Optical dispersion relations for amorphous semiconductors and amorphous dielectrics

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(∞)+($B_0$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(∞) 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.