Voxelbased Heterogenous Modeling for SurfaceMicromachined MEMS

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Voxel-based Heterogenous Modeling for
Surface-Micromachined MEMS

• Andy Perrin
• Venkat Ananthakrishnan
• Radha Sarma
• G. K. Ananthasuresh
• (NSF Grant DMI 99-70059)

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Motivation

• Surface-micromachined MEMS devices can have very
  complicated geometries.

MUMPS micromotor
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Motivation

• Two problems
• (Forward Problem) Given a process and the masks,
  what does the part look like?
• (Inverse Problem) Given a process and a desired
  part geometry, what do the masks look like?
• We care about the part geometry, so we want to
  solve the inverse problem, but to solve it, we
  need the forward problem.

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Forward Problem Strategy

• Define some mathematical operators that can be
  composed with each other to yield process steps.
• If each process step can be reduced to some
  composition of operators, it does not matter how
  that step is actually implemented.
• Develop a practical implementation.

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State-change operators
Query operators
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Forward Problem Voxels

• Voxels are well adapted to
• Heterogenous modeling (multiple materials)
• Layered manufacturing processes
• Creating meshes for later analysis (FEA, etc.)
• Topology optimization
• Etching multiple layers
• Problems with voxels
• Rendering speed
• Memory requirements

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Forward Problem Heterogenous Modeling

• Voxels can store local material information.
  (Currently, we store a string indicating the
  material in each voxel.)
• Our mathematical model can be combined with Kumar
  and Duttas (1998) representations of
  heterogenous solid models.

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Forward Prob Implementation

• Four layer types
• Conformal
• Stack
• Via
• Planar
• Two etch types
• anisotropic
• isotropic

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Kinds of Layers
Stack
Conformal
Via
Planar Via Stack
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Kinds of Etches Anisotropic
Before
After
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Kinds of Etches Isotropic
Before
After
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User Interface
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Example
'stack' 'Substrate' 0.06666 1 'stack'
'Oxide' 0.13332 2 'etch' 'etch1' 0.13333
'Oxide' 'anisotropic' 1 'conformal'
'Polysilicon' 0.06666 3 'etch' 'etch2'
0.066663 'Polysilicon' 'anisotropic' 2
'etch' 'etch3' 0.19998 'Oxide'
'isotropic' 2
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Inverse Problem Strategy

• For each step of the given process do the
  following
• If the process step is a deposit command, deposit
  that layer in a new intermediate model (IM).
• If it is an etch command, compare the current IM
  to the given model and extract a mask etch the
  IM with it.
• Check/correct masks if they need modification
  update IM.

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Inverse Problem Strategy

• Mask correction routine yields three
  possibilities
• No solutions (impossible to build with given
  process)
• One solution (convenient!)
• Many solutions (Develop a figure of merit and
  choose the best.)

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Inverse Problem Limitations

• Restricted to conformal layers
• Restricted to anisotropic etches

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Future Work

• Incorporate via, planar layers and isotropic etch
  in inverse problem
• Apply topology optimization and combine with
  inverse problem to automatically design
  structures.
• Feature based modeling

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Thanks to...

• Dr. G.K. Ananthasuresh, Venkat Ananthakrishnan,
  Radha Sarma for their work, help, and support.
• NSF Grant DMI 99-70059