Phase-plane analysis and classification of transient regimes for high-field electron transport in nitride semiconductors

Abstract

We present a detailed theoretical analysis of steady-state, transient time-dependent, and spatially dependent electron transport in the group-III nitrides at high and ultrahigh electric fields. To develop an analytical model, we derive time-dependent differential equations describing the hot-electron rates of momentum and energy relaxation in electron–polar-optical-phonon scattering and analyze them by employing phase-plane analysis. From the structure of the phase-plane partitioning based on the phase trajectories, the transient regimes are investigated and classified depending on various initial conditions. We have studied different subpicosecond regimes and found a considerable velocity overshoot effect. One of our findings is that when the velocity reaches the maximum, the electron temperature is of a moderate magnitude but increases considerably in the subsequent stage. Dynamic regimes with high electron temperature overshoot have been revealed. For the dominant electron–polar-optical-phonon scattering, the observed overshoot can be treated as a rudiment of the runaway effect typical for that mechanism. In nanoscale nitride diodes with space-charge limited transport, the transient processes are extended to sufficiently larger distances, the overshoot is weaker and the electron heating in the region of the peak velocity is greater than that found for time-dependent problem with a constant electric field throughout a homogeneous sample.