Sources of Wafer-Scale Nonuniformity

Sources of Wafer-Scale Nonuniformity a. Relative Velocity Mismatch Across the Wafer 

The Preston relationship provides a pointwise dependency of removal rate based on the relative velocity and pressure within some region of the wafer. A straightforward application of Preston s model is to study the 

Let the angular rotation of the wafer and table be CO2 id co (in radians per minute) respectively. Preston has obtained the relative velocity between pad and point Q on the wafer as 

This formulation assumes radial symmetry in the polishing process. With the substitution 6 = 2(p and cos 6=1 — 2 sin q , the effective radial velocity 

Preston s equation indicates a pressure dependency and if the pressure distribution across the surface of the wafer is not uniform, one expects a wafer-level removal rate dependency. Runnels et al, for example, report a model incorporating pressure dependencies to account for wafer scale nonuniformity [42]. The distribution of applied force across the surface of the wafer is highly dependent on the wafer carrier design, and significant innovation in head design to achieve either uniform or controllable pressure distributions is an important area of development. 

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