third int. conf. quantum, nano, and micro tech. (icqnm 2009) february 1-6, 2009 — cancun, mexico...

Third Int. Conf. Quantum, Nano, and Micro Tech. (ICQNM 2009) February 1-6, 2009 — Cancun, Mexico

Heat Transferin

Thin Films

Thomas Prevenslik

Berlin, GermanyHong Kong, China

1


Background

Over the past 30 years, heat transfer in thin films has been based on classical methods.

However, for films less than about 100 nm, classical heat transfer cannot explain the reduced thermal conductivity found in experiments.

2


Experiment

3

Pulse Method (Thin Solid Films, Kelemen, 36 (1976) 199-203)

Thermal Diffusivity

c

K

T/Tlnt4

xx

21

21

22

K = thermal conductivity = density, c = specific heat

X1

X2 T1

T2

Wire

F

Data Shows K 0 as 0

Substrate

Film

Problem

Diffusivity diverges as c 0 Can conductivity K be measured

by Pulse Method?

S

W


Current Approach

To explain reduced conductivity data, Fourier heat conduction theory is thought not

applicable to thin films having thickness smaller than the mean free paths of phonons.

Heat Transfer in thin films is modified to treat phonons as particles in the Boltzmann

Transport Equation (BTE).

4


Experiment and BTE Theory

Bulk Copper

0

100

200

300

400

500

10 100 1000 10000

Film Thickeness - - nm

The

rmal

Con

duct

ivity

- W

/ m

-K

.

Keff BTE PredictionsCopper Films

Electronics Cooling, 2007

5


Purpose

6

To provide a QM explanation

for thin film heat transfer based on

QED induced EM radiation using Standard Mixing Rules.

QM = Quantum Mechanics

QED = Quantum Electro Dynamics

EM = Electromagnetic


QED induced EM radiation

Classically, heat is conserved by an increase in temperature.

But at the nanoscale, QM forbids heat to be conserved by an increase in temperature

because specific heat vanishes.

QED allows heat to be conserved at the nanoscale by the emission of

nonthermal EM radiation

7


Nanoparticle or Quantum Dot

8

•

NP, QD

• •

Molecular

Collisions

No Temperature change

EM

Emission

Laser

Radiation


Thin Film

9

QED Heat Transfer QCond = QJoule -QQED

Standard Mixing Rules

eff= Keff /effceff ceff = cS and cF = 0 eff =(FKF+SKS)[(F/S)+1]/[cS(FF+SS] KF = eff cS [F +S(S/F)] - (S/F)KS

KF ~ KBulk

QQED

QCond

T1

T2

Current Approach QCond =QJoule

Kelemen

KF = KS [(F+S/S)-1SFKF << KBulk

QJoule

x2-x1


EM Confinement

2r2r

2r

2 n2

1

Ln2

1

Wn2

11

c

f rn2

rP n2

hcE

For << W and L, 2nr

Photons in Rectangular cavity resonator, nr > 1

10


Specific Heat Thin films cannot conserve the Joule heat by an

increase in temperature because specific heat vanishes

Specific heat by Debye/Einstein Model for atomic vibration gives slow phonon (ps) response.

Excitons in QDs produced promptly (fs).

Modify Einstein Model for atom vibration to photon vibration inside the thin film.

11


QM Restrictions

0.00001

0.0001

0.001

0.01

0.1

1 10 100 1000

Wavelength - - microns

Pla

nck

Ene

rgy

- E -

eV

1

kT

hcexp

hc

E

12

Film

Free Molecule


Thin Film as an Einstein Solid

1

kThc

exp

hc

N3U A

NA = Number of Atoms in Film 3 NA Degrees of Freedom

13


Einstein Specific Heat

T

UC

2

2

A1

kT

hcexp

kT

hcexp

kT

hc

kN3

C*C

14

0*Cas0 Einstein

1*Cas

Debye & Einstein


Thin Film Specific Heat

15

3 microns0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000

Thin Fim Thickness - nr microns

Dim

ensi

onle

ss S

peci

fic H

eat

C* EM

Emission Temp

Increase


QED Induced Heat Transfer

QEDJouleCond QQQ

16

dt

dNEQ PPQED

Non Thermal Emission

EP = Photon Planck Energy

dNP/dt = Photon Rate


Conductivity – Response Kelemen - 1976

17

Copper Film

Glass SubstrateMixing Rule

Substrate

Experiment


QED induced Heat Transfer

18

0

100

200

300

400

500

10 100 1000 10000

Film Thickeness - - nm

The

rmal

Con

duct

ivity

- W

/ m

-K

.

0510152025303540

E(d

N/d

t) /

A (

T-T

o)

x10

9 W

/ m

2- K.

Kbulk - Keff

Keff

EMEmission


QED induced Heat Transfer

19

0

10

20

30

40

10 100 1000 10000

Film Thickness - - nm

Pla

nck

Ene

rgy

- E

- e

V

1.E+25

1.E+26

1.E+27

1.E+28

(dN

/dt)

/A(T

-To)

/ m2- K

dN / dt

Ep Photomultiplier


UV Laser Emission

Zinc Oxide

Sapphire

He-Cd

Laser

325 nm

QED radiation ~ 388 nm

~ 388/2(2.03 ) = 95 nm

< 100 nm

Mat. Sci. Eng. B56 (1998) 239-245 (QED cavity by Refractive Indices-Not Film Conductivity )

20

QLaser ~ QQED

QCond ~ 0


Conclusions Thin film specific heat vanishes. Transient film

temperatures follow the substrate allowed by QM to have specific heat.

Bulk conductivity is maintained in the film, but there is no conductive heat loss parallel to the surface. The film loses heat normal to the surface by EM emission.

Pulse Method requires modification using Standard Mixing Rules to measure thin film thermal conductivity

QED induced EM emission can and should be measured with standard photomultipliers for 100 nm films.

21


Extensions

Nanocatalysts

Surface Chemical Reactions

22


Nanocatalysts

Reactants A, B kT ~ 0.0258 eV

VUVRadiation

A

A

B

B

NP Au kT ~ 0.0 eV

BA

VUVRadiation

Reactants A, B kT ~ 0.0258 eV

TiO2 Particle

VUVRadiation

A

B

B

NP Au/TiO2

kT ~ 0.0

BA

A

A

B

B VUVRadiation

A

UnsupportedSupported

23


Surface Chemical Reactions

Substrate

NPs

Gas Molecules

QED radiation

QEDradiation

A

A

A

A

A AA-

A-EEE+PE

EEE+PE

exo A -

24

“God made solids, but surfaces are the work of the Devil.” W. Pauli (1900-1958)


Questions & Papers

Email: [email protected]

http://www.nanoqed.net

25

third int. conf. quantum, nano, and micro tech. (icqnm 2009) february 1-6, 2009 — cancun, mexico...

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