Corrections to the calculation of bulk electron densities in quantum wells of HEMTs

摘要

This paper presents an improved quantum mechanical calculation of the electron density in a multi-layered high electron mobility transistor (HEMT) device structure. Extra terms arise in the integrals which describe this density, and an approximation to these extra terms is derived. This enables the integrals and their derivatives to be rapidly evaluated for the purpose of numerical simulation. The accuracy of the approximation is demonstrated. The effect of the correction terms is illustrated in the case of a four-layer one-dimensional structure with alternating layers of GaAs and AlGaAs. It is shown that certain components of the electron density are significantly increased when the extra terms are included. It is also shown that the use of a smaller number of eigensolutions of the Schrödinger equation produces greater accuracy when using the correction