Calibration of the Density-Gradient model by using the multidimensional effective-mass Schrödinger equation

Abstract

A calibration method is developed for the electron effective mass in the Density-Gradient model. This method uses the two- and three-dimensional effective-mass Schrodinger equations, which are solved for bounded quantum systems. The electron effective mass is computed by fitting the electron concentration computed by using the Density-Gradient model to the electron concentration computed by using the Schrodinger equation. Results for strongly confined silicon system with (100), (110), and (111) crystallographic orientations are presented. It is shown that the effective mass varies with the shape and dimensions of the quantum box. In device simulations, one should use the value of m_n that corresponds to the right shape and dimensions of the confinement region in the device.