Optical properties of crystalline semiconductors and dielectrics

A new formulation for the complex index of refraction, N(E)=n(E)-ik(E), as a function of photon energy E, for crystalline semiconductors and dielectrics is developed based on our previous derivation of N(E) for amorphous materials. The extinction coefficient k(E) is deduced from a one-electron model with finite lifetime for the excited electron state. The refractive index n(E) is then derived from the Kramers-Kronig relation as the Hilbert transform of k(E). It is shown that n(∞)>1. Excellent agreement is found between our equations for n(E) and k(E) and published measured values for crystalline Si, Ge, GaP, GaAs, GaSb, InP, InAs, InSb, SiC, cubic C, and α-${\mathrm{SiO}}_2$, over a wide range of energies (∼0–20 eV). Far fewer parameters, all of which have physical significance, are required and they can be determined for a particular material from the position and strength of the peaks in the k spectrum.