HETEROSTRUCTURE DEVICE SIMULATION USING THE

WIGNER FUNCTION

by

KIRAN KUMAR GULLAPALLI, Ph.D, MS.

DISSERTATION

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

THE UNIVERSITY OF TEXAS AT AUSTIN

May 1994

ABSTRACT

Kiran Kumar Gullapalli, Ph. D.

The University of Texas at Austin 1994

Supervisor Dean Neikirk

In the last decade advanced heteroepitaxial technology has allowed the exploration of a wide variety of semiconductor heterostructures in which the electronic properties can be varied significantly over atomic length scales. Semiclassical models of electron transport are not useful for the analysis of such structures. Perhaps the most dramatic phenomenon illustrating the need for advanced quantum transport models is resonant-tunneling across a double barrier quantum well structure. Since the early work on resonant tunneling, many devices have been proposed that incorporate double barrier quantum wells, the motivation being the increased functionality per device. Because significant regions in these devices can still be described by semiclassical equations, it is highly desirable that the quantum transport equation have the structure of the semiclassical Boltzmann equation, and reduce to it when appropriate. Such a model is afforded by the Weyl transform and the associated Wigner function. In this work, a quantum transport model based on the Wigner function is developed for the analysis of heterostructure devices. Past work on the use of the Wigner function has assumed that the effective-mass is spatially uniform, clearly not the case in heterostructure devices. In this work, the spatially varying effective-mass has been correctly incorporated in the Wigner transport equation. While past work using the Wigner function has been restricted to relatively unimportant Al_xGa_1-xAs / GaAs heterostructure devices, this work presents improvements in the numerical treatment of the Wigner transport equation that are necessary to extend its application to the study of the more important devices based on In_yAl_1-yAs / In_xGa_1-xAs heterojunctions.

With the aid of the quantum transport models developed during this work, an intriguing memory switching phenomena was discovered in double barrier resonant tunneling diodes that contain N^- - N⁺ - N^- spacers. Experimentally, the devices can be reversibly switched between two conduction curves. They retain memory of the curve last switched to, even after removal of the external bias. Within the scope of the quantum transport models, the phenomenon is explained by the existence of two self-consistent charge distributions in the device, even when no external bias is applied.

Table of Contents

List or Figures ............... x

Chapter 1. Introduction .................. 1

Chapter 2. Schrödinger-Poisson Model for Quantum Transport .................. 6

2.1 Effective-mass Hamiltonians .................. 7

2.2 The Schrödinger equation on a discrete lattice .................. 14

2.2.1 Boundary conditions .................. 16

2.2.2 Resonances .................. 18

2.2.3 Electron density .................. 19

2.2.4 Current density .................. 21

2.2.5 Self-consistent potential .................. 23

2.3 G - X bandstructure .................. 24

2.4 Resonant-tunneling diodes .................. 26

2.5 Summary .................. 31