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.

中文翻译：

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单斜晶系 Ga2O3 和 Al2O3 的第一性原理表面能以及 (AlxGa1−x)2O3 开裂的后果

裂纹的形成限制了 (AlxGa1-x)2O3 外延膜在 Ga2O3 衬底上的生长。我们采用第一性原理计算来确定这种薄膜在单斜结构的三个生长方向上的脆性断裂韧性：[100]、[010] 和 [001]。计算最终化合物（单斜 Ga2O3 和 Al2O3）的表面能和弹性常数，并用于插入 (AlxGa1-x)2O3 合金。确定每个方向的适当裂纹平面，并根据格里菲斯理论计算相应的临界厚度，该理论依赖于弹性能和表面能之间的平衡。我们获得了临界厚度的下限，这与可用的实验进行了很好的比较。我们还对松弛和未松弛表面的表面能进行深入分析，提供对决定不同表面相对稳定性的因素的重要见解。我们的研究为不同生长方向的 (AlxGa1-x)2O3 薄膜中的表面稳定性、裂纹平面和不同程度的裂纹形成提供了物理见解。