Statistics of crystallization kinetics in nanoscale systems

We investigate the statistics of the crystallization kinetics caused by the finite size of nanoscale samples. We define a characteristic length, LC, as a function of the material properties, in order to describe the sample size dependence of the statistics. We find that the samples smaller than LC undergo single-nucleus crystallization, which yields wide distributions of the half-transition time. Finally, we apply our theory to find a way to improve the data retention statistics of sub-20 nm phase-change memory.