## 4 Conclusions  
In this study, a numerical simulation of the LTA process was carried out using a three-dimensional transient heat transfer model. Through the simulation, the temperature distributions induced by different laser scan paths and beam overlap ratios were analyzed. In addition, the dopant diffusion behavior outcomes at various locations having different temperature distributions within the annealed area were numerically investigated. The major conclusions of this study are presented below.  
1. According to simulation result, a zig-zag pattern produces a hot-spot around the corner part of the beam path due to the greater heat accumulation per unit area. At an overlap ratio of 50%, the temperature difference induced by the corner is close to 96 \({}^{\circ}\)C, which is larger than that produced in the 0% overlap condition (-74 \({}^{\circ}\)C). Unlike the zig-zag pattern, a bidirectional pattern generates a cold spot around the corner part of the beam path because the laser beam is switched off while moving along the y-direction. For the bidirectional pattern, the temperature difference induced at an overlap ratio of 0% (-787 \({}^{\circ}\)C) is larger than that produced when the overlap ratio is 50% (-658 \({}^{\circ}\)C).
2. Regarding the beam overlap region, the temperature change induced by the overlap ratio is much more significant than the corresponding scanning pattern. The maximum temperature reachable in the beam overlap region is between 697 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C depending on the process condition, an outcome much lower than that (1337-1433 \({}^{\circ}\)C) obtained along the beam scanning path. Considering the maximum temperature reachable throughout the computational domain, it can be concluded that the most uniform heating is possible when the zig-zag pattern and the 50% overlap condition are used.
3. According to an analysis of the temperature distribution in the depth direction, the temperature decreases considerably near the surface; however, the change of the temperature is greatly reduced as the depth increases. Around a depth of 400 \(\upmu\)m, the temperature becomes close to the wafer preheating condition (400 \({}^{\circ}\)C). It was found that the temperature distribution obtained at the scan track is nearly identical regardless of the order of the scan track and the overlap ratio. However, the temperature distribution obtained in the beam overlap region depended somewhat on the overlap ratio.
4. According to dopant diffusion and concentration distribution analyses, it was found that for the hot spot produced by the zig-zag pattern and a 50% overlap ratio, the diffusion length increases by thirty times compared to the overlapped area.
5. In this study, only the numerical simulation for multipath laser dopant activation anneal process was handled. The authors of this study are planning to undertake experimental study for the process as a future work. One of the major research items in the future work is the experimental measurement of the dopant concentration distribution through secondary ion mass spectrometry (SIMS) analysis. Experimentally measured data will be also compared to simulation results for validation of the simulation study.  
D.C., Methodology, Visualization, Investigation, Data curation, Writing--original draft. J.S., Conceptualization, Methodology, Resources, Writing--review & editing. All authors have read and agreed to the published version of the manuscript.  
This research work was supported by the Technology Innovation Program (Grant No. 20010323, Development of the Rapid Annealing System for Semiconductor Device Using kW Fiber Laser) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).  
Not applicable.  
Data Availability Statement: Data are available from the corresponding authors upon reasonable request.