Generation and recombination processes via acoustic phonons in disordered graphene

Generation-recombination interband transitions via acoustic phonons are allowed in a disordered graphene because of violation of the energy-momentum conservation requirements. The generation-recombination processes are analyzed for the case of scattering by a static disorder and the deformation interaction of carriers with in-plane acoustic modes. The generation-recombination rates were calculated for the cases of intrinsic and heavily-doped graphene at room temperature. The transient evolution of nonequilibrium carriers is described by the exponential fit dependent on doping conditions and disorder level. The characteristic relaxation times are estimated to be about 150–400 ns for a sample with the maximal sheet resistance of $\sim 5$ k$\Omega$. This rate is comparable with the generation-recombination processes induced by the thermal radiation.

Figure 1

Interband generation-recombination transitions via acoustic phonons with energies $\sim \hslash {\omega }_{\text{ac}}$ (thick arrows) between broadened electron-hole (e-h, shown by gray) states in the low-energy region, $\varepsilon <\hslash {\omega }_0/2$. Thin lines show the ideal dispersion law.

Figure 2

(a) Density of states ${\rho }_{\varepsilon }$ vs energy at $g=0$ (1), 0.15 (2), 0.3 (3), and 0.45 (4). (b) Ratio $V_{\varepsilon }=\sqrt{{\overline{\rho }}_{\varepsilon }/{\rho }_{\varepsilon }}$ vs $g$ for $\varepsilon =20$ meV (1), 30 meV (2), 40 meV (3), and 50 meV (4). (c) Equilibrium concentration of nondoped graphene $n_{\text{eq}}$ vs $g$ normalized to $n_T\simeq 0.52{(T/\hslash \upsilon )}^2$.

Figure 3

Contour plots of dimensionless kernels $w(\varepsilon /T,{\varepsilon }^{\prime }/T)$ for $g=0.4$ (a) and $g=0.2$ (b).

Figure 4

Averaged kernel $w_g$ vs coupling constant $g$. Dashed curve corresponds to the quadratic fit.

Figure 5

Transient evolution of concentration $n_t$ at different initial conditions: $n_{t=0}=3n_{\text{eq}}$ (1,2), $n_{t=0}=2n_{\text{eq}}$, (3,4), and $n_{t=0}=0.5n_{\text{eq}}$ (5,6) for coupling parameters $g=0.25$ (1, 3, 5) and $g=0.5$ (2, 4, 6). Dotted curves correspond to exponential fits (19), with $\alpha =0.16$ (1), 0.125 (2), 0.19 (3), 0.155 (4), 0.22 (5), and 0.275 (6).

Figure 6

Transient evolution of hole concentration $n_t-n_s$ at different initial conditions: $n_{t=0}-n_s=3n_T$ (1), $n_{t=0}-n_s=2n_T$ (2), and $n_{t=0}-n_s=0.5n_T$ (3). Solid and dashed curves correspond to coupling parameters $g=0.5$ and $g=0.25$, respectively. Dotted curves correspond to the exponential fits.

Figure 7

Transient evolution of concentration due to interband radiative transitions for intrinsic (a) and heavily-doped (b) graphene at different initial conditions: $n_{t=0}=3n_T$ (1), $n_{t=0}=2n_T$ (2), and $n_{t=0}=0.5n_T$ (3). Dotted curves correspond to exponential fits.