A unified equilibrium treatment of modulation doped heterojunctions and grossly asymmetric homojunctions, and its application to MODFET design

Homo- and hetero- “grossly asymmetric junctions”, i.e., “junctions between a heavily doped and a lightly doped layer”, are important building blocks of modern p⁺-i-n ⁺ and n⁺-i-n⁺ diodes, BJTs and MODFETs. We establish a hitherto unhighlighted aspect of the unity underlying the physics of these junctions, based on a simple yet original deduction from available surface field-potential relations. We show that, apart from pursuing the scientific quest for unification, the deduction also leads to three new results of practical significance. Firstly, simple expressions are obtained for important parameters of the space-charge layer of a general grossly asymmetric junction under equilibrium. These parameters include the width of the partially depleted region on the heavily doped side of the junction, that could not be obtained from earlier analyses. Secondly, applying this partial depletion width expression to the MODFET heterojunction, a nonlinear MODFET 2-DEG charge versus gate voltage model is derived, which is very useful for accurately simulating the effects of gradual saturation charge-voltage nonlinearity on dc and ac performance of analogue circuits. This charge-voltage model is expressed directly in terms of device parameters and temperature, unlike earlier nonlinear charge-voltage models whose parameters were empirical and could be extracted only by fitting to experimental data or complex numerical calculations. Thirdly, a new concept has emerged, as per which the effects of electron confinement, partial impurity ionization, Fermi-Dirac statistics and small geometry in a grossly asymmetric junction can be treated simply as apparent band discontinuity narrowing phenomena, and thus represented in an additive form by dimensionally identical parameters. The concept facilitates a comparison of different modulation doped heterojunction systems. We present calculations illustrating the above results