## 3 Results  
We developed a prediction simulation to visualize the center of the conditioning disc, the trajectory of the working diamond abrasives, and the wear amount color contour using LabVIEW (National Instruments, Austin, TX, USA). Figure 5a shows an example of visualizing the trajectory made by the center of the conditioner disc on the pad. Figure 5b shows the visualization results of the trajectory of the entire working diamond abrasives. Figure 5c shows the wear amount color contour on a 2D plane. All the subsequent interpretations were performed on the basis of the aforementioned theory. Subsequently, the results of the prediction of the pad wear amount were compared with the profile in the pad radial direction considering the symmetrical motion characteristics of the CMP. Figure 4: (**a**) Conceptual diagram of a motion model comprising a rotating disc, a pad, and a swing arm, (**b**) Schematic of the integration of the trajectory length within a specific area for predicting the wear amount. Figure 5: (**a**) Disc-centered motion trajectory predicted by the developed simulation; (**b**) Trajectory of all working diamond abrasives; (**c**) Color contour through integration of the trajectory length. Based on the developed simulation shown in the example of Figure 5, the change in the pad shape was predicted for the rotational speed of the disc, the rotational speed of the pad, and the sweep speed of the swing arm. First, the rotation speed of the conditioner disc was fixed at 103 rpm, and the effects of the rotation speed of the pad and the sweep speed on the relative motion were analyzed. Figure 6 shows the results of the center trajectory of the conditioner disc under 12 conditions in which the pad speed was varied from 96 rpm to 99 rpm at a rate of 1 rpm, and the sweep speed was increased in steps of 1 sweep/min from 8 to 10 sweeps/min. When the sweep speed was 8 sweeps/min and the rotation speed of the pad was 96 rpm, the trajectory of the center did not spread evenly over the pad; it moved repeatedly in a certain trajectory. The same phenomenon was observed at 99 rpm and 9 sweeps/min. If the sweep speed is a divisor of the rotational speed of the pad, the center trajectory of the conditioner is not evenly distributed across the pad, and only the same path moves. In Figure 7, the trajectory of all the working diamond abrasives on the pad is confirmed, and the trajectory is unevenly distributed over the entire surface of the pad under the two conditions mentioned in Figure 6. Figure 8 shows the result of integrating this within a 1 cm square meter and expressing it as a color contour. In Figure 6, under a pad rotation speed of 96 rpm and a sweep speed of 8 sweep/min, the shape of the pad worn by the entire working diamond abrasives is uneven. Under the other conditions, except for the two conditions, the pad is expected to wear evenly over its entire surface. When the above conditions are applied to the actual process, wafer polishing may be adversely affected by the nonuniform wear and shape of the pad. This suggests that the pad shape may change into an undesired shape in some cases, despite a slight change of 1 rpm. Based on these  
Figure 6: Conditioner disc center trajectory on the pad with respect to pad rotation speed and conditioning arm swing speed. results, it is necessary to set the sweep speed such that it is not a divisor of the rotational speed of the pad. To confirm that the developed pad wear prediction simulation is in good agreement with the actual experimental results, a comparison of the predicted shape and the actual shape was made under the eight conditions explained in the Materials and Methods section. In addition to the even condition with the same ROT in all the zones, seven conditions were verified: linear center fast, linear edge fast, controlled, parabolic, inverse parabolic, step edge fast, and step center fast. For various types of ROT, we confirmed whether the actual pad wear shape and the shape predicted by the developed simulation match.