Efficient wave function matching approach for quantum transport calculations

TL;DR

This paper introduces an optimized wave function matching method for quantum transport calculations that significantly reduces computational costs by excluding unnecessary evanescent modes, demonstrated on a carbon nanotube FET device.

Contribution

It presents a modified WFM approach that efficiently excludes most evanescent modes, enabling iterative determination of essential bulk modes and reducing computational expense.

Findings

Efficiently excludes majority of evanescent modes in WFM calculations.

Demonstrates reduced computational cost on a carbon nanotube FET device.

Maintains accuracy comparable to traditional methods.

Abstract

The Wave Function Matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable with the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all the propagating and evanescent bulk modes of the left and right electrodes in order to obtain the correct coupling between device and electrode regions. In this paper we will describe a modified WFM approach that allows for the exclusion of the vast majority of the evanescent modes in all parts of the calculation. This approach makes it feasible to apply iterative techniques to efficiently determine the few required bulk modes, which allows for a significant reduction of the computational expense of the WFM method. We illustrate the efficiency of the method on a carbon nanotube field-effect-transistor (FET) device displaying band-to-band tunneling and modeled within the semi-empirical Extended H\"uckel theory (EHT) framework.