CMP Modeling

1
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
2
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
3
Model Theory

• 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

33
Tufts University Dept. of Mechanical
Engineering MS Thesis Defense Oct 17, 2002
4
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
5
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