Heteroepitaxy

Heteroepitaxy is epitaxy in which a crystalline film grows on a different material while maintaining an orientation relationship with the substrate. For example, a semiconductor layer can be grown on a different crystalline semiconductor to combine useful electronic properties.

A simple mismatch measure is $f=(a_f-a_s)/a_s$, where $a_f$ and $a_s$ are the relaxed film and substrate lattice parameters. A coherent layer can accommodate mismatch through elastic strain; increasing thickness increases the stored elastic energy and can favour relaxation through dislocations. Orientation, chemical compatibility and strain relaxation are therefore separate questions. An ordered epitaxial film need not retain the lattice parameter it would have in an unconstrained bulk crystal.