An Analytical Model of Contact Pressure Caused by 2-D Wafer Topography in Chemical-Mechanical Polishing Process

Topography on wafer surface affects chemical-mechanical polishing (CMP) greatly. In this paper, 2-D wafer topography's effects on the contact pressure in CMP are investigated and calculated. It is found that the wafer can be treated as a rigid punch and pad as an elastic half space when the effects of the pattern features on the wafer surface are investigated. Based on the linear small strain theory of elasticity, the formula of calculating the contact pressure between the wafer and the pad is given. The performance of CMP system is shown to be a linear time invariant (LTI) system in a mathematical way. The magnitude spectra and phase spectra of the system are obtained exactly by the formula. The contact pressure for 2-D wafer topography during CMP can be calculated easily by the formula.