Phonon Excitation by Electric Field in Semiconductors

Abstract

Calculations of electron and hole mobilities in semiconductors are generally based on the assumption that the phonon distribution is maintained at a fixed temperature $T_0$ even when the applied electric field is large. This assumption, however, is not always valid. One of us has shown that the phonon distribution deviates appreciably from its equilibrium value at low temperature ($T_0\approx 4$°K) and in strong electric fields. It was in fact shown that an increase in phonon density affects the mobility of electrons in high fields. Experiments on the mobility of $n$-type germanium were in reasonable agreement with the theory. We propose that a finite time is necessary for the phonons to build up to their saturation value. In the present paper, we calculate the phonon density and the electric current as a function of time. We show that, for a range of electric field $F$ and for semiconductors with dominant acoustic mode scattering, the current density decreases from the initial value $j\left(0\right)\mathrm{}$ to its saturation value $j\left(\infty \right)$ in a time ${\tau }_{\mathrm{ph}}$ of the order of the average phonon relaxation time.