48x48 poster template

1
Fast Yield-Driven Fracture for Variable
Shaped-Beam Mask Writing Andrew B. Kahng1, Xu
Xu1, and Alex Z. Zelikovsky2 1. CSE Dept.
University of California, San Diego 2. CS
Department, Georgia State University
ABSTRACT
Fracture in Mask Data Process
Gain Based Selection Heuristics
The aggressive use of RET techniques with each
successive process generation have presented new
challenges for current fracture tools, which are
at the heart of layout data preparation. One main
challenge is to reduce the number of small
dimension trapezoids (slivers) to improve mask
yield. Some commercial tools are available for
handling the sliver minimization problem in
fracture. The integer linear programming (ILP)
method can significantly reduce sliver number at
the expense of long runtime. In this work, we
propose a new ray-segment selection heuristic
which can find a near-optimal fracture solution
in practical time while being flexible enough to
take into account all specified requirements. We
also extend the heuristics with the introduce of
auxiliary ray-segments. Compared with
state-of-art sliver-driven fracturing tools, the
proposed method reduces the number of slivers in
the fractures of two industry testcases by 76.7
and 58.6, respectively, without inflating the
runtime and shot count. Similarly, compared with
the previous ILP based fracture, the new method
reduces the number of slivers by 56.1 and 2.2
respectively, with more than 60X speedup and
negligent shot count overhead.

• For any ray segment i, weight of i
• W(i) increased sliver number after using i
  
• For any conflict pair (i, j), gain of i
• G(i)W(j)-W(i) sliver number saved by
  using I
• Initially, the set S All ray
• segments from concave points
• While (S?Ø)
• - Choose one ray segment i with
• the largest gain, delete its
• conflict pair from the S
• - If there is a ray segment j connected
• with i, add j into S
• - Update the gains of ray segments
• in S

Circuit Design
Layout Extraction
RET
Tape Out
Fracture
Job Decomposition
-1
Tonality
1
0
Mask Data Preparation
PEC Fracture
0
Job Finishing
0
Writing
1
-1
Mask Making
Inspection
1
Metrology
-1
Fracture Decompose a list of polygons into
trapezoids (shots)
1
Sliver Minimization Challenge
In S
Chosen

• Sliver A shot whose minimum dimension lt e
• Sliver number
• Mask CD variation Mask yield

Auxiliary Ray Segments
lt ?
Yield Driven Fracture
Sliver number may be reduced with the
introduction of auxiliary ray segments Auxil
iary ray segment addition rule If two rays
form a sliver whose length grater than 3e,
and no rays partition the sliver in the
middle, add one auxiliary ray in the middle.

• Yield Driven Fracture Problem
• Given
• List of rectilinear polygons P
• Slivering size e
• Partition P into non-overlapping trapezoidal
  shots
• To minimize Number of shots and number of slivers

2 shots
No sliver with good fracture
gt3e
Ray-Segment Selection Formulation
CONCLUSIONS
0 sliver
sliver

• Grid graph Draw two rays from each concave
  point
• Rays are divided into non-intersected
  ray-segments
• Conflict pair two ray segments from the same
  point
• Rule 1 One of ray segments from any concave
  point must be used
• Rule 2 At most one ray segment in each conflict
  pair can be used
• Rule 3 No internal concave points
• Fracture select ray segments obeying the rules
  

• Compared with two commercial fracture tools
• - Reduce sliver number by 76.7 and 58.6
• - No runtime overhead
• Compared with previous ILP method
• - Reduce sliver number by 28.9
• - 60x speedup
• Future work fracture-friendly OPC

rays
ray segments
concave point
Experimental Results
Method Design A Design A Design A Design B Design B Design B
Method shots slivers CPU shots slivers CPU
Tool A 10754 6111 0 17335 11572 0
Tool B 10455 4451 0 17130 10797 0
Tool C 9755 786 2 17195 6502 3
ILP 9750 417 134 17684 2750 222
Proposed 9786 183 1 17656 2691 4
BIBLIOGRAPHY

• Kahng et al., Yield- and Cost-Driven Fracturing
  for Variable
• Shaped-Beam Mask Writing, BACUS 2004
• Nakao et al. A new figure fracturing algorithm
  for variable-shaped
• EB exposure-data generation , ECJ 2003
• Cobb et al. High performance Hierarchical
  fracturing SPIE 4754
• Cobb et al. Hierarchical GDSII based fracturing
  and job deck
• system SPIE 4562

Conflict pair
concave points
convex points