CMP Modeling – Current Status Goal is to develop a comprehensive CMP model that complements experimental program Begin with hydrodynamic slurry flow model and eventually include pad deformation, polishing, etc. Bramono (MS with L. Racz) - rigid, flat wafer Scarfo (MS with V. Manno) - curved wafer Taylor (MS now) – RR or Pad Deformation 30 Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002

Current Hydrodynamic Slurry Flow Model 2-D model of gap between pad and wafer Slurry film thickness and angle of attack adjust to satisfy hydrodynamic boundary conditions based on lubrication theory Calculates slurry film pressure on wafer surface Slurry is modeled as one phase with one set of properties Assumes both pad and wafer to be rigid and smooth 31 Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002

Model Theory 33 Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002 To calculate correct slurry film thickness, need to satisfy following condition: –Slurry must support applied down force – Zero moment is required about gimbal point Full Navier-Stokes and energy equations were solved using FIDAP version 8.52

Chemical Mechanical Planarization (CMP) Model 2D cross section to reduce computational time A user-defined subroutine written to specify new wafer surface position FIDAP calculates solution for velocities and pressure in fluid region 34 Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002

Summary (Modeling) Hydrodynamic slurry flow model predicts fluid film thickness and pitch angle to satisfy a force and moment balance Addition of wafer bow significantly increases FFT Degree of wafer curvature affects pitch angle Viscous heating results in max temperature change of.25 °C (increases with higher downforce) Increases in viscosity significantly increase FFT and pitch angle Results compare well with experimental measurements (on same order) 43 Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002