Atomistic calculation of the thermal conductance of large scale bulk-nanowire junctions

We have developed a stable and efficient kernel method to compute thermal transport in open systems, based on the scattering-matrix approach. This method is applied to compute the thermal conductance of a junction between bulk silicon and silicon nanowires with diameter up to 10 nm. We have found that beyond a threshold diameter of 7 nm, transmission spectra and contact conductances scale with the cross section of the contact surface, whereas deviations from this general trend are observed in thinner wires. This result allows us to predict the thermal resistance of bulk-nanowire interfaces with larger cross sections than those tractable with atomistic simulations, and indicate the characteristic size beyond which atomistic systems can in principle be treated accurately by mean-field theories. Our calculations also elucidate how dimensionality reduction and shape affect interfacial heat transport.

Figure 1

Silicon nanowire and bulk interconnect partitioning. The central defect is generally further subdivided in order to speed up the computation. The bulk and wire reservoirs are organized as a pile of periodic slices ($S$ and $S$${}^{\prime }$, respectively) indexed starting from the contact areas.

Figure 2

Transmission spectra (a) and thermal conductance as a function of the temperature (b) for a set of bulk-nanowire contacts. Both data sets are normalized with respect to the interface area expressed either in nm${}^2$ (conductance) or in number of atoms at the contact interface (transmission).

Figure 3

Band structure of the bulk contact (left panel) and reflection spectra of the nanowire modes normalized with respect to the diameter (center panel) and the surface area (right panel) of the SiNW.

Figure 4

Volumetric representation of the norm of the energy flux at the interface of a 10-nm-thick silicon nanowire, corresponding to channels with frequency of 0.25, 0.75, 2, and 4 THz. In the 0.75 and 2 THz case, thermal transport mainly occurs in a thin subsurface layer (red color area).

Figure 5

Number of transmission channels for a set of bulk-nanowire contacts of different diameter and shape. The data are normalized with respect to the interface area expressed in number of atoms. Data are compared to the number of channels in a three-dimensional periodic bulk to highlight the effect of dimensionality reduction. All the nanowires considered here are larger than the 7-nm diameter threshold.