text: Homoepitaxy is a kind of epitaxy performed with only one material, in which a crystalline film is grown on a substrate or film of the same material. This technology is often used to grow a more pure film than the substrate and to fabricate layers with different doping levels. In academic literature, homoepitaxy is often abbreviated to "homoepi".
  Homotopotaxy is a process similar to homoepitaxy except that the thin-film growth is not limited to two-dimensional growth. Here the substrate is the thin-film material.
  Heteroepitaxy is a kind of epitaxy performed with materials that are different from each other. In heteroepitaxy, a crystalline film grows on a crystalline substrate or film of a different material. This technology is often used to grow crystalline films of materials for which crystals cannot otherwise be obtained and to fabricate integrated crystalline layers of different materials. Examples include silicon on sapphire, gallium nitride (GaN) on sapphire, aluminium gallium indium phosphide (AlGaInP) on gallium arsenide (GaAs) or diamond or iridium, and graphene on hexagonal boron nitride (hBN).
  Heteroepitaxy occurs when a film of different composition and/or crystalline films grown on a substrate. In this case, the amount of strain in the film is determined by the lattice mismatch Ԑ:
  Where  and   are the lattice constants of the film and the substrate. The film and substrate could have similar lattice spacings but also different thermal expansion coefficients. If a film is grown at a high temperature, it can experience large strains upon cooling to room temperature. In reality,  is necessary for obtaining epitaxy. If  is larger than that, the film experiences a volumetric strain that builds with each layer until a critical thickness. With increased thickness, the elastic strain in the film is relieved by the formation of dislocations, which can become scattering centers that damage the quality of the structure. Heteroepitaxy is commonly used to create so-called bandgap systems thanks to the additional energy caused by de deformation. A very popular system with great potential for microelectronic applications is that of Si–Ge.
  Heterotopotaxy is a process similar to heteroepitaxy except that thin-film growth is not limited to two-dimensional growth; the substrate is similar only in structure to the thin-film material.
  Pendeo-epitaxy is a process in which the heteroepitaxial film is growing vertically and laterally simultaneously.
  In 2D crystal heterostructure, graphene nanoribbons embedded in hexagonal boron nitride give an example of pendeo-epitaxy.
  Grain-to-grain epitaxy involves epitaxial growth between the grains of a multicrystalline epitaxial and seed layer. This can usually occur when the seed layer only has an out-of-plane texture but no in-plane texture. In such a case, the seed layer consists of grains with different in-plane textures. The epitaxial overlayer then creates specific textures along each grain of the seed layer, due to lattice matching. This kind of epitaxial growth doesn't involve single-crystal films.
  Epitaxy is used in silicon-based manufacturing processes for bipolar junction transistors (BJTs) and modern complementary metal–oxide–semiconductors (CMOS), but it is particularly important for compound semiconductors such as gallium arsenide. Manufacturing issues include control of the amount and uniformity of the depositions resistivity and thickness, the cleanliness and purity of the surface and the chamber atmosphere, the prevention of the typically much more highly doped substrate wafers diffusion of dopant to the new layers, imperfections of the growth process, and protecting the surfaces during manufacture and handling.