Effect of a ${\mathrm{SiO}}_2$ layer on the thermal transport properties of $\langle 100\rangle \mathrm{Si}$ nanowires: A molecular dynamics study

The presence of a ${\mathrm{SiO}}_2$ layer on Si nanowires (SiNWs) has been found through molecular dynamics simulation to reduce their thermal conductivity $\left(\kappa \right)$, with $\kappa$ approaching the amorphous limit of Si as the oxide layer thickness is increased. Through analysis of the phonon energy dispersion and vibrational density of states (VDOS) spectrum, this decrease in $\kappa$ was attributed to dispersionless vibrational states that appear in the low energy range below 4 THz as a result of the lattice vibration of Si atoms near the ${\mathrm{SiO}}_2/\mathrm{Si}$ interface. The ${\mathrm{SiO}}_2$ layer also induced a low-frequency tail in the VDOS spectrum, the length of which was more closely correlated to the reduction in $\kappa$ than the frequency-integrated value of the VDOS spectrum. These findings provide a more refined explanation for the decrease in $\kappa$ than has been previously observed, and contribute to providing a greater understanding of the anomalistic vibration near the interface that is critical to determining the heat conductivity in nanoscale materials.

Figure 1

Molecular dynamics simulation models of a SiNW with (a) 0, (b) 2, (c) 3, or (d) 5 monolayers (ML) of oxide film.

Figure 2

Temperature gradient along the length of a SiNW. A linear fit is shown by the red solid line.

Figure 3

(a) Thermal conductivity $\kappa$ of a SiNW as a function of its cross-sectional area. Solid circles represent $\kappa$ values obtained by molecular dynamics simulation. Filled and open squares represent a simple estimation of $\kappa$ with a ${\kappa }_{{\mathrm{SiO}}_2}$ of 1.0 and 2.0 W/mK, respectively. The shaded area is the model prediction with $1.0<{\kappa }_{{\text{SiO}}_2}<2.0$ W/mK, in which ${\kappa }_{\mathrm{Si}}$ is assumed to be equal to the $\kappa$ of bare SiNW (7.6 W/mK).

Figure 4

Phonon dispersion relation of acoustic phonon modes. (a) Longitudinal and (b) transverse acoustic mode of a SiNW with 0, 2, 3, or 5 monolayers of oxide film.

Figure 5

Intensity of the dynamical structure factor as a function of frequency for a SiNW with 0, 2, 3, or 5 monolayers of oxide film. The wave vector is $(2\pi /a)(0.5,0,0)$.

Figure 6

Partial dynamical structure factor of a SiNW covered with 3 monolayers of oxide. (a) Whole body, (b) Si core encompassing the 11th to 13th atomic layers from the surface, and (c) the Si surface region between the second and fourth atomic layers.

Figure 7

Vibrational density of states for bare and oxidized SiNWs. (a) Whole body, (b) Si core region (11th to 13th atomic layer from the surface), and (c) Si surface region (second to fourth atomic layer).

Figure 8

Illustration of the four VDOS parameters used to characterize its shape: (i) area, (ii) slope, (iii) peak, and (iv) width of the VDOS curve. The VDOS curve was fitted at lower frequencies (1.0–4.0 THz) by a linear function, but a quadratic function was used at higher frequencies (4.0–9.0 THz).

Figure 9

Dependence of $\kappa$ on the (i) area, (ii) slope, (iii) peak, and (iv) width of the VDOS curve. The coefficient of determination $R^2$ is also shown in each graph.