LargeScale FullWave Simulation

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Large-Scale Full-Wave Simulation

• Sharad Kapur and David Long
• Integrand Software, Inc.

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Areas
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Current Inaccurate methods

• In IC-world R,L,C and substrate extracted
  separately
• Cobbled together
• Can be inaccurate
• Wire over high-resistivity substrate
• Strong frequency dependence
• Effective ground plane moves lower at high
  frequencies
• Problems with a-priori assumptions about
  current-return paths for inductance
• Real problem is fully coupled

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EMX

• Full-wave field solvers can be made practical
• Replace patchwork of point tools
• High accuracy for large RF chip-size problems
• Handle all electromagnetic effects in a unified
  manner
• Efficient and very accurate
• GDSII -gt S-Params/Spice like representation

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Fundamental problem

• Efficiency
• Structures are discretized into panels and
  unknowns to be solved for are things like
  charge/current
• Accurate simulations are computationally
  expensive
• Traditional full-wave EM simulation tools can
  take hours

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Solving the linear system efficiently

• Conventional methods O(N3) time
• In 80s-90s slew of techniques for solving these
  systems
• Iterative methods reduce time to O(N2)
• Fast Matrix-Vector methods O(N)
• Fast Multipole Methods, SVD methods, P-FFT
  methods
• Fundamentally changed computational
  electromagnetics
• Reached point of diminishing returns

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IC specific fast solutions

• Nebula capacitance using FMM (DAC 2000)
• had sufficient speed to do the electrostatic
  (capacitance) problem for block sized problems
• Homogenization of far-away geometry
• Cannot be applied to full-wave problem
• IES3 full-wave solution using SVDs (ICCAD 96)
• with a completely new direction of attack
• Several new ideas in EMX implementation
• Will talk about two of them

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Idea 1 Layout is regular

• Wires are paths of constant width
• Distance between adjacent routing is constant
• Routing is at 45 or 90 degrees
• Components, spiral inductors, capacitors, are
  symmetric
• Normal notion of regularity, repeated instances
  of subcircuits
• Layout space is actually a very small subset of
  all possible routing
• Can you take advantage of this?

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Conventional approach

• In all previous approaches, mesh generation and
  field solution viewed as orthogonal sub problems
• Mesh generation
• Typically unstructured Delauny triangulation
• Field solution
• Uses a fast solver method
• Independent of the underlying mesh
• Cannot take advantage of layout regularity

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• Unstructured Delauny mesh
• Pairs of interactions are dissimilar, because of
  the shapes and the distances between the
  triangles

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• Layout has a lot of structure
• This structure can be imposed on the mesh
• Identical interactions are repeated all over
• Few unstructured left over regions are a small
  part of the mesh

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Routing of a 16 bit bus line from a 10GHz chip
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Quadrature CMOS VCO (Gierkink, Frye, courtesy
Agere)
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(No Transcript)
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Algorithm for creating regular meshes

• Wire recognition algorithmwas developed
• Sweep through the layout identifying wires
• Grey regions areidentified wires
• Once the wires are identified
• A mesh is created from a small set of canonical
  shapes

The Jester RCF
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Algorithm for creating regular meshes

• Wire recognition algorithm was developed
• Sweep through the layout identifying wires
• Grey regions areidentified wires
• Once the wires are identified
• A mesh is created froma small set of canonical
  shapes

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Algorithm for creating regular meshes

• Wire recognition algorithm was developed
• Sweep through the layout identifying wires
• Grey regions areidentified wires
• Once the wires are identified
• A mesh is created froma small set of canonical
  shapes

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Exploiting the regularity

• Embedded in the FMM
• Direct interactions represented by sparse matrix
• Lot of structure in the sparse matrix with
  identical entries
• Substantially more compact representation
• Reduction in time for matrix construction
  (integral time)
• Reduction in storage

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Idea 2 Approximating the vector formulation

• Vector potential term isdominant cost
• With RWG basis functions
• 3 roof tops for each triangle
• 4 roof tops for each rectangle
• Between two shapes need to compute 9-16
  interactions
• 1 for scalar interaction

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Approximating the Vector potential

• To avoid ill-conditioning basis functions are
  decomposed into curl free and divergence free
  bases (loops and patches)
• Current flow through a triangle due to loop is a
  constant!
• Can be exactly represented by a scalar integral
  over source
• Approximation for other vector contributions

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Approximating the vector potential

• In the limit of fine mesh approximation is exact
• Intuition The current flow smoothly varies
  across shapes and very small amount of charge is
  deposited as current leaves a shape
• Approximation is valid for practical problems and
  frequencies

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Examples
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10s
35s
360s
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Comparsion to IES3
20x-40x saving in memory 20x-30x saving in
time Better accuracy than IES3
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• PBP001 blue
• PBP002 black
• Sim - red
• Inductance
• Q
• Resistance
• Impedance

L15
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Integrated Filter Design

• Integrated filter design
• Courtesy of STATS
• Circuit is a band pass filter with R,L,C and
  interconnect
• MIM caps

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Integrated Filter Design

• Comparison of EMX simulation to measurement
• Structure designed and measured by Bob Frye

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Conclusion

• Developed a new full-wave simulation tool
• Takes advantage of layout regularity
• New formulation for vector potential
• 50x faster than previous approaches
• Used for model generation and RF block level
  simulation, packaging, etc.
• Potential application in many other areas