Abstract First principles calculations are increasingly often used in device modelling. However, due to their complexity and high computational costs, simplified but reliable models are of great value. In this work, we present an original method of finding the 30-band k · p parameters on an example of Ge 1 - x Sn x alloy. It allows to reproduce the electronic band structure in the full BZ and in the full composition range. The method uses the state-of-the-art supercell based ab initio calculations as the reference. A direct fitting of the k · p parameters from ab initio supercell band structures is difficult since the assignment of the k · p bands to correct eigenvalues of the reference band structures may be ambiguous. For this reason, the ab initio computational alchemy is used as an intermediate step. Owing to its properties, the supercell unfolded eigenvalues are approximated with continuous curves, which enables a straigthforward way to fit the 30-band k · p parameters. As an example of application, the optical gain in bulk Ge 0.91 Sn 0.09 has been calculated. The advantage of using the 30-band over the often used 8-band k · p approach is clearly seen. The presented method can be applied to any mixed, isovalent and isostructural system, eg. III-V, or II-VI alloys.

中文翻译：

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半导体合金的电子能带结构：通过计算炼金术从 ab initio 到 k·p，以 Ge1-xSnx 合金为例

摘要 第一性原理计算越来越多地用于设备建模。然而，由于它们的复杂性和高计算成本，简化但可靠的模型具有很大的价值。在这项工作中，我们提出了一种在 Ge 1 - x Sn x 合金示例上找到 30 波段 k·p 参数的原始方法。它允许在完整的 BZ 和完整的组成范围内重现电子能带结构。该方法使用最先进的基于超胞的 ab initio 计算作为参考。从 ab initio 超胞带结构直接拟合 k·p 参数是困难的，因为分配 k·p 带以校正参考带结构的特征值可能不明确。出于这个原因，从头计算炼金术被用作中间步骤。由于其特性，超胞展开特征值用连续曲线近似，这使得能够以一种直接的方式拟合 30 波段 k·p 参数。作为应用示例，计算了块体 Ge 0.91 Sn 0.09 的光学增益。使用 30 波段的优势明显优于常用的 8 波段 k·p 方法。所提出的方法可以应用于任何混合、等价和同构系统，例如。III-V 或 II-VI 合金。