Strain accumulation and relaxation on crack formation in epitaxial AlN film on Si (111) substrate

The formation of cracks is often observed in the epitaxial growth of ultrawide-bandgap aluminum nitride (AlN) semiconductor films on economical and versatile silicon (Si) substrates due to the significant differences in in-plane lattice parameters and thermal expansion coefficients between the film and the substrate, which hampers the development of template, buffer layer, and device structure with a relatively thick AlN layer for devices. The present study aims to elucidate the conditions of crack formation through a simple but comprehensive estimation of strain energy accumulation and relaxation by lattice strain, misfit dislocation density, and crack formation. Strain energy in the epitaxial film from lattice and thermal mismatches is evaluated by an elastic strain equation tailored to the epitaxy of the hexagonal crystal structure. The effects of temperature, thickness, and dislocation density on the lattice and dislocation strain energies of the film are also considered. Finally, the comparison in the changes in the total strain energy and cleavage energy with decreasing temperature shows that cleavage energy is higher than strain energy if the film is thinner than 400 nm but becomes lower than the strain energy if the film is thicker than 400 nm during cooldown, suggesting the crack formation, which matches well with experimental observations.