Heat Flow Control From Thermal Transistor to Thermal Logic Gate

7/29/2019 Heat Flow Control From Thermal Transistor to Thermal Logic Gate

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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


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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 thatallow the flow of heat to be controlled are still not available.

To make thermal devices that control heat flowjust like what we have done for electric charge flow.


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Outline:1 Negative Differential Thermal Resistance

2 Model of Thermal transistor

3 Thermal Logic Gate


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1 Negative Differential Thermal Resistance (NDTR)

1.1 WAHT is Negative Differential Thermal Resistance

1

T

JR

Normally larger the temperature difference, largerthe heat current J, namely positive R.

Is the negative R, i.e., lower temperature

difference higher heat flow, possible?

When temperature difference exists, heat flows

from high temperature to low temperature,


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A water pipe

Low pressure,

low flow.

High pressure,

high flow.


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Pressure dependent valve

high pressure

narrow valve

high flow

low flow

Two factors compete, negative differential

resistance is thus possible!

low pressure

broad valve

low flow

high flow

?

?


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Match and mismatch of the power spectra of coupled materials

xtaxx cos20

22222

0 )(

)cos(

ab

tbx

Then, the response:

1.2 How to Make a Negative Differential Thermal

Resistance

Make a smart thermal valve.

0

Resonance phenomenon


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As the frequency of the external driven force equals

the own frequency of the linearoscillator, the

response reaches its maximum.

As the power spectra of two systems match each

other, energy can easily flow from one to the other.


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Suppose the power spectra of one of the two coupled

segments is temperature dependent.

TL TR

right segment

left segment

power

frequency

power

frequency

right segmentleft segment

Smaller TL

larger T

Large TL

smaller T

TL


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In principal power spectra of any nonlinear system

is temperature dependent.

Our choice: Frenkel-Kontorova (FK) model

iiii

i

y

V

yyKm

p

H 2cos)2()(2

1

2 22

1

2


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Sensitive temperature dependence

High frequency

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.


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0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

120

Power

J=2.8E-7

TL=0.01

frequency

particle at left

particle at right

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

120

frequency

J=9.5E-5

TL=0.06

particle at leftparticle at right

Power

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

120

Power

frequency

J=3.5E-4

TL=0.11


0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

120

Power

frequency

J=1.272E-4

TL=0.18


0.00 0.05 0.10 0.15 0.20

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

0.00040

J

TL

TL TR


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1.3 Why do we need a Negative Differential Thermal

Resistance?

Thermal transistor


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2 Model of Thermal transistor

G(Gate)

D(Drain)

S(Source)

VD(+)

VS(-)

IS

IDIG

2.1 Field-Effect-Transistor (FET):

IG 0

VG


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TS=T-

TO

JS JD

At steady state: JS=JD

Segment DSegment S

JD=J

S

Tos

T+T-

J

To

JD

JS

TD=T+

O

T+>T-


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JG=J

S-J

D

JS

JD

Tob

To

at NESS

T+T-

J

To

JD

JS

)/(/

/DSS

OO

OD

O

D RRRTJ

TJ

J

J

current amplification factor:


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Normal situation: RS,RD>0

Therefore:


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0.00 0.04 0.08 0.12 0.16

6

TO'

TO

"off"

"on"

TO

G

S D

(b)

(a)

JG

JS

JD

0

O

4

2J(

10-

4)

kintG

kint

TS=T

-T

D=T

+

TG

TG

JS

JDJ

G

O'

RG is negligible

thus TO=TG

At the three crosses, JG=0.

Heat flow switch


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In the working region: TG= 0.05 ~0.135

JD=5e-5~2e-4

While JG=-1e-5~1e-5

Heat flow

modulator


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3 Thermal Logic Gate

3.1 Thermal repeater

3.0 standard voltages (temperature)

Transistor-transistor logic (TTL):

Vhigh=5.0 v, Vlow=0.0 v

cinoff

cinon

out TTifT

TTifTT

,

,

Here we use Ton and Toff as the two

standard temperatures.

A repeater standardize the input, when it is

slightly different from Ton/Toff.


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0.00 0.04 0.08 0.12 0.16

6

TO'

TO

"off"

"on"

TO

G

S D

(b)

(a)

JG

JS

JD

0

O

4

2J(

10-

4)

kintG

kint

TS=T

-T

D=T

+

TG

TG

JS

JD

JG

O'

suppose TG is slightly greater than

Ton, then JS>JD, thus JG >0

suppose RG is taken into account,

Then TO


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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)

TO

TG


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0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

O' O'OO

D D

SS T-T-

T+

T+

OO'

(b) Ton

Toff

Toutput

Tinput

output of the 1st transistor

output of the 2nd transistor

output of the 6th transistor

ideal repeater

Tc

T+

D

G

S

input output

Thermal repeater

T-

(a)

......

Output of a six-transistor

repeater

If we connect them in

series, the final outputwill be closer and

closer to that of an

ideal repeater.


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3.2 Thermal NOT gate

oninoff

offinon

out TTifT

TTifTT

Notice: as Tin increases, Tout howeverdecreases.

Question: can we cool down one part of a

system by warming up another part?!


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0.00 0.04 0.08 0.12 0.16

6

TO'TO

"off"

"on"

TO

G

S D

(b)

(a)

JG

JS

JD

0

O

4

2J(

10-

4)

kint

G

kintTS=T- TD=T+

TG

TG

JS

JD

JG

O'

TO increases

JD increases, RD is nearly fixed

Temperature drop in

segment D ( TD-TO )increases

TD is fixed, thus TO

decreases

Lets study TO(TO).

This is in fact possible.


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0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.160.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

ideal NOT gate

(b)

Toutput

Tinput

T+

T-

T-

G

D

S

OO'

input

Thermal NOT gate

plug into a repeater

(a) temperature

divider

Vout

R2

V

R1

voltage divider

Vout=VR2/(R1+R2)


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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.


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0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0.02

0.04

0.06

0.08

0.10

0.120.14

0.16

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0.02

0.04

0.06

0.08

0.10

0.120.14

0.16

G

S

D

T-

T+

(c) Thermal OR gateT

input2=T

off=0.03

Toutput

Tinput1

plug into a repeater

input2

input1

Thermal AND and OR gates

SO

O'

(a)

T-

GD

O

O'T

+

ideal AND gate

(b) Thermal AND gateT

input2=T

on=0.16

ideal OR gate

It is clear that when the twoinputs 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.


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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


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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).


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Acknowledgement

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.

Collaborators


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Renmin University of China


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Renmin: peoples

: Peoples Republic of China

Our university is basically a social science university.

We are building a department of physics in a

social science university.


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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, financephysics, bio-physics etc.


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A young department needs your support

Welcome to Renmin University

Welcome to our department

Wang Lei

[email protected]


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Heat Flow Control From Thermal Transistor to Thermal Logic Gate

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