A Methodology to Optimize Design Pattern Context ...

A Methodology to Optimize Design Pattern Context Size Using Pattern Association Tree (PAT) Piyush Pathak, Shikha Somani, Piyush Verma, and Sriram Madhavan

Introduction : Configurations vs Patterns • Configurations are simple

geometric constructs like tip-to-line space • Patterns are configurations with

context • Configuration based DRCs are

insufficient to detect all design hotspots • Context plays a key role in the

design process interaction • Pattern based checks successful

alternative to complex rule based checks Dai. V., Proc. SPIE 6521, 65210A (March 28, 2007)

Conventional Pattern Deck Generation x

x

x x

x

x x

x x

x

x

x

VLSI design

Defect locations marked on VLSI design

Pattern classification with radius ‘r’

• All design hotspots classified into unique pattern

classes • All patterns in the deck have a fixed common radius

thus the same context size

Fixed radius pattern deck

Pattern context – Process correlation Etch

Photolithography

Pattern radius related to

Optical diameter

Chemical Mechanical Planarization

Microloading distance

Topography dependent radius of influence

VLSI design Variation in the density and geometry within a pattern

Design hotspots with varying context size depending upon the defect inducing process

Variable radius pattern deck Traditional fixed radius pattern deck

Variable radius pattern deck (generated using PAT)

•

A variable radius pattern deck consisting of ‘root cause’ patterns will have a much higher defect predictability than a fixed radius deck

•

‘Root cause’ patterns have optimal context for defect detection

•

A Pattern Association Tree (PAT) is used to build such a variable radius pattern deck

Pattern Association Tree (PAT) Parent

Child

Grandchildren

Features of PAT • A child node can have one and only one parent node • A parent node can have more than one children

• Number of children for a given parent node represents extent of

variation in context observed across different hotspots

PAT node annotation - Terminology Name

Description

Formula

Hit count (NC)

Hotspot markers covered

-

Match count (NM)

Total locations matched

-

Hotspot count (NH)

Total number of hotspots

-

Precision (P)

Fraction of matched locations that were true hotspots

NC/NM

Sensitivity (S)

Fraction of the total hotspots that were matched

NC/NH

Precision = 1/2, Sensitivity = 1/3

Step 1 – Generating nodes Pattern classification with radius r1 x

PAT construction set aka “Training set”

x

Generated pattern decks

FR–r1 Deck

x

x x x

x

x x

x

FR-r2 Deck

x

x

x VLSI design

Defect locations marked on VLSI design

x x

x

x x Pattern classification with radius r2

Step 2 – Building associations Pattern classification output x

FR-r1

x x

x x

x

FR-r2 x

x x

x x

x

Pattern Association Tree

Step 3 - Node annotation Generated pattern decks

Pattern matching with FR-r1

FR-r1

x Defect locations marked on VLSI design

Nm

P

S

4

9

4/9

4/6

2

6

2/6

2/6

Nc

Nm

P

S

1

3

1/3

1/6

3

4

3/4

3/6

1

2

1/2

1/6

1

2

1/2

1/6

x x

x x

x

x

Nc

x

FR-r2

x

x x

x

NH = 6

x

x x

x x

x Pattern matching with FR-r2

Filtering and ranking criteria PAT deck can be filtered based on the attribute of significance to the application  NmP* : Detect those design constructs which are rarely used in the design but which have high defect correlation  Nm > Nm* : Most frequently used  P > P* : high defect predictability

Number of patterns in PAT deck equals the number of unique traversal paths in PAT

Nc

Nm

P

S

2

3

2/3

2/6

1

2

1/2

1/6

1

2

1/2

1/6

1

2

1/2

1/6

Patterns in the PAT deck can be further ranked:  P : Patterns with higher correlation with defects  Nc : Patterns which have covered more hotspots  Nm: Patterns which are more frequently used  S: Patterns which have covered more hotspots given the design space of training pool

Step 4: Optimal context pattern selection GEN-I

GEN-II GEN-III

Precision

GEN-IV

Sharp transition

Pattern radius

 A significant transition in precision along a tree traversal path indicates the ‘root cause’ pattern  Only ‘root cause’ patterns are selected to construct the PAT deck.

Results: PAT snippet

• Three randomly chosen tree traversal paths • Selection based on significant transitions in precision results in variable

radius pattern deck

Results: PAT deck composition • Pattern statistics from

training set – ~10000 markers used Nm/Nc (Unique pattern classes at the classification radius)

for classification (Nc) – Precision increases with increase in pattern classification radii (1/P = Nm/Nc)

• PAT deck – Is obtained after

filtering the PAT – Consists of patterns

ranging from 3r radius to 6r radius.

Results: PAT deck performance • Number of patterns in the

deck increase as the pattern radius increases • Precision increases as the

pattern radius increases • Sensitivity decreases as the

radius increases • PAT deck has half as many

patterns as the FR-6r deck and almost the same number of patterns as FR-5r deck

• PAT deck has much higher

precision than all the traditional fixed radius decks

• PAT deck has a reasonable

sensitivity given the small training pool

Conclusions  Context sensitivity analysis to obtain ‘root cause’ patterns using

PAT  PAT Deck has higher predictive capability than other traditional FR

decks  The ranking and filtering criterion for PAT nodes can be fine tuned

for different applications.