# Simulation of Electronic Quantum Devices: Failure of Semiclassical Models
## 1 Introduction  
Despite its intrinsically quantum-mechanical nature, the steady-state electro-optical response of a conduction electron within a bulk crystal may be safely described via semiclassical models based on the Boltzmann transport theory [1]. This fact has allowed the development of a wide variety of semiclassical simulation strategies [2], and, during the last decades, the latter have provided a strong impetus to the development of semiconductor physics and technology [3]. The continuous progress in nanoelectronics and nanooptics, however, pushes device dimensions toward space- and time-scales where the semiclassical picture is questionable, and should at least be compared with authentic quantum approaches [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. The latter can be qualitatively grouped into two main classes: double-time approaches based on the nonequilibrium Green's function technique [16; 17; 18] and single-time approaches based on the density-matrix theory [19; 20], including phase-space treatments within the Wigner-function formalism [21]. The replacement of semiclassical simulation schemes with genuine quantum-mechanical treatments implies, in general, a considerable increase in computational effort and resources; indeed, a microscopic treatment of various scattering mechanisms via proper Monte Carlo simulations [2] is often computationally too demanding already within the conventional Boltzmann theory; for quantum-transport simulations, the situation is even worse. The design and optimization of new-generation nanomaterials as well as of related electronic and optoelectronic quantum devices is therefore frequently performed via partially phenomenologicaltransport models based on the Wigner-function formalism [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66]; within such simplified quantum-simulation schemes, energy dissipation versus decoherence phenomena are still described via local models borrowed from the semiclassical Boltzmann theory, namely relaxation-time treatments or Boltzmann-type scattering approaches. Such a local description is, however, intrinsically incompatible with the fully quantum-mechanical (i.e., non-local) nature of the dissipation-free carrier dynamics within the device active region. Indeed, during the last decades the intrinsic limitations of such hybrid treatments have been repeatedly pointed out, both for the case of thermalization models based on the conventional inflow-boundary-condition scheme [34; 37; 45; 46; 47; 47] and for the case of dissipation versus decoherence treatments based on the relaxation-time approximation as well as on Boltzmann-like scattering models [61; 64]. The aim of the present paper is twofold: on the one hand, we review and discuss selected simulated experiments pointing out these intrinsic limitations in different contexts, providing in addition a cohesive theoretical treatment able to clearly identify the origin of such diverse anomalies within the Wigner-function picture; and, on the other hand, starting from the density-matrix formalism, we discuss how to derive genuine quantum-mechanical dissipation models, able to overcome the intrinsic limitations just recalled. The main conclusion is that within the Wigner-function picture a correct treatment of both dissipation versus decoherence phenomena within the device active region and of the device-reservoir thermalization process requires the use of intrinsically non-local scattering models. The paper is organized as follows.