Dual Graph-Based Hot Spot Detection

Andrew B. Kahng1

Chul-Hong Park2

Xu Xu1

(1) Blaze DFM, Inc.(2) ECE, University of California at San Diego

University of California, San Diego

Outline Introduction of Hot Spot Detection Dual Graph Based Approach Experimental Results Conclusions

University of California, San Diego

Why Hot Spot Detection?

Hot spots = features whose CD variation > T Form under a variety of conditions Reduce manufacturing yield Should be detected and solved in the early stage

Commercial tools: ORC (Mentor) and LRC (Synopsys)

Hot spot

University of California, San Diego

Previous Methods

Park et al. (SPIE 1999) proposed rule based detection with look-up tables Number of parameters increase for complex patterns

Speed merit of rule-based approach is reduced Inaccurate

Simulation-based approach has been a mainstream Detect hot spots accurately Hot spots can be changed according to process

conditions Model generations are significant overhead

Key Question Can we detect the hotspots fast and accurately?

University of California, San Diego

How We Think About Hot Spot Hotspot is a 2-dimensional function of line and space

with traditional parameters of DOF and Exposure Detect too many hot spots to classify the real hot spots

Our approach: more topological / graph-oriented

Practical methodology: Filter the chip layout down to a small candidate

set of hotspots, which can then be checked using the golden ORC/LRC tool

University of California, San Diego

(a) (b) (c)90

100

110

120

130

a b c

C-1 C-2 C-3

Nominal CD

Lithography Simulation

Different complexity leads to different CD variation CD variation is affected by different process condition More complex pattern, higher probability of hot spot

Probability: Pattern(c) > Pattern(b) > Pattern(a)

Simulation Condition: C-1: NA=0.85, σ=0.96/0.76, C-2: NA=0.75, σ=0.75/0.55, C-3: NA=0.75, σ=0.75/045DOF=0.2um, Exposure=+10% of nominal exposure

University of California, San Diego

Outline

Introduction of Hot Spot Detection Dual Graph Based Approach Experimental Results Conclusions

University of California, San Diego

Hot Spot Detection ProblemGiven: Layout L simulation conditions hot spot definitionDetect: Hot spots whose CD variation >T

To Minimize:

Number of un-detected and falsely detected hot spots

University of California, San Diego

“ Bad” Patterns Lead to Hotspots

Corner effect Proximity effectIn general, single effect does not lead to hot spots.

Hot spots are accumulative effects.

4 proximity effects, 2 corner effects

University of California, San Diego

Proposed Hot Spot Detection Flow Layout

Layout Graph Construction

Graph Planarization

Three-Level Detection

Local Pattern Density Filter

Output Hot Spots

University of California, San Diego

Layout Graph Construction

Corner effect

Proximity effect

Feature node

Two features with corner/proximity effects edge

University of California, San Diego

Edge Weighting Scheme Closed-form formula based approach

Weights of corner edges: constant Weights of proximate edges: f(w1, w2, l, d)= (w1’w2’l’) /d

Here w1’= w1 when w1 <c0

= c0 otherwise

Lookup table based

lw1

w2d

University of California, San Diego

Graph Planarization Delete one edge of any pair of crossing edges Convert the layout graph into its dual graph

(face dual node)

Planarization Dual graph

University of California, San Diego

Three-Level Hot Spot Detection For each edge

If (its weight > T0) report hot spot For each face (dual node)

If (the total weight > T1 ) report hot spot Sort all dual nodes according to weights Iteratively merge two dual nodes with max merged weight For each merged face (dual node)

If (the total edge weight > T2 )report hot spot

Edge Face Merged Face

University of California, San Diego

Local Pattern Density Filter

Hot spotNot Hot spot

Hot spots depend on the local pattern density A hot spots filtering based local pattern density

to reduce falsely detected hot spots

University of California, San Diego

Outline Introduction of Hot Spot Detection Dual Graph Based Approach Experimental Results Conclusions

University of California, San Diego

Experimental Setup Testcase: alu128 core

8.7K instances 90nm technology Chip size is 335 um X 285 um The netlists from OpenCores.

CalibreOPC , CalibreORC from Mentor Graphics are used for model-based OPC, and optical rule check (ORC)

Our algorithms are implemented in C++

University of California, San Diego

An Example of Hotspot Filtering

2D function (width, space) finds too many hotspots to classify the real hotspots

Real hotspot can be detected by dual graph based approach with weighted cost function

Detect hotspots which missed by rule-based approach Result is similar to simulation-based approach

(b) Hotspot(a) No Hotspot

University of California, San Diego

Experimental ResultsSimulation Condition

Number of Hot Spots Run time(s)ORC Detected False

DetectedORC Our

DOF=0.1ET=0.36

17 17 13 690 1.37

DOF=0.1ET=0.37

21 21 22 690 1.52

DOF=0.1ET=0.38

25 25 46 690 2.32

DOF=0.2ET=0.38

152 152 1291 690 4.38

Total 215 215 1372 2760 9.59 Runtime of our method is more than 287X faster compared to ORC Achieves 100% hot spot detection with small falsely defected hot spots overhead

University of California, San Diego

Outline Introduction of Hot Spot Detection Dual Graph Based Approach Experimental Results Conclusions

University of California, San Diego

Conclusion A novel fast dual graph based hot spot

detection algorithm Our method can detect hot spots with small

false detected overhead Runtime improvement is more than 287X

compared with ORC Future works

Fast hot spot detection engine in detailed router Cool spot detection: a pattern that is known to be

ORC/LRC-clean through the OPC

University of California, San Diego