Mathematical Problems in Engineering
Volume 2 (1996), Issue 3, Pages 219-231

A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor; part II: The full quantum transport

R. Khoie

Department of Electrical and Computer Engineering, University of Nevada, Las Vegas, Las Vegas 89154, NV, USA

Received 24 March 1995

Copyright © 1996 R. Khoie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In Part I of this paper we reported a self-consistent Boltzmann-Schrödinger-Poisson simulator for HEMT in which only electrons in the first subband were assumed to be quantized with their motion restricted to 2 dimensions. In that model, the electrons in the second and higher subbands were treated as bulk system behaving as a 3 dimensional electron gas. In Part II of this paper, we extend our simulator to a self-consistent full-quantum model in which the electrons in the second subband are also treated as quantized 2 dimensional gas. In this model, we consider the electrons in the lowest two subbands to be in the quantum well forming the 2-dimensional electron gas, and the electrons in the third and higher subbands to behave as bulk electrons with no restrictions in their motion. We have further incorporated an additional self-consistency by calculating the field-dependent, energy-dependent scattering rates due to ionized impurities and polar optical phonons. The two higher moments of Boltzmann transport equation are numerically solved for the two lowest subbands and the bulk system; six transport equations, four for the two subbands and two for the bulk system. The Schrödinger and Poisson equations are also solved self-consistently. The wavefunctions obtained are used to calculate the ionized impurity scattering and the polar optical phonon scattering rates. The rates of transfer of electrons and their energies to and from each subband are calculated from these intersubband and intrasubband scattering rates.