This thesis is concerned with the study of certain aspects of semiconductor materials both from an analytical point of view as well as from an optimization perspective. On the one hand, we focus on a system of partial differential equations (PDE) which models the dynamics of negatively charged electrons and positively charged holes inside a semiconductor. This PDE-system generalizes the Shockley-Read-Hall-model which accounts for recombination, drift and diffusion of the charged particles by means of an additional internal energy level. Our main result states that the charge densities of electrons and holes converge to their equilibrium distributions at an exponential rate. Moreover, this convergence rate is independent of the mean residence time of electrons in the additional energy level. On the other hand, we investigate a material design problem in the context of photovoltaics. Given a density of positive nuclear charges inside a photovoltaic cell, we determine the resulting electronic density by solving the Kohn-Sham equations. In short, the structure of the charge density of the electrons may change under the influence of incident light due to internal electronic excitations. We prove that there exists a certain nuclear density which maximizes the change of the electronic density under the influence of a specific light. A 1D simulation of an atomic chain reveals a pronounced charge transfer for certain nuclear densities. Within a future application, one could use this charge separation to obtain an electric current. At the end, we study a PDE-model for electrons and holes in a semiconductor including the influence of the selfconsistent potential generated by these charge carriers. As the main result, we prove exponential convergence to the equilibrium for the corresponding charge densities.