Precise Measurement of Refractive Indices in Thin Film Heterostructures

TL;DR

This paper introduces a precise method combining transmittance spectra and layer thickness measurements to accurately determine the refractive indices of thin-film materials with minimal uncertainty.

Contribution

A novel approach using TMM-based curve fitting and Monte Carlo error propagation for simultaneous refractive index measurement in multilayer structures.

Findings

Achieved $10^{-4}$-level uncertainty in refractive index measurements.

Demonstrated method on GaAs and AlGaAs in a distributed Bragg reflector.

Applicable across various wavelength regions and material combinations.

Abstract

We present a robust, precise, and accurate method to simultaneously measure the refractive indices of two transparent materials within an interference coating. This is achieved by measuring both a photometrically accurate transmittance spectrum and the as-grown individual layer thicknesses of a thin-film multilayer structure. These measurements are used for a TMM-based curve-fitting routine which extracts the refractive indices and their measurement uncertainties via a Monte-Carlo-type error propagation. We demonstrate the performance of this approach by experimentally measuring the refractive indices of both, GaAs and Al$_{0.929}$Ga$_{0.071}$As, as present in an epitaxial distributed Bragg reflector. A variety of devices can be used to obtain the transmittance spectrum (e.g., FTIR, grating-based spectrophotometer) and layer thicknesses (e.g., SEM, TEM, AFM), the discussed approach is readily adaptable to virtually any wavelength region and many transparent material combinations of interest. The subsequent model-fitting approach yields refractive index values with $10^{-4}$-level uncertainty for both materials.