Nonlinear resistivity and heat dissipation in monolayer graphene

We have experimentally studied the nonlinear nature of electrical conduction in monolayer graphene devices on silica substrates. This nonlinearity manifests itself as a nonmonotonic dependence of the differential resistance on applied dc voltage bias across the sample. At temperatures below $\sim$70 K, the differential resistance exhibits a peak near zero bias that can be attributed to self-heating of the charge carriers. We show that the shape of this peak arises from a combination of different energy dissipation mechanisms of the carriers. The energy dissipation at higher carrier temperatures depends critically on the length of the sample. For samples longer than 10 $\mu$m the heat loss is shown to be determined by optical phonons at the silica-graphene interface.

Figure 1

(a) Differential resistance as a function of dc source-drain bias measured in sample A at different bath temperatures: $T_B=4.2$, 17, 26, 35, 83, and 107 K from bottom to top. (b) Dependence of the zero-bias differential resistance on the bath temperature. All measurements are taken at the Dirac point. The solid red line is a guide to the eye. Inset: Optical micrograph of sample A, with the flake indicated by a dotted outline; the scale bar is 10 $\mu$m.

Figure 2

(a) Differential resistance as a function of dc source-drain bias measured at $T_B=4.2$ K, for different gate voltages, $V_G=0$, $-6$, $-12$ V, with respect to the Dirac point (bottom to top). (b) The temperature dependence of the zero-bias resistance, for the gate voltages shown in (a): $V_G=0$, $-6$, $-12$ V, bottom to top. In (a) the zero-bias resistance has been subtracted from the curves to aid comparison, while in (b) $R_0(T=4.2\mathrm{K})$ has been subtracted. (c) Differential resistance as a function of source-drain bias, measured with different lengths between source and drain contacts, taken at 4.2 K. Measurements were taken for sample A in (a) and (b), and sample B in (c).

Figure 3

(a) Temperature dependence of the normalized zero-bias resistance of sample B at $V_G=-3$, $-10$, $-16$ V with respect to the Dirac point. (b)–(d) Differential resistance as a function of source-drain bias at different gate voltages, $V_G=-3$, $-10$, $-16$ V, respectively. The bath temperature $T_B=4$ K in (b) and (c), and 2 K in (d). The symbols are measured values, and the red lines are fits using Eq. (1).

Figure 4

(a)–(c) Measurements of $R\left(V_{\mathrm{sd}}\right)$ (black) in sample A for different gate voltages: $V_G=3$, $-6$, $-12$ V, respectively. The smooth curves are calculations for the case of no phonons (dashed green), acoustic phonons (dotted red), and both acoustic and optical phonons (blue). Note that in (c) the dotted and solid curves overlap. (d) The rate of energy loss of electrons due to scattering by acoustic phonons (dotted red line), and scattering by both acoustic and remote optical phonons (solid blue line). The dashed green line shows the inverse diffusion time. The inset shows this dependence over a larger range of temperature. (e) The calculated temperature distribution along the length of the sample for the three different models (same color coding) with an applied source-drain bias of 70 mV. The bath temperature is 4.2 K, and $V_G=3$ V.