``Epi-nucleation'' on Reconstructed Surface and a Model Study of Si(001) Homoepitaxy

We introduce the concept of ``epi-nucleation'' to distinguish nucleation and growth on a reconstructed surface from that on a non-reconstructed surface. The `critical nucleus' defined in the classical nucleation theory refers to a nucleus stable against dissociation, which is also implicitly assumed to have an epi-relation to the substrate. However, such assumption may fail on a reconstructed surface because although the ``classical'' nucleus is stable against dissociation, it may not yet establish the epi-relation with the substrate as the substrate surface underneath the nucleus remains reconstructed. Therefore, on a reconstructed surface, in addition to the stable ``classical'' nucleus, there must exist another ``epi-nucleus'' that is not only stable against dissociation but also has a epi-relation with the substrate (breaking the underlying substrate surface reconstruction). We illustrate the general concept of ``epi-nucleus'' using first-principles calculations of homoepitaxial nucleation on a reconstructed Si(001) surface and we find that here the epi-nucleus consists of six adatoms, in contrast to the classical nucleus of two adatoms.