Multi-Project Reticle Design & Wafer Dicing under Uncertain Demand Andrew B Kahng, UC San Diego Ion...
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Multi-Project Reticle Design & Wafer Dicing under Uncertain Demand ndrew B Kahng, UC San Diego on Mandoiu, University of Connecticut u Xu, UC San Diego Alex Zelikovsky, Georgia State Universi
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Transcript of Multi-Project Reticle Design & Wafer Dicing under Uncertain Demand Andrew B Kahng, UC San Diego Ion...
Multi-Project Reticle Design & Wafer Dicing
under Uncertain Demand
Andrew B Kahng, UC San DiegoIon Mandoiu, University of ConnecticutXu Xu, UC San DiegoAlex Zelikovsky, Georgia State University
2Images courtesy of EuroPractice and CMP
Multi-Project Wafers Mask set cost: >$1M for 90 nm technology Share cost of mask tooling between multiple designs!
Prototyping Low volume production
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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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Standard wafer dicing MPW dicing
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
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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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1 2
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1 2
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1 2
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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
1 2
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Maximal Independent Sets: {1, 4} {2} {3}
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!
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ILP for Restricted MDP
:Subject to
:Minimize pw nn
IyxN
xn
yn
DDNyDIQ
II
IIp
IIw
CDI
max
)(),(
otherwise 0 ,0 if 1
set indep. dice toused wafers#
II
I
yx
Iy
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CMP Floorplan
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9 wafers with SDP
SDP vs. MDP
5 wafers with MDP
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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
Shotmap #1
Shotmap #2
?
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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Given: Die sizes & production volumes Maximum reticle size
Find: Placement of dies within the reticle
To Minimize: Production cost (reticle cost, #wafers, …)
Reticle Floorplaning Problem
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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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Reticle Area = 2.30 (vs. 2.45)
HQ Floorplan of CMP Testcase
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 scheduleI will not pay you
after JuneBut, 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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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
Robust Reticle Floorplaning
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Compared Algorithms
HQ with production volume set to the expected customer demand
HQ+Cloning 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
