Characteristic wave speeds in the surface Brillouin scattering measurement of elastic constants of crystals

A simple and robust fitting procedure is presented for determining the three elastic constants of a cubic crystal from surface Brillouin scattering measurements carried out in the $⟨100⟩$ and $⟨110⟩$ directions in a (001) surface. The input data utilized are the Rayleigh surface wave velocity, the Lamb shoulder threshold velocity, and the longitudinal lateral wave velocity measured in the two directions. In fitting these velocities, use of simple closed-form expressions is made for the secular functions determining them. Corresponding expressions for the $⟨010⟩$ and ⟨101̄⟩ directions in the (101) plane are also provided. The formulas for the Lamb shoulder threshold, which have not previously been available in the literature, should prove to be particularly useful, as they apply also to thin supported film structures. The procedure is applied to the determination of the elastic constants of the ternary semiconductor alloy InAs0.91Sb0.09, yielding C₁₁=74.4 GPa, C₁₂=40.5 GPa, and C₄₄=37.8 GPa.