ABSTRACT
This chapter aims to review the assumptions behind the Boltzmann transport equation and to present how a hierarchical set of equations for the moments of the distribution can be derived from it. It discusses advantages and limitations of different approaches to go beyond the semiclassical limit, from quantum-corrected semiclassical to quantum kinetic models in which dissipative carrier transport and quantum optics are described on equal footing. High-field nonstationary effects, phase coherence, tunneling, and other quantum features of electronic transport may have barely found mention in a handbook of optoelectronic devices, were it not for the developments in novel material systems, highly nanostructured to offer unprecedented performance. Moving from quantum-corrected semiclassical models to genuine quantum-kinetic descriptions, one has to face the fact that two closely related aspects of the problem, namely carrier transport and optical generation, are traditionally considered from different perspectives.
