# Analysis of Wafer Warpage in Diamond Wire Saw Slicing Sapphire Crystal
## 5 Results and Discussion  
### Analysis of Wafer Temperature Field and Thermal Deformation  
Figure 8 shows the temperature field nephogram generated by the cut crystals and wafers at cutting depths of 2 mm and 8 mm. The temperature in the cutting area is the highest, and the temperature in the sawed part is lower than that in the uncut part. This is because the coolant is directly sprayed on the sawing area and then flows down along the newly formed surface, causing the temperature to drop faster. The temperature field at both sawing depths is symmetrically distributed, and the temperature of the wafers is lower than that of the surrounding uncut sapphire material. This is because the wafers absorb relatively less heat and have a large heat dissipation area.  
\begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Wire Speed \(V_{\text{s}}\) (m/min)** & **Feed Rate \(V_{\text{w}}\) (mm/min)** \\ \hline
1 & 800 & 0.1 \\
2 & 800 & 0.3 \\
3 & 1200 & 0.1 \\
4 & 1200 & 0.3 \\ \hline \end{tabular}
\end{table}
Table 2: Processing parameters for the sawing experiment.  
Figure 7: Sawing unit in the experiments: (**a**) appearance, (**b**) schematic.  
From Figure 8b, it can be seen that there is a relatively larger area of deep red stress distribution zone (high stress value) on the middle slice, and the temperature field of multiple wafers is symmetrically distributed. Therefore, during the sawing process, the temperature of the middle slice may be the highest, which means that the temperature distribution of wafers 1 and 5, as well as wafers 2 and 4, is consistent. Therefore, the variation of maximum temperature of slices 1, 2, and 3 with sawing depth was analyzed, as shown in Figure 9. In addition, it was found that as the sawing depth increases, the temperature of the wafer gradually increases and tends to stabilize, with a stable sawing temperature of about 34.5 \({}^{\circ}\)C. The lower temperature at the beginning of the sawing stage is due to the pouring of coolant from top to bottom. At this time, the cutting depth is shallow, and the coolant can directly enter the sawing area. But as the cutting depth increases, the coolant cannot be directly poured into the cutting area and needs to flow into the cutting area along the cut surface. Therefore, the flow rate of coolant entering the cutting area will inevitably decrease, resulting in an increase in temperature.  
Figure 8: Nephogram of temperature field distribution during sawing: (**a**) sawing depth of 2 mm, (**b**) sawing depth of 8 mm.  
Figure 9: The variation of wafer maximum temperature with cutting depth.  
The deformation nephogram of wafer No. 3 in the \(z\)-direction was extracted when the sawing depth was 4 mm, as shown in Figure 10. The deformation at the sawing position is the largest, reaching up to 54.8 um, which corresponds to the highest temperature in the sawing area. According to the selected test points on the wafer surface shown in Figure 6, to extract the thermal deformation positions at the maximum temperature of each point, the wafer warpage can be calculated by using the method shown in Figure 5.