Interplay of latent heat and time-dependent nucleation effects following pulsed-laser melting of a thin silicon film

We propose a simple-form mathematical description that allows us to account simultaneously for the effects of time-dependent nucleation and of latent heat during rapid cooling of a thin film. The method is based on a combination of analytical description of nucleation and a numerical (or, semianalytical) description of thermal effects due to postnucleation growth of crystallites. The accuracy of the treatment is tested against numerically exact solutions of the Farkas-Becker-Döring master equation, and is applied to several realistic cooling histories consistent with experimental studies of silicon on silicon oxide films of Stiffler et al. [Phys. Rev. B 43, 9851 (1991)] and Sameshima and Usui [J. Appl. Phys. 70, 1281 (1991)], respectively. Special attention is paid to the region of high cooling rates (very thin films of less than 100 nm) where the transition to complete amorphization occurs. For such cooling rates the time-dependent nucleation effects turn out to be especially important, and their neglect would lead to significant overestimates of the critical cooling rate that separates the recrystallization and the amorphization regions.