Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide

Infrared laser interferometry was used to measure the temperature dependence, β(T), of the refractive index of Si, GaAs, and InP at λ=1.15, 1.31, 1.53, and 2.39 μm. Semiconductor wafer samples that had been polished on both sides were either heated or cooled while measuring the sample temperature and the transmitted or reflected intensity of an infrared laser beam. The changing optical path length within the material causes alternating constructive and destructive interference between reflections off the front and back surfaces of the wafer. By subtracting the contribution of thermal expansion, α(T), which is small and accurately known, β(T) was obtained. Representative values of β (293 K) at 1.53 μm are 5.15×${10}^{\mathrm{-}5}$ ${\mathrm{K}}^{\mathrm{-}1}$, 6.65×${10}^{\mathrm{-}5}$ ${\mathrm{K}}^{\mathrm{-}1}$, and 5.95×${10}^{\mathrm{-}5}$ ${\mathrm{K}}^{\mathrm{-}1}$ for Si, GaAs, and InP. Polynomial expressions are presented for Si, GaAs, and InP, yielding values of β(T) that are accurate to within ±5%. $beta (T)— increases with increasing temperature and decreases with increasing wavelength. There is a large resonance enhancement of β(T) in direct-gap semiconductors as the photon energy ${\mathit{E}}_{\mathit{h}\nu }$ approaches the band-gap energy ${\mathit{E}}_{\mathit{g}}$. Absolute values and temperature dependences of β calculated from published theory agree reasonably well with the measurements. The extreme accuracy in β needed for interferometric thermometry, however, cannot be met by these theoretical calculations, and so requires the experimental measurements.