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

Abstract

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 × 10 19 cm −3 to 5·20 × 10 19 cm −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.

Phonon Scatterings in the Lattice Thermal Conductivity of Si_(1-x) Ge_x Alloy Nanowires: Theoretical Study

“…A detailed explanation of this effect can be found in previous work of GaN NWs [44] and Si NWs [46]. But a difference between previous work and present work is that while the specularity parameter depends on the size of GaN and Si NWs, in Si 1-x Ge x alloy NWs this depends on the alloy concentration, as shown in figure 2 ( the role of parameters will be discussed later).…”

“…Therefore, this parameter is used as an adjustable parameter. The change in Gruneisen parameter is small (as shown in Table 2) in these NWs, indicating that the Gruneisen parameter is not sizedependent, unlike Si and Ge NWs [46,47]. Thus, anharmonicity is not as powerful as alloy scattering of these alloy NWs at high temperatures.…”

“…This result is related to the phonon mean free path in various conditions, which suggests that dense surface features may enhance surface scattering, thereby hindering phonon transport and decreasing LTC [52]. Thus, size dependence is not as effective as alloy scattering, especially for relatively large diameters, and is not as significant as it is in the case of Si, Ge and GaN NWs [44,46,47].…”

“…Phonon confinement (which reduces phonon group velocity), however, can lead to considerable reductions of LTC in 147 nm Theoritical 147 nm Expt.data [21] 344 nm Theoritical 344 nm Expt.data [21] 229 nm Theoritical 229 nm Expt.data [21] 160 nm Theoritical 160 nm Expt.data [21] Soran Mohammed Mamand: Phonon Scatterings in the Lattice Thermal Conductivity of Si 1-x Ge x Alloy Nanowires: Theoretical Study NWs [25,45]. For the aforementioned sample of Si 1-x Ge x alloy NWs, phonon group velocities are assumed to be sizedependent (as a result of phonon confinement) and calculated using a thermodynamical approach, as used in previous work [44], with all the parameters of Si and Ge available at [46,47]. It is found that the decrease in the phonon group velocities is less than 5.5% of that of the bulk values of the samples, this is because of the relatively large diameter of the samples.…”

“…It is found that the decrease in the phonon group velocities is less than 5.5% of that of the bulk values of the samples, this is because of the relatively large diameter of the samples. The decrease in the phonon group velocity is significant for nanowires of diameter less than 100nm (called a small diameter in this work) [44][45][46]. So, the phonon group velocities of bulk Si and Ge (as shown in Table 1) were used (using Eq.…”