Numerical computation of the complex dielectric permittivity using Hilberttransform and FFT techniques

A procedure is described to efficiently obtain the complex dielectric permi ttivity of semiconductor materials with numerical routines available in cur rent software applications. This procedure calculates the real component of the dielectric permittivity from its imaginary component by making use of the Hilbert transform properties of the Kramers-Kronig relations. We show t he reliability of this approach by reconstructing the real component from t he experimentally known dispersion relations of GaAs and InAs. In addition, we use this procedure for the case when the imaginary component is obtaine d from analytical expressions as is the case for the Franz-Keldysh effect i n the absorption of photons in GaAs. We show how the spectral photoreflecti on of structures where this effect is present can be easily modeled and sim ulated by this method. (C) 1998 The Franklin Institute. Published by Elsevi er Science Ltd.