# Stitching-Based Resolution Enhancement in Wavefront Phase Measurement of Silicon Wafer Surfaces
## 4 Results  
A quarter-wafer sample from IMEC was utilized, with die-to-wafer bonding applied to specific regions of the wafer. A notable result of this work is to determine the shape (bow/warp) of dies that are thinned and then glued onto a carrier wafer, along with the resulting deformation. First, 196 images were taken in both defocused planes (see Figure 11). The full capture process is shown in Figure 12. After both stitched measurements were obtained, the quantitative phase algorithm was applied to obtain the shape of the wafer, as explained in the previous section. In Figure 13, it is possible to see the peak-to-valley difference between both types of die; die-to-wafer bonding is around 2.5 \(\upmu\)m, while non-die-to-wafer bonding is around 1.8 \(\upmu\)m. In addition, it is worth analyzing the full measurement in order to check whether  
Figure 11: Final composed image after stitching 196 images. Figure 12: Schematic representation of the complete detection process. The scanning head incorporates the 4f system. Scanning proceeds row by row, as illustrated in the right panel. The overlap between consecutive measurements is consistent with the overlap between rows. all die-to-wafer bonding dies have higher peak-to-valley values than for non-die-to-wafer bonding. Figure 14 shows a full measurement of a quarter of the wafer. In the same figure, both types of die are selected and numbered. To maintain consistency, each die-to-wafer bonding die is compared with its neighboring non-die-to-wafer bonding dies, positioned directly below and on the right of it, as depicted in the figure. From the same figure, it is evident that all die-to-wafer bonding dies exhibit greater deformation compared to the non-die-to-wafer bonding dies. Note that the global shape of the wafer affects the peak-to-valley, as expected. A similar comparison is presented in Figure 15, this time with the application of a high-pass filter to the original data. The use of a high-pass filter allows for the isolation of higher-frequency surface variations by removing long-wavelength features, making localized deviations more prominent. The high-pass filter used here is a double Gaussian filter which is defined in the SEMI Standards [42]. This filter can be expressed as follows:  
\[G_{DHP}=1-2\exp\left[-1.228\left(\frac{\lambda_{c}}{\lambda}\right)^{2}\right] +\exp\left[-2.456\left(\frac{\lambda_{c}}{\lambda}\right)^{2}\right] \tag{25}\]  
where \(\lambda_{c}\) is the cutoff frequency. The cutoff frequency used in Figure 15 is 200 \(\upmu\)m.  
As a result, it can be seen that the die-to-wafer bonding dies exhibit a noticeably higher peak-to-valley, suggesting increased surface irregularities or deformation after bonding. Furthermore, the high-pass filtering reveals a small defect on one of the dies. It is very interesting that different columns of dies exhibit different peak-to-valley patterns. For example, it can be seen from the two figures mentioned above that the first column, which includes dies 1, 4, 8, 13, 19, and 25, has higher peak-to-valley than the column with dies 2, 5, 9, 14, 20, and 26. Figure 13: Three-dimensional plot of IMEC wafer with die-to-wafer bonding die (**left**) and without die-to-wafer bonding (**right**). Continuing with die analysis, a very important parameter in the industry is the coplanarity between the die-to-wafer bonding and the surrounding area. Figure 16 shows the difference between the best fit plane of the die-to-wafer bonding (area of the red dashed line) and the surroundings (area between the red and black dashed lines). The angle differences between both planes are on the order of microdegrees. Lastly, one of the most interesting results is provided by the stress induced during die-to-wafer bonding. Process-induced overlay errors are a growing problem in meeting the ever-tightening overlay requirements for integrated circuit production. By calculating the stress, the overlay error can be minimized.