Study on mechanical behaviors and constitutive models of single-crystal silicon considering anisotropy and strain rate effect

Single-crystal silicon is one of the most common and widely used semiconductor materials. As the performance of single-crystal silicon exhibits obvious anisotropy, characterizing its physical and mechanical properties is crucial for its engineering applications. In this work, nanoindentation tests and finite element analysis were used to investigate the mechanical behaviors and constitutive models for P-type single crystals: Si(111), Si(110), and Si(100). The findings revealed that the mechanical properties of single-crystal silicon were significantly affected by anisotropy and strain rate. The critical phase transition pressure and the creep resistance of Si[111], Si[110], and Si[100] decreased sequentially. As the strain rate increased, the hardness of single-crystal silicon increased significantly, while the fracture toughness declined. The elastic modulus, hardness, and fracture toughness of Si[111], Si[110], and Si[100] declined gradually. In addition, three engineering usable formulas have been proposed to describe the relationship between hardness and strain rate. The strain rate sensitivities for Si[111], Si[110], and Si[100] were determined as 0.054, 0.057, and 0.077, respectively. Equations for fracture toughness were established as functions of strain rate. Finally, the constitutive models for single-crystal silicon related to strain rate were established using finite element inversion methods. The findings could provide a theoretical basis for the design, manufacture, and application of single-crystal silicon in engineering.