Heat Flow Control : from Thermal Transistor to Thermal Logic Gate

1. Heat Flow Control : from Thermal Transistor to Thermal Logic Gate Wang Lei Department of Physics, Renmin University of China, Department of Physics and Centre for Computational Science and Engineering, National University of Singapore Transmission of Information and Energy in Nonlinear and Complex Systems (TIENCS) 2008

2. Motivation: When it comes to transporting energy, nature has two vital tools: conduction by heat and by electricity. Electricity, by way of the electronic transistor and other devices that control the flow of charge, has enabled technological developments that have improved many aspects of our lives. But similar devices that allow the flow of heat to be controlled – are still not available. To make thermal devices that control heat flow just like what we have done for electric charge flow.

3. Outline: 1 Negative Differential Thermal Resistance 2 Model of Thermal transistor 3 Thermal Logic Gate

4. 1 Negative Differential Thermal Resistance (NDTR) 1.1 WAHT is Negative Differential Thermal Resistance When temperature difference exists, heat flows from high temperature to low temperature, Normally larger the temperature difference, larger the heat current J, namely positive R. Is the negative R, i.e., lower temperature difference higher heat flow, possible?

5. A water pipe High pressure, high flow. Low pressure, low flow.

6. Pressure dependent valve high pressure high flow ? narrow valve low flow low pressure low flow ? broad valve high flow Two factors compete, negative differential resistance is thus possible!

7. 1.2 How to Make a Negative Differential Thermal Resistance Make a smart thermal valve. Match and mismatch of the power spectra of coupled materials Resonance phenomenon Then, the response: ω0 ω

8. As the frequency of the external driven force equals the own frequency of the linear oscillator, the response reaches its maximum. As the power spectra of two systems match each other, energy can easily flow from one to the other.

9. Suppose the power spectra of one of the two coupled segments is temperature dependent. TL TL<TR TR Smaller TL larger ΔT Large TL smaller ΔT

10. In principal power spectra of any nonlinear system is temperature dependent. Our choice: Frenkel-Kontorova (FK) model

11. Sensitive temperature dependence Low frequency When the energy of particles is more or less the critical value, the temperature dependence reaches its maximum. Then we can see clear NDTR. High frequency

13. 1.3 Why do we need a Negative Differential Thermal Resistance? Thermal transistor

14. 2 Model of Thermal transistor 2.1 Field-Effect-Transistor (FET): VD(+) D(Drain) ID IG → VG G(Gate) IS S(Source) VS(-) IG≈ 0

15. Segment D Segment S JS JD O TS=T- TD=T+ TO T+>T- At steady state: JS=JD

16. current amplification factor:

17. Normal situation: RS,RD>0 Therefore: α<1 The transistor does NOT work!! If either RS or RD is negative, αcan be greater than 1 thus the thermal transistor works.

18. RG is negligible thus TO=TG Heat flow switch At the three crosses, JG=0.

19. Heat flow modulator In the working region: TG= 0.05 ~0.135 JD=5e-5~2e-4 While JG=-1e-5~1e-5

20. 3 Thermal Logic Gate 3.0 standard voltages (temperature) Transistor-transistor logic (TTL): Vhigh=5.0 v, Vlow=0.0 v Here we use “Ton” and ”Toff” as the two standard temperatures. 3.1 Thermal repeater A repeater standardize the input, when it is slightly different from “Ton /”Toff”.

21. suppose TG is slightly greater than Ton, then JS>JD, thus JG >0 suppose RG is taken into account, Then TO<TG, thus is closer to Ton.

22. As TG is closer to Ton/Toff, TO is always even closer, i.e., Ton and Toff are two stable fixed points of the function: TO(TG)

23. If we connect them in series, the final output will be closer and closer to that of an ideal repeater. Output of a six-transistor repeater

24. 3.2 Thermal NOT gate Notice: as Tin increases, Tout however decreases. Question: can we cool down one part of a system by warming up another part?!

25. This is in fact possible. Let’s study TO’(TO). TO increases JD increases, RD is nearly fixed Temperature drop in segment D ( TD-TO’ ) increases TD is fixed, thus TO’ decreases

26. Vout=VR2/(R1+R2)

27. 3.3 Thermal AND/OR gate AND/OR gate is a three terminal ( two inputs one output) device. If two inputs are the same, the output of AND/OR gate follows, otherwise AND/OR gate output “off”/“on”.

28. It is clear that when the two inputs are the same, the output must follow. By adjusting some parameters e.g., the critical temperature of the repeater, it is also easy to output “off”/“on”, thus a AND/OR gate is realized.

29. Summary: Based on the novel physical phenomenon Negative Differential Thermal Resistance, thermal transistor that control heat flow becomes possible. By combining thermal transistor in different ways, one can also build up thermal logic gates that realize all the basic logic operations. Although at this moment these are only pure theoretical (toy) models, this still opens the possibility that, heat energy already present in abundance in electronic devices, can be used to process information and even to do computation. Phononics

30. References: Baowen Li, Lei Wang, and Giulio Casati, Appl. Phys. Lett. 88, 143501 (2006); Lei Wang and Baowen Li, Phys. Rev. Lett. 99, 177208 (2007); Lei Wang and Baowen Li, Physics World 21, no.3, 27 (2008).

31. Acknowledgement Collaborators Prof. Baowen LI (NUS) Prof. Giulio CASATI (NUS/Como, Italy) Dr. Jinghua LAN (NUS, IHPC/A*STAR) Dr. Nianbei LI (NUS) Mr. Nuo YANG (NUS) Mr. Weichung LO (NUS, IHPC/A*STAR) ...... Other members in CCSE.

32. Renmin University of China

33. Renmin 人民: people’s 中华人民共和国: People’s Republic of China Our university is basically a social science university. We are building a department of physics in a social science university.

34. Groups in our department: 1, theoretical physics 2, condensed matter experiment 3, material computation and simulation 4, computational physics 5, atomic and molecular physics 6, complex systems: statistical physics, finance physics, bio-physics etc.

35. A young department needs your support Welcome to Renmin University Welcome to our department Wang Lei phywanglei@ruc.edu.cn

36. thanks