Simultaneous Measurement of Mid-Infrared Refractive Indices in Thin-Film Heterostructures: Methodology and Results for GaAs/AlGaAs

TL;DR

This paper introduces a novel methodology for simultaneously measuring the mid-infrared refractive indices of GaAs and AlGaAs in thin-film heterostructures, combining spectrometry, electron microscopy, and Monte Carlo analysis to achieve high accuracy.

Contribution

It presents a new integrated approach for precise refractive index measurement over a broad spectral range using existing techniques combined innovatively.

Findings

Achieved relative uncertainties of about 10^-4 in refractive index measurements.

Developed a dispersion model fitting method applicable to MBE-grown AlGaAs.

Provided updated refractive index values for GaAs and AlGaAs across 2.0 to 7.1 μm.

Abstract

We present our results for simultaneous measurement of the refractive indices of gallium arsenide (GaAs) and aluminum gallium arsenide (Al$_\mathrm{x}$Ga$_\mathrm{1-x}$As) from $2.0$ to $7.1\,\mathrm{\mu m}$ ($5000$ to $1400\,\mathrm{cm^{-1}}$). We obtain these values from a monocrystalline superlattice Bragg mirror of excellent purity (background doping $\leq 1 \times 10^{-14}\,\mathrm{cm^{-3}}$), grown via molecular beam epitaxy. To recover the refractive indices over such a broad wavelength range, we fit a dispersion model for each material. In a novel combination of well-established methods, we measure both a photometrically accurate transmittance spectrum of the Bragg mirror via Fourier-transform infrared spectrometry and the individual physical layer thicknesses of the structure via scanning electron microscopy. To infer the uncertainty of the refractive index values, we estimate relevant measurement uncertainties and propagate them via a Monte-Carlo method. This highly-adaptable approach conclusively yields propagated relative uncertainties on the order of $10^{-4}$ over the measured spectral range for both GaAs and Al$_{0.929}$Ga$_{0.071}$As. The fitted model can also approximate the refractive index for MBE-grown Al$_\mathrm{x}$Ga$_\mathrm{1-x}$As for $0\leq x \leq 1$. Both these updated values and the measurement approach will be essential in the design, fabrication, and characterization of next-generation active and passive optical devices in a spectral region that is of high interest in many fields, e.g., laser design and cavity-enhanced spectroscopy in the mid-infrared spectral region.