Microscopic theory of semiconductor-based optoelectronic devices

Since the seminal paper by Esaki and Tsu, semiconductor-based nanometric heterostructures have been the subject of impressive theoretical and experimental activity due to their high potential impact in both fundamental research and device technology. The steady scaling down of typical space and time scales in quantum optoelectronic systems inevitably leads to a regime in which the validity of the traditional Boltzmann transport theory cannot be taken for granted and a more general quantum-transport description is imperative. In this paper, we shall review state-of-the-art approaches used in the theoretical modelling, design and optimization of optoelectronic quantum devices. The primary goal is to provide a cohesive treatment of basic quantum-transport effects, able to explain and predict the performances of new-generation semiconductor devices. With this aim, we shall review and discuss a fully three-dimensional microscopic treatment of time-dependent as well as steady-state quantum-transport phenomena, based on the density matrix formalism. This will allow us to introduce in a quite natural way the separation between coherent and incoherent processes. Starting with this general theoretical framework, we shall analyse two different types of quantum devices, namely periodically repeated structures and quantum systems with open boundaries. For devices within the first class, we will show how a proper use of periodic boundary conditions allows us to reproduce and predict their current-voltage characteristics without resorting to phenomenological parameters. For the second class of devices, we will address the relevant issue of a quantum treatment of charge transport in systems with open boundaries (electrical contacts) when studying and simulating an at least two-terminal device