TEMPERATURE OF A HEATED THIN METAL FILM IN LIQUID 4He AT 0.1 K FOR LARGE VALUES OF ENERGY FLUX

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TEMPERATURE OF A HEATED THIN METAL

FILM IN LIQUID 4He AT 0.1 K FOR LARGE

VALUES OF ENERGY FLUX

E. Nothdurft, K. Luszczynski

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplement au n° 8, Tome 39, aout 1978, page C6-252

TEMPERATURE OF A HEATED THIN METAL FILM IN LIQUID

4

He AT 0.1 K FOR LARGE

VALUES OF ENERGY FLUX

E.E, Nothdurft and K. Luszczynski

Department of Physios, Washington University, St. Louis, Missouri 63130, U.S.A.

Résumé.- On a mesuré la température Ts d'un film mince d'or chauffé plongé dans ''He liquide maintenu

à 0,1 K pour des valeurs du flux d'énergie Q V Â comprises dans le domaine de 0,03 à 100 mW/mm2. Pour Q/A < 0,27 mW/mm2 (Ts < 1,1 K) les résultats sont décrits par la loi Q/A = 0,20 Tg'° et pour des

va-leurs plus élevées du flux d'énergie par Q/A = 0,16 T|* . Les vava-leurs de Ts mesurées paraissent

net-tement plus élevées que les températures effectives de la source, pour les valeurs de Q/A utilisées dans les techniques d'impulsion de chaleur à 0,1 K.

Abstract.- The temperature Ts of a heated thin gold film immersed in liquid ""Hemaintened af 0.1 K

has been measured for energy flux values Q/A#in the range between 0.03 and 100 mW/mm2. For Q/A<0.27 mW/mm2 (TS<1.1 K) the data are described by Q/A = 0.20 Tg"° and for higher energy flux values by

Q/A = 0.16 T|'5. The measured values of Ts appear to be substantially higher than the effective

sour-ce temperatures for values of Q/A used in heat pulse experiments at 0.1 K.

The problem of energy transport between a so-lid and liquid helium ''He has been studied extensi-vely/1/. A large body of work relates the amount of heat flow across the solid-liquid interface in res-ponse to a temperature difference AT = T - T, whe-re T is the temperatuwhe-re of the solid and T is the ambient temperature of the liquid. F o r A T » T , black body phonon radiation arguments give/2/

Q/A = H(AT)*/4 . (1) This situation is difficult to achieve for

conti-nuous energy flow, but is readily obtained with thin films heated by short electric current pulses, a technique which has been used extensively in heat pulse experiments in liquid ''He at low temperatures. In these experiments the surface temperature of the heater T is not accurately known nor is it clear

s

at this stage how T is related to the effective source temperature T. which characterizes the spec-tral distribution of phonon flux in liquid "*He. Sherlock et al/3/, on the basis of their analysis of observed heat pulses, conclude that T probably is substantially lower than a reasonable estimated value of T . It is clearly of considerable interest

s

to determine T experimentally and to find its de-pendence on the energy flux Q/A transfered into low temperature liquid ''He.

In the present experiment thin strips of tin and an aluminum alloy along with thick gold con-tact strips are vapor deposited on a glass micros-cope slide, as shown in figure 1. The central

por-Top View

Gold Contacts ( 5 0 0 0 1 )

-Gold \ Tin „ (500A)/(5OOA)

Fig. 1 : Schematic diagram of thin film bolometers and thin film heater ; each metal strip is 0.85 mm wide.

tion of these depositions is then covered with a o

1000 A layer of silicon oxide. Finally, a thin gold film with thick gold contact strips is deposited across the central portion. The substrate is placed in a sample chamber that is 3.5 cm across so that when the chamber is filled with low temperature li-quid ''He reflected phonons do not return in less than 180us. The strips are biased with a small cons-tant current and a uniform magnetic field is applied to use them as superconducting bolometers. The vol-tage appearing across the b'olometer is then calibra-ted as a function of ambient temperature.

The front gold strip is pulsed with a 50 ys long square pulse of varying powers. The resulting volta-ge signals from the bolometers are converted to tem-perature vs. time plots using the ambient temperatu-re calibrations. The observed temperatutemperatu-re temperatu-registetemperatu-red by the bolometers closely follows the input pulse. After the pulse is applied the temperature reaches Work supported in part by the National Science

Foundation Grant.

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98

%

of its maximum value within 6 ps, and it falls

to its initial value even more rapidly at the end

of the pulse. This response is consistent with re-

sults obtained from approximate solutions of the

heat flow equations which indicate that energy flux

into the glass substrate approaches zero within a

few microseconds after the beginning of the pulse.

Figure 2 shows the surface temperature T as

measured by the bolometers, for various values of

~ I A ,

with liquid helium maintained at

0.1

K and sa-

turated vapor pressure.

Fig. 2

:

Surface temperature Ts as measured by the

superconducting bolometers, as a function of eneFgy

flux from the gold film heater. Solid symbols

-

alu-

minum alloy bolometer

;

open symbols

-

tin bolome-

ter. Nominal values of magnetic field in gauss are

triangles

:

150

;

solid circles

:

210

;

open cir-

cles

:

300

;

squares

:

370. The measured values of T are relatively insensitive

to pressure over the entire range of $A values in-

vestigated here

;

at 24 atm there is a 5

+

2

%

reduc-

tion in the measured values of T

.

For i(/A

<

0.27 mw/m2 (T

<

1 .l

K) the data fit the relation

4/A

=

0.2;

'

:

T

',

indicated by the dashed line. For

higher values of $A the data are approximately des-

cribed by 6/A

=

0.16 T

:

"

,

represented by the solid

line.

Since the temperature of liquid helium is

maintahed at

0.1

K, the measured Ts is essentially

the same as AT in equation (1).

For values of G/A

below 0.27 mw/nrm2, the data clearly follow the re-

lation predicted by the black body phonon radiation

model. Results obtained for

$A i

0.27 mw/m2 show

significant

deviationsfrom the phonon radiation mo-

del and suggest that some different energy transport

mechanisms

may

become important in this region.

The values of the surface temperature T as

measured in the present experiment differ substan-

tially from the effective source temperature T1 cal-

culated by Sherlock et a1./3/ for values of

~ I A

used

in their heat pulse experiments. For example, for

energy flux of 50 mw/mm2 they calculate an effective

source temperature T 1 of 1.2 K. For the same energy

flux the present measurements correspond to T =2.8K,

as shown in figure

2.

The observed differences bet-

ween T and T may indeed arise if there is an in-

1

termediate layer between the heated solid and the

bulk low temperature liquid helium.

References

/l/ Anderson,A.C., in Phonon Scattering in Solids

edited by Challis. L.J. Ram~ton

* ~ - -