Design and Application of MEMS-Based Hall Sensor Array for Magnetic Field Mapping

micromachines

Article Design and Application of MEMS-Based Hall Sensor Array for Magnetic Field Mapping

Chia-Yen Lee 1 , Yu-Ying Lin 2, Chung-Kang Kuo 1 and Lung-Ming Fu 3,*

1 Institute of Materials Engineering, National Pingtung University of Science and Technology, Pingtung 912, Taiwan; [email protected] (C.-Y.L.); [email protected] (C.-K.K.) 2 Department of Materials Engineering, National Pingtung University of Science and Technology, Pingtung 912, Taiwan; [email protected] 3 Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan * Correspondence: [email protected]; Tel.: +886-7-27575752-63321

Abstract: A magnetic field measurement system based on an array of Hall sensors is proposed. The sensors are fabricated using conventional microelectromechanical systems (MEMS) techniques and consist of a P-type silicon substrate, a silicon dioxide isolation layer, a phosphide-doped cross-shaped detection zone, and gold signal leads. When placed within a magnetic field, the interaction between the local magnetic field produced by the working current and the external magnetic field generates a measurable Hall voltage from which the strength of the external magnetic field is then derived. Four Hall sensors are fabricated incorporating cross-shaped detection zones with an identical aspect ratio (2.625) but different sizes (S, M, L, and XL). For a given working current, the sensitivities and

response times of the four devices are found to be almost the same. However, the offset voltage increases with the increasing size of the detection zone. A 3 × 3 array of sensors is assembled into a

Citation: Lee, C.-Y.; Lin, Y.-Y.; Kuo, 3D-printed frame and used to determine the magnetic field distributions of a single magnet and a C.-K.; Fu, L.-M. Design and group of three magnets, respectively. The results show that the constructed 2D magnetic field contour Application of MEMS-Based Hall maps accurately reproduce both the locations of the individual magnets and the distributions of the Sensor Array for Magnetic Field magnetic fields around them. Mapping. Micromachines 2021, 12, 299. https://doi.org/10.3390/ Keywords: hall sensor; hall effect; ion implantation; MEMS; sensor array mi12030299

Academic Editor: Cheng-Hsin Chuang 1. Introduction Hall sensors based on CMOS (Complementary Metal-Oxide-Semiconductor Transistor) Received: 20 February 2021 technology are widely applied in the manufacturing, medical devices, consumer electronics, Accepted: 10 March 2021 Published: 12 March 2021 automobile, and aerospace ﬁelds nowadays due to their low cost, high integration ability, and good reliability [1–7]. Hall sensors have many practical advantages, including non-

Publisher’s Note: MDPI stays neutral contact operation, high linearity, physical sturdiness, and versatility [8–10]. As a result, with regard to jurisdictional claims in they have attracted significant attention throughout industry and academia in recent published maps and institutional affil- years [11–13]. In the last decade, many sensor fusion techniques have been developed iations. to improve sensing field mapping [14,15]. Such systems could be used for condition monitoring and prognosis of machines [16,17]. Lozanova et al. [18] fabricated a Hall magnetic sensor consisting of two parallel-field Hall devices for obtaining in-plane magnetic field measurements and one orthogonal Hall element for acquiring out-of-plane (i.e., vertical) magnetic field measurements. It was Copyright: © 2021 by the authors. shown that six contacts were sufficient to acquire simultaneous measurements of the three Licensee MDPI, Basel, Switzerland. This article is an open access article orthogonal magnetic field components. In a later study [19], the same group presented distributed under the terms and a single-chip device based on a rectangular n-type silicon substrate for measuring two conditions of the Creative Commons orthogonal magnetic-field components using a common transduction zone and just four Attribution (CC BY) license (https:// contacts. The lateral sensitivity and vertical sensitivity of the proposed device were shown creativecommons.org/licenses/by/ to be Sx = 17 V/AT and Sz = 23.3 V/AT, respectively. Furthermore, the channel cross-talk 4.0/). at an induction of B ≤ 1.0 T was found to be no more than 3%. Zhao et al. [20] integrated

Micromachines 2021, 12, 299. https://doi.org/10.3390/mi12030299 https://www.mdpi.com/journal/micromachines Micromachines 2021, 12, x 2 of 12

cross-talk at an induction of B ≤ 1.0 T was found to be no more than 3%. Zhao et al. [20] integrated six pairs of permanent magnets and six Hall sensors to realize a six-degree-of-freedom (6-DOF) measurement system for a precision positioning stage. The experimental results showed that the proposed system enabled the in-plane stage Micromachines 2021, 12, 299 displacement to be controlled to within 0.23 mm and the angular displacement to be2 of 11 controlled within 0.07°. Xu et al. [21] demonstrated the potential for realizing Hall element sensors based on graphene rather than silicon substrates. It was shown that the higher carrier sensitivity and atomically thin active-body of graphene made possible the realizationsix pairs of of a permanentmagnetic sensor magnets with and high six sensitivity, Hall sensors excellent to realize linearity, a six-degree-of-freedom and outstanding thermal(6-DOF) stability. measurement Jones et al. system [22] developed for a precision a Hall positioning effect tactile stage. sensor The for experimental hand splinting results applications.showed that The the design proposed parameters, system enabled mechanical the in-plane response, stage and displacement force range to of be the controlled pro- to within 0.23 mm and the angular displacement to be controlled within 0.07◦. Xu et al. [21] posed device were optimized by finite element simulations. The results obtained using a demonstrated the potential for realizing Hall element sensors based on graphene rather prototype device showed that the optimized design achieved a pressure range of 45 kPa than silicon substrates. It was shown that the higher carrier sensitivity and atomically in the normal direction and 6 kPa in the shear direction. Berus et al. [23] prepared Hall thin active-body of graphene made possible the realization of a magnetic sensor with high sensors capable of working over a broad range of temperatures based on heavily-doped sensitivity, excellent linearity, and outstanding thermal stability. Jones et al. [22] developed n-InSb epitaxial thin films. The proposed sensors exhibited a temperature coefficient of a Hall effect tactile sensor for hand splinting applications. The design parameters, mechan- the magnetic sensitivity of less than 0.01% per degree and were virtually independent of ical response, and force range of the proposed device were optimized by finite element the temperature up to 400 K. Uzlu et al. [24] fabricated a gate-tunable graphene-based simulations. The results obtained using a prototype device showed that the optimized Hall sensor on a flexible polyimide (PI) substrate. In the proposed device, the sig- design achieved a pressure range of 45 kPa in the normal direction and 6 kPa in the shear nal-to-noise ratio was improved through the use of an AC-modulated gate electrode, direction. Berus et al. [23] prepared Hall sensors capable of working over a broad range of which increased the sensitivity of the device and reduced the off-set voltage compared to temperatures based on heavily-doped n-InSb epitaxial thin films. The proposed sensors a traditionalexhibited aHall temperature sensor with coefficient a static operation. of the magnetic sensitivity of less than 0.01% per degree andAs wereshown virtually in Figure independent 1, when a of Hall the temperaturesensor is placed up to perpendicularly 400 K. Uzlu et al. within [24] fabricated an ex- a ternalgate-tunable magnetic graphene-basedfield, the current Hall flowing sensor through on a flexible the sensor polyimide is deflected (PI) substrate. toward one In theside pro- of theposed substrate device, and the creates signal-to-noise an orthogonal ratio was voltage improved (referred through to as the the use Hall of voltage) an AC-modulated with a magnitudegate electrode, proportional which increased to both the the sensitivityworking current of the device and the and strength reduced of the the off-set external voltage magneticcompared field. to In a traditionalphysics, the Hall Lorentz sensor force with is athe static magnetic operation. force acting on a point charge in the presenceAs shown of inan Figure electromagnetic1, when a Hall field. sensor In particular, is placed perpendicularly a particle of charge within q anmoving external withmagnetic velocity field,v in an the electric current field flowing E and throughmagnetic the field sensor B experiences is deflected a force toward of: one side of the substrate and creates an orthogonalF = q (E voltage + v  B) (referred to as the Hall voltage)(1 with) a magnitude proportional to both the working current and the strength of the external magneticIn other field.words, In physics,the electromagnetic the Lorentz force isacting the magnetic on charge force q is acting a combination on a point of charge a forcein in the the presence direction of anof electromagneticthe electric field field. E proportional In particular, to the a particle magnitude of charge of the q movingfield and with thevelocity quantity v of in the an electriccharge, fieldand a E force and magneticacting on fieldthe charge B experiences at right angles a force to of: the magnetic field B and charge flow direction proportional to the magnitude of the electric field, the charge, and the velocity. Similar formulaeF = q can (E + be v × usedB) to describe the magnetic force (1) acting on a current-carrying wire or wire loop moving through a magnetic field.

FigureFigure 1. Schematic 1. Schematic illustration illustration of Hall of Hall effect. effect. In other words, the electromagnetic force acting on charge q is a combination of a Generally speaking, Hall sensors made from III–V semiconductor materials, such as force in the direction of the electric field E proportional to the magnitude of the field and InSb tend to outperform those based on silicon. However, such devices are more expen- the quantity of the charge, and a force acting on the charge at right angles to the magnetic sive and difficult to fabricate than silicon devices. Moreover, they are less easily inte- field B and charge flow direction proportional to the magnitude of the electric field, the charge, and the velocity. Similar formulae can be used to describe the magnetic force acting on a current-carrying wire or wire loop moving through a magnetic field. Generally speaking, Hall sensors made from III–V semiconductor materials, such as InSb tend to outperform those based on silicon. However, such devices are more expensive and difficult to fabricate than silicon devices. Moreover, they are less easily integrated with the signal-processing circuits and functions required to carry out the sensing operation [11]. Accordingly, the present study fabricates a magnetic field measurement system based on an Micromachines 2021, 12, x 3 of 12

Micromachines 2021, 12, 299 grated with the signal-processing circuits and functions required to carry out the sens3 ofing 11 operation [11]. Accordingly, the present study fabricates a magnetic field measurement system based on an array of Hall sensors constructed on silicon substrates using simple microelectromechanical systems (MEMS) technologies. Four Hall sensors incorporating array of Hall sensors constructed on silicon substrates using simple microelectromechanical detection zones with an identical aspect ratio but different sizes (S, M, L, and XL) are de- systems (MEMS) technologies. Four Hall sensors incorporating detection zones with an signed, manufactured, and characterized. Finally, a 3 × 3 Hall sensor array is assembled identical aspect ratio but different sizes (S, M, L, and XL) are designed, manufactured, and into a 3D-printed frame to measure the magnetic field mapping of both a single magnet characterized. Finally, a 3 × 3 Hall sensor array is assembled into a 3D-printed frame to and an arrangement of three magnets, which will be an important tool in the Nonde- measure the magnetic ﬁeld mapping of both a single magnet and an arrangement of three structive-Testing (NDT) field. magnets, which will be an important tool in the Nondestructive-Testing (NDT) ﬁeld.

2.2. Principle andand DesignDesign WhenWhen aa currentcurrent passing passing through through a semiconductora semiconductor material material flows flows in ain direction a direction perpen- per- dicularpendicular to that to that of an of external an external magnetic magnetic field, field, the carriers the carriers in the in semiconductor the semiconductor are deflected are de- toflected one side to one and si producede and a produce potential a difference potential difference called the Hall called voltage the Hall with voltage a magnitude with a equalmagnitude to: equal to: VH = I × B × RH/d (2) VH = I × B × RH∕d (2) wherewhere I is the I is electrical the electrical current, current, B is theB is magnetic the magnetic field field strength, strength, d is thed is thicknessthe thickness of the of semiconductor material and RH = rH/nq is the so-called Hall resistivity, in which n is the semiconductor material and RH = rH∕nq is the so-called Hall resistivity, in which n is the density of the charge carriers, q is the carrier charge, and rH is the Hall scattering the density of the charge carriers, q is the carrier charge, and rH is the Hall scattering factor depending on the used semiconductor material and the dominant charge carrier factor depending on the used semiconductor material and the dominant charge carrier mechanism. mechanism. Figure2 presents a schematic illustration of the sensor proposed in the present study Figure 2 presents a schematic illustration of the sensor proposed in the present study consisting of a 4-inch silicon wafer, a silicon dioxide insulating layer, metal leads, and consisting of a 4-inch silicon wafer, a silicon dioxide insulating layer, metal leads, and a a cross-shaped phosphide-doped detection zone [25–27] For comparison purposes, four cross-shaped phosphide-doped detection zone [25–27] For comparison purposes, four devices are fabricated, in which the cross-shaped detection zones have the same aspect devices are fabricated, in which the cross-shaped detection zones have the same aspect ratio (L/W = 2.625), but different sizes, namely S, M, L, and XL. In the proposed devices, ratio (L/W = 2.625), but different sizes, namely S, M, L, and XL. In the proposed devices, the analog signals are amplified by a large-current operational amplifier (AD620) and then the analog signals are amplified by a large-current operational amplifier (AD620) and supplied to an analog-to-digital converter (MEGA2560). Utilizing interpolation elements to then supplied to an analog-to-digital converter (MEGA2560). Utilizing interpolation el- smoothen planar display, the digital signals are then processed in LabVIEW to determine theements corresponding to smoothen magnetic planar display, field strength the digital and distribution signals are then (Figure processed3). in LabVIEW to determine the corresponding magnetic field strength and distribution (Figure 3).

FigureFigure 2.2. SchematicSchematic illustrationillustration of Hall sensor design and dimensions of four sizes of cross-shapedcross-shaped detectiondetection zones.zones.

3. Fabrication Figures 4 presents schematic illustrations showing the basic steps of the sensor fabrication process. At first, a silicon oxide isolation layer with a thickness of 0.5 μm was deposited on the surface of the 4-inch P-type < 100 > Si wafer (Thickness: 525 +/ −25 µm, Internal Resistivity: 1–20 Ω-cm) using a High-Density Plasma Chemical Vapor Deposi-

Micromachines 2021, 12, x 4 of 12

Micromachines 2021, 12, 299 tion (HDPCVD) technique (Figure 4a) [28,29]. A photolithography method was4 of 11 employed to pattern (Figure 4b) and etch the cross-shaped detection zone in the Si substrate (Figure 4c) and the detection zone was then implanted with phosphide ions.

(a)

(b)

FigureFigure 3. Block3. Block diagrams diagram showings showing (a ()a analog) analog circuit circuit and and signal signal conversion conversion path path of of proposed proposed Hall Hall sensor array and (b) LabVIEW program of the visualization platform of the magnetic field map- sensor array and (b) LabVIEW program of the visualization platform of the magnetic ﬁeld mapping. ping. 3. Fabrication Figure4 presents schematic illustrations showing the basic steps of the sensor fabrication process. At ﬁrst, a silicon oxide isolation layer with a thickness of 0.5 µm was deposited on the surface of the 4-inch P-type < 100 > Si wafer (Thickness: 525 +/ −25 µm, Internal Resistivity: 1–20 Ω-cm) using a High-Density Plasma Chemical Vapor Deposition (HDPCVD) technique (Figure4a) [ 28,29]. A photolithography method was employed to pattern (Figure4b) and etch the cross-shaped detection zone in the Si substrate (Figure4c) and the detection zone was then implanted with phosphide ions.

Micromachines 2021, 12, x 5 of 12

Micromachines 20212021,, 1212,, 299x 5 of 1112

(a) Deposition SiO2 (f) Photolithography (i) Photolithography

(a) Deposition SiO2 (f) Photolithography (i) Photolithography (b) Photolithography (g) Wet etching (j) Deposition Cr and Au

(b) Photolithography (g) Wet etching (j) Deposition Cr and Au (c) Wet etching (h) Removing PR (k) Lift-off

(d) Ions implantation

(e) Annealing(d) Ions implantation

Figure 4. Schematic(e) Annealing illustration showing the main steps of the fabrication process of Hall sensor: (a) deposition of SiO2, (b) photolithography, (c) wet etching, (d) ion implantation, (e) annealing, (f) photolithography,Figure 4. Schematic (g) wet etching, illustration (h) removing showingthe PR, main (i) photolithography, steps of the fabrication (j) deposition process of of Cr Hall and sensor: Figure 4. Schematic illustration showing the main steps of the fabrication process of Hall sensor: (a) Au, and(a) ( depositionk) lift-off. of SiO2,(b) photolithography, (c) wet etching, (d) ion implantation, (e) annealing, (depositionf) photolithography, of SiO2, (b ()g photolithography,) wet etching, (h) removing (c) wet etching, PR, (i) photolithography,(d) ion implantation, (j) deposition(e) annealing, of Cr (f) and photolithography, (g) wet etching, (h) removing PR, (i) photolithography,15 (j) deposition2 of Cr and (DopingAu, and( kenergy:) lift-off. 100 KeV, Depth: 0.1 µm, Concentration: 10 ions/cm ) (Figure 4d). The residualAu, and (k photoresist) lift-off. (PR) was then stripped away in acetone solution and an annealing process(Doping was energy: performed 100 KeV, at 900 Depth: °C for 0.1 1 minµm,(Figure Concentration: 4e). Apparently, 1015 ions/cm a thin2 layer) (Figure of 4d). (Doping energy: 100 KeV, Depth: 0.1 µm, Concentration: 1015 ions/cm2) (Figure 4d). siliconThe oxide residual was photoresistoxidized on (PR) the wasdetection then stripped area. A awayPR layer in acetone was then solution deposited and an on annealing the The residual photoresist (PR) ◦ was then stripped away in acetone solution and an an- surfaceprocess of thewas silicon performed wafer using at 900 theC photolithography for 1 min(Figure 4methode). Apparently, [30,31] to a pattern thin layer (Figure of silicon nealing process was performed at 900 °C for 1 min(Figure 4e). Apparently, a thin layer of 4f) andoxide etch was the oxidized contact on windows the detection of the area. leads A PR ( layerFigure was 4g) then on deposited each branch on the of surface the of silicon oxide was oxidized on the detection area. A PR layer was then deposited on the cross-theshaped silicon detection wafer using zone the (Figure photolithography 4h). Finally, method the Electron [30,31 ]Beam to pattern Evaporation (Figure4 f)(EBE) and etch surface of the silicon wafer using the photolithography method [30,31] to pattern (Figure methodthe was contact used windows to pattern of the the sensor leads (Figure surface4g) with on eachAu/Cr branch leads offor the electrical cross-shaped connection detection 4f) and etch the contact windows of the leads (Figure 4g) on each branch of the purposeszone (Fig (Figureure 44ih).–k). Finally, the Electron Beam Evaporation (EBE) method was used to pattern cross-shaped detection zone (Figure 4h). Finally, the Electron Beam Evaporation (EBE) Figurethe sensor 5a presents surface witha photograph Au/Cr leads of the for complete electrical Hall connection sensors. purposes The sensors (Figure were4i–k). at- method was used to pattern the sensor surface with Au/Cr leads for electrical connection tached to Figurea glass5 fiberboarda presents using a photograph UV glue ofan thed encapsulated complete Hall in resin. sensors. Finally, The sensors2 × 2 pin were purposes (Figure 4i–k). headersattached were bonded to a glass to ﬁberboardthe sensors using using UV conductive glue and silver encapsulated glue to form in resin. the Finally,final sensor 2 × 2 pin Figure 5a presents a photograph of the complete Hall sensors. The sensors were at- assemblyheaders Figure were 5b. bonded to the sensors using conductive silver glue to form the ﬁnal sensor tachedassembly to Figurea glass5 b.fiberboard using UV glue and encapsulated in resin. Finally, 2 × 2 pin headers were bonded to the sensors using conductive silver glue to form the final sensor assembly Figure 5b.

(a) (b) Figure 5. Photographs of: (a) complete Hall sensor, and (b) resin- encapsulation of individual Hall Figure 5. Photographs of: (a) complete Hall sensor, and (b) resin-encapsulation of individual sensorHall. sensor. (a) (b)

Figure4. Results 5. Photographs and Discussion of: (a) complete Hall sensor, and (b) resin-encapsulation of individual Hall sensor4.1. Sensitivity. Test Figure6 illustrates the experimental setup used in the present study to characterize and

compare the four Hall sensors with different detection zone dimensions. The experiments

Micromachines 2021, 12, x 6 of 12

Micromachines 2021, 12, 299 4. Results and Discussion 6 of 11 4.1. Sensitivity Test Figure 6 illustrates the experimental setup used in the present study to characterize commencedand compare by the measuring four Hall the sensors voltage with response different of detection the four zone sensors dimensions. given different The ex- working periments commenced by measuring the voltage response of the four sensors given dif- currents (2, 7, and 10 mA) and magnetic field strengths in the range of 0–5200 Gauss. The ferent working currents (2, 7, and 10 mA) and magnetic field strengths in the range of corresponding0–5200 Gauss. Theresults corresponding are presented results in Figure are presented7. As expected, in Figure the 7. measured As expected, Hall the voltages ofmeasured each sensor Hall increase voltages with of each the increasing sensor increase working with current.the increasing Moreover, working for a current. given working current,Moreover, the for Hall a given voltage working increases current, linearly the Hall with voltage an increasingincreases linearly magnetic with fieldan in- strength 2 (Rcreasing= 0.9955–0.9982). magnetic field Finally, strength for (R a2 constant= 0.9955– magnetic0.9982). Finally, field strength for a constant and working magnetic current, thefield Hall strength voltage and increases working withcurrent, an the increasing Hall voltage size increases of the detection with an increasing zone. size of the detection zone.

Micromachines 2021, 12, x 7 of 12

offset voltage 1.302 1.069 0.737 0.330 (mV) working current sensitivity 2 mA 0.214 0.196 0.231 0.208 (μV/Gauss)

FigureFigure 6.6. Experimental setup. setup. R-square 0.9859 0.9851 0.9879 0.9897

Table 1 compares the sensitivities of the four sizes of devices at each of the considered working currents. It is seen that(a) even though the detection zones in the different(b) devices have different sizes, the devices have the same sensitivity since they conduct the same current in every case. The offset voltage increases with an increasing size of the detection zone at different identical working currents. In other words, the surface electrical properties of the detection zone are more susceptible to the effects of the mechanical stress caused by the manufacturing and packaging processes as the size of the detection zone increases.

Table 1. Offset voltage, sensitivity, and coefficients of determination of four sizes of Hall sensors under three different working currents.

XL L M S

offset voltage 7.640 5.063 3.744 1.668 (mV) working current sensitivity 10 mA 0.923 0.914 0.930 0.909 (μV/Gauss) (c) (d) R-square 0.9969 0.9955 0.9982 0.9963 offset voltage 4.083 3.541 2.613 1.056 (mV) working current sensitivity 7 mA 0.615 0.621 0.598 0.607 (μV/Gauss) R-square 0.9985 0.9953 0.9991 0.9978

Figure 7. Sensitivity results for Hall sensors of size (a) XL, (b) L, (c) M, and (d) S. Figure 7. Sensitivity results for Hall sensors of size (a) XL, (b) L, (c) M, and (d) S.

4.2. Hysteresis Test Hysteresis is the time-based dependence of the response on the current and past state of the input. Specifically, the output of the Hall sensor depends not only on the instantaneity of the input but also on its history. If the design is not good enough in the early stages, the hysteresis may make the measurement results different from the previous results [32]. To realize the overall characteristics of the proposed Hall sensor, it is necessary to observe the hysteresis phenomenon under different magnetic fields. The experimental results (Figure 8) show the voltage path used to increase and decrease the magnetic field when the operating current of the Hall sensor of size S is 10 mA. It can be seen that as the magnetic field is less than 4000 Gauss, the two paths are actually almost superimposed. When the magnetic field is greater than 4000 Gauss, the maximum observed hysteresis is 170 Gauss (4.25%). This phenomenon greatly reduces the deviation of the magnetic field measurement, especially at a magnetic field strength less than 4000 Gauss.

Micromachines 2021, 12, 299 7 of 11

Table1 compares the sensitivities of the four sizes of devices at each of the considered working currents. It is seen that even though the detection zones in the different devices have different sizes, the devices have the same sensitivity since they conduct the same current in every case. The offset voltage increases with an increasing size of the detection zone at different identical working currents. In other words, the surface electrical properties of the detection zone are more susceptible to the effects of the mechanical stress caused by the manufacturing and packaging processes as the size of the detection zone increases.

Table 1. Offset voltage, sensitivity, and coefﬁcients of determination of four sizes of Hall sensors under three different working currents.

XL L M S offset voltage (mV) 7.640 5.063 3.744 1.668 working sensitivity current 0.923 0.914 0.930 0.909 10 mA (µV/Gauss) R-square 0.9969 0.9955 0.9982 0.9963 offset voltage (mV) 4.083 3.541 2.613 1.056 working sensitivity current µ 0.615 0.621 0.598 0.607 7 mA ( V/Gauss) R-square 0.9985 0.9953 0.9991 0.9978 offset voltage (mV) 1.302 1.069 0.737 0.330 working sensitivity current µ 0.214 0.196 0.231 0.208 2 mA ( V/Gauss) R-square 0.9859 0.9851 0.9879 0.9897

4.2. Hysteresis Test Micromachines 2021, 12, x 8 of 12 Hysteresis is the time-based dependence of the response on the current and past state of the input. Specifically, the output of the Hall sensor depends not only on the instantaneity of the input but also on its history. If the design is not good enough in the compensation, and reduction of rotating current offset [33,34]. Figure 9 shows the rela- early stages, the hysteresis may make the measurement results different from the previous tionship between the offset voltage, sensitivity, and temperature of the S-size Hall sensor results [32]. To realize the overall characteristics of the proposed Hall sensor, it is necessary when the working current is 10 mA. It can be found that due to the overall temperature to observe the hysteresis phenomenon under different magnetic fields. The experimental resultscoefficient (Figure of resistance8) show the (TCR) voltage when path the used ambient to increase temperature and decrease is increased the magnetic from 30 field °C to when50 °C the at a operating rate of 0.1 current mV/°C, of the Halloffset sensor voltage of of size the S isHall 10 mA.sensor It canincreases be seen linearly, that as theand magneticthe sensitivity field isof less the thansensor 4000 also Gauss, increases the two with paths the increase are actually in temperature almost superimposed. at a rate of

When0.01 µV/Gauss the magnetic-°C. It field is obvious is greater that than as 4000the environmental Gauss, the maximum temperature observed exceeds hysteresis 50 °C, the is 170offset Gauss voltage (4.25%). and Thissensitivity phenomenon of the Hall greatly sensor reduces greatly the increase deviation due of to the the magnetic greater fieldinflu- measurement,ence of temperature especially on atthe a magneticsensor. Temperature field strength compensation less than 4000 can Gauss. be incorporated according to the results of the temperature effect test for accurate measurement.

FigureFigure 8. 8.Magnetic Magnetic hysteresis hysteresis curve curve for for the the Hall Hall sensor sensor of of size size S S at at 10 10 mA mA of of working working current. current.

Figure 9. Temperature effect on voltage offset and sensitivity of the S-sized hall sensors at 30 °C, 40 °C, 50 °C, and 60 °C as the working current is 10 mA.

4.4. Time Response Test The responsivity of the four sizes of Hall sensors was evaluated by covering the sensors with a non-metal plate and placing them within a magnetic field with a strength of 2000 Gauss. The plate was abruptly removed from the Hall sensors and the corresponded Hall voltages were recorded. In Figure 10, it is seen that the response time is 8 ms for all four sizes of devices as the working current was 10 mA.

Micromachines 2021, 12, x 8 of 12

compensation, and reduction of rotating current offset [33,34]. Figure 9 shows the relationship between the offset voltage, sensitivity, and temperature of the S-size Hall sensor when the working current is 10 mA. It can be found that due to the overall temperature coefficient of resistance (TCR) when the ambient temperature is increased from 30 °C to 50 °C at a rate of 0.1 mV/°C, the offset voltage of the Hall sensor increases linearly, and the sensitivity of the sensor also increases with the increase in temperature at a rate of 0.01 µV/Gauss-°C. It is obvious that as the environmental temperature exceeds 50 °C, the offset voltage and sensitivity of the Hall sensor greatly increase due to the greater influence of temperature on the sensor. Temperature compensation can be incorporated ac- Micromachines 2021, 12, 299 cording to the results of the temperature effect test for accurate measurement. 8 of 11

4.3. Temperature Effect Test One of the key characteristics of the Hall sensor is the effect of offset voltage and sensitivity on temperature. With the advancement of fabrication technology, different offset compensation methods are known, such as calibration, device symmetry, mutual compensation, and reduction of rotating current offset [33,34]. Figure9 shows the relationship between the offset voltage, sensitivity, and temperature of the S-size Hall sensor when the working current is 10 mA. It can be found that due to the overall temperature coefﬁcient of resistance (TCR) when the ambient temperature is increased from 30 ◦C to 50 ◦C at a rate of 0.1 mV/◦C, the offset voltage of the Hall sensor increases linearly, and the sensitivity of the sensor also increases with the increase in temperature at a rate of 0.01 µV/Gauss-◦C. It is obvious that as the environmental temperature exceeds 50 ◦C, the offset voltage and sensitivity of the Hall sensor greatly increase due to the greater inﬂuence of temperature on the sensor. Temperature compensation can be incorporated according to the results of the temperature effect test for accurate measurement. Figure 8. Magnetic hysteresis curve for the Hall sensor of size S at 10 mA of working current.

◦ FigureFigure 9.9. TemperatureTemperature effecteffect on voltage offset and and sensitivity sensitivity of of the the S S-sized-sized hall hall sensors sensors at at 30 30 °C,C, 40 40°C,◦ C,50 50°C,◦ C,and and 60 60°C ◦asC the as theworking working current current is 10 is mA. 10 mA. 4.4. Time Response Test 4.4. Time Response Test The responsivity of the four sizes of Hall sensors was evaluated by covering the The responsivity of the four sizes of Hall sensors was evaluated by covering the sensors with a non-metal plate and placing them within a magnetic field with a strength of sensors with a non-metal plate and placing them within a magnetic field with a strength 2000 Gauss. The plate was abruptly removed from the Hall sensors and the corresponded of 2000 Gauss. The plate was abruptly removed from the Hall sensors and the corre- Hall voltages were recorded. In Figure 10, it is seen that the response time is 8 ms for all sponded Hall voltages were recorded. In Figure 10, it is seen that the response time is 8 four sizes of devices as the working current was 10 mA. ms for all four sizes of devices as the working current was 10 mA. 4.5. Integration Test Having characterized the sensing performance of the proposed Hall sensors, nine sensors were assembled into a 3D-printed plastic frame to create a 3 × 3 sensing array (Figure 11). The size of utilized sensors is S, and the working current is 10 mA. The feasibility of the sensing array was investigated by detecting the magnetic field distributions of a single magnet and a group of three magnets attached to the underside of an iron plate, respectively (Figure 12a,b). The magnetic field strength of each circle magnet (Diameter: 18 mm, Thickness: 5 mm) is 1420 Gauss. The detection results are presented in Figure 12c,d respectively. It is seen that for both arrangements of the magnets, the 2D magnetic field contour maps constructed in LabView accurately detect both the locations of the individual magnets and the distributions of the magnetic fields around them. The operational video is attached. MicromachinesMicromachines 2021 2021, 12, ,12 x , x 9 of9 12of 12

4.5.4.5. Integration Integration Test Test HavingHaving characterized characterized the the sensing sensing performance performance of ofthe the proposed proposed Hall Hall sensors, sensors, nine nine sensorssensors were were assembled assembled into into a 3Da 3D-printed-printed plastic plastic frame frame to tocreate create a 3a ×3 3× sensing3 sensing array array (Figure(Figure 11 11). The). The size size of ofutilized utilized sensors sensors is isS, S,and and the the working working current current is is10 10 mA. mA. The The fea- fea- sibilitysibility of ofthe the sensing sensing array array was was investigated investigated by by detecting detecting the the magnetic magnetic field field distributions distributions of ofa singlea single magnet magnet and and a groa groupup of ofthree three magnets magnets attached attached to tothe the underside underside of ofan an iron iron plateplate, respectively, respectively (F igure (Figure 1 21a2,b).a,b). The The magnetic magnetic field field strength strength of of each each circle circle magnet magnet (Dia(Diameter:meter: 18 18 mm, mm, Thickness: Thickness: 5 mm) 5 mm) is 14is 14202 Gauss.0 Gauss. The The detection detection results results are are presented presented in in FigFigureure 12 1c,2dc ,respectively.d respectively. It Itis isseen seen that that for for both both arrangements arrangements of ofthe the magnets, magnets, the the 2D 2D Micromachines 2021, 12, 299 magneticmagnetic field field contour contour maps maps constructed constructed in inLabView LabView accurately accurately detect detect both both the the locations locations9 of 11 of ofthe the individual individual magnets magnets and and the the distributions distributions of ofthe the magnetic magnetic fields fields around around them. them. The The operoperationalational video video is attached.is attached.

Figure 10. Time responses of Hall sensors of various sizes: (a) S, (b) M, (c) L, and (d) XL. FigureFigure 10. 10. Time Time responses responses of ofHall Hall sensors sensors of ofvarious various sizes: sizes: (a) ( Sa), (Sb, )( bM,) M, (c) ( L,c) L,and and (d )( dX)L. X L.

Micromachines 2021, 12, x Figure 11. Photographs of: (a) 3D-printed Hall sensor frame, and (b) 310× of3 12 Hall sensor array

FigureconsistingFigure 11. 11. Photographs of Photographs 9 sensing modules.of: of: (a) ( 3Da) 3D-printed-printed Hall Hall sensor sensor frame, frame, and and (b )( b3 )× 3 3 × Hall 3 Hall sensor sensor array array con- con- sistingsisting of of9 sensing 9 sensing modules. modules.

(a) (c) (d)

10 mm (b)

10 mm

Figure 12.FigurePhotographs 12. Photographs of: (a,b) frontof: (a, andb) front rear and sides rear of sides the iron of the plate iron with plate attached with attached magnets; magnets; (c,d) single (c,d) magnet and three-magnetsingle detection magnet arrangements and three-magnet and corresponded detection arrangements 2D magnetic and ﬁeld correspond distributionsed 2D (unit: magnetic Gauss). field distributions (unit: Gauss).

5. Conclusions This study has designed and fabricated Hall sensors with application to magnetic field strength measurement. On a P-type silicon substrate, the device features a phosphide-doped cross-shaped detection zone and is fabricated using simple MEMS-based techniques, including HDPCVD sputtering, photolithography patterning, ion implantation, and EBE metal lead deposition. Four kinds of devices have been constructed with detection zones of identical aspect ratio (2.625) but different sizes (S, M, L, and XL). The experimental results have shown that all four sizes of devices have a linear response over the range of 0–5200 Gauss for working currents of 2 mA, 7 mA, and 10 mA. For a constant working current, the four sensors have an identical sensitivity and a similar response time (8 ms) despite the difference in the size of the detection zone. However, the offset voltage increases with an increasing detection zone size; indicating that the surface electrical properties of the detection zone are more susceptible to the effects of the manufacturing and packaging processes as the size of the detection zone increases. The practical feasibility of the proposed sensors has been demonstrated by measuring the magnetic field mapping of a single magnet and a group of three magnets, respectively, using a 3 × 3 array of sensors assembled into a 3D-printed frame, which will be an important tool in the NDT field.

Author Contributions: L.-M.F. and C.-Y.L. conceived and designed the experiments; Y.-Y.L. and C.-K.K. performed the experiments; L.-M.F. and C.-Y.L. analyzed the data; Y.-Y.L. and C.-K.K. contributed reagents/materials/analysis tools; Y.-Y.L., L.-M.F. and C.-Y.L. wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology in Taiwan, grant number MOST 108-2622-E-020-004-CC3; MOST 108-2622-E-006-026-CC2, and MOST 109-2221-E-006-043-MY3. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest

References

Micromachines 2021, 12, 299 10 of 11

5. Conclusions This study has designed and fabricated Hall sensors with application to magnetic field strength measurement. On a P-type silicon substrate, the device features a phosphide- doped cross-shaped detection zone and is fabricated using simple MEMS-based techniques, including HDPCVD sputtering, photolithography patterning, ion implantation, and EBE metal lead deposition. Four kinds of devices have been constructed with detection zones of identical aspect ratio (2.625) but different sizes (S, M, L, and XL). The experimental results have shown that all four sizes of devices have a linear response over the range of 0–5200 Gauss for working currents of 2 mA, 7 mA, and 10 mA. For a constant working current, the four sensors have an identical sensitivity and a similar response time (8 ms) despite the difference in the size of the detection zone. However, the offset voltage increases with an increasing detection zone size; indicating that the surface electrical properties of the detection zone are more susceptible to the effects of the manufacturing and packaging processes as the size of the detection zone increases. The practical feasibility of the proposed sensors has been demonstrated by measuring the magnetic field mapping of a single magnet and a group of three magnets, respectively, using a 3 × 3 array of sensors assembled into a 3D-printed frame, which will be an important tool in the NDT field.

Author Contributions: L.-M.F. and C.-Y.L. conceived and designed the experiments; Y.-Y.L. and C.- K.K. performed the experiments; L.-M.F. and C.-Y.L. analyzed the data; Y.-Y.L. and C.-K.K. contributed reagents/materials/analysis tools; Y.-Y.L., L.-M.F. and C.-Y.L. wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology in Taiwan, grant number MOST 108-2622-E-020-004-CC3; MOST 108-2622-E-006-026-CC2, and MOST 109-2221-E-006- 043-MY3. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Zhang, Y.; Hao, Q.; Xiao, G. Low-frequency noise of magnetic sensors based on the anomalous Hall effect in Fe–Pt alloys. Sensors 2019, 19, 3537. [CrossRef] 2. Lin, Y.N.; Dai, C.L. Micro magnetic field sensors manufactured using a standard 0.18-µm CMOS process. Micromachines 2018, 9, 393. [CrossRef] 3. Fujiwara, K.; Satake, Y.; Shiogai, J.; Tsukazaki, A. Doping-induced enhancement of anomalous Hall coefficient in Fe-Sn nanocrys- talline films for highly sensitive Hall sensors. APL Mater. 2019, 7, 111103. [CrossRef] 4. Collomb, D.; Li, P.; Bending, S.J. Nanoscale graphene Hall sensors for high-resolution ambient magnetic imaging. Sci. Rep. 2019, 9, 14424. [CrossRef] 5. Xuan, X. Recent advances in continuous-flow particle manipulations using magnetic fluids. Micromachines 2019, 10, 744. [CrossRef] 6. Stern, M.; Cohen, M.; Danielli, A. Configuration and design of electromagnets for rapid and precise manipulation of magnetic beads in biosensing applications. Micromachines 2019, 10, 784. [CrossRef] 7. Li, X.; Fukuda, T. Magnetically guided micromanipulation of magnetic microrobots for accurate creation of artistic patterns in liquid environment. Micromachines 2020, 11, 697. [CrossRef] 8. Lee, S.; Hong, S.; Park, W.; Kim, W.; Lee, J.; Shin, K.; Kim, C.; Lee, D. High accuracy open-type current sensor with a differential planar Hall resistive sensor. Sensors 2018, 18, 2231. [CrossRef][PubMed] 9. Fan, L.; Bi, J.; Xi, K.; Yan, G. Investigation of radiation effects on FD-SOI Hall sensors by TCAD simulations. Sensors 2020, 20, 3946. [CrossRef] 10. Yatchev, I.; Sen, M.; Balabozov, I.; Kostov, I. Modelling of a Hall effect-based current sensor with an open core magnetic concentrator. Sensors 2018, 18, 1260. [CrossRef] 11. Petruk, O.; Kachniarz, M.; Szewczyk, R. Novel method of offset voltage minimization in hall-effect sensor. Acta Phys. Pol. A 2017, 131, 1177. [CrossRef] 12. Lin, C.H. Precision motion control of a linear permanent magnet synchronous machine based on linear optical-ruler sensor and Hall sensor. Sensors 2018, 18, 3345. [CrossRef] Micromachines 2021, 12, 299 11 of 11

13. Roy, A.; Sampathkumar, P.; Kumar, P.S.A. Development of a very high sensitivity magnetic field sensor based on planar Hall effect. Measurement 2020, 156, 107590. [CrossRef] 14. Liang, C.; Zhang, Y.; Li, Z.; Yuan, F.; Yang, G.; Song, K. Coil positioning for wireless power transfer system of automatic guided vehicle based on magnetic sensing. Sensors 2020, 20, 5304. [CrossRef] 15. Ursel, T.; Olinski, M. Displacement estimation based on optical and inertial sensor fusion. Sensors 2021, 21, 1390. [CrossRef] 16. Martinez-Garcia, M.; Zhang, Y.; Wan, J.; McGinty, J. Visually interpretable profile extraction with an autoencoder for health monitoring of industrial systems. In Proceedings of the 2019 IEEE 4th International Conference on Advanced Robotics and Mechatronics (ICARM), Osaka, Japan, 3–5 July 2019. 17. Martinez-Garcia, M.; Zhang, Y.; Suzuki, K.; Zhang, Y.-D. Deep recurrent entropy adaptive model for system reliability monitoring. IEEE Trans. Ind. Inform. 2020, 17, 839. [CrossRef] 18. Lozanova, S.; Ivanov, A.; Roumenin, C. A novel three-axis hall magnetic sensor. Procedia Eng. 2011, 25, 539–542. [CrossRef] 19. Lozanova, S.; Noykov, S.; Roumenin, C. Two-axis silicon hall effect magnetometer. Sens. Actuators A Phys. 2017, 267, 177–181. [CrossRef] 20. Zhao, B.; Shi, W.J.; Zhang, J.W.; Zhang, M.; Qi, X.; Li, J.X.; Tan, J.B. Six degrees of freedom displacement measurement system for wafer stage composed of Hall sensors. Sensors 2018, 18, 2030. [CrossRef] 21. Xu, H.; Zhang, Z.; Shi, R.; Liu, H.; Wang, Z.; Wang, S.; Peng, L.M. Batch-fabricated high-performance graphene Hall elements. Sci. Rep. 2013, 3, 1207. [CrossRef] 22. Jones, D.; Wang, L.; Ghanbari, A.; Vardakastani, V.; Kedgley, A.E.; Gardiner, M.D.; Vincent, T.L.; Culmer, P.R.; Alazmani, A. Design and evaluation of magnetic Hall effect tactile sensors for use in sensorized splints. Sensors 2020, 20, 1123. [CrossRef] 23. Berus, T.; Oszwaldowski, M.; Grabowski, J. High quality Hall sensors made of heavily doped n-InSb epitaxial films. Sens. Actuators A Phys. 2004, 116, 75–78. [CrossRef] 24. Uzlu, B.; Wang, Z.; Lukas, S.; Otto, M.; Lemme, M.C.; Neumaier, D. Gate-tunable graphene-based Hall sensors on flexible substrates with increased sensitivity. Sci. Rep. 2019, 9, 18059. [CrossRef] 25. Jovanovic, E.; Pesic, T.; Pantic, D. 3D simulation of cross-shaped hall sensor and its equivalent circuit model. In Proceedings of the 24th International Conference on Microelectronics (MIEL), Niš, Serbia, 16–19 May 2004; pp. 235–238. 26. Wei, R.; Du, Y. Analysis of orthogonal coupling structure based on double three-contact vertical hall device. Micromachines 2019, 10, 610. [CrossRef][PubMed] 27. Fan, L.; Bi, J.; Xi, K.; Majumdar, S.; Li, B. Performance optimization of FD-SOI hall sensors via 3D TCAD simulations. Sensors 2020, 20, 2751. [CrossRef][PubMed] 28. Kim, Y.; Lee, M.; Kim, Y.J. Selective growth and contact gap-fill of low resistivity Si via microwave plasma-enhanced CVD. Micromachines 2019, 10, 689. [CrossRef] 29. Fraga, M.; Pessoa, R. Progresses in synthesis and application of SiC Films: From CVD to ALD and from MEMS to NEMS. Micromachines 2020, 11, 799. [CrossRef] 30. Lee, A.H.; Lee, J.; Laiwalla, F.; Leung, V.; Huang, J.; Nurmikko, A.; Song, Y.K. A scalable and low stress post-CMOS processing technique for implantable microsensors. Micromachines 2020, 11, 925. [CrossRef] 31. Puryear, J.R.; Yoon, J.; Kim, Y.T. Advanced fabrication techniques of microengineered physiological systems. Micromachines 2020, 11, 730. [CrossRef][PubMed] 32. Nguyen, P.B.; Choi, S.B.; Song, B.K. A new approach to hyeteresis modelling for a piezoelectric actuator using Preisach model and recursive method with an application to open-loop position tracking control. Sens. Actuators A Phys. 2018, 270, 136. [CrossRef] 33. Cholakova, I.M.; Takov, T.B.; Tsankov, R.T.; Simonne, N. Temperature influence on Hall sensors characteristics. In Proceedings of the 20th Telecommunications Forum TELFOR, Belgrade, Serbia, 20–22 November 2012; p. 967. 34. Tang, W.; Lyu, F.; Wang, D.; Pan, H. A new design of a single-device 3D Hall sensor: Cross-shaped 3D Hall sensor. Sensors 2018, 18, 1065. [CrossRef][PubMed]