# Numerical and Experimental Research on the Laser-Water Jet Scribing of Silicon
## 4 Results and Discussion  
### Ablation Mechanism of Silicon  
On the basis of Section 2, numerical simulations were carried out to investigate the temperature and stress distribution at the machining region. The laser power and repetition rate were set as 5 W and 50 kHz, respectively. Fifteen points along the central axis with a depth interval of 100 nm were selected as the sampling points. The temporal evolution of temperature on these sampling points and the highest temperature in the calculation domain are demonstrated in Figures 5 and 6. The comparison of temperature distribution at t = 50 ns and t = 200 ns is shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature** & **Thermal Conductivity** & **Specific Heat** & **Linear Thermal Expansion Coefficient** \\ /**K** & /**kW\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)** & /**J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)** & /**10\({}^{-6}\cdot\)K\({}^{-1}\)** \\ \hline
300 & 156 & 713 & 2.63 \\
400 & 105 & 785 & 3.24 \\
500 & 80 & 832 & 3.84 \\
600 & 64 & 849 & 4.00 \\
700 & 52 & 866 & 4.14 \\
800 & 43 & 883 & 4.24 \\
900 & 35.6 & 899 & 4.33 \\
1000 & 31 & 916 & 4.42 \\
1100 & 28 & 933 & 4.51 \\
1200 & 26.1 & 950 & \\
1300 & 24.8 & 967 & \\
1400 & 23.7 & 983 & \\
1500 & 22.7 & 1000 & \\
1600 & 21.9 & 1017 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Thermodynamic parameters of silicon [19].  
Figure 4: Demonstration of LWJ machining. (**a**) Laser waterjet coupling device; and (**b**) capture of machining process.  
During the first laser pulse, the temperature of sampling points in the surface layer reached the melting point and the highest temperature was obtained at t = 38 ns. When t = 50 ns, a shallow pit formed and the high temperature area was localized surrounding the pit. At the end of laser pulse, the temperature of the remaining sampling points started to drop. When t = 200 ns, the size of pit was fixed and the surrounding temperature remained at a low level. Once the second laser pulse was applied, the temperature of sampling points rose again and the highest temperature was obtained at t = 33 ns. This tendency was repeated in the following three laser pulses.  
To further clarify the ablation mechanism of the silicon substrate, the temporal evolution of major principal stress in the calculation domain is demonstrated in Figure 8. The generation of maximum compressive stress was always delayed after the tensile stress. Both of these two stresses increased during the laser pulse, then gradually dropped during the pulse interval. The compressive stress dropped much faster than tensile stress. The spatial distributions of maximum compressive and tensile stress in the calculation domain at t = 100 ns are illustrated in Figure 9. Both tensile and compressive stresses concentrated on  
Figure 5: Temporal evolution of temperature at sampling points.  
Figure 6: Temporal evolution of the highest temperature in the calculation domain.  
Figure 7: Temperature distribution at (**a**) t = 50 ns and (**b**) t = 200 ns.  
the right side of the domain and restricted within a relatively small area. Most importantly, the maximum compressive stress and tensile stress were far lower than the compressive strength and tensile strength, respectively.