Spatial dispersion in silicon

Spatial dispersion (SD) is a nonlocal effect that can introduce optical anisotropy in an otherwise isotropic material, causing the electromagnetic response at a given point to depend not only on the local field, but also on the field in the vicinity of that point. In this study, we investigate the impact of SD on a cubic semiconductorlike silicon, which is typically considered a negligible effect due to the small size of the lattice parameters with respect to the wavelength of light. However, our findings demonstrate that SD can be significant above the band gap, where transmission measurements are not feasible and reflection measurements are required for characterization. We utilize Mueller matrix ellipsometry spectroscopy to quantify the anisotropy caused by SD in (110) and (100) silicon wafers, and determine the complete permittivity tensor of silicon when spatial dispersion is included. In the most general case, this tensor is found to depend on two complex parameters.