Airy function analysis of Franz–Keldysh oscillations in the photoreflectance spectra of In1−xGaxAsyP1−y layers

Abstract

Room temperature photoreflectance (PR) has been performed on three In0.32Ga0.68As/ In0.76Ga0.24As0.53P0.47 tensiley strained single-quantum-well structures, with heavy Zn modulation p-doping (5×1017 cm−3) in the quaternary barriers, which are lattice matched to an InP substrate. The PR spectra exhibit strong, well-defined, and regular Franz–Keldysh oscillations (FKO) associated with the barrier layers. We study the FKO in detail, comparing two different techniques of analyzing them to obtain a measure of the built-in electric field: (i) the conventional simple graphical asymptotic technique; and (ii) least-squares fitting to the experimental spectra using the recently proposed electromodulation model based on complex Airy functions. In the second method, the PR spectra are best described by the sum of two Airy function expressions representing degenerate heavy- and light-hole band edges. Good fits are obtained without the need to use an empirical energy-dependent broadening term to account for the effects of nonflatband modulation and nonuniform fields. The results are consistent with FKO originating from heavy- and light-hole transitions under the same electric field, but having a partial destructive interference effect in the PR spectrum. The fitted field value of ∼17 kV/cm is essentially the same as that obtained in the graphical analysis which assumed that the FKO were heavy-hole dominated. However, contrary to previous suggestions, neither the heavy- nor light-hole contributions dominate the actual FKO spectrum.