Balance model for contactless chemo-mechanical polishing of wafers

Abstract

We developed a physical model for polishing. It makes it possible to determine physico-chemical processes occurring at contactless chemo-mechanical polishing (CMP) of crystal surfaces. A balance equation for diffusion, convection and chemical flows is used to describe processes that are proceeding in the stationary case. The analytical expressions are obtained that relate polishing rate and surface form for processed material to the physical parameters of the proceeding processes. It was found that macrorelief of the processed surface depends not only on the velocity of polishing plate motion but also on the gap between the processed wafer and polishing plate, as well as active component diffusion in the etching solution. One would expect that, at processing conditions discussed, the surface form is the same for different materials, whatever the active component concentration and chemical reaction constant. The polishing rate substantially depends on the concentration of the etchant active component, chemical reaction, physical properties of sample material and etching liquid. It is shown that the inverse rate of dissolution is the sum of inverse limiting rates of chemical, diffusion and convection stages of the process. The expressions are obtained that make it possible to optimize technological modes of polishing.