Recognizing that the processing window in conventional excimer laser crystallization corresponds mainly to the partial melting regime, and that this can be properly simulated using a one-dimensional model, we investigate numerically the melting and solidification of thin silicon films on SiO2. Here a portion of the silicon film is melted and subsequent vertical solidification is initiated from the lower interface bounding the unmelted region. Upper and lower energy density limits for this regime are calculated for crystal silicon films of thickness 10 to 300 nm, and for pulse duration ranging from 10 to 200 ns. These calculations show that increasing pulse duration requires proportionally more incident energy density to partially melt the film, while decreasing film thickness reduces the range of energy densities over which partial melting can occur. The results are explained in terms of characteristic thermal diffusion distances and the enthalpy change associated with melting. In view of the results we discuss optimization of the conventional excimer laser crystallization and the avoidance of complete melting during the process.