A new relation between the hot electron power loss and acoustic phonon limited mobility in Bloch-Grüneisen regime

Expressions for the electron power loss F(T) and mobility μp due to acoustic phonon scattering are given in the Bloch-Grüneisen (BG) regime for three- and two-dimensional electron gas in semiconductors and Dirac-fermions. We obtain a simple relation F(T) μp = ηevs2, where η (~ 1) is a constant, e is the electron charge and vs is the acoustic phonon velocity. It is found to be independent of temperature and electron concentration. This relation is applied to GaAs heterojucntions and graphene, to obtain μp from the measured F(T). We propose that, using this relation, the measurements of F(T), in BG regime, which depends exclusively upon the electron - acoustic phonon coupling, could serve as a tool to determine the low temperature μp, which is otherwise difficult to measure due to the contributions from the lattice disorders.