Electron escape via polar optical-phonon interaction and tunneling from biased quantum wells

Abstract

In this study, the escape of electrons from a biased quantum well through polar optical-phonon interaction is addressed for an ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum-well system. Unlike previous models, the redistribution of the density of states resulting from the applied electric field is included. The calculation of the density of states, wave functions, and energy levels is performed by solving the Schr\"odinger equation through the logarithmic derivative of the wave function. A comparison of the escape time of electrons through a polar optical-phonon interaction and through tunneling out of the quantum well is made. It is demonstrated that for shallow quantum wells, escape via tunneling dominates for fields greater than 20 kV/cm, whereas, with increasing Al concentration, the escape via polar optical phonons dominates over a larger range of electric fields. The temperature dependence of the tunneling and polar optical-phonon assisted escape time is addressed, demonstrating an exponential dependence.