Quantum calculations of the change of refractive index due to free carriers in silicon with nonparabolic band structure

Abstract

A quantum-mechanical approach used to calculate the change of refractive index, Δn, due to free carriers in various doped silicon is presented. This approach uses a numerical Kramers–Kronig relation to analyze a calculated carrier-related absorption spectrum below or near the energy-band gap. The absorption spectrum is obtained by considering the optical transitions between energy bands and impurity bands, and the free-carrier absorption due to acoustic phonons, optical phonons, and ionized impurities in a spherical nonparabolic band model. Values of Δn at wavelength λ=1.3 and 1.6 μm for different doping levels are obtained. The results are applicable to both the integrated-optics applications and optical-probing applications in silicon.