Fracture toughness and critical thickness of β-(InxGa1−x)2O3/Ga2O3 by first principles

Abstract

First-principles calculations were employed to determine the surface energy and fracture toughness of monoclinic Ga₂O₃ and (In_xGa_1−x)₂O₃ alloy with In content up to 37.5%. The lattice parameters and elastic constants of (In_xGa_1−x)₂O₃ alloys are calculated and followed Vegard's law with an increasing In concentration. The most probable crack planes for each growth orientation, [100], [010] and [001], are determined through comparison with the surface energy and fracture toughness of monoclinic Ga₂O₃. In addition, the critical thicknesses of the (In_xGa_1−x)₂O₃ epitaxial film grown on the Ga₂O₃ substrate in [100], [010] and [001] orientations were found to be 40 nm, 35 nm and 36 nm, respectively at an In content up to 37.5%, suggesting reasonable pseudomorphic growth conditions for (In_xGa_1−x)₂O₃/Ga₂O₃ heterostructure formation. Based on the analysis of bond lengths, dangling bonds and surface coordination, the stability of the surface in the (100) direction with surface terminations including Ga and O atoms was found to have lower fracture toughness than the other surfaces, implying that epitaxial growth with the (100) crack surface might result in lower defects with a higher film thickness. Overall, the cracking mechanisms in the (In_xGa_1−x)₂O₃ film grown on the Ga₂O₃ substrate with different orientations are elucidated.