Introduction

The main issue of downscaling in the Si field-effect transistors (FETs) is the short channel effect in which the gate control is weakened by the drain bias. Based on an analysis of the electrical potential distribution in the channel region, it is well known that the short channel effect can be neglected when the channel length is ~6 times longer than the scaling length 1,2, where N, εch, εox, tch and tox are the effective gate number, dielectric constants for the channel and gate insulator and thickness of the channel and the gate oxide. This perspective attracts great attention to two-dimensional (2D) layered channels in the FET application because of their rigidly controllable atomic thickness (tch < 1 nm), as well as the low dielectric constant (εch = ~4) for typical 2D layered channels3,4. Although old-but-new 2D channels, such as transition metal dichalcogenides, black phosphorus and so on, have been intensively investigated recently5,6,7,8,9, bilayer graphene with an electrostatically tunable band gap still has an advantage over the high performance device from the viewpoint of mobility due to the smaller effective mass (mBLG = ~0.03710, mBP = 0.1311 and mMoS2 = ~0.3712).

The suppression of conductivity in bilayer graphene has so far been reported by many researchers by applying an external electrical field13,14,15,16,17,18,19,20,21,22,23,24. Optical spectroscopic measurements, such as angle-resolved photoemission spectroscopy25 and infrared spectroscopy14,26,27, confirmed the band gap formation. However, the large current on/off ratio (Ion/Ioff) of ~106 is obtained only at the quite low temperature of 300 mK17, not at room temperature. The reason is explained by the variable range hopping in gap states13,15,17,18,19. Therefore, the main target issue for bilayer graphene is a low current on/off ratio at room temperature. At the zero-order approximation, there will intrinsically be no interface states in bilayer graphene because there are no dangling bonds on the basal plane, compared with Pb centers in the SiO2/Si system, assigned by the electron spin resonance measurement28,29,30. Although the strong disorder at the channel edge was expected to act as a main conduction path, the transport measurement in the Corbino geometry excluded this idea19. The origin of the gap states remains an open question. So far, detailed measurements on the density of states (Dit) and the time constant (τit) for gap states have not been reported.

Contrary to the transport measurement, the extraction of the quantum capacitance (CQ) through the capacitance measurements (C-V) of bilayer graphene provides direct information on the density of states (DOS) of bilayer graphene, consequently, the energy gap (EG), because it is regarded as the energy cost of inducing the carriers in graphene and is directly related as CQ = e2DOS31. Although there are a few reports on CQ measurement for bilayer graphene32,33,34, the comparison of EG estimated both from I-V and C-V has not been done yet. Moreover, in principle, the mobile carrier response to a small-signal alternating current voltage at a certain frequency is measured in the C-V measurement. The capture and emission process of mobile carriers at the trap levels distributed throughout the band gap can be extracted as a deviation from the ideal carrier response without any trap levels under the assumption of the equivalent circuit. This technique is known as the conductance method34.

In this work, we present the systematic extraction of EG as a function of the displacement field (), which determines the band structure of bilayer graphene, from both I-V and C-V. The conductance measurements are carried out to extract Dit and τit; then, the possible origins of the gap states are discussed.

Bilayer graphene FTEs with a high quality top gate insulator

Recently, we have demonstrated a considerable suppression of the low-field leakage through high-k Y2O3 on monolayer graphene by applying high-pressure O2 annealing35. The same process was applied to bilayer graphene FETs. The improved electrical quality of the insulators provides access to the large displacement field ( = ~3.1 V/nm) in this study. Although there are several conventions for , we adopt the most widely used definition of in this study14, where εBG, εTG, dBG, dTG, VBG and VTG are the dielectric constants, the insulator thickness and the gate voltages for back- and top-gate insulators, respectively. is the charge neutrality point to give the minimum resistance in the top-gated region.

To suppress the hysteresis in drain current—gate voltage curves, the SiO2 surface was converted to be hydrophobic (siloxane group) by annealing the SiO2/Si substrate in a 100% O2 atmosphere at 1000 °C prior to the graphene transfer36. Then, the conventional back-gated bilayer graphene FETs containing source and drain electrodes were fabricated on ~90 nm SiO2/n+-Si substrates by the mechanical exfoliation of Kish graphite. This device was annealed under Ar/H2 gas flow at 300 °C for 3 hours to remove the resist residue on the bilayer graphene channel. Subsequently, Y2O3, with a thickness of ~6 nm, was deposited on bilayer graphene FETs by the thermal evaporation of Y metal in the O2 atmosphere at PO2 = 10−1 Pa35. Then, high-pressure annealing was carried out in a 100% O2 atmosphere at ~100 atm and 300 °C. Finally, the top gate electrode was patterned, followed by annealing at 300 °C for 30 s under 0.1% O2 gas flow. The lack of a Raman D band measured through Y2O3 indicated that no detectable defects were introduced into the bilayer graphene by the high-pressure O2 annealing, as shown in Supplementary Fig. S1c.

Estimation of EG by C-V and I-V

We first focus on the capacitance measurement to determine EG through the CQ extraction. Figure 1a shows the total capacitance (CTotal) between the source and top gate electrodes, obtained by sweeping VTG at different VBG, which were measured at the frequency of 1 MHz in a vacuum of ~1 × 10−5 Pa at 20 K. Figure 1b is the counter plot of CTotal. The CTotal reduction at the Dirac point with increasing VBG indicates the decrease in the DOS by the gap formation because of the strong contribution of CQ. The hysteresis in the bidirectional C-V curves is quite small (~0.1 V for a VTG = ±4 V sweep)35. As shown in Supplementary Fig. S2, the frequency dependence of CTotal is clearly observed in the gap region, suggesting the existence of trap sites. The gradual saturation of the capacitance with increasing frequency from 200 kHz to 1 MHz suggests that CTotal measured at 1 MHz is close to the ideal capacitance without any response to the trap site. Therefore, the C-V measurement in Fig. 1a was carried out at 1 MHz.

Figure 1
figure 1

Capacitance characteristics of dual gated bilayer graphene FETs.

(a) CTotal between the source and top gate electrodes as a function of VTG for different VBG measured at 20 K and a frequency of 1 MHz. (b) Counter plot of CTotal. The charge neutrality point is  = 0.75, 9. The value is shown at the periphery of the counter plot. (c) Comparison of CTG with those reported previously for both monolayer and bilayer graphene. Closed and open circles indicate CTG obtained for oxide insulators deposited by the atomic layer deposition technique (ALD) and for insulators prepared by another technique, respectively. “EOT” and “EDL” indicate CTG obtained for 1 nm-thick-SiO2 and a typical electric double-layer, respectively. Several papers are included. a: Zhang, Z. et al. Appl. Phys. Lett. 101, 213103 (2012). b: Fallahazad, B. et al. Appl. Phys. Lett. 100, 093112 (2012). c: Zou, K. et al. Nano Lett. 13, 369 (2013). d: Meric, I. et al. Nature Nanotech. 3, 654 (2008). e: Liao, L. et al., Nature 467, 305 (2010). f: Kim, S. et al. Appl. Phys. Lett. 94, 062107 (2009). g: Wu, Y. et al. Nature 472, 74 (2011). h: Velasco Jr. J. et al. Nature Nanotech. 7, 156 (2012).

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The slope of the dotted black line at the charge neutrality point of  = 0.75, 9 in Fig. 1b corresponds to the capacitive coupling ratio between the top gate and back gate, that is, −0.0412 = −CBG/CTG. Using CBG = 0.038 μFcm−2 for SiO2 with dBG = 90 nm and εBG = 3.9, CTG is estimated to be 0.93 μFcm−2. In the course of this study, the typical CTG value is ~1.2 μFcm−2, depending on the Y2O3 thickness. The CTG value is considerably high compared with those reported previously for both monolayer and bilayer graphene, as shown in Fig. 1c. Based on CTG and CBG, the white dotted lines indicate the constant , whose values are shown at the periphery of the counter plot of Fig. 1b. The maximum at the Dirac point in this study is ~3.1 V/nm, which is quite high compared with other reports.

The simplified equivalent circuit model of the device is shown in Fig. 2a, where Vch and Cpara are the charging voltage and the parasitic capacitance. The Fermi energy (EF) and the band structure of bilayer graphene are independently controlled by changing VTG and VBG. It should be noted that the contribution of CBG is implicitly involved in CTotal through CQ and Vch, in Fig. 2a. Based on the equivalent circuit of Fig. 1a, CQ was extracted along the constant lines, i.e., the constant band structure, by using Cpara as a fitting parameter. Figure 2b shows CQ as a function of EF for different constant values. At  = 0 V/nm, the extracted CQ is fitted reasonably well with the theoretical value for bilayer graphene calculated by the tight-binding model37 by selecting Cpara = 0.91 μFcm−2. The charging energy required to induce carriers in bilayer graphene is denoted by EF, which is expressed as EF = eVch. Vch can be expressed by the equation for a series combination of capacitors according to , where and are defined as  = CTotal−Cpara and  = VTG−VDP, respectively. VDP is the Dirac point voltage. The detailed calculation method is explained in Supplementary Fig. S3. The CQ value at the Dirac point for  = 0 V/nm is consistent well with the theoretical value because the DOS for bilayer graphene at the Dirac point is larger than the residual carriers induced externally by the charged impurities at the SiO2 surface38. With increasing , the reduction of CQ is clearly observed because the scattering issue, which strongly contributes to the conductivity in I-V, can be neglected in C-V. It should be emphasized that the DOS within the gap region almost reaches zero, which is not observed in the previous report for bilayer graphene with the h-BN top gate33. Moreover, the van Hove Singularity (vHS) is also observed near the valence band edge, as shown by arrows. The appearance of the vHS is asymmetric, that is, a valence band edge for negative and a conduction band edge for positive (not shown in Fig. 2b), which is consistent with previous data33. This phenomenon is explained by the near-layer capacitance enhancement effect39. Figure 2c shows EG as a function of absolute value for , determined from the C-V data. EG was defined as the energy between inflection points for the conduction and valence sides in Fig. 2b. EG is roughly ~300 mV at  = 2.5 V/nm.

Figure 2
figure 2

Quantum capacitance and energy band gap.

(a) Simplified equivalent circuit for the bilayer graphene FET. (b) CQ as a function of EF at different ranging from ~0 to −2.5 V/nm. The right vertical axis indicates DOS. (c) EG and E0 as a function of absolute value for determined from the C-V data and I-V data.

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We now consider the transport properties for the same device. Figure 3a shows the conductivity (σ) measured as a function of VTG for different VBG at 20 K. The conductivity at the Dirac point decreases with increasing VBG, again indicating the band gap opening. The maximum Ion/Ioff is ~3 × 103 for  = ~3.1 V/nm. Figure 3b shows the maximum mobility as a function of for different regions of pnp, ppp and so on, whose positions are shown in Supplementary Fig. S4a. In terms of the determination of carrier mobility using the Drude model (σ = enμ), the carrier density (n) is estimated by the integration of the differential capacitance of , that is, , because of the large contribution of CQ. Otherwise, n is overestimated. However, the carrier density at the access region between the source (drain) and topgate is assumed to be consistent with that at the main channel region just below the topgate electrode for the mobility estimation. Shortening this access region by the self-alignment process40 is important to extract the mobility more precisely and to improve the device performance.

Figure 3
figure 3

Transport characteristics.

(a) σ as a function of VTG for different VBG measured at 20 K. The drain current is on the order of 50 mA for the drain voltage of 100 mV. The leakage current is ~107 orders of magnitude lower than the drain current, as shown in Supplementary Fig. S1d. (b) Maximum mobility as a function of for different regions of pnp, ppp, npn, and nnn. The mobility at the hatched region (0 <  < 1.2) is relatively low because of the contribution of the ungated region between the top gate and source/drain electrodes (Supplementary Fig. S4). (c) Subthreshold swing (S) as a function of temperature. The slope is nearly linear (dS/dT = ~1.1 mV/K). (d) Comparison of Ion/Ioff and mobility with those reported previously for bilayer graphene. The temperature for Ion/Ioff data was fixed at 20 K. For the mobility, the temperature is not limited to 20 K and both two-probe and four-probe data are shown here.

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Moreover, the subthreshold swing (S) is plotted as a function of temperature, as shown in Fig. 3c. The S value (~600 mV/dec) extrapolated to room temperature is considerably larger than the theoretical lower limit of 60 meV/dec at room temperature41, suggesting the large contribution of the gap states. Figure 3d compares the present mobility and Ion/Ioff at 20 K with previously reported data. All the data for Ion/Ioff are selected at 20 K from the literature, while the temperature for the mobility is not limited to 20 K. The mobility in the present study is not very high because it includes the contact resistance. In contrast, Ion/Ioff in the present study is quite high in spite of the direct deposition of high-k oxide on bilayer graphene without any organic buffer layer.

To determine EG from the viewpoint of the transport, we study the temperature dependence of σ at different ranging from 0 to 3.1 V/nm. Figure 4a shows the temperature dependence of σ as a function of VTG−VDP at VBG = −60 V. So far, the temperature dependence of the conductivity in bilayer graphene is explained by the sum of three terms, the thermal activation (TA) at the high temperature region, nearest neighbor hopping (NNH) at the intermediate temperature range and variable range hopping (VRH) in a two-dimensional system of localized states at the low temperature region, as follows17,18,

Figure 4
figure 4

Temperature dependence of conductivity at the Dirac point.

(a) Temperature dependence of σ as a function of VTG−VDP at VBG = −60 V. (b,c) σ at the Dirac point as a function of temperature for different VBG ranging from −60 to 0 V. All the data are fitted by a sum of TA and NNH for (b) and by a sum of TA and VRH for (c).

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where , and are prefactors and E0, T0 and kB are the activation energy, the hopping energy and the Boltzmann constant. Since the lowest temperature in this study is 20 K, the contribution of VRH may not be observed. The conductivity at the Dirac point is plotted as a function of temperature and fitted by two combinations of TA + NNH and TA + VRH, as shown in Fig. 4b,c, respectively. All the conductivity data are well fitted with respect to T−1 for TA + NNH, while the plot with respect to T−1/3 does not show clear linear behavior below T = 100 K. The present data can be explained by TA + NNH for the temperature range above 20 K. This is consistent with the previous report where VRH was observed at below 5 K13,17,18. Extracted EG and E0 are plotted as a function of in Fig. 2c, respectively, along with the results obtained in infrared absorption studies14. EG determined by I-V is reasonably consistent with the previous infrared absorption data, while EG determined by C-V is slightly larger. This difference is discussed later. Moreover, E0 increases with and reaches 2.8 meV at  = 3.1 V/nm, which is high compared with previous reports18.

Estimation of Dit and τ it

To gain insight into the interface properties, the gap states in the electrostatically opened-band gap are quantitatively analyzed using the conductance method. The equivalent circuit of the device is shown in the left of Fig. 5a, where Rit and Cit are the resistance and capacitance associated with the interface traps, their product CitRit is defined as τit and Rs is the series resistance. It should be noted that Rit and Cit have been neglected due to roughly no electrical communication of carriers with trap sites at 1 MHz in Fig. 2a. Here, when this equivalent circuit is converted into Cp, in parallel with Gp, as shown in the right of Fig. 5a, the relation between Gp and Dit can be given as the following42,

Figure 5
figure 5

Characterization of gap states.

(a) The equivalent circuits with τit = RitCit (left) and for the conductance method (right). (b) Gp/ω as a function of f at  = −1.5 V/nm, i.e., the constant band structure with EG = ~150 meV. EF was changed from −74 to −28 meV. (c) Dit of bilayer graphene (BLG) as a function of EG for different . For comparison, Dit for Si(100), Si(111)44 and MoS243 are also included as a function of normalized energy gap (top transverse axis). (d) Two possible origins of the gap states are shown. For the border trap (top), some defect sites in oxides, such as an oxygen vacancy (dotted box), work as trap sites. For A-B stack breaking (bottom), the band structure is not ideal but is like the dotted line. When the external electrical field is applied, the band gap is opened, like the solid line.

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where ω = 2πf (f: measured frequency). Finally, Dit and τit can be obtained as and , where f0 is the frequency at . The accurate estimation of Dit is possible because Gp/ω does not include CQ, which is the advantage of the conductance method. However, if there is leakage conductance (Gleak), indicated by the dotted line in the left of Fig. 5a, it is quite difficult to separate the two conductance contributions. The key issue to extract Dit quantitatively is the fabrication of a highly reliable top gate insulator on bilayer graphene without any leakage current. This has been achieved by the high-pressure O2 post-deposition annealing of Y2O3.

Figure 5b shows Gp/ω as a function of f for EF from −74 to −28 meV, where the band structure was fixed as constant at = −1.5 V/nm, i.e., EG = ~150 meV. It should be emphasized that Gp was measured under the constant band structure along the constant line by controlling VTG and VBG at the same time. To prevent the contribution of a minority carrier response to the conductance, especially for small band gap semiconductors, the measurement temperature was lowered as much as possible, i.e., 20 K (kBT = ~1.7 meV). This quite low temperature is only possible in bilayer graphene because the majority carriers do not freeze due to the doping by the external gate control, unlike substitutionally doped semiconductors. The more detailed measurement conditions are described in the method section. Clear peaks were observed in the Gp/ω-f relation, suggesting the detection of a trap-detrapping sequence of carriers with gap states. The τit value is evaluated to be ~4 μs. In Fig. 2a, it is assumed that the contribution of Cit is roughly negligible in CTotal, measured at 1 MHz. According to this τit value, this assumption is roughly, but not completely, reasonable. Therefore, EG estimated by C-V may be slightly overestimated due to the contribution of Cit. Figure 5c shows Dit as a function of EG for different . Dit is in the range from the latter half of 1012 to 1013 eV−1cm−2. The energy dependence of Dit is not so obvious. Although this value is slightly smaller than that for MoS243, it is larger compared with those of Si44. The large amount of gap states at the interface of high-k oxide/bilayer graphene limits Ion/Ioff at present. The much lower Dit could be achieved for dual-gate bilayer graphene heterostructure with h-BN.

In general, the conductance method is applied to the metal-oxide-semiconductor (MOS) capacitor, where the current is injected from the back side through the semiconductor substrate, whose series resistance, including back side contact, can be removed by measuring the impedance at the high-frequency limit (see Method). The interface trap conductance can be precisely measured. In contrast, in the present FET structure, the carriers are injected from the side of the channel through the source and drain43,45. The channel resistance may contribute to Gp in the equivalent circuit. To avoid this, a device with a relatively short channel was used at the expense of the channel area, which increased Cpara in this study compared with typical value of ~0.2 μFcm−2 35. Supplementary Figure S5b compares τit with the channel time constant (τch = RDPCDP, where RDP and CDP are the measured resistance and capacitance at the Dirac point), suggesting that τit is dominant. Therefore, the present Dit measurement is reliable.

Finally, let us discuss the origin of the gap states. As mentioned before, no detectable defects are observed by the Raman D band. Therefore, the trap sites formed by defects are ignored in this discussion. Two possible origins are discussed here, as shown in Fig. 5d. One is the external origin, that is, the border trap46. The carriers in bilayer graphene electrically communicate with trap sites, such as the oxygen vacancy (dotted box) at the surface of oxides, because π electrons stay on the surface of bilayer graphene. The other is the internal origin. The local breakdown of A-B stacking47,48 results in the stacking of two monolayers49, leading to the different band structure. In this case, EF stays within EG at some momentum space, while the real states exist at another momentum space, which may macroscopically act as gap states. Here, let us consider the dominant origin of the gap states. From the viewpoint of the time constant, the former origin will be a more time-consuming process than the latter because the rate limiting process is the tunneling between bilayer graphene and trap sites at the oxide surface50. On the other hand, if A-B stack breaking is the dominant origin of the gap states, Dit should decrease with increasing , which is consistent with the observation in Fig. 2b. This, however, does not appear to be clear in the conductance measurement in Fig. 5c because other devices show almost no difference in Dit for different . If T0 in VRH is extracted at the low temperature region below 5 K, the dependence of Dit can be discussed more in detail because T0 is inversely proportional to the density of states for the localized states51. Further detailed measurements are required to understand the dependence of Dit. Although it is difficult to determine the dominant origin of the gap states at present, the quantitative recognition of the current status for Dit in this study does provide the realistic comparison with other semiconductor channels in terms of the interface quality.

Conclusions

We have succeeded in extracting critical information on the interface quality, that is, Dit and τit for gap states. At the large displacement field of ~3 V/nm, they are in the range from the latter half of 1012 to 1013 eV−1cm−2 and ~4 μs, respectively. The large amount of gap states at the interface of high-k oxide/bilayer graphene limits the Ion/Ioff ratio at present. Many trials to characterize the interface properties for other 2D layered channels, as well as bilayer graphene, will help in understanding the origin of the gap states. The improvement of gap states below ~1011 eV−1cm−2 is the first step for bilayer graphene devices to be a promising candidate for future nanoelectronic applications.

Methods

The transport measurement of the device was performed using a Keysight B1500A semiconductor analyzer in a Nagase low-temperature prober in a vacuum of ~10−5 Pa. The capacitance measurement and conductance method under the constant conditions were performed by controlling both the Keysight 4980 A LCR meter and the Keithley 2450 source meter for the back gate. The top gate electrode was connected to the high terminal, while the source and drain electrodes was connected to the low terminal. For the conductance measurement, Gp should be measured accurately by reducing the contribution of Rs in the equivalent circuit in the right side of Fig. 5a. Therefore, ozone treatment was performed for 5 min before the metal deposition to remove the resist residue at the source/drain contact52, which reduces the contact resistance. Then, Rs was estimated as follows. For the equivalent circuit in Fig. 5a (right), the impedance (Z) is given by . Therefore, Rs at the accumulation side was estimated to be 29.4 kΩ by taking the high-frequency limit (ω→∞), as shown in Supplementary Fig. S5a. Finally, Gp can be accurately estimated by removing Rs in the equivalent circuit in the right side of Fig. 5a. For the Dit measurement at the valence band side, EF is scanned along negative (−1.5 and −3 V/nm). The access region modulated only by the back gate is always p-type (black line on the dashed-dotted vertical line at VTG = 0 V in Fig. 1b), from which a hole is injected into the main channel under the top gate to ensure majority carrier response and vice versa for the conduction band side at the positive . Therefore, Dit distributed throughout EG can be measured using the single FET device, unlike the MOS capacitor.

Additional Information

How to cite this article: Kanayama, K. and Nagashio, K. Gap state analysis in electric-field-induced band gap for bilayer graphene. Sci. Rep. 5, 15789; doi: 10.1038/srep15789 (2015).