Two-dimensional state of stress in a silicon wafer

Two-dimensional state of stress in (001) and (111) silicon wafer is studied with infrared photoelasticity. In two widely used groups of coordinate systems, the silicon piezo-optical coefficient tensors due to photoelastic anisotropy of silicon crystal are derived. The relation between stress ellipsoid and refractive index ellipsoid is analyzed with infrared polarized light transmitting through the silicon crystal in certain directions. The applicability of the stress-optical law in (001) and (111) silicon wafers is presented. A three direction observation method is developed to decide the magnitude and direction of principal stresses in silicon wafer. The stress states in (100) and (111) silicon wafers after certain device processes are also measured and calculated. Comparisons of experimental and calculated results are made.