# Experimental Study on Femtosecond Laser Processing Performance of Single-Crystal Silicon Carbide
## 3 Results and Discussions
### Experimental Results
#### 3.2.1 Analysis of Single Factor Experimental Results
The laser energy deposited into the material is directly proportional to the spot overlap rate (\(PO\)), and the spot overlap rate and effective pulse number (\(N_{0}\)) can be expressed as [7]:  
\[PO=\left(1-\frac{S}{fD}\right)\,100\% \tag{2}\]  
\[N_{0}=\frac{1}{1-PO}=\frac{fD}{S}. \tag{3}\]  
In the formula, \(D\) is the diameter of the laser spot on the workpiece, \(S\) is the scanning speed and f is the repetition rate. According to Equations (2) and (3), when the scan speed increases from 50 \(\upmu\)m/s to 450 \(\upmu\)m/s, the spot overlap rate decreases from 99.86% to 98.77%. As can be seen from Figure 5a,b, with the increase in scan speed, the overlap rate of light spot decreases, and the energy of injected material decreases, so the material removal decreases. It can be seen from Figure 5c,d that with the increase in scan speed, the number of effective pulses decreases and the HAZ decreases. Due to the decrease in groove depth, groove width and groove cross-sectional area, the inclination angle of the material sidewall decreases. Figure 4: Effect of fluence on groove size, MRR, HAZ and side wall inclination angle. (**a**) Depth and width; (**b**) MRR; (**c**) HAZ; (**d**) side wall inclination angle. Figure 5: _Cont._  
Figure 6 shows the effect of repetition rate on the size of groove, MRR, HAZ and side wall inclination angle. As shown in Figure 6a, the size of the groove increases with the increase in pulse repetition rate. When the repetition rate increases from 200 Hz to 1 kHz, the spot overlap rate increases from 97.95% to 99.59%, resulting in an increase in the laser energy received by the workpiece per unit time. Figure 5: Effect of scan speed on groove size, MRR, HAZ and side wall inclination angle. (**a**) Depth and width (**b**) MRR; (**c**) HAZ; (**d**) side wall inclination angle. Figure 6: Effect of repetition rate on groove size, MRR, HAZ and side wall inclination angle. (**a**) depth and width; (**b**) MRR; (**c**) HAZ; (**d**) side wall inclination angle. As shown in Figure 6b, with the increase in repetition rate, the MRR increases. Increasing the repetition rate of laser pulses can provide more energy for the target material of a given area at constant scan speed and laser fluence, thereby increasing the cross-sectional area and achieving a higher MRR. It can be seen from Figure 6c,d that with the increase in repetition rate, the energy of injected material increases and the HAZ and side wall inclination angle increase. Figure 7 shows the effect of multipass scans on the groove size, MRR, HAZ and side wall inclination angle. Figure 7a,b show that repeated scanning increases the laser energy injected into the groove, increases the material absorption rate induced by multipulse laser [23] and melts the amorphous material in the groove under the repeated high temperature caused by multi pulse laser. Therefore, the groove depth and MRR increase with the increase in multipass scanning. Due to the fixed diameter of the spot, the groove width slightly increases with the increase in multipass scanning. It can be seen from Figure 7c that with the increase in multipass scanning, the laser energy is injected, the laser energy at the edge of the spot accumulates and the HAZ increases. As shown in Figure 7d, as the number of scans increases, the inclination angle of the sidewall increases and the sidewall of the V-shaped groove become steeper. Figure 8 shows the influence of numerical aperture on the size of groove, HAZ and MRR. With the increase in the numerical aperture, the focus energy of the processing area increases while the focus energy of the HAZ decreases in the direction of the laser radius. It can be seen from Figure 8a-c that with the increase in numerical aperture, the groove  
Figure 7: Effect of multipass scans on groove size, MRR, HAZ and side wall inclination angle. (**a**) depth and width (**b**) MRR; (**c**) HAZ; (**d**) side wall inclination angle. depth increases and the groove width and HAZ decrease.