S. Karmalkar, A UNIFIED EQUILIBRIUM TREATMENT OF MODULATION-DOPED HETEROJUNCTIONS AND GROSSLY ASYMMETRIC HOMOJUNCTIONS, AND ITS APPLICATION TO MODFET DESIGN, I.E.E.E. transactions on electron devices, 45(10), 1998, pp. 2187-2195
Homo- and hetero- ''grossly asymmetric junctions,'' i.e., ''junctions
between a heavily doped and a lightly doped layer,'' are important bui
lding blocks of modern p(+)-i-n(+) and n(+)-i-n(+) diodes, BJT's and M
ODFET's. We establish a hitherto unhighlighted aspect of the unity und
erlying the physics of these junctions, based on a simple yet original
deduction from available surface field-potential relations. We show t
hat, apart from pursuing the scientific quest for unification, the ded
uction also leads to three new results of practical significance. Firs
tly, simple expressions are obtained for important parameters of the s
pace-charge layer of a general grossly asymmetric junction under equil
ibrium. These parameters include the width of the partially depleted r
egion on the heavily doped side of the junction, that could not be obt
ained from earlier analyses. Secondly, applying this partial depletion
width expression to the MODFET heterojunction, a nonlinear MODFET 2-D
EG charge versus gate voltage model is derived, which is very useful f
or accurately simulating the effects of gradual saturation charge-volt
age nonlinearity on dc and ac performance of analogue circuits. This c
harge-voltage model is expressed directly in terms of device parameter
s and temperature, unlike earlier nonlinear charge-voltage models whos
e parameters were empirical and could be extracted only by fitting to
experimental data or complex numerical calculations. Thirdly, a new co
ncept has emerged, as per which the effects of electron confinement, p
artial impurity ionization, Fermi-Dirac statistics and small geometry
in a grossly asymmetric junction can be treated simply as apparent ban
d discontinuity narrowing phenomena, and thus represented in an additi
ve form by dimensionally identical parameters. The concept facilitates
a comparison of different modulation doped heterojunction systems. We
present calculations illustrating the above results.