Direct measurement of the free-energy barrier to nucleation from the size distribution of dendritic crystallites ina-Si thin films

We introduce a method to determine the free-energy barrier to nucleation of crystallites, independent of any model for the nucleation free-energy barrier, and independent of the energy barrier to the growth. This model-independent method is developed based on the dynamic scaling of the cluster size distribution and other universal kinetics in the early stages of nucleation and growth. The method is applied to determine the free-energy barrier to nucleation of the amorphous-to-crystalline transformation in a-Si thin films. After considering the dendritic nature of Si crystallites, we obtain the free-energy barrier to nucleation ${\mathit{W}}_{\mathrm{*}}$≊2.15–2.18 eV, the enthalpic (i.e., the activation energy) barrier Δ${\mathit{H}}_{\mathrm{*}}$=1.32 eV, and the entropic barrier Δ${\mathit{S}}_{\mathrm{*}}$=-9.57×${10}^{\mathrm{-}4}$ eV ${\mathrm{K}}^{\mathrm{-}1}$, within the temperature range of T=863–893 K. The entropic contribution to ${\mathit{W}}_{\mathrm{*}}$ is found to be considerably large. We also show that the magnitude of the measured ${\mathit{W}}_{\mathrm{*}}$ could not be accounted for by the classical expression for the free-energy barrier with the previous suggested values for its parameters.