# Study of non equilibrium phase transitions in silicon under femtosecond laser excitation

Tatiana Itina, Dmitry S Ivanov

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Tatiana Itina, Dmitry S Ivanov. Study of non equilibrium phase transitions in silicon under femtosecond laser excitation. FORUM ILP: 13ème Forum Lasers et Plasmas, Invited talk, ILP, CPHT, France, Jun 2025, Le Plan de la Tour (Var), France. ujm-05118193

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Submitted on 18 Jun 2025

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# Study of non-equilibrium phase transitions in silicon under femtosecond laser excitation

Tatiana E. ITINA, Dmitry S. IVANOV

Lab. Hubert Curien, UMR CNRS 5516, UJM, Campus Manufacture, 42000 St-Étienne, France

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# MOTIVATIONS

Currently, contact silicides are critical building blocks of micro and nanoelectronic devices that are widely integrated in Complementary Metal Oxide Semiconductors (CMOS).

For these contacts to be optimal, it is necessary that the silicide layers meet specifications, namely the requirements for ultrathin silicides layers (between 10 and 20 nm), for which *pre-amorphization* of silicon surface is usually introduced prior the reactive metal deposition.

**Si amorphization for microelectronics:** femtosecond laser-based treatments for an efficient alternative processing holding promises to meet the requirements of the highly demanding sector (microelectronics).

<figure><img src="image_8.png" /><figcaption>TEM C54-TiSi₂ contacts, ST-Microelectronics</figcaption></figure>

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www.afs-jena.de/applications/silicon-processing

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https://link.springer.com/rwe/10.1007/978-3-319-69537-2_15-1

ANR LAMORSIM:
LabHC, LP3 and
ST-Microelectronics
Technological advances in amorphization of Si

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https://global.sharp/corporate/news/180327.html

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A. Engel, Th. Pflug, M. Olbrich, and A. Horn

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Laserinstitut
Hochschule Mittweida

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David Grojo et al, Laser Photonics Rev. 2024, 2301327

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C. Florian et al. Materials 2021, 14(7), 1651
Examples of previous experimental results

<figure><img src="image_22.png" /><figcaption>Femtosecond laser-induced amorphization
at $\lambda_{laser} = 1.55$ µm on Si<111></figcaption></figure>

https://www.sciencedirect.com/science/article/pii/S0038109803010111

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M. Garcia-Lechuga at al.,
Advanced Optical Materials 9(17):2100400, 2021

C. Florian et al. Materials 2021, 14(7), 1651
Examples of previous experimental results

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For Si<111> the fs-laser-induced melt layer transfers completely into amorphous material.

For Si<100> only an upper part of the melt pool finally turns amorphous.
# Our main objectives

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Adv. Optical Mater. 2021, 2100400

<caption>Laser-induced surface modifications</caption>

* Better understanding is required of the mechanisms involved in fs laser -induced amorphization of Si under conditions of typical microelectronics applications

* Laser-amorphized layer thickness should be smaller than ~ 50 nm and ideally reach ~10 nm.

* To find the optimum laser parameters for the ultra-thin amorphization of initially crystallin Si near the surface. This should be done firstly on blankets wafers and then for the nano-structured (patterned) wafers.

* The main technological objective is to develop a novel and reliable laser-based method of the optimized and minimized surface amorphization to satisfy the requirements of not only the above considered application, but also to open the way for numerous other laser applications in microelectronics.
Theoretical models of Si melting, annealing, amorphization

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M. He et al. J. Appl. Phys. 136, 213103 (2024)

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# Modeling of ultra-short laser interactions

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## 1. **Thermal (TTM) models**

$$C_e \frac{\partial T_e}{\partial t} = \frac{\partial}{\partial z} \left( k_e \frac{\partial T_e}{\partial z} \right) - \gamma (T_e - T_i) + Q_{abs}$$

$$C_i \frac{\partial T_i}{\partial t} = \frac{\partial}{\partial z} \left( k_i \frac{\partial T_i}{\partial z} \right) + \gamma (T_e - T_i)$$

⇒ **Melting without ablation**

⇒ **Many assumptions**

⇒ **No motion**

⇒ **Hard to describe phase changes**

⇒ **Have to know many coefficients**

## 2. Molecular dynamics approach (MD or TTM-MD)

⇒ **melting, ablation**

⇒ **interaction potential is often assumed to be constant**

## 3. Hydrodynamics (1T, 2T, one fluid, two fluids, etc.)

⇒ **Need all transport coefficients**

⇒ **Need equation of state (EOS)**

⇒ **Need additional sub-models for ionization**
Material ejection in femtosecond laser ablation

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Two-temperature model (TTM)

$$C_e(T_e) \frac{\partial T_e}{\partial t} = \nabla [K_e(T_e) \nabla T_e] - G(T_e - T_l) + S(z,t),$$

$$C_l(T_l) \frac{\partial T_l}{\partial t} = \nabla [K_l(T_l) \nabla T_l] + G(T_e - T_l),$$

Kaganov et al. Sov. Phys. JETP 4, 173 (1957)

TTM-MD model

Ivanov & Zhigilei, (2003)

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$$C_e(T_e) \frac{\partial T_e}{\partial t} = \frac{\partial}{\partial z} \left( K_e(T_e) \frac{\partial}{\partial z} T_e \right) - G(T_e - T_l) + S(z,t), \quad \text{TTM}$$

$$m_i \frac{d^2 \mathbf{r}_i}{dt^2} = \mathbf{F}_i + \xi m_i \mathbf{v}_i^T, \quad \text{MD}$$

$$\xi = \frac{1}{n} \sum_{k=1}^{n} G V_N (T_e^k - T_l) / \sum_i m_i (\mathbf{v}_i^T)^2$$
nTTM-MD for Semiconductors (Si)

* Modification of the classical TTM-MD model

* Carriers (electrons and holes)

* Conduction band modifications

* Including carrier excitation/relaxation

* Ambipolar diffusion

* Different potentials

* Etc.
n - Model for silicon

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$$ \frac{\partial n}{\partial t} = Source_n(\vec{r}, t) + \theta n - \gamma n^3 - \text{div}(J) $$

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Combined MD-nTTM model

$$
\begin{align*}
\frac{dI(z, t)}{dz} &= -(\textcolor{red}{\boldsymbol{\alpha}} + \textcolor{green}{\boldsymbol{\alpha}_{FCA}}(\boldsymbol{\varepsilon}(N_e))) I(z, t) - \textcolor{blue}{\boldsymbol{\beta}} I^2(z, t) \\
\frac{\partial n_e}{\partial t} &= \frac{\textcolor{red}{\boldsymbol{\alpha}} I(z, t)}{h\nu} + \frac{\textcolor{blue}{\boldsymbol{\beta}} I^2(z, t)}{2h\nu} + \delta n_e - \gamma N_e^3 - \nabla \cdot \vec{J}(n_e, T_e, E_g) \\
\frac{\partial U_e(N_e, T_e, E_g)}{\partial t} &= (\textcolor{red}{\boldsymbol{\alpha}} + \textcolor{green}{\boldsymbol{\alpha}_{FCA}}(\boldsymbol{\varepsilon}(N_e))) I(z, t) + \textcolor{blue}{\boldsymbol{\beta}} I^2(z, t) \\
&\quad - \nabla \cdot \vec{W}(N_e, T_e, E_g) - \frac{C_{e-h}(N_e, T_e, E_g)}{\tau_e} (T_e - T_l) \\
C_l \frac{\partial T_l}{\partial t} &= \vec{\nabla} \cdot (\kappa \vec{\nabla} T_l) + \frac{C_{e-h}(N_e, T_e, E_g)}{\tau_e} (T_e - T_l) \rightarrow m_i \frac{d\vec{r}_i}{dt^2} = - \sum_{j=1,N} \vec{\nabla} U(\vec{r}_{ij}, T_e) + \xi m_i \vec{V}_i^T
\end{align*}
$$

1. TTM + additional eq for the
density of carriers

2. Implicit Crank-Nicolson
algorithm needs parallel.

3. Drude-Lorenz model for
reflectivity and free car abs

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MD-nTTM model verification

* 100 fs pulse at 800 nm, $F = 0.3 \text{ J/cm}^2$

* Total energy is conserved

* Can account for a pre-pulse

* Electron temperature deviation

* Free carrier excitation and conductivity are well coupled to Molecular Dynamics

NB: Non-reflecting boundary conditions at the bottom of the sample

Typical laser fluences ranging from 0.3 to 1.5 J/cm².

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Melting kinetics in <001> and <111> crystal orientation and depth of melting

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1. Two identical samples with <001> and <111>

2. 100fs, 0.3 J/cm2

3. Heterogeneous vs homogeneous melting mechanism

4. <001> results in 26% more melt

5. Speed of sound in <111> is 8% larger

6. Optical properties are refined
Melting kinetics of Si vs metals

<figure><img src="image_55.png" /><figcaption>Ni
1 ps pulse, fluence 129 mJ/cm², 100 nm Ni film</figcaption></figure>

<figure><img src="image_56.png" /><figcaption>Ni
4500 m/s
Time, ps</figcaption></figure>

<figure><img src="image_57.png" /><figcaption>Si
270 fs pulse, fluence 400 mJ/cm², 1000 nm Si film
P, GPa</figcaption></figure>

<figure><img src="image_58.png" /><figcaption>Si
800 m/s
Time, ps</figcaption></figure>

Ni: face
center cubic

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1. Well distinguished solid-liquid interface propagation

2. T/P interplay results in both heterogeneous and homogeneous melting mechanism

3. Melting starts upon the **drop** in pressure

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Si: Diamon cubic

1. Rapid/instant advancement of the melting front

2. T/P interplay results in mainly homogeneous melting mechanism

3. Melting starts upon the **rise** of pressure
Crystal structure effect on the solid-liquid transition in metals and Si

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$$ \begin{gathered} \text{At P} = 0 \text{ Pa} \\ T_m = 1439 \text{ K} \end{gathered} $$

Face center cubic structure: $V_{\text{melt}} = 5\%$

Volume expands resulting in internal stresses increase

$$ \left(\frac{dT}{dP}\right)_m = \frac{\Delta V_m}{\Delta S_m} = \frac{T_m \Delta V_m}{\Delta H_m} $$

1. For metals **dT/dP > 0**, so increase of P reinforce the crystal stability against of melting.

2. For Si **dT/dP < 0**, so the increase of pressure destabilize the crystal structure and facilitates the onset of melting.

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$$ \begin{gathered} \text{At P} = 0 \text{ Pa} \\ T_m = 1699 \text{ K} \end{gathered} $$

Open diamond crystal structure: $V_{\text{melt}} = -7.5\%$

Volume contracts resulting in internal stresses drop
Melting kinetics of Si vs metals

<figure><img src="image_63.png" /><figcaption>Ni
1 ps pulse, fluence 129 mJ/cm², 100 nm Ni film</figcaption></figure>

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<figure><img src="image_65.png" /><figcaption>Si
270 fs pulse, fluence 400 mJ/cm², 1000 nm Si film</figcaption></figure>

<figure><img src="image_66.png" /><figcaption>Ni: face
center cubic</figcaption></figure>

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1. At the fluences around melting threshold the solid-liquid transition via **heterogeneous mechanism** is more energetically favorable.

<figure><img src="image_68.png" /><figcaption>Si: Diamon cubic</figcaption></figure>

1. At the fluences around melting threshold, the **homogeneous melting** mechanism plays a determinant role and makes formation of the solid-liquid interface at a significant depth instantly.
Central Symmetry Parameter (CSP)

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CSP = 0.97 threshold value

1. The effect of crystal structure makes the homogeneous mechanism of melting in Si **dominant and the only** mechanism at fluences above the melting threshold.

2. Due to instant relaxation of the laser-induced stresses at the surface, the heterogeneous melting mechanism is observed within **few presurface nm only**.

3. Negative volume of melting for Si make the formation of **amorphous phase preferable**.

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Due to ~ 10% higher speed of sound in <111> the melting threshold is lower, but the optical properties during the laser light absorption must be considered carefully.
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<001>

50 ps

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<001>

100 ps

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Position, nm

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<111>

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red: T, K

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<111>

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red: T, K

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1000 nm Si target after 270fs at 0.32 J/cm2 at 800nm

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Depth of melting vs. fluence

1. Melting threshold is ~0.3 J/cm²

2. The results are for <001>

3. There some experimental results matching our measurements

4. Two melting mechanisms at low fluence

5. Heterogeneous mechanism is suppressed at high fluences

Agreement and some discrepancy

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Theory vs experiment : comparison

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$$d_{\text{melt}} = A \ln(F/F_{\text{th}}) + B$$

$$A = 600\text{nm and } B = -220\text{nm}$$

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David Grojo et al, Laser Photonics Rev. **2024**, 2301327
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Investigation of the
amorphization mechanism
in Si due to rapid
quenching (laser-induced)

☐ Prepare an initial (1,0,0) Si 300 K

☐ Introduce a rapid heating to 2000 K of the surface layers

☐ Follow the equilibration procedure

☐ This is a model to study cooling mechanism due to free carrier's flux and their thermal diffusion process
Amorphization of Si upon a short laser pulse

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1. Re-crystallization procedure

2. We want to provide strong enough cooling rate

3. Solid-liquid interface is uncapable of moving fast enough

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4. CSP does not distinguish melt from amorphous

5. Jump in density up to 7%
Amorphization of Si upon a short laser pulse

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CSP: liquid < 0.97 < solid

There are nucleation sites of the
amorphous phase

MD requires T drop rate 30K/ps

nTTM modeling : only 2.5 K/ps

Standard Stillinger-Webber
F. Stillinger and T.A. Weber, *Phys. Rev. B* **31**, 5262 (1985).

Modified Stilinger-Webber
R.L.C. Vink, G.T. Barkema, W.F. vaan Weg, and N. Mousseau,
*Journal of Non-Crystalline Solids* **282**, 248-255 (2000).

K. Schelling, *Comput. Mater. Sci.* **44**, 274–279 (2008).
<figure><img src="image_91.png" /><figcaption>Amorphization of Si upon a short laser pulse</figcaption></figure>
Cooling rate of Si surface vs fluence

<figure><img src="image_92.png" /><figcaption>100 fs pulse, fluence 0.16 J/cm² at 800nm</figcaption></figure>

Fast cooling rate makes it possible for the
formation of the amorphous phase

<figure><img src="image_93.png" /><figcaption>100 fs pulse, fluence 0.18 J/cm² at 800nm</figcaption></figure>

Relatively slow cooling rate facilities the recrystallization
process during the liquid-solid transition

Working just above the melting threshold warrant the surface melting ~ (10-20)nm with fastest cooling rate, which makes the amorphization possible
Conclusions

The study emphasizes that atomistic modeling not only enhances our understanding of these complex phenomena but also guides the development of innovative applications in advanced technologies.

A comprehensive investigation of ultrafast laser-induced phase transitions in silicon (Si) using a hybrid atomistic-continuum model (nTTM-MD). By incorporating a refined Drude-Lorentz approach for the description of free carrier absorption process, the model accurately captures the interplay between electronic excitation, energy transfer, and structural transformations under femtosecond laser irradiation

The hybrid nTTM-MD model determines the melting threshold to be approximately 0.3 J/cm², in agreement with experimental data, whereas conventional continuum models such as the standalone nTTM significantly underestimate this value at 0.16 J/cm².

the benefit of atomistic modeling in capturing the fundamental mechanisms governing ultrafast laser-induced phase transitions in silicon.

A strong dependency of the melting dynamics on crystal orientation is revealed. Under an incident fluence of 0.3 J/cm², Si samples oriented along <001> exhibit ~25% greater resulting melted volume than <111>-oriented samples, an effect attributed to faster pressure relaxation along the <111> direction. This anisotropy has direct implications for laser-based surface modifications, where controlled energy deposition is essential for achieving uniform material processing in applications such as photonic circuits and advanced semiconductor manufacturing.

Our simulations provide insight into the conditions required for laser-induced amorphization of Si, a technologically significant phenomenon in phase-change memory and semiconductor device engineering. The results indicate that achieving a stable amorphous layer necessitates rapid cooling rates on the order of 30 K/ps—significantly exceeding the ~2.5 K/ps predicted by conventional nTTM models.
ACKNOWLEDGEMENTS

We acknowledge the financial support of the French National Research Agency (ANR) under LAMORSIM project [Project-ANR-23-CE08-0029], and CINES of France for the computational resources needed for large-scale simulations.

Thank you very much
for your attention!

tatiana.Itina@univ-st-etienne.fr