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

# Study of anomalous effects in thermal conductivity in c-GaN/a-SiO₂ nano-composites

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

Desmarchelier Paul¹² Termendzidis Konstantinos¹, Tanguy Anne²

¹CETHIL, INSA Lyon, Villeurbanne, France, ²LaMCoS, INSA Lyon, Villeurbanne Cedex, France.

## 1 Introduction and Configurations

With the increasing demand of efficiency in electronic devices, a good thermal management starts to be crucial. In this regard nanocomposite can be a good solution to tune the conductivity of materials. Here we further investigate previous results [5], that shows that the thermal conductivity can depend significantly on the relative orientation of

c-GaN inclusion in a a-SiO₂ matrix. Which is not taken into account in the Effective Medium Approach. We try to understand how this percolation can take place through molecular dynamics simulation.

<figure><img src="image_3.png" /><figcaption>"ANISO": rotated crystals</figcaption></figure>

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

<table><thead><tr><th></th><th>c - GaN</th><th>a - SiO<sub>2</sub></th><th>ISO</th><th>ANISO</th></tr></thead><tbody><tr><td>κ W/mK</td><td>160</td><td>1.1</td><td>24,9</td><td>14.8</td></tr></tbody></table>

## 4 VDOS nano sphere Composites

The VDOS is influenced by the size of the nano inclusion

### ► Inclusions Size

<figure><img src="image_5.png" /><figcaption>VDOS free GaN sphere</figcaption></figure>

### ► Matrix Interface

<figure><img src="image_6.png" /><figcaption>VDOS GaN sphere in a-SiO₂</figcaption></figure>

### ► Red Shift of the acoustic peak

* Modes relative importance [4]

### ► More high frequencies modes

* little to no existing studies

### ► In both case with the reduction of the radius

* filling of the band gap

* reduction of the sharpness of the main peaks

### ► Influence on the thermal conductivity

* tailoring of the EMA

## 6 Wave packet propagation

Comparison of the propagation of an excitation from the inclusion in the middle

### ► No obvious differences at 0.5 THz

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

## 2 Energie transport

### ► Orientation dependent thermal conductivity

* Coherent wave transmission between inclusions

* Possible if Mean Free Path in SiO₂ ~ l_incl

* If possible at low frequency for longitudinal waves

► Coherent with experimental results[7, 6]

<figure><img src="image_8.png" /><figcaption>Mean Free Path in SiO₂ from wave packet attenuation [1]</figcaption></figure>

## 3 Vibrational Density of State

To be transmitted mode of the frequency that travels should be allowed in both matrix and inclusion

### ► Overlap between the DOS at low frequency

* in DOS of the disjunct materials

<figure><img src="image_9.png" /><figcaption>Transverse as non compressive [2]</figcaption></figure>

## 5 Dynamical Structure Factor

We use the mode resolved dynamical structure[3]

### ► for Bulk a-SiO₂

* From the slope of the first phonons

* v_L(v) > v_T(v)

<figure><img src="image_10.png" /></figure>

### ► ISO/ANISO

* Apparition of a new band frequency corresponding to the GaN peak

* no obvious differences

<figure><img src="image_11.png" /><figcaption>S(q, v) ISO (L)</figcaption></figure>

## Summary and prospective

### ► Non trivial effect of size / interface to the VDOS

### ► No obvious difference one the propagative part

* no supplementary channel in S(q, ω)

### ► Prospective

* Computation of κ via another method (NEMD)

* Test of the propagation at characteristic frequencies

► Size of the inclusions

► Distance between inclusion

## References

[1] Y. M. Beltukov, C. Fusco, D. A. Parshin, and A. Tanguy. "Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: The effect of bond directionality". In: *Physical Review E* 93.2 (2016). [5]

[2] Y. M. Beltukov, C. Fusco, A. Tanguy, and D. A. Parshin. "Transverse and longitudinal vibrations in amorphous silicon". In: *Journal of Physics: Conference Series* 661.1 (2015). [6]

[3] T. Damart, V. M. Giordano, and A. Tanguy. "Nanocrystalline inclusions as a low-pass filter for thermal transport in a -Si". In: *Physical Review B - Condensed Matter and Materials Physics* 92.9 (2015). [7]

[4] U. F. Savoie, E. Salazar, J. A. Páez, and J. L. Corzán. "Size and shape dependence of the vibrational dynamics". In: *Physical Review B - Condensed Matter and Materials Physics* 56.2 (1997).

K. Termentzidis, V. M. Giordano, M. Katsikini, E. Paloura, G. Pernot, M. Verdier, D. Lacroix, I. Karakostas, and J. Kioseogloud. "Enhanced thermal conductivity in percolating nanocomposites: a molecular dynamics investigation". In: *Nanoscale* 10.46 (2018).

R. Vacher, J. Pelous, and E. Courtens. "Mean free path of high-frequency acoustic excitations in glasses with application to vitreous silica". In: *Physical Review B - Condensed Matter and Materials Physics* 56.2 (1997).

J. Yang, Q. Zhang, Z. Cui, M. Gerboth, Y. Zhao, T. T. Xu, D. G. Walker, and D. Li. "Ballistic Phonons in Amorphous Nanocomposites". In: *Physical Review B* 88.011101 (2013).