Method for calculating photo- and electroreflectance spectra from semiconductor heterostructures

A method for calculating photo- and electroreflectance spectra from weakly inhomogeneous layers of semiconductor heterostructures is developed. Transfer matrices are used in order to solve the propagation of light between different layers and perturbation theory in order to obtain the transfer matrix for a single layer. If applied to an infinite half space, the method reproduces the result by Aspnes and Frova [Solid State Commun. 7, 155 (1969)]. The electric field profiles of the heterostructures are calculated by means of an integral equation which holds under quite general conditions including incomplete dopant ionization and carrier degeneracy. The application of the general theory is demonstrated by calculating photoreflectance spectra of homogeneously n-doped semi-infinite GaAs samples with different doping levels, and of a (Al,Ga)As heterostructure with an interface charge between buffer layer and substrate. Due to its speed and accuracy the method has the potential for an on-line simulation of photo- and electroreflectance spectra.