Phenomenological synthesis of nanometric patterning in ballistically formed MBE silicon between 450 and 713K

The comprehensive 673K steady-state data set of Perovic et al. (D.D. Perovic, G.C. Weatherly, J.-P. Noel, D.C. Houghton, J. Vac. Tech. B9 (1991) 2034 and D.D. Perovic, G.C. Weatherly, P.J. Simpson, P.J. Schulz, T.E. Jackman, G.C. Aers, J.-P. Noel, D.C. Houghton, Phys. Rev. B43 (1991) 14257) was later expanded to substrate temperature variations from 450 to 687K with transients up to the steady state. Our particular experimental emphasis on temperature dependence and atomic force microscopy (AFM) at the nanostructure scale is combined and organized so as to exhibit complete systematics as a function of temperature. We show that the kinetics and instability patterns map with consistency to the steady-state 3D microstructures observed and predicted in binary cellular forced velocity solidification of metallic alloys. Adapting the solidification phenomenological algorithm to the MBE case, we are able to extract a plausible and useful Arrhenius expression for the diffusion of occluded vacant sites in ballistically formed Si. It is further illustrated that the MBE instability margin maps in some detail to the interface Rayleigh droplet-forming morphology of 3D binary solidification. We offer this example of universality in kinetics as a contribution to the non-linear science of pattern formation, as well as complementing the often preferred analyses within a molecular dynamics paradigm.