Optical dispersion relations for amorphous semiconductors and amorphous dielectrics

Abstract

An expression for the imaginary part, k, of the complex index of refraction, N=n-ik, for amorphous materials is derived as a function of photon energy E: k(E)=A(E-${E}_{g}$${)}^{2}$/(${E}^{2}$-BE+C) where A, B, and C are positive nonzero constants characteristic of the medium such that 4C-${B}^{2}$>0. ${E}_{g}$ represents the optical energy band gap. The real part, n, of the complex index of refraction is then determined to be n(E)=n(\ensuremath{\infty})+(${B}_{0}$E+${C}_{0}$)/ (${E}^{2}$-BE+C) using Kramers-Kronig analysis, where ${B}_{0}$ and ${C}_{0}$ are constants that depend on A, B, C, and ${E}_{g}$, and n(\ensuremath{\infty}) is a constant greater than unity. Excellent agreement was found between these formulas and experimentally measured and published values of n and k of amorphous silicon, hydrogenated amorphous silicon, amorphous silicon nitride, and titanium dioxide.