Magic matching in semiconductor heterojunctions

Matching of m crystal planes of a grown layer to n planes of the substrate is observed in many cases, when the difference in the lattice parameters is large. This kind of magic matching is explained by coincidence planes. Two examples are shown in this paper. SiC grains perfectly oriented to the substrate were prepared by high temperature ion implantation of Si into natural diamond. Considering the (111) lattice planes and the cases, when 5 planes of SiC match to 6 planes in diamond, or 4 planes of SiC match to 5 planes in diamond, the misfit is reduced to about 2% in both cases having opposite signs. High resolution images taken at the SiC/diamond interface were investigated and both of the above mentioned domains were found. When we consider the regular distribution of the above two domains, i.e. matching of 9 SiC lattice planes to 11 diamond planes a misfit value below 0.1% is obtained. This explains how the ion beam synthesised SiC can grow epitaxially despite the huge difference in lattice parameters. GaN synthesised in GaAs by ion implantation is presented as another example where magic matching of 5:4 reduces the misfit to 0.8%. That value is low enough to be compensated by elastic deformation of the lattice, therefore the insertion of another domain is not needed.