= 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.
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