Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations

It is shown that in a semiconductor, where impurity and polar optical phonon scatterings are not involved, the transient velocity is the solution of a relaxation time equation. Relaxation times can be defined as functions of the stationary energy, thus leading to relaxation time equations which are good approximations for describing the transient average energy and drift velocity. Comparisons between the relaxation time description, and the transient response obtained by iterative or Monte Carlo methods, are performed on p-Ge and n-Si, and show an agreement better than 10% in a wide range of electric fields and lattice temperatures.