Simulation of Electronic Quantum Devices: Failure of Semiclassical Models

To simplify the design and optimization of new-generation nanomaterials and related electronic and optoelectronic quantum devices, energy dissipation versus decoherence phenomena are often simulated via local models based on the Wigner-function formalism. Such a local description is, however, intrinsically incompatible with the fully quantum-mechanical (i.e., non-local) nature of the dissipation-free carrier dynamics. While the limitations of such hybrid treatments have already been pointed out in the past in diverse contexts, the spirit of the present work is to provide a more cohesive and critical review. To this aim, we focus on the fundamental link between the Wigner-function picture and the density-matrix formalism. In particular, we show that, starting from well-established density-matrix-based models, the resulting Wigner-function dissipation and/or thermalization dynamics is necessarily non-local. This leads to the conclusion that the use of local Wigner function models borrowed from the semiclassical Boltzmann theory is formally not justified and may produce unreliable results, and that such simplified local treatments should be replaced by fully non-local quantum models derived, e.g., via the density-matrix formalism.