By Nidhi DhullReviewed by Lexie CornerAug 20 2024
A recent article published in npj Computational Materials explored the phenomenon of phonon funneling to improve the thermal conductivity of semiconductor thin films through systematic atomistic simulations.
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This study demonstrated that nanoscale boundary scattering could increase the phonon thermal conductivity in thin films, surpassing the limitations of traditional macroscale heat diffusion.
Background
Energy diffusion from hot to cold, as dictated by the second law of thermodynamics, influences the efficiency and failure of various technologies. However, in nanoscale devices, temperature gradients are highly dependent on interfaces and boundaries.
Such devices exhibit local thermal hot spots (due to size-dependent effects), where most heat carriers, with mean free paths longer than the device's characteristic length scales, are scattered at the boundaries.
This non-diffusive transport significantly reduces the thermal conductivity of semiconducting thin films compared to bulk materials. The spacing between nanoscale heat sources in a thin film can further impact thermal transport.
The complex dynamics of energy carriers, which conduct heat in various directions, limit our understanding of nanoscale devices and challenge efforts to overcome size-dependent thermal transport issues. This study employed computational methods to demonstrate increased thermal conductance across thin films through phonon funneling.
Computational Methods
Systematic atomistic simulations were conducted on silicon and germanium thin films using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package to investigate their thermal properties. The Stillinger-Weber (SW) potential was employed to model the interatomic interactions in both systems.
Nano-heaters were periodically placed on top of the thin films, with a width equal to half of the period length, while nano-coolers were positioned at the opposite ends. These nanostructures had a fixed duty cycle of 50 %, and the thin film thickness varied from 15 to 59 nm.
After the initial structure creation, energy minimization was performed, followed by raising the system's temperature from 0 to 300 K and allowing it to equilibrate.
The number of atoms in the simulations varied between approximately 71,000 and 800,000, depending on the nano-heater/nano-cooler period and film thickness. However, the total number of nano-heater/cooler periods remained constant across all cases.
The thermal conductivity of the thin films was directly determined using Fourier's law via the non-equilibrium molecular dynamics (NEMD) method. The temperature gradient was averaged over the in-plane direction of the film to calculate the effective cross-plane thermal conductivities.
After equilibration, the heat baths were activated by adding or subtracting 3 eV/ps of energy from the hot and cold baths to establish a temperature gradient. One-dimensional temperature gradients were then extracted to calculate the effective thermal conductivity of the thin films.
Finally, individual atomic kinetic energies were calculated to visualize the temperature profiles in the silicon and germanium systems.
Results and Discussion
The steady-state temperature profiles resulting from the nanostructures on the top and bottom of the thin films differed significantly from those produced by conventional diffusive heat flow. Replacing uniform heat baths with nano-heaters and nano-coolers led to a substantial increase in the effective cross-plane thermal conductivities (Keff) of germanium thin films, with the effect being enhanced at shorter periods.
The maximum increase in Keff was observed in the thinnest (15 nm) film, attributed to the phonon wavelength spectrum of 1-15 nm in bulk germanium. Additionally, germanium thin films with nano-heaters on top and a heat sink at the bottom did not show significant dependence of Keff on the period of nano-heaters.
However, Keff in the nano-heater/cooler configuration was highly dependent on the period, providing greater control over thermal transport across semiconducting thin films. This enhanced cross-plane heat conduction in the thin films with nanoscale heat baths was due to efficient phonon funneling along the applied heat flux and a reduction in specular back-reflection of phonons from the heat baths.
Keff increased with the height of the nanoscale heat baths up to approximately 9 nm, owing to enhanced phonon scattering at these longer heat baths, which further reduced specular backscattering. Notably, even small heat bath heights (<3 nm) led to a substantial increase in Keff compared to uniform heat baths, highlighting the critical role of phonon funneling in thin films with periodic nano-heaters and nano-coolers.
Conclusion
Overall, the researchers demonstrated a more than 7-fold increase in thermal conductance across thin films by strategically placing periodic, closely spaced nano-heaters on top of the thin films and tightly packed nano-coolers at the opposite ends.
The enhancement in thermal conductivity was driven by phonon funneling, which became more pronounced with increased anharmonicities resulting from the interaction of ballistic phonons originating from adjacent heat baths. This anharmonic scattering of phonons was evidenced by the 'light-bulb'-shaped temperature profiles observed in the thin films.
Limiting specular backscattering of phonons at the film/heat bath interfaces further enhanced the cross-plane heat conduction in thin films. This proposed nanostructure configuration offers a promising approach to improving the effective cross-plane thermal conductivities of semiconductor thin films.
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Journal Reference
Dionne, C. J., Thakur, S., Scholz, N., Hopkins, P., Giri, A. (2024). Enhancing the thermal conductivity of semiconductor thin films via phonon funneling. npj Computational Materials. DOI: 10.1038/s41524-024-01364-w, https://www.nature.com/articles/s41524-024-01364-w
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