We present a new analytical model to predict the spatial location of amorphous phases in ion-implanted single-crystalline silicon using results of multidimensional Monte Carlo simulations. Our approach is based on the concept of the critical damage energy density. Additionally, the self-annealing of radiation damage during ion implantation is taken into account because this effect is crucial for a correct prediction of amorphization. Two aspects of self-annealing are considered, namely, the temperature and the spatial dependence. The latter is related to the local damage energy density, which is simulated by one-, two-, and three-dimensional modules of our Monte Carlo program MCIMPL of the technology CAD framework VISTA. Therefore, the formation and the shape of amorphous regions in single-crystalline silicon can be predicted as a result of Monte Carlo simulations of ion implantation. The suggested model accurately reproduces the results of direct microscopic observations (XTEM measurements) of amorphous layers in silicon after a silicon self-implantation, which are available for a temperature range of 82-296 K.