Refractive index of n-type gallium arsenide

The index of refraction for n-type GaAs is calculated as a function of photon energy by a method which accounts for the contribution of the fundamental absorption edge to the index of refraction. The absorption coefficient for n-type GaAs near the band-gap energy is determined from experimental data; free-carrier absorption is not included in the calculations; however, its contribution to the index of refraction is estimated to have a negligible effect compared to that due to the fundamental edge. Some applications to single- and double-heterojunction (AlGa)As–GaAs laser structures are discussed. The results indicate that occasionally the most important factor contributing to radiation confinement to the optical cavity in laser structures is the index-of-refraction change due to the differences in doping of various regions. Index calculations are made by using absorption data on GaAs at 77 and 300°K. The difference in the index of refraction of a material with different doping can be pronounced. For example, an index change of 1.3% occurs due to differences in the absorption edge of crystals with dopings n = 2 × 1016 cm−3 and n = 6.5 × 1018 cm−3 at an energy of 1.48 eV and T = 77°K. However, the same crystals had a 0.89% index differential at E = 1.37 eV and T = 300°K. These calculations agree extremely well with the index-of-refraction differentials determined from radiation pattern characteristics of laser devices.