1. Thermal Model of a Thinned-Die Cooling System N. Boiadjieva … NPTest, Inc P. Koev… MIT, Dept. of Mathematics

2. Outline Optical Probing and Cooling Problem Statement System Characterization Mathematical Model Development Conclusions

3. Optical Probing & Cooling Socket & Clamp Cooling system Load Board Die Carrier Tapered Final Lens Element Transparent Diamond Window (Heat Sink) Detector Stimulus

4. Optical Probing

5. Cooling System setup DUT Heat Exchanger Heat Spreader, Diamond window Clamp Lens

6. Cooling System X-Section Transparent Diamond k=1800 W/m-K Device clamp Thermocouple, T B Thermocouple, T HS Lens Copper k=374 W/m-K

7. Thermal System Characterization T DUT =f(Wattage, air Flow rate, cooling air T AIR ) Heat Spreader Thermocouple, T DIA during characterization only Diamond window Thermocouple, T B Heat Exchanger Thermocouple, T HS DUT Center line Package Heat Exchanger Cooling air, T AIR Flow rate

8. Problem Statement Develop a mathematical model so that both device temperature and device power could be derived through the analytical expression. T DUT TBTB T HS T AIR Flow rate T DUT =f 1 (Wattage, T AIR, FLOW, T HS ) Wattage=f 2 (T HS,T AIR, FLOW)

9. Thermal System Characterization T DIA TBTB T HS T AIR Air Flow rate

10. Mathematical model development Thermocouple, T DIA Diamond window Thermocouple, T B Cooling air, T AIR Thermocouple, T HS DUT x T DUT T HS TBTB T AIR T DIA ~T DUT,

11. Mathematical model … cont’d x T DUT T HS TBTB T AIR 3D case  1D non uniform rod In Steady State 1D Heat equation Uniform rod Non uniform rod

12. Mathematical model … cont’d x T DUT T HS T AIR l1l1 l2l2 Solution Uniform rod Non uniform rod

13. Non uniform rod…cont’d x T DUT T HS T AIR T FP Flow T FP =f (T AIR, Flow) Need to define measure ???

14. T FP =f (T AIR, FLOW) x T DUT T HS T AIR c T FP d T AIR T3T3 T3T3

15. Final Formula(s) measure??? T DUT TBTB T HS T AIR Flow rate

16. Results Comparison T DUT TBTB T HS T AIR Flow rate, Error was less that 10% over the entire temperature and power range

17. Conclusions Cooling system for thinned 150W microprocessor - characterized 3-D Heat Transfer simplified to a 1-D non uniform rod case Device temperature and input power can be determined through an analytical expression Future software control capabilities.