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 ele- ment 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 increasedto both the the sensitivityworking current of the deviceand 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