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Nanoscale Heat Transfer at Contact Between a Hot Tip

and a Substrate

Stphane Lefvre

Laboratoire dEtude Thermiques, UMR CNRS !"

E#o$e Nationa$e Suprieure de M#anique et d%rote#hnique, "&!

'uturos#ope Cede(

Sebastian )o$* and +ierre-$ivier Chapuis

Laboratoire dEner.tique Mo$#u$aire et Ma#ros#opique, Combustion, U+R

CNRS /""

E#o$e Centra$e +aris, &//&0 Ch1tena2Ma$abr2

Corresponding Author 3

Sebastian )o$*, +h454

EM/CEC+, &//&0 Ch1tena2 Ma$abr2, 'ran#e

T 3 66787767!8& ' 3 66789!/"!60, vo$*:em/#4e#p4fr

Abstract

;ot tips are used either for #hara#teri*in. nanostru#tures b2 usin.

S#annin. Therma$ Mi#ros#opes or for $o#a$ heatin. to assist data


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Nomenclature3

%3 a##ommodation #oe>#ient

a3 therma$ di?usivit2 @m/4s7A

b3 #onta#t radius @mA

Cv,p3 heat #apa#ities @B4.74D7A

E3 oun.Fs modu$us3 @+aA

e3 G$m thi#ness @mA

'3 for#e bet#ient @=4m/4D7A

I3 e$e#tri#a$ #urrent @%A

L3 ha$f $en.th of the rhodiump$atinum


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*!3 #oordinate on the +tRh #ient @D7A

: temperature amplitude(K)

3 heat #apa#ities ratio

: thermal conductivity (W.m-1.K-1)

3 e$e#tri#a$ resistivit2 @4mA

Subscripts3

%3 air

C3 tota$ #onta#t #ondu#tan#e probe #urvature radius

Eq3 #onta#t and samp$e #ondu#tan#es in series

+3 probe

S3 so$idso$id #onta#t

=3


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Thermoe$e#tri# ener.2 #onversion


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measurements are not dependent on the temperature distribution on the

samp$e surfa#e4

Homes et a$ K su..ested that the


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properties Jma.neti#, e$e#tri#, e$asti#, O4 %nd in 7&", D4 =i#ramasin.he

K7! proposed to mount a thermo#oup$e tip in a #onventiona$ %'M4 =hi$e

the temperature


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90mi#rons and shaped as a tip4 The si$ver #oatin. is removed at the tip

samp$e #onta#t to un#over the p$atinumrhodium


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the tip and the ambient4 ppand apare the probe perimeter and therma$

di?usivit24

#! The solid$solid and water meniscus contact conductances

The #onta#t bet


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bet


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estimated to !4/07nm from this si.na$4 !4/0nm is the


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%!Conduction through air

=e


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h x0y

0( )=C

vv.z

0 3

z0

1+ 2(2A) A +1( )$r , @7A


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transfer #oe>#ient h bet


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enhan#ement of heat u( in the ba$$isti# area be#ause the 'EM predi#tions

sho< that the heat transfer in the ba$$isti# area is mu#h $ess than the tota$

heat transfer4 The tip is assimi$ated to an e$$ipsoid


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#ondu#tan#e is hi.her than the ba$$isti# one


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the heat u( #rossin. the samp$e surfa#e b2 usin. our 'EM4 The tip hei.ht

is /!nm so that no so$idso$id heat #ondu#tion is invo$ved4 'i.ure " reports

a s$i.ht di?eren#e in the u( distributions


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and


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'()('(NC(S

[1] R. Venkatasubramanian, E. Siivola, T. Colpitts and B. OQuinn, Thin-film thermoelectric

devices with high-room temperature figures of merit, Nature, 413, (2001), 597.

[2] P. Vettiger et al., The Millipedenanotechnology entering data storage, IEEE

Transaction on Nanotechnology, 1, (2002), 39.

[3] C.L. Tien and G. Chen, Challenges in microscale conductive and radiative heat transfer,

ASME J. Heat Transfer, 116, (1994), 799.

[4] D.G. Cahill et al., Nanoscale thermal transport, Journal of Applied Physics, 93, (2003),

793-818.

+ . %hi and . 4a5umdar 'hermal transport mechanisms at nanoscale point contact

6ournal of 7eat 'ransfer 12! (2002) 328.

[6] S. Gomes, Contribution thorique et exprimentale la microscopie thermique sonde

locale: calibration dune pointe thermorsistive, analyse des divers couplages thermiques,

Ph.D. Report, Reims University, France (1999).

%. ef9vre et al. 'hermal conductivity cali"ration for hot wire "ased dc scannin# thermal

microscope :eview of %cientific ;nstruments ! (2003) 2!1


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[12] O. Kwon, L. Shi and A. Majumdar, Scanning thermal wave microscopy, Journal of Heat

Transfer, 125, (2003), 156.

[13] D.G. Cahill and R. Pohl, Thermal conductivity of amorphous solids above the plateau,

Physical Review B, 35, (1987), 1259-1266.

[14] M.M. Yovanovitch, General expressions for circular constrictions resistances for

arbitrary flux distribution, Progress in Astronautics and Aeronautics: Radiative transfer and

thermal control, 49, (1976), 381-396.

[15] W.M. Rohsenow and H. Choi, Heat, Mass and Momentum Transfer, chapter 11,

Prentice-Hall ed, 1961.


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CAPTIONS

Table 1: Contact radius bW corresponding to heat conduction in the water meniscus for

different water film thickness.

Table 2: Thermal conductances and radii for the four heat transfer modes involved in the tip-

sample heat transfer.

Figure 1: Schematic of the probe-sample interaction including conduction through air,

through the water meniscus and through the solid-solid contact.

Figure 2: Scanning Electronic Microscope image of the thermal probe. The Wollaston wire is

a silver coating 75 microns in diameter and a Pt-Rh core 5 microns in diameter. The mirror

ensures the laser reflection to control the tip deflection.

Figure 3: Thermal conductances of the contact and the sample versus the force applied by the

tip on the sample.

Figure 4: Thermal contact conductance through the water meniscus versus the meniscus

thickness.

Figures 5(a) and 5(b): Thermal resistance of the contact and the sample versus the tip

altitude. Figure 5(a) reveals a convective regime when z>20m and a linear regime

corresponding to conduction in air when z


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Figure 8: Flux versus radius (small ellipse axis direction) when the tip is in contact and for

different values of sample thermal conductivities. The insert reveals that the contact radius

due to air conduction may vary with the sample thermal conductivity by a factor of 2.

.


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Table 1:

Table 2:

Heat Transfer Mode Conductance (W.K-1) Contact Radius b (nm)

Radiation

Solid-solid

Conduction through air

Water Meniscus

1-!

" 1.#

$.%

% - !

-

$

1 " !

1 - $

Fig 1:

Fig 2:

&ilm Thic'ness W(nm) bW(nm)

0.25

0.5

1

100

140

200


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Fig 3:

Fig 4:


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Fig 5:


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Fig 6:

Fig 7:


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Fig 8:

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