Title:

Instabilities and distribution functions associated with photoexcited carriers in semiconductors

Some aspects of photoexcited carriers in semiconductors are investigated theoretically. Three distinct phenomena are studied namely, photoluminescence, oscillatory photoconductivity and trap modified Gunn domains. Distribution functions are calculated for photoexcited electrons in gallium arsenide and are discussed within the context of recent photoluminescence experiments. The calculations apply to conditions of continuous, monochromatic photoexcitation and lattice temperatures in the liquid helium range. A Boltzmann equation approach 1s used to take account of Injection of electrons into the conduction band, electron scattering and electron recombination. The effects of Inelastic scattering by acoustic phonons, longitudinal optical phonons and other electrons are considered. The equation is solved numerically using an Iterative technique. The steady state distribution function and its time evolution from an initial state in which there are no electrons in the band are both computed. Under conditions such that electronelectron scattering has a negligible effect, the steady state distribution function is found to have a nonMaxwellian form. It has a high energy plateau which has some fine structure close to the injection energy (or energies). The origin of the plateau and the fine structure are explained in terms of the phonon scattering events undergone by the photoexcited electrons. Two models for electronelectron scattering are studied. Within a large screening model, distribution functions are computed without recourse to further approximations to the electronelectron scattering rates. Distribution functions applicable to situations in which the screening is not large are computed using a Taylor series approximation to the electronelectron scattering rates. The computations are of a preliminary nature but it is found that at an electron density of ~ 3 x 1016 m3 electronelectron scattering could cause heating of those electrons whose energy is greater than the injection energy. Electronacceptor luminescence spectra for C doped GaAs, under photoexcitation conditions such that electronelectron scattering has a negligible effect, are derived from the computed distribution functions and are compared with the results of some recent photoluminescence experiments. Fair agreement is obtained. The theory of oscillatory photoconductivity is studied, with special reference to negative current and instability effects. The theory is used to investigate a one dimensional model for the spacetime dependence of the electric field in a semiconductor under conditions such that oscillatory photoconductivity occurs. The semiconductor is taken to be in a resistive circuit. The appropriate equations are solved numerically and thus the stability of the negative current state is investigated. It is shown that this state could be stable with respect to space charge formation if the circuit resistance is sufficiently high. In addition a numerical study is made of the types of domain instability which could otherwise form.
