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

作者：Yu, Chengjiao^*; Wang, Zhanjiang; Sun, Fred; Lu, Shaoning; Keer, Leon M.; Wang, Q. Jane

来源：ECS Journal of Solid State Science and Technology, 2013, 2(9): P368-P374.

DOI：10.1149/2.017309jss

• FINITE-ELEMENT-ANALYSIS
• ELASTIC-PLASTIC MODEL
• MATERIAL-REMOVAL RATE
• DISCRETE CONVOLUTION
• MATHEMATICAL-MODEL
• MICRO-CONTACT
• AREA
• PRESSURE
• STRESSES
• BEHAVIOR

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.

• 出版日期2013
• 单位西北大学; 机械传动国家重点实验室; 重庆大学