We have applied real time spectroscopic ellipsometry (RTSE) to characterize the formation of polycrystalline silicon (poly-Si) films by a rapid thermal annealing process at relatively low temperatures, ranging from 580 to 625 degrees C. A gradual transition of the silicon films from amorphous to polycrystalline with annealing time at constant temperature was quantified by RTSE using the Bruggeman effective medium theory (EMT). Grain grow th processes were studied by critical point (CP) analyses applied to the deduced poly-Si dielectric functions. The resulting CP broadening parameter provides information on the average grain size within the top similar to 0.3 mu m of the film. The EMT and CP analyses suggest that crystallization occurs from isolated nuclei uniformly distributed within the film. RTSE analysis results for poly-Si formation at different temperatures, further provides information on the crystallization kinetics. We found that poly-Si having a somewhat larger grain size was generated at the lower crystallization rates obtained under lower annealing temperatures.