Electron Wave Filters from Inverse Scattering Theory

TL;DR

This paper presents a method to design semiconductor electron wave filters with prescribed transmittance properties by combining inverse scattering theory, Padé approximation, and unitary transformations, resulting in practical layered structures.

Contribution

It introduces a novel approach integrating inverse scattering and Padé approximation to design energy-specific electron filters with realizable layered profiles.

Findings

Designed a narrow band-pass AlGaAs filter with a high energy peak twice narrower than others.

Demonstrated the feasibility of translating continuous profiles into rectangular-well structures.

Provided specifications for a 12-layer electron filter with targeted transmittance features.

Abstract

Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: {\em a)} Pad\'e approximant reconstruction of the S-matrix; {\em b)} inverse scattering theory for Schro\"dinger's equation; {\em c)} a unitary transformation which takes into account the variable mass effects. The resultant continuous concentration profile can be digitized into an easily realizable rectangular-wells structure. For illustration, we give the specifications of a 2 narrow band-pass 12 layer $Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twice narrower} than the other.