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First-principles surface calculations for monoclinic Ga2O3 and Al2O3 and consequences for cracking of (AlxGa1-x)2O3 films

The wide-bandgap semiconductor Ga2O3 is a promising candidate for high-power electronics. Alloying with Al for (AlxGa1-x)2O3 films enables heterostructures that are essential for device applications. However, the limited thickness of (AlxGa1-x)2O3 films grown on Ga2O3 substrates is a serious obstacle. Here 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 growth orientation is determined, and the corresponding critical thicknesses of (AlxGa1-x)2O3 films are calculated based on Griffith’s theory. Our in-depth analysis of surface energies for both relaxed and unrelaxed surfaces provides important insights into the factors that determine the relative stability of different surfaces. We conclude that the critical thickness is largest for (AlxGa1-x)2O3 films grown along [100].