Energy relaxation rate and power loss density in graphene on GaAs substrate due to piezoelectric surface acoustic phonons

Abstract

Electron-piezoelectric phonon interaction provides a significant extrinsic channel for energy relaxation in a graphene sheet placed on a polar substrate. We report in this paper our analytical and numerical investigations on energy relaxation rate and power loss density in graphene sheet on a polar substrate considering the electron-piezoelectric phonon scattering channel in the Boltzmann transport approach. We overcome the earlier crude approximations made to achieve the reported analytical results and compare the obtained results for their compliance with the numerical findings for the graphene sheet on the GaAs substrate. The obtained analytical expression for energy relaxation rate is valid for all temperatures and electron energies. The analytical result for power loss density limits its validity for low electron densities [Formula: see text]. It is observed that the relaxation rate due to surface piezoelectric phonons in graphene on GaAs substrate is directly proportional to temperatures above [Formula: see text], below which temperature independence is seen. Also, it is observed that the relaxation rate is linearly dependent on electron energy, [Formula: see text] at low temperatures, and [Formula: see text] independent at high temperatures. Moreover, the relaxation rate is electron density-independent for all (low to high) temperatures. The seemingly odd (from earlier reported behavior) temperature-independent, linearly dependent [Formula: see text] and n independent relaxation rate behavior for low temperatures is attributed to the approximation used so far in the phononic statistical occupation factor in deriving the relaxation rate in the low-temperature Bloch-Gruneisen (BG) regime. In undoped graphene, we have found that the power loss behavior follows a crossover from [Formula: see text] to [Formula: see text] behavior while moving from low [Formula: see text] to high [Formula: see text] electron temperature. This behavior contradicts the study by Zhang et al. [Phys. Rev. B 87, 075443 (2013)] and M. Ansari [Physica E: Low Dimens. Syst. Nanostruct. 131, 114722 (2021)] which reported low-temperature BG behavior of [Formula: see text]. This behavior is again attributed to using BG regime approximation for statistical occupation factors. Our findings are in agreement with the experimental work by Chen et al. [Nature Nanotechnol. 3, 206 (2008)] and You et al. [Appl. Phys. Lett. 115, 043104 (2019)].