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

The Wigner-function formalism is a well-known approach to model charge transport in semiconductor nanodevices. The primary goal of the present article is to point out and explain the intrinsic limitations of the conventional quantum-device modeling based on such a 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 dissipation and decoherence phenomena are taken into account via a relaxation-time approximation, the solution, although unique, is not necessarily a physical Wigner function. © 2013 American Physical Society.