Global Routing Method for 2Layer Ball Grid Array Packages

1
Global Routing Method for 2-Layer Ball Grid
Array Packages

• Yukiko Kubo, Atsushi Takahashi
• The University of Kitakyushu
• Tokyo Institute of Technology

2
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

3
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

4
Introduction

• Old package design
• Circuits were small
• Number of I/O terminals of packages was small
• -gt Terminals were put on perimeter of package
  board
• Radial routing
• Manual design or simple automatic design

5
Introduction
Ball Grid Array

• Recent package design
• Circuits are large
• Number of I/O terminals
• of packages is large
• Ball Grid Array (BGA)
• Routing design is difficult
• Reduction of design term
• Routing automation

6
Previous Works for BGA Package Design

• Net generation and global
• routing (single layer)
• Yu and Dai ICCAD95
• Shibata etc. JIEP97(in Japanese)
• Layer Assignment and single layer routing
• Tsai, Wang and Chen TCAD98
• Chen, Chen, Tsai and Chen ICCD99
• Existing algorithms are for single layer routing
• Global routing method for 2-layer BGA packages
  is proposed

7
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

8
Our target
Ring wire for plating

• Target 2-layer BGA package with plating leads
• Plating lead a wire connecting outer ring to
  plate wires
• Finger (on layer1) connecting BGA board and chip
• Ball (on layer2) connecting BGA board and PCB
• Net 2-terminal (a finger and a ball) with
  plating lead

chip
finger
ball
Plating lead
via
Route on layer1
finger
via
ball
Route on layer2
9
Via assignment
Vias are on grid array Radius of vias are
large for ball pitch At most one via is
allowed between four adjacent balls
10
Routing strategy Monotonic routing

• Monotonic Routing
• never snakes in horizontal direction
• crosses any horizontal line at most once

Monotonic routing
Non-monotonic routing
11
Condition for Monotonic Routing

• Monotonic routing is possible
• if and only if via assignment is monotonic
• Monotonic via assignment
• Net labels of vias on each row are
• subsequence of net labels of fingers
• In monotonic via assignment,
• Monotonic global routes are determined uniquely
• Global routing Monotonic via assignment

12
Routing Strategy Routes on Each Layer

• Layer1 Monotonic routes with plating tales
• Via assignment is monotonic
• Global routes are determined uniquely
• Layer2 Short routes
• Each via is put near
• corresponding ball

0, 1, , 14
Layer2
Layer1
13
Evaluation of Routes

• Via assignment is monotonic
• -gt Global routes can be determined uniquely
• Global routes are evaluated by via assignment
• Evaluation wire length (layer1), wire length
  (layer2) and wire congestion

0, 1, , 14
14
Evaluation Wire Length
Wire length (Layer1) the number of crosses of
vertical grid line and global routes
2 5

• Monotonic routes
• If wire length is long,
• routes snake
• routes cross vertical grid line

Len2
Len0
15
Evaluation wire length
Wire Length (Layer2) Manhattan distance between
a ball and a via
2 5
5
Len2
5
Len1
2
2
16
Evaluation Wire congestion

• Routing failure occurs
• Congestion is dense
• Congestion is not
• ballanced

Difference of congestion 3-52
Congestion between adjacent 2 vias
Reciprocal of wire pitch
Congestion evaluation Sum of
difference of adjacent congestion
17
Problem Definition

• 2-Layer BGA Package Routing
• Input 2-terminal nets (pair of a ball and a
  finger)
• Output Global routes including vias
• Objective
• To minimize
• Costawire length(layer1) bwire
  length(layer2) cwire congestion
• Constraints
• Monotonic via assignment
• Plating leads

18
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

19
Routing Optimization Approach

• Greedy algorithm
• Give initial via assignment
• Select via-assignment modification with maximum
  gain under monotonic constraint
• If maximum gain gt 0, apply the modification and
  go to 2

20
Routing Optimization Approach

• Greedy algorithm
• Give initial via assignment
• Select via-assignment modification with maximum
  gain under monotonic constraint
• If maximum gain gt 0, apply the modification and
  go to 2

21
Initial via assignment

• Vias are generated according to ball sequences
• Each via sequence is divided into monotonic
  sub-sequences
• Vias of sub-sequences for same ball sequence are
  put on different rows of via grid array

0, 1, , 14
4
10
11
13
1
5
6
7
12
14
0
3
8
2
9
22
Initial via assignment

• Vias are generated according to ball sequence
• Each via sequences are divided into monotonic
  sub-sequences
• Vias of sub-sequences for same ball sequence are
  put on different rows of via grid array

Vias of sub-sequences in different ball
sequences can share same row of via grid array
0, 1, , 14
11
4
10
5
13
1
6
7
2
9
12
14
0
3
8
23
Initial via assignment

• Vias are generated according to ball sequence
• Each via sequences are divided into monotonic
  sub-sequences
• Vias of sub-sequences for same ball sequence are
  put on different rows of via grid array

Vias of sub-sequences in different ball sequence
can share same row of via grid array
0, 1, , 14
11
4
10
5
13
1
6
7
2
9
12
14
0
3
8
24
Routing Optimization Approach

• Greedy algorithm
• Give initial via assignment
• Select via-assignment modification with maximum
  gain under monotonic constraint
• If maximum gain gt 0, apply the modification and
  go to 2

25
Via assignment modification

• Modification patterns
• 2-via exchange
• 3-via rotation
• Sequential via movement

26
2-via exchange, 3-via rotation

• 2-via exchange
• Adjacent 2 vias are exchanged
• 3-via rotation
• 3 vias on a unit grid are rotated

u
u
j
i
k
j
i
k
l
l
d
d
2-via exchange
3-via rotation
27
Sequential via movement

• Vias are moved to their adjacent grid one by one
  without overlaps

0, 1, , 14
11
4
10
5
2
13
9
1
6
7
12
14
0
3
8
28
Complexity

• Modification with maximum gain
• enumerating all modifications
• calculating the gain of them
• Complexity to obtain modification with maximum
  gain (n number of nets)
• 2-via exchange O(n)
• 3-via rotation O(n)
• Sequential via movement O(n2)
• Total O(n2)

29
Routing Optimization Approach

• Greedy algorithm
• Give initial via assignment
• Select via-assignment modification with maximum
  gain under monotonic constraint
• If maximum gain gt 0, apply the modification and
  go to 2

30
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

31
Experiments

• Proposing method is implemented by C
• CPU 3GHz, 1GB memory
• Cost function
• length(layer1) length(layer2) congestion
• ( a b c 1 )
• Comparison
• ALL (Proposing method) 2-via exchange, 3-via
  rotation, and sequential via movement
• SEQ Sequential via movement only

32
Experimental results
Calculation Time (s)

• ALL generates better routes than SEQ
• ALL takes much more time than SEQ
• Tradeoff between quality of solution and
  calculation time

33
Experimental result (data3)
Length(layer1) 252 ? 53 Length(layer2) 160 ?
193 Congestion 414.3 ? 129.8 Time(s) 1.90
(sec)
34
Contents

• Introduction
• Problem Definition and Strategy
• Global Routing Method
• Experiments
• Conclusion

35
Conclusion

• Global routing method for 2-layer BGA packages
  was proposed
• Monotonic routing was introduced
• Global routing method by monotonic via assignment
  was proposed
• The method gives initial via assignment and
  improve it by via assignment modification
• Experimental results
• Our method generates good global routes
• Tradeoff between quality of solution and
  calculation time

36
Future work

• Reduction of calculation time without degrading
  solution
• Accurate design rule consideration for both
  layer1 and layer2
• Plating leads planning
• Whether is the plating lead of each net routed on
  Layer1 or Layer2?

37
BGA Package Design

• Consideration
• Multi-layer routing
• Obstacles
• Plating lead
• Chip scale package
• Multi-chip on board
• Electrical effects

die
Au bonding wire
bonding finger
board
solder ball
38
Evaluation Wire length on layer1
11
len 1
4
10
5
2
13
9
1
6
7
len 3
12
14
0
3
8
39
Routes distribution

• Many obstacles on layer2
• For short routes
• Little obstacles on layer1
• For long routes
• Plating leads is on layer1

Layer2
Layer1
40
Sequential via movement
0, 1, , 14
0, 1, , 14
Layer1 Layer2 Congestion
41
Local change of the cost

• Local change of cost is possible to calculate if
• Adjacent vias of the target via are known
• Two previous vias and a next via in the movement
  are known
• Sum of local change of cost gain

u
k
j
i
i

k
l
j
l
d
d
The direction of movement is restricted to
right, left or above, below
42
Cost graph
Nodes target via and two previous vias Edges
the direction of next via
j, k, u
u
j
i
k
l
j, k, l
i, j, k
d
j, k, d
43
Cost graph
Nodes target via and two previous vias Edges
the direction of next via
a
j, k, u
k, u, a
u
b
j, k, l

i
k
j
l
c
k, u, b
i, j, k
d
j, k, d
Weight of edges are local change of cost
k, l, b
44
Cost graph

• Directed acyclic graph
• Calculate longest path
• Longest path sequential movement with maximum
  gain
• Sequential via movement with maximum via is
  selected
• For all starting nodes,
• Generate cost graph
• Search longest path
• Select path with maximum gain among all

45
Experimental results
46
Experimental results

• Comparison
• ALL
• Proposing method
• SEQ
• sequential via movement only
• Via movement starts with via of large cost

47
Our Strategy

• Strategy
• Layer1 Monotonic routes with plating leads
• Layer2 Short routes

Layer2
Layer1