1. An Approach to Thermal Placement in MCM Using Thermal Force Model 黎 靖 南台科技大學電子系

2. Problem Assign chips to chip sites such that the system failure rate of a MCM is minimized.

3. Failure rate Failure rate of a chip is estimated by. System failure rate is

4. Typical MCM

5. II. Multiple Reflection Technique Transform a bounded substrate into an unbounded region.

6. III. Thermal-Force model 1. Force on C i caused by C j : 2. Thermal-force exerts on C i 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.

7. PLACEMENT PROCEDURE Initial placement Zero-force placement Chip Assignment

8. Initial placement

12. MCM Information ModulesChips Power dissipation value (power × chip number) A29 30W×12 、 27W×2 、 25W×4 、 16W×8 、 13W×2 、 7W×1 B31 30W×14 、 27W×2 、 25W×4 、 16W×8 、 13W×2 、 7W×1 C110 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

13. Results ABC IBMOurIBMOurIBMOur T max 108107115112228185 T min 80828885100145 282527 12840 S 10.8910.9610.23

14. IBM

15. Our

16. TCM, 1981

17. 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.