## 4 Summary  
In this paper, we presented the kinematic modeling of three-motion disc rotation, pad rotation, and sweep of the conditioning arm in CMP conditioning. Based on this, a simulation was developed to visualize the center trajectory of the disc and the entire trajectory of the working diamond abrasives. In addition, the trajectory density was quantified by integrating the trajectory of the working diamond abrasives within a certain area, and based on this, a simulation to predict the wear shape of the pad was developed. Based on the developed simulator, the trajectory with respect to the pad rotation speed and the sweep speed was visualized, and when the sweep speed became a divisor of the pad rotation speed, the center trajectory did not move evenly across the pad and only moved in a specific trajectory. Furthermore, the predicted results and the actual shape of the pad profile were compared and analyzed in the simulation developed for eight pad wear patterns through ROT control using an in situ pad profile device. The predicted results and the actual shape of the pad profile were found to have similar overall shapes, and in particular, the positions of the inflection points where the inclination changes were largely identical. The shape of the pad could be maintained, which is the purpose of CMP conditioning, by changing the size of the disc and the returning point. In addition, as the overhang length increased, the pressure effect increased, and it was experimentally proven that a flat area can be ensured over the entire pad. The final results showed that the maximum pad thickness deviation was less than 10 \(\upmu\)m even after 2 h of conditioning. The developed simulation is expected to not only be able to quickly verify the various conditions of conditioning, but also ultimately help in deriving conditions that can maintain a constant shape of the pad. Maintaining the pad shape can help maintain the shape of the wafer in the CMP process.  
The following are available online at [[https://www.mdpi.com/article/10.3390/app11104358/s1](https://www.mdpi.com/article/10.3390/app11104358/s1)]([https://www.mdpi.com/article/10.3390/app11104358/s1](https://www.mdpi.com/article/10.3390/app11104358/s1)), Videos S1 and S2: Pad profile measuring system.  
Conceptualization and developed the idea, H.C. and H.K.; methodology, H.C., H.K., and T.L.; validation, D.K. and T.L.; investigation, D.K.; resources, H.K.; writing--original draft preparation, H.C.; writing--reviewing, H.K.; supervision, H.K.; project administration, H.K. All authors have read and agreed to the published version of the manuscript.  
This study has been conducted with the support of the Korea Institute of Industrial Technology as \"Research equipment coordination project (KITECH JH-21-0008)\". Additionally, this research was funded by the Ministry of Trade, Industry and Energy of the Republic of Korea (grant number 20013589).  
Not applicable.  
We thank Saeosol Diamond Co. for providing us the diamond disc.  
Figure 12: (**a**) Pad wear profile under a controlled condition with a 375 mm overhang, (**b**) Pad thickness variation over time under even and controlled conditions with an overhang of 375 mm.