Multi-Project

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Multi-Project Reticle Design Wafer Dicing
under Uncertain Demand
Andrew B Kahng, UC San Diego Ion Mandoiu,
University of Connecticut Xu Xu, UC San
Diego Alex Zelikovsky, Georgia State University
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Multi-Project Wafers

• Mask set cost gt1M for 90 nm technology
• Share cost of mask tooling between multiple
  designs!
• Prototyping
• Low volume production

Images courtesy of EuroPractice and CMP
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Design Flow for MPW
Die Sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Design Flow for MPW
Die Sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Why is Dicing a Problem?

• Side-to-side dicing!
• Correctly sliced out dies
• Cut lines along all four edges
• No cut line partitioning the die

Standard wafer dicing
MPW dicing
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Side-to-side Dicing Problem

• Given
• Production volume for each die
• Reticle floorplan
• Wafer shot-map
• Find
• Horizontal and vertical dicing plans for each
  wafer
• To Minimize
• wafers required to meet production volumes

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Dicing Strategies

• Wafer Dicing Plan (DP) all horizontal and
  vertical cut lines used to cut a wafer
• Row/Column DP cut lines through row/column of
  reticle images

• Single wafer dicing plan (SDP) ISPD04
  KahngR04
• The same wafer DP used for all wafers
• Different DPs used for different rows/cols in a
  wafer
• Multiple wafer dicing plans (MDP)
• Restricted MDP the same DP used for all
  rows/cols of a wafer
• Graph coloring based heuristic in Xu et al. 04

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Independent Dies

• Under restricted MDP dicing, all reticle images
  on wafer yield the same set of dies
• Independent set set of dies that that can be
  simultaneously diced from a reticle image
• Only maximal independent sets are of interest!

2
1
4
3
Maximal Independent Sets 1, 4 2 3
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ILP for Restricted MDP
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CMP Floorplan
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SDP vs. MDP
9 wafers with SDP
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4-Part Dicing

• Partition each wafer into 4 parts then dice each
  part separately using side-to-side cuts

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Design Flow for MPW
Die sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Shotmap Definition Problem
?
Reticle Floorplan

• Simple grid-based shotmap definition algorithm
  yields an average reduction of 13.6 in wafers

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Design Flow for MPW
Die sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Reticle Floorplaning Problem

• Given
• Die sizes production volumes
• Maximum reticle size
• Find
• Placement of dies within the reticle
• To Minimize
• Production cost (reticle cost, wafers, )

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Reticle Floorplaning Methods

• Key challenge cost estimation
• Previous approaches
• Simulated annealing ISPD04
• Grid-packing Andersson et al. 04, KahngR04
• Integer programming WuL05
• Our approach Hierarchical Quadrisection (HQ)

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Hierarchical Quadrisection Floorplan

• At most one die assigned to each region at
  lowest level
• Region widths/heights easily computed from die
  assignment
• HQ mesh more flexible than grid

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HQ Algorithm

• Random initial assignment improved using
  simulated annealing
• SA moves region exchange, die rotation
• Max reticle size enforced throughout the
  algorithm
• Hierarchical structure enables quick cost
  estimation

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HQ Floorplan of CMP Testcase
Reticle Area 2.30 (vs. 2.45)
4 wafers with MDP (vs. 5)
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Design Flow for MPW
Die sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Project Cloning

• Motivation
• Die-to-die inspection Xu et al.
• Reduced wafer cost when there is large variation
  in production demands
• Post-processing approach WuL05
• Insert clones in white space left on reticle
• Our approach
• Before floorplaning number of clones
  proportional to square root of production volume
  clones arranged in clone arrays
• During floorplaning clone arrays assigned to
  single cell in HQ new SA moves add/delete clone
  array row/column
• After floorplaning insert additional clone array
  rows/columns without increasing cell size

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Design Flow for MPW
Die sizes Production Volumes
Project Partitioning
Project Cloning
Reticle Floorplaning
Shotmap Definition
Dicing Plan Definition
Reticle, Wafer Shotmap, Wafer Dicing Plans
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Schedule Aware Partition

• More decision knobs fabrication schedule

I will not pay you after June
But, money will be saved if waiting for other
orders
?

• Project Partitioning Problem
• Given Reticle size, set of projects
• Find Partition of projects into reticles
• To minimize Sum of manufacturing cost and delay
  cost
• BACUS05 Schedule-aware partitioning leads to an
  average cost reduction of 63.8 vs.
  schedule-blind partitioning

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Demand Uncertainty

• Customer demands (over reticle life period) may
  not be fully known at design time
• Only rough customer demand distribution available
  (e.g., min/max demand)
• MPW become even more attractive in this context
  sharing of demand misprediction risks
• Online wafer dicing combined with production of
  larger wafer lots can bring further economies of
  scale (see paper)
• Feasible when there are no IP protection issues

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Robust Reticle Floorplaning

• Given
• Die sizes
• Maximum reticle size
• Distribution of customer orders
• Find
• Placement of dies within the reticle
• To Minimize
• Expected wafers required to meet customer
  orders over a fixed time horizon

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Compared Algorithms

• HQ with production volume set to the expected
  customer demand
• HQCloning with production volume set to the
  expected customer demand
• Distribution-driven simulated annealing
• Use expected production cost for evaluating SA
  moves
• Monte-Carlo simulation used to estimate expected
  cost

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Robustness Results - Normal
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Robustness Results Uniform
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Conclusions Future Research

• Improved MPW design flow
• Schedule-aware partitioning 60 average cost
  reduction
• Project cloning 10 average wafer cost reduction
• HQ reticle floorplan 15 average wafer cost
  reduction
• Wafer shot-map definition 13 average wafer cost
  reduction
• MDP wafer dicing 60 average wafer cost
  reduction
• Future work
• Multi-layer reticle design