A cryogenic fast response thermometer

Multipurpose carbon thin film resistance thermometers have been developed for cryogenic use. Carbon was electron beam evaporated onto polycrystalline alumina substrates with copper films as electrical contacts. The thermometers were coated with thin glass layers. The desired electrical resistance of the sensors was obtained with a final heat treatment. Their sensitivity at 4.2 K is approximately 300 f l K -I. Between 4.2 and 20 K the film resistance can be expressed as a function of temperature by a usual correlation of the form In R = Ao + AI In T + A2 (In T)2. These sensors have been developed as separate devices to be soldered or glued onto experiments Nevertheles& their response is fast at 4.2 K their thermal relaxation time is better than 1 ms and their thermal delay time is of the order of 70 ps.

A cryogenic fast response thermometer W.B. Bloem Key words: thermometers, carbon, thin film, fast response, low temperature

Heat transfer to boiling and supercritical helium plays an important role in ensuring stable performance of large superconducting magnets. Stationary heat transfer can be measured with relatively slow thermometers like germanium and carbon resistors. For transient effects, however, the use of fast sensors such as thermocouples is required, but they have a low sensitivity. Thus, available data on transient heat transfer are mostly the results of experiments in which the intrinsic electrical resistance of the sensor is used as heater and as thermometer. Schmidt ~ studied in this way transient effects with a NbTi wire, Steward 2 and Giarratano et al. a carried out similar work with a carbon film deposited onto a quartz substrate. A basic drawback of their technique is that it cannot be generally applied in other experimental set-ups. Seki and Sanokawa + constructed a fast response germanium thin film thermometer which measured the temperature of a stainless steel ribbon. Here, the sensor was indissolubly linked with the heating strip: for measurements on other samples one has to evaporate new germanium films. Thus, a sensitive cryogenic fast response thermometer which can be contacted to the experiments in a flexible way, is still very desirable. Such a fast response thermometer should have a high thermal diffusivity and a small size. In this study the construction of a carbon film resistance thermometer is examined and its thermal relaxation time is determined. Carbon was chosen as sensing material because of its large negative temperature coefficient of resistivity while allowing measurements in high magnetic fields. Another possibility was to use germanium, but we had a preference for carbon films because of the smaller influence of magnetic fields on their electrical resistance? The carbon films are often made by painting or spraying with a suspension of colloidal carbon in water. A severe disadvantage of these methods is the vulnerability of the film, while the absorption of gases causes resistivity changes? Making the films by vacuum deposition is a promising option to satisfy requirements like film thickness, small size and stability. 0011-2275/84/003159-07

CRYOGENICS . MARCH 1984

C o n s t r u c t i o n of t h e c a r b o n t h i n f i l m thermometer Fast response thermometers must have a low heat capacity pc o per volume unit and a high thermal conductivity X. So, the thermal diffusivity a, defined as a = h/(pCp), has to be optimized by proper selection of the materials for the thermometer construction. The thermal diffusivity and the thickness d of the sensor define the response time r. For example, when one side of an infinite slab gets a temperature j u m p from To up to T~, then after a long time t, that is if at/d 2 > 0.5, the temperature T on the other insulated side of the slab is given by

T =~" T, - ( T 1 -

To) 4~- exp ( -

lr2 4 da: t )

(1)

As usual in heat transfer phenomena the response time r is defined as

r = d 2/a

(2)

or just the time when at/d 2 .= 1. After time r the temperature increase on the insulated side of the slab equals 89% of the original temperature difference. To be applicable a thermometer should have a substrate with good thermal properties, which can easily be fixed on all kinds of experimental devices. Soldering generally gives a perfect thermal contact between the sensor and the sample, so that the best performance can be expected from metallic substrates. The first carbon thin film thermometers which we produced, were based on thin copper substrates covered with insulation layers to avoid electrical contact between the substrate and the carbon film. Several insulators have been applied like vacuum evaporated alumina, silicon-monoxide and glass. However, the results were often not satisfactory. Because of the relatively good thermal properties and insulating character, sintered alumina slabs (thickness 0.5 ram) were next chosen as substrates for these sensors. On one side of the alumina slabs carbon films (0.34 p,m) and copper contacts (0.5/.tm) were deposited

$ 0 3 . 0 0 © 1 984 Butterworth f:t Co. (Publishers) Ltd.

159

I" . . . .

."1

--'1

-____, Substrate

Carbon

Copper

Glass

Atz03

,.i--.---i.-

6 mm ~

Glass, I/J.m Cu, 0.5/.t.m C, 0.54 p.m I

AtzO3 substrate, 0.5 turn

Cr, o o2 m Cu, 0.5/J.m Fig. 1 Structure of the carbon thin film thermometer

and covered by glass films of 1/xm. The glass layers protect the carbon films and prevent the absorption of gases. On the backside of the alumina slabs 0.5/xm copper films were deposited. This allows soldering of the thermometers onto metallic components of test units. Fig. 1 shows schematically the final structure of these thermometers. All the deposited films were prepared at room temperature by electron beam evaporating in a conventional bell jar at a pressure of about 10-3 Pa. Each step of the deposition process was made through photo-etched copper masks of 0.15 m m thickness. The resistance varied between 1250 fI and 2500 II, even within one batch. Most of these sensors showed a resistance of more than 20 M N at 4.2 IL This latter value makes this type of thermometer unsuitable for cryogenic application. The thin film carbon thermometers got their desired electrical resistance by a final heat treatment at 150°C for 1 h in vacuum. The resistance of the thermometers was then about 250 fl at 300 K and about 2600 N at 4.2 IL The carbon film is a rectangle of 2 × 4 mm, on the short side for 1 m m overlapped by the copper contacts. The effective resistor is thus a square film of 2 × 2 m m (Fig. 1). Copper wires of 0.05 m m diameter were attached to each copper electrode with the aid of colloidal silver. This allowed for a four point resistance measurement. From transmission-electron-microscopy observations it was seen that the deposited carbon films were highly amorphous in character. For these observations a few films were deposited on glass substrates, so that they could be easily floated off. Annealing the carbon film reduces the electrical resistance, but its amorphous character did not vanish. This effect was also observed by other authors, eg K u p p e r m a n et al. 7 Hauser and PlateP explain the changes of the electrical properties by stating that amorphous carbon contains a mixture of graphite bonds and d i a m o n d bonds. The localized conduction states in amorphous carbon are situated in the graphite bonds. It was found by HauseP that during the

160

annealing process the film recrystallizes to a greater part in the graphite configuration. Hence, there will be more localized conduction states and a reduced electrical resistivity.

Method of response time measurement For use as a temperature probe the sensor will be soldered or glued onto the experimental components. The temperature variations have to pass the alumina substrate before they are registered by the thermal sensitive carbon layer. The thermal relaxation time of the alumina slab, as defined by (2), determines the response time of the thermometer. Due to lack of reliable data it is difficult to calculate the response time from the sensor dimensions and material properties. Furthermore, the four electrical leads, the conductive silver paint and the solder will influence the real sensor response time. Therefore, it will be determined from measurements. In first approximation the thermal behaviour of the sensor is comparable with the behaviour of an infinite slab of thickness d. One side of the slab (x = 0) is thermally insulated; on this side the carbon film is situated. The temperature variations are imposed on the other side (x = d), the so-called copper side of the thermometer. The influences of the carbon-, copperand glass film on the response time are neglected because these layers are very thin in comparison with the alumina substrate. When the infinite slab with temperature To undergoes at time t ---- 0 on x = d a temperature j u m p up to T~, the temperature distribution T(x, t) will be given by ~°

4

T ( x , t) = T1

-~

(Tt

To)

-

~~ '

(- 1)n 2n + 1

n=0

08/o4O6 1.0-

o

0.2

06--

f

]

~

~--'d-~l"

0.2

I

I

0.4

0.6

I

0.8

ID

¢1 Fig. 2 The non-dimensional temperature changes of two parallel planes of an infinite slab as function of the Fourier parameter a = at/d =, when a constant heat flux ¢ib0 is flowing into the slab at x = d. At x =- 0 the slab is thermally insulated

CRYOGENICS . MARCH 1 9 8 4

After a long time the temperature at x = 0 is approximately given by (1). From (2) it follows that v is is given by the time when the temperature ratio [T(0, t) -- To]/[T~ -- To] reaches a value of 0.89. Because it is physically very difficult to create a well-defined temperature jump at the copper side of the slab, this method is unsuitable for deriving the response time r. On the other hand it is possible to create a constant heat flux at the copper side of the thermometer. The electrical resistivity of copper is practically constant at low temperatures. So, a constant electrical current generates a constant heat dissipation and when the whole slab is placed in vacuum, the heat can only flow into the alumina substrate. Again considering an infinite slab, the temperature distribution T(x, t), when a constant heat flux q~o is flowing into the slab at x = d, is given bye°:

pcpd

2

2

+ -X-- [

6~

+

H2 n=l

(4)

exp ( - a n 2 rfl t/d 2) cos (n zr x/d) } The physical properties ~ O and Cp are considered to be constant. The Fourier parameter a is defined as a = at/d 2. Rewriting (4) for the temperatures at the carbon film- and copper side results in: X[T(O, t ) - To]

¢o d

(

1

= ot + / - 6

~

2 rt2

(-1) n n 2

n---1

exp ( - ot n 2 ~.2)}

(T--To)=

(5)

/

(carbon film side, insulated, x = 0), and

lim

tp--~ *o

(% {a tp/d2 - 1 1

aE

"8"

The final temperature T® will always prevail in the slab after absorption of an amount of heat E, independent of the manner of how the heat is supplied and assuming there are no heat losses. Thus on the other hand the amount of heat E (per unit area) is given by E =

(-1)n

Tr2

then at T(O, t) = T o the delay time is found. Let us now consider the case that the constant heat flux is only supplied during a limited period of time: tp (pulse time). The total absorbed heat is then E ---- 00. t p . The same amount of heat can be delivered for various pulse times.t v at appropriate flux levels dpo = E/tp. For a long time tp (7) is valid. In that case the temperature T= at the carbon side at the end of the pulse is given by

v P c----E---PdT A

(9)

To where A is the surface of the slab and V its volume. When equal energy E is absorbed at x = d during a short time tp, there will still exist a temperature gradient in the slab. Neglecting the heat losses, during the time tp the momentary value of T(0, t) is given by (5). After time tp the temperature x = 0 will rise until it reaches the final value as given by (8). This behaviour allows a second method for measuring the response of the thermometer. It is possible to vary experimentally the pulse time tp and heat flux ~b0 in such a manner that the total amount of absorbed heat is constant. During the heat pulse the temperature T(0, t) rises until the value T(0, tp) is reached at the end of the pulse. After the pulse the temperature at x = 0 will rise still further until it has reached the final temperature T , as given by (8); then the temperature profile in the sensor has leveled out completely. The ratio between T(0, tp) and T~ can be derived from (5) and (8) for various pulse times tp:

T(O' t p ) - TT° o - 1+ { - 61

rr 22

~

n2

rl=l

~od

= or+

~'2

=

exp ( - a n 2 rr2)}

exp ( - n 2 rr ap)}/0tp

~-

(6)

(copper side, constant heat flux, x = d). Calculated values of both temperatures are shown in Fig. 2. From this figure it can be seen that after a short time the temperature at the carbon side (measuring position) rises linearly in time and parallel to the temperature on the opposite side, but somewhat delayed by a time vd, that is given by rd: a Vd/d 2 = 1/6. Because the response time r is defined for a = 1 it follows that r = 6 ra. The delay time ra can be derived from the measured temperature response on a constant heat flux. Starting the flux at t = 0 and extrapolating the straight part of the measured curve

-d-)~ [ T ( O ' t ) - T ° ]

=Co(a-

CRYOGENICS . M A R C H 1 9 8 4

6-1)'

(7)

(10)

The right hand side of (10) depends only on Otp = a tp/d ' = tp/r and is a unique function of the response time v = d 2/a. Formula (10) has been plotted in Fig. 3. The ratio [T(0,/p) - - T o ] / [ T ~ - - To] can be derived from the temperature curve which is measured on the carbon side for various heat pulses, During the measurements the temperature increase should be small in order to keep the physical properties h, p and Cp sufficiently constant.

Characteristics of the carbon film thermometer The resistance of the carbon thin films was measured by a four wire potentiometric system. Excitation currents of 1 p,A and 10 p,A supplied by a constant current source were passed through the films. The potential difference across the films were measured by digital voltmeters. Two calibrated carbon glass and one germanium thermometer (Lake Shore,

161

% 1.0

1~)

I I

2 I

3 I

4 I

5 _

0.8

~P I ~8 0,6

0.4

-

d ~-- o.2

00

I

I

I

I

0.2

0.4

0,6

0.8

1.0

01p Fig. 3 Plot of the temperature ratio IT(0, tp -the Fourier parameter % as given in (10)

To]/[T

= --

TO] as function of

Model CGR-I-1000. GR-200A-1000) were used as temperature standards. All the thermometers were mounted on a copper block. Four stainless steel wires (diameter 0.2 mm) and three nylon spacers were used to keep the calibration block in its proper position inside a vacuum vessel. This vessel was surrounded with liquid helium of 4.2 K to minimize the heat input by radiation. The vessel was evacuated to about 5 • 10-4 Pa after which it has been cooled down by liquid helium. The potential differences across the various thermometers were scanned at normal and inverted polarities by a cryogenic multiplexer. Fig. 4 is a schematic view of the experimental set-up and Fig. 5 shows the calibration copper block as it is mounted before assembling the cryostat.

Fig. 5

thermometers

View onthecalibrationblockforthethinfilm

3000r

Vocuum 'DUmD tube R

,

=~~~Rodiation

2500

shield Stainless steel wire

~ 2000

o ¢)

1500

film

thermomeler

Vacuum

Liquid helium Fig. 4 Schematic view of the equipment for the calibration of the carbon thin film thermometer

1 62

IOO0 [

I

I

4

6

8

I

I

I0 12 Temperature,

I

I

14

16

CRYOGENICS

. MARCH

18

K Fig. 6 Resistance versus temperature for a few carbon thin film thermometers

1984

I° t°l

Fig. 6 shows plots of the resistance versus temperature for a few carbon thin film thermometers. The resistance temperature curves of the thermometers can be correlated by the logarithmic function In R = A0 + A, In T + A 2 (In T)2

voltmeter

(11)

The sensitivity S, defined as S = -T/R dR/dT, of the carbon films is plotted in Fig. 7. The thermometers were exposed to more than 30 thermal cycles from helium temperature up to about 15 K and a few cycles up to room temperature. No noticeable resistance change appeared: the reproducibility is better than 0.1%. Influences of liquid and gaseous helium, air and moisture on the film resistance have not been noticed.

Carbon thin film thermometer amplifier i

Response time One of our carbon film thermometers was mounted inside a vacuum vessel, which was surrounded by liquid helium of 4.2 K, for determining its response time. The thin copper film on the backside of the alumina substrate was used as heater. The current leads of the heater were stripped monofilament NbTi wires (diameter 0.2 mm), the potential leads were two constantan wires (diameter 0.04 mm) with synthetic fibre insulation. The leads of the heater were soldered on the copper film with indium. The wires of the carbon film were attached to the copper contacts with colloidal silver. Constant currents of 10 #A and 100 pA through the carbon film were supplied by a battery. The signals across the film were amplified by a dc as well as an ac amplifier and recorded on a transient recorder with sample time of 5 #s. A pulse generator could supply heat pulses up to 400 W with pulse times in the range from 0.1 ms to 9 s. Fig. 8 shows the schematic diagram of the measuring circuit and the data acquisition system. As mentioned the thermal relaxation time r can be derived from the measured temperature response to a heat pulse. During a series of measurements the total heat input was kept constant for various pulse durations, starting at 0.1 ms and increasing in steps of

Transient recorder

1'

I1 generator Flesponse time measuring circuit and data acquisition system

Fig. 8

3E

~ 0.2 E

'~ O.i

0 I

I

I

I

I

I

I

T 0.64 .> > tO

0.62

o (3

I" 060

.= 0.58

j 0

0.56

~urrent

pulse

i

I

i

I

I

I

0.2

0.4

0.6

0.8

I.O

1.2

I

1.4

t , ms Fig. 9 Temperature response of a carbon thin film thermometer to a heat pulse. The heating current causing the pulse was monitored across a 0.595 El resistor. The resistance of the copper film heater was 0.011 El

0.54

/x

052

7 1

2

,

,

I

,

,~,1

5

J

I0

I

20

,

J

I,,,

50

Temperature, K Fig. 7 The sensitivity S = -dOn R)/d(In 7) versus temperature for a few thin film thermometers

CRYOGENICS . M A R C H 1 9 8 4

IOO

0.1 ms to a maximum time of 1 ms. The behaviour of the sensor to a 0.5 ms pulse is shown in Fig. 9. Also the current pulse is shown. Fig. 10 shows a few records of temperature responses on different heat pulses of constant time but different power. Extrapolation of these curves gives a delay time r d of about 70 #s. Following the theory of the thermal delay time (r = 6 rd) the response time is 0.42 ms.

163

To,(O, tp)

r(o,t°) Current pulse

0.2

.

.

.

.

Too

,¢

I--

Temperature responses

._= o

g E

I

TO

B

"6

I I I

o

o=

fO

tp Time

Fig. 1 1 The temperatures of the thin film thermometer at the heater side [7(d, t)] and carbon side [7(0, t)] during and after a heat pulse starting at t = t o and ending at t = tp

1.0 O

0.1

,

0.2 f, ms

,

O.3

I

T* = 7(0, t . L

~..--e--'-'-

,

,

0.8

Fig. 10

The determination of the delay time from different temperature responses to different current pulses at constant pulse time .'

The second method of determining the response time was based on measuring the temperature ratio IT(0, tp) - - T o l / I T = - - T.i. The temperature T(0,/p) of the carbon film is reached at the end of the pulse and T= is the constant final temperature of the thermally insulated thermometer. During the experiment small heat losses to the environment causes a temperature decrease and thus T® will not be reached, as can be seen from Fig. 9. In order to estimate the temperature T®, experiments with small values of the heat flux and large pulse times (> 5 ms) were carded out. During the pulses there exists a negligible temperature gradient in the slab. The results showed that the temperature decrease at the end of the pulse started after an additional 70/xs, which is identical to the reported delay time rd. This time is necessary to build up the temperature gradient belonging to the losses and from this it can be concluded that the heat leaked from the copper side and not from the carbon side. This conclusion is confirmed by the fact that the relatively thick superconducting wires were connected to this copper side. A value of T** might be derived by backwards extrapolation of the temperature curve after the pulse to the time tp. This temperature Tax(0, tp) (Fig. 11) will be higher than the sensor average temperature, because during the losses the carbon side temperature T(0, t) is higher than the copper side temperature T(d, t). On the other hand the maximum measured temperature 7(0, te) will be lower than the theoretical value of T~ due to the fact that the heat losses occur immediately, when the temperature of the sensor rises. From this it follows that T(0, te) < T < Tax(0, tp). When T . is replaced by these boundaries in the temperature ratio T f [(0, tp) - - T o I / I T , . - - Tel an interval estimation of the thermal response time is possible. From Fig. 12 it can be seen that r is lying between 0.4 ms and 0.6 ms, which confirms the results

164

0.6

t_=

20 0.4 d ~ 0.2 I 0.2

I I

0.4 0.6 Pulsetime fp, ms

1 0.8

Fig. 1 2 Plot of the measurement results of the temperature ratios [7(0, tp) - - To]/[Tax(O,tp) - - TO] and [7(0, tp) - - 7"01/[7"10, re) - - T0] versus the pulse time t D. The thermal relaxation time is defined by the temperature ratio of 5 / 6

derived from the delay time (r = 6 rd = 0.42 ms). These results show that the response time of the thin film carbon thermometer is indeed lower than 1 ms.

Conclusion A practical multipurpose cryogenic temperature sensor has been developed. It is based on a thin carbon layer deposited onto a relatively thick, but mechanically strong and thermally well conducting, alumina substrate. It has a sensitivity of about 300 f~ K-L At cryogenic temperatures the film resistance is a smooth function of temperature and can be expressed by a doubly logarithmic correlation. The sensor has a thermal response time better than 1 ms. The carbon film was coated with a thin glass layer; influences of gases, liquid helium and moisture have not been noticed on the film resistance. The characteristics of the thin carbon film thermometer can even be improved when smaller dimensions are chosen or when monocrystalline sapphire is used as substrate instead of sintered alumina.

CRYOGENICS.

MARCH1984