Validity of vegard's rule for the lattice parameter and the stiffness elastic constant ratios of the AlGaAs ternary compound

A new procedure for the determination of the Poisson ratio, the elastic stiffness constant ratios and the lattice parameter of epitaxial films is presented which is based on the strain tensor determination by high-resolution X-ray diffraction by using epitaxial layers simultaneously grown on three different substrate orientations and different alloy compositions. Our method allows us to verify the validity of the Vegard's rule and/or evidence a difference in the incorporation of group-III-elements in ternary III-V semiconductor films. We discuss the results obtained from Al _xGa _{1- x}As epilayers coherently grown simultaneously on (1 0 0)-, (2 1 0)- and (3 1 1)-GaAs substrate crystals. Assuming a GaAs lattice parameter d_GaAs=0.565325±0.000002 nm our experiment yields the AlAs lattice parameter d_AlAs=0.566139±0.000005 nm. The stiffness elastic constant ratios for AlAs are c₁₂/ c₁₁=0.475±0.003, which leads to a Poisson ratio ν=0.322±0.001 and c₄₄/ c₁₁=0.517±0.003. An analogous analysis for the ternary Al _xGa _{1- x}As compound with x=0.5 yields a lattice parameter value and elastic constant ratios which are in agreement with the Vegard's rule. Within the accuracy of our method no deviation for the Al incorporation in the differently oriented samples has been observed.