Scattering and Screening Processes

Abstract

As we have seen, the temporal evolution of electrons and holes in a semiconductor is influenced by a rich variety of possible scattering processes. In the simplest case, these scattering processes transfer energy or excitation from a part of the semiconductor — often referred to as “the system” — to the rest of the semiconductor — “the bath”. This artificial distinction of the system from the bath is perfectly obvious in the example of electron-phonon scattering. In Chaps. 4 and 6, we have described these processes by simple phenomeno-logical effective scattering rates γ₁ = T ^-1₁ and γ₂ = T ^-1₂ for the relaxation of the distribution functions and of the transition amplitude, respectively. This picture is — if at all — justified if a single transition such as the Is exciton dominates. If continuum states come into play the effective scattering rates become dependent on the energy and on the wave vector. At this level, the decay of a transition amplitude or occupation is thought of as scattering out of a given state in terms of Fermi’s golden rule:¹ for example, an electron in state |a〉 has either not emitted a phonon or has emitted a phonon and ends in state |b〉. The rates γ and γ are proportional to the transition probability from |a〉 to |b〉. Obviously, this simple picture fails — in particular, in the case of carrier-carrier scattering — if the scattering rates are dependent on the occupation of the final states,