## 4 Results and Discussion  
### Shape Evolution of DEE Process Conditions  
A copper layer was deposited on the stainless steel surface through an electrodeposition process. A copper-deposited layer was formed under the conditions of 0.5 M of sulfuric acid, 0.5 M of copper sulfate mixed solution, an applied voltage of 2 V, and an electrodeposition time of 60 s. [PERSON] et al. [13] suggested laser beam irradiation conditions to minimize damage to the surface of stainless steel, the base material. In this study, the copper layer was removed under conditions that minimized the surface damage of stainless steel, which is the base material [13]. The laser patterning conditions of the deposited layer in the DEE process are shown in Table 2. In order to minimize damage to the base material, the copper layer was removed by performing laser patterning three times under the laser beam conditions in Table 2. Figure 3 shows the result of the actual patterning of the copper layer under the conditions of Table 2 as an optical image. The dark areas are the copper layer, and the light areas are the surface of the stainless steel from which the copper layer has been removed. Figure 2: Procedures for DEE process; (**a**) electrodeposition, (**b**) patterning by laser irradiation, and (**c**) electrochemical etching. The electrochemical etching of metals is basically isotropic etching. Therefore, in the DEE process, the etching shape changes depending on the etching step conditions. Figure 4 shows the shape change of the cross-section in isotropic etching. As shown in Figure 4, in electrochemical etching, the etch factor is determined by the side etch and etching depth. Since the electrochemical etching of the DEE process is based on the isotropic etching of the metal, in order to increase the overall etching depth in the DEE process, side etching should be minimized. In the electrochemical etching of metal, the limit of the physical etch factor is about 1.5 [1; 2; 3]. If the etching time is excessive in the electrochemical etching step of the DEE process, it means that the etching proceeded even after the deposited layer protecting the sidewall was removed. If the side wall is not protected, the surface profile of the cross-section proceeds in a hemispherical shape, so the taper angle of the vertical wall in the etched final shape increases. The big taper angle of the vertical wall per cycle of the DEE process means that the precision of the overall machining shape is lowered after the DEE process is finished. Therefore, it is necessary to select an electrochemical etching depth per cycle of the DEE process that can minimize the taper angle. In the DEE process, the etch factor can be calculated by measuring the width before electrochemical etching as L\({}_{1}\), the width at the repeated cycles as L\({}_{2}\), and the total depth in the cycle as d. \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristics** & **Value** \\ \hline Average power & 4 W \\ Pulse repetition rate & 80 kHz \\ Moving speed of spot & 600 mm/s \\ Line spacing of beam spot & 10 \(\upmu\)m \\ Number of repeated laser patterning & 3 times \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Laser patterning conditions of copper layer. Figure 4: Shape evolution and etch factor in electrochemical etching. Figure 3: Optical image of laser-patterned copper layer. Figure 5 shows the result of a square pattern performed by repeating the DEE process 10 times at an excessive etching time of 10 s. Figure 5b is an enlarged picture of the white square dotted line in Figure 5a. As shown in Figure 5b, it can be seen that the taper angle is large in the vertical wall formed from the top surface to the bottom surface. This means that the more the DEE process was repeated under excessive etching conditions, the greater the taper angle was generated. In Figure 6, it can be confirmed that a big taper angle occurred as a result of measuring the surface profile of the cross-section of line AA' in Figure 5a.