Effects of the absorption coefficient on the refractive index of germanium in a fiber optic-semiconductor temperature sensor

Abstract

This paper introduces a theoretical model which reveals the relation between the absorption and the refractive index of germanium within absorption region, which is crucial to a new fiber optic-semiconductor film temperature sensor developed lately in our lab. The new designed sensor is based on the effect of the temperature dependence of the refractive index of semiconductor. Many efforts on the effect of the temperature-dependent refractive index of semiconductor are reported in transparent region mostly by empirical model such as Sellmeier model[1]. We analyze the temperature dependence of the refractive index of semiconductor near the absorption edge other than in the transparent region. From the Kramers-Kronig relations, the refractive index is an integral of the absorption coefficient over the whole energy spectrum.Taking advantage of the model that explained the contribution of the integral cloesd to the absorption edge to the refractive index by Frank Stern [2] we are able to calculate the variation of the refractive index due to the thermal shift of absorption edge. The contribution of the temperature-dependent absorption coefficient to the refractive index is enhanced dramatically at the absorption edge of semiconductor, where the temperature dependence of the energy gap Eg can be used to get the absorption edge shift with Yu-Brook's model[3]. While the contribution of the absorption shift far away from the absorption edge to un is negligible comparing to that near the edge according to Frank Stern[2]. Further demonstration experiments will be carried out to support our theory, in which refractive indexes of germanium are measured at specific wavelengths of 1310nm, 1550nm and 2000nm. Since the direct absorption edge of germanium is at about 0.82eV, corresponding to the wavelength of 1550nm, we estimate that the thermo-optic coefficient dn/dT of germanium at 1550nm would be larger than that at 1310nm and 2000nm.