Lattice-constant-adaptable crystallographics. I. Heteroepitaxial growth of semiconductors and other specific compounds on lattice-constant-adapted garnets, spinels and perovskites; a systematic geometrical (not experimental) evaluation

Crystals of garnets, spinels and perovskites have the interesting property that various ions can be substituted on different lattice sites. This property implies that the lattice constants of these materials are adaptable. From a geometrical treatment of heteroepitaxial growth on such materials having a (large) non-adapted lattice constant it is found that two lattice-matching relations have to be fulfilled: (1) an axial-matching relation which determines the value of the lattice constant of the substrate material to be grown and (2) a cross-sectional relation which determines the appropriate growth plane to be cut from that crystal. A large variety of cubic compounds like Si, GaAs, Ge, InP and In ₂O ₃, and also non-cubic compounds like hexagonal LiNbO ₃, can be lattice-matched to prescribed samples of these crystalline groups. Circumstances of in-plane rotation of the crystallographic plane of the epilayer, as compared to the plane of the substrate, are discussed. In this approach to heteroepitaxial growth, crystallographic planes as well as interplanar spacings play an essential role in the basic framework.