Defects play an important role for surface reconstructions and therefore also influence the substrate growth. In this work we present a first principle calculation for the Ge(001) surface without and with tin impurities incorporated into the top surface layer. By mapping the system onto an Ising-type model, with interaction constants taken from density functional theory, the stability of the surface reconstructions under the influence of different concentrations of tin impurities is explored. This approach allows us to simulate the possible phase transitions for the different surface reconstructions including the local structure around the tin impurity atoms. In addition, we compare our theoretical results with experimental STM images on clean and Sn-doped Ge(100) surfaces.

缺陷对表面重建起着重要作用，因此也会影响基板的生长。在这项工作中，我们提出了 Ge(001) 表面的第一原理计算，没有和有锡杂质掺入顶面层。通过将系统映射到 Ising 型模型，并利用密度泛函理论中的相互作用常数，探索了不同浓度锡杂质影响下表面重建的稳定性。这种方法使我们能够模拟不同表面重构的可能相变，包括锡杂质原子周围的局部结构。此外，我们将我们的理论结果与干净和 Sn 掺杂的 Ge(100) 表面上的实验 STM 图像进行了比较。