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 length scales lambda(perpendicular to) (the branch width) and lambda(parallel to) (the branching distance) which are perpendicular and parallel to the growth direction and (ii) the typical angle theta between the branches. We find a qualitative similarity between films with various component concentrations and crystallization temperatures. However, these parameters enounce the two length scales in a different fashion, thus influencing the angle between the branches. We further find that lambda(perpendicular to) similar to v(-1/4), while lambda(parallel to) depends 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 features of the Eden model (for the growth of the Al crystal rim) and the diffusion-limited aggregation model (for the growth of the branched Ge fingers). The predictions of the model are compared with our experimental data.