Microscopic theory of vertical-transport phenomena in semiconductor heterostructures: Interplay between two- and three-dimensional hot-carrier relaxation

A theoretical analysis of vertical-transport phenomena in semiconductor heterostructures is presented. In particular, the scattering coupling between two- and three-dimensional states in multiple quantum wells is investigated. To this purpose, a fully three-dimensional approach for the description of both localized and extended states in the heterostructure is proposed. Starting from such three-dimensional states, obtained from a self-consistent Schrödinger-Poisson calculation, a Monte Carlo solution of the corresponding Boltzmann transport equation is performed. In contrast to various phenomenological transport models, the present simulation scheme allows a kinetic description, i.e., based on microscopic scattering rates, of vertical transport across a generic heterostructure. Our results provide a rigorous description of hot-carrier relaxation between extended and localized states. This simulation scheme has been applied to finite multiple quantum wells with different geometries and doping profiles. A detailed analysis of the electron current as a function of temperature in quasiequilibrium conditions shows good agreement with experimental results. Moreover, in non-equilibrium conditions (i.e., hot-carrier regime) the scattering coupling between three- and two-dimensional states is found to play a significant role in modifying the carrier mobility as well as the fraction of conducting electrons.