Growing a crystal on top of another so that its atoms line up with the ones underneath and carry on the pattern of the crystal below. It is how most chips, lasers and LEDs are built, and it works cleanly only when the two crystals’ atomic spacings match closely – a restriction that layered largely escape.
Going deeper
Left: in ordinary epitaxy the film is bonded to the substrate and squeezed to its spacing, storing strain until a misfit dislocation – an extra row of atoms – relieves it and defects run up through the film. Right: a layered crystal grown by van der Waals epitaxy rests on the substrate without bonding to it, so it keeps its own spacing and the mismatch costs almost nothing.
Carrying a crystal on
Epitaxy is Greek for “arranged upon”. Deposit atoms slowly on a clean surface, hot enough for them to move about, and they settle where the surface offers the best sites, so the new layer carries on the crystal below. Homoepitaxy, silicon on silicon, makes the purest material; heteroepitaxy – aluminium gallium arsenide on gallium arsenide, gallium nitride on sapphire, silicon–germanium on silicon – is how lasers, LEDs and fast are built. , and are all ways of doing it.
The quality of the result depends on how well the two lattices fit. The lattice mismatch is the fractional difference in their atomic spacings. A film bonded to the is forced to take the substrate’s spacing and stores energy that grows with thickness; beyond a critical thickness it becomes cheaper to insert misfit dislocations – extra or missing rows of atoms at the interface – and each sends defects threading up through the film. At a mismatch of about one percent the critical thickness is of the order of ten nanometres; germanium on silicon, four percent apart, stays coherent for only a few atomic layers.
What changes for 2D materials
A layered crystal has no bonds pointing out of its faces, so a 2D layer grown on another layered crystal, or on a passivated substrate, is aligned by weak but not bonded. Mismatches of tens of percent then cost almost nothing – the growth-side counterpart of the fact that any two layers can be stacked. The weakness cuts both ways: alignment is weak too, and on many substrates islands nucleate in two orientations 60° apart and meet in . Growing single-crystal therefore needs substrates that break that symmetry, such as sapphire or copper cut slightly off a crystal plane so that surface steps set one orientation.
Graphene grown on silicon carbide is epitaxial in the conventional sense: heating the crystal drives silicon off its surface, and the remaining carbon forms graphene locked to the lattice below through a bonded buffer layer. That registry makes it uniform over whole wafers, which is why it is used for resistance standards.
Remote epitaxy, oxide interfaces and the evidence to ask for
Two further variants matter here. In remote epitaxy a single graphene sheet is laid on a substrate before growth; it is thin enough for the substrate’s electrostatic potential to reach through it, so a semiconductor film grows aligned to a crystal it never touches – and can then be peeled off and the substrate reused. In oxide epitaxy, layers grown one at a time by pulsed laser deposition produce interfaces with properties neither material has: LaAlO3 grown on SrTiO3 traps a conducting sheet of electrons at the boundary between two .
Because “epitaxial” claims an orientation relationship, it needs diffraction evidence: reflection electron diffraction during growth, X-ray or electron diffraction over the whole sample afterwards, and for 2D layers the fraction of domains in each orientation. A single well-aligned in a microscope image shows that alignment is possible, not that the growth is epitaxial.
For specialists
Growth of a crystalline film whose orientation is fixed by a single-crystal substrate: homoepitaxy on the same material, heteroepitaxy on a different one. A bonded film strains to the substrate’s lattice until, beyond a critical thickness that falls steeply with mismatch, misfit dislocations relax it, so mismatches above a few percent permit only very thin coherent films. In the film is aligned but not bonded and mismatch is largely irrelevant; in remote epitaxy the substrate’s potential aligns the film through a graphene interlayer.