Piezo-resistive pressure sensor applicable for in situ pressure measurement at cryogenic temperatures under magnetic fields

Piezo-resistive pressure sensor applicable for in situ pressure measurement at cryogenic temperatures under magnetic fields K. Nara, M. Okaji and H. Kato National Research Laboratory of Metrology, 1-4, Umezono 1-chome, Tsukuba, Ibaraki 305, Japan

Received 10 June 1992; revised 27 August 1992 A commercial piezo-resistive pressure sensor, PD116S, is reported to be suitable for use in a cryogenic environment. The temperature dependence of its pressure sensitivity, its stability after thermal cycling and its performance under magnetic fields of up to 8 T are studied to assess its applicability. Its pressure sensitivity changes by not more than 5% from room temperatures down to 6 K. Its characteristics are also found to stabilize after several thermal cycles between room temperature and liquid nitrogen temperature. The effect of the magnetic field on pressure sensitivity does not exceed 2% under a magnetic field of up to 8 T between 6 and 40 K.

Keywords: pressure sensors; magnetic fields; piezo-resistive sensors

The pressure of liquefied gas is one of the most important parameters to determine when operating cryogenic apparatus such as cryostats, refrigerators and flow meters. As there are few reliable and compact pressure sensors which function at cryogenic temperatures, the pressure o f cryogenic fluids is often measured using a pressure measurement system held at room temperatures via a pressure sensing capillary. This arrangement has undesirable consequences. Firstly, the heat input along the capillary from the room temperature section can disturb the operation of the system. Secondly, the response of the pressure measurement system can be poor if the capillary is too thin. Thirdly, the volume within the capillary can also introduce error which cannot easily be corrected when one is monitoring a gas pressure which is varying, such as that within a cryocooler. To tackle these problems, a compact and reliable pressure sensor applicable to cryogenic temperatures is needed. To date, several in situ pressure sensors have been developed for application in a cryogenic environment. Most of these are based on a Be-Cu diaphragm and a capacitive measurement system to detect deflection of the diaphragm ~-3. As such systems consist of metal bodies and metal electrodes, with adhesives and insulators between them, they have been considered to be too complicated for practical use. Recently, integrated piezo-resistive pressure sensors have become commercially available for room temperature use. These sensors convert pressure to a change in resistance, which is easy to measure. They are

small and their construction, involving silicon piezoresistive strain sensors on a silicon diaphragm, is also desirable from the viewpoint of avoiding large stresses due to differences in thermal contraction. In this report, the low temperature characteristics of a commercial piezo-resistive pressure sensor are measured and an assessment of its applicability for operation in a cryogenic environment is made. As the superconducting magnet is one of the most important applications of cryogenic systems, this report also includes the study of the sensor under magnetic fields.

Preparation of sensors The piezo-resistive pressure sensor chosen for the study is PD116S made by Toyoda Machine Works Ltd (Aichi, Japan), which is the same model as that used in an earlier report 4. As shown in Figure 1, it has a ceramic gas inlet at its base. As the end of the inlet is gold plated, any metallic tube can be easily soldered to the sensor. The sensing elements, a silicon diaphragm and four silicon strain gauges formed on it, are packaged in a metal can, with nitrogen gas at ---1 atm sealed in it. Thus, the basic design of the sensor is similar to that of an absolute pressure sensor, with the exception that the reference pressure is 1 atm rather than null. As the reference pressure changes with variation in temperature, a vent hole is made on one of the five sensors tested to clarify the effect of the sealed gas. In the case of this special sensor, the sensor operates as a gauge-type pressure sensor. The original specifications

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Cryogenics 1993 Vol 33, No 5

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Piezo-resistive pressure sensor: K. Nara

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of the sensor and the sensor with a vent hole are listed in Table 1.

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The experimental arrangement is shown in Figure 2. Three sensors, A, B and C, are thermally anchored to a temperature-stabilized copper base in a vacuum can, which is cooled down by cold helium gas flowing outside the vacuum can. The measurement procedure is the same as that devised to study thermometers under magnetic fields at cryogenic temperatures 5. 4He gas is used as the working gas throughout the experiment. A helium leak detector constantly monitors the vacuum to detect possible leakage of helium through the sensors. Leakage is not observed as long as the pressure is kept below the upper limit of 3 MPa for the entire temperature range. The measuring system is shown in Figure 3 along with a list of the apparatus in Table 2. An excitation current of 0.1 mA is applied throughout the experiment. As the pressure sensitivity of the sensor depends on the resistance of the strain gauges in the constant current mode, the voltage drop along the current (referred to as the series voltage, hereafter) is measured in addition to the output voltage of the sensor (referred to as the differential voltage, hereafter). Both voltages are converted to resistance and are called the series resistance and differential resistance, respectively.

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In the present pressure sensors, four p-type piezoresistive strain gauges comprising a resistance bridge are formed on a silicon diaphragm. The resistance change

where B and o~are the magnetic field strength and gauge factor, respectively. As the temperature dependences of R(T, B) and or(T, B) depend on the concentration of the carrier np, np has been used as a design parameter to obtain a small temperature dependence of the pressure sensitivity, by cancelling the temperature dependence of the resistance, R(T, B), with that of the gauge factor, tx(T, B) 6. The four strain gauges used in PD116S are heavily doped with boron to give np as high as 1 0 21 c m - 3 (reference 7). In the case of heavily doped silicon, the temperature dependence of the resistance is expected to behave as in a metallic system, due to impurity conduction at low temperatures 8'9. The temperature dependence of the series resistance averaged for three sensors is shown in Figure 4. It decreases monotonously when the sensors are cooled down from room temperature to low temperature. The power consumption determined by the series resistance

Table 1

Table 2

Temperature dependence of characteristics

Original specifications and modification of sensor

Pressure range (full scale) Over-pressure tolerance Vent hole

3 MPa 1 5 0 % of full scale Yes: sensor C No: sensors A, B, D and E

542 Cryogenics1993 Vol 33, No 5

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The pressure sensitivity of the sensors is measured at several temperatures from 5.9 to 256 K. To treat the results quantitatively, the change in the differential resistance AR is fit by the following function of pressure P (2)

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The parameters A(T) and B(T) will, hereafter, be called the sensitivity and non-linearity of the sensor, respectively. The temperature dependence of the sensitivity of the sensors normalized at 256 K is shown in Figure 7. The change in the sensitivity is a smooth function of temperature and small enough to be easily corrected. The variation of the temperature dependence among the sensors is smaller than 1%. The temperature dependence of the present sensor is smaller than that of 100% recently reported for a pressure sensor developed for cryogenic use m. The small temperature dependence of the present sensor makes it suitable for measuring pressure changes accompanied by temperature changes, such as pressure measurement inside a cryocooler. The non-linearity of the sensor at the limit of 3 MPa is shown in Figure 8. The non-linearity is also a smooth

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function of temperature and smaller than 4 %. The origin of the increase in sensitivity below room temperature and the additional increase observed below 40 K is not clearly known at present. The smooth increase from room temperature down to 40 K might be explained by the deformation of the diaphragm due to relative thermal contraction between the silicon diaphragm and its base material, known as the balloon effect n. The increase in non-linearity also supports the origin proposed above. The change in the gauge factor might be another possible cause. The additional increase below 40 K is clearly caused by the change in the gauge factor, as the thermal expansion coefficient of the materials comprising the sensing part is close to null. Therefore, the change in sensitivity might be explained by degeneration of carriers at low temperatures. All these results support that idea that the present pressure sensor is a suitable candidate for an in situ pressure sensor at cryogenic temperatures.

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Performance under magnetic fields There are many instances where cryogenic instruments have to be used under magnetic fields, as in superconducting magnet systems. When a sensor is used under magnetic fields, for the sensor to be reliable the effect

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Cryogenics 1 9 9 3 Vol 33, No 5

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of the magnetic field on its operation must be small and predictable. In addition, the sensor must not disturb the magnetic field profile around it. The present sensor clearly satisfies the former condition. The effect of magnetic fields is measured at several temperatures under magnetic fields up to 8 T. The results of operation at 40.75 K under magnetic fields are shown in Figure 10 as a typical example. The effect is as small as 1%, as is clearly seen from the figure.

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Qualitatively, the effects of the magnetic fields can be classified in two ways. The first effect is the Hall effect, which is linear with respect to magnetic field. This effect is observed in the change of the differential resistance at null pressure under magnetic fields, as shown in Figure 11. It is caused by the arrangement of the voltage terminals for the strain gauges. A slight change in this arrangement will be enough to reduce the effect, which is currently smaller than 1% of the full range. The second effect of the magnetic field is the direct effect on the two parameters, R(T, B) and cKT, B), in Equation (1). The origins of the change can be divided into the increase in the series resistance (magnetoresistance) and the change in the gauge factor c~. The sensitivity, as a result, changes as shown in Figure 12. Its increment under a magnetic field of 8 T is smaller than 1.5% between 6 and 41 K. As shown in Figure 13, the magnetoresistance increases with magnetic field and decreases with temperature. As the increment in sensitivity and magnetoresistance is of the same order as shown in Figure 12, the change in sensitivity can be explained mainly by the magnetoresistance. The effect of the magnetic fields on the gauge factor gives rise to an additional effect. As the increase in the pressure sensitivity is larger than magnetoresistance above 20 K, and smaller below 20 K, magnetic field increases the gauge

12 T e m p e r a t u r e d e p e n d e n c e of pressure s e n s i t i v i t y under m a g n e t i c field of 8 T b e t w e e n 6 and 41 K for sensors A, B and C. The data are normalized b y t h e s e n s i t i v i t y u n d e r null m a g n e t i c field. The m a g n e t o r e s i s t a n c e of t h e averaged series resistance for t h e three sensors is also s h o w n in t h e figure

factor above 20 K and decreases it below 20 K. The overall effect of magnetic field is smaller than 1.5% of the null field value. The discussion above clearly supports the applicability of the sensor for use under magnetic fields. However, the sensor is very likely to disturb the. field profile as its metal can is made of iron. As the material is chosen so as to seal the sensor using Kovar, it might not be easy to change it 7. Therefore, at present it is advisable to use the sensor primarily in a null magnetic field environment. It can be used under magnetic fields with a small correction, provided that the disturbance caused to the magnetic field by the pressure sensor is not a serious problem. Conclusions

The results summarized in Table 3 support the prospect of using the present sensors as in situ pressure sensors

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Cryogenics 1993 Vol 33, No 5 545

Piezo-resistive pressure sensor: K. Nara e t al. Table 3

sensor, such as a long t e r m p r e s s u r e c y c l i n g test, w o u l d be n e c e s s a r y .

Summary of results

Change in pressure sensitivity (from room temperature to 6 K) Averaged temperature coefficient of span Change in zero value (with vent hole) (from room temperature to 6 K) Averaged temperature coefficient of zero Stability against thermal cycling Sensitivity (initial) (after 10 cycles) Zero (initial) (after 10 cycles) Change under magnetic fields Sensitivity (at 8 T) Zero (at 8 T)

<5% + 0.02% K - 1

< 1% of span 0.005% of span K 0.1% 0.03% 0.1% of span 0.03% of span 1.5% 1% of span

at c r y o g e n i c t e m p e r a t u r e s . Its v e r y small d e p e n d e n c e on t e m p e r a t u r e is e s p e c i a l l y d e s i r a b l e for a p p l i c a t i o n to the study o f p r e s s u r e c h a n g e in c r y o c o o l e r s , as the t e m p e r a t u r e variation f o l l o w s p r e s s u r e v a r i a t i o n in this case. To assess its a p p l i c a b i l i t y , a further study on the

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Acknowledgements The authors gratefully a c k n o w l e d g e helpful discussions with S. Sakurai and T. N a g a t a o f T o y o d a M a c h i n e Works.

References l Straty, G.C. and Adams, E.D. Rev Sci [nstrum (1969) 40 1393 2 Helvensteijn, B.P.M. and VanSciver, S.W. Rev Sci lnstrum (1990) 61 1127 3 Nara, K., Rusby, R.L. and Head, D.I. Cryogenics (1990) 30 952 4 Nara, K., Okaji, M. and Kato, H. Technical Digest of the 11th Sensor Symposium Institute of Electrical Engineers of Japan, Tokyo, Japan (1992) 139 5 Nara, K., Kato, H. and Okaji, M. Cryogenics (1991) 31 16 6 Shimada, S., Nishihara, M., Yamada, K., Tanabe, M. et aI. Trans Soc lnstrum Control Eng (Jpn) (1984) 20 74 (in Japanese) 7 Sakurai, S. Toyoda Machine Works, Japan, private communication (1991) 8 Morin, F.J. and Maita, J.P. Phys Rev (1954) 96 28 9 Yamanouchi, C., Mizuguchi, K. and Sasaki, W. J Phys Soc Jpn (1967) 22 859 10 Juanarena, D.B. and Rao, M.G. Cryogenics (1992) 32 39 11 Tufte, O.N., Chapman, P.W. and Long, D. JAppl Phys (1962) 33 3322