On calculation of elastic properties in silicon and germanium single crystals

We present a study of the structural, elastic, and thermo dynamical properties of the single crystal silicon, using density-functional theory within the generalized gradient approximation of the exchange-correlation functional. The optimized lattice parameter, elastic moduli, Zener anisotropy factor (A), Poisson's ratio (ν), Young's modulus (Y), shear modulus (C'), are systematically investigated and compared with other experimental and theoretical calculations. Our structural results are well consistent with experimental works presented earlier. single crystal silicon is anisotropic. The crystalline directions of interest include the <;100>, the <;110>, and the <;111> crystal directions. Material properties in these crystalline directions can be calculated from basic crystal properties. Crystalline silicon {100} and {111} oriented wafers are used mainly for fabrication of Micromechanical sensors and actuators. A primer on anisotropic elasticity of a cubic symmetric silicon crystal is presented. This program code can also be used for single crystal Germanium.