Towards a Low Current Hall Effect Sensor

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Sensors and Actuators A 279 (2018) 278–283

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Sensors and Actuators A: Physical

journal homepage: www.elsevier.com/locate/sna

Towards a low current Hall effect sensor

a b a,∗

Yossi Sharon , Bagrat Khachatryan , Dima Cheskis

The Physics Department, Ariel University, Ariel 407000, Israel

The Physics Department, Technion, Haifa 3200003, Israel

a r t i c l e i n f o a b s t r a c t

Article history: Many modern electronic devices utilize linear Hall sensors to measure current and the magnetic ﬁeld, as

Received 30 January 2018

well as to perform switching and latching operations. Smartphones, laptops, and e-readers all work with

Received in revised form 10 June 2018

very low (sub-milliampere) currents. To perform a switching function in low-power devices, however,

Accepted 11 June 2018

Hall sensors must work in the microampere regime. This paper demonstrates, for the ﬁrst time, the ability

Available online 18 June 2018

of a standard Hall detector to work linearly in the microampere regime between√ 0 and 0.7 Tesla. To do so,

we developed a current source with RMS noise on the order of 10–100 pA/ Hz. An optimized electronic

Keywords:

circuit with minimal connections feeds current to the Hall sensor, and the Hall voltage is measured with

Hall sensors

Magnetism an industrial nanovoltmeter. After cooling this system down to temperatures as low as 77 K, we found

mostly 1/f noise. In this regime the thermal noise was negligible. We demonstrate the capabilities of this

Low current

system by precisely measuring the slope of the Hall effect with a four-point probe at current intensities

of 100, 10, and 1 ␮A. We expect that our system can work as a microampere Hall sensor using external

voltage detectors.

1. Introduction output current of the Hall sensor is in the mA regime. This current

level gives a good signal-to-noise ratio (SNR), and its Hall voltage

Many modern devices, such as smartphones, tablets, e-readers, can be easily detected. This paper presents work towards the devel-

GPS units, and heart rate monitors, are controlled remotely and opment of a Hall sensor that can work in the microampere regime

operated continuously for long stretches of time. These features and still react while a device is in the sleep mode. In order to achieve

come with a practical design constraint: the devices spend most of this goal, it is necessary to ﬁrst greatly reduce SNR and then ﬁnd

their time in a low-power sleep mode, using a battery or a DC low- a voltage sensor capable of detecting the signal. The present work

power bus to deliver current in the sub-milliampere (mA) regime. focuses on the ﬁrst factor. We demonstrate for the ﬁrst time a lin-

When transmitting information, the devices switch to high-power ear DC Hall sensor working in the microampere regime, with a SNR

radio frequency (RF) activity, and the current increases to the mA similar to the mA regime used by current technologies. We mea-

or even Ampere scale. To control these switching behaviors, precise sure magnetic ﬁelds in the range 0–0.7 Tesla, for three very low DC

sensors must be used that are capable of measuring both low and current sources.

high currents. Usually, noninvasive current control is done using The basic relation between Hall voltage, current and magnetic

Hall sensors. The current ﬂowing through the Hall sensor creates a ﬁeld is:

perpendicular Hall voltage, which is proportional to the current and

detectable through the material of the sensor. Weak magnetic ﬁelds VHall RH BI/t (1)

can be measured by various techniques, such as superconducting

quantum interference (SQUID) devices [1] or magnetoresistance

where RH is Hall resistivity, B is the magnetic ﬁeld, I is the electrical

sensors (“giant”, “anomalous”, or “tunneling”, respectively denoted

current and t is a thickness of material.

GMR, AMR, or TMR) [2–4]. Hall sensors are also cheap, so are used

RH is equal to:

in many devices. However, to conserve battery life, the energy used

by different types of sensors needs to be minimized. Usually, the =

RH rh/nq (2)

where n is the density of charge carriers, q is the carrier charge, and

∗ rh is the Hall scattering factor that different from one, depending

Corresponding author.

on the material and the dominant charge carrier mechanism.

E-mail address: [email protected] (D. Cheskis).

https://doi.org/10.1016/j.sna.2018.06.027

Y. Sharon et al. / Sensors and Actuators A 279 (2018) 278–283 279

Fig. 1. Current source.

2. Current source

As was previously described, our main innovation is to use a

power source with very low noise. This device is shown in Fig. 1.

We use a 9 V battery as the source of voltage, and disconnect the

measurement circuit completely from the external network. The

load on the source should be no more than 9 V, and ideally much

less, in order to reduce noise. To create a constant current through

the sample, we use a Texas Instruments lm 234 current source and

adjustable system.

The formula which connects output current and resistivity R2

on an adjustable wire is shown below:

Iout (227 ␮V/K)/R2 (3)

If the voltage load is no larger than a few millivolts, and ﬂuctu-

ations in the load are small, then the noise in the current is very

small.

In order to test our sensor, we built an experiment which per-

forms Hall effect measurements on an industrial GaAs sensor.

3. Noise treatment

Fig. 2. Current source noise.

Having reduced the current by three orders of magnitude, it

is necessary to understand how the signal-to-noise (SNR) ratio

changes. In order to measure small magnetic ﬁelds with the same

accuracy, we need to reduce the noise level. DC systems mainly

We place our circuit consisting of current source and Hall sensor

harbor two types of noise: the non-thermal 1/f (ﬂicker) noise,

inside a cryostat. Its connections are a coaxial cable, Fisher con-

and broadband noise which depends on temperature. Our system

nectors and cryogenic wires. The nanovoltmeter is connected in a

includes three main parts: the current source, the circuit compris-

similar manner, and will have its own noise. The noise generated

ing current source and sensor, and the detector. This paper focuses

by the coaxial cables, connectors, and the Hall sensor itself has a

on the ﬁrst two. First we need to understand the noise in the cur-

thermal origin. We perform measurements at 300 K and at 77 K in

rent source, then we will look at the noise in the electronic circuit

order to see how this thermal noise inﬂuences our system.

that includes the Hall sensor.

In electronic circuits, the main type of broadband resistance

Fig. 2 illustrates the noise spectral density as function of fre-

noise at room temperature in DC circuits is Johnson–Nyquist noise.

quency in the range of 10 Hz–100 kHz in the logarithmic scale in

The noise level of the sensor voltage equals [5]:

our system:

According to deﬁnition, the 1/f noise decreases until some “cor-

ner frequency” is reached, and then levels off to a constant value.

V 4kbTRf (4)

This ﬁgure clearly shows that the corner frequency is around 100 Hz

for the 3 and 5 mA current sources. At 100 ␮A, the corner frequency

where k is the Boltzmann constant, T is the temperature, R is the

lies between 10 and 100 Hz. As expected, 1/f noise climbs in these b

resistance, and f is the frequency bandwidth.

plots as we move left from the corner frequency. Although this is

Laboratory power supplies are designed to provide currents

not shown, we expect that√ the noise spectral density for the 100 ␮A

and waveforms over a wide range of intensities and frequencies.

source reaches 100 pA/ Hz for some frequency around 1 Hz. For the

They are therefore built with many electronic components, which

10 ␮A source, the noise curve is ﬂat and we expect that it does not

increase the noise in the system. Moreover, the alternating voltage

change drastically between 1 and 10 Hz. The 1/f noise curve for the

of the power supply grid introduces additional noise. The standard

1 ␮A source is not shown, but we expect that will be lower than the

way to reduce noise is to decrease the bandwidth using a modu-

10 ␮A curve.

lated signal and a lock-in ampliﬁer. In our case, we instead use a DC

For comparison, the Keithley 6221 current source√ has approved

battery to supply a small amount of current without introducing

broadband RMS noise levels on the order of nA/ Hz. The level of

any noise from extraneous electronic components or the external

1/f noise achieved by our source is 3 orders of magnitude smaller

grid.

than any industrial current source connected to the external grid.

280 Y. Sharon et al. / Sensors and Actuators A 279 (2018) 278–283

Table 1

Hall coefﬁcients for 1 ␮A, 10 ␮A, 100 ␮A current sources at 300 K.

Current 1 ␮A 10 ␮A 100 ␮A 100 mA (manuf.)

VH/T 0.371 ␮V/T 3.955 ␮V/T 39.85 ␮V/T 39.93 mV/T

(VH/T) 1.5 nV/T 6.5 nV/T 81 nV/T 80 ␮V/T

(VH/T)/VH/T*100% 0.42% 0.16% 0.21% 0.2%

from 77 K to 300 K. This control is achieved by cooling the gas or

adjusting the heater with the help of a Cernox temperature sen-

sor and a controller from Lake Shore Cryotronics, Inc. [11]. This

control system stabilizes the sample area to a temperature con-

stant within 0.1 K. Measurements of the Hall voltage are performed

under a constant magnetic ﬁeld. The ﬁeld can be adjusted from 0

to 0.8 Tesla, in both directions. The sample that we use is the HSP-

T Hall Sensor of the Cryomagnetic, Inc. [12]. The sample type is a

Hall bar with one voltage output. The sample is completely isolated

from the external environment in the evacuation chamber of the

cryostat, which makes it possible to avoid oxidation. Although we

do not know the material of the sample or its exact thickness, the

manufacturer provides the dependence of the Hall voltage on the

Fig. 3. Experimental setup.

magnetic ﬁeld. Hence, we can compare our measurements with

those of the manufacturer. As it was shown previously, the Hall

voltage depends on the magnetic ﬁeld, the current, the charge of

4. Experimental setup

the carriers, the population density of the charge carriers, and the

thickness of the sample. Changes to the measured Hall voltage can

Our setup for making Hall effect measurements is shown in

only occur because either the magnetic ﬁeld B or the electric current

Fig. 3. This system consists of a DC current source, a very accu-

I changes. All other factors are constant for the sample.

rate nanovoltmeter, Helmholtz magnetic coils, and a liquid nitrogen

cryostat.

With this system, we can measure both the resistance and the 5. Experimental results

Hall Effect. This can be done using two different conﬁgurations: a

Hall bar [6,7] and the Van der Pauw sample arrangement [8–10], The Hall bar calibration sample has a linear Hall effect when

as shown in Fig. 4. In the Van der Pauw arrangement, the electrical the magnetic ﬁeld is perpendicular to the current passing through

contacts are connected to the boundaries of a square sample and the the sample. The manufacturer provides the ratio of the Hall volt-

Hall voltage is measured diagonally. In a Hall bar, the current ﬂows age to the magnitude of the magnetic ﬁeld for a current of 100 mA.

through an elongated plate and the Hall voltage is measured at the In order to test our system and learn its sensitivity, we measured

cross section. In both cases, the voltage is measured perpendicular the Hall voltage as a function of the external ﬁeld using our four-

to the current, and the voltage and current contacts are separated. point probe. Due to our assumption that the density of carriers

Such conﬁgurations are called four-point probes. Measurements of does not depend on the current, we can measure this relation for

resistance effects in these conﬁgurations are only related to the different currents and check whether it is proportional to the manu-

properties of sample, not to the measurement circuit. facturers values. We measured the Hall effect under three currents:

The sample is attached to a special holder with connected wires. 100 ␮A and 10 ␮A and 1 ␮A. The dependencies of the Hall voltage

The plane of the holder is perpendicular to the axis of the magnetic as function of magnetic ﬁeld are shown in Fig. 5.

coils and can rotate 180 degrees. The holder is inserted into the This ﬁgure shows an approximately linear dependence of the

evacuation area of the cryostat. This allows us to hold the sam- Hall voltage on magnetic ﬁeld for all current values. In Table 1, we

ple either in vacuum or at a low constant gas pressure. The gas compare the slopes of the Hall effects measured at all currents to

delivered to this region is pure helium. The outer walls of the cryo- the slope provided by the manufacturer at 100 mA. with statistical

stat are cooled by liquid nitrogen. The inside cools to 77 Kelvin, errors on the slopes derived from least-squares linear ﬁts.

so the helium remains gaseous at a pressure of a few millibars. The slopes at 1 ␮A and 10 ␮A differed from the slope at 100 ␮A

The temperature of the area containing the sample can be adjusted by factors of 107 and 10.07, respectively. These deviations were

Fig. 4. Hall measurement conﬁgurations.

Y. Sharon et al. / Sensors and Actuators A 279 (2018) 278–283 281

Fig. 5. Measured Hall voltage, VHall, as a function of the magnetic ﬁeld for three current intensities at 300 K.

Fig. 6. Hysteresis deviation in VHall [V] for the 1,10 and 100 ␮A signals, as a function of the magnetic ﬁeld at 300 K.

Table 2

very close to the expected factors of 100 and 10. The most precisely

RMSE(accuracy limit) and hysteresis deviation for 1 ␮A, 10 ␮A, 100 ␮A current

determined slope in this series of measurements was for the 10 ␮A

sources at 300 K.

current, which had a relative error of only 165 m%. The uncertain-

Current 1 ␮A 10 ␮A 100 ␮A

ties in the slopes (reported in Table 2) are directly proportional to

the root-mean-squared error (RMSE) of the Hall voltage measure- RMSE (accuracy limit) 10.4 nV 48.7 nV 530 nV

␮ ␮ ␮

ments. RMSE, measured in nanovolts, deﬁnes the real limit of our Hysteresis deviation 0.09 V 0.1 V 0.6 V

282 Y. Sharon et al. / Sensors and Actuators A 279 (2018) 278–283

Fig. 7. Hysteresis deviation in VHall [V] for 100 ␮A signals, as 300 K and 77 K, full scale in the left side and zoomed on the right side.

Table 3

three different current intensities, and also measured hysteresis in

␮

Hall coefﬁcients for 1 A, 10 ␮A, 100 ␮A current sources.

the Hall voltage at these currents.

Temperature 300 K 77 K We observe a general trend that the hysteresis deviation

decreases with increasing magnetic ﬁeld, both at room tempera-

VH/T 39.85 ␮V/T 39.68 mV/T

␮

(VH/T) 81 nV/T 78 ␮V/T ture and at 77 K. For very low currents (1 A), the Hall sensor started

(VH/T)/VH/T*100% 0.203% 0.197% to lose its linearity. By comparing the accuracy limits and linear-

ity of the 1 ␮A and 10 ␮A currents, √we estimate the 1/f noise in the

0.1–10 Hz range to be below 20 nV/ Hz. It is impossible to see such

low noise levels using a standard DC current source. However, it is

ability to resolve nonlinear phenomena in the sample. For example,

achieved in our system,√ because we start with a current noise level

the Hall voltage curve displays hysteresis, being differently shaped

of at most 100 pA/ Hz. These interesting results have motivated us

for increasing and decreasing magnetic ﬁelds. One possible source

to design additional low-noise current sources, to see if we can fur-

of hysteresis is a small amount of spontaneous magnetization in

ther decrease the RMSE of individual voltage measurements while

the sample. The manufacturer does not emphasize the hystere-

preserving Hall linearity.

sis deviation, but this effect is well known in the literature. Fig. 6

In our system, we use a doped GaAs Hall sensor whose Hall resis-

shows zoomed-in plots of the hysteresis deviation normalized by

tance is almost independent of temperature. The thermal noise is

Hall voltage for all three currents. The hysteresis deviations were a

reduced by stabilizing the temperature of the system within a liquid

major source of uncertainty in the slopes.

nitrogen cryostat.

Table 2 reports the maximal separations in Hall voltage due to

The focus of this work has been on testing the linearity of Hall

hysteresis. The hysteresis deviation was larger than the precision

voltage/magnetic ﬁeld dependence. Trying to achieve a high reso-

of the voltage measurements, characterized by the RMSE. As the

lution in magnetic ﬁeld strength was beyond the scope of this work.

current decreased from 100 to 10 ␮A, the normalized hysteresis

The long-term goal of this research is to develop low-cost, acces-

deviation does not change drastically, but it strongly increases at

sible methods to accurately characterize the electronic behavior of

1 ␮A. In our experiment, 10 ␮A is the minimal current which gives

thin ﬁlms. Modern technological devices offer many advantages,

a linear Hall effect.

but also require sophisticated power management circuits that

As mentioned before, we want to know whether or not the noise

increase the noise in the system. This issue can only be solved

in our system is thermal. To answer this question, we performed

by measuring low-intensity magnetic ﬁelds with stable and sim-

measurements with a 100 ␮A current source at 300 K and at 77 K.

ple systems. Our experiment shows a new way to understand and

The results are shown in Fig. 7.

measure such small effects, and may eventually lead to the devel-

We see from Fig. 7 that at 77 K, the sensor has almost exactly

opment of new equipment that can take full advantage of currents

the same Hall voltage/Magnetic ﬁeld dependence, with a little less

in the microampere regime.

error. These results are summarized in Table 3. Comparing them to

Table 1, we see that reducing the noise by cooling has much less

effect than simply choosing a lower current source with lower 1/f

Acknowledgements

noise. This is one additional proof that the main part of the noise is

not thermal.

We would like to thank to Prof. Boris Ashkinadze from Technion,

Haifa, Israel, for his advice and expertise in the area of transport

measurements. This study was partially funded by the Kamin pro-

6. Conclusion

gram of the Israel Innnovation Authority.

We have shown that a standard industrial Hall sensor exhibits

a linear response for currents in the microampere range. We were

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