Group-IV SiGeSn ternary alloy is a hot spot in the field of fabricating high-efficient Si-based light source due to its large lattice constant and bandgap variation range. However, due to the high cost and low speed of experimental and computational research, it is difficult to obtain their lattice constants comprehensively and quickly. Machine learning prediction based on statistics is an advanced method to solve this problem. In this paper, based on the existing data of group IV alloys, three machine learning methods such as Random Forest (RF), Support Vector Regression (SVR) and Gradient Boosting Decision Tree (GBDT) have been built to predict the lattice constants of SiGeSn. Firstly, the lattice constants of Group-IV alloys are collected to construct data set; Then, the data set are used to train the machine learning models which describe the quantitative relationship between concentrations and lattice constants; Finally, the prediction performance of these models are compared with each other, and the concentrations with appropriate lattice constants are predicted. The results show the comprehensive performance of SVR model is better than the other two, which means the SVR model can be used to directly predict the lattice constants of SiGeSn.

Silicon-based materials are significant candidates for electronic and optoelectronic applications because of their high electron and hole mobility. Si1-xGex, Si1-xSnx and Ge1-xSnx are currently hot materials in the field of fabricanting silicon-based light-emitting sources. At present, GeSn has been experimentally proved to have a direct band gap structure and achieve photoluminescence. But the more practical electroluminescence has not been realized. There are two reasons of these: one is the cost of experiment is high, which makes it impossible to conduct a comprehensive and in-depth study on these materials; Additionally, the variational laws of the lattice constants have not been reported due to the lack of theoretical and experimental data. In this paper, the lattice constants and bowing factor of Si1-xGex, Si1-xSnx and Ge1-xSnx have been studied by the first-principles method based on density functional theory (DFT) combined with the Special Quasirandom Structures (SQS) and hybrid function of Heyd-Scuseria-Ernzerhof (HSE) functional correction. Comparing the calculated data with the reported theoretical and experimental data, the results show our method is more accurate. In addition, the lattice constant fitting formulas of Si1-xGex, Si1-xSnx and Ge1-xSnx are given, it shows Si1-xSnx can reduce the lattice mismatch when Si1-xSnx as the buffer between Si and GeSn alloy.