Shape and orientation effects on the ballistic phonon thermal properties of ultra-scaled Si nanowires

The effect of geometrical confinement, atomic position, and orientation of silicon nanowires (SiNWs) on their thermal properties are investigated using the phonon dispersion obtained using a Modified Valence Force Field (MVFF) model. The specific heat (C_ν) and the ballistic thermal conductance (κ_l^bal) shows anisotropic variation with changing cross-section shape and size of the SiNWs. The C_ν increases with decreasing cross-section size for all the wires. The triangular wires show the largest C_ν due to their highest surface-to-volume ratio. The square wires with [110] orientation show the maximum κ_l^bal because they have the highest number of conducting phonon modes. At the nano-scale a universal scaling law for both C_ν and κ_l^bal are obtained with respect to the number of atoms in the unit cell. This scaling is independent of the shape, size, and orientation of the SiNWs, revealing a direct correlation of the lattice thermal properties to the atomistic properties of the nanowires. Thus, engineering the SiNW cross-section shape, size, and orientation open up new ways of tuning the thermal properties in the nanometer regime.