A Current Driven Routing and Verification Methodology for Analog Applications

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A Current Driven Routing and Verification
Methodology for Analog Applications

• Thorsten AdlerInfineon Technologies
  AGThorsten.Adler_at_infineon.com
• Hiltrud Brocke, Lars Hedrich, Erich
  BarkeInstitute of Microelectronic
  SystemsUniversity of Hanover

This work was supported by the German BMFT
under contract 01 M 3034 Research was done at
IMS, University of Hanover
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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Introduction

• Current driven routing of multi-terminal nets

• Power ground nets

• Signal nets in analog integrated circuits

• Variable width routing per wire segment used to

• Avoid electromigration

• Save routing space

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Standard Flow
Introduction

• Current driven routing using

• Standard unified values, e.g. minimum values

• Manually specified current values

• Layout extraction simulation

• Layout modification if needed

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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Proposed Design Methodology

• Current Characterization

• Current Driven Router (CDR)

• Layout correct by construction

• Layout verification for existing layouts (CDXCDS)

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New Design Flow
Proposed Design Methodology
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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Current Characterization

• Determination of realistic current values per
  terminal

• Simulation

• Standard circuit simulator

• Netlist

• Designer or Monte Carlo Stimuli

• Postprocessing

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Postprocessing
Current Characterization

• Simulate circuit and gather all terminal currents

• For all terminals

• Extract maximum positiveand negative current
  value

• Copy those two snapshotsinto the current vector

• For n terminals that may lead to up to 2n current
  vectors

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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Current Driven Router (CDR)
Current driven routing of multi-terminal nets

• Power ground routing

• Signal nets in analog applications

• Guided by terminal currents

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Problem Definition
CDR
ST2
?
?
ST2
ST1
ST1

• Current flow between two Steiner points unknown
  prior to Steiner tree topology construction

• Valid Steiner tree topology construction only
  possible if all currents are known

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Power Ground Routing
CDR

• Power Ground routing is done sequential

• Steiner tree topology

• Calculation of unknown currents

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• Steiner tree layout generation

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Power Ground Routing
CDR

• Power Ground routing is done sequential

• Steiner tree topology

• Calculation of unknown currents

• Steiner tree layout generation

• Layout modification

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Routing for Analog Applications
CDR

• Signal net routing ? crowded routing levels

• Analog circuits highly sensible to parasitic
  effects

? Placement modifications not allowed

• CDR has to generate layout correct by
  construction

• Sequential generation of Steiner tree topology

• Simultaneous computation of unknown currents

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Principle
CDR

• Steiner tree generation based on Hanans algorithm

w2
w1
w1w2w3
w3

• Single trunk Steiner tree problem ? O(n)

• Unknown current flow between two Steiner points
  calculated on the fly during Steiner tree
  generation

• Modified Three-Point-Steinerization algorithm

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Database
CDR

• Connection graph

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Basic Algorithm
CDR

• While more than one terminal to connect

• While more than one terminal to connect

• Find the optimum Steiner point between the last
  Steiner point and the next two terminals (P3S)

• Find the optimum Steiner point between the last
  Steiner point and the next two terminals (P3S)

• Generate the wire between the two Steiner points

• Generate the wire between the two Steiner points

ST1

• Connect the first terminal to the new Steiner
  point

• Connect the first terminal to the new Steiner
  point

• Connect the remaining terminal to the last
  Steiner point found

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Basic Algorithm
CDR

• While more than one terminal to connect

• While more than one terminal to connect

• Find the optimum Steiner point between the last
  Steiner point and the next two terminals (P3S)

• Find the optimum Steiner point between the last
  Steiner point and the next two terminals (P3S)

• Generate the wire between the two Steiner points

• Generate the wire between the two Steiner points

ST2

• Connect the first terminal to the new Steiner
  point

• Connect the first terminal to the new Steiner
  point

• Connect the remaining terminal to the last
  Steiner point found

• Connect the remaining terminal to the last
  Steiner point found

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Three-Point-Steinerization
CDR

• Start a graph search from the actual Steiner
  point to the next two unconnected terminals

• At every graph node evaluate a cost function that
  estimates the final routing area

• Compute the exact distance to the next two
  terminals using a modified detour algorithm

• Estimate the routing area needed to connect all
  remaining terminals

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Steiner Point Search
CDR
v current node u node last reached d Distance
between LAST_ST and u M Manhattan distance
widtht1detour(v,t1,widtht1)
cost(v) widthLAST_ST(dM(u,v))
widtht2detour(v,t2,widtht2)
estimate_route_area(v)
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Steiner Point Search
CDR
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T2
v current node u node last reached d Distance
between LAST_ST and u M Manhattan distance
T4
-8
v
u
T1
T3
-4
6
LAST_ST
widtht1detour(v,t1,widtht1)
cost(v) widthLAST_ST(dM(u,v))
widtht2detour(v,t2,widtht2)
estimate_route_area(v)
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Steiner Point Search
CDR
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T2
v current node u node last reached d Distance
between LAST_ST and u M Manhattan distance
T4
v
-8
u
T1
T3
-4
6
LAST_ST
widtht1detour(v,t1,widtht1)
cost(v) widthLAST_ST(dM(u,v))
widtht2detour(v,t2,widtht2)
estimate_route_area(v)
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Steiner Point Search
CDR
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T2
v
v current node u node last reached d Distance
between LAST_ST and u M Manhattan distance
T4
u
-8
T1
T3
-4
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LAST_ST
widtht1detour(v,t1,widtht1)
cost(v) widthLAST_ST(dM(u,v))
widtht2detour(v,t2,widtht2)
estimate_route_area(v)
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Steiner Point Search
CDR
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T2
ST
T4
-8
T1
T3
-4
6
LAST_ST
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Steiner Point Heuristics
CDR

• Cost function finds local optimums only

• Heuristics used to find the global optimum

• Terminal swapping during path searching

• Steiner points above terminals

• Generation of hierarchical Steiner trees

• etc.

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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Current Density Simulator (CDS)
Validation tool used to check current densities

• Extraction of interconnection network (CDX)

• Calculation of unknown currents between Steiner
  points

• Computation of current densities

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Geometry Extraction (CDX)
CDS
Correlation between wire segments and resistors

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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Example 1 Terminal Swapping
Examples - CDR
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Example 2
Examples - CDR
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Example 3 Hierarchical Steiner Tree
Examples - CDR
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Example 1 An industrial example
Examples - CDS
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Outline

• Introduction
• Proposed Methodology
• Current Characterization
• Current Driven Router (CDR)
• Current Density Simulator (CDS)
• Examples
• Summary Outlook

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Summary

• Work supported by German BMFT (SSE-PARASITICS)

• Cooperation between IMS Hanover, Bosch and TEMIC

• Prototype system available

• Current characterization

• Current driven routing of multi-terminal nets

• Layout validation

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Outlook

• CDR

• Two layer routing

• Manual specification of Steiner points to be used

• Coupling with in-house routers from Bosch and
  TEMIC

• CDS

• Proper treatment of irregularities

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