Abstract
Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.
Highlights
To accurately model the high-field transport in silicon inversion layers, several authors [3, 4] have introduced a nonparabolicity correction in the subband dispersions
Position-dependent material parameters are taken into account
As a result each subband is characterized by three parameters, En, mn, an, which denote the subband energy, mass and nonparabolicity coefficient, respectively
Summary
To accurately model the high-field transport in silicon inversion layers, several authors [3, 4] have introduced a nonparabolicity correction in the subband dispersions. In this work we quantitatively analyze nonparabolicity effects in various two-dimensional electron gases. For this purpose a self-consistent Schr6dinger-Poisson solver has been developed, capable of dealing with silicon inversion layers and heterostructures. As a result each subband is characterized by three parameters, En, mn, an, which denote the subband energy, mass and nonparabolicity coefficient, respectively. This set of parameters is intended to serve as input for high-field transport calculations. Our approach relies on the effective-mass approximation which is applicable if the confining potential, V(z), satisfies two conditions [3]: 1. V(z) is slowly varying over a unit cell, 2. matrix elements of V(z) between Bloch functions of different bands are negligible
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