Epitaxial layer thickness measurement of double heterostructures using reflectance spectroscopy

Reflectance spectroscopy has been applied to the study of A-B-A double-heterostructure (DH) layer sequences in the AlGaAs and InGaAsP materials systems, consisting of an A epitaxial layer on a B epitaxial layer on a substrate of material A. In the spectral regime where the materials are transparent, the reflectance spectrum exhibits periodic oscillations due to thin-film interference. Both epitaxial layer thicknesses may always be determined by performing computer simulations of the DH reflectance spectrum, obtaining a best fit to spectral data. Simple algorithms far less computation intensive than curve fitting the spectrum are developed here, which can be used to deduce both epitaxial layer thicknesses in many cases. The choice of algorithm depends primarily on the thickness of the B layer. Fourier transform infrared measurements have been used to apply this technique to a variety of A-B-A DH systems for B layers ranging from 0.01 to 3.8 μm thick. The simulated and measured reflectance spectra are in good agreement. The optical results show a systematic offset of 2% from transmission electron microscopy measurements with a standard deviation of 1%. An analytical expression for the modulation amplitude of the reflectance spectrum oscillations, which depends on the thickness and composition of the epitaxial layers, is developed. This theoretical expression justifies the thickness algorithms and predicts a nearly linear relationship between the modulation amplitude of the reflectance spectrum and the refractive index (composition) of the B layer.