Carrier scattering

Abstract

So far, the present work has considered only the static behaviour of carriers in nanostructures. In other words, the states that carriers could occupy within a structure have been calculated, along with the Fermi-Dirac distributions of carriers in thermal equilibrium. However, the equilibrium distribution of carriers is broken in real heterostructure devices (e.g. by the injection of an electric current or an optical 'pump'), and it is therefore important to consider the dynamic behaviour of carriers in such systems in order to predict their distribution accurately.In principle, a complete model of the behaviour of a carrier within a heterostructure could be obtained by finding a Hamiltonian that describes all possible interactions between the carrier and its surroundings, and then solving the time-dependent Schrödinger equation to observe the evolution of the carrier wave function over time. However, this is a formidable computational task, which is further complicated by the random nature of many of the interactions (e.g. randomly distributed impurities). To simplify the problem, carrier dynamics may be approximated by two distinct types of process: coherent processes in which wave functions evolve smoothly between their initial and final states; and incoherent, scattering processes. The latter are the focus of this chapter, and are defined as random, infrequent but very rapid events that transfer a carrier between two states. This could be caused by interactions between carriers and any kind of perturbing potential, including other carriers, impurities, and defects in the heterostructure, or with lattice vibrations (phonons) and photons.Since scattering is assumed to be infrequent, the system can be assumed to stabilise to its static, unperturbed state between events. As such, the eigenstates of the unperturbed system can be calculated (as in Chapters 2 and 3) independently from the scattering dynamics. The very rapid nature of scattering events introduces a further simplification: carriers effectively 'hop' instantaneously from one state to another, and the only necessary task is to compute the rate of scattering (i.e. the number of events per second) for any combination of initial and final states, which is the focus of this chapter. After determining these scattering rates for appropriate interaction processes, the results are used in Chapter 12 to compute the populations of states and current density in devices.