Modeling of chemical mechanical polishing at multiple scales

Abstract

Chemical Mechanical Polishing (CMP) has grown rapidly during the past decade as part of mainstream processing method in submicron integrated circuit manufacturing because of its global or near-global planarization ability. However, CMP process is influenced by many factors and is poorly understood. It makes process control and optimization very diffi­ cult. This study focuses on the modeling and simulation to facilitate better understanding and better control of the CMP process. The thesis outlines the modeling of CMP process in three scales: particle scale for material removal mechanism, wafer scale for within wafer nonuniformity issues and feature scale for dishing and erosion in metal CMP. At the particle scale, material removal mechanism is assumed to be due to local plastic deformation of wafer surface at the abrasive wafer interface. Pad is assumed to deform like a beam to obtain an approximate force partition between abrasives and direct wafer-pad contact. A mechanistic material removal model is derived that delineates the influence of abrasive (shape, size and concentration), pad (rigidity) and process parameters (pressure and relative velocity) on the material removal rate (MRR). Wafer scale model is based on the solution of indentation of elastic half space by a rigid fhctionless polynomial punch. The elastic solution is derived through potential theory and complex analysis method. It is valid for any polynomial punch with integer power or noninteger power. The load-displacement relationship is also derived and the conditions for unbonded or bonded contact are obtained from the boundary condition at punch edge. The corresponding viscoelastic solution is obtained through Laplace transform and elastic-viscoelastic analogy. The elastic solution is used to explain the edge effect. The elastic analytical