The Effect of Different Pulse Widths on Lattice Temperature Variation of Silicon under the Action of a Picosecond Laser
Abstract
:1. Introduction
2. Theoretical Model and Parameters
2.1. Free Electrons Excitation
2.2. Energy Absorption and Heat Transfer in Electrons
2.3. Electron–Lattice Energy Coupling
3. Results and Discussion
3.1. Simulation
- Step 1: Calculating the free electron concentration by Equations (1) and (2).
- Step 2: The electron heat capacity and electron–lattice relaxation time were calculated according to the calculated free electron concentration.
- Step 3: Calculating the electron temperature by Equation (3).
- Step 4: The electron diffusion coefficient and electron heat transfer coefficient were calculated according to the calculated electron temperature.
- Step 5: Calculating the lattice temperature by Equations (4) and (5).
- Step 6: The single photon absorption coefficient, reflection coefficient, lattice heat capacity and lattice heat transfer coefficient were calculated according to the calculated lattice temperature.
- Step 7: Resolving formula (2) according to the calculated reflection coefficient and single-photon absorption coefficient and repeating the above steps.
3.2. Simulation Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|
[20] | 2.98 × | m2/s | [19] | fs | |
[27] | 3.8 × 10−43 | m6/s | [26] | J/(m3·K) | |
[20] | 2 + 9.967 × 5 | 1/m | [26] | −1.23 | W/(m K) |
[20] | 1.5 × 10−11 | m/W | 15 | μm | |
[26] | ) | 300 | K | ||
[27] | 1.12 | eV | 0.8 | ||
[25] | J/(Kg·K) | [17] | 5.67 × 10−8 | W/m2·K4 | |
[25] | W/(m·K) |
No. | 1 | 2 | 3 | 4 | 5 | Average | Simulation |
---|---|---|---|---|---|---|---|
Depth | 195.5 nm | 204.7 nm | 200.4 nm | 195.2 nm | 215.1 nm | 202.2 nm | 196 nm |
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Yang, J.; Zhang, D.; Wei, J.; Shui, L.; Pan, X.; Lin, G.; Sun, T.; Tang, Y. The Effect of Different Pulse Widths on Lattice Temperature Variation of Silicon under the Action of a Picosecond Laser. Micromachines 2022, 13, 1119. https://doi.org/10.3390/mi13071119
Yang J, Zhang D, Wei J, Shui L, Pan X, Lin G, Sun T, Tang Y. The Effect of Different Pulse Widths on Lattice Temperature Variation of Silicon under the Action of a Picosecond Laser. Micromachines. 2022; 13(7):1119. https://doi.org/10.3390/mi13071119
Chicago/Turabian StyleYang, Jianjun, Decheng Zhang, Jinye Wei, Lingling Shui, Xinjin Pan, Guangren Lin, Tiande Sun, and Yicheng Tang. 2022. "The Effect of Different Pulse Widths on Lattice Temperature Variation of Silicon under the Action of a Picosecond Laser" Micromachines 13, no. 7: 1119. https://doi.org/10.3390/mi13071119