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Hall sensor applicable to cryogenic temperatures for magnetic fields up to 25 T
Hall sensor applicable to cryogenic temperatures for magnetic fields up to 25 T A. Sawada, S. Sakatsume*, T. Goto t, S. Nakamura t, H. Matsui t, R. Settai t, Y. OhtanP, K. Watanabe* and A. HoshP Department of Physics, Tohoku University, Sendal 980-77, Japan *Cryogenics Center, Tohoku University, Sendai 980-77, Japan tResearch Institute for Scientific Measurement, Tohoku University, Sendai 980-77, Japan *Institute for Materials Research, Tohoku University, Sendal 980-77, Japan Received 23 March 1994; revised 18 April 1994 An investigation was carried out on commercial Hall sensors used to measure the magnetic field of a superconducting magnet. Surprisingly, one of the GaAs Hall sensors, THS-119A, did not show Shubnikov-de Haas oscillations under high field conditions. This sensor, which is available as an electrical component for commercial circuits, was suitable for measuring magnetic fields up to 25 T at temperatures from 1.5 to 300 K. Keywords: Hall sensors; GaAs; Shubnikov-de Haas oscillation
In experiments for measuring various physical quantities as a function of applied magnetic field, the determination of the magnetic field strength is an important task. The magnetic field is proportional to the current at the superconducting magnet. But, because the field responds to the current with a delay time L/R, where L and R are the self-inductance of the magnet and the shunt resistor, respectively, the magnetic field is not proportional to the external current. The field strength is independent of the current in the persistent mode. Consequently it is necessary to measure the field profile of the magnet. One precise way to measure the magnetic field is using NMR. But NMR equipment is generally complicated and the field strength able to be measured using one set of NMR equipment is limited. One practical method used is to measure the magnetoresistance of a pure thin copper wire wound in a non-inductive form. However, this method is rather poor in terms of sensitivity and reproducibility. Furthermore, this set-up is liable to break very easily due to the use of a thin wire. Another method involves using a Hall sensor having adequate characteristics, which has been calibrated by means of a previously known magnetic field. Taking into account sensitivity, reproducibility, easy handling, and other factors relevant to sensors, it is quite effective to use a Hall sensor to measure the strength of a magnetic field 1-9. In this paper, the characteristics of several pieces of commercial Hall sensors are described. Their adequacy as magnetic field measuring sensors is also discussed.
0011-2275/94/110953-04 1994Butterworth-HeinemannLtd
©
M e a s u r e m e n t s and results The measurement of the Hall effect was conducted at 300, 77, 4.2 and 1.5 K under a magnetic field of up to 25 T generated by a hybrid magnet composed of a superconducting and a Bitter magnet. The magnetic field was calibrated by the induction method to within ___0.3%1°. The specimens with which the measurements were made are three types of Hall sensors, namely GaAs 1 (Matsushita OH002-2HR, ion implantation type, Matsushita Electronics Corp, Kyoto, Japan), GaAs 2 (Toshiba THS-119A, ion implantation type, Toshiba Co., Tokyo, Japan) and InAs (F.W. Bell BHT921, F.W. Bell, Inc., Orlando, FL, USA). These sensors are commercially available. The GaAs sensors are used as an electrical component in the circuits of a brushless motor, a floppy disk, etc., whereas the InAs one is used as a cryogenic sensor for a superconducting magnet. GaAs 1 had been found to be useful in magnetic fields up to 6.8 T at 4.2 K 5. The results of the observations at 4.2 K are shown in Figures 1-3. In each figure, part a shows the observed values of the Hall voltage. With the GaAs sensors, the measurements using the various sensors of the same type were conducted simultaneously. However since no remarkable difference was noticed among the individual sensors, just typical results are presented in the figure. The control currents supplied to the sensors are 0.5 mA with GaAs and 10 mA with InAs, respectively. The magnetic field intervals of the measuring points are 7 - 1 0 mT. The sensitivity estimated from the observed values of Hall voltage is 0.1266VT--lmA -~ with GaAs 1, 0.2336 V T-~mA-~ with GaAs 2 and 81.2/~V T-~mA-I with
Cryogenics 1994 Volume 34, Number 11 95:!
Hall sensors for cryogenic temperatures: A. Sawada et al.
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Figure 1 Hall effect of GaAs 1. The control current supplied to the sensor is 0.5 mA. (a) Hall voltage; (b) deviation from linearity
Figure 2 Hall effect of GaAs 2. The control current supplied to the sensor is 0.5 mA. (a) Hall voltage; (b) deviation from linearity
InAs, respectively. The GaAs sensors are roughly 10 3 times higher in sensitivity than InAs. The deviation from linear dependence of the Hall voltage is illustrated in Figures 13 parts b. The deviation of GaAs 1, GaAs 2 and InAs is less than ---5, ___10 and ___2.0%, respectively. It is notable that the GaAs sensors are still tending to increase even at 25 T. It is possible to explain these tendencies in terms of the heterogeneous phase of the carrier6. The characteristics which are generally taken into account for Hall sensors include linearity, sensitivity, offset voltage, temperature coefficient, input resistance and superposition of Shubnikov-de Haas ( S - d H ) oscillations. The most important of these is the problem of superposition of S - d H oscillations on the Hall voltage. The period of the S - d H oscillations is proportional to the inverse of the magnetic field and changes with the direction of the magnetic field, and the amplitude of the oscillation depends on the temperature. Therefore, it is very difficult to transform the Hall voltage value into the magnetic field value exactly. Consequently, a sensor with no S - d H oscillations is preferable. The results of the InAs clearly indicate S-dH oscillations; the data for GaAs 1 meander a little bit; and we cannot see the oscillations from the GaAs 2 results. As the mobility /x of the GaAs sensors is 5000 cm 2 V-~s-1, we get /.~B~I at 2 T, where B is the magnetic field. Because a magnetic field higher than 2 T is used as the high field for these sensors, S-dH oscillations
would usually be observed. However this is not the case for the GaAs 2. We assume that the carrier concentration of the GaAs 2 is dependent on the depth from the surface, since the conducting layer is made using the ion implantation method. As the period of the S - d H oscillations is dependent on the carrier concentration, the heterogeneous phase of the specimen causes the disappearance of the oscillations. Although GaAs 2 shows the largest deviation of these samples, its simple deviation from linear dependence can be easily fitted by the higher order terms of a polynomial. Therefore, the GaAs 2 with no S - d H oscillations is the most promising of these magnetic field sensors. The temperature dependence of the Hall voltage is not a serious problem. As the superconducting magnet is usually immersed in liquid helium at 4.2 or 2.2 K ()t point), the Hall sensor can also be immersed directly in the liquid He. In Figure 4, the temperature dependence of the Hall voltage under a magnetic field of 10 T is shown. In all sensors, the Hall voltage below 4.2 K shows very slight temperature dependence. The input resistances in the absence of a magnetic field are 1 kl~ with the GaAs sensor and 1 I~ with the InAs one, respectively. Due to the magnetoresistance effect, the input resistance increases to 3 kl~ with GaAs and 10 l~ with InAs under a magnetic field of 15 T. The control currents shown in Figures 1-3 are so selected as to limit the power dissi-
954
Cryogenics
1994 V o l u m e
34, N u m b e r
11
Hall sensors for cryogenic temperatures: A. Sawada et al. 25
I
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Discussion
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.=,.,
.... , (0x0o2-~m/
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where/, n, e and d are the electronic current, the carrier density, the carder charge and the thickness of the sensor, respectively. The more n or d decrease, the more the sensitivity increases. It is difficult to decrease the carder density to less than 1017 cm -3. However, GaAs with an impurity concentration higher than 1017 cm -3 shows excellent Hall probe properties, because the temperature dependence of the resistance and the amplitude of the S - d H oscillations are small. The InSb Hall sensors for electronic circuits that we investigated previously had too high an electrical resistance at 4.2 K to measure the magnetic field. We assume that these were intrinsic semiconductors. The carder concentration is strongly dependent on temperature, as the band gap is 0.17 eV. Consequently, the only way to increase the sensitivity is to decrease d~ Compared to a bulk element cut from crystal homogeneously containing the carriers, it is easy to obtain a thin sensor by ion implantation, d for GaAs 2 is 0.4/zm. These GaAs sensors, made by an integrated circuit technique, have small sensitive areas, i.e. 0.2 x 0.2 nLrn 2, and regular shapes 5.6. Therefore, they can be used to measure the magnetic field of a limited small area, and have a small offset voltage. From a comparison with respect to the characteristics shown above, GaAs 2 is the most favourable magnetic field sensor of the various specimens examined. The Hall voltage of this sensor behaves as a simple function of the magnetic field. The problem of the poor linearity of the Hall voltage can be settled by translating the Hall voltage value to the accurate magnetic field value using a polynomial. Since the GaAs Hall sensor is commercially available as an electronic circuit component of a plastic package, a problem might arise concerning the matter of reproducibility due to heat cycling. Contrary to this fear, GaAs 2 did not break and maintained reproducibility after 4 thermal cycles. Furthermore, this sensor can be used without anxiety because it is far less expensive compared with the InAs Hall sensor for the cryogenic element.
,
,
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,
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Temperature dependence of Hall voltage under a field strength of 10 T. VRTis the Hall voltage at 300 K
Using a GaAs Hall sensor, we have successfully performed magnetic field strength measurements on a superconducting magnet, where the field was being swept in a time dependent way. This sensor has also been used effectively for measuring the field distribution from 10-4 to 101 T. As the magnetic field is not proportional to the external current in the persistent mode, we need to monitor the magnetic field directly. As these GaAs sensors are very sensitive, the field can be measured at the outside of the Dewar. Acknowledgements
pation below 1 mW. An excess self-heating of the sensor might cause insufficient heat exchange with the liquid helium due to the bubbles of helium gas formed on the surface of the sensor. This would lead to instability of the Hall voltage.
The authors would like to thank M. Kudo, K. Sai, Y. Ishikawa, S. Ohtomo, H. Miura, S. Tanno, Y. Ishigami, K. Hosokura and the members of the machine shop at the Faculty of Science of Tohoku University for their helpful discussions and technical support.
Cryogenics 1994 Volume 34, Number 11 955
Hall sensors for cryogenic temperatures: A. Sawada et al. References 1 Thanallakis, A. and Cohen, E. Solid State Electron (1969) 12 997 2 Rubin, L.G., Nelson, D.R. and Sample, H.H. Rev Sci Instrum (1975) 12 1624 3 Sample, H.H and Rnbin, L.G. 1EEE Trans Magn (1976) MAG12 810 4 Poole, M.W. and Walker, R.P. IEEE Trans Magn (1981) MAGI7 2129 5 Hara, T., Milmra, M., Toyoda, N. and Zama, M. 1EEE Trans Electron Devices (1982) ED-29 78
956
Cryogenics 1994 Volume 34, Number 11
6 Doi, H. and Noto, H. Report of the Institute for Materials Research, Tohoku University, Sendal. Japan (1985) (in Japanese) 7 IOdo, G., Nakagawa, Y., Noto, K., Hoshi, A. et al. Sci Rep RITU (1986) A33 289 8 Inoue, K., Nakanisi, K., Takigami, H., Itoh, K. et al. Proc 48th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo. Japan (1992) 105 (in Japanese) 9 Hiromoto, N., Aold, T.E., Fijiwara, M. and Itabe, T. Proc Japan Soc Applied Physics: $4th Autumn Meeting (No. 1) Japan Soc Applied Physics, Tokyo, Japan (1993) 58 (in Japanese) 10 Kido, G. and Nakagawa, Y. Proc 9th lnt Conf on Magnet Technology Zurich, Switzerland (1985) 821
In experiments for measuring various physical quantities as a function of applied magnetic field, the determination of the magnetic field strength is an important task. The magnetic field is proportional to the current at the superconducting magnet. But, because the field responds to the current with a delay time L/R, where L and R are the self-inductance of the magnet and the shunt resistor, respectively, the magnetic field is not proportional to the external current. The field strength is independent of the current in the persistent mode. Consequently it is necessary to measure the field profile of the magnet. One precise way to measure the magnetic field is using NMR. But NMR equipment is generally complicated and the field strength able to be measured using one set of NMR equipment is limited. One practical method used is to measure the magnetoresistance of a pure thin copper wire wound in a non-inductive form. However, this method is rather poor in terms of sensitivity and reproducibility. Furthermore, this set-up is liable to break very easily due to the use of a thin wire. Another method involves using a Hall sensor having adequate characteristics, which has been calibrated by means of a previously known magnetic field. Taking into account sensitivity, reproducibility, easy handling, and other factors relevant to sensors, it is quite effective to use a Hall sensor to measure the strength of a magnetic field 1-9. In this paper, the characteristics of several pieces of commercial Hall sensors are described. Their adequacy as magnetic field measuring sensors is also discussed.
0011-2275/94/110953-04 1994Butterworth-HeinemannLtd
©
M e a s u r e m e n t s and results The measurement of the Hall effect was conducted at 300, 77, 4.2 and 1.5 K under a magnetic field of up to 25 T generated by a hybrid magnet composed of a superconducting and a Bitter magnet. The magnetic field was calibrated by the induction method to within ___0.3%1°. The specimens with which the measurements were made are three types of Hall sensors, namely GaAs 1 (Matsushita OH002-2HR, ion implantation type, Matsushita Electronics Corp, Kyoto, Japan), GaAs 2 (Toshiba THS-119A, ion implantation type, Toshiba Co., Tokyo, Japan) and InAs (F.W. Bell BHT921, F.W. Bell, Inc., Orlando, FL, USA). These sensors are commercially available. The GaAs sensors are used as an electrical component in the circuits of a brushless motor, a floppy disk, etc., whereas the InAs one is used as a cryogenic sensor for a superconducting magnet. GaAs 1 had been found to be useful in magnetic fields up to 6.8 T at 4.2 K 5. The results of the observations at 4.2 K are shown in Figures 1-3. In each figure, part a shows the observed values of the Hall voltage. With the GaAs sensors, the measurements using the various sensors of the same type were conducted simultaneously. However since no remarkable difference was noticed among the individual sensors, just typical results are presented in the figure. The control currents supplied to the sensors are 0.5 mA with GaAs and 10 mA with InAs, respectively. The magnetic field intervals of the measuring points are 7 - 1 0 mT. The sensitivity estimated from the observed values of Hall voltage is 0.1266VT--lmA -~ with GaAs 1, 0.2336 V T-~mA-~ with GaAs 2 and 81.2/~V T-~mA-I with
Cryogenics 1994 Volume 34, Number 11 95:!
Hall sensors for cryogenic temperatures: A. Sawada et al.
2.0
I
I
I
T-- .2K ~__~1.5
4.(
I
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(a)
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Figure 1 Hall effect of GaAs 1. The control current supplied to the sensor is 0.5 mA. (a) Hall voltage; (b) deviation from linearity
Figure 2 Hall effect of GaAs 2. The control current supplied to the sensor is 0.5 mA. (a) Hall voltage; (b) deviation from linearity
InAs, respectively. The GaAs sensors are roughly 10 3 times higher in sensitivity than InAs. The deviation from linear dependence of the Hall voltage is illustrated in Figures 13 parts b. The deviation of GaAs 1, GaAs 2 and InAs is less than ---5, ___10 and ___2.0%, respectively. It is notable that the GaAs sensors are still tending to increase even at 25 T. It is possible to explain these tendencies in terms of the heterogeneous phase of the carrier6. The characteristics which are generally taken into account for Hall sensors include linearity, sensitivity, offset voltage, temperature coefficient, input resistance and superposition of Shubnikov-de Haas ( S - d H ) oscillations. The most important of these is the problem of superposition of S - d H oscillations on the Hall voltage. The period of the S - d H oscillations is proportional to the inverse of the magnetic field and changes with the direction of the magnetic field, and the amplitude of the oscillation depends on the temperature. Therefore, it is very difficult to transform the Hall voltage value into the magnetic field value exactly. Consequently, a sensor with no S - d H oscillations is preferable. The results of the InAs clearly indicate S-dH oscillations; the data for GaAs 1 meander a little bit; and we cannot see the oscillations from the GaAs 2 results. As the mobility /x of the GaAs sensors is 5000 cm 2 V-~s-1, we get /.~B~I at 2 T, where B is the magnetic field. Because a magnetic field higher than 2 T is used as the high field for these sensors, S-dH oscillations
would usually be observed. However this is not the case for the GaAs 2. We assume that the carrier concentration of the GaAs 2 is dependent on the depth from the surface, since the conducting layer is made using the ion implantation method. As the period of the S - d H oscillations is dependent on the carrier concentration, the heterogeneous phase of the specimen causes the disappearance of the oscillations. Although GaAs 2 shows the largest deviation of these samples, its simple deviation from linear dependence can be easily fitted by the higher order terms of a polynomial. Therefore, the GaAs 2 with no S - d H oscillations is the most promising of these magnetic field sensors. The temperature dependence of the Hall voltage is not a serious problem. As the superconducting magnet is usually immersed in liquid helium at 4.2 or 2.2 K ()t point), the Hall sensor can also be immersed directly in the liquid He. In Figure 4, the temperature dependence of the Hall voltage under a magnetic field of 10 T is shown. In all sensors, the Hall voltage below 4.2 K shows very slight temperature dependence. The input resistances in the absence of a magnetic field are 1 kl~ with the GaAs sensor and 1 I~ with the InAs one, respectively. Due to the magnetoresistance effect, the input resistance increases to 3 kl~ with GaAs and 10 l~ with InAs under a magnetic field of 15 T. The control currents shown in Figures 1-3 are so selected as to limit the power dissi-
954
Cryogenics
1994 V o l u m e
34, N u m b e r
11
Hall sensors for cryogenic temperatures: A. Sawada et al. 25
I
I
I
Discussion
I
(a) ~
T=4.2K
20
The Hall voltage is derived from
/
VH = B l / n e d
"~ 10
0 ~
5
0
10
15
20
25
Magnet~ field intensity 0")
0.6
I
I
I
I
T=4.2K 0.4
(b)
I=10mA
•
+2.0%
0.0 ".~ - 0 . 2 -0.4 -0.6
, 5
0
, 10
I 15
i 20
25
Magnetic field intensity (T) 3 Hall effect of InAs. The control current supplied to the sensor is 10 mA. (a) Hall voltage; (b) deviation from linearity. a is calculated in the range of m a g n e t i c f i e l d below 10 T Figure
10
.=,.,
.... , (0x0o2-~m/
0
. . . . . . . . . . - - ~ J _ _. . . ........ . .
@..--
'0
/ "
,_, 0
Conclusions 03m~1)
I -5
-10
Figure4 magnetic
where/, n, e and d are the electronic current, the carrier density, the carder charge and the thickness of the sensor, respectively. The more n or d decrease, the more the sensitivity increases. It is difficult to decrease the carder density to less than 1017 cm -3. However, GaAs with an impurity concentration higher than 1017 cm -3 shows excellent Hall probe properties, because the temperature dependence of the resistance and the amplitude of the S - d H oscillations are small. The InSb Hall sensors for electronic circuits that we investigated previously had too high an electrical resistance at 4.2 K to measure the magnetic field. We assume that these were intrinsic semiconductors. The carder concentration is strongly dependent on temperature, as the band gap is 0.17 eV. Consequently, the only way to increase the sensitivity is to decrease d~ Compared to a bulk element cut from crystal homogeneously containing the carriers, it is easy to obtain a thin sensor by ion implantation, d for GaAs 2 is 0.4/zm. These GaAs sensors, made by an integrated circuit technique, have small sensitive areas, i.e. 0.2 x 0.2 nLrn 2, and regular shapes 5.6. Therefore, they can be used to measure the magnetic field of a limited small area, and have a small offset voltage. From a comparison with respect to the characteristics shown above, GaAs 2 is the most favourable magnetic field sensor of the various specimens examined. The Hall voltage of this sensor behaves as a simple function of the magnetic field. The problem of the poor linearity of the Hall voltage can be settled by translating the Hall voltage value to the accurate magnetic field value using a polynomial. Since the GaAs Hall sensor is commercially available as an electronic circuit component of a plastic package, a problem might arise concerning the matter of reproducibility due to heat cycling. Contrary to this fear, GaAs 2 did not break and maintained reproducibility after 4 thermal cycles. Furthermore, this sensor can be used without anxiety because it is far less expensive compared with the InAs Hall sensor for the cryogenic element.
,
,
,
I
,i,,i
,
s 10 Temperature OK)
,
*
I
se
, ,,
100
Temperature dependence of Hall voltage under a field strength of 10 T. VRTis the Hall voltage at 300 K
Using a GaAs Hall sensor, we have successfully performed magnetic field strength measurements on a superconducting magnet, where the field was being swept in a time dependent way. This sensor has also been used effectively for measuring the field distribution from 10-4 to 101 T. As the magnetic field is not proportional to the external current in the persistent mode, we need to monitor the magnetic field directly. As these GaAs sensors are very sensitive, the field can be measured at the outside of the Dewar. Acknowledgements
pation below 1 mW. An excess self-heating of the sensor might cause insufficient heat exchange with the liquid helium due to the bubbles of helium gas formed on the surface of the sensor. This would lead to instability of the Hall voltage.
The authors would like to thank M. Kudo, K. Sai, Y. Ishikawa, S. Ohtomo, H. Miura, S. Tanno, Y. Ishigami, K. Hosokura and the members of the machine shop at the Faculty of Science of Tohoku University for their helpful discussions and technical support.
Cryogenics 1994 Volume 34, Number 11 955
Hall sensors for cryogenic temperatures: A. Sawada et al. References 1 Thanallakis, A. and Cohen, E. Solid State Electron (1969) 12 997 2 Rubin, L.G., Nelson, D.R. and Sample, H.H. Rev Sci Instrum (1975) 12 1624 3 Sample, H.H and Rnbin, L.G. 1EEE Trans Magn (1976) MAG12 810 4 Poole, M.W. and Walker, R.P. IEEE Trans Magn (1981) MAGI7 2129 5 Hara, T., Milmra, M., Toyoda, N. and Zama, M. 1EEE Trans Electron Devices (1982) ED-29 78
956
Cryogenics 1994 Volume 34, Number 11
6 Doi, H. and Noto, H. Report of the Institute for Materials Research, Tohoku University, Sendal. Japan (1985) (in Japanese) 7 IOdo, G., Nakagawa, Y., Noto, K., Hoshi, A. et al. Sci Rep RITU (1986) A33 289 8 Inoue, K., Nakanisi, K., Takigami, H., Itoh, K. et al. Proc 48th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo. Japan (1992) 105 (in Japanese) 9 Hiromoto, N., Aold, T.E., Fijiwara, M. and Itabe, T. Proc Japan Soc Applied Physics: $4th Autumn Meeting (No. 1) Japan Soc Applied Physics, Tokyo, Japan (1993) 58 (in Japanese) 10 Kido, G. and Nakagawa, Y. Proc 9th lnt Conf on Magnet Technology Zurich, Switzerland (1985) 821