Design and Test Trends from Physical Design perspective - PowerPoint PPT Presentation

Loading...

PPT – Design and Test Trends from Physical Design perspective PowerPoint presentation | free to download - id: 39527-ODlmY



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Design and Test Trends from Physical Design perspective

Description:

1. Session III. Dr. Parthasarathi Dasgupta. MIS Group. Indian Institute of Management Calcutta ... Local wiring Pitch (nm) 105 750. Minimum Global wiring Pitch ... – PowerPoint PPT presentation

Number of Views:152
Avg rating:3.0/5.0
Slides: 160
Provided by: Part95
Learn more at: http://www.cse.iitb.ac.in
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Design and Test Trends from Physical Design perspective


1
Interconnect Synthesis
Session III Dr. Parthasarathi Dasgupta MIS
Group Indian Institute of Management Calcutta
2
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

3
ITRS02 Interconnect Projected Parameters
ITRS 2002 Update - I
Solution known
Solution exists
Solution Unknown
Year of Production
2010
2016
DRAM Tech node(nm) 45
22 No. of metal levels 10
11 Total interconnect length(m/cm2) (active
wiring only, excluding global levels)
16063 33508 Interconnect RC
delay- 1mm line (ns) 565
2008
4
ITRS02 Interconnect Projected Parameters
ITRS 2002 Update - II
Solution known
Solution exists
Solution Unknown
Year of Production
2010
2016
Effective dielectric constant of inter-level
metal insulator
2.1 1.8
Local wiring Pitch (nm) 105 750
Minimum Global wiring Pitch (nm) 205
100 Intermediate wiring Pitch (nm)
135 65 Conductor effective resistivity
(microOhm-cm) 2.2 2.0
5
ITRS02 Some Grand Challenges - I
  • Near Term (Through 2007)
  • Mask-Making (Lithography)
  • Process Control (Lithography)
  • Integration of New Processes and Structures
  • (Interconnect)
  • Power Management (Design)

6
ITRS02 Relevant Grand Challenges - II
  • Long Term (2008 Through 2016)
  • Next-Generation Lithography (Lithography)
  • Identify Solutions Addressing Global Wiring
    Issues
  • (Interconnect)
  • Error-Tolerant Design (Design)

7
Why are DSM Interconnects Important ?
  • Signal Delay
  • Reduction of chip size K times
  • increases wire resistance K times
  • increases wire capacitance K times, and hence
  • increases global interconnect delay K2 times
  • reduces gate switching time K times
  • local interconnect delay remains unchanged

8
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

9
Why bother about Signal Delay?
  • Global Routing trees often need to be
    constructed with an objective of minimizing
    circuit delay
  • Minimum circuit delay preferred to increase
    speed of the circuit
  • Accurate measurement of signal delay is thus
    very important
  • Exact signal delay measurement is too complex
    and time consuming
  • Hence there is a need to have an accurate delay
    estimation

10
Estimating Signal Delay
  • Elmore Delay
  • Delay through an on-path resistor its
    resistance ?
  • downstream capacitance
  • Delay through a path (driver to a sink pin)
  • sum of delays through individual edges on the
    path
  • First moment of the interconnect under impulse
    response
  • Based on the 50 delay

r
Source
Rest of circuit
C1/2
C1/2
C2
Delay through interconnect r.(C1/2 C2)
11
Elmore Delay Characteristics
  • Fairly accurate estimate of delay at nodes far
    from source
  • Expressible as a closed-form expression
    involving only
  • resistors and capacitors
  • Provable upper bound on actual delay for all
    inputs
  • Additive

Source, S
A
B
Delay (S, B) Delay(S, A) Delay(A, B)
12
Elmore Delay - An Example
i 1
j 1
I 1
j i
13
Elmore Delay Computation
RC tree is traversed depth-first twice Pass 1
Compute the effective capacitance at each node of
the RC tree Pass 2 At a node, compute the
actual Elmore delay from the source, using the
sum of (a) delay upto the predecessor node, and
(b) the product of the resistance between the
predecessor node and the current node, and the
effective capacitance at current node obtained in
Pass 1.
1 k
1 k
1 k
1 k
1 k
A
B
500
500
500
500
500
?AB 1k ohm x 500 Ff x 5 1k ohm x 500 Ff x 4
1 k ohm x 500 Ff x 3 1 k ohm x 500 Ff x 3 1
k ohm x 500 Ff x 2 1 k ohm x 500 Ff x 1 2500
2000 1500 1000 500 7.5 n seconds.
14
Bounds on Signal Delay
Lower bound and Upper Bound Computation Define
Rii resistance between source and node i Rki
resistance of the subpath common to the path
between source and node i, and that between
source and node k. The 3 Ts with dimension of
time are artificially constructed to simplify
bound computation. TP ?kRkkCk, TDi
?kRkiCk, TRi (?kR2kiCk)/Rii Let signal delay
at node i bet . Then, TDi - TRi lnTRi / TP(1 -
vi(t)) lt t lt TDi /(1 - vi(t)) -
TRi where v0 1, vi(t) 0.5
J Rubinstein, P Penfield and M A Horowitz,
Signal Delay in RC Tree Networks, IEEE Trans.
on Computer-Aided Design, CAD-2, 3, July, 1983.
15
Bounds on Signal Delay - An Example
16
Other delay Metrics
Higher order moments and using R, L and C have
also been tried by several researchers, but most
of them are rarely used due to the difficulty of
their computation inspite of their better
accuracy.
Bonding Wire
Chip
L
Mounting
Cavity
L
Lead Frame
Pin
17
  • Fidelity of a delay estimator
  • Degree to which an optimal or near-optimal
    solution according to a
  • delay estimator correlates to a nearly optimal
    according to actual delay.
  • For a set of possible solutions obtained using
    the estimator, how
  • close are the ranks correlated to those for the
    solutions obtained by
  • the actual delay measurement?
  • Measure of fidelity in the context of finding
    Optimal RST
  • Portion of the pair-wise inequality relations
    among the optimal
  • solutions that are correctly determined by the
    heuristic solution
  • If there are m instances of RST and hi, si are
    respectively the
  • objective values of the heuristic and optimal
    solutions to
  • instance j,then fidelity
  • f (i, j) 0 lt i lt j lt m, ((hi - hj)(si
    -sj)gt 0) or (si sj) / mC2

How effective are Delay Estimators?
P. Dasgupta, et al, Relative Accuracies of
Estimators and their use in VLSI Routing, IIM-C
Tech. Report.
18
Relative Accuracy of Delay Estimators
  • Existing work
  • Used in constructing near-optimal routing trees
    based on
  • Elmore delay (Boese et al, ICCAD. 1993)
  • Used for optimum wire sizing in routing trees
  • (Cong et al, ACMTODAES, 1996)
  • Major drawback of existing work
  • Fidelity measured on all possible samples
  • Main ideas
  • Fidelity should be computed on a reasonably
    diverse set of
  • relevant (near-optimal?) samples
  • Should be dimensionless
  • Preferably in the range (-1, 1)
  • Relevant, I.e., act as a discriminator for
    good solutions, and
  • not for the bad solutions
  • Should be least affected by ties

19
New Delay Metric?
  • Can we use the bounds to have a better delay
    metric?
  • Preferable characteristics of this delay metric ?
  • Compact and closed-form expression
  • Easily computable
  • - Efficient lower bound of actual delay (this
    helps!!)

20
Practical use of delay minimization
Required Arrival Times
s1
s2
s0
sn
RAT(s0) lt RAT(si ) delay(s0, si ), I 1,
n RAT(s0) lt minimumi1, n (RAT(si ) delay(s0,
si )) Slack(s0, si ) (RAT(si ) delay(s0, si
)) - RAT(s0)
21
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

22
Routing Tree Construction
  • Mostly based on finding minimum-cost Steiner
    trees (SMT)
  • Some are based on Rectilinear Steiner
    Arborescences
  • which are minimum-cost Steiner trees (RSMT)
    with shortest source-sink paths
  • Algorithms exist for simultaneous cost
    minimization and
  • tree-diameter reduction
  • Extended Prim with bounded diameter also
    proposed
  • In DSM range, driver resistance / unit wire
    resistance
  • hence, distributed interconnect structure /
    capacitance

23
Routing Tree Construction
  • P-tree heuristics (Lillis et al)
  • Iterated 1-steiner (Kahng Robins)
  • Geo-Steiner (Best Steiner tree construction
    method!)
  • Bounded PRIM (BPRIM)
  • Shallow-Light trees (BRBC)
  • Rectilinear Steiner Arborescence (RSA)
  • (A-tree construction of Cong et al)

24
RSMT Problem - Key Results
  • Reduction to discrete grid
  • NP-hard
  • Iterated 1-Steiner heuristic
  • Greedily adds Steiner points to the tree
  • Almost 11 improvement over MST on average
  • Fast batched implementation (BI1S)
  • Exact algorithm GeoSteiner 3.0
  • Branch-and-cut
  • 11.5 improvement over MST on average

25
A-Tree Construction
A Rectilinear Steiner Tree is an A-tree if every
path from the source to any node in the tree is a
shortest path. A-Tree algorithm (in a nutshell)
  • Start with a forest of n single-node
    arborescences
  • Apply a sequence of moves
  • Grows an existing arborescence
  • Combines two arborescences to form a new one
  • Stop when ONE arborescence is left
  • Move may be safe (optimal) / heuristic
    (possibly sub-optimal)

J. Cong, K-S. Leung, D. Zhou, Performance-Driven
Interconnect Design based on Distributed RC
Delay Model, Design Automation Conference, 1993.
26
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

27
Topological Routing - A new idea
Our goal Partitioning routing area into
zones of pins with geometric proximity for better
area / topological routing and finding ways of
prioritizing zones. Why ??
Sinha, Sur-Kolay, Dasgupta and Bhattacharya,,
Partitioning Routing Areas into Zones with
Distinct Pins, IEEE International Conference
on VLSI Design, Bangalore, India, 2001.
28
Forming Zones in a Placement

Objective all pins in a zone belong to distinct
nets and are reachable through connected
regions Rationale First, connect nets among
zones, then route in detail each zone
within its connected region Bus lines
are likely to be routed together.
29
Graph for Zone Partitioning
  • Pins in a placement
  • gt Point set
  • gt Voronoi diagram
  • gt Delaunay triangulation
  • gt Planar triangulated graph, G

Net name for pin gt color of point, i.e., vertex
in G
30
Formulation of the problem
  • Input Planar triangulated graph G with vertices
    having different colours.
  • MIN_ZONE_PART
  • Find minimum set of connected sub-graphs, which
    partitions G such that vertices in each
    sub-graph have distinct colors.
  • Proposed algorithm is based on Genetic Algorithm.

31
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

32
Can we reduce Interconnect delay?
  • Buffer allocation
  • New directions
  • Wire sizing
  • Non-tree routing

33
Why use Buffers in Routing Trees?
  • Added buffer shields the heavy load downstream
    on
  • the branch from the rest of the tree.
  • Recover the slope of the signals transition
    edge and
  • screen out the noise.
  • Boost driving power and reduce delay.

34
Buffer allocation schemes
  • Classical technique of Van Ginneken
  • Permutation tree (P-tree)-based method to
    combine
  • topology construction and buffer-insertion
    searches,
  • with wire sizing
  • Okamoto-Congs work

35
Ginnekens DP-based Method
Input a) A routing tree. b) Required arrival
times (RAT) at sinks. c) Legal buffer positions
(at vertices of routing tree) Output Find the
optimal buffer placement s.t. the RAT at source
is maximum. Method Two stage dynamic
programming-based algorithm. Stage 1. For each
vertex of routing tree, find best choices for
buffer assignment giving larger RAT at vertex
(Bottom-up). Stage 2. Top-down traversal from
root to leaves corresponding best choice for root
obtained in Stage 1. Actual buffer placement.

L.P.P.P. van Ginneken, Buffer Placement in
Distributed RC-tree Networks for Minimal Elmore
Delay, Int Sym on Circuits Systems, 1990, pp.
865-868.
36
Ginnekens DP-based Method ..Contd.
s1
B total number of legal buffer positions Time
complexity O(B2)
buffer
s2
s0
Without buffer - Tk Tk rlLk 0.5rcl2,, Lk
Lk cl With buffer Tk Tk Dbuf RbufLk,
Lk Cbuf
s3
s4
s5
s6
  • An option is strictly worse if
  • load is larger, and (ii) required time is
    earlier.
  • At each vertex, the worst options are not saved.
    At root, the
  • best option is chosen.

37
Okamoto-Congs Method - I
  • existing techniques mostly works in two stages
  • optimum Steiner tree construction
  • optimum buffer insertion in this tree
  • This method - DP-based simultaneous application
    of
  • van Ginnekens buffer insertion
  • Congs A-tree construction

S1 (Critical)
S1 (Critical)
S2
S2
S3
S3
Source
S4
Source
S4
Minimum-delay buffered tree
Minimum-delay tree followed by buffer insertion
38
Okamoto-Congs Method - II
  • Characteristic features
  • Critical path isolation - root gate drives
    critical sinks and a smaller additional load due
    to buffered non-critical paths
  • If RATs at sinks are within a small range,
    balanced load decomposition is applied in order
    to decrease the load at output of root gate.

Critical Signal
Critical Signal Isolation
Balanced Load Decomposition
T. Okamoto and J. Cong, Interconnect Layout
Optimization by Simultaneous Steiner tree
construction and Buffer insertion, ICCAD, 1996.
39
Okamoto-Congs Method - III
  • Overview
  • Critical path isolation (CPI) - root gate drives
    critical sinks and a smaller additional load due
    to buffered non-critical paths
  • If RATs at sinks are within a small range,
    balanced load decomposition (BLD) is applied in
    order to decrease the load at output of root
    gate.
  • Bottom-up DP followed by top-down buffer
    placement
  • CPI and BLD are taken into account when choosing
    two subtrees to be merged into a single root.
  • For a given set of options of two nodes u, v,
    and for root node r, the distances dist(r,u),
    dist(r, v), and characteristics of buffer to be
    placed at r, the set of options at r are computed
  • Using a cost criteria for different roots in the
    A-tree, the best subtree is formed.
  • In 2nd phase, option at root which gives max
    RAT(root) is chosen, and the tree is traversed in
    top-down manner using the best chosen nodes in
    the previous phase.

40
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

41
Improving Delay by Wire Sizing
  • Why wire sizing ?
  • In DSM, when wire resistance becomes
    significant, proper sizing of the interconnects
    can reduce the interconnect delay.
  • First proposed by Cong, Leung and Zhou in 1993.
  • When driver resistance is much larger than wire
    resistance of the interconnect, the interconnect
    can be modeled as a lumped capacitor without
    losing much accuracy, and conventional minimum
    wire-width solution often leads to an optimal
    design.
  • When driver resistance falls below unit wire
    resistance, optimal wire-sizing can lead to
    substantial delay reduction.

J. Cong, K.S. Leung, "Optimal Wire sizing under
the Distributed Elmore Delay Model," ICCAD, 1993.
42
P-tree-based method
  • Salient features
  • Uses the notion of permutation of sinks
  • Constructs binary search trees as the routing
    trees
  • Finds an optimal sink permutation P based on
    minimum length of tour
  • on the sinks, and searches for the optimal
    binary tree for P
  • Based on DP as in Ginnekens algorithm
  • Uses load and RAT as cost parameters in DP
  • Performs simultaneous wire sizing for the
    constructed tree


s0
s0
s1
s2
s3
s4
s5
s1
s4
s5
s2
s3
Two different trees induced by a sink permutation
Lillis, Cheng, Lin, New Performance Driven
Routing Techniques with Explicit Area/Delay
Tradeoff and Simultaneous Wire Sizing , 33rd
Design Automation Conference, pp. 395-400, 1996.
43
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

44
Battling with Manufacturing Defects
  • Wire doubling
  • Simple, easy to integrate in current design flows
  • Can be applied to all nets

Can the use of Graphs (with cycles) instead
of (conventional) Trees for Routing Topologies be
useful ?
  • Non-tree routing (NTR)
  • Still easy to integrate in current flows
    (post-processing approach)
  • Appropriate for non timing-critical nets
  • Potentially more effective

45
NTR increases Reliability
  • Open fault missing material (or extra oxide
    where via should be formed)
  • Predominant for reduced feature size
  • Manufacturing defects and electro-migration tend
    to be
  • acute problems for DSM
  • Reliability ability of the interconnect to
    tolerate open
  • faults increases for NTR topology

46
Spot Defect Classification
(Source Ion Mandoiu, Fujitsu Lab Talk)
47
Probability of Failures
48
NTR Problem formulation
Optimal Routing Graph (ORG) Problem Given a
signal net N (n1, n2, , nm) with source s0,
find a set S of Steiner points and a routing
graph G (N U S, E), such that the maximum
source-sink signal propagation delay is
minimum. Result. ORG problem is NP-hard.
B. A. McCoy and G. Robins, Non-Tree Routing,
IEEE Transactions on CAD/ICAS, Vol 14, No. 6,
June 1995.
49
Other uses of Non-tree Routing
  • May reduce signal propagation delay
  • Wire capacitance Wire resistance
  • Observation Often, for DSM designs,
  • decrease in R gt increase in C
  • Capable of reducing signal skew
  • Signal skew improved by an average of 63 over
    Steiner routing

50
Augmenting Paths for NRT Construction
(C) Paths connecting tree nodes or projections
of tree nodes onto adjacent tree edges
(C)
(Source Ion Mandoiu, Fujitsu Lab Talk)
51
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

52
Achieving High Clock Speed!
  • Factors determining the operating speed of a
    circuit
  • Delay
  • Clock distribution
  • Clock skew
  • Measures the asymmetric clock distribution
  • Maximum clock delay - Minimum clock delay
  • Ideally should be Zero (Zero Skew Trees)

source
Reducing Clock Skews
53
Zero Skew Routing
  • Greedy Deferred Merge Embedding for Zero skew
  • Greedy bottom-up method
  • Set of merging segments, initially each segment
    having a
  • sink
  • Iteratively finds the pair of closest segments
  • Determine the position of parent such that the
    delays from
  • parent to the children are equal

M. Edahiro, A Clustering-based Optimization
Algorithm in Zero-Skew Routings, 30th Design
Automation Conference, 1993.
54
Bounded-Skew Routing
  • Problems with Zero-skew Tree construction
  • Very difficult to achieve
  • Increased wiring area
  • Higher power dissipation
  • Practical case Circuits operate correctly within
    some non-zero skew bound.
  • BST/DME
  • Form merge regions instead of merge segments
  • Bottom-up region formation followed by top-down
    process to
  • determine the exact location of the internal
    nodes.

Cong et al, Bounded-Skew Clock and Steiner
Routing, ACMTODAES, Vol 3, 1998.
55
Semi-Synchronous Circuits
  • Cluster-based method for Semi-Synchronous Circuit
  • A circuit in which the clock is assumed to be
    distributed periodically to
  • each individual register, though not
    necessarily simultaneously
  • Clock period minimization is of prime importance
  • Registers are partitioned into clusters
    depending on their geometric
  • positions
  • Registers within a cluster are in close
    proximity and have identical
  • clock timing requirements
  • Clusters are then modified to improve the clock
    period while keeping
  • the radius small
  • Each cluster of registers is driven by a buffer
  • Clock period is 18 shorter than zero-skew
    method
  • Wire length and power consumption are comparable
    to zero skew

Saitoh, Azuma and Takahashi, A Clustering Based
fast Clock Schedule Algorithm for Light Clock
Trees, IEICE Trans. Fundamentals, Dec, 2002.
56
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

57
Early Design Planning Needs
  • Interconnect Planning (Otten, others)
  • Buffer Block Planning
  • Interconnect Architecture (IA)
  • Performance Prediction
  • Others .

58
Buffer Block Planning for Interconnects
  • Why planning for buffers?
  • Early works were for one net at a time, and had
    no global
  • planning for buffer placement for all the nets
  • Buffers can not be placed anywhere as they will
    be in the
  • silicon, and require connections to
    power/ground
  • networks.
  • Arbitrary buffer placement may affect use/reuse
    of IP
  • blocks

59
A Method for Buffer Block Planning
  • Salient features of Congs method
  • Introducing the concept of feasible region (FR)
    for buffer
  • placement under some delay constraint
  • FR can be quite large and can be used to place
    buffer
  • clusters
  • an effective algorithm proposed for finding FRs
    which can
  • be used for subsequent Floorplanning and
    Interconnect
  • Planning

J. Cong, T. Kong and Z. Pan, Buffer block
Planning for Interconnect Planning and
Prediction, IEEE TCAD/ICAS, December, 2001.
60
Routing Tree for Fixed Buffer Locations
  • High performance design requires using a large
    number of
  • buffers
  • In practice, buffers are organized into buffer
    blocks which
  • are pre-planned
  • Buffer positions are fixed prior to routing tree
    construction

obstacle
Buffer block
Logic Block
Pin
Routing Graph for a floorplan with buffer block
planning
61
Routing Tree for Fixed Buffers - A Method
  • Summary of the method
  • given the RAT values at sinks, and feasible
    regions of buffers, to construct a routing tree
    and assign buffers such that the RAT at source is
    maximum.
  • Each node v is identified by a tree below it,
    and characterized by (i) load capacitance at v in
    its subtree, (ii) RAT(v) in the subtree, (iii)
    RE reachable sink set in the subtree, and (iv) a
    flag buf indicating if a buffer is inserted in
    subtree at v.

J. Cong and Xin Yuan, Routing Tree Construction
under Fixed Buffer Locations, Design Automation
Conference, 2000.
62
Routing Tree for Fixed Buffers - A Method
  • Summary of the method Contd.
  • Expansion of nodes (subtrees), and merging of
    nodes (subtrees) are done at each node and the
    corresponding labels generated.
  • A label-queue stores all the labels at any stage
    of the algorithm, and at each iteration of the
    algorithm, a new label with maximum RAT is
    selected.
  • Subtrees are not deleted on immediately on
    merging.
  • Stops when algorithm fetches a label from queue
    for for the whole tree

63
Routing Tree for Fixed Buffers - Example
64
Outline
  • Interconnect synthesis
  • ITRS challenges (http//public.itrs.net)
  • Delay models and estimators
  • Routing tree construction methods
  • Topological routing
  • Delay reduction
  • Buffer insertion
  • Wire sizing
  • Non-tree routing methods
  • Clock tree routing
  • Early interconnect planning
  • Buffer block planning
  • Interconnect architecture and metrics

65
Can we Predict IA Performance?
  • Performance of Interconnect Architecture (IA)
    traditionally predicted using delay, congestion,
    etc.
  • Previous works lack in considering several
    factors like materials, use of vias, repeaters,
    number of layers, etc
  • Helps to choose the dynamic parameters related
    to process and materials for an IA

66
Interconnect Architecture
An Interconnect Architecture (IA) is a collection
of pairs of wiring layers (tiers), with all wires
in a given layer pair having uniform width (w),
height (h), spacing (s) and thickness (t)
Layer-pair j
Layer-pair (j1)
Repeater
Repeater
via
Schematic of an IA
Repeater
67
Proposing a Novel Metric
  • Novel metric for IA performance evaluation
  • Efficient dynamic programming method for exactly
    computing the metric
  • for given Interconnect Architecture
  • for given Wirelength Distribution (WLD)
  • Studies of effects of materials, geometry,
    frequency, design parameters, repeater resources
    on IA metric

Dasgupta, Kahng and Muddu, A Novel Metric for
Interconnect Performance, Design and Test
Automation in Europe (DATE) 2003.
68
Performance-, WLD-Aware Routing Model
  • All connections (wires) are two-pin, L-shaped
  • Each segment of an L is assigned to one layer of
    a tier
  • For a given WLD, longer wires always routed on
    upper tiers shorter wires always routed on lower
    tiers
  • Every wire has a target delay (proportional to
    clock period)
  • Repeaters inserted as needed to meet delay
    targets
  • Starting from longer wires first
  • All repeaters used in wires of a tier are of
    same size
  • Repeater resource is specified as fraction of
    total die area
  • Repeaters inserted until repeater area budget is
    exhausted

69
Rank Metric for IA
  • Determines IA quality in terms of how completely
    target performance is met while embedding all
    wires
  • Rank of a wire its index in the WLD, where
    wires have been arranged in order of
    non-increasing length
  • Rank of an IA index of the highest-rank wire in
    the WLD that meets its target delay, subject to
    the constraints
  • The given repeater area budget is not exceeded
  • Lower-rank ( longer) wires in the WLD meet
    target delays
  • All wires in the WLD can be assigned to the IA
  • The rank of an IA is zero if not all the wires of
    the WLD can be assigned to the IA, even without
    meeting any delay targets

70
Rank of IA Dependencies
WLD
Number of wires
IA of layer pairs W, H, S and T, tech node,
gate count and gate parameters
TWirelength
Target Delays
Rank of the IA
Repeater area budget AR
Via blockage
71
The Rank Computation Problem
  • Given
  • IA with fixed number of layer-pairs with fixed
    geometry
  • WLD W with n wires
  • Available repeater area AR
  • Upper bound di target delay for each wire
  • Find
  • An assignment of wires from the WLD to the IA
  • using repeater insertion within the repeater area
    budget
  • to meet target delays of wires
  • such that rank of first wire failing to meet
    target delay is maximized

72
Rank Computation
  • Rank of an IA is computed by assigning maximum
    number of wires from the WLD to tiers of the IA
  • by making ActualDelay ? TargetDelay
  • within AR
  • Maximizing the Rank requires optimum combination
    of
  • wires assigned to tiers
  • repeaters assigned to wires
  • Exhaustive search over wires, tiers and repeaters
    is infeasible
  • How to compute Rank efficiently?
  • Greedy approach or Dynamic Programming (DP)

73
Layout Enhancement for Manufacturability
Session III Dr. Parthasarathi Dasgupta MIS
Group Indian Institute of Management Calcutta
74
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

75
Process flow for IC Manufacturing
Layout Design
Pattern Generation
Mask or Reticle
Chip Production
76
IC Manufacturing Terminology
Reticle - A photographic plate developed from a
sequence of polygonal patterns for a single layer
of an IC Depth of focus - a plus or minus
deviation from a defined reference plane wherein
the required resolution for photolithography is
still achievable Photoresist - A
radiation-sensitive material used as a coating on
wafer prior to doping
77
Photolithography
RADIATION
MASK
RESIST
RESIST
RESIST
OXIDE
OXIDE
SILICON
SILICON
78
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

79
IC Manufacturing in DSM - Problems?
  • Feature dimensions (lt 350 nm) lt Wavelength of
    the incident light
  • Effects?
  • Optical diffraction.
  • Resist process effects.
  • Distortion or disappearance of features.
  • Rayleigh limit (resolution ? ? / NA2)
  • Compensation Schemes (Amp / Phase)
  • Optical Proximity Correction.
  • Phase-Shifting Masks.
  • ...

Resolution Enhancement Techniques (RET)
80
Optical Proximity Correction (OPC)
  • Perturb the shapes of transmitting apertures in
    the mask in a systematic manner to address
    optical lithographic distortions.
  • OPC correction primitives
  • Serif small L-shaped geometry added to
    (subtracted from) convex (concave) corner to
    nullify rounding
  • Hammerhead A U or inverted-U to compensate for
    line-end shortening
  • Notch local thinning of a feature to compensate
    for linewidth variation
  • Outtrigger disconnected, non-printing geometry
    that uses diffraction effects to enhance
    linewidth control

81
OPC Example
A. B. Kahng and Y. C. Pati, "Subwavelength
Optical Lithography Challenges and Impact on
Physical Design", Proc. ISPD, April 1999, pp.
112-119.
82
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

83
Phase Shifting Mask (PSM)
Proposed in M.D. Levenson, et al. Improving
Resolution in Photolithography with a
Phase-Shifting Mask, IEEE Trans. Electron
Devices, 29, p. 1812, Dec. 1982. By using a
coating based on Chromium or Molybdenum Silicide
(MoSi), two adjacent clear regions of a mask are
enabled to transmit light with pre-defined
phase-shifts. For a phase-shift 180 degrees,
diffracted light in the intermediate dark region
interfere destructively. Effect - Better
resolution and depth of focus (DOF).
84
PSM Example
Phase shifter
Light Intensity
Regions of Interference
Without Phase-shifting mask
With Phase-shifting mask
85
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

86
Phase Assignment Problem
Input A given set of features in a mask
layout Objective Assign phases to all the
features of the layout such that no two
conflicting features are assigned the same phase.
87
New Thoughts?
Constrained Physical Design !!
Layout Geometry Mask
Geometry
Actual geometry on Wafer
88
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

89
Chemical-Mechanical Polishing (CMP)
  • Requirements for ULSI --
  • smaller feature size
  • higher resolution
  • multi-layer interconnects
  • global planarity on ILD and metal layers for
    better
  • depth of focus
  • CMP
  • - can be performed on both ILD and metals
  • - polishes wafer surface flat
  • - uses chemical slurry and circular action

90
Problems with CMP
Wafer
Slurry
Rotating Pad
  • Associated Problems
  • wearing out of Polishing Pad over metal features
  • dishing in sparse regions of layout
  • greater ILD thickness over dense regions of
    layout

91
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

92
Uniform Feature Density?
  • The density of a layer in any particular region
    is the
  • total area covered by the drawn features on
    that
  • layer divided by the area of the region
  • ILD thickness ? Local Feature density
  • Uniform (feature) density achieved by
  • Post-Processing Insertion of Dummy
    (electrically
  • inactive) features

93
Uniform Feature Density - Tiling
Dummy feature
Normal feature
Cross-sectional view
Top view
94
(Dummy) Fill Synthesis Problem (Tiling)
  • Foundry rules specify minimum and maximum
    feature densities to reduce effect of CMP on
    yield (e.g., each metal layer, every 2000 um x
    2000 um window must be between 35 and 70 filled
  • Problem
  • Input A post-CMP feature distribution on a
    layout
  • Objective The amount and location of dummy
    features to be placed into the layout.
  • Constraints Feature density gt a prescribed
    minimum, variation in feature density is within a
    prescribed range, electrical and physical design
    rules are observed.

95
Solving Tiling Problem
  • Outline of A Generic Approach
  • For every prescribed window size, find the
    available
  • area for dummy features
  • fixed dissection
  • arbitrary dissection
  • Compute amounts and locations of dummy fills
  • satisfying the constraints
  • Generate Fill Geometry

96
Methods for Dummy Feature Placement - I
  • rule-based (widely used in Industry)
  • boolean operation
  • tiles of a single prescribed density
  • fills ONLY open space

97
Methods for Dummy Feature Placement - II
  • model-based
  • analytical expression of the relation between
    local
  • density and ILD thickness
  • more accurate than rule-based

R. Tian, D. F. Wong and R. Boone, Model-Based
Dummy Feature Placement for Oxide CMP
Manufacturibility, DAC 2000.
98
Outline
  • Issues in lithography
  • Resolution enhancement
  • Optical process correction
  • Phase Shift Masking
  • Phase assignment
  • Chemical mechanical polishing
  • Dummy fill synthesis
  • Layout data representation and compaction

99
Dummy Fills Is DENSITY the ONLY factor?
  • Representing fill patterns (GDSII)
  • Generating compressed fill patterns
  • Compressing existing fill patterns

100
Defining Layouts - GDSII
  • A standard (binary) file format
  • Used for transferring / archiving 2D graphical
    design data
  • Records
  • Header (record type)
  • Information (GDSII BNF)
  • Contains hierarchy of structures
  • Structure
  • Boundary / polygon, path, text, box
  • Structure references (SREF)
  • Array of structures references (AREF)

101
GDSII AREFs
X3, Y3
SREF / AREF
Inter row spacing
X1, Y1
Inter column spacing
X2, Y2
102
GDSII File Description Example
Header Bgnlib Lib1 Bgnstr Struct1
(ltelementgt) Endstr Endlib Element -
ltboundarygt ltpathgt ltarefgt lttextgt ltnodegt
ltboxgt Endel Header Bgnlib Libname LIB1
Bgnstr Strname CELL1 Boundary Layer 0
Datatype 0 XY 6 X -1000.000 Y
0.000 X 163000.000 Y 0.000 X
163000.000 Y 177000.000 X 80000.000 Y
260000.000 X -1000.000 Y
260000.000 X -1000.000 Y 0.000
Endel Endstr
103
GDSII File Description Example
Bgnstr Strname AREF_SAMPLE1 Aref
Sname CELL1 Strans 0,0,0 Colrow 7 , 3 XY
3 X -5114000.000 Y -3006000.000 X
-3095600.000 Y -3006000.000 X
-5114000.000 Y -1891800.000 Endel
Endstr
104
GDSII File Description Example
Bgnstr Strname SREF_SAMPLE1 Sref Sname
AREF_SAMPLE1 XY 1 X
-7114000.000 Y -2006000.000 Endel
Endstr Bgnstr Strname LAYOUT Aref
Sname SREF_SAMPLE1 Strans 0,0,0 Colrow 9 ,
5 XY 3 X -114000.000 Y -2006000.000
X -2095600.000 Y -2006000.000 X
-114000.000 Y -2891800.000 Endel
105
GDSII File Description Example
Aref Sname CELL1 Strans 0,0,0 Colrow 2 ,
3 XY 3 X -3140000.000 Y
-2006000.000 X -3240000.000 Y
-2006000.000 X -3140000.000 Y
-3891800.000 Endel Endstr Endlib
Aref Sname CELL1 Strans 0,0,0 Colrow 2 , 3
XY 3 X -3140000.000 Y
-2006000.000 X -3240000.000 Y
-2006000.000 X -3140000.000 Y
-3891800.000 Endel Endstr Endlib
106
Why Layout Data Compaction is needed?
  • Drastic increase in Layout data
  • pattern modification due to OPC and PSM
  • fracturing of layout data (partitioning into
  • primitive patterns, like triangles,
    trapezoids, etc.)
  • fill pattern generation

107
A Method for Layout Data Compaction
  • Basic figure a rectangle or a trapezoid
    corresponding
  • to a fractured mask pattern.
  • Grouped figure group of multiple basic figures
  • Array a reference to grouped figures with
    pitch and
  • number of repetitions in each of X and Y
    directions.
  • Cell has some references and one definition.
    Cell
  • includes grouped figures.

Effective Data Compaction Algorithm for Vector
Scan EB Writing System, S. Ueki et. Al., Proc.
of SPIE, Vol. 4186, 2001.
108
Compaction Steps in Uekis Algorithm
Step 1. Search arrays of same type of figure
(array search algorithm) Step 2. Classify arrays
by array type and create cells that include
multiple figures for each array type. Step 3.
Search cells from all figures that are not
positioned in array. (cell search algorithm)
109
Example - I
Shape A A1, A2, A3 Shape B B1, B2, B3 Figures
classified by shape
B1
B2
B3
A1
A3
A2
Array of A1, A2, A3 Array of B1, B2,
B3 Array figures of same type
B1
B2
B3
A1
A3
A2
Grouped figure AB One array AB1, AB2, AB3
AB1
AB3
AB2
Cell extracted for arrays of same pitch and same
of figures
110
Example - II
Three cell references
5 x 1 array
111
Open Artwork System Interchange Standard
  • OASIS Salient Features
  • Proposed in February, 2003 by SEMI TWG
  • Achieve gt10x (order of magnitude) file size
    reduction
  • compared to GDSII
  • Allow integers to extend to gt 64 bits, when
    required
  • Efficiently handle flat geometric data,
    including array
  • of figures
  • Make format publicly available to academic and
  • commercial entities

New Stream Format Progress Report on
Containing Data Size Explosion, DSM Technical
Notes, Mentor Graphics
112
OASIS Repetition Types
Type 1
Type 2
Type 4
Type 5
Type 3
Type 7
Type 6
Type 8
113
References
1. J. Rubinstein, P. Penfield and M. A. Horowitz,
"Signal Delay in RC Tree Networks", IEEE Trans.
on Computer-Aided Design, CAD-2, 3, July,
1983. 2. J. Lillis, C. K. Cheng, T. Y. Lin and
C. Y. Ho, "New Performance Driven Routing
Techniques with Explicit Area/Delay Tradeoff and
Simultaneous Wire Sizing",33rd Design Automation
Conference, pp. 395-400, 1996. 3. J. Cong and
Xin Yuan, "Routing Tree Construction under Fixed
Buffer Locations", Design Automation Conference,
2000. 4. P. Dasgupta, "Relative Accuracies of
Estimators and their use in VLSI Routing", IIM-C
Tech. Report, 2003.
114
References
5. K. Sinha, S. Sur-Kolay, P. Dasgupta and B. B.
Bhattacharya, "Partitioning Routing Areas into
Zones with Distinct Pins", Proc. International
Conference on VLSI Design (IEEE-CS Press),
Bangalore, India, 2001. 6. L.P.P.P. van
Ginneken, "Buffer Placement in Distributed
RC-tree Networks for Minimal Elmore Delay",
International Symposium on Circuits Systems,
1990, pp. 865-868. 7. T. Okamoto and J. Cong,
"Interconnect Layout Optimization by Simultaneous
Steiner tree construction and Buffer insertion",
International Conference on Computer-Aided Design
(ICCAD), 1996.
115
References
8. J. Cong and K.S. Leung, "Optimal Wiresizing
Under the Distributed Elmore Delay Model",
International Conference on Computer-Aided Design
(ICCAD), 1993. 9. B. A. McCoy and G. Robins,
"Non-Tree Routing", IEEE Transactions on
CAD/ICAS, Vol 14, No. 6, June 1995. 10. M.
Edahiro, "A Clustering-based Optimization
Algorithm in Zero-Skew Routings", 30th Design
Automation Conference, 1993. 11. J. Cong, A. B.
Kahng, C-K.Koh and C.-W. A Tsao, "Bounded-Skew
Clock and Steiner Routing, ACM Transactions on
Design Automation of Electronic Systems, Vol 3,
No 3, 1998, pp. 341-388.
116
References
12. M. Saitoh, M. Azuma and A. Takahashi, "A
Clustering Based fast Clock Schedule Algorithm
for Light Clock Trees", IEICE Transactions
Fundamentals, Vol E85-A, No. 12, Dec, 2002. 13.
J. Cong, T. Kong and Z. Pan, "Buffer block
Planning for Interconnect Planning and
Prediction", IEEE Transactions on CAD/ICAS,
December, 2001. 14. J. Cong and Xin Yuan,
"Routing Tree Construction under Fixed Buffer
Locations", DAC, 2000. 15. P. Dasgupta, A. B.
Kahng and S. V. Muddu, "A Novel Metric for
Interconnect Performance", Design and Test
Automation in Europe (DATE), 2003.
117
References
16. A. B. Kahng and Y. C. Pati, "Subwavelength
Optical Lithography Challenges and Impact on
Physical Design", Proc. International Symposium
on Physical Design, April 1999, pp. 112-119. 17.
R. Tian, D. F. Wong and R. Boone, "Model-Based
Dummy Feature Placement for Oxide CMP
Manufacturibility", Design Automation Conference,
2000. 18. S. Ueki, et al, "Effective Data
Compaction Algorithm for Vector Scan EB Writing
System", S. Ueki, Proceedings of SPIE, Vol.
4186, 2001.
118
References
19. "New Stream Format Progress Report on
Containing Data Size Explosion", DSM Technical
Notes, Mentor Graphics, 2003. 20. A. B. Kahng
and G. Robins, "A New Class of Steiner Tree
Heuristics with Good Performance The Iterated
1-Steiner Approach", Proc. International
COnference on Computer-Aided Design, pp. 428-431,
1990. 21. International Technology Roadmap for
Semiconductors (ITRS), http//public.itrs.net. 22
. J. Cong, K-S. Leung, D. Zhou,
"Performance-Driven Interconnect Design based on
Distributed RC Delay Model", Design Automation
Conference, 1993.
119
Session IV Analyzing Layout Databases for
Improving Test Quality
Dr. Sujit T Zachariah Intel India Development
Centre, Bangalore (sujit.t.zachariah_at_intel.com)
120
Outline
  • HVM Test Basics
  • Case Studies
  • Defect Based Testing
  • Shorts
  • Bridge defects (Random two-node and multi-node)
  • Opens
  • Open defects (Random and systematic)
  • Circuit Marginality Testing
  • Power Supply Droop
  • Q A

121
High Volume Manufacturing (HVM)Test Basics
122
HVM Testing Approaches An Overview
  • Functional testing
  • Exorbitant cost of testers (at-speed application)
  • Need for frequent tester upgrades
  • Cost of manual test generation
  • Structural testing
  • Low cost, re-usable structural testers
  • Automated approaches for test pattern generation
  • Use of fault models
  • Classical approach stuck-at fault model

123
But
  • Most manufacturing defects behave electrically as
    shorts or opens
  • Marginality issues introduced by design tool
    approximations and process variations on the rise
    with device scaling
  • Stuck-at fault model inadequate for both cases
  • We need to rethink fault models!
  • Adequately model failing behavior
  • Simple enough for targeting test generation

124
Also
  • For realistic fault models
  • Number of possible faults is extremely large
  • Current ATPG techniques limit target size
  • Implies need for fault extraction prior to fault
    modeling
  • Enumerate all failure sites
  • Prioritize failure sites as a ranked list
    (probability)
  • Analysis at lower level of design abstraction
  • Circuit (schematic) Example cross talk
    analysis
  • Physical (layout) Layout Analysis
    for Test

125
Layout Databases Assumptions
  • All standard industry formats converted to
    standard hierarchical database format
  • Rectilinear polygons converted to set of non
    overlapping rectangles
  • Non Manhattan geometry approximated as
    rectilinear polygons

126
Case Study 1 Defect Based TestingExtraction
of Random Bridge Defects
127
Bridge Fault Extraction Overview
  • Identify potential bridge failure sites in a
    layout
  • Useful for yield estimation, test generation and
    failure analysis
  • Approaches
  • Capacitance Extraction Based Approaches Stroud,
    Emmert et al 00
  • Inductive Fault Analysis (IFA) Based Approaches
    Ferguson, Shen 88
  • Uses defect information from manufacturing
    sources
  • Likelihood of occurrence modeled using Weighted
    Critical Area (WCA)

128
Inductive Fault Analysis (IFA) Overview
129
Bridge Faults Types
Multi-Node Bridge Faults
Two-Node Bridge Faults
ltn2,n3gt 1.8 ltn1,n2gt 0.7 ltn2,n3gt 0.6 ltn1,n2,n3gt 0.4
ltn2,n3gt 2.2 ltn1,n2gt 1.1 ltn2,n3gt 1.0
  • Why Multi-Node Bridge Analysis?
  • Accuracy of extracted bridge list
  • Impact on test quality and yield estimation

130
IFA Based Approaches
  • CARAFE Jee, Ferguson 92
  • CREST Nag, Maly 95
  • LOBS Gonclaves, Teixeira, Teixeira 96,97
  • Eiffel Chakravarty, Zachariah 00
  • FedEx Walker, Stanojevic 01

131
IFA Based Approaches CARAFE
  • Straightforward implementation of the WCA
    definition
  • For each layer L (or layer pair)
  • For each defect size S
  • Expand each feature by the defect size S
  • Determine CARs as the intersection area of the
    expanded rectangles
  • Annotate CARs with net name pair and collect them
    into a global list
  • Find union of CARs by selectively merging the
    rectangles from the global list
  • Repeat computations for each given defect size

132
IFA Based Approaches CARAFE
  • Sources of inefficiency
  • Linear increase in run time with the number of
    defect sizes processed
  • Sub optimal line sweeping rectangle intersection
    algorithm
  • Overhead due to global processing of CARs
  • Limits use to very small layouts

133
IFA Based Approaches CREST
  • Uses layout hierarchy (no flattening)
  • WCA computations performed one instance at a time
    - bottom up approach
  • Through-the-cell routing and net name propagation
    issues
  • Accuracy issues with generated fault list (WCA
    values ranking)

134
IFA Based Approaches LOBS
  • Uses sliding window algorithm for computing CARs
    based on maximum defect size
  • Algorithm for determining union of CARs based on
    the cube generation of the intersections
  • When two CARs A and B overlap,
  • CA computed as Area(A) Area(B) - Area (A
    intersection B)
  • Potential explosion in number of computations if
    number of overlapping CARs is large

135
IFA Based Approaches Eiffel
  • Process multiple defect sizes
  • Results deduced for all defect sizes from the
    calculations for maximum defect size
  • Interval tree based algorithm to determine
    rectangle intersections
  • Novel algorithm for finding the union of
    rectangles constituting the critical area for a
    bridge
  • Resulting Algorithm is
  • Able to process large number of defect sizes
  • Able to handle larger layout databases

136
Algorithm Outline
  • For each layer L (or layer pair)
  • Step1 Determine CAR for the maximum defect size
  • Expand each feature by the maximum defect size
    Smax
  • Determine max_CARs as the intersection area of
    the expanded rectangles
  • Efficient computation using interval trees
  • Annotate CARs with net name pair and collect them
    into buckets, with each net pair having its own
    bucket

137
Algorithm Outline
  • Step 2 Process each bucket of max_CARs
  • For each net name pair ltN1,N2gt (bridge)
  • For each defect size S
  • Shrink max_CARs by (Smax-S) to obtain CARs for
    the size S
  • Merge CARs to obtain CA(N1,N2,S,L)
  • (Efficient merging using novel algorithm)
  • Weigh CA(N1,N2,S,L) with pL(S) and update
    WCAltN1,N2gt
  • (Bridges and their associated WCA maintained in
    balanced AVL tree for efficiency of update
    process)

138
Experimental Results
300X improvement
139
Experimental Results
140
IFA Based Approaches FedEx
  • Algorithm targeted for fast results
  • Capable of handling large VLSI layout databases
  • Accuracy traded to achieve speed

141
Multi-Node Bridges
  • Computation more challenging than two-node
    analysis
  • Eiffel Algorithm
  • Compute two node critical area rectangles
  • Performed only for the maximum defect size
  • Efficient interval tree based solution
  • Resulting critical areas collected into a global
    list
  • Critical area rectangles for all defect sizes
    deduced from critical areas corresponding to the
    maximum defect size

142
Multi-Node Bridges (Continued)
  • Compute multi-node WCA value increments from
    critical area rectangles
  • Novel line sweep based solution

143
Experimental Resul
About PowerShow.com