The thermodynamic stability of germanium tin alloys is investigated across the composition range by applying density functional theory together with the cluster expansion formalism (CE). It is known that GeSn alloys are immiscible and that non-equilibrium growth techniques are required to produce metastable films and nanostructures. Insight into the driving forces behind component segregation is gained by investigating the equilibrium thermodynamics of GeSn systems. The alloy free energy of mixing is computed by combining enthalpies from the CE with entropy terms for configurational and vibrational degrees of freedom. Volume deformations due to the large mismatch in ionic radii are readily found to be the key driving force for immiscibility at all temperatures of relevance. This leads to a study of epitaxial stabilisation by employing latticed matched substrates to favour growth of alloys with fractional compositions of x = 0, approximately x = 0.5 and x = 1. The reduction in the free energy of mixing due to epitaxial strain in thin films is quantified for each substrate leading to indicators for growth of kinetically stable films.

在成分范围内研究了锗锡合金的热力学稳定性通过将密度泛函理论与集群扩展形式主义 (CE) 结合使用。众所周知，GeSn 合金是不混溶的，需要非平衡生长技术来生产亚稳态薄膜和纳米结构。通过研究 GeSn 系统的平衡热力学，可以深入了解组分偏析背后的驱动力。合金的混合自由能是通过将 CE 的焓与构型和振动自由度的熵项相结合来计算的。很容易发现由于离子半径大不匹配导致的体积变形是所有相关温度下不混溶的关键驱动力。这导致通过使用晶格匹配衬底来促进具有以下成分组成的合金的生长来研究外延稳定性x  = 0，大约x  = 0.5 和x  = 1。由于薄膜中的外延应变引起的混合自由能的减少被量化为每个基板，导致动力学稳定膜的生长指标。