Microscopic modeling of energy dissipation and decoherence in nanoscale materials and devices

Primary goal of this thesis work is to develop and implement microscopic modeling strategies able to describe semiconductor-based nanomaterials and nanodevices, overcoming both the intrinsic limits of the semiclassical transport theory and the huge computational costs of non Markovian approaches. The progressive reduction of modern optoelectronic devices space-scales, triggered by the evolution on semiconductor heterostructures at the nanoscale, together with the decrease of the typical time-scales involved, pushes device miniaturization toward limits where the application of the traditional Boltzmann transport theory becomes questionable, and a comparison with more rigorous quantum transport approaches is imperative. In spite of the quantum-mechanical nature of electron and photon dynamics in the core region of typical solid-state nanodevices, the overall behavior of such quantum systems is often governed by a highly non-trivial interplay between phase coherence and dissipation/dephasing. To this aim, the crucial step is to adopt a quantum mechanical description of the carrier subsystem; this can be performed at different levels, ranging from phenomenological dissipation/decoherence models to quantum-kinetic treatments. However, due to their high computational cost, non-Markovian Green’ s-function as well as density-matrix approaches like quantum Monte Carlo techniques or quantum-kinetics are currently unsuitable for the design and optimization of new-generation nanodevices. On the other end, the Wigner-function technique is a widely used approach which, in principle, is well suited to describe an interplay between coherence and dissipation: in fact it can be regarded both as a phase space formulation of the electronic density matrix and a quantum equivalent of the classical distribution function. The evolution of this quasi-distribution function is governed by the Wigner-equation, which is usually solved by applying local spatial boundary conditions. However, such a scheme has recently shown some intrinsic limits. In this thesis work we analyze both the reasons for these unphysical features –pointing out the needing of different and purely quantum approaches– and the limits in which they should not appear, thus justifying why these problems had not been encountered in numerous quantum-transport simulations based on this procedure. For these reasons here we present a novel single-particle simulation strategy able to describe the interplay between coherence and dissipation/dephasing. In the presence of one- as well as two-body scattering mechanisms, we apply the mean-field approximation to the many-body Lindblad-type (hence, positive-definite) scattering superoperators provided by a recently proposed Markov approach, and we derive a closed equation of motion for the electronic single-particle density matrix. Although the resulting scattering superoperator turns out to be, at finite or high carrier densities, nonlinear and non-Lindblad, we prove that it is able to guarantee the positivity of the evolution (in striking contrast with conventional Markov approaches) independently of the scattering mechanisms, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices; furthermore, it may be extended to the cases of quantum systems with open spatial boundaries (in this regard, it provides a formal derivation of a recently proposed Lindblad-like device-reservoir scattering superoperator). The proposed theoretical scheme is able, one the one hand, to recover the space-dependent Boltzmann equation and, on the other, to point out the regimes where a relevant role may be played by scattering-nonlocality effects, e.g. scattering-induced variations of the spatial charge-density which may not be provided by semiclassical treatments. Supplementing our analytical investigation with a number of simulated experiments in homogeneous as well as inhomogeneous GaN-based systems, we provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures: in particular, we show how the scattering-nonlocality effects (i) are particularly significant in the presence of a carrier localization on the nanometric space scale, (ii) cause a speedup of the diffusion and (iii) in superlattice structures induce, with respect to scattering-free evolutions, a suppression of coherent oscillations between adjacent wells. These genuine quantum effects may be predicted also by other simplified treatments of the dissipation/decoherence like, e.g., the Relaxation Time Approximation: the latter however turns out to be, contrary to the proposed microscopic theoretical scheme, totally nonlocal, e.g. it is unable to recover the local character of the Boltzmann collision term in the semiclassical limit and it leads, especially for the case of quasielastic dissipation processes, to a significant overestimation of the diffusion speedup.