Modulated photoluminescence (MPL) is an optoelectronic characterization technique of semiconductor materials. Going to high frequencies enables one to characterize fast phenomena, and so materials with a short lifetime such as chalcogenides or III-V absorbers. Some typical signatures have already been experimentally observed. However, physical mechanisms and quantitative analyses are not well understood yet. Here, using both an analytical approach and a full numerical modeling, we study how the energy position of a defect level, its electron and hole capture cross sections, its density, influence the frequency dependence of the MPL phase. We show that quantitative information can be extracted. We also study the effect of additional surface recombination, and of non homogeneities created by carrier generation profiles or asymmetric top surface and bottom surface recombination velocities, where diffusion of the carriers plays a role and can be limiting at high frequency. Finally we apply our model to an experimental result to extract defect parameters of the sample. Our analysis highlights the usefulness of MPL and the importance of having a proper modeling of the experiment.