New approach to the high quality epitaxial growth of lattice-mismatched materials

We have reconsidered the problem of the critical layer thickness hc for growth of strained heterolayers on lattice-mismatched substrates, using a new approach which allows us to determine the spatial distribution of stresses in a bi-material assembly and include the effects of a finite size of the sample. The possibility of dislocation-free growth of lattice-mismatched materials on porous silicon substrates is discussed as an example of a more general problem of heteroepitaxial growth on small seed pads of lateral dimension l, having a uniform crystal orientation over the entire substrate wafer. It turns out that for a given mismatch f, the critical film thickness hlc strongly depends on l, rising sharply when the latter is sufficiently small, l≲lmin. The characteristic size lmin( f ) below which, effectively, hlc( f )→∞, is determined in terms of the experimentally known (or calculated for growth on a monolithic substrate) function h∞c( f )≡hc( f ). When l≲lmin, then the entire elastic stress in the epitaxial film will be accommodated without dislocations.