Evolution of the grain size distribution during solid-phase crystallization of silicon

Abstract

This thesis characterizes the time dependence of the Grain Size Distribution (GSD), N(r, t), during crystallization of a d—dimensional solid. A Partial Differential Equation (PDE) including a source term for nuclei and a growth law for grains is solved analytically. We obtain solutions for processes described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model for Random Nucleation and Growth (RNG). The analysis presents how model parameters, the dimensionality of the crystallization process, and time influence the shape of the distribution. The calculations show that the dynamics of nucleation and growth play an essential role in determining the final form of the distribution obtained at full crystallization. For one class of nucleation and growth rates we show that the distribution evolves in time into a lognormal form. The theory is applied to solid-phase crystallization of Silicon (Si) thin films and is shown to describe well the experimental data except for early stages of crystallization. The discrepancy is explained and a modification of the model is proposed.