Quantum theory of the dispersion of the refractive index near the fundamental absorption edge in compound semiconductors

A calculation of the real part of the refractive index near the fundamental absorption edge is given, which is based on a quantum mechanical calculation of the complex dielectric constant using the quantum density matrix method. An analytical expression is obtained in terms of experimentally known quantities for a given semiconductor and compared with available experimental data. The band structure of the Kane theory, which applies to direct gap III-V and II-VI compounds, is assumed. The expression obtained is a function of the bandgap energy, the effective electron and heavy hole masses at the bandedge, the spin orbit splitting energy, the carrier concentration for n-type or p-type materials, the temperature, and the frequency of the incident radiation. The temperature dependence occurs through the dependence of the bandgap energy and the effective mass on temperature for degenerate n-type or p-type materials, and there is an additional temperature-dependent factor for nondegenerate materials. The expression also involves the value of n at the absorption edge which is not accessible to measurement. However, an equation for n at the absorption edge can be found in terms of experimentally obtainable values of n near the absorption edge and solved to give the desired quantity