Modulation ellipsometry measurements and density matrix modeling of a p-i-n-i superlattice optoelectronic modulator

Abstract

Differential reflection measurements are performed on a n-i-p-i modulator with superlattice in the active layer. We use a modulation ellipsometer with pulsed laser excitation of the sample, avoiding electrical contacting of the device. We present for the first time a density matrix model which can be used for calculating the dielectric function of both superlattices as well as multiple quantum wells. The model includes the off-diagonal Coulomb coupling potentials, which are crucial for superlattice structure modeling, and the applied electric field which is required in a modulator device. An optical transfer-matrix model is used to obtain the differential reflection spectra of the device, using the dielectric function of the superlattice calculated with the density matrix model. Thus a direct and quantitative comparison with the experimental spectrum is shown.