Novel Probability Density Function of Pad Asperity by Wear Effect over Time in Chemical Mechanical Planarization
Abstract
:1. Introduction
2. Theorectical Background
2.1. Contact Theory in CMP
2.1.1. Contact: PDF of Pad Asperity
2.1.2. Contact: Wear Affect in CMP
2.2. Multivariate Gaussian Normal Distribution (MVN) Theory
3. Model Development
3.1. Pad Asperity Evolution According to CMP Time
3.2. Novel PDF Model with MVN Theory
3.3. Material Removal Rate Model
- Initialize to and to ;
- Solve for the load-balancing separation using balance equation of force as in Equations (15) and (16);
- Calculate the actual contact-force , the actual contact area , and the number of contact asperities as in Equations (17)–(19);
- Integrate the evolution equation for the PDF for one time step;
- Calculate the material removal rate as in Equation (20);
- Increment the time and repeat from step 2 until complete.
4. Results and Discussion
4.1. Experimental Condition for CMP
4.2. Comparison of CMP Result and Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
CMP | Chemical mechanical planarization |
MVN | Multivariate normal distribution |
GW | Greenwood–Williamson |
MRR | Material removal rate |
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Bef. | 1 min | 2 min | 3 min | 4 min | 5 min | 10 min | Cond. | |
---|---|---|---|---|---|---|---|---|
2 psi | 109 | 121 | 103 | 113 | 97 | 91 | 56 | 114 |
3 psi | 106 | 103 | 116 | 110 | 98 | 96 | 52 | 120 |
4 psi | 121 | 118 | 101 | 99 | 80 | 82 | 60 | 110 |
5 psi | 114 | 96 | 72 | 81 | 60 | 46 | 108 |
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Jeong, S.; Shin, Y.; Jeong, J.; Jeong, S.; Jeong, H. Novel Probability Density Function of Pad Asperity by Wear Effect over Time in Chemical Mechanical Planarization. Materials 2024, 17, 1817. https://doi.org/10.3390/ma17081817
Jeong S, Shin Y, Jeong J, Jeong S, Jeong H. Novel Probability Density Function of Pad Asperity by Wear Effect over Time in Chemical Mechanical Planarization. Materials. 2024; 17(8):1817. https://doi.org/10.3390/ma17081817
Chicago/Turabian StyleJeong, Seonho, Yeongil Shin, Jongmin Jeong, Seunghun Jeong, and Haedo Jeong. 2024. "Novel Probability Density Function of Pad Asperity by Wear Effect over Time in Chemical Mechanical Planarization" Materials 17, no. 8: 1817. https://doi.org/10.3390/ma17081817