Simultaneous measurement of mid-infrared refractive indices in thin-film heterostructures: Methodology and results for GaAs/AlGaAs

We present our results for simultaneous measurement of the refractive indices of gallium arsenide (GaAs) and aluminum gallium arsenide (AlₓGa₁₋ₓAs) in the spectral region from 2.0 µm to 7.1 µm (5000 cm⁻¹ to 1400 cm⁻¹). We obtain these values from a monocrystalline superlattice Bragg mirror of excellent purity (background doping 1×10⁻¹⁴/cm³), 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 Al₀.₉₂₉Ga₀.₀₇₁As. The fitted model can also approximate the refractive index for MBE-grown AlₓGa₁₋ₓAs for 0≤x≤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.