The controlled generation of single photons on demand is a basic requirement of the quantum-information technology. In this context, two-photon Raman processes in three-level systems in -configuration have been thoroughly investigated. The system is excited by a control-laser pulse such that it makes a transition from one to the other ground state via the emission of a single photon. This photon inherits the spectral properties of the laser. However, until now on-demand emission has not been observed. The theoretical study presented in this thesis is connected with the further development of Raman-photon sources in two respects. On the one hand, we consider a certain two-photon process in semiconductor-quantum dots, namely the two-photon process between the biexciton and ground state. We show that frequency, linewidth and line shape of the emission are determined by the control laser. On the other hand, we use the fact that on-demand performance has not yet been achieved in experiments as the starting point to investigate two-photon Raman processes in a fundamentally reoriented manner. We develop a microscopic framework based on the Heisenberg equation in combination with the cluster expansion. This method allows for an unambiguous definition of a Raman-Photon. In a first step, we analyze Raman processes in three-level systems and identify two types of Raman processes. We find that Stark shifts as well as quantum interference can occur. We show that taking these effects into account, Raman processes actually allow for on-demand performance. Finally, we generalyze our framework to describe the single-photon emission from the biexciton. We present first fundamental insights for the optimization potential of the system and excitation design to bring the Raman emission of the biexciton into the on-demand regime.