Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-22T14:23:19.947Z Has data issue: false hasContentIssue false

A Fast, Experimentally validated, Particle Augmented Mixed Lubrication Framework to Predict CMP

Published online by Cambridge University Press:  13 August 2013

Gagan Srivastava
Affiliation:
Mechanical Engineering. Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh PA 15213
C . Fred Higgs III
Affiliation:
Mechanical Engineering. Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh PA 15213
Get access

Abstract

Fabrication of integrated circuits is a multi-step process that involves chemical mechanical polishing (CMP) for planarizing the deposited layers. Although dependent on the consumables and machine operating conditions, most CMP researchers assume that the polishing occurs in the mixedlubrication regime, where the applied load on the wafer is supported by the hydrodynamic slurry pressure and the contact stress generated during the pad-wafer contact. The particle augmented mixed lubrication (PAML) approach has been employed by Terrell and Higgs (2009) as a high-fidelity asperity-scale mixed-lubrication CMP model. The current work introduces a more computationally efficient wafer-scale PAML model, called PAML-lite, which employs a two-dimensional average flow Reynold's Equation incorporating spatial dependence of entrainment velocities to model the hydrodynamic pressure. The contact mechanics are modeled using a Winkler elastic foundation in cylindrical polar coordinates. The resulting slurry hydrodynamic pressure distribution and contact stress are used to determine the equilibrium configuration of the system in the form of a nominal clearance and rolling and pitch angles. Local and wafer scale material removal rate (MRR) is predicted by assuming a uniform distribution of particle sizes. The prediction of PAML-lite were then benchmarked against experimental results. Upon verification, parametric studies were conducted to understand the effect of some unexplored CMP parameters.

Type
Articles
Copyright
Copyright © Materials Research Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Terrell, E. J. and Higgs, C. F., “A Particle-Augmented Mixed Lubrication Modeling Approach to Predicting Chemical Mechanical Polishing, ” J. Tribol., vol. 131, no. 1, p. 012201, 2009.CrossRefGoogle Scholar
Johnson, K. L., “Contact mechanics, ” 1985. .CrossRefGoogle Scholar
Luo, J. and Dornfeld, D. A., “Material removal mechanism in chemical mechanical polishing: theory and modeling, ” IEEE Trans. Semicond. Manuf., vol. 14, no. 2, pp. 112133, 2001.Google Scholar