We have investigated the crystallization of a-Si films by means of pulsed KrF excimer laser annealing as a function of irradiation energy density (E(L)), using transmission electron microscopy (TEM), Raman scattering spectroscopy and secondary ion mass spectrometry (SIMS). The grain size increased gradually at 0.2-0.4 J/cm(2), while a drastic enlargement of grains occurred with lateral growth at 0.6-0.8 J/cm(2). The stress in the films decreased with a decrease in the thickness of the fine grain (FG) layer until the FG layer finally disappeared. We proposed a model in which a drastic enlargement of grains at high E(L) is controlled by the nucleation fate, the solidification velocity, and the nucleus density of initial growth. It was found that poly-Si films with large grains (0.5-0.9 mu m), high purity of C (similar to 3 x 10(16) cm(-3)) and low stress were obtained in the high E(L) regime (0.6-0.8 J/cm(2)).