In the case of sapphire crystals, the lattice constant “a” corresponds to the distance between sites along the a-axis, as shown in the figure above, because it is considered as a hexagonal unit cell. The lattice mismatch is defined as (|a f- a s|)/[ (a f+a s)/2] (a f, a s : the lattice constants of the film and the substrate), and the smaller the value, the better the lattice matching and the less likely it is that lattice distortion will occur between the substrate and the film, resulting in a high-quality film. In epitaxial thin film growth, the lattice mismatch is used to quantify the matching between a substrate and a film.
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