Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation

Optical constant spectra for silicon and thermally grown silicon dioxide have been simultaneously determined using variable angle of incidence spectroscopic ellipsometry from 0.75 to 6.5 eV. Spectroscopic ellipsometric data sets acquired at multiple angles of incidence from seven samples with oxide thicknesses from 2 to 350 nm were analyzed using a self-contained multi-sample technique to obtain Kramers–Kronig consistent optical constant spectra. The investigation used a systematic approach utilizing optical models of increasing complexity in order to investigate the need for fitting the thermal ${\mathrm{SiO}}_2$ optical constants and including an interface layer between the silicon and ${\mathrm{SiO}}_2$ in modeling the data. A detailed study was made of parameter correlation effects involving the optical constants used for the interface layer. The resulting thermal silicon dioxide optical constants were shown to be independent of the precise substrate model used, and were found to be approximately 0.4% higher in index than published values for bulk glasseous ${\mathrm{SiO}}_2$ . The resulting silicon optical constants are comparable to previous ellipsometric measurements in the regions of overlap, and are in agreement with long wavelength prism measurements and transmission measurements near the band gap.