Some Studies on the Effect of Size on Various Semiconductor Structure used in Device Design

TL;DR

This paper develops an analytical transfer matrix method to model quantum tunneling in semiconductor structures, applied to device design, offering a balance between physical insight and computational accuracy.

Contribution

The paper introduces a transfer matrix method for modeling quantum tunneling in arbitrary potential wells, improving analysis of semiconductor device structures.

Findings

Successful application to three electronic device models

Provides accurate tunneling probabilities for arbitrary potentials

Balances physical insight with computational precision

Abstract

The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb Approximation (3) Numerical Calculation.Instaton method is helpful to understand the physical insight of quantum tunneling but the validity is restricted to the case of large separation between the two potential minima. WKB approximation is widely used in its simple mathematical form, but the result is inaccurate due to its inherent defect in connection formula. Recently WKB approximation has been developed by changing the phase lose at the classical turning points but no above approximation have provide the perfect result to the best of knowledge of Author. Using numerical methods, one can get the solution up to the desired accuracy, but a considerable deal of physical insight is lost in this process. In this paper, the Author presented the developmentof models of multiple quantum wells or barriers potential by using analytical Transfer matrix method (TMM), which has been applied to any arbitrary potential wells and barriers successfully. The author applied the above theory to three electronic device models and got satisfactory results.