A Dynamic Thermal Modeling of Chemical Mechanical Polishing Process

화학기계적 연마 프로세스의 동적 열전달 모델링 연구

  • Published : 2004.05.01


This paper describes a dynamic thermal model for a representative dual axis rotational Chemical-Mechanical Polishing (CMP) tool. The model is one-dimensional but configured in the two-dimensional space and consists of three sub-models (pad, wafer and slurry fluid), with the first and the second that are time-dependent heat conduction-convection models with linear stationary (wafer) and nonlinear moving (pad) boundary conditions, and the last one that is a heat transport-convection model (slurry fluid). The modeling approach is validated by comparing the simulation results with available experimental data.


CMP;Dynamic Thermal Modeling;Material Removal Model;Transient Thermal Analysis


  1. Mathworks, $Matlab^{TM}$ Version 6.1, 2001, Mathworks Inc.
  2. Bejan, A., 1988, Advanced Engineering Thermodynamics, New York, John Wiley & Sons
  3. White, D., Melvin, J. and Boning, D., 2003, 'Characterization and modeling of dynamic thermal behavior in CMP,' J. Electrochem. Soc., Vol. 150, No. 4, pp. G271-G278
  4. Incropera, F. P. and DeWitt, D. P., 1985, Introduction of Heat Transfer, New York, John Wiley & Sons
  5. Kwon, D. H., Kim, H. J., Jeong, H. D., Lee, E. S., Shin, Y. J., 2001, 'A Study of Temperature Behavior and Friction Force Generated by Chemical Mechanical Polishing,' Proceedings of the Korean Society of Precision Engineering Fall Meeting, pp. 939-942
  6. Cho, S. H., Kim, H. J. Kim, H. Y., Seo, H. D., Kim, K. J. and Jeong, H. D., 2001, 'A Study on the Improvement of the Slurry Dispersibility in CMP,' Journal of the Korean Society of Mechanical Engineers A, Vol. 25, No. 10, pp. 1535-1540
  7. Runnels, S. R., Eyman, L. M., 1998, 'Tribology Analysis of Chemical-Mechanical Polishing,' J. Electrochem. Soc., Vol. 141, No. 6, pp. 1698-1701
  8. Shan, L., Levert, J. A., Tichy, J. and Danyluk, S., 2000, 'Interfacial Fluid Mechanics and Pressure Prediction in Chemical Mechanical Polishing,' Journal of Tribology, Vol. 122, No. 3, pp. 539-543
  9. Seok, J., Sukam, C. P., Kim, A. T., Tichy, J. A. and Cale, T. S., 2003, 'Multiscale Material Removal Modeling of Chemical Mechanical Polishing,' Wear, Vol. 254, pp. 307-320
  10. Greenwood, J. A. and P.Williamson, J. B., 1966, 'Contact of Norminally Flat Surfaces,' Proceedings of the Royal Society London, Vol. A 295, pp. 300-319
  11. Preston, F., 1927, 'The Theory and Design of Plate Glass Polishing Machines,' J. Soc. Glass Technol. Vol. 11, pp. 214-256
  12. Luo, J. and Dornfeld, D. A., 2001, 'Material Removal Mechanism in Chemical Mechanical Polishing: Theory and Modeling,' IEEE Trans. Semicon. Manufact. Vol. 14, No. 2, pp. 112-133
  13. Steigerwald, J. M., Muraka, S. P. and Gutmann, R. J., 1997, Chemical Mechanical Planarization of Microelectronic Materials, New York, John Wiley & Sons