Benchmarking of analytical photoionization models for solids using photoionization-induced reflection

First-principle simulations of photoionization processes in solids can quickly become a numerically very demanding task. In some cases, simple analytical expressions for the photoionization rates can help. However, choosing the most appropriate analytical model can be difficult, with no standard solution. We show how the best formalism can be determined based on the wave form of the pulse reflected from a sample due to photoionized, nearly free electrons in the conduction band. For the typical case of diamond, we compare three analytical models and benchmark them against highly accurate first-principles, time-dependent density functional theory (TDDFT) simulations by analyzing the match between the reflected pulses calculated with the different methods in the time and frequency domains. We also show that for very short sub-10-fs pulses, due to interband contributions, a semiclassical description based on analytical photoionization models does not provide an adequate description. The software package piglet developed for the finite-difference time domain simulations of photoionization-governed propagation is made available to the scientific community.