# GeTe/a-C Superlattices: Thermal Conductivity and Wave-Propagation

Paul Desmarchelier, Anne Tanguy, Valentina M Giordano, Konstantinos Termentzidis

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Paul Desmarchelier, Anne Tanguy, Valentina M Giordano, Konstantinos Termentzidis. GeTe/a-C Superlattices: Thermal Conductivity and Wave-Propagation. Nanoscale and Microscale Heat Transfer VII Eurotherm seminar No 114, May 2022, Palerme, Italy. hal-04787008

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https://hal.science/hal-04787008v1

Submitted on 16 Nov 2024

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
DESMARCHELIER Paul¹, TANGUY Anne²,³,GIORDANO Valentina³, TERMENTZIDIS Konstantinos¹

¹Univ Lyon, CNRS, INSA Lyon, CETHIL, UMR5008, ²Univ Lyon, INSA Lyon, CNRS, LaMCoS, UMR 5259, ³Univ Lyon 1-CNRS, ILM, UMR 5306, ⁴ONERA, University Paris-Saclay

## 1. c-GeTe/a-C Superlattice

GeTe has promising properties for both phase change memory and thermoelectric generation applications. One of them is its low thermal conductivity, the nanostructuration in superlattice can further decrease it. Here, we study the impact of the structure on thermal properties.

<figure><img src="image_2.png" /></figure>

[Chahine, Thesis, 2020]

## 3. Modelisation: Molecular Dynamics

* Simplified approach with a 3 body potential used for Si

* GeTe as a single atom

* Tuning of the impedance Z = ρν

* ν via Intensity the interaction

* ρ via Atomic Masses

Reproduction of a high impedance mismatch crystalline amorphous superlattice.

<table><thead><tr><th></th><th>SW</th><th>Ref.</th></tr></thead><tbody><tr><td>ν<sub>sound</sub> (km s<sup>-1</sup>)</td><td>a-C</td><td>9 14.5</td></tr><tr><td></td><td>GeTe</td><td>4 1.9</td></tr><tr><td>κ (W m<sup>-1</sup> K<sup>-1</sup>)</td><td>a-C</td><td>.93 ≈ 1<sup>1</sup></td></tr><tr><td></td><td>GeTe</td><td>44 ≈ 3.3</td></tr></tbody></table>

¹[Bullen et al., JAP, 2000]

## 6. Diffusivity

* Energy diffusivity (D) after a non coherent excitation

* Orientation change and interdiffusion create obstacle

* decrease of D<sub>CP</sub> and D<sub>IP</sub>

* Roughness periodicity also increases D<sub>IP</sub>

<figure><img src="image_3.png" /></figure>

## 7. Transmission in the In-Plane Direction

<figure><img src="image_4.png" /></figure>

* Interdiffusion of C decrease Λ<sub>L</sub> at high frequency

* Periodicity increases Λ<sub>T</sub> on a large spectrum

### A. q-Bandgap and Interaction Potential

* Variation of GeTe-C interaction

* Pot. 1 (this study): GeTe-C = averaged

* Pot. 2: GeTe-C = GeTe-GeTe

With Pot. 2 bandgap opening in the IP dir.

<figure><img src="image_5.png" /></figure>

## 2. Studied Geometries

Study the effects:

* of a-C thickness on dispersion (1-2 nm)

* of a-C layer roughness (via shape)

* Periodicity of the roughness

* Diffusion of a-C in the GeTe

<figure><img src="image_6.png" /></figure>

## 4. Thermal Conductivity (Equilibrium MD)

<table><thead><tr><th>(W m<sup>-1</sup> K<sup>-1</sup>)</th><th>Smooth</th><th>Double t<sub>a-C</sub></th><th>Period Rough</th><th>Rand. Rough</th><th>Orientation Change</th><th>Carbon Diffusion</th></tr></thead><tbody><tr><th>κ<sub>IP</sub></th><td><strong>3.4±.6</strong></td><td><strong>2.0±.5</strong></td><td>4.2±.4</td><td>3.7±.5</td><td>4.3±.5</td><td>3.4±.3</td></tr><tr><th>κ<sub>CP</sub></th><td><strong>1.3±.2</strong></td><td><strong>0.5±.3</strong></td><td>1.7±.1</td><td>0.94±.1</td><td>1.2±.2</td><td>1.1±.2</td></tr><tr><th>κ<sub>Total</sub></th><td>2.6±.2</td><td>1.5±.4</td><td>3.4±.1</td><td>2.8±.1</td><td>3.3±.1</td><td>2.6±.2</td></tr><tr><th>κ<sub>IP</sub>/κ<sub>CP</sub></th><td>2.6</td><td>3.7</td><td>2.5</td><td>4</td><td>3.6</td><td>3.2</td></tr></tbody></table>

* Impact of a-C thickness (t<sub>a-C</sub>) on κ<sub>IP</sub> and κ<sub>CP</sub>

* At constant t<sub>a-C</sub>

* Little impact of the geometry on κ<sub>IP</sub>

* Impact of the roughness periodicity on κ<sub>CP</sub>

## 6. Transmission in the Cross-Plane direction

* MFP (Λ) via the attenuation of wave-packet amplitude at low temperature

* Little difference between the configurations

* Smoothness marginally decreases Λ

<figure><img src="image_7.png" /></figure>

## 8. Transverse IP Propagation at 2 THz

<figure><img src="image_8.png" /></figure>

* Periodic roughness increases the coherent transmission

* Random roughness increases the diffusivity

## 9. Conclusion and Perspectives

* Low impact of geometry on κ<sub>IP</sub>

* The roughness periodicity

* Increases D and Λ<sub>IP</sub>

* Increases κ<sub>CP</sub>

* Orientation and interdiffusion affect D and Λ but not κ

* Importance of phonon scattering
However, there is a dependence on the C-GeTe interactions: study with a more realistic potential on-going.

## Acknowledgement

This work was done thanks to the project MAPS ANR-20-CE05-0046, and was granted access to the HPC resources of IDRIS under the allocation

2021-A0110911092, made by GENCI.