Determination of thicknesses and temperatures of crystalline silicon wafers from optical measurements in the far infrared region

Optical measurements of transmittance in the far infrared region performed on crystalline silicon wafers exhibit partially coherent interference effects appropriate for the determination of thicknesses of the wafers. The knowledge of accurate spectral and temperature dependencies of the optical constants of crystalline silicon in this spectral region is crucial for the determination of its thickness and vice versa. The recently published temperature dependent dispersion model of crystalline silicon is suitable for this purpose. Because the linear thermal expansion of crystalline silicon is known, the temperatures of the wafers can be determined with high precision from the evolution of the interference patterns at elevated temperatures.