Effects of nanoscale size dependent parameters on lattice thermal conductivity in Si nanowire

The effects of nanoscale size dependent parameters on lattice thermal conductivity are calculated using the Debye-Callaway model including transverse and longitudinal modes explicitly for Si nanowire with diameters of 115, 56, 37 and 22 nm. A direct method is used to calculate the group velocity for different size nanowire from their related calculated melting point. For all diameters considered, the effects of surface roughness, defects and transverse and longitudinal Gruneisen parameters are successfully used to correlate the calculated values of lattice thermal conductivity to that of the reported experimental curve. The obtained fitting value for mean Gruneisen parameter has a systematic dependence on all Si nanowire diameters changing from 0·791 for 115 nm diameter to 1·515 for the 22 nm nanowire diameter. The dependence also gave a suggested surface thickness of about 5–6 nm. The other two parameters were found to have partially systematic dependence for diameters 115, 56, and 37 nm for defects and 56, 37 and 22 nm for the roughness. When the diameters go down from 115 to 22 nm, the concentration of dislocation increased from 1·16 × 10¹⁹cm⁻³ to 5·20 × 10¹⁹cm⁻³ while the surface roughness P found to increase from 0·475 to 0·130 and the rms height deviation from the surface changes by about 1·66 in this range of diameter. The diameter dependence also indicates a strong control of surface effect in surface to bulk ratio for the 22 nm wire diameter.