Wigner-function formalism applied to semiconductor quantum devices: Failure of the conventional boundary-condition scheme

TL;DR

This paper critically examines the Wigner-function formalism for semiconductor quantum devices, revealing fundamental limitations of the conventional boundary-condition approach, especially regarding solution uniqueness and physical validity in different regimes.

Contribution

It identifies intrinsic issues with the standard boundary-condition scheme in Wigner-function modeling, providing insights into its limitations in both coherent and dissipative regimes.

Findings

Solution non-uniqueness without energy dissipation

Non-physical solutions with dissipation and relaxation-time approximation

Highlights the need for revised boundary-condition schemes

Abstract

The Wigner-function formalism is a well known approach to model charge transport in semiconductor nanodevices. Primary goal of the present article is to point out and explain intrinsic limitations of the conventional quantum-device modeling based on such Wigner-function paradigm, providing a definite answer to open questions related to the application of the conventional spatial boundary-condition scheme to the Wigner transport equation. Our analysis shows that (i) in the absence of energy dissipation (coherent limit) the solution of the Wigner equation equipped with given boundary conditions is not unique, and (ii) when decoherence/dissipation phenomena are taken into account via a relaxation-time approximation the solution, although unique, is not necessarily a physical Wigner function.