Refractive index of n-type gallium arsenide

Abstract

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.