Microscopic Origin of the Reduced Thermal Conductivity of Silicon Nanowires

We designed nanowires with a tailored surface structure and composition and with specific core defects to investigate the microscopic origin of the reduced thermal conductivity of Si at the nanoscale. We considered a diameter (15 nm) comparable to that of systems fabricated in recent experiments and we computed the thermal conductivity using equilibrium molecular dynamics simulations. We found that the presence of a native oxide surface layer may account for a tenfold to $\sim 30$-fold decrease in conductivity, with respect to bulk Si, depending on the level of roughness. However it is only the combination of core defects and surface ripples that enables a decrease close to 2 orders of magnitude, similar to that reported experimentally.

Figure 1

Representative silicon nanowires generated in MD simulations. (a) Different surface terminations investigated in this study: reconstructed (sample N1), composed of an amorphous Si layer (sample N3) and of an amorphous silica layer (sample N6). (b) Samples with rippled surfaces (N7-N9) and with core defects (1 nm voids in N8 and grain boundaries in N9). The left hand side shows two cross sections of the wires grown along the $z$ direction: upper part, ($x$, $z$) plane and lower part ($x$, $y$)plane. The parameter $a$ represents the length of the unit cell in our MD simulations; $c$ is the distance between two ridges; and $d$ is the depth of the valleys of rippled surfaces. For samples N7, N8, and N9: $a=10\mathrm{nm}$, $c=3\mathrm{nm}$, and $d=1.5\mathrm{nm}$. All samples are described in detail in the text.

Figure 2

The normalized heat current autocorrelation function of samples N3 (a) and N7 (b) shown in Fig. 1, as a function of the correlation time ($t_{\mathrm{corr}}$) at room temperature. The insets show the calculated thermal conductivity as a function of the truncation time ($t_{\mathrm{tr}}$) used in the evaluation of the integral in Eq. (1).

Figure 3

Ratio between the computed thermal conductivity of bulk, crystalline Si (${\kappa }_{\mathrm{bulk}}$) and eleven Si nanowire (${\kappa }_{\mathrm{wire}}$) samples of 15 nm diameter, with different surface structure and composition, and with core defects (in the case of N8, N9, N10, and N11). N1 and N11: samples without amorphous surfaces; N2 to N5: samples with amorphous silicon surfaces; N6to N10: samples with amorphous silica surfaces. All samples are described in detail in the text (see also Fig. 1).

Figure 4

Comparison of the vibrational density of states (VDS) of samples N1, N6, N7, and N9 (see Fig. 1), computed from the autocorrelation function of the atomic velocities. (a) full VDS; (b) contributions to VDS of the velocities of core atoms; and (c) contributions to VDS of the surface shells.