A Deterministic Semi-Analytical Model for the Contact of a Wafer and a Rough Bi-Layer Pad in CMP

• Published in: ECS journal of solid state science and technology Vol. 2; no. 9; pp. P368 - P374
• Main Authors: Yu, Chengjiao, Wang, Zhanjiang, Sun, Fred, Lu, Shaoning, Keer, Leon M., Wang, Q. Jane
• Format: Journal Article
• Language: English
• Published: The Electrochemical Society 01.01.2013
• ISSN: 2162-8769; 2162-8777
• DOI: 10.1149/2.017309jss

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.