## 4 Results and Discussion  
### Numerical Simulation Results  
The mass fraction of each monitoring point as described above is shown in Figure 7 for the R0 and R32 pads. The whole process of simulated fluid flow included 30 s DIW flow and 30 s slurry flow. Thus, the slurry mass fraction only shows the data from the last 30 s. As the slurry was supplied, the mass fraction of these five points all rose rapidly for both the R0 and R32 pads. Values below 0.95 are hidden to make the trends more obvious. The slope of the slurry mass fraction with time is presented in Figure 8 by taking the first derivative of data in Figure 7. The SSTs of the five monitoring points are labeled with double-headed arrows. The time at which each monitoring point reached the ideal target mass fraction of 1.00 was defined as the SST, and the average SST of the five points was regarded as the final value. In the case of the R0 pad, the mass fraction slope of the fresh slurry fluctuated significantly because the old slurry was recirculated beneath the wafer surface. Even if fresh slurry is supplied continuously, it cannot escape from the polishing interface completely until around 50 s. As for the R32 pad, the mass fraction slope of the fresh slurry fluctuated slightly around 45 s, which means there is little old slurry recirculation. Compared to the R32 pad, the fresh slurry is not evenly supplied throughout the wafer for the R0 pad, and the average SST is 4.90 s slower.  
Taking atmospheric pressure as a reference, the gauge pressure of the slurry at the wafer-pad interface is depicted in Figure 9. The pressure difference between the two cases occurs on the trailing edge and the leading edge in dynamic conditions. This is consistent with reported experiment results [19]. Quantitatively, the R0 pad and R32 pad showed negative pressures of \(-\)8 kPa and \(-\)6 kPa, respectively, at the trailing edge. The negative pressure caused recirculation of the old slurry and delayed the supply of fresh slurry, a phenomenon known as the back mixing effect [38; 39; 40]. The greater the absolute value of negative pressure, the more obvious the back mixing. This suction caused by the uneven pressure distribution can tilt the wafer opposite to the sliding direction, making the wafer-pad contact unstable and causing variations in slurry film thickness [41]. This phenomenon eventually acts as a destabilizing NU near the wafer edge.  
Figure 8: The slopes of slurry mass fraction and the relevant slurry saturation time on the (**a**) R0 pad, and (**b**) R32 pad in the 100-mm wafer polisher.  
Figure 7: Simulated slurry mass fraction of five monitoring points with time on the (**a**) R0 pad, and (**b**) R32 pad in the 100 mm wafer polisher.  
In terms of the overall slurry distribution beneath the wafer, Figure 10 shows the mass fraction of the fresh slurry as a function of time at the surface of Y = 0.9 mm. The slurry mass fraction of the R32 pad had a more uniform distribution than that of the R0 pad because the fresh slurry supply was slower when using the R0 pad, as discussed above. The confirmed theory revealed that the slow feed rate and discharge rate of fresh slurry increased the scratching and NU, but reduced the MRR [42; 43].  
Figure 10: Simulated mass fraction of fresh slurry distribution in the wafer–pad interface with increasing flow time.  
Figure 9: The gauge pressure field distribution at the wafer–pad interface.