Determination of refractive index of crystalline silicon in the infrared region on the basis of interference pattern observed in thick slab

The precise values of the refractive index of crystalline silicon are determined in the infrared region based on the measurements of the interference pattern in 0.25 mm thick wafer. The interference pattern observed for one particular incidence angle allows us to determine the optical thickness precisely, however, the wafer thickness and refractive index, whose product gives the optical thickness, can be determined with much worse accuracy. This limitation could be overcome by using several incidence angles because if the dependence of the period of interference pattern on the incidence angle is considered, it is possible to determine both the thickness and refractive index with high accuracy. The FTIR infrared ellipsometer is used for measurements at oblique incidence angles, while the FTIR spectrophotometer is utilized for measurements at near-normal incidence. To correctly interpret the experimental data, it is necessary to consider the influence of the finite spectral resolution and beam divergence of the instruments and the thickness non-uniformity of the sample. These effects significantly alter the observed interference patterns. The formulae needed to accomplish this task are derived in this work. The values of the refractive index determined using the proposed method for the crystalline silicon show differences smaller than $10^{-3}$ from the values obtained by the minimum deviation method.