High-Accuracy Measurement of Mid-IR Refractive Indices of GaAs/AlGaAs in Thin-Film Multilayers

Thin film optical coatings are essential for a wide range of photonic applications. However, meeting design targets without resource-intensive iterations in fabrication relies on precise knowledge of the optical properties of the deposited thin films, especially their refractive index. Accurate knowledge of the refractive index for GaAs-based materials is required for the design of a plethora of optical devices in the near- (NIR) and mid-infrared (MIR) spectral region, among them vertical-cavity surface-emitting lasers [1] and high-performance substrate-transferred optical interference coatings [2].
Typically, the refractive index shows variability depending on deposition conditions, and are therefore often insufficiently accurate [3]. This motivates the need for routine characterization of as-produced thin film structures. While several measurement methods for refractive indices exist – among them (spectroscopic) ellipsometry, the prism method, and Fourier-transform Infrared (FTIR) refractometry [3] – they all rely on specialized samples and measurement equipment.
We present a novel, robust method to measure the refractive indices of transparent materials over the NIR and MIR spectral regions, involving the following steps: Obtaining a photometrically-accurate low-resolution transmittance spectrum of a quarter-wave-type GaAs/AlGaAs structure via FTIR; extraction of individual layer thicknesses from cross-sectional imaging of the structure via calibrated scanning electron microscopy; using these thickness values, together with a single effective oscillator model [4] for the refractive indices, to fit a transfer-matrix-method model to the FTIR spectrum. Uncertainty propagation is done via a Monte-Carlo-type propagation method, including uncertainties in both, layer thicknesses and FTIR, measurements.
This method allows us to simultaneously extract the refractive indices of both materials in the as-deposited thin film structure with per-mille-level relative uncertainty over the 2–7 μm range.
1. C. W. Wilmsen, H. Temkin, and L. A. Coldren, eds., Vertical-Cavity Surface-Emitting Lasers (CUP, 2001).
2. G. Winkler, L. W. Perner, et al., “Mid-infrared interference coatings with excess optical loss below 10 ppm,” Optica 8, 686 (2021).
3. S. G. Kaplan, L. M. Hanssen, et al., “Fourier transform refractometry,” Proc. of SPIE 3425, 203 (1998).
4. C. Palmer, P. N. Stavrinou, et al., “Mid-infrared (λ ~2–6 μm) measurements of the refractive indices of GaAs and AlAs,” Semicond. Sci. Tech. 17, 1189 (2002).