## 2 Theoretical Analysis of the Influence of Water-Jet-Assisted Laser Etching  
Water-jet-assisted laser processing introduces a water jet to traditional laser processing. The auxiliary gas removes slag and debris generated in the laser processing, thereby improving the processing quality of the materials and reducing slag accumulation, the generation of microcracks, formation of recast layers during processing, and the heat-affected zone. Figure 1 schematizes the water-jet-assisted laser technique. Note that the water jet consumes part of the laser energy. In contrast, when jetted at appropriate velocity, the water jet washes away slag and the recast layer in an appropriate time, which reduces the heat-affected zone and improves processing quality. Water-jet-assisted laser processing also reduces photothermal efficiency and suppresses secondary adhesion of the etched material via laser-induced liquid cavitation, water cooling, and water flow.  
Conventional gas-assisted and water-jet-assisted laser processing techniques remove material via laser irradiation, which smells or vaporizes the material surface. In the conventional technique, most laser energy is absorbed by the material. The material's thermal properties will transfer excess heat around the laser action zone, which enlarges the heat-affected zone and increases slag accumulation. In water-jet-assisted laser etching technology, conventional laser etching is supplemented by water jets  
Figure 1: Schematic of water-jet-assisted laser processing.  
applied at a certain angle and velocity. This technology combines the high efficiency of traditional gas-assisted laser processing with the advantages of water jets. The laser primarily acts as a softening material that melts or vaporizes the material as it is heated. The water jet strikes the laser processing area and cools it by heat transfer. Generally, the specific heat capacity of water is greater than that of the material matrix, which implies that water absorbs excess heat from the material surface and provides a cooling effect. In addition, increasing the water-jet velocity increases the impact force on the material. Within a certain range, the impact force is sufficient to flush the slag and other defects generated by the laser action. Then, the flowing water removes the slag or recast layer from the tank in sufficient time. Note that reducing slag and the recast layer from the bottom and walls of the trench can improve processing quality [20].  
In this study, the effects of water jet pressure at different angles and velocities on the material were compared in fluent simulations. Herein, the water-jet angle was set to 30\({}^{\circ}\) or 60\({}^{\circ}\), and the velocity was varied between 16, 20, 24, and 28 m/s (Figure 2). Note that many factors were simplified during simulation; thus, the results are theoretical rather than practical. As shown in Figure 2, increasing jet velocity at a fixed incident angle gradually increased the impact force of the water jet on the material. In addition, for a fixed water-jet velocity, the impact force was \(\sim\)1.5 times higher at an impact angle of 60\({}^{\circ}\) than at 30\({}^{\circ}\). Thus, it is theoretically demonstrated that 60\({}^{\circ}\) water-jet-assisted laser etching of the polysilicon material demonstrates groove depth and width greater than that of the 30\({}^{\circ}\) water-jet-assisted laser etching polysilicon material. In actual machining, greater jet velocity is advantageous for material removal; however, if the water flow velocity is excessive, the water jet will shake the experimental device, which will also deflect the impact center of the jet on the material. A significantly diverted water beam will cause splashing, which will generate \"water mist\" that affects the focused laser spot and incurs large laser energy loss.