First-principles surface energies for monoclinic Ga2O3 and Al2O3 and consequences for cracking of (Al<i>x</i>Ga1−<i>x</i>)2O3

Abstract

Crack formation limits the growth of (AlxGa1−x)2O3 epitaxial films on Ga2O3 substrates. We employ first-principles calculations to determine the brittle fracture toughness of such films for three growth orientations of the monoclinic structure: [100], [010], and [001]. Surface energies and elastic constants are computed for the end compounds—monoclinic Ga2O3 and Al2O3—and used to interpolate to (AlxGa1−x)2O3 alloys. The appropriate crack plane for each orientation is determined, and the corresponding critical thicknesses are calculated based on Griffith’s theory, which relies on the balance between elastic energy and surface energy. We obtain lower bounds for the critical thickness, which compare well with available experiments. We also perform an in-depth analysis of surface energies for both relaxed and unrelaxed surfaces, providing important insights into the factors that determine the relative stability of different surfaces. Our study provides physical insights into surface stability, crack planes, and the different degrees of crack formation in (AlxGa1−x)2O3 films for different growth orientations.