Thermal time constants of germanium thermometers at liquid helium temperatures

Thermal time constants of germanium thermometers at liquid helium temperatures

90 p. is made of stainless steel. The cylinder is electrowelded along a generator. The spherical end faces are made of the same material and welded to...

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90 p. is made of stainless steel. The cylinder is electrowelded along a generator. The spherical end faces are made of the same material and welded to the cylinder with an argon arc welder. The vessel is 60 mm in diameter and 250 m m long. The lower part of the vessel is connected by tube 3 to the 10 I. capacity liquid hydrogen tank. Evaporation tube 2 connects to the upper part of



Figure 2. Arrangement of operating part of the target

Thermal time constants of germanium thermometers at liquid helium temperatures C. E. S A R V E R and J. S. B L A K E M O R E ~

R E S ] S I A N C E thermometers are widely used for temperature measurement in the cryogenic range, and sensors employing the temperature-dependence of resistance in single crystal germanium have found increasing acceptance in recent years as a result of their stability and reproducibility. 1-3 When measurements must be made as a function of time during a short interval, it can be important to know the thermal response time, or time constant, of the sensor. This is certainly the case for a thermometer used in a flowing cryogenic fluid system (whether liquid or gaseous), or in applications involving level sensors, bubble chambers, etc. We have made measurement of the change in resistance with time when the thermal environment of a germanium thermometer was abruptly changed. For all of our measurements, the change with time was essentially exponential, thus the quantity we call 'thermal time constant' or 'response time' was the time necessary for the temperature differential to decrease to (I/e) = 0.37 of its "~ Physics Department, Florida Atlantic University, Boca Raton, Florida, 33432, U.S.A. Received 10 September 1967. CRYOGENICS • OCTOBER 1967

the vessel and makes it possible to empty and refill the target quickly to measure the background. The vessel is contained in a vacuum jacket made of 6 m m thick sheet stainless steel. 60 m m diameter circular windows are cut in the end walls along the axis of the primary beam and 70 x 280 mm 2 windows in the side walls to let out the slow secondary particles. The windows are covered with 90 ta thick stainless steel foil soldered to the jacket with tin solder. A cylindrical shield of 30 la thick aluminium foil is placed between vessel 1 and the vacuum jacket to reduce the heat influx. The position of the hydrogen vessel and the thermal shield inside the vacuum jacket is fixed by the needles 4. Vessel 1 was tested to 4 arm pressure before assembly. The vacuum jacket of the target is connected by tube 5 to tube 7 of the vacuum jacket of the reservoir. The connection is demountable and is sealed by a rubber sleeve which can be clearly seen in Figure 1. The feed tube 3 and evaporation tube 2 are soldered to the hydrogen vessel with tin solder. This connection is made at the joint of flange 8, so that the hydrogen vessel can be rapidly disconnected or changed if necessary. The target has been tested. After 2 h of operation, a total of 0.9 1./h of liquid hydrogen is evaporated from the target and reservoir vessel.

initial value. Some measurements were made with the sensor immersed in liquid helium at 4,2" K, and others with the thermometer suspended in helium vapour at atmospheric pressure. Most observations used sensors for which the germanium element was contained in a hermetically sealed case (Figure l), so that the time constant would be controlled by the parallel conduction paths along the metallic leads and through the helium transfer gas within the case. A few measurements used a thermometer with a deliberately perforated case, and the results were surprisingly similar to those for sealed sensors. The thermometers used in our study were commercially produced, 4 constructed in a manner generally similar to those previously described in the literature 1,5 except for a slight reduction in overall size, and the omission of the Teflon liner used in some early thermometers. Figure I shows how the bridge-shaped single crystal germanium element is supported within a copper case, with a hermetic seal at one end carrying the four electrical connections. The overall dimensions of the case for each thermometer were 0.85 cm long by 0.32 cm diameter; the complete sensor had a mass of 0.31 gm and a thermal capacity at 4-2 ° K of 4 x 10-s J/deg. The single crystal

Figure 1. Cutaway view showing the bridge-shaped germanium bar supported within the thermometer case 299

germanium bar suspended inside the case was approximately 0.55 cm long, with a cross-section 0-04 x 0.04 cm z, so that the mass of germanium was only 0.005 g for a thermal capacity at 4.2 ° K of 2 x 10-7 J/deg. Response time measurements were made by a simple method, using the arrangement illustrated schematically in Figure 2. Current was admitted to the thermometer from its end contacts this current did not change when the sensor temperature was modulated because the external circuit impedance was much larger than the end-to-end resistance of the sensor. The potential drop



' I I





Figure 2. A simplified s c h e m a t i c of t h e circuit u s e d for t h e observation of transient response to t h e r m a l change

between the probe contacts to the sensor was monitored with a Hewlett-Packard Type 419A infinite impedance voltmeter, and with a Tektronix Type 561 oscilloscope using a Type 2A61 differential amplifier input. Changes in the thermal environment were produced by passing current on a manually controlled intermittent basis through a multi-turn resistance-wire heater wrapped around the sensor case and cemented in place with G.E. 7031 cement. For the first series of measurements, with No. 218(a), a rather bulky heater was used, and it was realized that the thermal mass of this probably slowed down the sensor response. In all subsequent experiments, a single layer configuration was used (of negligible thermal capacity), care being taken that there was no inductive transfer from the heater circuit to the sample output. As noted previously, measurements were made either with the thermometer immersed in liquid helium or in T A B L E 1. T H E R M A L


Sample Thermometer No.

Series load resistor RL (~)

helium vapour. We found that when the sensor was suspended 5 cm above the liquid level in a helium storage dewar that the temperature (as determined from the sensor resistance) was inappreciably different from that of the liquid itself. Higher temperature environments could be provided by suspending the thermometer at a considerable height above the liquid level. The results obtained at 4.2 ° K are summarized in Table 1. By analysis of photographically recorded oscilloscope traces, it was established that the fall in resistance (rise in temperature) occurring when the heater was activated, and the subsequent increase of resistance (fall in temperature) when heater power was terminated, were essentially exponential. For the range of modulation employed, (AR/Rs) was never larger than 0.07, (which corresponds with a temperature change of less than 0.2 deg at 4.2 ° K); thus the time constants of 'resistance' and of 'temperature' are identical. Figures 3 and 4 show typical oscilloscope traces, from which time constants can readily be determined. The response time which is most meaningful for the internal structure of the thermometer is that for operation immersed in the liquid helium. This we may take from the appropriate column in Table 1 as averaging some 0.028 + 0.005 s for the group of thermometers tested. The curves of temperature rise and fall were not always identical in details of shape, but there was not a significant difference of time constant between the two situations. In studying the curve of Figure 3, a typical temperature decay curve for an immersed sensor, the droop in the trace following the rapid rise can be ignored; it is a consequence of the finite low-frequency limit in the a.c. coupled differential input system. Similarly, the high frequency component of small amplitude reflects the electronic imperfections of the system. Since a multi-layer heater was used for the first tests on No. 218, a fresh set of observations was made using a single layer heater of much smaller thermal capacity. This did not make a major change in measured time constant under immersion conditions, (though a much more significant reduction was seen when tested in helium vapour, to be discussed next). Rather to our surprise, the response time of sensor No. 651 (with a perforated can to permit direct liquid immersion of the germanium element) was no shorter than for hermetically sealed units, at any rate by the present method of measurement. Our method is probably

Tested while immersed in liquid helium

/ (A)

resistance between probes R~ (~)

of Resistance (AR/Rs)

Time constant ~" (s)




A T 4.2 ° K

Tested while suspended in helium vapour Modulation

of resistance (AR/Rs)

Time constant

T (s)

218 la)

1.00 × 10s

1.00 x 10-5

1 300

0.002 to 0,01


0.01 to 0.07


218 (b)

1.00 x 104

1.00 x 10-5

1 294

0.002 to 0.02


0.005 to 0.02



1.00 x 104

1.00 x 10 -5

1 075

0.01 to 0.03


0.005 to 0.03



1.00 x 108

1.00 x 10 -4


0.002 to 0.01


0.005 to 0.03


651 (e)

1.00 x 10~

1.00 x 10 -5


0.01 to 0.07


0.005 to 0.02


(a) First series of measurements with this unit, using multi-layer heater. (b) Second series of measurements with the same unit, using single-layer heater. (c) Unit with perforated copper can.





Figure 3. Increase of resistance (decrease of temperature) with time for sample No. 218 immersed in liquid helium at 4.2 ° K when heater power is terminated. Bias conditions as in first line of Table 1. Vertical scale is 20 I~V per major division. Horizontal sweep is 0.1 s per major division. Time constant = 0.035 s

not a fair one in the circumstances, since in order to modulate the germanium resistance for No. 651 in the liquid, it was necessary to supply enough heater power to produce local boiling. It would be more proper to test such a unit by exposing it to a step-function heat wave in pressurized liquid so that no boiling would occur. When a sensor is suspended above the surface of liquid helium, in helium vapour at 4.2 ° K, the thermal coupling between the sensor and the cryogenic fluid is much weaker. In consequence, we found for our own arrangement that a temperature rise AT requiring heater power AP for an immersed sensor required only about 0.02 AP for the same sensor suspended in the cold vapour. As exemplified by Figure 4, the time response curves for sensors suspended in helium vapour were accurately exponential in form. With the sensor and heater suspended above the liquid, one is measuring the time constant of the combined thermal masses with respect to the environment. This probably has little to do with the internal heat conduction paths, but a lot to do with the total 'effective system' thermal mass. Such a view is borne out by the 25 per cent reduction in time constant for No. 218 when most of its heater was stripped off. The average of the response times reported in the final column of Table 1 is some 0.17 + 0.03 s, and it seems reasonable to suppose that ~




i/? j

~ O'4

Figure 4. Increase of resistance (decrease of temperature) with time as heater power is terminated to thermometer No. 659while suspended in helium vapour at 4.2 :~K. Vertical scale is 50 I~V per major division. Horizontal sweep is 0.1 s per major division. Time constant = 0.13(5) s

appreciable shorter time constants might have been observed had we been able to divorce the thermal capacity of the support system completely from the sensor. As expected, the response time of No. 651 with a perforated case was no shorter in helium vapour than for hermetically sealed units under the same conditions (since the thermal conduction through an 'ideal' gas is independent of pressure provided that this is large enough to make the molecular mean free path smaller than the dimensions of the system). Thus heat transport through helium gas to the element is as efficient with a few tort pressure of transfer gas as it is with full atmospheric pressure. Moreover, the heat conduction path along the platinum supporting leads is probably several times more efficient than that through the helium gas at any pressure. The time constant as measured for a sensor suspended in helium vapour increases with increasing temperature, a result entirely to be expected from the rapid increase in thermal capacity. Figure 5 illustrates the typical manner in which the effective response time increases with temperature, a result which should be interpreted qualitatively rather than quantitatively as to what might be expected for a different degree of coupling between the sensor itself and its support structure. Thanks are due to Mr. C. S. Monroe for his assistance with some of the measurements, and to Mr. T. H. Herder of CryoCal Inc. for his cooperation in making sealed and perforated sensors available to us. This research has been supported by the U.S. Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under AFOSR Grant number AF/AFOSR/1259/67.








6 1 Temperature


2 (°K)




Figure 5. Temperature dependence of response time for thermometer No. 259, when suspended in helium vapour at 1 atm pressure at the various temperatures CRYOGENICS

• O C T O B E R 1967

1. KUNZLER, J. E., GEBALLE, T. H., and HULL, G. W. Rev. sci. lnstrum. 28, 96 0957) 2. LINDENFELD,P. Rev. sci. Instrum. 32, 9 (1961) 3. CATALAND, G . , and PLUMB, H. H. J. Res. nat. Bur. Stand. A70, 243 (1966) 4. Prepared for us through the courtesy of Mr. T. H. Herder of CryoCal, Inc., of Riviera Beach, Florida 5. BLAKEMORE, J. S., SCHULTZ, J. W., a n d MYERS, J. G . Rev. sci. lnstrum. 33, 545 (1962) 30t