# Photothermal Effects and Heat Conduction in Nanogranular Silicon Films

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Micro-Raman Spectroscopy

^{−1}. The pixel size on the iCCD camera and entrance slit to the spectrometer were 13 and 150 μm, respectively. All reported intensities, positions and linewidths of measured Raman peaks are the results of the Lorentzian fitting.

#### 2.3. Local Temperature Measurements

#### 2.4. FDTD Electromagnetic and FEM Heat Modeling

_{2}were taken from Lumerical software material libraries (Ansys, Canonsburg, PA, USA) for Si NPs and glass substrate, respectively.

## 3. Results and Discussion

#### 3.1. FDTD Modeling of Light Penetration

#### 3.2. Laser-Induced Phase Transition in Si Nanogranular Films

^{−1}. These bands differ from the well-known cubic lattice with the Raman peak at 520 cm

^{−1}at room temperature. This phase transition is supposed to be not purely thermally induced but also photo-induced. The formation of the hex-Si phase is accompanied by the absorption of electromagnetic radiation and a reduction in the overall mechanical stresses and, consequently, by partial quenching of the splitting between LO and TO phonon modes [22].

^{−1}correspond, respectively, to the LO and TO phonon modes of cubic c-Si under photo-thermal and mechanical stresses caused by a temperature gradient through Si NP films. At the threshold laser power of 3.2 mW, the photo-induced structural relaxation in the overheated part of Si NPs leads to the formation of the hexagonal (hex-Si) phase characterized by Raman bands centered at 504 and 497 cm

^{−1}.

#### 3.3. Laser Induced Heating and Thermal Conductivity of Si Nanogranular Films

^{−1}shifts towards lower phonon frequencies when the laser power increases. The frequency shifts of the Stokes and anti-Stokes peaks are symmetric with respect to the Rayleigh line because they correspond to the energy difference between the same upper and lower resonant states [62]. A laser heating-induced red-shift of the Raman peak as high as 20 cm

^{−1}over the 0.07–3.2 mW range of the incident laser powers is also accompanied by a characteristic spectral line broadening.

_{2}shells and leading to an additional decrease in their $k$ [68].

## 4. Conclusions

## Supplementary Materials

^{3}, ×10

^{15}) at different depths (z) of 4 µm thick porous Si NPs film on 4 µm thick glass substrate: (a) z = 0.1 µm, (b) z = 1 µm, (c) z = 2 µm, (d) z = 3 µm. Table S1: Room temperature thermal conductivity values of nanostructurely voided Si.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**SEM images of Si nanogranular film (

**a**) and a closer view of Si NPs (

**b**) within a film with a typical NP size of 100 ± 50 nm (

**c**).

**Figure 2.**FDTD simulated (

**a**) nanogranular porous Si NP film on a continuum SiO

_{2}glass substrate, and (

**b**) in−depth distribution of incoming light (532 nm wavelength) field intensity in normalized units (n.u.) in the nanogranular porous Si NP film (70% porosity, 4 µm depth (along z-direction) and (1.6 µm × 1.6 µm) lateral area within xy-plane with the laser beam diameter (2 µm) fitting into this lateral area). The incident laser beam is shown with wave-vector $\overrightarrow{k}$ and polarization $\overrightarrow{P}$. * absorption depth of the incoming light (532 nm), ** porous Si NP film/silica glass substrate interface.

**Figure 3.**Deconvoluted Raman spectra of the films formed by Si NPs with average size of 100 nm demonstrating a photo-induced transition of phase from cubic (

**a**–

**c**) to hexagonal one (

**d**).

**Figure 4.**(

**a**) Measured Stokes and ant-Stokes Raman spectra at various laser powers and (

**b**) corresponding laser induced temperature rises in the Si NP films with various thicknesses and a bulk crystalline silicon substrate (c-Si) versus laser power densities.

**Figure 5.**In-depth $T$ distribution for porous Si NP films deposited on 1 mm thick SiO

_{2}glass substrate with the film thickness of (

**a**) 50 µm and (

**b**) 2 µm. Film heating is induced by a 532 nm wavelength laser beam of 2 µm diameter focused on the film surface.

**Figure 6.**Measured thermal conductivity values of our Si nanogranular films with 70% porosity in comparison with other types of nanostructurally voided Si films (taken from the literature) versus different film thicknesses.

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**MDPI and ACS Style**

Kurbanova, B.A.; Mussabek, G.K.; Timoshenko, V.Y.; Lysenko, V.; Utegulov, Z.N. Photothermal Effects and Heat Conduction in Nanogranular Silicon Films. *Nanomaterials* **2021**, *11*, 2379.
https://doi.org/10.3390/nano11092379

**AMA Style**

Kurbanova BA, Mussabek GK, Timoshenko VY, Lysenko V, Utegulov ZN. Photothermal Effects and Heat Conduction in Nanogranular Silicon Films. *Nanomaterials*. 2021; 11(9):2379.
https://doi.org/10.3390/nano11092379

**Chicago/Turabian Style**

Kurbanova, Bayan A., Gauhar K. Mussabek, Viktor Y. Timoshenko, Vladimir Lysenko, and Zhandos N. Utegulov. 2021. "Photothermal Effects and Heat Conduction in Nanogranular Silicon Films" *Nanomaterials* 11, no. 9: 2379.
https://doi.org/10.3390/nano11092379