Brittle fracture toughnesses of GaN and AlN from first-principles surface-energy calculations

Cracks are a major limitation for the growth of III-nitride bulk crystals and thick epitaxial films. The propensity for a crack to propagate on a given plane is determined by the anisotropic fracture toughness, Γ. Using first-principles surface-energy calculations, we have determined toughnesses for brittle fracture (Γb) in GaN and AlN, for cracks on the nonpolar {101¯0} m-and {112¯0} a planes, and the polar (0001)+(0001¯) c plane. For both materials, Γb values for cracks on the nonpolar planes are similar, and significantly smaller than for the c plane. Calculated critical thicknesses for AlGaN grown on GaN correctly predict the fracture planes in polar and nonpolar growth.