Lineshape analysis for optical transitions in III-V semiconductors using a sequential simplex procedure

Abstract

A computer lineshape analysis for optical transitions in III-V semiconductors is presented. The routine utilizes the Nelder–Mead version of the sequential simplex optimization procedure embodied in a pascal program that can be executed on a personal computer. The sequential simplex routine allowed the optimum fitting of experimental data with a function or group of functions with n-independent parameters. The routine was successfully applied to two types of optical spectra. First, convolved Gaussian and asymmetric Gaussian bands in low temperature (4.2 K) Fourier-transformed photoluminescence spectra of lattice-matched InxGa1−xAs on InP substrates were fit. As a result of applying the sequential simplex routine to the InxGa1−xAs/InP system, three optical transitions (excitonic band, donor-to-acceptor pair band, and defect/impurity or exciton LO replica band) were identified in all spectra and a fourth transition was found in some samples. A second application of the routine was the fitting of the Aspnes third derivative lineshapes (TDLS) to room temperature, low electric field photoreflectance spectra of high purity GaAs. In applying the routine to photoreflectance spectra, it was found that the two-dimensional critical point, n=3 form of the TDLS best fit the photoreflectance spectra of high-purity GaAs at room temperature. In both applications of the sequential simplex routine, the lineshape analysis contributed valuable insight into the nature of the optical phenomena occurring in the analyzed material.