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

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.