A deterministic semi-analytical model for the contact of a wafer and a rough Bi-layer pad in CMP

Chengjiao Yu, Zhanjiang Wang, Fred Sun, Shaoning Lu, Leon M. Keer, Q. Jane Wang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Precise understanding of the pad-wafer contact is needed for designing polishing pads and planarization processes. This paper presents a deterministic semi-analytical model for investigating the elastic contact between a rough bi-layer porous body (pad) and a rigid plane (wafer). Homogenized or equivalent material properties are obtained and utilized for modeling each layer. The frequency response functions (FRF) for contact involving a bi-layer material, based on the Papkovich-Neuber potentials, are used, and the model is solved with the conjugate gradient method (CGM) and a fast Fourier transform (FFT) approach. The simulated pad-wafer contact areas are compared with the results from optical contact measurements for model verification. The application region of the bi-layered model is determined, and a map for the use of the bi-layer contact model is generated. The impacts of materials and layer thicknesses on contact ratio are analyzed.

Original languageEnglish (US)
Pages (from-to)P368-P374
JournalECS Journal of Solid State Science and Technology
Volume2
Issue number9
DOIs
StatePublished - 2013

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials

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