Hot-electron cooling by acoustic and optical phonons in monolayers of MoS$_2$ and other transition-metal dichalcogenides

Kristen Kaasbjerg, K. S. Bhargavi, S. S. Kubakaddi

Published 2014-09-05Version 1

A theory for hot-electron cooling by acoustic (APs) and optical (OPs) phonons is developed in monolayers of MoS2. The cooling power P is investigated as a function of electron temperature $T_e$ and carrier density $n$ taking into account all the relevant electron-phonon (el-ph) couplings. $P$ due to APs is dominant at low $T_e$ and the cross over to OP dominated cooling happens at $T_e\sim 50$-$75$ K. The unscreened deformation potential (DP) coupling to the TA phonon is shown to dominate $P$ due to acoustic phonon scattering over the entire temperature and density range considered. The cooling power due to screened DP coupling to the LA phonon and screened piezoelectric (PE) coupling to the TA and LA phonons is orders of magnitude lower. In the Bloch-Gruneisen (BG) regime, $P\sim T_e^4$ ($P\sim T_e^6$) and $P\sim n^{-1/2}$ are predicted for unscreened (screened) el-ph interaction. With increasing $T_e$, the exponent decreases to smaller values of nearly 1. The cooling power due to OPs is dominated by zero-order deformation potential and Frohlich interactions and is found to be significantly reduced by the hot-phonon effect at large values for the phonon-relaxation time due to phonon-phonon scattering $\tau_\text{ph}$ and $n$. The dependence of the optical phonon lifetime due to el-ph scattering, the effective hot-phonon temperature and hence the hot-phonon distribution function on carrier density $n$ and $T_e$ is also studied. These results for monolayer MoS2 are compared with those in conventional two-dimensional electron gases (2DEGs) and graphene.