MORPHOLOGY OF GE-AL THIN-FILMS - EXPERIMENTS AND MODEL

We report measurements on the branched morphology of the Ge core which grows inside the Al crystal during the crystallization of Ge:Al thin films. We quantitatively characterize this morphology by (i) two lengt h scales lambda(perpendicular to) (the branch width) and lambda(parall el to) (the branching distance) which are perpendicular and parallel t o the growth direction and (ii) the typical angle theta between the br anches. We find a qualitative similarity between films with various co mponent concentrations and crystallization temperatures. However, thes e parameters enounce the two length scales in a different fashion, thu s influencing the angle between the branches. We further find that lam bda(perpendicular to) similar to v(-1/4), while lambda(parallel to) de pends more weakly on v (lambda(parallel to) similar to v(-1/6)), where v is the growth velocity. Finally, we propose a model that combines f eatures of the Eden model (for the growth of the Al crystal rim) and t he diffusion-limited aggregation model (for the growth of the branched Ge fingers). The predictions of the model are compared with our exper imental data.