Acoustic phonons play a critical role in energy transport in nanostructures. The dispersion of acoustic phonons strongly influences thermal conductivity. Recent observations show lower values of thermal conductivity in finite dimensional nanostructures than in the bulk material. In this work, we will present results for guided acoustic phonon modes in (a) a bilayered GaAs-Nb nanowire of rectangular cross section and (b) a trapezoidal Si nanowire. The former has been used for phonon counting in a nanocalorimeter for measuring thermal conductivity and the latter is commonly used in MEMS applications. A semi-analytical finite element (SAFE) analysis technique has been used to investigate the effects of layering, anisotropy, and boundaries on the dispersion of modes of propagation. Many interesting features of group velocities are found that show confinements around the corners, in the low velocity layer, and coupling of the longitudinal and flexural modes. These would strongly influence thermal conductivity and might provide means of nondestrutive evaluation of mechanical properties.

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