Mathematical Problems in Engineering
Volume 2 (1996), Issue 3, Pages 205-218

A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor; part I: The Boltzmann-Poisson-Schrödinger solver

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.


A self-consistent Boltzmann-Poisson-Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current-voltage characteristics, transconductance, gate capacitance, and unity-gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7 μm, and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity-gain frequency of 47.8 GHz.