A Physically Based Analytical Model to Predict Quantized Eigen Energies and Wave Functions Incorporating Penetration Effect

TL;DR

This paper introduces a new analytical model for predicting quantized eigen energies and wave functions in quantum wells, incorporating penetration effects, and validated against numerical simulations for improved accuracy.

Contribution

The model is the first to accurately predict all eigen energies without fitting parameters for both silicon and III-V quantum well devices.

Findings

Model accurately predicts all eigen energies

Significantly better agreement with numerical simulations

Applicable to both silicon and III-V devices

Abstract

We propose a physically based analytical compact model to calculate Eigen energies and Wave functions which incorporates penetration effect. The model is applicable for a quantum well structure that frequently appears in modern nano-scale devices. This model is equally applicable for both silicon and III-V devices. Unlike other models already available in the literature, our model can accurately predict all the eigen energies without the inclusion of any fitting parameters. The validity of our model has been checked with numerical simulations and the results show significantly better agreement compared to the available methods.