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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. Multi-Project Wafer s. Mask set cost: >$1M for 90 nm technology

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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


Multi-Project Wafers

  • Mask set cost: >$1M for 90 nm technology

  • Share cost of mask tooling between multiple designs!

    • Prototyping

    • Low volume production

Images courtesy of EuroPractice and CMP


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


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


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


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


Dicing Strategies

2

2

2

1

1

1

3

3

3

4

4

4

  • 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]


Independent dies
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

3

4

Maximal Independent Sets: {1, 4} {2} {3}




SDP vs. MDP

5 wafers with MDP

9 wafers with SDP


4 part dicing
4-Part Dicing

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


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


Shotmap #1

Shotmap #2

Shotmap Definition Problem

?

Reticle Floorplan

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


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


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, …)


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)


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


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


HQ Floorplan of CMP Testcase

Reticle Area =2.30(vs. 2.45)

4 wafers with MDP (vs. 5)


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


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


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


Schedule Aware Partition

  • More decision knobs: fabrication schedule

I will not pay you afterJune

?

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


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


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


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




Conclusions future research
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


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