Strain and charge carrier coupling in epitaxial graphene

Diedrich A. Schmidt, Taisuke Ohta, and Thomas E. Beechem

Phys. Rev. B 84, 235422 – Published 5 December 2011

Abstract

We report a striking coupling between strain and carrier concentration variations at micrometer scale in single-layer graphene grown on silicon carbide (SiC) (0001). The in-plane compressive strain (up to 0.4%) and carrier concentration are probed using Raman spectroscopy. We show that the large strain inhomogeneities in graphene initiate at the growth stage and develop further by strain relaxation along the mismatched symmetry axes of the graphene and the underlying substrate. The strain relaxation is accompanied by a locally larger electron concentration, suggesting that charge transfer reduces the strain energy in the overall system. Our work establishes the strain and doping variations as coupled, intrinsic properties of epitaxial graphene growth on SiC(0001).

Received 11 October 2010

DOI:https://doi.org/10.1103/PhysRevB.84.235422

Authors & Affiliations

Diedrich A. Schmidt^1,*, Taisuke Ohta^2,†, and Thomas E. Beechem²

¹Department of Physical Chemistry II, Ruhr-University Bochum, Bochum D-NRW 44780, Germany
²Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

^*Corresponding author: Diedrich. Schmidt@rub.de; On leave: Department of Physics, North Carolina A&T State University, Greensboro, North Carolina 27411, USA.
^†tohta@sandia.gov

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Vol. 84, Iss. 23 — 15 December 2011

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Images

Figure 1
Inhomogeneous Raman spectra in 1ML epitaxial graphene: (a) AFM topography; (b) Raman $G$ -band intensity map integrated over 1580–1605 cm $^{- 1}$ ; (c) false-color Raman cluster map; (d) overlay of $G$ -band peak position map (color scale below; blue: shift to higher wave number, yellow: unshifted with respect to $ω_{G}^{0}$ = 1582 cm $^{- 1}$ ) on AFM phase image shown in gray scale; and (e) average spectra from clusters in (c) with bare SiC (black) for reference, color coding same as in (c). Scan size is 30 × 30 μm $^{2}$ . Labels in (c) and (e) correspond to each cluster categorized by its strain state. RML stands for relaxed ML (cyan); PRML, partially relaxed ML (yellow); PSML, partially strained ML (blue); SML, strained ML graphene (green); and greater than 1ML coverage (red). Note the lack of any significant defect-induced $D$ band for all clusters.Reuse & Permissions
Figure 2
Strain and carrier concentration mapping: (a) mechanical strain-field map; (b) histogram of strain values for (a) categorized by the clusters in Fig. 1c; (c) electron concentration map; and (d) histogram of electron concentrations for (c) categorized by the clusters in Fig. 1c. Regions of more than 1ML graphene are not shown [blackened out in (a) and (c)]. Scan size is 30 × 30 μm $^{2}$ . Right bottom: legend for the histogram plots and color-bar scales for strain and carrier concentration.Reuse & Permissions
Figure 3
The surface of partially graphitized SiC: (a) AFM phase map; (b) false-color Raman cluster map; (c) strain and carrier concentration (inset) histograms of the clusters shown in (b); (d) average spectra from strain clusters in (b) with bare SiC (dashed curve) for reference, color coding same as (b); and (e-f) schematic of the step-flow and irregular growth mode fronts, respectively. Scan size in (a) and (b) is 12 × 12 μm $^{2}$ . Labels of clusters in (b) correspond to the spectra shown in (d).Reuse & Permissions
Figure 4
Residual mechanical strain vs normalized relative peak shift as determined from the $G$ - and 2 $D$ -band peak shifts for sub-ML (red) and ML coverage (black). Inset: uncorrected strain vs relative peak shift not considering carrier concentration dependence of the Raman peak shift. Circles and squares correspond to $G$ -band positions, and up- down-triangles to 2 $D$ -band positions. The interface (Int.) and relaxed monolayer (RML) data points are noted for reference. The dashed lines are linear fits to the data points, with their slopes proportional to the Grüneisen parameters for the $G$ and 2 $D$ bands.Reuse & Permissions
Figure 5
A model accounting for the strain-doping correlation based on $v_{F}$ renormalization. (a) Schematic illustration of the π and π $^{*}$ states (Dirac cone) for 1ML graphene with and without compressive strain. Inner cones (blue) show unstrained, doped 1ML, and outer cones (green) compressively strained, doped 1ML (corresponding to the cases of, for example, RML and SML, respectively). Varying the $v_{F}$ changes the opening of the cones, thus modifying the carrier concentration for the doped graphene. (b) Tight-binding (TB) band structure for unstrained (inner band, blue) and compressively strained (outer band, green) 1ML for the parameters described in the text. The dash line is the unstrained, undoped case. The electron energy is plotted with respect to the Fermi level.Reuse & Permissions

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