# Atomistic-Continuum Modeling of Laser-Induced Phase Transitions in Silicon: Melting, Ablation, Solidification, and Amorphization

Dmitry S. Ivanov, Tatiana Itina, Martin E. Garcia

► To cite this version:

Dmitry S. Ivanov, Tatiana Itina, Martin E. Garcia. Atomistic-Continuum Modeling of Laser-Induced Phase Transitions in Silicon: Melting, Ablation, Solidification, and Amorphization. 13th INTERNATIONAL CONFERENCE ON PHOTOEXCITED PROCESSES AND APPLICATIONS (ICPEPA 2025), Anna Paola Caricato, Maria Dinescu, Maurizio Martino, Leonid Zhigilei, Sep 2025, Lecce (ITALY), Italy. ujm-05291760

HAL Id: ujm-05291760

https://ujm.hal.science/ujm-05291760v1

Submitted on 1 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Atomistic-Continuum Modeling of Laser-Induced Phase
Transitions in Silicon: Melting, Ablation, Solidification,
and Amorphization

Dmitry S. Ivanov*,¹,², Tatiana E. Itina², and Martin E. Garcia¹

ICPEPA-13 conference, 17th of Sept 2025, Lecce, Italy

UNIKASSEL
VERSITÄT

Theoretical Physics Department, University of Kassel, Germany

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

Université Jean Monnet Saint-Etienne, Laboratoire Hubert Curien, Saint-Etienne, France
Technological advances in amorphization of Si

CMOS Technology:

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

(a)

TFT Technology

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

(b)

Vishwas Acharya et al, *Mater. Res. Express* **10**, 082002 (2023)

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

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

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

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

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

Laserinstitut
Hochschule Mittweida

<figure><img src="image_9.png" /></figure>

David Grojo et al, *Laser Photonics Rev.* **18**, 2301327 (2024)

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

Feiyu Xu et al, *Chemical Engineering Journal* **430**, 133140 (2022)
The combined MD-nTTM model

$$
\left\{
\begin{array}{l}
\displaystyle \frac{dI(z,t)}{dz} = -(\alpha + \alpha_{FCA}(\varepsilon(N_e)))I(z,t) - \beta I^2(z,t) \\[1.5ex]
\displaystyle \frac{\partial N_e}{\partial t} = \frac{\alpha I(z,t)}{h\nu} + \frac{\beta I^2(z,t)}{2h\nu} + \delta n_e - \gamma N_e^3 - \nabla \cdot \vec{J}(n_e, T_e, E_g) \\[1.5ex]
\displaystyle \frac{\partial U_e(N_e, T_e, E_g)}{\partial t} = (\alpha + \alpha_{FCA}(\varepsilon(N_e)))I(z,t) + \beta I^2(z,t) \\[1.5ex]
\displaystyle -\nabla \cdot \vec{W}(N_e, T_e, E_g) - \frac{C_{e-h}(N_e, T_e, E_g)}{\tau_e}(T_e - T_l) \\[1.5ex]
\displaystyle c_l \frac{\partial T_l}{\partial t} = \vec{\nabla} \cdot (\kappa \vec{\nabla} T_l) + \frac{C_{e-h}(N_e, T_e, E_g)}{\tau_e}(T_e - T_l) \rightarrow m_i \frac{d\vec{r}_i}{dt^2} = -\sum_{j=1,N} \vec{\nabla} U(\vec{r}_{ij}, T_e) + \xi m_i \vec{V}_i^T
\end{array}
\right.
\quad
\begin{array}{l}
1) \text{ TTM + additional equation for free carriers } \rightarrow \text{nTTM} \\
2) \text{ Explicit methods are hampered, implicit are difficult to parallelize} \\
3) \text{ Drude-Lorenz model is used for reflectivity and free carriers' absorption} \\
4) \text{ Tersoff Modified Potential is utilized}
\end{array}
$$

<figure><img src="image_11.png" /></figure>
Melting Dynamics of the irradiated Si target

<figure><img src="image_12.png" /></figure>

$F = 0.31 \text{ J/cm}^2$

Si <001>
100 fs
800 nm

Z
X

Y

25 nm

$CSP_{thr} = 0.97$

<figure><img src="image_13.png" /></figure>

CSP

10 ps

20 ps

30 ps

40 ps

50 ps

70 ps

100 ps

150 ps
Clapeyron equation for metals and Si, the crystal structure effect

<figure><img src="image_14.png" /></figure>

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

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

Melting results in the 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.

<figure><img src="image_15.png" /></figure>

$$ \begin{gathered} \text{At P = 0 Pa} \\ T_m = 1696 \text{ K} \end{gathered} $$

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

Melting results in internal stresses drop
Central Symmetry Parameter Dynamics

Laser pulse

<figure><img src="image_16.png" /></figure>

1. The effect of crystal structure makes the homogeneous mechanism of melting in Si **dominant** due to laser-induced pressure increase

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

$F_{\text{inc}} = 0.31 \text{ J/cm}^2$

<figure><img src="image_17.png" /></figure>

$CSP_{\text{thr}} = 0.97$

<figure><img src="image_18.png" /></figure>

crystal
orientation <001>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

$F_{\text{thr}} = 0.30 \text{ J/cm}^2$

<figure><img src="image_22.png" /></figure>

CSP
liquid < 0.97 < solid

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>
The Effect of Crystal Structure Orientation

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

crystal
orientation <111>

<figure><img src="image_27.png" /></figure>

CSP
liquid < 0.97 < solid

<figure><img src="image_28.png" /></figure>
The Effect of Pulse Duration

$F_{\text{thr}} = 0.30 \text{ J/cm}^2 \rightarrow 0.28 \text{ J/cm}^2$

$F_{\text{inc}} = 0.29 \text{ J/cm}^2$

<figure><img src="image_29.png" /></figure>
The Effect of Pulse Duration

$F_{\text{thr}} = 0.28 \text{ J/cm}^2 \rightarrow 0.26 \text{ J/cm}^2$

$F_{\text{inc}} = 0.29 \text{ J/cm}^2$

<figure><img src="image_30.png" /></figure>
<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

## Depth of melting vs. fluence

1. 800 nm wavelength, 100 fs pulse, <001>

2. There some experimental results matching our measurements (Jörn Bonse)

3. Logarithmic fit is applied

<figure><img src="image_33.png" /></figure>

$$d_{\text{melt}} = A \ln(F/F_{\text{th}}) + B \qquad A = 600\text{nm and B} = -220\text{nm}$$
# Ablation/Spallation mechanism of Si vs fcc Metals

Laser Pulse

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /><figcaption>Ni
1 ps pulse, fluence 129 mJ/cm², 100 nm Ni film</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>Si
270 fs pulse, fluence 400 mJ/cm², 1000 nm Si film</figcaption></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

Ni: face
center cubic

<figure><img src="image_39.png" /></figure>

1. At the fluences around melting threshold the **heterogeneous** mechanism is energetically favorable.

2. **Spallation** is due to temperature/pressure interplay

Si: Diamon cubic

<figure><img src="image_40.png" /></figure>

1. At the fluences around melting threshold, the **homogeneous** melting mechanism already plays a determinant role

2. **Spallation** mechanism is **suppressed**
Investigation of the amorphization mechanism of Si

$F = 0.31 \text{ J/cm}^2$

$T < T_m$ and NO mechanical
equilibrium!

<figure><img src="image_41.png" /></figure>

1. The melting process is over by 1000 ps

2. The surface oscillations are due to thermal expansion and melting contraction interplay

3. At the time of 1000ps the temperature gradient provides the cooling

4. Used MD-nTTM model is computationally expansive
Choosing the criteria to increase the numerical efficiency

<figure><img src="image_42.png" /></figure>

Lattice temperature gradient
provides the cooling rate due to
normal phonon thermal conductivity

a) By the time of 1000 ps the surface temperature drops below the equilibrium melting point with remaining gradient

b) The carriers' density drops 25 times as compared their value upon the pulse deposition by 200ps and the effect of free carriers can be discarded

<figure><img src="image_43.png" /></figure>

MD-nTTM with 1 processor → MD MPI

<caption>(b)</caption>
Investigation of the amorphization mechanism of Si with <001>

$F_{\text{inc}} = 0.31 \text{ J/cm}^2$

<figure><img src="image_44.png" /></figure>

$T \sim 1600 \text{ K}$

$T_m = 1683 \text{ K}$
Investigation of the amorphization mechanism of Si with <111>

<figure><img src="image_45.png" /></figure>

$t_{pulse} = 100$ fs

$F_{inc} = 0.3$ J/cm$^2$

crystal orientation
<111>

CSP
liquid < 0.94 < solid

$F_{thr} = 0.28$ J/cm$^2$ is lower than for <001>

$F_{inc} = 0.31$ J/cm$^2$

<figure><img src="image_46.png" /></figure>

T ~ 1600 K

T_m = 1683 K
Metals: Face center cubic structure: $V_{\text{melt}} = 5\%$

Solid-liquid interface advancement is favored

<figure><img src="image_47.png" /></figure>

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

Solid-liquid interface advancement is hampered

<figure><img src="image_48.png" /></figure>

Possible mechanism of
amorphization of Si due
to laser cooling

<figure><img src="image_49.png" /></figure>

$$G(P,V) = U + PV - TS \Leftrightarrow \Delta G = \Delta H - T\Delta S$$

Also, diffusion coefficient $D = f(T)$
Conclusion

➤ The atomistic-continuum MD-nTTM model is proposed for laser-Si interactions

➤ Homogeneous melting mechanism was found dominant

➤ The melting depth vs fluence was related to the experimental measurements

➤ The effect of crystal orientation and the pulse duration was investigated

➤ The amorphization mechanism is attributed to the cooling rate in the absence of mechanical (acoustic) equilibrium

Thank you for your attention!