Phonon-assisted impact ionization of electrons inIn0.53Ga0.47As

Abstract

Using perturbation theory, phonon-assisted impact ionization in semiconductors is investigated and its transition probability is compared to ``normal'' impact ionization processes with phonons not participating. Since phonon-assisted impact ionization is a second-order process, whereas ``normal'' impact ionization is of first order, phonon-assisted impact ionization has not been considered to be important in the past. A careful analysis shows, however, that this difference in the matrix elements has to be balanced against the higher number of final states in case of phonon-assisted processes. It turns out that, especially in small-band-gap materials with high satellite valleys, such as ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ or InAs, phonon-assisted impact ionization can dominate over ``normal'' impact ionization. With this knowledge, it has been possible to explain the anomalous temperature dependence of the electron ionization coefficient in ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ consistent with experimental data. Further, it is shown that the temperature dependence of the band gap is not sufficient alone to cause the reported positive temperature dependence of the ionization coefficient. Performing Monte Carlo transport simulations and using a simple approximation of the energy-dependent phonon-assisted ionization rate, good agreement between the theoretical calculation and the experimental data of both the temperature and the electric-field dependence of the electron impact ionization coefficient in ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ is obtained.