Characterization of Electronic Materials by Optical Reflectance Spectroscopy and Digital Signal Processing

Abstract

AbstractIon implantation, diffusion, epitaxy, oxidation and ion exchange are common processing steps which alter the refractive index of dielectric media. These changes can be probed non-destructively by optical methods such as infrared and ultraviolet-visible spectroscopy, and related to material structure. An overview is given of the bilinear transform of reflectance and its use in conjunction with Fourier spectral analysis for thickness and refractive index estimation. Closed-form solutions are presently available for the bilinear transformed reflectance of heteroepitaxial multilayer structures, and for materials containing graded refractive index profiles. Salient features such as positions of interfaces and refractive index steps in multilayer media; depth and width of buried inhomogeneous layers; and width of a transition region between layers of constant refractive index can be determined directly. Under certain restrictive assumptions the bilinear transformed reflectance is shown to be invertible, which allows one to determine the complete refractive index profile. Examples are presented which illustrate the determination of thickness and refractive index of individual layers in multilayered structures. Specific examples include silicon-on-insulator, and Il-V heteroepitaxial structures such as InP/InGaAs/lnP. Analysis of the reflectance of medium to high energy implanted Si or GaAs allows determination of mean damage depth and standard deviation. The invertibility of the bilinear transformed reflectance is illustrated by estimating the refractive index profile of nitrogen implanted silicon.