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

30Tufts 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

31Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002

Model Theory

33Tufts 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

dAFd n

surfacewafer gf dA

_nRM

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

34Tufts 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)

43Tufts University – Dept. of Mechanical Engineering – MS Thesis Defense –Oct 17, 2002