authors: jia-wei fang,chin-hsiung hsu,and yao-wen chang dac 2007 speaker: sheng yi an integer linear...

Authors: Jia-Wei Fang,Chin-Hsiung Hsu,and Yao-Wen Chang

DAC 2007

speaker: sheng yi

An Integer Linear Programming Based Routing Algorithm for Flip-Chip Design

Outline

2

IntroductionProblem formulationRDL routing algorithmExperimental resultsConclusions

Introduction

3

The increasing complexity and decreasing feature size of VLSI designs make the demand of more I/O pads a significant problem to package technologies.

An advanced packaging technology, the flip-chip (FC) package[Fig.1.(a)] is created for higher integration density and larger I/O counts.

However, in recent IC designs, the I/O pads are still placed along the boundary of a die. This placement does not suit for the flip-chip package well. As a result, the top metal or an extra metal layer, called a Re-Distribution Layer (RDL)[Fig.1.(b)] is used to redistribute the wire-bonding pads to the bump pads without changing the placement of the I/O pads

Introduction

4

Introduction

5

There are two kinds of the RDL routing problems for flip-chip design.

1.free-assignment routing

:a router has the freedom to assign a wire-bonding pad to

bump pads during routing.

2.pre-assignment routing

:the mapping among wire-bonding pads and bump pads are

defined before routing and can not be changed.

ps: pre-assignment problem is more popular in practice since

the functions of wire-bonding and bump pads are

typically pre-defined by IC and packaging designers.

Problem formulation

6

}p,...,p,{p pads bonding- wirel ofset a of consists :r

package. theofboundary

at the rings pad bonding- wireg ofset a :}r,...,r,{rR

}b,...,b,{b pads bump q ofset a of consists :r

package. theof

center in the rings pad bump f ofset a :}r,...,r,{rR

pads. bump ofset the:B

pads. bonding- wireofset the:P

:notations

jl

j2

j1

pj

pg

p2

p1p

iq

i2

i1

bi

bf

b2

b1b

Problem formulation

7

segments.adjacent twoof middle in the line a :linecut

pads. bump and pads bonding

-reconnect wi topoints passing hese through tpass :Nets

points.

passingor pads connectsnet which a ofpart a :segment

]connected. be should that pad bump

a and pads) bonding- wireofset pad(a bonding

- wireaby defined is Nin n net pin)-pin(multi-2each :[ps

routing.for

nets)pin -multior pin -2 be nets(could ofset the:N

:notations

Problem formulation

8

design]

chip-flip eperformanc-high ain routing for the considered be also

shouldnets, obetween twgth in wirelen difference theskew, signal [the

path.turn - Uno with

route a is routing monotonic a ,informally :routing monotonic

.]r ring same in the

pads bonding-ireadjacent w obetween twsegment or pads

bumpadjacent obetween twsegment thebe Uu interval[an

intervals. ofset a :U

pj

:notations

interval.an through pass net to afor point the:point passing

Problem formulation

9

Problem formulation

10

Problem formulation

11

Problem 1 :The single-layer pre-assignment routing problem in the flip-chip design is to connect a set P of wire-bonding pads and a set B of bump pads according to pre- defined netlist with wire width and signal skew constrains so that no wire crosses each other, no signal skew constrain is violated, and the total wirelength is minimized under the 100% routability

guarantee.

RDL routing algorithm

12

Algorithm overview


13

Notations and construct the routing network G:

E)B,D(PGnetwork routing a

rings.) pad (bump)

bonding-ireadjacent w obetween tw ))b,b,b,((b

)p,p,p,(p rectangle a represents M m(each

tiles.ofset a :M

ring.) pad bonding

- wireain )b,(p intervalan or pads bumpadjacent two

between ))b,((b )b,(b intervalan through pass

net to a of node candidate a represents node ILP(each

nodes. ILPh ofset a :}dd{dD

B

1i1z'

1iz'

i1z

iz

1j1y'

1jy'

j1y

jy

j1y

jy

1iz

iz

i1z

iz

,...,,h21

[global routing : ILP Formulation]


14

Notations:

E: a set of edges which are the candidate segments of the

global routing paths of nets.

There are four types of edges:

1.the directed edge from a wire-bonding pad to a bump pad.

2.the directed edge from a wire-bonding pad to an ILP node.

3.the directed edge from an ILP node to a bump pad.

4.the directed edge from an ILP node to another ILP node.



15

5. Figure



16 [global routing : ILP Formulation]



.0)e,C(e

otherwise,;1)e,C(e ,e crosses e If .e

and ebetween crossing thedenoteshat function t :)e,C(e

.nnet of width wire thedenoteshat function t:)W(e

.e oflength thedenoteshat function t:)L(e

.n ofpath routing

-global theof jsegment candidate a denotes that edge:e

otherwise.,0xchosen; is jsegment the

if 1 x.nnet ofpath routing-global in thechosen is j

segment candidate a if denotes that riableinteger va 1-0 :x

:follows as aren formulatio ILP in the used notations The

qp,ji,

qp,ji,qp,ji,qp,

ji,qp,ji,

iji,

ji,ji,

i

ji,

ji,

ji,i

ji,

RDL routing algorithm Constraint (1): avoids the crossing Constraint (2): is used to avoid the congestion overflow of a

tile . Constraint (3): avoids the congestion overflow of an interval

between two pads.(for the edges passing through

the same interval.) Constraint (4): formulates the signal-skew constraint between

two nets. Constraint (5): guarantees that at least one edge of the wire-

bonding pad pi of net ni be chosen.

Constraint (6): flow conservation.


RDL routing algorithm Two ILP reduction techniques to reduce the size of network G

and the number of variables and constraints in the ILP:

(1).Constraint Graph Based Pruning

(2).ILP Node Merging

22 [global routing:ILP reduction]


23[ 出處 :2006 IEEE Monotonic Parallel and Orthogonal Routing for single-layer Ball Grid Array Package]

A single netlist is monotonic if and only if nets on each row are in increasing order.

RDL routing algorithm (1).Constraint Graph Based Pruning:



28 [global routing:Non-monotonic]

RDL routing algorithm Passing point assignment

:passing points are transformed from ILP nodes in order to distribute nets pass through the same interval, according to their wire widths and further signal-skew constraints.

Net-Ordering Determination

29[Detail routing:passing point and Net-order Determination]


30 [Detail routing:X-based Gridless Routing]

Experimental results

31

#Nets: the number of nets#Skew pairs: the number of matched nets with skew constrains#Wire widths: the number of variable wire widths#Rp: the number of wire-bonding rings#p: the number of the wire-bonding pad#Rb: the number of bump pad rings#b: the number of bump pads


32

Imp. Of CG(%):the reduction rate of the variables by using constrain graph pruning.Imp. Of NM(%):the reduction rate over the results listed in the Column “Imp. Of CG(%)” by using the ILP node merging.Total: the final resulting number of variables (constraints)


33

Conclusions

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The first algorithm for the pre-assignment RDL routing problem, consider signal skews variable wire widths, U-turn routes, and total wirelength minimization.

authors: jia-wei fang,chin-hsiung hsu,and yao-wen chang dac 2007 speaker: sheng yi an integer linear...

Documents

ilp formulation slide

rdl routing problems

algorithm overview slide

freeassignment routing

routing network g

global routing paths

wirebonding pads

flipchip design slide