Near infrared Brillouin scattering and high resolution x-ray diffraction is used for a precise determination of the elastic constants and the relaxed lattice parameters of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ epitaxial layers $(0.1\mathrm{}<~x<~1.0).$ The composition of the layers is specified by inductively coupled plasma atomic emission spectroscopy, photoluminescence, and Raman spectroscopy. For the elastic constants we get a composition independent value of $118.9\pm 0.7\hspace{0.5em}\mathrm{GPa}$ for ${\mathrm{C}}_{11},$ a nonlinear increase in ${\mathrm{C}}_{12}$ and a linear decrease in ${\mathrm{C}}_{44}$ with increasing Al composition. The Poisson ratio shows a linear increase for $x<\mathrm{}0.8\mathrm{}$ and a downward bowing for higher Al concentrations to the AlAs value of $\nu =0.325\mathrm{}\pm \mathrm{0.004.}$ The effect of lattice mismatch induced strain on the elastic properties is investigated on free standing epitaxial layers. The trend in ionicity from the GaAs to the AlAs bonds are deduced from phenomenological expressions for the bond-bending and bond-stretching forces which are calculated from the elastic constants. The lattice parameters of the unstrained crystals are obtained from the measured full metric of the tetragonally strained layers and the Poisson ratios. The combined results of Brillouin scattering, x-ray diffraction, and compositional analysis confirm the deviation of the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ lattice parameter from Vegard’s law, and provides the first direct and accurate determination of the quadratic bowing parameter.

• Received 1 March 1999

DOI:https://doi.org/10.1103/PhysRevB.60.11601