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.