Ph.D. Dissertation Defense by Sum Huan Ng
Monday, February 21, 2005
(Dr. Steven Danyluk, Chair)
"Measurement and Modeling of Fluid Pressures in Chemical Mechanical Polishing"
A theory of the sub-ambient fluid pressure phenomenon observed during the wet sliding of a disk on a polymeric pad is presented. Two-dimensional fluid pressure mapping using membrane pressure sensors reveals a large, asymmetrical sub-ambient pressure region occupying about 70 percent of the disk-pad contact area. At the same time, a small positive pressure region exists near the trailing edge of the disk. This phenomenon is believed to be present during chemical mechanical polishing (CMP) and can contribute to the contact pressure, affecting the material removal rate and removal uniformity. Depending on the load and pad speed, the real contact pressure can be more than 2 times the nominal contact pressure due to the applied load. Tilt measurements of the disk carried out by a capacitive sensing technique indicate that the disk is tilted towards the leading edge and pad center when the pad is rotating. In addition, wafer bow is found to be less than 2 µm and wafer tilt with respect to the wafer carrier is 5 to 7 µm in the CMP configuration. A two-dimensional mixed-lubrication model based on the Reynolds equation is developed and solved using a finite differencing scheme. The pad is modeled as two layers: a top asperity layer described by the Greenwood and Williamson equation, and the bulk pad as linearly elastic. The orientation of the disk is determined by balancing the fluid and solid forces acting on it and solving using a modified Newton 's method. It is found that the tilt of the disk and the pad topography play important roles in the distribution of fluid pressure through affecting the film thickness distribution. For a pad with severe topography, minimum and maximum fluid pressures of -90 kPa and +51 kPa respectively are detected. The model is able to recreate the experimental pressure maps. A material removal rate model based on mechanical abrasion and statistics has also been developed. The model assumes that only abrasives trapped between the tips of the pad asperities and the wafer are responsible for material removal. Abrasives that are too large to get between the pad asperity tips and wafer are filtered out. Taking into account the relative velocity distribution and contact pressure distribution across the wafer, the model is able to create the material removal rate distribution. Comparisons of model predictions and silicon oxide polishing results show agreement.