## 3 Results and Discussion  
### Analysis of the Surface Temperature Distribution  
The temporal profiles of the maximum surface temperature (the temperature at beam spot center) under different simulation conditions are shown in Figure 3. Early in the annealing process, the temperature increases significantly. However, the temperature becomes quickly stabilizes in a few milliseconds, and it mostly does not change until the first scanning track of the laser beam ends. When the laser beam moves along the y direction, the temperature increases dramatically (for zig-zag pattern) or decreases (for bidirectional pattern) depending on the scanning pattern. At the corner region of the scanning track, the zig-zag pattern produces a hot spot due to the greater heat accumulation per unit area. For the overlap ratio of 50%, the maximum temperature at near the starting point of the second track increases by approximately 22 \({}^{\circ}\)C more compared to that at an overlap ratio of 0% because the preheating effect at the end of the first track is substantial. A temperature fluctuation is observed between the end of the first track and the start of the second track when the overlap ratio is 0%. A decrease in the temperature in this region occurs as the beam spot leaves the area preheated by the first track. Unlike the zig-zag pattern, the bidirectional pattern generates a cold spot because the laser beam is switched off between the first and second scanning tracks. The temperature reduction is more significant (decreases approximately 129 \({}^{\circ}\)C more) when beam overlapping is not used, as shown in Figure 3c,d. It was also found that at an overlap ratio of 0%, more time is required for the temperature to recover to the previous level. Table 3 shows the temperature change induced by the corner zone of the beam path. As shown in the Table 3, the bidirectional scanning pattern at an overlap ratio of 0% causes the largest temperature difference, which in turn worsens the temperature uniformity. The beam overlap effect in sequentially scanned lines was also investigated. Figure 4 shows the temperature with time at the midpoints (points 1 and 2 in Figure 4) between two adjacent scanned lines. At the beginning of the annealing process, the temperatures at the designated points are nearly constant given that these points are far from the start pointing of the annealing. However, as the laser beam approaches points 1 and 2, the temperature at point 1 rises rapidly, as shown in the figure. The temperature of point 2 also increases with a slight time lag, although the degree of the temperature increase is relatively small. This indicates that annealing of the first track could preheat the second and third tracks. As shown in Figure 4, the maximum temperature of the peaks (the three high peaks shown in graphs) tends to increase slightly owing to the effect of the preheating induced by the scanning of the former track. When the laser beam scans the second track, points 1 and 2 undergo rapid increases and decreases of the temperature, with the temperature variations at the two points being identical regardless of the simulation condition, as shown in the figure. During the scanning of the third track, the temperature of point 2 increases greatly again as the laser beam approaches point 2, with the temperature at point 1 also increasing slightly with a time lag, as shown in the figure. The temperature profiles do not change much according to the difference in the scanning pattern. However, the temperature difference caused by the degree of beam overlapping is considerable. At an overlap ratio of 50%, the temperature of the peaks increases by approximately 54% compared to that at an overlap ratio of 0%. It was also found that the 50% overlap ratio condition generates higher heating and cooling rates than the 0% overlap ratio condition. The differences between the heating and cooling rates in the 0% and 50% overlap conditions are 130% and 150%, respectively (see Table 4).