Thermalization of excitons

Abstract

Thermalization means the achievement of thermal equilibrium. In this article we will be interested in how physical systems achieve thermal equilibrium after optical excitation. Actually we are not always interested in how a system returns to true thermal equilibrium. Often we are interested only in how a part of the system attains thermal equilibrium and this is sometimes known as a quasi-equilibrium. However, for the sake of brevity, I will refer to all processes which enable a system or subsystem to relax towards thermal equilibrium or quasi-equilibrium as thermalization. The word exciton n will also be used in this article in a broad sense. Exciton usually denotes a bound state of an electron and a hole in solids, I will consider mobile electrons and holes not bound to each other as continuum states of an exciton. This more general definition of excitons allows me to discuss the thermalization of electron-hole plasmas in semiconductors also. The study of how systems relax and thermalize has been going on for years. This review article becomes necessary as a result of recent advances in short laser pulse technology. In solids there are typically a large number of electrons. In addition to electron-electron interactions, the electrons interact with lattice vibrations and with electromagnetic radiations. These interactions are often strong in solids and as a result excitons relax and thermalize in times varying from nanoseconds to femtoseconds. Such short time durations made a real time study of thermalization of excitons very difficult if not impossible in the past. Recent advances in short laser pulse technology made it possible for the first time to study these thermalization processes in condensed systems in real time. The purpose of this article is to review some of the recent time-resolved studies of thermalization of excitons in semiconductors. This article is not meant to be exhaustive and only representative examples have been chosen to illustrate the physical principles involved. In particular I want to point out some of the subtleties in the interpretation of the time-resolved photoluminescence experiments. It is hoped that by comparing the results in different systems this article will serve as a guide to understanding time-resolved studies of thermalization in less understood solids. The organization of this article is as follows. In the next section I will survey the present status of experimental techniques available for performing time-resolved studies. Since many articles have already appeared on the generation of short laser pulses, the emphasis of that section will be on matching the detectors to the available light sources. As will be shown, the time resolution of an experiment is often not limited by the light source but rather by the detector. In Section III the theortical background for understanding relaxation processes in solids is reviewed. In the section