LatticeMismatch

Lattice mismatch is the relative difference between the lattice spacings of two crystalline materials, typically a substrate and a film grown on it. In epitaxial deposition, the film may be forced to adopt the substrate’s lattice constant, creating strain. The mismatch is commonly expressed as M = (a_s - a_f)/a_s, multiplied by 100%, where a_s is the substrate lattice constant and a_f is the film lattice constant. The sign indicates whether the film is stretched (tensile) or compressed.

When the mismatch is small, the film can grow coherently and adopt the substrate lattice constant up to a critical thickness. Beyond this thickness, misfit dislocations or other defects form to relieve strain, leading to partial or complete relaxation, degraded crystal quality, and possible surface roughness or defect formation. Large mismatches can also promote island growth, cracking, or poor adhesion.

Strategies to manage lattice mismatch include using buffer layers with intermediate lattice constants, gradually grading the film composition to ease transitions, employing compliant or patterned substrates, or using van der Waals epitaxy for some two-dimensional materials. In some cases, relaxation is deliberate to achieve a desired composition or phase. Characterization methods such as X-ray diffraction with reciprocal-space mapping, transmission electron microscopy, and related techniques are used to quantify strain, relaxation, and defect densities.

Examples illustrate the range of challenges: nearly zero mismatch for GaAs on GaAs substrates; about 4% mismatch for GaAs on Si (or InP on GaAs); and a large mismatch for GaN on sapphire, which drives substantial strain management. Lattice mismatch is a central consideration in designing semiconductor heterostructures, LEDs, lasers, and high-electron-mobility transistors, where strain influences electronic and optical properties.