The refractive index of $AlxGa1−xAs$ below the band gap: Accurate determination and empirical modeling

The refractive indices of $AlxGa1−xAs$ epitaxial layers $(0.176⩽x⩽1)$ are accurately determined below the band gap to wavelengths, λ<3 μm. The layers are grown on GaAs substrates by molecular beam epitaxy metal organic and chemical vapor deposition with thicknesses ranging from 4 to 10 μm. They form improper waveguide structures with the GaAs substrate. The measurements are based on the excitation of the improper waveguide modes with grating couplers at 23 °C. The refractive indices of the layers are derived from the modal propagation constants in the range of 730 nm<λ<830 nm with an estimated uncertainty of $Δn=5×10−4.$ The temperature coefficient of the refractive index is investigated in the same spectral range. From the effective indices of the TE and TM modes, we derive the strain-induced birefringence and the elasto-optic coefficients. High-resolution x-ray diffraction is used to determine the strain of the layers. The layer compositions are obtained with inductively coupled plasma atomic emission spectroscopy. The measurement range of the refractive index is extended from the direct gap to λ<3 μm by observing the Fabry-Pérot interference fringes of the transmission spectra of isolated layers. The measured values of the refractive index and the elasto-optic coefficient are compared to calculated data based on semiempirical models described in the literature. Published data of the index of refraction on GaAs, AlAs and GaP are analyzed to permit the development of a modified Sellmeier approximation. The experimental data on $AlxGa1−xAs$ can be fitted over the entire composition range $0⩽x⩽1$ to provide an accurate analytical description as a function of composition, wavelength, and temperature.