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 less than or e qual to x less than or equal to 1) are accurately determined below the band gap to wavelengths, lambda < 3 mu m. The layers are grown on GaAs substrat es by molecular beam epitaxy metal organic and chemical vapor deposition wi th thicknesses ranging from 4 to 10 mu m. They form improper waveguide stru ctures with the GaAs substrate. The measurements are based on the excitatio n of the improper waveguide modes with grating couplers at 23 degrees C. Th e refractive indices of the layers are derived from the modal propagation c onstants in the range of 730 nm <lambda < 830 nm with an estimated uncertai nty of Delta n=5x10(-4). The temperature coefficient of the refractive inde x 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 el asto-optic coefficients. High-resolution x-ray diffraction is used to deter mine the strain of the layers. The layer compositions are obtained with ind uctively coupled plasma atomic emission spectroscopy. The measurement range of the refractive index is extended from the direct gap to lambda < 3 mu m by observing the Fabry-Perot interference fringes of the transmission spec tra of isolated layers. The measured values of the refractive index and the elasto-optic coefficient are compared to calculated data based on semiempi rical models described in the literature. Published data of the index of re fraction on GaAs, AlAs and GaP are analyzed to permit the development of a modified Sellmeier approximation. The experimental data on AlxGa1-xAs can b e fitted over the entire composition range 0 less than or equal to x less t han or equal to 1 to provide an accurate analytical description as a functi on of composition, wavelength, and temperature. (C) 2000 American Institute of Physics. [S0021- 8979(00)04811-8].