Ge $_{1-x}$ Sn $_{x}$合金的能带结构：全区30带$k$ $p$模型
Band structure of Ge$_{1-x}$Sn$_{x}$alloy: a full-zone 30-band $k$$\cdot$$p$ model
摘要：
建立了一个全区30带的$k$ $\cdot$ $p$模型，该模型是计算Ge $_{1-x}$ Sn $_{x}$合金电子能带结构的有效和可靠的工具。该模型首次被用于再现由经验紧束缚和\textit{ab initio}方法得到的Ge和$α$ -Sn的电子能带结构。30波段$k$ $\cdot$ $p$模型的输入参数根据先前的经验预测和实验数据进行仔细校准。重要的材料特性，如电子和空穴的有效质量，Luttinger参数，和态密度的Ge $_{1-x}$锡$_{x}$合金的组成范围$0<x<0.3$。30-band $k$ $\cdot$ $p$模型需要的计算资源少得多，是优化由Ge $_{1-x}$ Sn $_{x}$合金制成的复杂器件的必要能力，需要探索大的参数空间。
英文摘要：
A full-zone 30-band $k$$\cdot$$p$ model is developed as an efficient and reliable tool to compute electronic band structure in Ge$_{1-x}$Sn$_{x}$ alloy. The model was first used to reproduce the electronic band structures in Ge and $α$-Sn obtained with empirical tight binding and \textit{ab initio} methods. Input parameters for the 30-band $k$$\cdot$$p$ model are carefully calibrated against prior empirical predications and experimental data. Important material properties such as effective mass for electrons and holes, Luttinger parameters, and density of states are obtained for Ge$_{1-x}$Sn$_{x}$ alloy with the composition range $0<x<0.3$. The 30-band $k$$\cdot$$p$ model that requires far less computing resources is a necessary capability for optimization of sophisticated devices made from Ge$_{1-x}$Sn$_{x}$ alloy with a large parameter space to explore.
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