## 4 Experimental Procedures  
The movement of polishing slurry being acted upon by DEP force in a non-uniform electric field is observed in real-time by using a high-speed camera recording system, as shown in Figure 7. The observing experimental results are shown in the Figure 8. It could be seen from Figure 8, compared with other frequencies, that the maximum movement displacement of the polishing slurry is achieved at the frequency of 40 Hz. The displacement of the polishing slurry at 40 Hz is shown in Figure 9. Therefore, among these frequencies, when the frequency is 40 Hz, the largest DEP force is exerted on the polishing slurry. The 40 Hz was thus chosen as the frequency of subsequent processing experiments. Figure 10 shows the maximum displacement of polishing slurry under different electric field intensities. It can be seen from the Figure 10 that the electric field intensity is directly proportional to the displacement of the polishing slurry, the DEP effect and the DEP force on the polishing slurry. The DEP phenomenon is obvious at 300 V/mm, and the displacement of the polishing slurry at 300 V/mm is close to that of 450 V/mm. In fact, 450 V/mm is the maximum electric field intensity of the power supply, and considering the stability and reliability of the power supply, 300 V/mm was chosen as the electric field intensity for polishing experiments. Figure 5: The magnitude and direction of DEP force on the abrasive between the upper and lower electrodes. Figure 6: The simulation of movement of SiO\({}_{2}\) abrasive under both DEP force and centrifugal force. Figure 8: Maximum displacement of polishing slurry under different frequencies. Figure 10: Maximum displacement of polishing slurry under different electric field intensities. Figure 7: Experimental apparatus for observing polishing slurry: (**a**) schematic and (**b**) actual apparatus. Figure 9: The displacement of the polishing slurry at 40 Hz: (**a**) initial state and (**b**) 40 Hz. There were two groups of polishing experiments, one group utilized DEPP for sapphire substrate polishing, and the other group utilized traditional CMP. Most experimental settings for both groups were the same, the only difference between the two experiments being whether there is a non-uniform electric field. Detailed setting parameters for both experiments are shown in Table 1. The experiments were carried out on a Nanopoli-100 precision polishing machine and Figure 11 shows the picture of the actual DEPP machine. Turning off the power supply switches the machine to a traditional CMP polishing machine. The polishing pad is a cross-patterned polyurethane pad and its parameters are listed in Figure 8.0 The diameter and thickness of the sapphire substrates used in both experiments are 2 inches and 0.45 mm, respectively. The initial surface roughness of both substrates is about 1 um. Figure 12 shows the initial surface morphology and micrographs of the substrates, and it can be seen that there are many damages on the surface. Four diameters (0 mm, 16 mm, 32 mm and 48 mm) were selected as the research objects, and four locations were marked at every same diameter on the sapphire surface, the marked locations shown in Figure 8.1 The surface roughness of the marked locations was measured every 30 min; add the four surfaces roughness values at the same diameter, then the average surface roughness of each diameter was achieved. The measuring equipment was a VEECO white light interferometer. The change of surface roughness of sapphire at different diameters can be obtained from the average surface roughness. The surface morphology and the flatness of the sapphire substrates are observed after polishing. Initial weight and thickness of sapphire substrates are M and H, respectively. The weight after polishing is \(M_{0}\), polishing time is t, and \(MRR\) is the material removal rate:  
Figure 8.2Figure 8.3 Initial state of sapphire substrate: (**a**) surface micrograph; (**b**) 2D surface morphology; and (**c**) 3D surface morphology.