  Al-induced layer exchange crystallization of amorphous Ge thin films has been
demonstrated recently, and provides a suitable system to characterize, model
and control Ge crystal growth on non-crystalline substrates. Direct observation
of Ge transfer to the surface of Al through an interposed GeOx interfacial
layer allows independent measurement of the density and average area of
crystalline Ge islands formed on the surface. Based on these experimental
observations, the Johnson-Mehl-Avrami-Kologoromov phase transformation theory
is extended to model nanoscale nucleation and growth of Ge islands in two
dimensions. The Ge island growth mechanism switches from
atomic-attachment-limited to surface diffusion-limited kinetics with increasing
time. The transition point between these regimes depends on the Ge nucleation
site density and the annealing temperature. Finally, we show that local
bias-voltage stressing of the interfacial layer controls the areal density of
nucleated Ge islands on the film surface.
