Si and Ge are two key semiconductor elements to construct CMOS-based devices and IC transistors, while the lattice mismatch of these two elements may decrease the quality and stability of heterojunction bipolar transistors based on Si_1-xGe_x alloy. In this work, by using the first-principles calculations and the virtual crystal approximation (VCA) in material structures, we studied the lattice mismatch and the fundamental mechanical parameters in Si_1-xGe_x alloys. The numerical results are consistent with those reported in some previous works. Moreover, the lattice-compensation effect induced by B-doping in Si_1-xGe_x alloy is also studied, confirming further that the VCA is an efficient way to study the multi-component alloy systems doped by other kinds of atoms. Our work puts forward a feasible theoretical method to study the lattice constants, the lattice mismatch, the mechanical properties and the lattice-compensation effects in multi-component alloy systems.

Si和Ge是构建基于CMOS的器件和IC晶体管的两种关键半导体元素，而这两种元素的晶格失配可能会降低基于Si _1-x Ge _x合金的异质结双极晶体管的质量和稳定性。在这项工作中，通过使用第一性原理计算和材料结构中的虚拟晶体近似（VCA），我们研究了 Si _1-x Ge _x合金的晶格失配和基本力学参数。数值结果与之前一些工作中报道的结果一致。此外，Si _1-x Ge _{x 中}B 掺杂引起的晶格补偿效应还研究了合金，进一步证实了 VCA 是研究其他类型原子掺杂的多组分合金系统的有效方法。我们的工作提出了一种可行的理论方法来研究多组分合金体系中的晶格常数、晶格失配、力学性能和晶格补偿效应。