Figure 1

(a) Optical micrograph of a device on ${\mathrm{SiO}}_2/\mathrm{\text{doped}}$ Si substrate. The graphene flake is outlined in a dashed red line. (b) Resistivity $\rho (V_{bg})$ of a device before (black line) and after [lighter (red) line] high-bias measurements. (c) Temperature-dependent resistivity $\rho (T)$ at $n=1.30(2)\times {10}^{12}{\mathrm{cm}}^{-2}$. The coupling strength of longitudinal acoustic (LA, graphene) and SO (${\mathrm{SiO}}_2$ substrate) phonons is extracted from the fitting (solid line). See Ref. 17 for details. (d) Two-terminal magnetoresistance $R_{2\mathrm{pt}}$ vs magnetic field. The contact resistance is $R_{\mathrm{con}}=340\Omega$, determined by extrapolating the magnetoresistance at the quantum hall plateaus, $R_{2\mathrm{pt}}(B)=R_{\mathrm{con}}+\frac{h}{e^2\nu }$ (with the integer filling factor $\nu$ shown on the figure), to $B=0$. (e) The measured (circles) and calculated (lines) drift velocity (in units of Fermi velocity, $v_{\mathbf{F}}$) vs electric field. The conduction of our devices tends to drop sharply and irreversibly near $E\approx 1\mathrm{V}/\mu \mathrm{m}$, presumably due to burning at local hot spots. Dashed line: theory with only impurities and the LA and longitudinal optical (LO) phonons of graphene. Dash-dotted line: theory with only impurities and the SO phonons of the ${\mathrm{SiO}}_2$ substrate. Upper solid line: the full theory including all scattering mechanisms. Lower solid line: instantaneous emission model. The density of holes is $n=2.09(2)\times {10}^{12}{\mathrm{cm}}^{-2}$, and the density of charged impurities is $n_{\mathrm{imp}}=5.8\times {10}^{11}{\mathrm{cm}}^{-2}$. The experimental error bar is smaller than the size of the symbol. (f) Comparison of experimental and theoretical drift velocity for several electron (right) and hole (left) densities at $E=0.6\mathrm{V}/\mu \mathrm{m}$.Reuse & Permissions

Figure 2

The electron drift velocity, electron temperature, and power dissipation in graphene field effect transistors. Panels (a), (b), and (c) consider a low-temperature device, with $T_L=T_s=100\mathrm{K}$, whereas the remaining panels assume $T_L=T_s=600\mathrm{K}$, which corresponds to a typical room-temperature device with current induced heating. In panels (a), (b), (d), and (e), results are shown including all phonons (solid lines), LA and LO phonons (dash-dotted lines), LA phonons (dashed lines), and SO phonons (open circles). Panels (c) and (f) show total power dissipation (dashed line) and also the power dissipation into the SO phonons (solid line). For all plots, we take carrier density $n=2\times {10}^{12}{\mathrm{cm}}^{-2}$ and density of charged impurities $n_{\mathrm{imp}}=5\times {10}^{11}{\mathrm{cm}}^{-2}$, and neglect neutral impurities.Reuse & Permissions

Figure 3

The saturation current density $j_{\mathrm{sat}}$ vs carrier density $n$ for graphene on $\mathrm{Si}{\mathrm{O}}_2$. $n_{\mathrm{imp}}=5\times {10}^{11}{\mathrm{cm}}^{-2}$ (solid line) and $n_{\mathrm{imp}}=5\times {10}^{10}{\mathrm{cm}}^{-2}$ (dashed line). Neutral impurities are neglected. $j_{\mathrm{sat}}$ is approximately linear for $n\gtrsim 5\times {10}^{12}{\mathrm{cm}}^{-2}$ and is slightly lower for the higher $n_{\mathrm{imp}}$. $j_{\mathrm{sat}}$ is defined as $j$ at $E=2\mathrm{V}/\mu \mathrm{m}$; as seen in the inset, all currents have reached saturation at this field. Inset: current vs electric field $j(E)$ for three representative carrier densities, $n=5\times {10}^{11}$ (cyan, bottom curve), $2\times {10}^{12}$ (blue, middle curve), and $1\times {10}^{13}{\mathrm{cm}}^{-2}$ (green, top curve). Solid and dashed curves correspond to the higher and lower $n_{\mathrm{imp}}$, respectively. All data in this figure are calculated at the representative substrate and lattice temperatures $T_s=20\mathrm{K}$ and $T_L=500\mathrm{K}$.Reuse & Permissions