Refractive index of ternary and quaternary compound semiconductors below the fundamental absorption edge: Linear and nonlinear effects

The index of refraction n is calculated as a function of frequency and mole fraction x for the following compounds: Hg/sub 1-x/Cd/sub x/Te, Al/sub x/Ga/sub 1-x/As, and In/sub 1-x/Ga/sub x/As/sub y/P/sub 1-x/ lattice matched to InP. Lattice matching of In/sub 1-x/Ga/sub x/As/sub y/P/sub 1-y/ to InP requires that x = 0.466 y. The theoretical result for the refractive index is obtained from a quantum mechanical calculation of the dielectric constant of a compound semiconductor. It is given in terms of the basic material parameters of band gap energy, effective electron mass m/sub n/, effective heavy hole mass m/sub p/, spin orbit splitting energy, lattice constant, and carrier concentration n/sub e/ or p for n type or p type materials, respectively. If these quantities are known as functions of mole fraction x, there are no adjustable parameters involved. A negative change in the refractive index near the fundamental absorption edge is predicted on passing radiation through a crystal if the change in carrier concentration of the initially unoccupied conduction band is assumed proportional to internal intensity 1.