Comparison of electron transport in polar materials for the models of low-density and high-density electron gas. Application to bulk GaN - Korotyeyev, V.V.; Syngayivska, G.I.; Kochelap, V.A.; Klimov, A.A. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2009)
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.