, requiring the minimization of volatile organic compounds [514]. Second, the GRM concentration in these solvents is low (<1 g l⁻¹). Thus, in order to produce a functional (e.g. conductive) film, many print passes are required. The increase of GRM fillers could determine a problem with the solvent evaporation and in-series printability. In this context, the use of high boiling point solvents requires post-processing annealing for solvent removal [515], thus posing limitations on target substrate.

By increasing η, it is possible to obtain a paste, needed for screen printing. FLG-based conductive-pastes (i.e. FLG [516], RGO [517–519] and flakes [520, 521]) are emerging as possible alternatives to those based on metal NPs.

A paste based on FLG powder dispersed in terpineol, with ethylcellulose as a binder was prepared in [516]. The paste contained flakes at a concentration of ~80 g l⁻¹, having a η up to ~10 Pa·s at a shear rate of 10 s⁻¹. The as-deposited paste required a thermal treatment at 300 °C for 30 min to remove ethylcellulose. Another FLG-based paste, having shear thinning behaviour, was discussed in Ref. [522], which a gelation approach starting from the dispersion of expanded graphite in methyl ether dipropylene glycol in the presence of polyvinyl acetate and polyvinylpyrrolidone acting as binders. However, many parameters still need to be optimized for the development of optimal GRM-based inks/pastes for screen printing.

Figure III.4 shows a selection of polymers at 1 wt% loading that can be added to water or 50:50 water/ethanol solutions to modify the rheology. Polymers such as polyvinylpyrrolidone (PVP) can be added, with increased viscosity with increasing molecular weight (M_W). Celluloses which are commonly used, provide high viscosity at low loadings, and impart thixotropic behaviour. E.g. aqueous FLG-based inks produced by microfluidization [178] have FLG loading  >100 g l⁻¹ and are formulated using 1 wt% sodium carboxymethylcellulose (NaCMC) to provide η up to 1800 mPa · s.

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NaCMC is not easily dissolved and its preparation can be affected by factors including the NaCMC particle size, rotational speed of the mixer, the rate at which solutes are introduced, and the solution T [523]. Heating the FLG dispersion should be avoided as this may promote flocculation. NaCMC is water-absorbent and has high water retention, therefore it clumps. To prevent this, NaCMC is added until dissolved completely and stirred to avoid bubbles. Bubbles and clumps need to be removed prior to printing.

The rheological properties of inks were investigated by monitoring the elastic modulus G'[J m⁻³  = Pa] [524], representing the elastic behavior of the material and a measure of the energy density stored under a shear process [524], and the loss modulus G''[J m⁻³  =  Pa] [524], representing the viscous behavior and a measure of the energy density lost during a shear process due to friction and internal motions [524]. Flow curves measured by increasing $\boldsymbol{\dot{\gamma }}$ from 1 to 1000 s⁻¹ at a gap of 0.5 mm, because this $\boldsymbol{\dot{\gamma }}$ range is applied during screen printing. Figure III.5(a) plots the steady state viscosity of an ink produced from microfluidization (100 cycles) containing 73 wt% flakes as a function of $\boldsymbol{\dot{\gamma }}$. NaCMC imparts a drop in viscosity under shearing, from 570 mPa · s at 100 s⁻¹ to 140 mPa · s at 1000 s⁻¹. This is thixotropic [525], since the viscosity reduces with $\boldsymbol{\dot{\gamma }}$.

This behavior is shown by some non-Newtonian fluids, such as polymer solutions [526] and biological fluids [527]. It is caused by the disentanglement of polymer coils or increased orientation of polymer coils in the direction of the flow. In contrast, in Newtonian liquids, the viscosity does not change with $\boldsymbol{\dot{\gamma }}$[527]. Refs. [528, 529] reported that thixotropy in NaCMC solutions arises from the presence of unsubstituted (free) OH groups. Thixotropy decreases as the number of OH groups increases [528, 529]. Figure III.5(b) plots the viscosity at hundred s⁻¹ as a function of wt%FLG flakes (70 microfluidic process cycles). The NaCMC polymer (10 g l⁻¹ in water) has a µ ~0.56 Pa · s at hundred s⁻¹, and drops to 0.43 Pa · s with the addition of 5 wt% flakes. The loading wt% of flakes affects $\boldsymbol{\dot{\gamma }}$, which increases at 51 wt% and reaches 0.6 Pa · s at 80 wt.%.

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III.2.2.1. Graphene/polymer blends

III.2.2.2. Graphene/CNT films

III.2.2.3. Inks with conductive polymers

Vacuum filtration is a simple technique whereby a GRM dispersion can be filtered through an underlying porous membrane to obtain nm-to-several micron thick films [535, 536]. These can be removed from the underlying support to produce a freestanding film, or transferred to rigid and flexible substrates and the porous membrane removed e.g. by chemical dissolution [536]. Although this technique may be unsuitable for the production of GRM-containing structures for commercial purposes, its low cost and its simplicity makes it ideal for research purposes. The main advantage is the possibility to wash away surfactants and solvent residues that usually affect the performance (e.g. conductivity) of the final films. Films with different thicknesses and composition can be produced by tuning the amount of dispersion, the pore size of the membrane and the vacuum pressure. GRM dispersions can be filtered on to various membranes, selected based on their pore size and chemical compatibility. Membrane types include cellulose, polycarbonate, anodized alumina, PVDF or PTFE. This allows to produce composites such as layered oxides combined with SWNTs for supercapacitor electrodes [239, 537], and TMDs/SWNT composites for electrocatalysis [452, 538] can readily be fabricated.

A wide range of filtration membranes are available with different surface chemistries and pore-sizes, the choice of which depends on the nature of the dispersion media, the size of the dispersed materials to be filtered and the desired approach to carry out film transfer. As the flakes produced by LPE often have lateral dimensions in 10s-hundreds nm, it is often necessary to use filtration membranes with the smallest possible pore diameters. Mixed cellulose membranes with 25 nm pore size are compatible with aqueous/surfactant dispersion media and can be subsequently dissolved using acetone to achieve transfer of the filtered film.

FLG films with thickness ~150 nm, transmittance ~50%, roughness ~8 nm and R_s ~ 1–2 kΩ sq⁻¹ were prepared as conductive electrodes for biological applications [432]. These were also exploited in photonic applications, demonstrating sub-50 fs compressed pulses from a FLG-mode locked fiber laser [539], power scaling lasers [540], and monolithic waveguide lasers [541]. To produce these, a 25 mm diameter membrane filtration setup was used. 500 µl of dispersion with concentration ~0.1 g l⁻¹ was diluted in 1 ml DI water. The dilution is necessary when the amount of the filtered dispersion is less than 1 ml to ensure uniform coverage of the membrane. If the dispersion has a high surfactant concentration, the presence of foam on the liquid surface has to be avoided before vacuum filtration. FLG is filtered through a 100 nm pore-size nitrocellulose (NC) filter membranes (Millipore). In order to remove the residual surfactant, the film on the membrane can be rinsed by filtration of 20 ml DI water. The filtering process requires ~2 h, which will increase with the film thickness prepared.

These films can be transferred on to glass coverslips (25 mm diameter) using the following procedure: 1. the FLG/NC membrane is cut to the size required and soaked in deionized water. 2. The FLG/NC is placed on the glass substrate with the FLG side face down. 3. A sheet of cleanroom paper is pressed by hand on the back of the NC to remove the excess water and trapped air between the film and glass. This is a critical step, as trapped air can leave some FLG non-transferred and, therefore, holes or fractures in the final film. The substrate is then clamped with two bulldog clips between two glass slides (30  ×  30 mm). 4. The sample is left to dry in an oven for ~2 h at 90 °C. 5. The glass slides are removed and the coverslip left to soak in a covered beaker of acetone to dissolve the NC (at least 24 h) then soaked in isopropyl alcohol (1 h) and in deionized water (1 h). 6. The final FLG/glass sample is then dried in an oven for 2 h at 90 °C. Transfer on flexible substrates can be done with the same procedure. For improved transfer it is possible to use a hydraulic press in step 3.

Another method to make large free-standing membranes is electrophoretic deposition [542]. A suspension of GO with a concentration of 3 mg ml⁻¹ is prepared and used as the electrolyte. Two identical pieces of well-polished Cu sheets (30  ×  50  ×  2 mm) are used as anode and cathode. A constant current of 2 mA is applied between the two electrodes for 2 min. The anode coated with GO is then dried under vacuum overnight, and then the free-standing GO membrane can be peeled off.

The printing of FLG inks is an attractive approach for developing electronic applications, such as transparent conductive films, printed electrodes and sensors. Inkjet printing is the ideal tool to produce prototype electronic devices at the lab scale. Indeed, it enables high resolution (~25 µm) of the pattern associated with the possibility of easily changing the pattern and the printed material. Several examples of inkjet printing of nanomaterials have been reported [201, 447, 543, 544]. In order to have a good jettability an ink has to satisfy particular requirements on Z, γ ρ, η and nozzle diameter. If Z is in the 4–14 range, satellite droplets recombine before reaching the substrate, but Ref. [447] demonstrated the possibility of having good printing also outside this range. Most lab-scale inkjet printers equipped with disposable cartridges, (e.g. Fujilm Dimatix 2800, Ceradrop X, LP50) mount cartridges with 50 µm diameter, so the flakes dispersed in the ink have to be at least 1/20 of the nozzle diameter to avoid printing instability and nozzle clogging. Dispersions produced by LPE followed by centrifugation are particularly suitable for inkjet printing, since they contain flakes with lateral sizes  <2–3 µm [164]. Inks made by electrochemical exfoliation contain larger flakes even after centrifugation. These should be filtered before printing.

Inkjet printing can be performed on a variety of rigid (glass, Si/SiO₂) and flexible (PET, PEN, PI) substrates. However, the wettability of ink droplets, defined by the contact angle, varies significantly. The most common procedures for changing the surface properties is to reduce the contact angle (improve wettability) by treating substrates. To increase contact angles, the substrate can be silanized by spin coating hexamethyldisilazane (HMDS) (40 s at 1000 rpm, followed by annealing at 80 °C for 2 min) [447]. Silanization requires surface hydroxyl groups to bind to. For flexible substrates, a preliminary UV ozone or oxygen plasma treatment will help to generate surface oxides. This results in more confined droplets, less spreading of the ink and higher resolution [447].

Flexible substrates already optimized for inkjet can be found on the market i.e. glossy papers, Novele (PET/SiO₂/PVA) [545], etc which allow the quick wicking away of solvent, reducing the coffee ring effect thanks to their porosity.

Below, we report different examples for the production of strain sensors on flexible substrates from inkjet-pronted FLG. A flexible integrated platform, with four linear strain gauges 3 mm  ×  20 mm and a central Wheastone bridge strain gauge of 1.5 cm  ×  1.5 cm was printed on Novele substrate. A FLG-NMP ink with a concentration ~1 g l⁻¹ and FLG flakes lateral size up to 600 nm was printed for 50 printing passes with an interdrop distance ~27 µm, inter-layer delay time ~ 120 s, and printer platform T ~60 °C. Annealing was performed at 80 °C in vacuum overnight. The strain gauges with a resistance ~100 kΩ show had gauge factor(GF ~20 at 25 mm bending radius with a change in resistance ~5% after 1000 bending cycles. FLG-based strain gauges with similar properties were printed on planarized PEN using a FLG-ethanol ink (2 g l⁻¹) to make fully flexible wearable devices. The sensors are aligned with the proximal inter-phalangeal joints of the first and second digit of the hand, allowing the extension-flexion movements of these digits to be monitored. 20 printing passes, 22 µm inter drop distance and RT were used with an additional annealing at 80 °C in vacuum for 2 h.

With aqueous-surfactant based inks, one problem is the formation of foam bubbles following agitation of the print-head. This is observed at surfactant concentrations  >6 g l⁻¹. The presence of non-conductive species (surfactants, polymers) in the resulting printed films will reduce FLG network connectivity and, thus, conductivity. The ability for microfluidic processing to stabilize FLG at low surfactant concentrations (0.5 g l⁻¹) meant foaming does not occur. The suitability of 0.5 g l⁻¹ SDC stabilized FLG inks after 20 process cycles and centrifuged at 10 krpm, 1 h can be tested for inkjet printing (figure III.6(6)). Serpentine-type FLG resistors are printed on to photo quality paper (HP Advanced) at room temperature using an interdrop distance of 18 µm, with 20, 40 and 80 printing passes (figure III.6(b)). Prints are left to dry at RT for 60 s between passes. Although minimum optimization is required, prints with over 20 layers suffer bleeding, due to insufficient drying time, and nozzles could become partially clogged. During printing, the head is cleaned by an automated Spit-Purge-Spit cycle every 180 s. Patterns are printed for 20 passes at a time and the nozzles wiped by hand with IPA prior to printing more layers. After 20, 40 and 80 passes the resistance of the patterns decreases from~220, to 31, 3.7 MΩ, respectively, over ~40 mm (track width ~0.9 mm) as shown in figure III.6(b). The resistance response of these devices is tested with strain (3-point bending) and in different gas environments.

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Three-point bending is performed with a 300 N/2 kN Deben vertical three point tensile stage. The samples are bent with an extension rate of 0.5 mm min⁻¹ and measured under tension (positive strain) and compression (negative strain), to a maximum of 5 mm displacement. The electrical resistance of the printed strain gauge varies, depending on the amount of axial bending strain in the device. Printed structures at 20 and 40 passes show very similar resistance versus strain curves (figure III.6(c)) with significant response to  +0.4% strain (ΔR ~  +35%) and  −0.4% strain ΔR ~  −25%). The 80 printed pass sample show significantly lower response (ΔR ~  ±10%) in line with the higher sample thickness. These changes are a result of conductivity variations, due to changes in length, as well as the distance between flakes. The relative change in electrical resistance (ΔR/R₀) is related to the mechanical strain (ε) by the gauge factor (G  =  (ΔR/R₀)/ε). These are 93, 85 and 39 for the 20, 40 and 80 print pass samples, respectively and thus comparable to other FLG devices produced by drop-casting or spray coating (G: 75–150 at 0.2% strain) [546]. These gauge factors are higher than graphite-based ink strain sensors (G: 19.3  ±  1.4) [547], and considerably higher than conventional strain gauges [548] or inkjet-printed metal strain gauges [549] in which G_Factor ~ 2.

In addition we used inkjet printing to print heterostructure devices by placing one material on top of the other. Inkjet printed MoS₂/FLG photodetectors (PDs) using LPE inks were demonstrated on PET. The devices were fabricated using a Dimatix 2800. A 40 µm MoS₂ channel contacted by two inkjet printed FLG electrodes on top. 100 passes of both FLG and MoS₂/NMP based inks were printed at 60 °C using 25 µm interdrop distance and 300 s interdelay time. MoS₂ was annealed at 90 °C in vacuum for 9 h before printing FLG. Finally the entire device was annealed overnight at the same conditions. The good performance of the PD showed that the MoS₂ properties could be retained after printing. Similar results were reported in Refs. [201, 550], confirming that inkjet-printing can become an efficient method to produce functional devices for a variety of applications including photonics, optoelectronics and energy storage.

For flexible electronic devices, e.g. organic photovoltaics (OPVs), R_s  <  10 Ω □⁻¹ is required [255], while for printed radio-frequency identification (RF-ID) antennas one needs a few Ω □⁻¹ [257]. To minimize R_s, µm range films are deposited using screen printing [551–554]. Screen printing is a commonly used industrial technique for fast, inexpensive deposition of films over large areas. It also allows patterning to define which areas of the substrate receive deposition. The screen is typically a polyester mesh with a cured lacquer stencil on top that provides the desired pattern. Mesh grades vary from ~10 up to 180 threads cm⁻¹. The film or emulsion stencils range from a minimum of 12 µm to  >300 µm. The ink must have high viscosity (>500 mPa s) [555, 556], because lower viscosity inks run through the mesh rather than dispensing out of it [555]. To achieve this, typical formulations of screen inks contain a conductive filler, such as Ag particles,[557] and insulating additives [558]at a total concentration higher than 100 g l⁻¹ [558]. Of this, >60 g l⁻¹ consist of the conductive filler needed to achieve high σ ~ 10² S m⁻¹ [557, 559]. A squeegee is used to fill the mesh with ink before a high pressure is applied to force the ink through the mesh onto the substrate [558]. Figure III.7 shows a schematic of the screen printing process. Ref. [560] provides a good introduction to screen printing.

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The printability of inks with ~80 wt%FLG flakes after 70 microfluidic processing cycles formulated with 1 wt%NaCMC was tested using a semi-automatic flatbed screen printer (Kippax-2012-BU) and a Natgraph screen printer (figure III.8(a)), both equipped with screens with 120 mesh count per inch. Trials were made onto (PET) (125 µm thickness, PMX729 HiFi Industrial Film Ltd) and paper substrates. Figure III.8(b) shows a 29 cm  ×  29 cm print on paper with a line resolution ~100 µm (figure III.8(c)). The printed pattern (figure III.8(b)) can be used as a capacitive touch pad in a sound platform that translates touch into audio [561].

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The vertical induction heated furnace shown in figure IV.3 consists of a coil to produce a uniform electro-magnetic field in the semi-close graphite platform called crucible on which the T is measured with an optical pyrometer, a quartz tube with a diameter of 100–200 mm depending on the size of the crucible, porous graphite insulation which is slightly smaller than the quartz tube [607]. The role of the radiofrequency (RF) field is to produce Eddy current in the crucible and that heat up the crucible (figure IV.3(b)). The long RF coil in the reactor provides a uniform electro-magnetic field distribution in order to ensure a uniform T on the substrate. This design allows treatment of SiC wafers up to 50 mm in diameter. Other furnace designs with fully automated T controls were also reported [613].

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As the T distribution in the crucible influences the thickness uniformity, a symmetric crucible was designed for good T uniformity, with optimization by modelling the T distribution (figure IV.3(c)). The SiC substrate position should be in the centre of the RF coil. Prior to growth, the substrates are cleaned in organic solvents, then in solutions based on sequential oxidative desorption and complexing with H₂O₂–NH₄OH–H₂O (RCA1) followed by H₂O₂–NCI–H₂O (RCA-2) to remove organic contaminations and dipping in diluted HF. The substrates are then placed in the middle of the graphite crucible followed by the placement in the porous graphite insulation. After that, the whole assembly is loaded in the growth chamber (quartz tube), locked and pumped down. The chamber is ready for heating when the pressure reaches 5  ×  10⁻⁷ mbar.

To slow the Si sublimation while being close to equilibrium conditions, growth was performed under 1 atm of Argon (Ar) [588, 589, 614]. At 2000 °C Si sublimation in 1 atm of Ar SLG on a large area and thickness uniformity [614]. Figures IV.4(a) and (b) show LEEM images of graphene layers (small domains of 1–2 µm size and thickness  >5LG) grown in Ar atmosphere with a better thickness uniformity and quality for graphene grown in Ar [588]. Note that LEEM is performed instead of conventional SEM, because by counting the number of minima in the LEEM reflectivity as a function of the electron beam intensity, the N can be determined at the resolution of the LEEM image. Details about T-time profile can be described as setting T ramps (~20 per minute) up to at least 1150 °C and once the desired graphitization T (usually  >1150 °C) is reached keeping this T during the growth time. Then decreasing it down to RT with a slow ramping (70 min⁻¹).

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CCS[597] relies on SiC being in near equilibrium conditions with the Si vapour. Graphene growth is controlled by encapsulating the SiC crystals in graphite so as to sequester the evaporated Si (see figure IV.5). A SiC crystal is placed in a closed graphite box (called crucible) provided with a very small calibrated hole of typical diameter 1 mm. As the T of the furnace is increased above 1200 °C and Si sublimates from SiC, the built-up Si vapour remains confined inside the crucible and escapes slowly through the hole (figure IV.5(b)). The SiC chip is therefore in a uniform Si vapour as defined by the PS_i versus T of figure IV.2, ensuring uniform graphene growth. Because the Si vapour is confined, the growth T is substantially increased (by ~300 K for CCS [597]) compared to vacuum growth. Details about the full furnace design and operating conditions can be found in Ref. [597, 615]. The Si escape rate that ultimately determines the growth rate, is defined by the geometry of the hole (diameter 0.5 to 2 mm) [597, 615]. The rate of graphene formation by CCS can be reduced by a factor  >1000 compared to UHV sublimation, where 1LG grows on the C-face in ~1 min at T  =  1.200 °C [597]. The graphene formation rates can be reduced by an additional factor of up to 10³ by introducing 1 atm of Ar into the enclosed crucible [597]. The system is compact for fast pumping speed and small thermal inertia, allowing fast heating and cooling rate up 150 °C s⁻¹ in the T range from RT to 2100 °C. The T profile is computer automated [615, 616]. The whole process can be performed in less than two hours, being scalable to full wafer sizes.

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An alternative method to CCS is to cover the SiC substrate with a piece of graphite, which provides some Si vapour confinement. The Si escapes on the side providing a non uniform Si vapour gradient that produces narrow tapered stripes of graphene [617].

To grow EG on hexagonal 4H- or 6H-SiC wafers by CCS [615] the key step after pumping out the cell to below 10⁻⁶ mbar, is the Si sublimation at high T (1400 °C–1650 °C). The exact T profile depends the geometry of the graphite crucible and geometry of the hole [615], and on the background pressure (with or without additional Ar backpressure). Optimum T and growth times are specific for each crucible adapted to each type of grown graphene. Typically, a 1LG in 20 min at 1520 °C [594] on the Si-face, a graphene buffer layer °C lower than the Si monolayer in the same crucible [594]. On the C-face, N is determined by both T (1450 °C–1525 °C) and time (1 min to several hours for very thick films)[597, 615] [606] (see section IV.1.3 and figures IV.5(a)–(c)). Templated graphene growth of nanostructures (e.g. SiC sidewalls [618–620]) on non-polar facets (i.e. other that (0 0 0 1) and $\left( 0\,0\,0\,\overline{1} \right)$) is finely tuned close to the buffer layer growth conditions.

The surface state of the substrate prior to growth is essential, because rough surfaces have multiple disordered nano-steps acting as nucleation centres for graphene growth. The first step is therefore SiC surface flattening. For SiC surfaces polished to optical quality, the deep polishing scratches can be removed by SiC etching at high T in a hydrogen environment [621]. Successful flattening is obtained at 1500 °C for 15 min in a flow rate of 200 sccm in 1 atm of a mixture of 5% H₂ in Ar [621], which produces a surface with no observable scratches in AFM section IX.1.2 and with a step-terrace structure with atomically flat terraces. However, on the 6H(0 0 0 1) face, the average width and step height of terraces after treatment do not have a clear correlation with hydrogen etching, T and time, but are related to the local miscut angle (the local angle θ of the surface relative to the on-axis orientation, generally θ  <  0.2° for commercial wafers of on-axis wafer [621]. Commercial SiC wafers can be purchased with so-called 'epiready surfaces' treated by a chemical mechanical process. These provide excellent starting surfaces, with rms  <  0.2–0.3 nm, with no need for etching prior to graphene growth.

On the 4H- or 6H-SiC carbon face, continuous MLG containing 5–10 LG [622] are grown by annealing for 15 min at T in the range 1450 °C–1525 °C. Repeated cycles produce much thicker films up to 50 LG [623, 624]. Shorter times and lower T are required to produce 1LG. They appear in patches on the SiC substrate (see inset of figure IV.7(a)) because of the rapid growth rates on the C-face and the multiple nucleation sites [604, 606, 615, 625].These 1LG have excellent electronic properties, despite draping over steps and making pleats [604].

Sample quality is revealed in AFM (see section IX.1.2) and STM images (see section IX.1.4) in multiple spectroscopy techniques (see section IX)), magneto-optical, photoemission, see (section IX), ultrafast optics and electronic transport (see section IX.3 Raman spectroscopy shows a vanishing D peak attesting the low defect density (see figure IV.7). All spectroscopy studies [622, 624, 627–629] confirm that the MLG behaves as electronically decoupled, i.e. as a stack of graphene layers with a non gapped linear dispersion down to a few meV from the Dirac point, not like graphite and exhibit the quantum Hall effect [604, 625, 630] and high mobility (up to µ  =  39 800 cm² V⁻¹ s⁻¹ at charge density n  =  0.19  ×  10¹² cm⁻² [604]). The se MLGare continuous over the entire SiC, drape over SiC steps and have rms  <  5 pm as measured by x-ray diffraction [596]. STM shows extended moiré regions [600, 627] providing evidence that adjacently stacked graphene layers are rotated creating a superstructure. On a larger scale, smooth graphene pleats are observed, as seen as bright lines in figures IV.6(c) and (e), which originate from the differential contraction of graphene and SiC upon cooling.

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MLGs have been used as a model system to study graphene properties [585]. This stems from a combination of factors: (i) Excellent structural quality (small Raman D peak observed, see figure IV.7 and [630]), (ii) Flatness of the layers (rms  <  5 pm as measured by x-ray diffraction [596]) which excludes strain-related gauge field effects [632] and broadening effects in k-resolved spectroscopy measurements (see figure S1 in supp of [620]), (iii) Small interaction with the substrate and the environment, particularly for the layers in the middle of the stack that are quasi-neutral [629, 633] (charge density n ~ 5  ×  10⁹ cm⁻², that is at most 8 meV away from the Dirac point) with high mobilities at RT [628, 633]. (iv) graphene electronic structure for all layers [634], due to the rotational stacking, providing a large signal intensity very much sought in optical measurements.

MLG on Si-face (see figure IV.4) is the most studied as for realization of quantum resistance standards (as multiples of h/e²  =  25.812 807 kΩ) at 4.2 K in small (<1 Tesla) magnetic fields. With a quantum Hall resistance quantization accuracy of 3  ×  10⁻⁹ that rivals the best 2d electron gas standards [612, 635]. As growth on the Si-face starts from the SiC steps [601, 603, 636], BLG (or MLG) tend to form at step edges when a 1LG fully covers the terrace (see figure IV.4), which makes it difficult to produce extended 1LG. Additionally, the step edges add electronic scattering due to the presence of BLG/MLGH, or to the reduction of the carrier concentration on the step [585], which is detrimental to the homogeneity of the quantum Hall effect [637]. Better control of growth on the Si-face was obtained by providing carefully balanced methane and H₂ [638]. Ref. [639] reported MEG draped continuously over the steps by graphitization of a polymer deposited on the bare SiC.

During annealing above 1200 °C, the SiC surface undergoes microscopic restructuring by forming steps and terraces. This process, known as step bunching [1745], is different from atomic surface reconstruction and refers to surface morphology. Step bunching, i e. the bunching of straight steps on vicinal crystal surfaces, which is governed by energy minimization on different terraces is a fundamental phenomenon in SiC. Graphene formation has been analyzed with respect to step bunching of SiC, by studying the influence of the crystal structure at the atomic level for each SiC polytype [640]. As illustrated in figure IV.8(a), the 4H-SiC polytype has two decomposition energies, terraces 4H₁ (−2.34 meV) and 4H₂ (6.56 meV), respectively, and the 6H-SiC (figure IV.8(b)) has three distinct terraces, 6H1 (−1.33 meV), 6H2 (6.56 meV) and 6H3 (2.34 meV), while 3C-SiC (figure IV.8(c)) has only one kind of terrace, 3C1 (−1.33 meV) [640].

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The growth process is schematically shown for 4H-SiC in figure IV.8(d). Since Si and C atoms are bonded more weakly in the vicinity of step edges, Si desorbs from these areas faster in comparison with the terraces [601, 603, 636]. Based on the terrace energies, removing a 4H1 terrace costs less energy and the step decomposition velocity is faster (figure IV.8(a)). As shown in figure IV.8(d), from the edge of the 4H1 terrace on the graphene-free surface, C atoms are released onto the terrace as Si atoms leave the surface (stage 1). The C atoms coalesce and nucleate into graphene islands (stages 1 and 2), which act as a sink for subsequently released C atoms. After the 4H1 terrace step catches the 4H2 step, the newly formed two SiC bilayer step provides more C atoms as compared to the one-bilayer step and the first graphene layer extends along the step edge (stage 2). The large percentage of bunched steps with four Si-C bilayers, an increased source of C, will impose the formation of a second layer of graphene (figure IV.8(d), stage 3) since some extra C will be released. Therefore, a full coverage of the 4H-SiC substrate surface by just 1LG may be an issue.

A similar mechanism of energy minimization is expected in the 6H-SiC polytype (figure IV.8(b)). As a result, first the step 6H1 will catch step 6H2 and forms two Si-C bilayers. Then step 6H3 will advance and merge with the two-bilayer step. The growth process for 6H-SiC is the same as the 4H-SiC [640]. However, on 3C-SiC all terraces have the same decomposition energy [640] (figure IV.8(c)) and no energetically driven step bunching should be expected. In this polytype, a non-uniformity of sublimation may be induced by the presence of extended defects such as stacking faults, which are characteristic of this material [641].

A capping technique can be employed to localize the step bunching [642]. The cap consists of an amorphous carbon layer evaporated on the bare SiC grid evaporated on the bare SiC. Amorphous carbon is then patterned by plasma etching or lift-off to produce typically micron size structures. Upon annealing to produce graphene, the carbon layer pattern pins the SiC steps under it so that the SiC steps bunch against one enclosure wall and align along the amorphous C grid, as shown in figure IV.9(a). Several geometries have proven effective, and it is reasonable to position an edge of the cap perpendicular to the SiC substrate miscut to maximize step bunching against the cap wall. The slight SiC surface roughness induced by the mild plasma etch used to pattern the carbon layer (see figure IV.9(c) top) is smoothed out by the step bunching at the high T of the graphene growth (see figure IV.9(c) bottom). This technique provides large flat terraces (figure IV.9(c)-bottom) at a predefined location. The amorphous C is finally removable by plasma etching after annealing to access the graphene layer for further device patterning [642]. In that case a graphene protection layer is used (this can be the dielectric of a subsequent top grid).

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Growth conditions can be developed to increase the size of the SiC substrate to 20  ×  20 mm² and ultimately to 100 mm diameter wafers. The furnace is similar to that of figure IV.3, but with longer RF-coil with uniform distance between the pipes [643]. The coil can be moved up and down to change the T gradient if necessary and it is fully automatic. The key to achieve large area 1LG on SiC is to (a) understand the role of the buffer layer [590, 592, 610] and of the step bunching [607] which takes place during its formation and to monitor the effect of (b) T (in the range 1700 °C–1950 °C); (c) Ar pressure (in the range 750–950 mbar) (d) and growth time (from 0 to 15 min). AFM topography and phase images show that the formation of the buffer layer (at 1850 °C and Ar pressure 950 mbar) can start at any place on the substrate, but preferably on the kink of steps, as shown in figure IV.10(a). The C atoms coalesce and nucleate into graphene islands on the step kinks (marked with a circle) and these islands act as a sink for other C atoms. As the step edges are the main source of C, the growth rate is two times higher along the step edge compared to that on terraces and for this reason a graphene layer first covers like a ribbon the sidewall of steps (figure IV.10(a)) [602, 618, 620, 644].Then growth continues from the edge of a step to the (0 0 0 1) terraces, where the graphene layer interacts with the surface and becomes the buffer layer. Studies show that the graphene layer first covers the steps with larger terrace [643]. A critical issue is to fully cover the substrate surface by a buffer layer, before lifting it up as a 1LG by growing another buffer under it. A good quality buffer layer exhibits a particular pattern in LEED, as illustrated in figure IV.10(b) (see also figure IV.10(b), and [584, 592, 611, 645–647]. The pattern for a buffer layer grown in the reactor of figure IV.3 at 1850 °C and 850 mbar is similar over the whole surface.

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Similarly to the amorphous C corral [642], the buffer layer can stop the step bunching process on 4H and 6H-SiC [648]. This means that the surface energy becomes uniform all over the substrate surface after the formation of the buffer layer subsequently resulting in a uniform and continuous 1LG coverage, which does not exclude the growth of BLG at the steps. The T dependence of the buffer layer formation and SLG coverage is sublinear (that is close to linear, not exponential [643]), which suggests that the synthesis is surface kinetics limited on both SiC polytypes [601, 643]. The results from graphene samples grown Ar indicate that there is an optimal Ar pressure (~850 mbar) yielding under this condition a high growth rate.

The time dependence of SLG and BLG growth under Ar pressure shows that graphene spreads faster on 4H-SiC substrates than on the 6H polytype from the start of the growth, and that 1LG coverage increases approximately linearly with time. After the SLG is complete, increasing annealing time does not significantly increase the BLG coverage for both 4H and 6H-SiC polytypes [643].

Based on the above results, a growth protocol was defined to optimized SLG coverage. The result, shown in figure IV.11 indicate the growth of ~99% 1LG on 20  ×  20 mm² SiC substrates and 99.8% 1LG for 7  ×  7 mm² substrate (figure IV.11). The SLG coverage is determined by optical reflectance maps. Experiments showed that the reflectance of graphene on SiC normalized to the reflectivity of bare substrate (the contrast) increases linearly ~1.7% per layer for up to 12L, which agrees with theory [649]. The wavelength dependence of the contrast in the visible is investigated using the concept of ideal Fermions and compared with existing experimental data for the optical constants of SLG [649].

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The results for SLG on 4-inch SiC wafer showed that the growth rate on the edge of the wafer is higher than in the centre, due a faster Si escape at the wafer edges [597]. Quasi-equilibrium growth [597] provides a way to mitigate these problems. Figure IV.12 shows the recipe for growth of SLG on large area substrates, including on 4 inch SiC wafer. These operation conditions assume different T ramps up to 1150 °C and to the growth T, according to figure IV.12.

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Graphene layers are best grown on 4° and 8° off-axis 4H-SiC (0 0 0 1) substrates to have the right terrace width for performing step flow growth [650, 651]. A general recipe is provided in Ref. [652]. Figure IV.13 shows a side view of the off-axis SiC substrate used for graphene growth, where the off-axis surface is tilted at a specified angle (off-axis angle) from the basal plane surface toward the $[1\,1\,\overline{2}\,0$] SiC direction. Controlling the tilt angle allows to change step heights, terrace widths and a growth rates.

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A direct comparison of graphene formation on an 8°-off axis (0 0 0 1) 4H-SiC epitaxial layer and on-axis (0 0 0 1) 6H-SiC [653], performed by uniform graphitization of 1 cm  ×  1 cm SiC substrates at 2000 °C for 30 min (with a base pressure in the chamber ~5  ×  10⁻⁶ mbar and an argon pressure ~1 atm during the growth) shows that the growth of graphene on off-axis SiC starts from the edge and follows the surface of the large terraces (0.5 to 1 µm width), running parallel to the original steps of the off-axis wafer.

Off-axis samples present significant step bunching after high T annealing (rms  =  16 nm), while flatter surfaces (rms  =  2.4 nm) are obtained on the on-axis sample. In comparison with on axis SiC wafers, off-axis SiC wafers contain a lot of steps due to their cuting angle. For this reaseon, during annealing they easily bunch. Step bunching is higher in off-axis samples with dense step edge, because etching or erosion start from on step edges, which is not the case in on-axis samples. A more uniform and homogeneous graphene coverage was found on on-axis 6H-SiC [653]. The 100 to 200 nm wide terraces of the 4H-SiC (0 0 0 1) 8° off-axis samples are covered by FLG spreading like a carpet for all growth T in the range 1600 °C to 2000 °C (growth under Ar) [654], with an increase in the N as a function of T (from 0 to 10 LG) (figure IV.14).

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Similarly to the on –axis surface, the graphitization rate is much higher for the C-face off axis substrates while it is almost an order of magnitude smaller for the Si-face on-axis substrate compared to off axis substrates (figure IV.15). AFM analysis showed the presence of the steps with different heights. An ~0.35 nm and ~1.1 nm step height can be associated to 1 and 3LG, respectively, over the substrate or stacked over other graphene layers [601]. In fact, like for the (0 0 0 1) on-axis face, the graphitization starts from the step edges and propagates gradually to the centre of the terrace [601–603, 655]. In this case, the C atoms at terrace kinks and step edges have a lower coordination number, thereby leading to an easier breaking of the bonds at these sites. For this reason, the probability of SiC decomposition and further surface diffusion of C atoms is increased and graphitization of the SiC surface occurs [655]. Regarding the growth kinetics, anisotropy of the Si desorption rate is always present and, thus, different SiC steps have different evaporation rates [601]. In addition, increase in the miscut angle increases the step density, thereby leading to an increase in graphene thickness at this region [601].

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Another interesting finding (see figure IV.14—right) is that the presence of the atomic steps leads to the formation of pleats similar to the MEG on the 4H/6H on-axis C- face (~1 to 2 nm high and 10 to 20 nm wide) preferentially oriented in the direction perpendicular to the step edges of the SiC terraces (figures IV.14(e) and (f)) [654]. Such a parallel orientation of pleats is particular to SLG grown on a vicinal SiC surface, while for SLG grown on on-axis 4H-SiC it is characterized by a preferentially hexagonal mesh-like network of pleats interconnected into (often) triangular nodes [585] (see figure IV.14(c)).

The presence of the buffer layer on the Si-face is often argued to degrade the electronic properties of the SLG above it [656–659]. In quasi -free standing SLG the buffer layer is converted into SLG by intercalation. An alternative to intercalation is the direct graphitization of non-polar SiC surfaces where there is no buffer layer [660, 661], or to master the graphitization on 1LG on the C-face, where high mobilities are measured [604].

According to the crystallography of the hexagonal family of SiC, there are three non-polar planes available for graphene formation: the m-plane $1\,\overline{1}\,0\,0$, a-plane $1\,\overline{1}\,2\,0$ and r-plane $1\,0\,\overline{1}\,2$ [661]. Figures IV.16(a) and (b) show the possible polar and non-polar SiC planes for graphene growth. In addition, the growth of graphene can be performed using thermal decomposition of (0 0 1)-oriented cubic SiC [661]. However, the commercial production of 3C-SiC substrates is limited, and in contrast to 4H and 6H-SiC, large single crystals 3C-SiC are not available. Polycrystalline 3C-SiC are often grown as epilayers on SiC or on Si-wafers. Figures IV.16(c) and (d) demonstrates the important crystallographic planes in the cubic structure of SiC.

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Synthesis of graphene on on-axis (0 0 1) cubic SiC substrates can be performed at T  >1800 °C for 20 min in a C rich atmosphere [661]. To provide reliable control of graphene formation a low growth rate (~1LG per five minutes) should be maintained, which is realized in a close crucible at a Ar gas pressure of 800 mbar.

Optimization of parameters (e.g., lowering T from 2000 °C to 1800 °C) can be effective for obtaining graphene layers with desired thicknesses and domain sizes ~100 nm. The optimizacion of the rest of parameters, like pressure, flow rate, step bunching, time, etc follow the same trend that for samples grown on non-polar faces and that are described in previous paragraphs. Figure IV.17 shows the LEEM images of graphene before and after optimization i.e at T  =  1800 °C in the reactor of figure IV.3.

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A (0 0 1) cubic SiC substrates with rather flat surface and low surface roughness (rms~2 nm) obtained by substrate polishing (rms ~0.6 nm) promotes growth of more homogeneous EG with large domain sizes as shown in figure IV.17. Growth on $\left( 1\,\overline{1}\,0\,0 \right)$ 6H-SiC resulted in non uniform coverage exhibiting areas of fragmented graphene and some micrometre large areas (figure IV.18—left). Similar results were reported in Ref. [662] for the $\left( 1\,1\,\overline{2}\,0 \right)$ plane (figure IV.18—right).

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Growth on non-polar SiC surfaces is limited by the vertical growth rate (graphene growth on the polar face proceeds laterally) [641]. Such vertical growth produces scattered islands of graphene on the surface with higher density of grain boundaries (see figure IV.19). The latter causes a greater amount of Si out-diffusion from the substrate, leading to a thicker (up to 8LG) subsequent [607] MLG growth on the nonpolar faces in comparison to growth on polar faces [607]. As graphene growth on the low-packed non-polar planes is faster than that on the high densely packed non-polar planes, it is assumed that the surface density is a key factor limiting Si desorption and the graphene growth rate.

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Graphene grown on SiC(0 0 0 1), by sublimation resides on top of a buffer layer [590, 592], as schematically depicted in figure IV.20. The buffer layer (denoted also by 6  √  3) is formed at the early stages of heating of the samples, i.e. before graphene is formed, and it has been observed in several experimental studies of of SiC(0 0 0 1) surfaces [586, 663–665] and also in an atomistic simulation of graphene formation on SiC(0 0 0 1) [590, 666]. The buffer layer has a (6  √  3  ×  6  √  3)R30° periodicity with respect to SiC(0 0 0 1) substrate surface.

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This layer consists of C atoms in a graphene arrangement [590, 592, 668]. This means that the structure is has C hexagons with a C–C distance like in graphene. The (6  √  3  ×  6  √  3)R30° periodicity with respect to the SiC surface corresponds to a (13  ×  13) super cell. Thus, the super cell contains 169 graphene unit cells. Due to a hybridization of states of the C atoms of the buffer layer with states from the SiC substrate surface, it lacks the typical π-bands of graphene and therefore has no Dirac cone [592]. On the other hand, the σ-bands of the buffer layer are fully developed and indistinguishable from those of graphene [592]. These observations are in agreement with theoretical studies [590, 669].

The buffer layer (6  √  3) induces electron doping in SLG. Typical values for the charge carrier density in SLG are n ~ 1  ×  10¹³ cm⁻² [589, 671–674]. The buffer layer is also partly responsible for the relatively low µ and its T dependence [658]. Furthermore, the reduction in spin transport in SLG is attributed to the buffer layer [656]. Typical values for µ ~ 1000 cm² V⁻¹ s⁻¹ at n ~ 1  ×  10¹³ cm⁻² and T  =  300 K and µ ~ 2000 cm² V⁻¹ s⁻¹ at n ~ 1  ×  10¹³ cm⁻² and T  =  25 K [584, 589, 658, 675, 676].

The structural similarities between the buffer layer and graphene suggest that it should be possible to convert the former one into the latter by cutting the bonds between buffer layer and substrate through intercalation, as depicted in figure IV.21 schematically for the case of hydrogen. Similar procedures have been studied before for SLG on metal surfaces like, e.g. Ni(1 1 1) [677]. In this case, different metals like Au, Yb, or Cu were intercalated between the metal substrate and graphene [677]. Several authors showed that different elements can be intercalated between the buffer layer and the SiC substrate. E.g., the intercalation of H [645–647, 658, 678–681], O [682–685], F [686, 687], N [688], Si [689, 690], Ge [691, 692], Au [693–696], Cu[697], Li [698, 699], Na [700] and subsequent transformation of the buffer layer into graphene have been confirmed.

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For applications, it is important that the intercalated species does not give rise to electronic states at the Fermi level, since these would short-circuit the graphene layer on top of it. This is the case for hydrogen which saturates the SiC(0 0 0 1) surface with Si–H entities.

The doubly filled bonding and empty anti-bonding Si–H states are located below and above the valence band minimum and valence band maximum, respectively, leaving the surface electronically passivated [701–703]. A similar situation can be expected for oxygen and fluorine passivation of the SiC(0 0 0 1) surface.

The first study of the intercalation of hydrogen under the buffer layer on SiC(0 0 0 1) was reported in Refs. [645, 646] who annealed SiC(0 0 0 1) substrates covered by the buffer layer in one atmosphere of hydrogen at T between 600 °C and 1000 °C. Similar processes can be employed to intercalate hydrogen under the buffer layer even if an additional graphene layer already exists on top of it [645, 646, 657, 680, 704–706], although the exact conditions may vary. In this case, SLG becomes a quasi-freestanding BLG (see figure IV.21).

The successful decoupling of the buffer layer and conversion into so-called quasi-freestanding SLG was confirmed by LEED, ARPES, XPS and LEEM. Figure IV.22(a) shows typical XPS spectra of the C1s core level of various samples [707]. The spectrum of the buffer layer is has 3 components. S1 and S2 are caused by the C atoms of the buffer layer [592]. In addition, a component due to C atoms in the SiC substrate is visible. These are also seen in the spectra of SLG, BLG and TLG indicating that the buffer layer forms the interface. Upon H-intercalation, the buffer layer is converted to SLG which is evident from the disappearance of the components S1 and S2 and the formation of a graphene-related component. This is also the case for SLG/BLG. The component of the SiC substrate is shifted to lower binding energy due to a change of surface band bending. Figure IV.22(a) shows examples of the band structure near the K-point of the hexagonal Brillouin zone as measured by ARPES [707] for SLG, BLG.

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The charge carrier type is changed from electrons in SLG/BLG on the buffer layer to holes in QFSLG/QFBLG on the H-terminated (0 0 0 1) surface of hexagonal SiC polytypes [645, 646, 658, 704, 707, 708]. This is due to the spontaneous polarization of hexagonal SiC [708, 709], which varies with the polytype due to their different ratio of hexagonal to cubic stacking sequences [708–710]. For semi-insulating 6H- and 4H-SiC(0 0 0 1)-H substrates hole densities of 6.2  ×  10¹² cm⁻² and 8.6  ×  10¹² cm⁻², respectively, as determined by ARPES in good agreement with theoretical predictions [708–710]. In the case of QFSLG on n-type doped cubic 3C-SiC(1 1 1)-H a slight electron doping is observed, which agrees with the fact that this SiC polytype has no spontaneous polarization. In this case the excess electrons in QFSLG is due to alignment of the Fermi levels as described by the Schottky model for metal–semiconductor interfaces [708]. Refs. [658, 704] have provided evidence for the hydrogen at the interface by measuring the Si–H stretch mode vibration using FTIR absorption spectroscopy as shown in figure IV.22(c). This was later confirmed by surface enhanced Raman spectroscopy [711, 712]. Raman spectroscopy also provided evidence for the conversion of the buffer layer to a QFSLG [658, 705, 711, 712]. In the case of QFSLG a narrow 2D line is observed while for QFBLG a broad 2D line indicative for AB stacking is found (see figure IV.22(d)). Electronic transport studies on simple Hall bar structures and FET have shown that QFSLG on 4H- of 6H-SiC(0 0 0 1)-H exhibits a higher charge carrier mobility (typically ~4000 cm² V⁻¹ s⁻¹) than SLG on the buffer layer and that it has a considerably reduced T dependence [658, 704, 705, 713–718].

Decoupling of the buffer layer from the SiC substrate and saturation of the SiC(0 0 0 1) surface with hydrogen can be carried out in an apparatus depicted in figure IV.23 [719], initially designed for the hydrogenation of SiC surfaces [703, 719, 720]. The system consists of a quartz tube in which the sample can be heated in an atmosphere of purified hydrogen in a contact-less manner by means of halogen lamps. In the hydrogenation process, the chamber is first filled with hydrogen and then the sample is raised to the desired value. Typical process parameters are listed in table IV.1.

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Variations of the above procedure have been reported for the synthesis of quasi-freestanding graphene layers on SiC(0 0 0 1). Ref. [645], reported preparation T in the range from 600 to 1000 °C at atmospheric pressure without mentioning the annealing time. Ref. [713] annealed in molecular hydrogen to convert SLG to QFBLG. They reported a H₂ pressure of 800 mbar, T of 600 to 1200 °C, and process times between 30 and 120 min. Ref. [721] carried out the hydrogen annealing directly after the growth of graphene in a Hot-Wall CVD reactor. After graphene growth in Ar at 100 mbar at 1650 °C, the sample was cooled to 1050 °C. At this T, the gas a exchanged to H₂ and the pressure increased to 900 mbar. After 30 min, the sample was allowed to cool to 700 °C in H₂. Finally the system was evacuated and the sample allowed to cool to RT. Ref. [715] annealed their buffer layer samples in H₂ at 1013 mbar and temperatures between 600 and 1200 °C for 60 min. In Ref. [706], QFSLG was produced by annealing in a furnace at 800 °C and a H₂ flow of 0.2 slm for 1 h at an unspecified pressure. The process time was 60 min. The highest mobility was observed for at of 700 °C. In [706] QFBLG by annealing Hall-bars made from SLG at 1250 °C in H₂ at ~33 mbar was reported. Ref. [680] employed a plasma source as well as an atomic hydrogen source to convert SLG to QFBLG. They reported that the plasma treatment induces a disorder. Kinetic Monte Carlo simulations performed in Ref. [722] have shed light on the atomistic mechanism of H intercalation of the buffer layer, in good agreement with experiments.

Surface analytical tools such as LEED, XPS(see section IX.2/XPS for an introduction to the technique), ARPES (see section IX.2.3 for an introduction to the technique), LEEM and STM (see section IX.1.4 for an introduction to the technique) along with FTIR and Raman are ideally suited to characterize the quasi-freestanding graphene layers on H-terminated SiC(0 0 0 1). Table IV.2 lists several methods together with the expected observation and relevant references.

Oxygen intercalation was suggested a means for decoupling the buffer layer from the SiC(0 0 0 1) surface by annealing the buffer layer [682] in one atmosphere of molecular oxygen at 250 °C for 5 s, using a special oxidation chamber. In the first approach in Ref. [685] the buffer layer samples was annealed in situ, i.e. directly in the UHV chamber used for XPS and ARPES analysis, at 750 °C in ~10⁻⁴ mbar of molecular oxygen. The second procedure in Ref. [685] was carried out ex-situ by annealing in O₂ with best results at 270 °C at 200 mbar. The Raman spectra, however, demonstrated that both processes lead to the formation on numerous defects. In Ref. [683] the oxygen intercalation to transform SLG into a BLG was carried out by annealing in air at 600 °C for 40 min. A heat up ramp of 50° per minute was used. They confirmed the decoupling of the buffer layer and the formation of a high quality BLG.

In Ref. [684] buffer layer samples as well as SLG were annealed up to 500 °C and 650 °C, respectively, in a water vapour in order to decouple the buffer layer by oxidation of the SiC(0 0 0 1) substrate surface. Raman spectroscopy indicated numerous defects. However, like as for Ref. [683], the QFBLG formed by treating SLG showed a negligible D band. This was also evident from Hall effect measurements, which indicated µ ~ 790 cm² V⁻¹ s⁻¹ at a rather high hole concentration of 2  ×  10¹³ cm⁻². While oxidation of the SiC interface by oxygen or water intercalation leads to highly defective QFSLG, this technique is promising for the synthesis of decoupled QFBLG on SiC(0 0 0 1). One may speculate that the buffer layer, which is highly corrugated and in which C atoms are partially sp³ hybridized [723], is more prone to be attacked by the oxygen during intercalation. On the other hand, in the case of SLG, the buffer layer is protected by the graphene layer on top of it.

Intercalation with other elements was also studied. Contrary to Si, that intercalates only at T  >  800 °C through migration at graphene domain boundaries and other defects, Li [698, 699] was found to penetrate into the C layer already at RT through the formation of Li-compounds. Na partial and inhomogeneous intercalation occurs already at RT directly after deposition, although most of the Na remained on the surface and formed Na droplets. Na intercalation is promoted both by electron/photon beam exposure and by moderate annealing at ~100 °C. Annealing at higher T results in de-intercalation and Na desorption from the surface [700]. Other elements intercalation would be appealing, such as nitrogen, that is predicted to provide charge neutral QFSLG [726]

Finally, we review studies on Ge [691, 692] and Au [693–696] intercalation between buffer layer and SiC(0 0 0 1) surface. In both cases, the preparation is performed using the following scheme. First, a thin layer (up to 5 monolayers) of the intercalant (Ge or Au) is deposited on the buffer layer using thermal evaporation. Then, the sample is annealed in UHV to induce intercalation. The properties of the QFSLG formed by intercalation depend on the amount of material present at the interface. For Au two phases were observed [693]: a highly n-type doped one with the Dirac point located ~0.9 eV below the E_F for 1 monolayer Au at the interface and a weakly p-type doped phase with the Dirac point at 0.1 eV above E_F for one third of a monolayer Au at the interface. Spin-resolved ARPES indicated a Rhasba-type spin–orbit coupling in the π-band of QFSLG at energies where it interacts with Au bands [696]. In the case of Ge [691], an n-type doped QFSLG is obtained when 1 monolayer of Ge resides at the interface while a p-type doped QFSLG is observed when 2 monolayers of Ge are intercalated. The hole and electron concentrations in the QFSLG were ~p   =  4.1  ×  10¹² cm⁻² and n  =  4.8  ×  10¹² cm⁻². This means that the shift of the Dirac point with respect to E_F is almost symmetric. Note that a mixed phase can also be prepared in which n- and p-type regions coexist.

This was employed by Baringhaus et al [692] to fabricate pn-, np-, pnp- and npn-junctions which were investigated by 4-point probe transport measurements. Evidence for Klein tunnelling of charge carries across such barriers was observed.

The fact that growth starts at a step edges on the SiC(0 0 0 1) face (see above), can be used to produce graphene nanostructures for electronics. Masking methods, for selective growth using AlN [727], SiN [728] and amorphous C masks [642] with tens of nm precision have been proposed. The template growth method on sidewalls of SiC trenches [604, 615, 618, 619] is described below. It circumvents the detrimental effect of traditional plasma etching [729, 730] and resulting sidewall nanoribbons show RT ballistic transport properties [620].

The idea is to tune the parameters so to stop growth just as graphene covers the step sidewalls. Steps can be either natural steps obtained by step bunching at the SiC surface, or the sidewall of trenches of various shape etched in the SiC substrate. The width of the ribbon is then set by the step height and the angle with the basal (0 0 0 1) plane (~27°). Upon heating in the 1400 °C–1600 °C range for graphitization, the SiC steps flow to produce the equilibrium facets at that T. E.g., for ribbons oriented along the graphene armchair direction, stable facets are found at $\left( \overline{1}\,1\,0\,7 \right)$, $\left( \overline{1}\,1\,0\,6 \right)$, and symmetrically at $\left( 1\,\overline{1}\,0\,7 \right)$, $~ \left( 1\,\overline{1}\,0\,6 \right)$ [731].

For growing graphene on natural steps, SiC surface treatments are used to organize the step-terrace structure prior to graphene growth. These include [615] annealing the chemically and mechanically processed polished SiC substrate in vacuum, in Ar, in a face-to-face SiC configuration or with a refractory capping grid [642]. The key is to obtain a stable step configuration prior to graphene growth. The T for surface structuring are chosen according to the background pressure to prevent graphene growth, i.e. 1100 °C–1200 °C in vacuum, 1300 °C–1700 °C in Ar or face to face. Step bunching by annealing in these controlled conditions produces arrays of straight steps and terraces with uniform width and height (figure IV.24). The step structure depends on the polytype [732] the local miscut of on-axis SiC wafers (see above), which may vary up to  ±0.1° across the whole wafer, and other factors such as the heating method. A complete systematic study is still lacking. After treatment, the terraces are up to 10–30 µm in width and extended over several hundreds µm in length (figure IV.24). Examples of ribbons grown on the sidewall of natural sidewall steps (obtained by step bunching) and on etched trenches are shown in figure IV.24.

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In a more controllable manner, nano-structured graphene can be grown on various shapes etched in SiC(0 0 0 1) [733]. Trenches can be etched along the 4H-SiC$\left( 1\,\overline{1}\,2\,0 \right)$, and 4H-SiC$\left( 1\,\overline{1}\,0\,0 \right)$ directions to produce GNRs along the zigzag or armchair orientation, owing to the epitaxial orientation of graphene on SiC (see figure IV.1(a)). For this, an e-beam or a photoresist is patterned on SiC(0 0 0 1). Plasma etching is used to etch SiC with the resist as a mask for shallow etching. Various recipes have been reported [615, 618–620]E.g., reactive ion etching (RIE) (using SF₆ and O₂ ratio 20:7) with etching rates ~0.3 nm s⁻¹, or 43% SF₆/23% O₂/33% Ar RIE operating at 30 mTorr where the radiofrequency power was tuned to give a SiC etch rate ~0.8 nm s⁻¹ [616], allowing fine control of the etch depth. For deeper etching, a Ni mask can be used, that is evaporated on the resist and lifted up. The Ni mask is removed after RIE etching by an ultrasonic treatment in nitric acid [618].

The resist pattern is transferred to the SiC as a template for graphene growth, and complex interconnected graphene structures can be designed (see Refs. [604, 618, 733]), including pillars to produce nanometric graphene rings [604]. Although trenches of any height can be etched, well-formed graphene ribbons are best grown on sidewalls 15–35 nm deep. This is because shallow trenches (⩽10 nm) tend to get washed out upon annealing in the CCS furnace and deep trenches tend to break into multiple facets revealing multiple parallel ribbons [615].

In the CCS furnace, the structured SiC chip is then heated to 1100 °C to allow the vertical etched sidewalls to crystallize into the equilibrium facets [735] onto which the GNRs grow at~1500 °C–1600 °C [618]. The exact T and time depend on the specifics of system, such as the Si escape leak in the furnace CCS method [597, 620]. The sidewall ribbons produced this way are ballistic conductors at RT on micrometre distances [620]. Similar sidewall ballistic ribbons have been produced with the same technique, but by a dc current annealing of conducting SiC wafers (6H-SiC N-doped) in an Ar atmosphere of 4  ×  10⁻⁵ mbar (sample clamped by graphite contacts) [620]. Well-ordered crystal facets from at~1150 °C, and further annealing to 1300 °C results in growth of extended GNRs [620, 736].

Because the steps in SiC are etched and annealed prior to graphene growth, the facets onto which graphene grows are smooth and atomically defined. This is demonstrated in cross-sectional transmission electron microscopy [734] (figure IV.24(d)), and in ARPES [731] where measurement integrating thousands of parallel GNRs show graphene electronic-bands.

GRNs of any nominal orientation can in principle be produced. By design, tens of thousands of sidewall nano-structures can be produced all at once, following the recipes above [604, 618, 731, 733], in particular long straight parallel GNRs [615]. However, sidewalls may in some cases show restructuring after annealing [604, 620, 733] with rounding and faceting [597, 615]. The effects are sensitive to a number of factors such as the step direction, growth condition (both T, time, and also possibly the type of heating), the pinning of steps (e.g. under amorphous C pads such as in, figure IV.9, or by defects), or the polytype. The most prominent feature of the GNRs, i.e. RT quantized ballistic transport, is however a very sturdy result and was observed for straight as well as curved GNRs [620].

As mainstream electronics and very large scale integration is based on Si technology, schemes to integrate graphene grown on SiC with Si wafers have been devised. Two routes have been investigated. The first is based on the standard SOI technology, where a thin monocrystalline Si layer ready for CMOS processing is bonded on top of graphene on SiC. Figure IV.25 shows the principle of the design. This 3d integration, inspired by the industrial development of 3d integration stacking thin-film electronic devices, realizes the interconnection of the SiC supported graphene platform, preserving the integrity of graphene, with a Si wafer, enabling, in principle, the full spectrum of CMOS processing. [737].

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The main steps consist in the fabrication of graphene structures (either from patterned or from template growth on SiC sidewalls), evaporation of an alumina film by ALD as a bonding layer between the SiC and the oxidized Si wafer, wafer bonding in a pressure module and finally splitting of the Si wafer by annealing at 400 °C (smartcut) to leave a thin crystalline Si layer on top. The main advantage of the process is that the growth T (1400 °C and above) is not limited by the presence of Si (melting point 1414 °C). The Si wafer resides on top of SiC and is therefore fully accessible. Finally, the stacking of SiC and Si wafers increases the areal density inspired by the 3d stacked layers Very Large Scale Integration Technology.

The second strategy, so called graphene on-silicon (GOS), takes advantage of the heteroepitaxy growth of 3C-SiC on Si to produce graphane on SiC covered Si substrates (3C-SiC is the only SiC polytype known to grow on Si) [738–740] (see figure IV.25). The polar Si-terminated 3C-SiC(1 1 1)/Si(1 1 1) surface grown in UHV shows graphene Bernal stacking with an interfacial buffer layer, similarly to the 4H- or 6H-SiC(0 0 0 1) surfaces [738]. Conversely, the C-terminated 3C-SiC(1 1 1)/Si(1 1 0) shows a non-Bernal stacking, with the absence of an interfacial buffer layer, consistent with a C-face termination [738].

The quality of these graphene films is modest as shown by large Raman D peaks. The disorder results from Si diffusion through SiC grain boundaries (due to a large ~20% lattice mismatch between Si and 3C-SiC) and the lower T allowed for graphene growth (limited by the Si melting point) [741]. Process optimization is being developed. E.g., growing an epitaxial AlN layer on Si prior to SiC growth reduces Si out-diffusion and helps grow higher quality graphene [738]. Catalytic growth of SiC on Si with a NiCu coating [742] allows growth of graphene on predefined locations. For electronic application requiring high quality graphene, alternative schemes have been developed (see figure IV.25(a)).

Growing an epitaxial AlN layer on Si prior to SiC growth significantly reduces Si out-diffusion and helps grow higher quality graphene [738], as well as and interface NiCu layer [742].

The initial motivation to use Cu as a catalytic surface to grow graphene was to take advantage of the very low C solubility in Cu up to the melting point of Cu [776, 777]. This was expected to eliminate the need for a diffusion/precipitation mechanism[753, 778]. The binary phase diagram for Cu and C is shown in figure V.1. The solid solubility of carbon in Cu at 1100 °C is ~0.0076 w% at a T slightly above the melting point of Cu [777, 779, 780]. Mostly on this basis, it is argued that as CH₄ dissociates on the metal surface to form CH_x radicals at high T with the aid of the metal catalyst the resulting carbon atoms arrange in the form of graphene on the surface of Cu, thus creating SLG. This contrasts that on metals with a higher C solubility, where the C atoms dissolve and diffuse into the metal with subsequent segregation and precipitation at the metal surface upon cooling. Growth on Cu is limited largely to one monolayer [765, 781] for a low-pressure catalytic CVD process. The growth details were studied by using ¹²C isotopes to try to understand whether graphene was growing directly on the Cu surface or precipitating from the bulk of the Cu substrate [781]. The Raman map of the isotopically labelled graphene transferred on a SiO₂ substrate showed that at least macroscopically graphene was growing directly on the surface at high T and not upon cooling as in the case of Ni [781]. The growth of single-crystal graphene domains with controlled edges with orientations that range from zig-zag to armchair via a CVD growth–etching–regrowth process was reported [782]. FLG are also observed on Cu. There are multiple sources of carbon that lead to the presence of the adlayers. First, some of the C dissociated on the surface of Cu dissolves into Cu and after growth at high T it diffuses to the Cu surface because of the lower solubility as the Cu cools, and forms FLG under the already grown graphene [783]. These layers grow under the graphene on Cu as a result of precipitation upon cooling [783]. Even though it was reported that C might diffuse under the growing graphene to form FLG [784], it is more difficult to accept this mechanism since it does not take into account the C dissolved into Cu. If only the intentional C from the dissociation of methane were present, then a small percentage of the surface area would be covered with adlayers. However, in some cases many FLG have been observed across the surface of Cu/graphene and this can only be explained by the presence of other sources of C, and isothermal growth as a result of supersaturation [785]. It was also reported [791] that the surface of Cu can be covered with a high concentration of unwanted C from ambient, poor cleaning and cleaning using hydrocarbons. This can give rise to a high concentration of nuclei as well as FLG beyond the solubility limit of C in Cu [785]. The presence of the uncontrolled and unwanted C is also supported by anecdotal reports indicating that graphene can be grown on metal surfaces in the absence of a C precursor. Ref. [786], pointed out the importance of a high H₂/CH₄ ratio in the growth of SLG. The benefit of a high hydrogen concentration may arise from the details of the reactions at the metal surface, but also from the presence of excess oxygen in the growth chamber. This is highlighted by the fact, that graphene is etched during cooling in the absence of H₂ or CH₄ [787]. The effect of growth parameters such as T, and CH₄ flow rate and partial pressure on the growth rate, domain size, and surface coverage of graphene led to the definition of a 2-step CVD strategy for the growth of large single crystal graphene [788]. High-throughput growth of graphene on Cu foil was achieved at ambient pressure, interesting to reduce costs [789].

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The graphene growth process on Cu surfaces to first order can be described by the following steps, [784, 786, 791–794]:

• 1.  
  Cu surface cleaning/preparation prior to loading into the growth chamber
• 2.  
  Surface cleaning and annealing in the growth chamber
• 3.  
  Exposure to a hydrocarbon precursor with subsequent adsorption of the same on the Cu surface
• 4.  
  Nucleation of graphene by the dissociating CH_x radicals and local supersaturation of C to form graphene nuclei
• 5.  
  Surface diffusion of CH_x radicals and attachment onto the graphene edges
• 6.  
  Dehydrogenation of the CH_x radicals attached to the graphene edges and dehydrogenation of some of the isolated CHx radicals with subsequent diffusion into the Cu
• 7.  
  Coalescence of the growing graphene domains to form continuous polycrystalline films or single crystals.

Substrate selection, surface preparation, growth T and process are critical to achieve films that meet device requirements. Substrate surface quality, surface impurities, surface roughness and gas composition and pressure have large effects on the surface roughness, defects (Raman D-band), amount of FLG, and electrical properties. Graphene films of varying sizes, on Cu as well as other metal films have been grown in vertical single wafer cold wall reactors, horizontal furnaces [765], open continuous furnaces as well as in plasma enhanced single wafer systems [966]. Each one of these approaches requires optimization in order to achieve the desired results. Typically, growth conditions, such as reactor design, vertical versus horizontal, gas delivery system, precursor selection, heater, low versus high T growth, low pressure versus atmospheric pressure, must be considered and optimized. The aforementioned factors depend on material requirements as well as cost needed by a particular application.

Typically, graphene is grown on Cu foils [332], Cu thin film on sapphire, and bulk Cu single crystal foils [782, 794–796]. The most commonly used Cu foils are of a high-purity 99.9999% in a variety of thicknesses and sizes. In addition, oxygen [783, 791], carbon and other impurities [785] in or on Cu are have large effects on the growth mechanism. The quality of graphene will depend on the quality of the Cu surface morphology and crystallographic orientation. The surface of the metal can be improved by electropolishing [769, 770, 786] Many experiments have been performed on Cu annealing [797, 798], heating the substrate to T above the melting point of Cu,[799, 800], Cu surface oxidation, [786, 790, 802], using Cu with controlled crystal orientation [786] and oxygen free Cu [791]. Growth of graphene on bulk single crystals or single thin films of Cu would be advantageous. It would be ideal to grow high quality graphene directly on a dielectric surface Ref. [802] diffused C on thin Cu on SiO₂ to grow graphene directly on the dielectric surface. However, at the films grown using this process are still not of high enough quality to compete with films grown directly on the metal surface. For a more extensive discussion on the growth of graphene on dielectrics, see section V.3.

Growth of graphene on Cu metal has been carried out in horizontal tube furnaces [765] as well as in cold walled single wafer tools [766, 803] and even at higher T [799, 804] than the Cu melting point, 1084 °C, using any one of several hydrocarbons (such as methane or ethylene), ethanol hydrogen and argon are also used [799, 804]. The effect of the H₂/CH₄ ratio on the shape of graphene domains has been widely reported [786, 800, 801]. Low pressure CVD with very low precursor flow rate has been effective in growing large area graphene filmsVarious other methods of heating the substrate have been use in addition to resistive heating, such as magnetic inductive heating [805] and a hybrid process combining hot filament and resistive (thermal) heating [806], but these techniques have not been widely adopted yet. Growth has also been carried out in the presence of a plasma in an attempt to reduce the growth T well below 800 °C.

A typical growth procedure is shown schematically in figure V.2. Prior to growth high purity Cu substrates (foils) having a thickness ranging from 25 to 35 µm and of a desired surface area are procured. The are then cleaned in acetic acid for ~10 min and then transferred in de-ionized water for additional 10 min and dried with N₂. After, the Cu foil is introduced in the growth chamber and the chamber is evacuated and back filled with H₂ to a desired pressure. CH₄ and H₂ are usually circulated to purge the lines (50:50 sccm) at pressure  <4 mbar prior to substrate heating. The chamber T is then increased to 1000 °C under 20 sccm of H₂ in 70 min (see figure V.2 upper frame). T is then kept constant at 1000 °C for an additional 30 min. During this last step, the Cu substrate T and microstructure are stabilized. Heating of the Cu foil to the growth T can be performed also in Ar and then in H₂ gas flow at a pressure  <100 mbar. The purpose of this step is to promote grain growth of the Cu foil. A 'standard' graphene growth process follows: 5 sccm of CH₄ or C₃H₈ are then flowed for several minutes (typically ~30 min), after the growth phase, the substrate is cooled to RT by translating the furnace away from the substrate. The cooling can be done with the precursor flowing, hydrogen flow or under vacuum. The ambient during cooling is also critical especially in cases where the base pressure of the chamber is too high. In this case leaking oxygen can etch the graphene at the highest T. Once T is near RT, the gasses are closed off and the chamber is evacuated and back filled with an inert gas to one atmosphere. Growth of graphene on polycrystalline Cu foils using this process flow usually yields films with a grain size ~10 µm. By applying a longer annealing time, higher T, lower pressures, and by maintaining optimal hydrocarbon flow or melting the Cu, the domain size can reach several millimeters [807]. The lower frames in figure V.2 illustrate that domains ~800 µm can obtained systematically optimizing the CVD growth conditions and also show the corresponding Raman spectrum.

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Optical microscopy with Nomarski contrast, i.e. differential interference contrast (DIC) microscopy, is very useful (see figure V.3) to explore the quality of the Cu substrate surface as well as the grown graphene. DIC microscopy can expose cracks and micro-holes in the graphene layer and can provide information on microstructural changes before and after anneal that can be correlated with graphene film quality.

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Raman spectroscopy has been demonstrated to be the best characterization technique to confirm the presence of SLG on the Cu substrates [1748]. The technique is introduced in section IX.2.1, where representative spectra of SLG, BLG, etc are also given. Measurements performed by SEM plotted in figure V.4 can identify dark areas interpreted as adlayers of graphene. In addition, wrinkles formed during cooling from high T because of the large difference in the coefficient of thermal expansion between graphene and Cu are also visible as narrow lines criss-crossing the surface of the graphene. If Cu of lower quality (purity 99.9% or 99.999%) is used, e.g. Cu_5N and Cu_3N, the films are heterogeneous mainly in terms of their thickness. In figure V.4 light grey color represents areas with SLG.

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Atomic resolution images of graphene on Cu as measured by STM (see section IX.1) presented in figure V.5 show the configuration of the carbon atoms in SLG. The corresponding Fourier transform of the STM image (upper right inset) indicates that the maxima correspond to the pattern formed as a result of the orientation of the SLG in relation to the substrate (lattice mismatch). The figure V.5 shows an area 3  ×  2.2 nm with a graphene unit cell drawn upper left inset) exhibiting a lattice constant of 2.44 Å [812]. The shape, orientation, edge geometry, and thickness of CVD graphene domains can be controlled by the crystallographic orientations of Cu substrates [1749]. At the inception of the growth phase, during the nucleation stage, the Cu roughness plays a key role. The Cu-active sites are imperfections on the Cu surface, such as grain boundaries, irregularities or areas of coarseness, or surface impurities. It is at these defects that most of the graphene nuclei are formed. The higher the density of nucleation sites, the smaller the size of the graphene domains. The density of these grain boundaries is expected to affect electrical, chemical, and thermal properties, and it is thus necessary to optimize the graphene film properties according to the application requirements [808–811].

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For some applications large (square meters) areas of graphene may be needed, as it is the case for the functional coating of large pieces of other materials. When growing graphene on 500  ×  500 mm² Cu substrates, the T uniformity across the metal substrate must be controlled since the nucleation and growth characteristics has a large T component [755]. The control of the Cu metal foil T is critically important when growing films at T close to the Cu melting point as shown in figure V.6, where part of the Cu foil melted at the edges, due to an uneven T distribution across the Cu film. Ref. [794] reported the growth of 5  ×  50 cm² single-crystal graphene on industrial Cu foils. They first transformed industrial polycrystalline Cu foils into single-crystal Cu(1 1 1) by thermal annealing using a T-gradient-driving technique. Then graphen grains growon the Cu(1 1 1) substrate and seamlessly mergeto form a large single-crystal graphene film.

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This technique allows the synthesis of large-size single-crystal graphene films, with superior properties for various high-end applications, especially in electronics, such as large-scale fabrication of THz devices and transparent conductive film to replace ITO. It will also enable the growth of various other single-crystal LMson graphene

There are many alternatives for substrate heating, ranging from magnetic inductive heating [805] to hybrid processes, combining hot filament and resistive (thermal) heating [806]. Among them, photothermal heating (PT-CVD) provides up to 100 °C min⁻¹ heating and cooling rates [767, 772] while keeping the chamber walls cold. The system is based on a halogen lamp-heated rapid thermal processing (RTP) (for up to 300 mm wafers), where gas lines (CH₄, H₂ and Ar) and their mixing manifolds are incorporated. While keeping the RTP chamber walls cold. This, together with the fast growth process, less than 1 min, helps to reduce the contamination from the walls. In this case, the cleaned Cu foil is placed between two silica plates on a photothermally heated Si- or SiC-coated graphite susceptor. Silica is needed between Cu and Si to prevent reactions between them. The growth process starts by annealing the Cu foil for 5 min at ~935 °C (as measured by a pirometer) and pressure ~7–20 mbar. Next, CH₄at a flow rate of 15 sccm (CH₄/H₂ mixture 4:1) is introduced into the chamber. Under this condition a continuous SLG film is grown on Cu in a few tens of seconds, one order of magnitude faster than in thermal CVD using similar growth parameters. The SLG coverage is ~94% in films grown in 60 s at 950 °C. The SLG contains very small adlayer flakes, and defects (~3  ×  10⁷ cm⁻²) [775, 813]. The light from the RTP lamps enhances the catalytic effect of CH₄ on the Cu surface without generating defects. The grain size is in the µm range. Ref. [773] reported a rapid thermal CVD (RT-CVD) suitable for mass-production. In this setup, Cu foils are loaded vertically in the reactor, in which 24 lamps heat vertical graphite receptors around the Cu foil. They obtained a growth rate 7 times higher than thermal CVD using hydrogen-free N₂ carrier gas [773].

It would be desirable to grow graphene at low T for ease of process, equipment, contamination, as well as potential substrate melting issues. Ref. [814] reported growth of graphene on SiO₂/Si, plastic and glass at close to RT (25–160 °C). However, in most cases the reported reduction in growth T_g/T_mp(C) is very small (⩽0.30) and for most materials the quality of the grown crystals is higher when the growth T is close to the melting point. There have been some reports on the growth of graphitic films at low T by CVD [815], plasma assisted [816] and from solid sources [814, 817] on or under Ni films but not on Cu. Growth at low T on Cu, Ni or Cu-metal alloys could be of great interest, but the grown graphene could contain many defects, as in the case of low T crystal growth of many other electronic and optical materials.

As in the case of crystalline semiconductor materials, it may be advantageous to grow single crystal graphene films in order to minimize scattering effects by pure grain boundaries and grain boundaries that may react with ambient species such as OH, hydrocarbons, etc. Also, the presence of grain boundaries and their tilting has been studied in relation to the mechanical properties of the synthesized graphene [811].

Graphene has been demonstrated to grow on Cu surfaces by a nucleation and growth mechanism [765, 781, 818] predominantly by a surface limited process, because of the low solubility of C in Cu. The films grown using this process are polycrystalline, with a grain size that depends on the specific growth process conditions and they can range from less than one micron to hundreds of microns. Therefore, in order to increase the grain size, one would have to reduce the nucleation density on the surface of the metal. Various approaches were developed to achieve this, such as reducing precursor flow by using a Cu pocket [128, 766, 819, 820]. An example of such pocket is shown in figure V.7(a).

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The growth of large graphene single crystals led to the demonstration of very high µ in CVD graphene comparable to that of mechanically exfoliated flakes [821]. This is an important result since it has led to focused efforts on further understanding of the graphene single crystal growth as well as transfer [807, 822–824].

Further reduction of graphene nucleation density was investigated by Ref. [783, 791], who showed that graphene single crystals on polycrystalline Cu of over 1 cm could be grown after treating the surface of Cu with oxygen. However, this process is time consuming, growth times of over 10 h were used to grow 1 cm single crystals. Oxygen not only passivates the Cu surface, leading to reduced nucleation density, it also significantly speeds up the growth of graphene crystals by changing the growth regime from diffusion to edge-attachment-limited. A further explanation on the decrease of the nucleation density on the surface of Cu was provided by Ref. [785], where they observed that the surface and the bulk of the Cu foils may be contaminated with impurities including C which can aid in the formation of graphene nuclei. In this case, Cu oxidation prior to graphene growth removes carbons from the Cu surface leading to a lower nucleation density. Following the Refs. [791, 826], Ref. [825] used a solid source of oxygen, A_xO_y—e.g. SiO₂/Si, to provide a continuous source of oxygen under the Cu substrate while providing the hydrocarbon precursor at atmospheric pressure (see figure V.7(c)). This process led to a growth rate~60 µm s⁻¹ instead of~0.3 µm s⁻¹ of Ref. [791]; this is a major improvement. Another approach to reducing the graphene nuclei density on the Cu surface was performed by treating the surface with melamine [827]. This process led to the growth of 1 cm graphene domains with µ reaching 25 000 cm² V⁻¹ s⁻¹ for graphene transferred onto SiO₂/Si. Another method was proposed taking advantage of the residual oxygen in the CVD furnace for increasing the graphene domain size beyond one millimeter, and simultaneously promote recrystallization of a polycrystalline Cu foil in the (1 1 1) structure through a peculiar 'abnormal grain growth' mechanism [828]. The process yields aligned high-quality graphene single crystals smoothly merging together, with a crystal alignment maintained over few centimeters (in 1 hr).

In general, the following critical conditions should be met in order to grow large crystals: (1) suitable substrate, (2) substrate surface cleaning and polishing prior to loading in growth chamber, (3) surface pre-treatment (oxidation, the use of melamine or other surface treatment), (4) enclosing the sample to limit precursor flow, and (5) a non-reducing surface treatment at high temperature prior to growth.

Substrate preparation is a very important first step in order to create a clean and flat surface. Many approaches can be found in literature [583, 819] on mild surface etching using acidic solutions [791, 820, 829]. However, the most reproducible surfaces have been prepared by electropolishing [766, 807]. The solution used for electropolishing has a volumetric composition of 45% water, 25% phosphoric acid, 25% ethanol and 5% isopropanol. To increase viscosity, 0.5% (weight) of urea is added. Electropolishing is performed by applying a voltage between the sample (anode) and a Cu plate cathode. A typical electropolishing procedure is 30 s at 12 V, with a cathode-anode distance of 4 cm. To ensure homogeneous polishing, it is important to keep the electrodes parallel. For this one can employ a Coplin glass staining jar as the electropolishing vessel (figure V.8(a)), which has grooves to keep the foil and the counter electrode in place, figure V.8(b). Following the electropolishing, it is important to rinse the samples under running DI water to completely remove the viscous electrolyte, followed by a quick rinse with isopropanol. Finally, the samples are dried with compressed nitrogen.

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Owing to the catalytic nature of the Cu surface, it is important to reduce the carbon precursor flow impinging on the sample in order to reduce the nucleation density [755]. One of the most commonly-used approaches is to grow large SLG crystals inside 'pockets' formed from Cu foil, [128, 783, 791, 819, 820]. The discovery of large graphene crystals inside a Cu pocket led to the investigation of other methods to achieve similar results, for example a Cu tube [807], a sapphire cap over the Cu surface to minimize evaporation and the 'hydrocarbon' concentration [830], or placing a quartz plate on top of a flat Cu foil at a desired distance from the Cu surface [766]. The process conditions to achieve the largest single crystals will have to be optimized and perhaps combined with the use of Cu single crystals. Ref. [796] reported a comprehensive study of the evolution of the crystal morphologies grown inside Cu enclosures as a function surface orientation, absolute pressure, hydrogen-to-methane ratio (H₂:CH₄), and nucleation density At low pressure and low H₂:CH₄, circular graphene islands initially form. After exceeding ~1.0 µm, Mullins-Sekerka instabilities [1750] evolve into dendrites extending hundreds of micrometers in the 〈1 0 0〉, 〈1 1 1〉, and 〈1 1 0〉 directions on Cu(1 0 0), Cu(1 1 0), and Cu(1 1 1), respectively, indicating mass transport limited growth. Increasing H₂:CH₄ results in compact islands that reflect the Cu symmetry.

The nucleation density and growth rates are affected by the growth pressure and gas flow rates. While low pressure can help to radically reduce the nucleation density, it can also lead to extremely slow crystal growth. With a gas flow of~1 sccm CH₄, 900 sccm Ar and 100 sccm H₂, the graphene nucleation density is on the order of several crystals per mm² and typical growth rates are ~15 µm min⁻¹, allowing the synthesis of 1 mm-sized crystals in ~1 h. The use of Ni–Cu alloys will enable much higher growth rates due to the higher catalytic activity of Ni [831]. Figure V.9 illustrates the effect of using a nonreducing atmosphere and sample enclosure on oxidised Cu.

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When hydrogen annealing is used, the nucleation density is ~10 000 cm⁻² (a). Annealing in an Ar atmosphere reduces the nucleation density to ~1000 grains per cm⁻² [128, 791]. Substrates annealed in argon and placed inside an enclosure have a nucleation density ~10 grains per mm⁻² or lower, enabling the growth of large crystals. Figure V.10 shows a schematic diagram of the graphene growth process in a pocket and the image of a graphene single crystal grown inside the pocket. The interface between SLG and Cu (1 1 1) oxidises under ambient conditions within a few days, making SLG visible and decoupled from Cu. This is required for a reliable dry pick-up using h-BN [832].

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There have been many observations on the shape of graphene domains on different Cu grains having varied crystallographic orientation [786, 1751]. The shape varies depending upon the Cu orientation as well as the growth conditions and Cu oxidation state [755, 791]. It has also been reported that growth of graphene domains on oriented Cu(1 1 1) foils [794] and Cu(1 1 1) thin films on sapphire [830] under certain process conditions are aligned. As the domain growth progresses, the domains merge to form single crystals as the Cu surface becomes fully covered by a boundary-free stitching. This is true in the case where the domains are aligned and the Cu surface is nearly atomically flat [583, 833]. The advantage of this process, if large area Cu(1 1 1) films or foils are available, is that the growth time can be significantly reduced in comparison to the single nuclei approach. Efforts have been dedicated to the growth large Cu single crystal foils [833] and [831]. More recently, a gas-flow-driven aligned growth of graphene on liquid Cu has been achieved [834]. Another method of preparing large area Cu(1 1 1) crystals is to take advantage of the epitaxial nature of Cu on c-plane sapphire and thicken the thin film using an electrodeposition process, after which Cu(1 1 1) can be peeled off from the sapphire substrate [835]. Significant activities are ongoing to optimize the growth of graphene on controlled Cu surfaces in an effort to grow high quality crystals in production worthy growth systems [836].

It would be advantageous to be able to grow single crystal graphene from a single nucleus as for bulk single crystals. Wu et al [837] used Ni–Cu alloys to increase the catalytic activity in conjunction with a localized precursor delivery technique to grow graphene single crystals over 3 cm in diameter. The growth mechanism of graphene on Ni–Cu is more complex than on Cu or Ni and further development would require precise composition identification/selection in order to ensure single layer growth and full coverage by a single graphene grain. Ref. [838] reported the synthesis of single-crystal-like SLG on polycrystalline substrates. The method relies on 'self-selection' of the fastest-growing domain orientation, which eventually overwhelms the slower-growing domains and yields a single-crystal continuous film.

In summary, the growth of high quality, large area, single crystal graphene can be performed in several ways on:

• (1)  
  Growth on conditioned Cu substrates (oxidized or treated with melamine) under low pressure conditions (slow growth rates, size up to 1 cm)
• (2)  
  Growth on Ni–Cu substrates with a localized precursor delivery (relatively high growth rates)
• (3)  
  oriented single crystal Cu(1 1 1) foils
• (4)  
  thin Cu(1 1 1) films on sapphire substrates
• (5)  
  thick predominantly Cu(1 1 1) on sapphire followed by a peeling process so as to facilitate sapphire re-use.

Seeded graphene growth was reported by Ref. [839] patterned and etched CVD graphene patches were used as nuclei for the subsequent single crystal graphene growth. However, because of the polycrystalline nature of the starting graphene film, the resulting crystallites were not aligned but each crystal was hexagonal. In a subsequent study [840] pre-annealed foils were patterned with arrays of crosslinked PMMA, then used as a carbon source for the growth of single-crystal arrays. In both cases the array periodicity was ~20 µm and crystal size of up to ~15 µm. Due to the much lower nucleation densities required for large-crystal graphene, carbon-based seeding was found not to be robust enough for controlled growth of large-periodicity arrays. Metallic nucleation seeds were chosen instead for large-crystal graphene arrays. Ref. [841] used Cr as the nucelation sites for localized single crystal growth of graphene.

The nucleation seeds can be patterned by performing optical lithography on electropolished Cu using positive photoresist, followed by thermal evaporation of 25 nm Cr and lift-off in acetone. Cr was chosen because of its high melting point [1752], ensuring that thin films are not evaporated during the annealing of the foil and instead form particles that can act as nucleation points on passivated Cu. Spots with a diameter ~5 µm and a thickness ~25 nm lead to the most reproducible results [841]. Smaller seeds or lower film thickness did not ensure reliable seeding, whereas larger spots were sometimes found to initiate the nucleation of several separate crystals. By changing such flow ratio, it is possible to control the presence of residual Cr seeds during the growth by changing the CH₄:H₂ flow ratio. After growing graphene using a H₂:CH₄ ratio of 20:1, particles of Cr are found at the centre of seeded crystals, whereas when using a H₂:CH₄ ratio of 100:1, Cr seeds are removed. Growth was carried out in a 4-inch Aixtron BM Pro. All gases used in the CVD process had purities of 99.9999%. As shown in figure V.11(a), arrays with a periodicity of 200 µm show high nucleation control, with less than 10% of non-seeded nucleation. At larger periodicities (see figure V.11(b)), sporadic nucleation was slightly higher. Well-ordered arrays of crystals with a diameter of several hundred microns can be synthesised [841].

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We now discuss the growth of single crystal graphene with controlled edge structure. Two types of graphene crystals have been grown: (1) dendritic, and (2) hexagonal [791]. The shape of the graphene crystals was controlled by the presence (dendritic) or absence (hexagonal) of oxygen on the surface of the Cu for low pressure CVD. Ref. [842] reported the growth of 100 µm hexagonal graphene crystals on polished Cu foils at one atmosphere, with limited carbon flow, with the crystal edges dominated by the zigzag direction. Controlling the graphene edges may be important for some electronic applications and growth conditions to optimize quality and growth rate(cost) should be investigated. Another important point is the growth of edge-controlled graphene in the smallest dimensions (nm scale) and the treatment of graphene after patterning and etching to set the edge structure.

It is desirable to grow film at low T not only because of the integration device flows, but also to overcome problems associated with substrates like Cu. One issue with CVD of graphene on Cu from CH₄ is that the optimum growth conditions are typically at T  >  1000 °C, very close to the Cu melting point of 1084 °C or even above its melting point. Cu has a vapor pressure ranging from 8.1  ×  10⁻⁸ atm to 5.7  ×  10⁻⁷ atm for the T range ~ 1000 –1084 °C [843]. During annealing and graphene growth at low background pressures a measurable amount of Cu is transported by the flowing gasses away from the Cu surfaces. The presence of Cu on the surface of the quartz tubes in the case of a furnace or the metal surfaces in the case of cold wall reactor can make the cost of ownership high, since the growth systems has to be cleaned on a regular basis to prevent Cu deposits flaking and particle formation. As a result there have been several activities to (1) reduce the growth T to address the evaporation and the potential integration of graphene directly in a device flow and (2) finding alternative metals or alloys as discussed above to minimize the Cu evaporation problem. It should be added that the cost and reliability of precursor delivery systems should also be considered when designing a CVD. in order of preference, gases are preferred over liquids and liquids are preferred over solids. In an effort to reduce the growth T researchers have used liquid precursors such as alcohols [844], or aromatic molecules, such as hexane [845, 846], benzene [847] and toluene [848]. In the case of benzene, high quality mostly monolayer graphene was synthesized at 300 °C with µ of 2500 cm²·V⁻¹·s⁻¹ by APCVD [849]. Evaporation of the catalyst was avoided and oxygen removed from the deposition chamber to minimize contamination or structural disorder of the film. Deposition of graphene at 100 °C was observed by this method but with lower quality [1753]. With extended time deposition, BLG or TLG started to form, indicating that the synthesis is not self-limiting [817]. At 160 °C continuous graphene films of reasonable quality (µ~667 cm²·V⁻¹·s⁻¹) were deposited on SiO₂, however N was barely controlled. At lower T (from 60 to 160 °C) the deposition of continuous films was not achieved, being the coverage from 60% to 98% and the grain size and quality of the deposits deteriorated. At 60 °C on glass and PMMA the Raman signal showed the deposition of highly defective graphene layers with nanometric grain size.

Thus, the quality of the films is inferior to that grown on Cu at higher T using CH₄. In addition, the delivery system for the liquids may be more complicated and more costly, not to mention the toxicity issues. Ref. [850] reported on the CVD growth of high-quality, large-area predominantly SLG films with domains o~1 µm² and FWHM(2D)~35 cm⁻¹ on Cu foils using C₂H₄at 850 °C. Spectroscopic and electrical measurements show that these films display high uniformity and crystalline quality with reasonable µ~1000 cm² V⁻¹ s⁻¹ [850]. Figure V.12(a) shows the average Raman spectrum of a ~20  ×  20 µm² area (red) and a discrete spectrum taken at the centre of a SLG domain. I(2D)/I(G) is lower for the averaged spectrum as this includes the regions of secondary island growth. Figure V.12(b) plots a I(D)/I(G)map with brighter areas corresponding to regions of higher defect levels, highlighting the low defect levels throughout the film. The defects that are present here are attributed to domain boundaries. Figure V.12(c) plots FWHM(2D) across the same area of the film with brighter regions corresponding to wider FWHM(2D). The majority of the film FWHM(2D) ~35 cm⁻¹, typical of SLG [96, 105].

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Further characterization was carried out by fabricating GFETs. Al₂O₃ pre-patterning of the Cu foil passivates the areas, giving a patterned graphene film on the final substrate. Electrical measurements were performed with source-drain voltage (V_SD) ~20 mV while the gate voltage was swept to  +60 V and  −60 V. I_DS versus V_GS curves in figure V.13 give hole and electron µ~1100 and 700 cm² V⁻¹ s⁻¹ at RT. These fall short of the best reported values for CVD graphene [851], due to the smaller domains (~1 µm) compared to films grown at higher T.

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Ref. [849] investigated the growth process of graphene at ~300 °C, using C₆H₆as precursor at ambient pressure. They used a pump purge process multiple times to minimize residual oxidizing species in the growth chamber and annealed the Cu substrates at 1000 °C under H₂ and Ar gasses for 30 min to grow the Cu grains as well as clean the surface through evaporation of potentially damaged surfaces as well as surface adsorbates. This process produced films with 100% surface coverage, 97.6% transmittance, and µ~1900 to 2500 cm² V⁻¹ s⁻¹. This may become useful for back-end-of-line (BEOL) integration of graphene.

Another approach is the use of PECVD. However, the typical quality of graphene has not been significantly better than thermal CVD. PECVD synthesis on Cu foil was reported via simultaneous removal of native Cu oxide and film growth (<420 °C) [852]. This shows the importance of smoothing Cu and the differences in the deposition on top and bottom sides. The bottom side near the sample holder suffers a confinement that allows preparing smooth Cu metallic surface and growth of mostly SLG continuous films in one step. However the process is not self-limiting and the thickness was time dependent. Contamination of the process tube with Cu affects the lifetime of furnace as well as reproducibility.

Growth of graphitic carbon on Ni was achieved asfar back as the 1960s [746] and to the 1970s [753, 853]. Using PECVD, vertically oriented graphene nanosheets (VOGNs) on Ni can be prepared [854–856]. Carbon on metals is either soluble or it reacts to form a carbide. The majority of efforts on growth on metals have focussed on the use of non-carbide forming metals such as Cu, Ni, Co, Pt, Ru, Ir, and Au. There have been interesting reports on the growth of graphene on carbide forming as well [1754]. In this section we focus on the growth of graphene on Ni and Co, and similar metals. The solubility of C in Ni and Co is fairly high in comparison to that of C in Cu [857, 858], and it is much higher than that in Cu [790] ~1 at% (C in Ni) versus 8–10 ppm (C in Cu). The higher solubility makes it difficult to grow uniform SLG on the metal surface [756, 761]. In both growth on Ni and Co, one can grow produce patchy SLGs. Even by decreasing the Ni or Co thickness and growth T, single layer control is very challenging. This also does not solve the equivalent challenging problem of coefficient of thermal expansion difference between metal and graphene [859].The growth of graphitic C on Ni, Co, Pt and other elements that have high C solubility occurs principally by a diffusion and precipitation mechanism from the bulk of the metal [753, 754, 788]. Depending upon T and microstructure the C diffusion can be dominated by grain boundaries or bulk diffusion. Ref. [781] showed using C isotope labeling that while in the case of Cu, graphene growth is dominated by surface growth, on Ni this takes place by dissolution followed by diffusion and precipitation upon cooling to RT. Growth on Ni and Co alloys of Cu on the other hand has given better results, including growth of large area single crystals [1755]. This is due to a number of reasons, the principal being that at low Ni concentrations in Cu, the catalytic activity of the metal surface is much higher than just on Cu, leading to a higher surface growth rate [837]. While growth on elemental Ni and Co resulted in uncontrollable graphene layers, growth on Cu alloys (Ni_Cu, Co–Cu, etc) may lead to controlled larger single crystals of graphene [837]. The presence of metals with higher catalytic activity could also enable growth at lower T.

The integration of graphene into accessible and scalable 3d materials is an issue that is inspiring a growing field of research [860]. Free-standing interconnected porous graphene materials, called graphene foams (GF), attract interest due to their ability to transfer many of the unique properties of graphene to a larger scale, with high surface area  >850 m² g⁻¹ high electrical conductivity (>10 S cm⁻¹) and good structural integrity, retaining the form of the metallic template on which they were synthesized [861]. Applications include variable geometry elastic conductors [861], lithium ion batteries [862], EMI shielding [863], supercapacitors [864, 865] and lithium sulphur batteries [866, 867].

Structures such as papers [542] and hydrogels [343] can be prepared starting from chemically exfoliated graphene and/or GO [304]. These often suffer from poor electrical conductivities (e.g. only 5  ×  10⁻³ S cm⁻¹) [343] and thermal properties, mainly because of defects and their non-continuous nature. Graphene may be grown on templates of virtually any shape by CVD and continuous structures can be obtained starting from custom porous templates. Synthesis of graphene foams by CVD on metal foam templates was reported in Ref. [861]. The authors used commercially-available Ni foam templates to fabricate tunable, macroscopic structures consisting of high quality interconnected graphene sheets. The resulting materials were highly conductive, light and flexible with high surface area, and subsequent infiltration with PDMS led to robust composites that exhibited a resistance change when subjected to mechanical deformation, such as bending or stretching, indicating their potential in the field of stretchable electronics. This work inspired a lot of new research around graphene foams, for many different applications, such as lithium storage [347], high sensitivity detection of NH₃ (ppm in air at RT and NO₂)[868] supercapacitors [869], conductive scaffolds for the proliferation of neural stem cells [870], superhydrophobic coatings [871] combined with Teflon, or stretchable strain sensors [872] combined with PDMS.

The growth process depends on the metal catalyst. In the case of Cu, the process is self-limited, i.e. growth mostly ceases as soon as the Cu surface is fully covered with graphene principally because of the negligible C solubility and C diffusivity in Cu [781]. In the case of Ni, the carbon atoms diffuse into the bulk of the metal due to the high carbon solubility, ~0.9% at 900 °C [781], and graphene is formed both by the isothermal growth on the surface and carbon precipitation from the bulk upon cooling [115]. The shortcoming of graphene growth on Ni is the poor control on N, which is strongly influenced by the Ni thickness, T and exposure time to the hydrocarbon, and the cooling rate, not yielding uniform SLG but rather FLG [791]

In Ref. [873] GF were grown on commercially-available Ni foam templates by CVD in a hot-wall tube furnace (diameter 5 cm) using CH₄. The templates were washed by ultrasonication in dilute hydrochloric acid, then de-ionised water, and finally acetone, before being placed inside the furnace and heated to 1000 °C under a H₂ flow of 50 sccm. After annealing under these conditions for 30 min, the flow of H₂ was increased and CH₄ introduced (H₂:CH₄  =  500:50 sccm). Following a 10 min deposition time, the sample was removed from the furnace and allowed to cool in flowing Ar or N₂ for at least 2 h. To remove the sacrificial Ni templates, the samples were immersed overnight either in 17 vol% nitric acid (HNO₃) or in 4.5 vol% iron (III) chloride (FeCl₃) followed by 10% hydrochloric acid (HCl) heated to 80 °C. Finally, they were thoroughly rinsed in deionised (DI) water then allowed to dry completely before further handling.

Figure V.14 shows the characterization of the synthesized GF. From SEM observations, the wall thickness is estimated to be 10–20 nm, characteristic wrinkles are observed in the foam, arising from the mismatch in thermal expansion coefficients between Ni and graphene [874].The interior is hollow, indicating that Ni etching was successful. XRD measurements on foams etched with HNO₃ showed residual Ni (figure V.14(g)), most likely due to the produced by the reaction of Ni with HNO₃. These gas bubbles could block the infiltration of etchant to some channels of the internal structure. To overcome this, etching was instead performed in FeCl₃, which has no gaseous products on reaction with Ni, only soluble salts. These were [873] washed away in hot HCl, which also served to complete the etching process. XRD measurements confirmed that the resulting GF had few traces of Ni when FeCl₃ was used at RT (figure V.14(g)), and no traces of Ni when it was at 80 °C. However, in this case there was some residual Fe (figure IV.14(g)).

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TEM diffraction measurements confirmed the polycrystalline graphite nature although the thickness of the walls was too large to observe the individual layers of graphene (figures V.14(e)–(f)). The quality of the sample was further investigated by Raman spectroscopy (figure V.14(h) The small D peak indicates negligible defects. The 2D is consistent with that of FLG. Thinner GF featuring fewer layers of graphene may also be grown by varying parameters such as the amount of CH₄, the growth time and/or T and the cooling rate. However, thinner foams are less robust and require a PMMA support during etching, so that they do not collapse [861].

The structures described above are limited by the commercially-available templates, which typically have pore sizes in the range of 200–400 µm. In this case, most of the volume is occupied by void space rather than graphene, which is a disadvantage in applications such as energy storage, where a high volumetric energy density is required. Thus, a smaller pore size is often desirable.

High density scaffolding have been produced, as described in [875] as follows: Ni and Cu metal powders with typical particle sizes between 0.5 and 150 µm were purchased from Sigma Aldrich (figure V.15(a)). In the case of Cu powder below 1 µm, the powder was additionally mixed with MgCO₃ powder to prevent the agglomeration of the metal particles and compressed. The powder was placed into a quartz combustion vessel inserted into a quartz tube in a horizontal tube furnace. An annealing step with a flow of 400 sccm argon and 100 sccm hydrogen at high T for 45 min was used to connect the metal particles (thus forming the metal scaffold, see figure V.15(b)) as well as to remove metal oxides and contamination. The minimum T for preparing the scaffold was 600 °C for Ni and 800 °C for Cu. Carbon feedstock was provided by a CH₄ flow of 10 sccm under a constant Ar flow of 400 sccm and a total pressure of 50 mbar and 400 mbar for the case of the growth on Ni and Cu, respectively. These were the minimum pressures yielding closed graphene layers on the metal templates for all the investigated temperatures (figure V.15(c)).

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Figure V.16(a) plots a typical Raman spectrum at 532 nm of GFs grown on Cu at 900 °C and Ni at 600 °C. This gives Pos(2D) ~2695 cm⁻¹ and 2699 cm⁻¹ for GFs (Cu) and GFs (Ni), respectively, with FWHM(2D) ~61 cm⁻¹ and 80 cm⁻¹ for Cu and Ni-grown GFs, respectively, indicating FLG. I(D)/I(G) ~ 0.16 and ~0.25 for Cu- and Ni-grown GFs, indicating defects.

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For SEM analysis the GFs were freeze-dried at low pressure in liquid N₂ for several hours in order to prevent the collapse of the foam. A SEM picture of a GF is in figures V.16(b) and (c) depicts an optical image of two Ni foams fabricated at different T.

A similar process was described in Ref. [873], in which a combination of Ni and NiO NPs compressed into a pellet were used as the template. Despite the presence of NiO, the mechanism for the subsequent growth of graphene did not change, since during the annealing process in a high-T (1000 °C) H₂ atmosphere NiO was reduced to Ni, leading to the same behaviour as for Ni templates. After growth, the sacrificial template was removed. A long period (several days) of immersion in the etching solution was required before no more colour change was observed, indicating that all the Ni had been removed.

Figure V.17 reports the characterization of the GF produced in this way. The pellet subjected to high pressure (~440 kg cm⁻²) was too compact (figure V.17(a)), while the GF synthesized from pellets subjected to low pressure (~50 kg cm⁻²) shows a well-controlled particle size distribution (figures V.17(b) and (c)), with a network of interconnected hollow branches of graphene. The pores are in the 1–10 µm range, around 2 orders of magnitude less than the GF grown on commercially-available Ni foam templates. As estimated from the SEM images, the thickness of graphene is less than 10 nm. Indeed, by TEM, 10–30 layers of graphene could be observed (figures V.17(e)–(f)) and the polycrystalline graphite nature was confirmed as before by diffraction measurements (figure V.17(g)). To analyze the quality of the graphene, Raman spectroscopy was employed at 632.8 nm (figure V.17(d)). The sample was first fragmented slightly to ensure that measurements were taken from the inside of the foam. No significant D peak was visible in the Raman spectrum, indicating negligible defects and the 2D peak was consistent with FLG.

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Selection of the proper alloy could address some of the shortcomings of Cu. Ref. [876] studied the use of Mo-Ni alloys to grow SLG without the precipitation of diffused C into the bulk, because Mo traps C by forming a Mo-carbide. In principle, this approach could be extended to other metal alloys with the objective of finding a substrate with better CTE matching with graphene than Cu, and lower vapor pressure at the growth T. Another widely studied alloy is Ni–Cu in order to take advantage of the low solubility of C in Cu, the higher catalytic activity of Ni and the non-linear behavior of C solubility on Ni concentration in Cu_1−xNi_x [857]. Additionally, some of the metal alloys could be much better catalysts than Cu, enabling growth at much lower T [877, 878]. Refs. [877, 878] grew predominantely SLG by an admixture of Au to polycrystalline Ni. This allows a controlled decrease in graphene nucleation density, at low T ~450 °C. The graphene films exhibit an average I(D)/I(G)~0.24 and domain sizes  >220 µm² were reported via the design of alloy catalysts.

Carbide forming metals were also suggested to to grow SLG [879, 880]. Commercially available polycrystalline groups IVB-VIB metals (Ti, Zr, Hf, V, Nb, Ta, Mo and W) were used to grow graphene by CVD at ~1050 °C. However, the Raman spectra showed many defects, as exhibited by the presence of a high intensity D-band.

To get some insights into the atomic mechanisms ruling the growth of on metals by CVD, understanding the specific CVD kinetics [881] is crucial for advancing graphene processing and achieving a better control of graphene thickness and properties. Although the thermodynamics of the synthesis system remains the same, based on whether the process is performed at atmospheric pressure (AP), low pressure (LP) (0.1  −  1 Torr) or under ultrahigh vacuum (UHV), the kinetics are different, leading to a variation in uniformity. Graphene synthesis using a Cu catalyst in APCVD processes at higher CH₄concentrations revealed that the growth is not self-limiting, which is in contrast to previous observations for the LPCVD case [1756]. Hydrogen acts as an inhibitor for CH₄ (and for other widely used precursors like C₂H₄) on Cu and other metals, supressing deposition onto the surface [882]. Besides, hydrogen plays a key role in forming form C—H out of plane defects (as efficient nucleation points) in CVD graphene on Cu, defining an optimal (and desired) CH₄/H₂ ratio [882].

Several theoretical studies predicted that carbon atoms are thermodynamically unfavourable on the Cu surface under typical experimental conditions, and the active species for graphene growth should thus mainly be CH_x instead of atomic carbon [883]. Based on this [882, 883] the nucleation behaviour could be understood (see figures V.18(A) and (B)), explaining many experimental observations and providing a guide to improve graphene simple quality [883]. Other studies were conducted combining ideas from step flow growth augmented by detailed first-principles calculations [792]

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A combination of in situ LT-STM experiments and DFT-based calculations (see figure V.18(C)), revealed the growth intermediates of CVD graphene on Cu(1 1 1) via thermal decomposition of CH₄at different growth stages, comprising various carbon clusters (i.e. carbon dimers, carbon rectangles, 'zigzag' and 'armchair'-like carbon chains) and defective graphene [884]. Saturation of these carbon clusters on Cu(1 1 1) resulted in the transformation into defective graphene, with pseudo-ordered corrugations and vacancies due to lattice mismatching. These defects were healed by high T annealing in the presence of CH₄ and transformed into vacancy-free SLG. Such atomic insights of the structural evolution at different stages of graphene grown on Cu(1 1 1) can help better understand the growth mechanism of CVD graphene, and provide design rules for large scale growth of single crystalline graphene films.

The kinetics of graphene growth on Cu were also studied using Raman spectroscopy taking advantage of the mass difference of ¹²C and ¹³C [781, 791] where the time dependence of graphene growth on the surface of Cu was presented as shown for oxygen rich and oxygen free Cu surfaces in figure V.19

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On Ni another interesting growth mechanism can take place. This arises from the decomposed on-surface C atoms, catalytically produced from the CVD CH₄ [888] (or other precursors like C₂H₄, among others) at high T (see figure V.20(A)). The favourable solubility and diffusivity permits the decomposed C atoms to diffuse into the Ni bulk during the annealing stage at high T [889]. Then, the inward carbon atoms precipitate (segregate) on the catalyst during the cooling period due to supersaturation of the diluted carbon into Ni. This supersaturation-by-cooling leads to the segregation of carbon atoms on the cooled Ni surface, which will promote the formation of the graphene domains. It is worth mentioning that this mechanism has been validated by a complex theoretical computer modelling protocol accounting for a large variety factors affecting the CVD graphene synthesis (solubility in Ni, growth time, growth T, cooling rate, Ni thin film thickness, among others) [886], and will naturally lead to the formation of MLG easier than in other metal substrates by the nature of the segregation mechanism. Another growth mechanism of graphene on Ni(1 1 1) was suggested in Ref. [887] at T  <  460 °C. A surface-confined nickel-carbide phase coexists with SLG (see figure V.20(B)). This grows by in-plane transformation of the carbide along a phase-boundary, unlike other growth processes on other transition metals and on Ni above 460 °C, where carbon atoms attach to 'free' edges of graphene islands [887].

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Other low-interacting substrates have been explored. Ref. [108] reported the growth of graphene on Pt. This hand high crystal quality with lowest wrinkle height ~0.8 nm and µ  >  7100 cm² V⁻¹ s⁻¹ under ambient conditions. The repeatable growth of graphene with large single-crystal grains on Pt is nondestructive after electrochemical delamination of the grown graphene [108]. The growth of can be designed to control the graphene edges that range from zigzag to armchair orientations via growth-etching-regrowth by CVD on Pt [782]. Ref. [890] reported the nucleation and growth of graphene islands on Pt(1 1 1) at T ~ 1000 K by CVD of ethylene. Using a CVD method followed by a repeated etching-regrowth process on Pt Ref. [891], single-crystal graphene domains were reported up to 13 000 cm² V⁻¹ s⁻¹ under ambient conditions. Ref. [892] engineered the grain size of SLG grown on Pt with a limitted carbon solubility, by a segregation–adsorption CVD yielding a grain size ranging from ~200 nm to ~1 µm, which enabled the determination of the scaling laws of thermal and electrical conductivities as a function of grain size. They concluded that the thermal conductivity of graphene decreases with grain size, while the electrical conductivity slowly decreases with a small grain boundary transport gap ~0.01 eV and resistivity ~0.3 kΩ µm. CVD-graphene growth on Pt substrates can provide an extra added-value, as it may exhibit catalytic properties towards H₂ dissociation [893]. Pt is one of most commonly used materials for electrodes due to its thermal stability and chemical resistance.

The thermal expansion coefficient difference of Pt with graphene is smaller than for other transition metals [894]it is possible to tune the edge termination of the crystals via growth–etching–regrowth [108, 782, 793].

Efforts have been made not only in the growth of millimetre-sized hexagonal single-crystal graphene films on Pt but also in developping transfer methodologies. A bubbling method, was used to transfer SLG grown on Pt to arbitrary substrates, using a nondestructive process not only to graphene, but also to the expensive Pt substrates [108]. There are also studies focused on the growth on other noble metals, such as Ir [895], Ru [896] and Rh [896]. Moiré patterns have been explored on graphene on Rh(1 1 1) using in situ STM [897]. The synthesis of large-scale uniform graphene films on high carbon solubility substrates of Rh foils at ambient-pressure CVD was reported [898].The thickness of graphene can be tuned from multilayer to monolayer by increasing the cooling rate in the growth process graphene prefers to stack deviating from the Bernal geometry, with the formation of moiré patterns. Ref. [899] grew SLG on Ir(1 1 1) by LP CVD. The graphene layer had a very low density of defects. These are edge dislocation cores consisting of heptagon–pentagon pairs of carbon atom rings, related to small-angle in-plane tilt boundaries. Using Ir(1 1 1) as substrate at 750 °C–900 °C, growing rotated islands are more faceted than islands aligned with the substrate [895]. Further, the growth velocity of rotated islands depends not only on the C adatom supersaturation but also on the geometry of the island edge. Different growth mechanisms were proposed to explain the differences in the graphene edge binding strength to the substrate. Graphene growth by CVD of ethylene on a Ru(0 0 0 1) surface was also explored. At low pressures and high T the metal surface facets into large terraces, leading to ordered graphene layers [900]. Engineering of Ru surfaces with Ar⁺ sputtering to produce subsurface bubbles led to a tailored growth of graphene on Ru(0 0 0 1) and to anysitropic oxygen interacalation [896].

The substrate Ir(1 1 1)/YSZ/Si(1 1 1) in principle allows integration with Si technology. However, the growth is ruled by the outermost Ir atoms, and therefore the process may be generalized to many other transition metals like Ir [895], Ru [896] or Rh [896].

In the case of Ir and Pt, the interaction with the substrate is rather low, and this presents pros and cons. As an advantage graphene can be transferred to other substrates. However, the main disadvantage is the small domain size, as many rotational domains can be generated [901, 902]. Work is underway in the search of optimization methods for enlarging domain sizes, even to millimeter scales. Ru and Rh are substrates were the graphene-substrate interaction is very strong and it is possible to grow large grains on single-crystal substrates, however transfer is difficult [1757, 1758].

SLG on Ir(1 1 1) thin films on YSZ-buffered Si(1 1 1) wafers [903] was reported [905]. The substrate was first cleaned by Ar sputtering (0.8 keV, 5 µA, 15 min) and annealing to 900 °C followed by an oxygen treatment (p(O₂)  =  5  ×  10⁻⁸ to 1  ×  10⁻⁷ mbar, T between 400 °C and 550 °C) and a final flash annealing (to desorb the oxygen) up to 900 °C.

SLG was grown using ethylene as a precursor CVD at T  =  850 °C, starting from very low ethylene partial pressures (ideally  <1  ×  10⁻⁸ mbar for the first 20–30 min), then progressively increasing the pressure up to 2  ×  10⁻⁷ mbar. This approach prevents the formation of multiple nucleation centers, which would result in the appearance of many rotational domains (mosaicity). The substrate should first be heated to the setpoint T and only then should ethylene be admitted into the chamber[905]. Surface processes such as oxidation and overlayer (including graphene) formation modify the work function of the metal substrate, the photoelectron yield measured while irradiating the sample with a pulsed UV source can be used to track the onset of the surface process under study and to monitor its evolution until saturation is reached [905].

Several physical evaporation methods employing sublimation from a carbon source have been used, like electron beam evaporator [906, 907], or a resistively-heated piece of graphite [790, 908]. The growth of nanometer-sized SLG on hBNby MBE was reported [909].

Ref. [910] used a solid carbon source consisting of a glassy carbon filament connected by two refractory metal bars to a DC current source. Thanks to a 10 times higher resistivity of glassy carbon versus graphite, it is possible to use moderate electrical current ~14–18 A [911]. This makes this method simple and easy to install in a UHV system, significantly reducing contamination. Ref. [910] showed that for MBE growth of graphene, the substrate can be at lower T than in other methods [912, 915, 916]. This enables growth on dielectric substrates in an inherent transfer free process. Also, in situ surface science analysis techniques (LEED, RHEED, STM, XPS) can be used in a highly controllable growth environment (growth rate, substrate type, substrate temperature, in situ doping).

The evaporation growth rates are generally very as low as 3  ×  10⁻⁴ ML s⁻¹ to avoid a rapid degeneration of the glassy carbon filament. This requires a sample-to-source distance of tens of millimeters. At this distance the sample is radiatively heated.

An evaporation carbon source can be fabricated [913], using a resistively heated piece of glassy carbon [914], [915].

Using a 0.3 mm thick glassy carbon plate cut in the desired shape (see figure V.21) by laser or water-jet cutting, one gets the carbon source as shown in figure V.21(b). The glassy carbon filament is mounted on a standard UHV feedthrough, terminated with Ta rods, and fixed with Mo screws.

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The C Source is placed in a deposition UHV system, base pressure 1  ×  10⁻¹⁰ mbar heated using a DC current. The T calibration of the cell is performed in a separate UHV system with a base pressure 1  ×  10⁻⁸ mbar. The T in the hottest spot of the filament is measured using a dual-color optical pyrometer through an optical window located in front of the cell. Evaporation of carbon starts above 2000 °C. Using a DC current ~14 A (~100 W) the filament is at 2014 °C. A clear correlation of the increase of the partial pressure of atomic mass unit number 12 (a.m.u.) is observed in a residual gas analyzer (quadrupole) with source temperature. The presence of amu 12 can be associated to the evaporation of monoatomic carbon. The deposition rate is 3  ×  10⁻⁴ SLG s⁻¹.

By exposing a clean Pt(1 1 1) substrate to the carbon source the formation of carbon structures is observed [910]. First, the glassy carbon filament his held at T  >  2000 °C for degassing for 15 min. The pressure is kept  <1  ×  10⁻⁸ mbar. Before growth, the Pt single crystal is cleaned by cycles of Ar⁺ sputtering and annealing at 850 °C. The cycles are repeated until a sharp LEED pattern is observed, where only Pt peaks appears and/or STM images showing clean and flat extended regions. Then, one places the Pt (1 1 1) substrate at ~650 °C in front of the carbon source at 2000 °C with a distance between them of 20 mm. After 30 min 0.5 ML SLG is attained. During the process the pressure is ~7  ×  10⁻⁹ mbar. The procedure works equally well if the sample is annealed after growth. The graphene formation is demonstrated by in situ LEED and STM. The LEED diagram in figure V.22(a) shows the spots corresponding to the Pt(1 1 1) plus a surrounding ring characteristic of graphene. Brighter spots along the ring are indicative of the preferential orientations of the carbon periodicity with respect to the Pt crystal orientation. Figure V.22(b) shows an STM image measured on the graphene areas. The bigger periodicity (bright bumps) of the image corresponds to one of the possible moirés. The smaller periodicity (diagonal lines) is the atomic corrugation of the graphene. Graphene covers extended regions of the surface with a surface morphology similar to growth from decomposition of hydrocarbons or aromatic molecules.

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The MBE growth mechanism on Pt(1 1 1) by the evaporation of C atoms can be understood on the basis that the evaporated C atoms will not interact with each other or with gases until they reach the surface. This guarantees a continuum flux of atomic C on the surface, heated up to the desired T. The synergistic effect of surface T with the kinetic energy of the C atoms reaching the surface catalyses the initial graphene nucleation by atomic on-surface aggregation: C atoms reaching the surface are free to move until finding correct (stable) positions on the surface crystal lattice to bond and the epitaxial graphene growth undergoes by aggregation of on-surface diffusing C atoms or nucleated nanostructures (see figure V.23).

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T-assisted on-surface diffusion of C nucleation centers, able to collide with others, favours graphene formation, which will epitaxially grow in their most stable graphene domains. The CI-NEB approach [916, 917] yields a minimum diffusion barrier of a C atom on Pt(1 1 1) of 0.45 eV, and a C  +  C  →  C2 on-surface aggregation reaction barrier  <0.8 eV (with a net enthalpy gain ~3 eV), to be compared with barriers of 0.6 and 1.1 eV, respectively, reported for the Cu(1 1 1) surface [918], or the 0.58 eV for the atomic O diffusion barrier on Pt(1 1 1) [919]. These energy barrier values are easy to overcome in seconds at the typical surface temperatures in the MBE process on Pt(1 1 1). In addition, the graphene epitaxial growth-by-aggregation will be favoured as the nanopatches increase their size, which will be able to stabilize the incorporation of new diffusing C atoms and larger nucleated C nanostructures.

The use of Au as a substrate is difficult, since the T needed to obtain graphene is too close to Au melting point [906, 907]. A solid-carbon source can be used to decrease the T.

The Au (1 1 1) substrate is kept at 550 °C, with a well degassed carbon filament. This step can last for days because the freshly new filaments are porous containing many impurities. The degas pressure needs to be  <5  ×  10⁻⁹ mbar when the glassy carbon filament is at ~1600 °C (12 A, 83 W).If this step is not performed correctly, the samples get covered by an amorphous layer and the substrate has to be cleaned again.

In case of graphene growth by supersonic molecular beam epitaxy (SuMBE) from C₆₀ [920, 921], the two major issues to take into account are the substrate type and kinetic energy (KE). The main steps are the following:

• Surface preparation. Numerous (up to 40) Ar ion sputtering (0.5 keV) and annealing cycles of the Cu substrate (T  >  700 °C for optimal LEED diffraction pattern) to avoid the presence of unwanted contaminants, such as oxygen, sulphur or remaining carbons, during growth.
• Carrier gas choice. He or H₂The use of noble gases prevents strong interactions between carrier gas and the substrate and does not affect C₆₀ internal dynamics, which is frozen unlike ordinary heating that increases the molecular vibrations.
• Aerodynamical acceleration of the highly diluted (less than 1% of the mixture) C₆₀ beam by isentropic expansion of the flux out of the injection cell into vacuum through a nozzle. By changing the carrier gas and the seeding parameters (source T, gas inlet pressure), fullerene KE can be tuned, being inversely proportional to the carrier gas mass. KE ~ 10–15 eV using He carrier gas up to 30–40 eV using H₂.
• Collimation of the expanded flux and impact of the organic molecules on the Cu reconstructed surface, keeping the substrate at RT.
• Thermal activated growth of graphene islands by increasing T to 645 °C.

Refs. [922, 923] showed that substrate T must be raised to 645 °C to synthesize graphene islands as C₆₀ high-energy deposition on Cu, even at the highest KE reachable by SuMBE, does not lead to immediate C₆₀ cage rupture.

The ultimate evidence of the presence of defected nanometric graphene islands comes both STM and Raman spectroscopy [923]. This process is expected to be self-limiting and to stop completely as soon as the Cu surface is entirely covered by a monolayer of carbon atoms [923].

Ref. [923] reported a coating of graphene-like material at 645 °C using H₂ as carrier gas. These nanoislands also contain pentagons, which come from the original buckyball structures. Thus, at this stage this is just a proof of principle approach. The technique might be applied to a wide range of substrates, such as semiconductors and insulators, avoiding transfer.

This method consists in the growth of graphene in a UHV environment, using surface decomposition of C₆₀ [924] as a carbon source. The same method applies to Pt(1 1 1) and Ir (1 1 1), Cu(1 1 1)single crystals [901, 912, 925] and Cu foil [926].

The combination of a UHV environment together with the use of C₆₀ molecules provides some advantages with respect to conventional CVD [927, 928]. On one hand, this procedure is self-limited, which assures the growth of SLG. On the other hand, the controlled and clean environment (UHV chamber with a base pressure ~10⁻¹⁰ mbar) results in samples almost free of impurities with a lower growth T than CVD.

Ref. [926] used commercial C₆₀ (Sigma, 98% purity). To control the evaporation rate, a molecular evaporator is needed, that can be either commercial or homemade, as in this case. Figure V.24 shows a homemade one with a Ta crucible on which a type-K thermocouple is spot-welded. The molecules are placed inside the crucible. Acurrent is passed through the Cu rods and the molecules are evaporated at 450 °C–500 °C. Molecules are outgassed in UHV conditions prior to growth. To this aim, C₆₀ is heated 10 °C above the growth T, until the initial pressure is restored (~10⁻¹⁰ mbar) after elimination of impurities (water, CO, CO₂). Usually the crucible is spot welded to two pieces of steel that are clamped to Cu rods. It is important to have a good electrical contact between Ta crucible and rods, otherwise the whole evaporator will be heated and the result will be a rise in the base pressure of the chamber and, therefore, a dirty evaporation.

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Cu, used as a substrate, is cleaned with several sputtering and annealing cycles. A standard preparation consists in five cycles of 10 min Ar sputtering and 10 min annealing by electron bombardment at 800 °C. For the first cycle the sample current is 10 µA. For the last cycle, the sample current is reduced to 5 µA to prevent large surface roughness. With this sample current value a surface roughness of 0.4 nm is obtained. T  >  800 °C may promote the diffusion of impurities from the bulk to the surface as well as an excessive Cu sublimation, leading to higher roughness.

Figure V.25(a) shows a Cu foil mounted on a typical sample holder by using two lateral Ta wires to support it. Other fixing procedures, like the use of glue or carbon tape, are not possible in UHV. The way the sample is mounted is important because the sample might bend during annealing if the thermal contact with the sample holder is not homogenous (figure V.25(b)). The simplest and more efficient way of improving the thermal contact is the use of thicker Cu substrates.

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In situ surface techniques such as LEED, AES or STM can provide valuable information with no need to expose the sample to the air, thus avoiding surface contamination. Figure V.26 is a LEED pattern of a Cu foil after cleaning, where multiple spots, corresponding to different grain orientations, are observed.

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Once the substrate is clean and the molecules purified, the growth consists in exposing the substrate to the molecules at the chosen growth T. Typical parameters are: evaporation T ~ 450 °C, substrate size ~15  ×  20 mm², 10 cm evaporator/sample distance and growth time ~90 min. Coverage can be tuned by changing the exposure time. An important step is to have initially the substrate at the growth T before the C₆₀ molecules start to sublimate, avoiding any C₆₀ arriving to the sample surface when this is still cold. Different growth trials have been made by first depositing the molecules on the cold surface and making a post-annealing, but this procedure shows less satisfactory results. Once the evaporation is finished, it is important to keep the sample hot until the evaporator gets cold.

This procedure provides polycrystalline SLG on Cu. The next step involves sample characterization. Figures V.27(a) and (b) exhibit LEED patterns taken at of 50 and 56 eV with a typical ring of a polycrystalline graphene surface. AFM images (figures V.27(c) and (d)) show very large and flat Cu terraces (hundreds of nanometers) free of contaminants where graphene wrinkles cross all over the area, assuring a complete coverage. Figure V.27(e) shows a Raman spectrum at 532 nm, after background subtraction, taken in the area delimited in the optical image that appears in the inset. The spectrum exhibits a symmetric and narrow 2D peak located at ~2703 cm⁻¹ with FWHM(2D) ~28 cm⁻¹, compatible with SLG [105], with a significant D peak that could be due to grain boundaries and defects.

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As the solubility of carbon in Cu decreases with decreasing T with this method the solubility is reduced four times with respect to CVD [790]. For this reason, with this process mainly SLG is growth, without contribution of BLG.

The growth of graphene on single crystals by thermal decomposition of C₆₀ does not differ much from the polycrystalline ones. All surfaces must be clean, several sputtering and annealing cycles are mandatory, otherwise defective samples are obtained. Figure V.28 shows three STM images of graphene grown by on Cu(1 1 1) and Pt(1 1 1), Ir(1 1 1) for comparison. Some of the typical moiré patterns that depend on the substrate can be seen. These appear due to the mismatch of the graphene and metal network, meaning that only SLG has grown. This leads to a clean graphene not only because it takes place in a UHV environment but also because the precursor contains only C atoms.

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The same method works for other metals like Pt or Ir. Table V.1 shows the differences between the growths on the various substrates.

There is still a lack of a precise atomic mechanism rationalizing the thermally-assisted on-surface decomposition of fullerenes on metals, whose foundations still remain unclear. The process needs the synergistic effect of surface T and availability of enhanced reactivity sites on the metal surface: such as atomic metal vacancies, kink/add surface metal atoms or metal surface steps. The combination of these factors favours the anchoring of the C₆₀ molecules to the surface strongly enough to disrupt their stable geometrical arrangement (see figure V.29). A strong interaction of C₆₀ with the sites with enhanced-reactivity could lead to an efficient weakening of the C–C bonds within the cage-like configuration contacting with the surface, in particular, of the C–C bridges participating in pentagon-rings of the C₆₀ molecules, which store less energy than those connecting hexagon-rings. The process will start with the molecular cage rupture toward the on-surface disaggregation of the molecules into C atoms or other flatter C-based structures, free to diffuse on the metal surface by effect of the T.The epitaxial graphene growth will undergo by aggregation of the mentioned on-surface diffusing C atoms or C-based nanostructures (see figure V.29), which will lead to the formation of the most stable graphene domains on the metal substrates.

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It would be desirable to grow graphene on high quality single crystals. Graphene on SiC is of high quality and may satisfy some applications. However, these are limited to the use of SiC as a substrate. Other than on SiC, most of the high-quality isolated graphene has been grown on metal surfaces because of their high catalytic activity and limited C solubility. While as a single crystal is not widely used in the semiconductor industry, it is used as an alloy with Si (SiGe) in the sources and drain of advanced transistors and it could also be deposited selectively onto Si. With respect to its ability to be a good graphene substrate, Ge like Cu has an extremely low C solubility and it does not form a carbide, [930] thus potentially making it a good candidate for graphene growth. Ref. [931] took advantage of this and found CVD growth conditions for SLG. Additional work was performed on the growth of graphene using other techniques such as APCVD, [932] and MBE, [933] on Ge(1 1 0), Ge(1 0 0) and Ge(1 1 0)/Si(1 1 0) and Ge(1 0 0)/Si(1 0 0). Although Ge is more 'compatible' in Si device flows, there are still challenges: transfer and crystallinity. These could be overcome by developing growth selective techniques on isolated Ge/Si post transistor fabrication. Ref. [934, 935] reported the CVD growth of graphene on monocrystalline Ge(1 0 0) on Si(1 0 0), the preferred orientation of Si for CMOS technology. The growth took place between 900 and 930 °C with a ramp-up rate of 1–20 °C min⁻¹ and CH₄ flow in the (0.4–5 sccm) range. The optimal roughness of the substrate was achieved when the step growth was preceded by annealing at 750 °C–800 °C in pure H₂ to reduce native oxides in situ [936, 937]. Ref. [934, 935] also grew SLG on Ge(1 0 0)/Si(1 0 0) under laminar conditions with a Aixtron VP508 horizontal CVD hot wall reactor. The SLG growth was perfromed at 890 °C–910 °C with a ramp-up rate ~1 –10 °C min⁻¹ and a pressure ~850–990 mbar. CH₄ at flow rate ~0.1–0.5 sccm was used in an Ar flow ~3 l min⁻¹. The step growth was preceded by substrate annealing at 800 °C–850 °C in H₂.

The production of large area polycrystalline graphene and graphene single crystals has been demonstrated via chemical vapor deposition (CVD) on metal catalyst. Currently, the major drawback is the transference of the large area graphene film to the desired substrate for applications that normally induces contamination, wrinkles or even breakage of graphene. In this scenario, the game changing breakthrough would be the development of processes to deposit directly high quality graphene films and single crystals on arbitrary substrates avoiding the transference step and, if possible, at lower T than catalytic approaches. The first route involves the direct CVD synthesis on insulators or dielectrics at T  >  1000 °C with examples of synthesis surpassing 1500 °C [943]. Along the high T, atmospheric pressure and CH₄ as precursor diluted typically in Ar and/or H₂ are the most common parameters. Synthesis of SLG and FLG films was on reported on Si₃N₄ [938, 939], sapphire (Al₂O₃) [940–943] and silicon oxides in different structures [944–946] with final R_s between 5 kΩ [944] and 800 Ω [945]. FLG grains were also deposited on h-BN flakes at 1000 °C in atmospheric pressure CVD [947] and on MgO nanocrystal powder by LP CVD at lower T between 325 and 875 °C [948]. Other substrates include SiC [611] and SrTiO₃ [949] with µ ~1800 and 1050 cm²·V⁻¹·s⁻¹. Even though, the typical grain size is smaller (between 0.5 and 10 µm) and the amount of defects higher in comparison with the graphene synthesized with the catalytic approach, the final properties of the deposited graphene resemble transferred material grown on catalytic metals [945].

SiO₂ whether in bulk form as transparent quartz or fused silica or on thin films grown on Si wafers (SiO₂/Si), are the most frequently used insulators to directly growth graphene. In the case of the transparent substrates, the typical features of these films include transparency from 80% to 95%, nearly maintaining the transmittance of the substrate itself in some cases, and tunable R_s depending on process parameters [950–954] with values ranging from 1 kΩ sq⁻¹ [954] to few kΩ sq⁻¹ [952]. Those transparent materials have demonstrated potential for a broad range of daily life applications as heating elements in smart windows, high performance defoggers with fast response (one minute) [951], anti-icing glasses or as mechanical strain or rupture sensors (demonstrated G_F ~600 [955]), to name a few. The main limitation to transfer this knowledge to the industrial environment is the high growth T.

Given that Si based electronic technology is the established standard, it would be also extremely interesting to grow graphene on SiO₂/Si wafers so as to integrate graphene in Si-based devices. Many approaches have been developed in this area, but the temperature required, typically over 1100 °C [944, 945, 951, 954, 956–958], poses some problems derived from the poor thermal stability of SiO₂. Among them, desorption of SiO_x from the exposed surface [956] and diffusion of carbon or silicon species from the interface) [951] are well known phenomena that play an undesirable role during synthesis, affecting the structure and quality of the deposited graphene. These effects are more pronounced in thin oxide layers (less than 90 nm) [951] that, in turn, are an important issue in CMOS technologies [959]. Confinement of the substrate was suggested to eliminate desorption [956]. Even so, the final µ ranged from 410 to 760 cm²·V⁻¹·s⁻¹much lower than catalytic CVD. In order to manage the stability issue, PECVD has been considered as an alternative approach to direct deposit graphene at lower T [962].

PECVD enables catalyst free direct growth by the activation of molecules in gas phase and reduces the high T in conventional CVD or in attempts to use pyrolysis [938, 939, 941, 942, 944–948]. The most important drawback is the resulting small grain size.

PECVD has been reported on non-metallic substrates, resulting in films with small grain sizes -from 2 to 30 nm-, and amorphous carbon [816, 960, 961]. Ref. [774] reported an enlargement of grain size by a 'two-step' growth strategy in remote electron cyclotron resonance plasma assisted chemical vapor deposition, r-(ECR-CVD), figure V.30. The entire protocol is shown in figure V.31.

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The various parameters (time (t), T and partial pressures of C₂H₂ and H₂, PC₂H₂ and PH₂) were tuned 'in situ' in the nucleation (t₁, T₁, P₁C₂H₂/P₁H₂) of high quality graphitic seeds and growth from the seeds edges (t₂, T₂, P₂C₂H₂/P₂H₂) stages. A post-growth annealing is applied in UHV, improving the final properties of the film. The detailed procedure is usually as follows:

• Evacuation down to 10⁻⁵ mbar, introduction molecular H₂ at a P₁H₂  =  10⁻² mbar (typical flow of H₂  =  55 sccm) and increase T up to T₁  =  500 °C–700 °C in 40–60 min (t₀, figure V.31) for stabilization. Subsequently, annealing the substrate for 5 min. In some cases is interesting to bias the substrate with a positive potential (0 V–50 V) if the auto polarization due to the plasma is not positive.
• Step 1 (NUCLEATION): Introduction of C₂H₂, at a P₁C₂H₂  =  10⁻⁴ mbar, typical flow  =  0.25:0.20 sccm and turn on the plasma (100 W) during 5 min (t₁, figure V.31).
• Step 2 (GROWTH): Modify T₂ in a range of 30 °C–100 °C or P₂C₂H₂/P₂H₂ in the 0.1–0.9 · 10⁻⁴ mbar range (between 10%–20%), maintaining it for few hours (t₂, figure V.31), until the substrate is completely covered. As a general rule, P₂C₂H₂ is modified, due to its minimal relevance in the final pressure.
• Turn the plasma and bias off and cut the flow of precursor (P₂C₂H₂), cooling down in hydrogen atmosphere (P₂H₂) during 40 min (t₃, figure V.31) preventing oxidation. Post growth annealing in UHV at 650 °C, to desorb some chemical species attached to grain boundaries and to improve the coalescence among the grains.

Following the above protocol graphene was deposited on quartz as depicted in figure V.32. AFM images of lateral force contrast are shown in figures V.32(a)–(c). Raman analysis indicates the formation of predominantly highly defective SLG at 650 °C, figure V.32(d).

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Figure V.33 presents an AFM characterization of continuous film, confirmed by four point probe measurements, with a R_S ~ 3.4 kΩ·sq⁻¹. The coalescence of graphene grains follows two different trends (figures V.33(a) and (b)). Hexagonal graphene domains of similar orientation often generate a smooth lateral merging, presenting boundaries without linear defects (figure V.33(b), black arrows) [611, 931, 962–965]. On the other hand, rough lateral merging also takes place at many points, where linear defects occur (figure V.33(d), pink line). On these defects, carbon species accumulate as in vertical graphene deposition [966] that indicates that the process is not completely self-limiting. From UV–vis-NIR spectrophotometry transmittance (figure V.33(c)), it is also clear that there is an influence of this accumulation (values ~95%).

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After growth, the sample can be annealed in UHV to improve the final properties. Ref. [774] increased T stepwise up to 600 °C. The height and density of the linear defects is lower after annealing. R_S decreased from ~3.4 kΩ·sq⁻¹ to ~900 Ω·sq⁻¹, with transmittance  >  92%. The protocol is scalable it is likely accelerated by changing plasma power and pressure.

The r-(ECR-CVD) mode activated by microwave (MW) source provides higher efficiency in the dissociation of gases than other plasma and it is especially efficient in the dissociation of H₂. It is one order of magnitude more efficient than other DC (continuous polarization) and RF (radiofrequency) plasma sources. Along with the activated species and neutral radicals, ions and electrons coexist, being mostly the highly energetic ions a potential cause of etching of films. From a geometric point of view, a minimum distance between the plasma zone and the substrate (20 cm) should be respected ('remote plasma activation'). Moreover, the inhomogeneous plasma activation (plasma ball) results in different deposition rates on different sites. For this reason, to make de process reproducible the position of the sample in the holder is critical and must be respected. Apart from geometric considerations, one parameter that can minimize the presence of remaining ions reaching the sample is the positive bias of the substrate [967–969]. The activation of the substrate is also minimized preventing high nucleation density. The last fundamental plasma parameter is the power; the higher the power, the grater is the gas activation. However, as this protocol is a competitive process between etching and growth, assessing the role of power is not straightforward. The increase of power itself does not reflect a proportional increase of all species.

A T increase keeping the other parameters fixed, results in an increase of the reaction rate but at the expense of an enhanced nucleation density due to the present dangling bonds in freshly activated oxide surfaces. As a minimum T  >  400 °C is needed for graphitization, the key is to favor the reaction at the graphene edge instead of reaction with substrate by carefully playing with the local saturation of carbon. In figure V.32, a deviation in T from the established recipe affects the nucleation density, growth rate, microstructure and N. Figure V.32(a) shows single layer grains at 650 °C. At 700 °C, figure V.32(c) more flakes of few layers are predominant. Side chemical and topological effects take place, as covalent bonding with substrate or etching, hindering the desired van der Waals interaction. Formation of carbide phases or volatilization of oxide species (CO, H₂O, OH, SiO...) can be produced. There are interdependence between pressure and T, as the unbalanced pressure has similar effects, as observed in figure V.34 (variation of 20% of gas flow). If hydrocarbon flow is below the critical value at a given T, there is no deposition in the nucleation step. If it is over, the deposited nuclei suffer from amorphization. In the second step, a similar effect occurs with (T₂) or partial pressures relation, P₂(C₂H₂)/(P₂H₂), resulting in secondary nucleation or etching of the deposited material. In figures V.34(a) and (c) a deposition of submonolayer graphene can be seen in topography and friction images. In figures V.34(b)–(d) more few layer flakes are deposited increasing pressure.

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The precursors and atomic hydrogen, also play a critical role. An appropriate H/C_xH_y ratio in the atmosphere is necessary to grow crystalline material [970]. There is a competition between growth from C_xH_y radicals and etching of amorphous deposits by atomic H [971, 972]. The etching rate depends on T and N.

Ref. [774] found that C₂H₂ is a suitable precursor for low T, and no relevant differences between the films deposited with CH₄ and C₂H₂ diluted in hydrogen, once the appropriate H/C_xH_y relation and T) settings are selected. For C₂H₂ the activation is much higher due to combination of plasma and thermal activation (that does not happen with CH₄) [973]. This enhances the reaction rate because the plasma environment is full of activated carbon dimmers, postulated as the main precursor, or at least the main intermediate product, in the case of the synthesis of graphene, due to their higher mobility [974, 975].

Ref. [774] used fused silica at high T up to 700 °C. However, some kind of modification was detected in the surface and changed to quartz.

Dangling bonds in freshly activated surfaces (oxides or insulators) promote strong chemical interaction between the surface and gases. To overcome this limitation the two step process was developed Ref. [774] where the edge growth from seeds is highly favored over the nucleation on substrate. Even so, some limitations continue as the process is slow and not completely self-limiting as can be seen in figure V.34(d) where several layers conforming a multilayer deposit (rose petals shape) is apparent. The origin of this multilayer deposits is the slight reduction of the quartz surface.

The reduction process of the quartz surface has been computationally simulated by modelling the quartz [1 1   −  2 0] facet (x-cut), assessing the activation energies for the most probable reaction paths within the CI-NEB approach [916, 917] (see figure V.35(a)). Protonation of surface oxygen with atomic hydrogen from plasma and subsequent water vapour release are highly probable in this surface at Si synthesis T[774]. The passivation of the silicon enriched surface with hydrogen prior growth is also favoured because the Si detachment is more energy demanding. Simultaneously to the different steps along the reduction of the quartz surface (figure V.35(a)), plasma products, acting as reaction precursors toward the formation of graphene, start to adsorb on the surface, which will lead to their decomposition and dehydrogenation, favouring the nucleation at specific enhanced-reactivity sites, depending on the surface reduction stage (see figure V.35(b)). Graphene nanopatches will grow from the incorporation of dehydrogenated carbon atoms, as well as from nucleation centers catalysed by the surface. The coexistence of these processes with the plasma atomic hydrogen maintains the H-passivation and de-passivation (by surface-assisted H₂ formation) equilibrium in the surface promoting the plasma precursors into graphene.

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PECVDis as an alternative approach to directly deposit graphene at low T. Several studies were reported on the grown of graphene by PECVD over Si/SiO₂ with thick (250–300 nm) and medium oxide layers [977, 978], resulting in BLG or FLG [979, 980]. Ref. [981] addressed the direct growth of graphene on Siwafers with ultrathin native oxide by r-(ECR-CVD) using the two-step protocol discussed throughout this section to separately control nucleation and growth stages [977, 774], enabling tuning of grain size and thickness.

Figure V.36 is one example of graphene nuclei obtained at 550 °C following the two step protocol using two C₂H₂ flows. The increase of C₂H₂ flow in the nucleation step from 0.8 to 0.9 promotes a moderately increase of the nucleation density for a particular nucleation time (~30 nuclei µm⁻²). Also, the increase of C₂H₂ flow from 0.7 to 0.8 sccm increases the grain size during a given growth time. The height profiles in figures V.36(a) and (b) evidenced that, despite the different graphene nuclei sizes, for both experimental conditions, the thickness of the nuclei remained below 1 nm, resembling the features of SLG on quartz [774]. During the synthesis, the SiO_x surface is not affected in terms of surface roughness.

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After nucleation, the enlargement of the nuclei in figure V.37(a) follows to complete the deposition of a continuous film. Figure V.37(a) shows the submonolayer coverage of the substrate. Longer t₂ (seven hours) enables the creation of graphene domains up to 300 nm in lateral size. Flake thickness, as shown in figure V.37(b), corresponds typically to SLG. The coalescence of the domains occurred without vertical growth at the grain boundaries as seen in figure V.37(c) but the surface of the film is not completely flat. Inhomogeneous stitching between grains is apparent, along with lack of continuity in some others (darker contrast). Figure V.37(d) presents the corresponding Raman spectra before and after annealing. The Raman spectrum from submonolayer coverage shows the characteristic graphene peaks. I(2D)/I(G)~1 and 2 and FWHM(2D) 38 cm⁻¹. The high I(D)/I(G)~ 1 is due to the high density of grain boundaries and defects. Along with grain boundaries, another source of defects could arise from the hydrogen enriched atmosphere during deposition, which functionalizes the graphene grains and boundaries, inducing some re-hybridization in the corresponding carbon atoms [982]. The Raman spectrum in black from the continuous film in figure V.37(c) shows similar results. The continuity of the film in figure V.37(c) was also confirmed by four point probe measurements (R_s~15 kΩ·sq⁻¹) This high value can be related to these aspects mentioned: incomplete stitching in some grain boundaries due to randomly oriented grains and functionalization [972]. Thisdecreased to 8 kΩ·sq⁻¹ after annealing at 650 °C in vacuum at 10⁻⁶ mbar, lower than reported for low T procedures [977]. After annealing, I(D)/I(G)decreases from ~1.1 to 0.9. This could be related to H desorption from the film inducing sp² hybridization in the carbon atoms [774]. The decrease of R_safter annealing could be also related to the same reason: H desorption from grains and boundaries and conversion of carbon hybridization [774, 982, 983].