Modeling of the Effect of Wafer Topography on Chemical Mechanical Polishing Processes Based on 3D Analysis

In this paper, removal rate variation caused by wafer surface topography during chemical mechanical polishing (CMP) is studied based on the three-dimensional (3D) solid-solid contact model. In the model, the height of the wafer topography is a function of two dimensions as TG(x,y). A new way to calculate the contact pressure P(x,y) between the wafer and the pad during CMP is proposed. It is found by the simulation results that when TG(x,y) is represented as a linear combination of cos(omega(alpha)x)cos(omega(beta)y) (two-dimensional Fourier cosine expansions), the contact pressure P(x,y) can be represented as a linear combination of cos(omega(alpha)x)cos(omega(beta)y) with the same frequencies and different amplitudes. A broad class of signals can be represented as a linear combination of cos(omega(alpha)x)cos(omega(beta)y). The contact pressure P(x,y) will be obtained easily when the 3D magnitude spectra and 3D phase spectra of the system are known. The evolution of the wafer topography consisting of two square wave features with different densities is simulated and compared with the experimental data. This new method will be very helpful to establish the model for CMP with a complicated 3D wafer pattern structure. It will also help to specify the polishing parameters during CMP. The new method provides a general model to obtain contact pressure distribution when a rigid body with complicated 3D topography contacts with the flat flexible base completely. (C) 2011 The Electrochemical Society. [DOI: 10.1149/1.3527980] All rights reserved.