This thesis describes the simulation of high-energy charge transport in single photon avalanche diodes by means of the full-band Monte Carlo technique. A computationally efficient formulation of the scattering rates, while keeping the main physical features, renders the CPU-intensive calculation of the breakdown characteristics of single photon avalanche diodes feasible on standard computer clusters. \textit{CarloS}, a novel full-band Monte Carlo simulator, is applied to the high-field charge dynamics of the multiplication process. Compared to previous works employing simple charge transport models, the solution of the Boltzmann transport equation and the incorporation of the full-band structure puts the evaluation of the breakdown probability, the time to avalanche breakdown and its jitter on deeper theoretical grounds. Additionally, this thesis presents an impact ionization model for the scattering rates and secondary carrier energies based on the random-$\mathbf{k}$ approximation.weiterlesen