The Refractive Index of Gallium Antimonide

Abstract

Gallium antimonide (GaSb) is a key material for near- and mid-infrared photonics, enabling high-performance laser architectures and detectors. Design and simulation of such devices depend on accurate optical material data, especially the complex refractive index $n^*_{\text{GaSb}} = n_{\text{GaSb}} +ik_{\text{GaSb}}$, consisting of the real part $n_{\text{GaSb}}$ (refractive index) and the imaginary part $k_{\text{GaSb}}$ (extinction coefficient). However, GaSb refractive index values are based either on theoretical models, typically informed by legacy experimental data, or on experimental measurements without quantified uncertainties. This limits their reliability for state-of-the-art devices. Here, we present measurement results of $n^*_{\text{GaSb}}$ in the near- to mid-infrared range from \SIrange{1}{3.1}{\micro \metre} with a relative uncertainty <\num{7.8e-5} for $n_{\text{GaSb}}$, and <\num{2.0e-3} for $k_{\text{GaSb}}$. As a side result of our method, we also report $n_{\text{AlAsSb}}$ for aluminium arsenide antimonide ($\mathrm{AlAs_{0.08}Sb_{0.92}}$) with a relative uncertainty <\num{3.9e-4}. Our results are based on two complementary measurements on a GaSb/AlAsSb-based heteroepitaxial structure under controlled environmental conditions: photometric transmission and layer-thickness analysis by cross-sectional scanning electron microscopy. We simultaneously retrieve the refractive indices of the two materials by fitting a Sellmeier equation and a theoretical dispersion model by Djurišić \textit{et al.}~\cite{djurisic_modeling_2000}. The uncertainties of $n^*_{\text{GaSb}}$ and $n_{\text{AlAsSb}}$ are quantified using a Monte Carlo-based approach. Our results provide accurate complex refractive index values for GaSb, which are vital to advance photonics-related technologies in the near- and mid infrared spectral region.

Figures (7)

• Figure 1: Overview of the workflow. (a) We measure the photometric transmission $T$ and (b) record cross-sectional images of the structure to extract the layer thicknesses {$d_{\text{i}}$}. (c) With literature values for $n_{\text{Sub}}$, we (d) perform a nonlinear fit of a theoretical model for $n^*_\text{GaSb}$ and the Sellmeier coefficients of $n_\text{AlAsSb}$ to $T$ with {$d_{\text{i}}$} as additional input. We use the fit parameters to calculate (e) $n^*_\text{GaSb}$ and (f) $n_\text{AlAsSb}$.
• Figure 2: (a) The baseline-corrected transmission of the heteroepitaxial sample, measured using a Varian Cary 5 in the wavelength range from 13.1. (b) 1$\sigma$ standard uncertainty of the mean measurement shown in panel (a).
• Figure 3: Representative cross-sectional grayscale image of the sample with (a) 30k X and (b) 50k X magnification, respectively. The green line shows the column-wise mean grayscale intensity for (c) 30k X and (d) 50k X magnification. The orange and blue stripes indicate the extracted layer thicknesses.
• Figure 4: (a) The extracted physical layer thicknesses $\{d_{\text{i}}\}$. Red circles corresponds to GaSb and green squares to AlAsSb, respectively. (b) The 1$\sigma$ standard uncertainty $s(\{d_{\text{i}}\})$ of the individual layer thicknesses. Note the scaling factor $10^{-4}$ in front.
• Figure 5: (a) The measured photometric transmission $T$ (thick yellow line) together with the best-fit result (thin blue line). (b) The corresponding residual, obtained via Eq. \ref{['equ:residuals']}.