# High Surface Phonon-Polariton in-Plane Thermal Conductance along Coupled Films

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## Abstract

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## 1. Introduction

## 2. Method and Model

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scheme of (

**a**) a single SiO${}_{2}$ film and (

**b**) a three-layer structure (SiO${}_{2}$/Si/SiO${}_{2}$).

**Figure 2.**Real and imaginary parts of the relative permittivity of SiO${}_{2}$ reported in Ref [28].

**Figure 3.**Dispersion relations of SPhPs propagating along a SiO${}_{2}$ (1 $\mathsf{\mu}$m)/Si (10 $\mathsf{\mu}$m)/SiO${}_{2}$ (1 $\mathsf{\mu}$m) structure.

**Figure 4.**(

**a**) The in-plane propagation length and (

**b**) thermal conductance of SPhPs. The structure consists of the layered system, SiO${}_{2}$ (1 $\mathsf{\mu}$m)/Si (10 $\mathsf{\mu}$m)/SiO${}_{2}$ (1 $\mathsf{\mu}$m).

**Figure 5.**A comparison of the SPhPs thermal conductances of the SiO${}_{2}$/Si (10 $\mathsf{\mu}$m)/SiO${}_{2}$ three-layer structure and of a single SiO${}_{2}$ film at 300, 500 and 700 K, for different SiO${}_{2}$ thicknesses.

**Figure 6.**Cross-plane decay length in different media: Si (red solid line) and vacuum (black solid line) of the three-layer structure, and vacuum in the vicinity of the single film structure (black dashed line).

**Figure 7.**Normalized Poynting vector along the cross-plane direction for (

**a**) the single SiO${}_{2}$ film and (

**b**) the three-layer structure surrounded by vacuum.

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**MDPI and ACS Style**

Tachikawa, S.; Ordonez-Miranda, J.; Wu, Y.; Jalabert, L.; Anufriev, R.; Volz, S.; Nomura, M.
High Surface Phonon-Polariton in-Plane Thermal Conductance along Coupled Films. *Nanomaterials* **2020**, *10*, 1383.
https://doi.org/10.3390/nano10071383

**AMA Style**

Tachikawa S, Ordonez-Miranda J, Wu Y, Jalabert L, Anufriev R, Volz S, Nomura M.
High Surface Phonon-Polariton in-Plane Thermal Conductance along Coupled Films. *Nanomaterials*. 2020; 10(7):1383.
https://doi.org/10.3390/nano10071383

**Chicago/Turabian Style**

Tachikawa, Saeko, Jose Ordonez-Miranda, Yunhui Wu, Laurent Jalabert, Roman Anufriev, Sebastian Volz, and Masahiro Nomura.
2020. "High Surface Phonon-Polariton in-Plane Thermal Conductance along Coupled Films" *Nanomaterials* 10, no. 7: 1383.
https://doi.org/10.3390/nano10071383