Temperature dependent refractive index of silicon and germanium

Abstract

Silicon and germanium are perhaps the two most well-understood semiconductor materials in the context of solid state device technologies and more recently micromachining and nanotechnology. Meanwhile, these two materials are also important in the field of infrared lens design. Optical instruments designed for the wavelength range where these two materials are transmissive achieve best performance when cooled to cryogenic temperatures to enhance signal from the scene over instrument background radiation. In order to enable high quality lens designs using silicon and germanium at cryogenic temperatures, we have measured the absolute refractive index of multiple prisms of these two materials using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA Goddard Space Flight Center, as a function of both wavelength and temperature. For silicon, we report absolute refractive index and thermo-optic coefficient (dn/dT) at temperatures ranging from 20 to 300 K at wavelengths from 1.1 to 5.6 microns, while for germanium, we cover temperatures ranging from 20 to 300 K and wavelengths from 1.9 to 5.5 microns. We compare our measurements with others in the literature and provide temperature-dependent Sellmeier coefficients based on our data to allow accurate interpolation of index to other wavelengths and temperatures. Citing the wide variety of values for the refractive indices of these two materials found in the literature, we reiterate the importance of measuring the refractive index of a sample from the same batch of raw material from which final optical components are cut when absolute accuracy greater than +/-5 x 10^-3 is desired.