# Phononic thermal resistance due to a finite periodic array of nano-scatterers

## Abstract

The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetric objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.

- Authors:

- Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, F-69621 Villeurbanne (France)

- Publication Date:

- OSTI Identifier:
- 22597725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 120; Journal Issue: 4; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DIFFRACTION; FOURIER TRANSFORMATION; FREQUENCY DEPENDENCE; HOLES; KAPITZA RESISTANCE; PHONONS; POLARIZATION; ROUGHNESS; SILICON; TEMPERATURE DEPENDENCE; TEMPERATURE RANGE 0013-0065 K; TEMPERATURE RANGE 0065-0273 K; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Trang Nghiêm, T. T., and Chapuis, Pierre-Olivier.
```*Phononic thermal resistance due to a finite periodic array of nano-scatterers*. United States: N. p., 2016.
Web. doi:10.1063/1.4959803.

```
Trang Nghiêm, T. T., & Chapuis, Pierre-Olivier.
```*Phononic thermal resistance due to a finite periodic array of nano-scatterers*. United States. doi:10.1063/1.4959803.

```
Trang Nghiêm, T. T., and Chapuis, Pierre-Olivier. Thu .
"Phononic thermal resistance due to a finite periodic array of nano-scatterers". United States.
doi:10.1063/1.4959803.
```

```
@article{osti_22597725,
```

title = {Phononic thermal resistance due to a finite periodic array of nano-scatterers},

author = {Trang Nghiêm, T. T. and Chapuis, Pierre-Olivier},

abstractNote = {The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetric objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.},

doi = {10.1063/1.4959803},

journal = {Journal of Applied Physics},

number = 4,

volume = 120,

place = {United States},

year = {Thu Jul 28 00:00:00 EDT 2016},

month = {Thu Jul 28 00:00:00 EDT 2016}

}