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摘要
In this paper, wafer topography's effects on the contact pressure distribution during CMP are investigated and calculated based on 3D solid-solid contact model. In the model, wafer is treated as a rigid punch and pad as a half-elastic space. The height variation on the wafer surface is assumed as a function of two dimensions and is described by TG(x, y). Based on the linear elasticity theory, a formula of calculating the contact pressure distribution between the wafer and the pad is deduced in an analytical way. The performance of CMP system is shown to be a linear system. The formula shows that when the wafer topography is expressed as 2-D Fourier expansions, the contact pressure between the wafer and the pad can be represented as a linear combination of e(-i(omega alpha x+omega beta y)) with the same frequencies and different amplitudes. The 3D magnitude spectra of the CMP system are obtained exactly by the formula. The evolution of the wafer topography consisting of two square wave features with different densities is simulated and compared with experimental data. The formula proposed in the paper will help to specify the polishing parameters during CMP. It also provides a novel method to calculate contact pressure distribution when a rigid body with complicated 3D topography contacts with flat flexible base completely.
- 出版日期2012
- 单位兰州理工大学
