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

摘要

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