epitaxy

Epitaxy is the art of growing one crystal on top of another so that the new layer copies the arrangement of the surface it lands on, like laying a new row of bricks that lines up exactly with the course beneath. The word comes from Greek: epi means upon and taxis means arrangement, so epitaxy literally means arranged upon. The atoms of the deposited film do not pile up randomly; they take their cue from the substrate crystal and line up with its lattice.

In homoepitaxy the film is the same material as the substrate (silicon grown on silicon), so the fit is perfect. The interesting and useful case is heteroepitaxy, growing one material on a different one (say a semiconductor alloy on a silicon or gallium-arsenide wafer). Here the two lattice parameters usually differ, and the mismatch is measured by the misfit delta = (a_film - a_substrate)/a_substrate. If delta is small, the film grows strained but coherent, stretching to match the substrate; beyond a critical thickness it relaxes by forming misfit dislocations and becomes semicoherent. So epitaxy is the growth process, and the coherent / semicoherent interface ideas describe its interface.

Epitaxy is the foundation of the entire semiconductor and optoelectronics industry: LEDs, laser diodes, high-speed transistors, and solar cells are all built from precisely lattice-matched epitaxial layers grown by techniques like molecular-beam epitaxy (MBE) and metal-organic vapour-phase epitaxy (MOCVD). Engineers even use the leftover strain deliberately (strained silicon) to boost device speed. Honest note: too much misfit ruins a film, because the misfit dislocations that relieve strain are also electrically harmful defects, so device layers are kept below the critical thickness or the substrate is chosen to minimise misfit.