Temperature and intensity dependence of the refractive index of a compound semiconductor

An investigation of the effect of high-intensity radiation at frequencies below the fundamental absorption edge on the refractive index of a compound semiconductor must include consideration of effects due to generated carriers and effects due to heating. The latter include the change of band-gap energy with temperature and thermal expansion, both of which change the refractive index. A calculation of the refractive index of a semiconductor with the band structure of the Kane theory is given for the case of arbitrary spin–orbit splitting energy. Theoretical results are expressed in terms of the following experimental parameters: band-gap energy, effective electron mass, effective hole masses of the three valence bands, the spin–orbit splitting energy, and the lattice constant. An expression for the thermo-optic coefficient dn/dT is given that makes possible the numerical evaluation of the refractive index as a function of temperature. The nonlinear intensity-dependent refractive index is calculated, assuming that the change in carrier concentration is generated by an applied radiation field of high intensity, and theoretical results are compared with experiment for InAs and InSb.