an approach to thermal placement in mcm using thermal force model 黎 靖...
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An Approach to Thermal Placement in MCM Using
Thermal Force Model
黎 靖
南台科技大學電子系
Problem
• Assign chips to chip sites such that the system failure rate of a MCM is minimized.
x
Chips Chip sites Active substrate
py
p
Realsubstrate
Failure rate
• Failure rate of a chip is estimated by
. System failure rate is
T
1
298
1
kEaexpo
m
1iiS T
Typical MCM
Heat Sink
Cap
Thermal Grease
C4
Multi-layer Substrate ChipI/O Pad
II. Multiple Reflection Technique
Q
(a) A rectangle region with insulated boundaries (b) An unbounded region with infinite mirror heat sources .
Q Qi iQi
Qi
Qi
Qi
Qi
Qi
Qi
Qi
QiQi
Qi
W
L
Qi
Qi
Qi
Qi
QiQi
Qi
Qi
Qi
Qi
L
W iQj Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Qj
Y
X
row=0
row=1
row=2
row=-1
row=-2
column=2column=1column=0column=-1column=-2
Qi Qi
Transform a bounded substrate into an unbounded region.
III. Thermal-Force model
1. Force on Ci caused by Cj :
2. Thermal-force exerts on Ci
m
1j
1a
1ar
a)(r,ji,
a)(r,ji,
1a
a
ac
c)(a,ji,
c)a,(ji,
(0,0)ji,i fffffF
2ji,
jji,
)r(
qf
3. Thermal placement problem is reduced to the problem of solving a set of simultaneous linear equations to determine zero-thermal-force locations for chips.
4. A modified Newton-Raphson method is used to solve this system of equations.
PLACEMENT PROCEDURE
• Initial placement
• Zero-force placement • Chip Assignment
Initial placement
Ring I Ring II Ring III
1
1
1
1
2
2
2
2
3
3
3
34
4
4
4
5
5
5
5
1
2
3
4
5
8
6
7
9
10
11
12
13
14
15
16
17
18
19
20
C
C
C
C
C
C C
C
CCCC
C C C C C
C
C
C
MCM Information
Modules Chips Power dissipation value
(power × chip number)
A 29 30W×12、 27W×2、 25W×4、 16W×8、13W×2、 7W×1
B 31 30W×14、 27W×2、 25W×4、 16W×8、13W×2、 7W×1
C 110 20W×17、 19.5W×4、 17.3W、 16.9W×8、 15W×2、14.7W×1、 14.3W×1、 13.9W×1、 13.8W×1、 13.6W×1、 10.9W×1、 10W×1、 8.9W×71
ResultsA B C
IBM Our IBM Our IBM Our
Tmax 108 107 115 112 228 185
Tmin 80 82 88 85 100 145
28 25 27 27 128 40
S 1 0.89 1 0.96 1 0.23
maxT
IBM 128(8.9)
173(16.9)
134(8.9)
137(8.9)
134(8.9)
138(8.9)
141(8.9)
141(8.9)
139(8.9)
135(8.9)
128(8.9)
124(8.9)
142(8.9)
149(8.9)
152(8.9)
158(8.9)
171(15)
157(8.9)
149(8.9)
144(8.9)
139(8.9)
131(8.9)
148(8.9)
192(16.9)
185(10.9)
191(16.9)
172(16.9)
147(8.9)
136(8.9)
138(8.9)
150(8.9)
166(8.9)
204(20)
218(20)
220(19.5)
218(20)
205(20)
167(8.9)
152(8.9)
139(8.9)
135(8.9)
148(8.9)
168(8.9)
213(20)
226(20)
228(19.5)
227(20)
216(20)
174(8.9)
156(8.9)
139(8.9)
170(10)
215(20)
215(14.3)
216(13.6)
214(13.9)
217(20)
194(17.3)
169(14.7)
135(8.9)
148(8.9)
168(8.9)
213(20)
226(20)
227(19.5)
222(20)
208(20)
170(8.9)
154(8.9)
139(8.9)
138(8.9)
150(8.9)
165(8.9)
204(20)
217(20)
218(19.5)
210(20)
159(8.9)
150(8.9)
138(8.9)
137(8.9)
148(8.9)
173(16.9)
192(16.9)
190(13.8)
187(16.9)
168(16.9)
146(8.9)
136(8.9)
133(8.9)
127(8.9)
141(8.9)
148(8.9)
151(8.9)
157(8.9)
171(15)
156(8.9)
148(8.9)
145(8.9)
140(8.9)
131(8.9)
133(8.9)
137(8.9)
140(8.9)
140(8.9)
139(8.9)
138(8.9)
136(8.9)
131(8.9)
125(8.9)
Our179(20)
183(19.5)
179(20)
176(20)
174(20)
176(20)
155(8.9)
166(13.6)
179(20)
155(8.9)
160(8.9)
158(8.9)
154(8.9)
168(16.9)
167(16.9)
169(14.7)
157(8.9)
160(8.9)
177(16.9)
154(8.9)
158(8.9)
167(13.8)
152(8.9)
145(8.9)
152(8.9)
156(8.9)
160(8.9)
180(20)
179(19.5)
161(8.9)
157(8.9)
152(8.9)
148(8.9)
147(8.9)
148(8.9)
152(8.9)
157(8.9)
175(16.9)
160(8.9)
184(20)
158(8.9)
152(8.9)
150(8.9)
150(8.9)
150(8.9)
153(8.9)
157(8.9)
162(8.9)
182(20)
178(20)
161(8.9)
156(8.9)
153(8.9)
151(8.9)
151(8.9)
152(8.9)
155(8.9)
160(8.9)
164(8.9)
185(20)
170(15)
156(8.9)
153(8.9)
152(8.9)
151(8.9)
152(8.9)
156(8.9)
183(20)
177(15)
161(8.9)
173(20)
174(16.9)
156(8.9)
153(8.9)
152(8.9)
152(8.9)
152(8.9)
152(8.9)
171(13.9)
180(19.5)
153(8.9)
153(8.9)
154(8.9)
154(8.9)
154(8.9)
154(8.9)
156(8.9)
155(8.9)
152(8.9)
157(8.9)
154(8.9)
154(8.9)
152(8.9)
16.7(16.9)
165(14.3)
176(16.9)
172(16.9)
177(20)
158(8.9)
154(10)
173(20)
157(10.9)
172(19.5)
146(8.9)
174(20)
150(8.9)
146(8.9)
151(8.9)
171(17.3)
173(20)
TCM, 1981
Conclusion
• A force-directed technique based on thermal force model is proposed for the reliability-driven placement problem.
• The experimental results show that the present method can generate placements with lower system failure rate than their original designs.