Comparison of electron transport in polar materials for the models of low-density and high-density electron gas. Application to bulk GaN

Abstract

We analyzed the steady-state electron transport for bulk GaN in frame of two opposite approaches: the electron temperature approach that assumes a high-density electron gas and numerical single-particle Monte-Carlo method that assumes a lowdensity electron gas and does not take into account electron-electron (e-e) scattering. We have also presented an analytical solution of the Boltzmann transport equation based on diffusion approximation. The transport characteristics such as the drift velocity electric field, V d (E), and mean electron energy electric field, ε(E), have been calculated at nitrogen and room temperatures in the wide range of applied electric fields from zero fields up to runaway ones (~100 kV/cm) for both approaches. Our calculations were performed for doped semiconductor with equal impurity and electron concentrations, Ni = n =10¹⁶ cm⁻³. The electron distribution functions in various ranges of applied fields have been also demonstrated. Within the range of heating applied fields 0– 300 V/cm, we found a strong difference between the transport characteristics obtained by means of the balance equations (electron temperature approach) and Monte-Carlo procedure. However, the Monte-Carlo calculations and diffusion approximation show a good agreement at 77 K. Within the range of moderate fields 1–10 kV/cm at 77 K, we established that the streaming effect can occur for low-density electron gas. In spite of significant dissimilarity of a streaming-like and a shifted Maxwellian distribution functions, the calculated values of Vd(E) and ε(E) show similar sub-linear behavior as the functions of the applied field E. In the high-field range 20–80 kV/cm, the streaming effect is broken down, and we observe practically linear behavior of both Vd(E) and ε(E) for both approaches. At higher fields, we point out the initiation of the runaway effect.