Hall Plate Research Articles

A Hybrid Magnetic Current Sensor With a Multiplexed Ripple-Reduction Loop

This article presents a hybrid magnetic current sensor for galvanically isolated measurements. It consists of a CMOS chip that senses the magnetic field generated by current flowing through a lead-frame-based current rail. Hall plates and coils are used to sense low-frequency (dc to 10 kHz) and high-frequency (10 kHz to 5 MHz) magnetic fields, respectively. With the help of on-chip calibration coils, the biasing current of the Hall plates is trimmed to match the sensitivity of the Hall and coil signal paths. The sensitivity drift of the coil path with temperature is compensated by using temperature-dependent gain-setting resistors, while the drift of the Hall path is compensated by biasing the Hall plates with a proportional-to-absolute-temperature (PTAT) current. The resulting sensitivity drift is less than 9% from –40 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C to 80 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C. The offset of the Hall plates is reduced by the current spinning technique, and the resulting ripple is suppressed by a multiplexed ripple-reduction loop (MMRL). Fabricated in a standard 0.18- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu$</tex-math> </inline-formula> m CMOS process, the current sensor occupies 4.6 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and draws 7.8 mA from a 1.8-V supply. It achieves a gain variation of only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 2% in a 5-MHz BW. It also achieves high energy efficiency, with an figure of merit (FoM) of 1.6 fW/Hz.

Multiply-connected complementary Hall plates with extended contacts

Multiply-connected complementary Hall plates with extended contacts

Implementation of Optimized Planar Hall Effect Sensor as Tunable Resistors With DC Bias Control

The emerging requirements of tunable resistors or pseudoresistors for electrical and electronic circuits demand the rigorous attention of engineers in recent times. The frequency-dependent behavior of conventional pseudoresistors operating with gate-controlled metal oxide field effect transistors (FET) creates a subtle challenge to operate in high-frequency applications. Therefore, this letter investigates a tunable resistor with a planar Hall plate to eliminate the frequency-dependent limitations of FETs. The proposed design of a tunable resistor with an optimized Hall effect sensor is able to achieve resistance tuning in the range of 1.8 Ω–247 KΩ. Apart from that, this letter investigates different geometries of planar Hall plate devices and their impact on biasing and magnetic fields that produce a compelling choice for tunable resistors. The proposed scheme exhibits a THD value of 1.4e-8% for a 10-MHz input signal, which is superior to its counterparts based on gate-controlled field effect devices.

Complementary symmetric Hall plates with a hole and four outer extended contacts

The electrical properties of Hall plates are described by the resistance matrix. Its even part corresponds to a resistor network, its odd part reflects the Hall output voltage. For singly connected and symmetric Hall plates closed formulae of the resistance matrix are known. There are also relations between complementary geometries, where contacts and insulating boundaries are swapped. This work gives the resistance matrix and relations between complementary geometries for Hall plates with one hole. The contacts may have arbitrary sizes, yet the plates must have two perpendicular axes of mirror symmetry, and the magnetic field has to be small.

Contactless Current Sensor With Novel Coil Designs and Hall-Effect Based Electron Device for Dynamic Precision Adjustment

The conventional approach of contactless current sensing using Rogowski’s coil is associated with unavoidable design constraints that limit the sensitivity, rise time, settling time, and bandwidth of operation. This article discusses some novel coil designs for contactless current measurement along with an electron device that works based on a brace-shaped Hall plate for dynamic precision adjustment. Experimentally, these proposed coil models achieve a sensitivity of 5.76 mV/A and a nonlinearity of 0.09%, which are better than their conventional counterparts. Apart from this, a mathematical analysis related to this work with different core materials and geometrical parameters confirms that these coils are also superior based on rise time, peak time, settling time, and sensitivity compared with their conventional counterparts. The dynamic precision adjustment device, made up of a brace-shaped Hall plate, utilizes novel materials, such as TiO2 and NiO, to make the device impedance more sensitive to control frequency and voltage. Experimentally, the impedance across the electron device varies between 0.0153 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{M}\Omega $ </tex-math></inline-formula> and 0.387 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{M}\Omega $ </tex-math></inline-formula> for every change in voltage and frequency in MHz of the switched mode control signal. This impedance-sensitive characteristic makes the output of the proposed sensor more efficient in achieving dynamic precision control even at a small range of operating conditions.

Determination of the Hall voltage for the case of a Hall plate having piecewise constant Hall angle

Determination of the Hall voltage for the case of a Hall plate having piecewise constant Hall angle

A 2 MS/s Full Bandwidth Hall System with Low Offset Enabled by Randomized Spinning.

In this paper, a Hall plate readout with a randomized four-phase spinning-current scheme is proposed. The goal is to remove the maximum number of offset components, including the offset associated with spike demodulation. The outcome is that only the smallest possible offset remains, corresponding to the residual offset of the Hall plate which cannot be distinguished from the Hall signal. An additional innovation is to operate various offset-reduction loops in spread-spectrum mode, allowing the removal of error components without notching out any in-band signals. The resulting approach delivers a very large notch-free bandwidth while simultaneously reducing the Hall plate residual offset, making it an enabler for high-bandwidth Hall-based current sensors. To demonstrate the proposed techniques, we have realized a mixed-mode experimental circuit, where the analog part is implemented in a custom integrated circuit, and the digital control system in an FPGA is connected to the analog chip. Measurement results feature a Hall readout system with a notch-free bandwidth up to 820 kHz and a 47 Trms noise floor. The input-referred Hall plate offset, based on statistical measurements on 10 samples from a single wafer, is reduced from to only .

Analysis of a Hall-Corbino disk plate having a point current source at the center

The paper presents an analytical theory for a disk-shaped Hall plate having three peripheral contacts and a point contact at the center. The central contact is modeled as a Corbino source. Its potential function contains a multivalued function. On the boundary, besides the exit contact, the positions of the other two (sensing) contacts were determined in such a way as to maximize the Hall voltage. The numerical results show that, in the case of this type of sensing element (referred to as the Hall-Corbino element), the Hall voltage is of the same order as that corresponding to a Hall disk having only peripheral contacts.

Drift of the sensitive direction of Hall-effect devices in (1 0 0)-silicon caused by mechanical shear stress

Conventional Hall effect devices are designed to respond to a single magnetic field component in 3D space. However, if plastic encapsulated Hall effect devices in cubic crystals are exposed to poorly defined and unstable mechanical shear stress, small portions of unwanted, perpendicular magnetic field components will show up in the Hall output signals. Mathematically, any such crosstalk – may it originate from mechanical stress or not – can be expressed as a Taylor series in powers of the magnetic field. The even powers are the well known planar Hall effect at zero mechanical stress. In practice powers of even order are irrelevant, because they are eliminated by the widely used spinning current schemes. In this paper we address the odd powers of the magnetic crosstalk and their drift versus mechanical stress. The effect is small for Hall plates but large for Vertical Hall devices in (100)-silicon. It is fully described by piezo-resistance and piezo-Hall tensors. We present results of numerical simulations and measurements. Thin devices are less affected than thick devices. If magnetic angle sensors are made of Vertical Hall devices, in-plane shear stress leads to small orthogonality errors. This article lays the foundations for compensation circuits to eliminate such shear-stress induced orthogonality errors.

Residual Offset in Silicon Hall-Effect Sensor: Analytical Formula, Stress Effects, and Implications for Octagonal Hall Plate Geometry

The Hall-effect magnetic sensors suffer from large offset that is described by the resistance mismatch in the Wheatstone bridge-like equivalent electrical circuit model of the Hall plate. After a first order cancellation of the raw offset using spinning current technique, a residual offset still exists, significantly limiting the accuracy of the Hall sensor in the detection of low magnetic field. In this paper we analyzed the residual offset in silicon Hall sensor using a nonlinear lumped resistor network model to derive a closed form expression. We further analyzed the residual offset in silicon Hall sensor under the influence of stress. Using these results, we show that eight-terminal, octagonal-shaped silicon Hall sensors employing eight-phase spinning current technique provide greater immunity to stress effects on residual offset due to a second order cancellation compared to the conventional four-phase spinning. The measurement results suggest superior offset performance of eight-terminal silicon Hall sensor.

Modeling of Three-Axis Hall Effect Sensors Based on Integrated Magnetic Concentrator

In this paper, we develop computational model to analyze the magnetic concentrating effect of integrated magnetic concentrator (IMC) on surrounding external magnetic field. We present an IMC-based three-axis Hall sensor model that enables to measure both inclination angles and absolute strength of a random external magnetic field. An IMC changes surrounding parallel magnetic components into perpendicular components, and therefore allows the horizontal Hall plates to measure both the strength and inclination angles of parallel external magnetic fields. We develop a finite element method (FEM) based model in COMSOL Multiphysics for the three-axis Hall sensor. Key factors influencing IMC's magnetic concentrating effect, including material property and sensor structure, are investigated and discussed using the developed model. Comparing to traditional IMC-based three-axis angular sensors, a reference permanent magnet is no longer needed in the sensor. A measurement accuracy of 0.8 and 1.2 degrees are achieved respectively for the angles of α and θ of external magnetic field.

Low Offset and Noise in High Biased GaN 2DEG Hall-Effect Plates Investigated With Infrared Microscopy

This article presents GaN two-dimensional electron gas (2DEG) Hall plates with low residual offset and noise at 3 V input bias. We studied devices made from three consecutive fabrication generations through current spinning offset measurements in a zero-field chamber. When operated above 1 V, the first-generation devices charted high residual offsets >1 mT. We reduced these residual offsets by three orders of magnitude in later device generations. Two experiments were performed to confirm the improvements. First, the GaN 2DEG Hall-effect plates were measured with infrared microscopy during current spinning to investigate current crowding and Joule heating. The low offset devices had minimal thermal gradients while the high offset devices had large thermal variations during current spinning. Second, zero-field current spinning was used to compare GaN 2DEG Hall-effect plates against typical commercial silicon Hall-effect plates. The Si devices had residual offsets $> 10\mu \text{T}$ biased at 3 V and AlGaN/GaN devices had residual offset $ at 3 V, and an InAlN/GaN devices operated at 2 V had a residual offset $ . Thus, for the first time, GaN 2DEG Hall-effect plates were shown to operate with high bias with low offsets and noise, which enables high fidelity sensing applications in extreme environments. [2020–0176]

Basic relationships for Hall half-plane structures with multiple extended contacts on the boundary: Applications to the extraction of physical parameters and optimization of graphene and vertical Hall devices

The basic relationships for a Hall plate with N non-symmetric contacts placed in an arbitrary magnetic field are a set of N-1 relationships that are necessary and sufficient for the existence of a complex electrostatic potential function. By the application of the boundary conditions, they turn into a linear system of N-1 compatibility conditions involving the terminal voltages and currents. The construction of the basic relationships requires the positions of the contact extremities on the real axis of the canonical domain (the upper half-plane) as well as the electric and magnetic parameters of the Hall device. The conduction and resistance matrices can be obtained easily from the basic relationships. They give an effective method for predicting the performance of both horizontal and vertical Hall effect devices and provide a useful method for designing these types of planar devices.

The Ultimate Noise Limit for Hall Plates in Voltage, Current, and Hybrid Operating Modes

If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contacts. In this paper we study more general operating conditions of Hall plates with an arbitrary number of contacts. In such hybrid operating modes current sources are connected to a first set of contacts and voltage sources to a second set of contacts. Output voltages are tapped at the first set of contacts and output currents are measured at the second set of contacts. All these output signals are multiplied by coefficients and added up. The purpose of this work is to figure out which operating mode and which Hall plate achieve maximum signal at minimum thermal noise and power dissipation. To this end we develop a theory, which gives the ratio of signal over noise and power as a function of the resistance matrix of Hall plates, of the supply voltages and currents, and of the coefficients. Optimization is done analytically in closed form and numerically for specific examples. The results are: 1) all operating modes have identical noise performance if their parameters are optimized; 2) for any Hall plate one can measure its resistance matrix and insert its values into our formulae to obtain the optimum supply currents and coefficients for optimum noise performance.

90% &amp;lt;i&amp;gt;SNR&amp;lt;/i&amp;gt; Improvement with Multi-Port Hall Plates

For Hall plates, the ratio of signal over thermal noise is determined by material properties, thickness, layout geometry, magnetic field, and the electric power at which the plate is operated. For traditional Hall plates with four contacts, the optimum choice is a symmetrical device with medium-sized contacts. This paper shows that the signal-to-noise-ratio (SNR) can be further increased by up to 90% for Hall plates with more than four contacts. Supply currents flow through several pairs of contacts, while a signal conditioning circuit taps output voltages at all pairs of contacts and sums them up. We compute the total thermal noise of the sum of correlated noise voltages and relate it to the total magnetic sensitivity. We also prove that for electrically linear devices a spinning current scheme cancels out zero point errors (offset errors) in a strict sense. All our investigations use the definite resistance matrix of multi-port Hall plates. We develop an analytical theory based on recent advances in the theory of Hall plates, and then we compute the integrals and matrices numerically for symmetrical Hall plates with six to 40 contacts. We also present measurements in accordance with our theory.

A Statistical Investigation into Assembly Tolerances of Gradient Field Magnetic Angle Sensors with Hall Plates

Magnetic field-based sensors are used for reliable applications in automotive and aerospace industry because of their robustness. The electrification of powertrains and propulsion requires gradiometric sensing principles, because they suppress ubiquitous electromagnetic disturbances very efficiently. A prominent solution for the mass market uses a small permanent magnet attached to the end of a rotatable shaft and a small sensor chip with four Hall plates placed on the rotation axis and ahead of the magnet. Small misplacements of chip and magnet lead to errors in the detected angle of the shaft. The lateral position errors and tilts of the magnet and the chip give eight degrees of freedom (DoF). This large number of DoF and the nonlinearity of the system obscure the view on how to optimize such angle sensor systems. Therefore, this work presents a statistical description of angle errors caused by assembly tolerances. Probability distributions of angle errors are given and marked differences to Gaussian distributions are shown. The influence of spacing between sensor and magnet and the dominant influence of the shape of the magnet are clarified. The results obtained by numerical computations are in excellent agreement to recently published analytical theories. This work gives evident conclusions for statistical optimizations of such angle sensor systems.

An Analytical Geometry Optimization Model for Current-Mode Cross-Like Hall Plates.

This paper presents a new analytical geometry optimization model to depict the optimal current sensitivity and signal-to-noise ratio (SNR) for the current-mode Hall devices. The conformal mapping calculation is performed to study the influence of device geometry on the current sensitivity and SNR of the current-mode cross-like Hall plates. The analytical model indicates that a current-mode cross-like Hall plate can achieve optimal current sensitivity and SNR in the device length-to-width ratio (L/W) range of 0.4–0.5 when the thermal noise is taken into account. Three-dimensional (3D) technology computer aided design (TCAD) simulation validates the accuracy of the analytical model. The proposed analytical model provides a geometry design rule to achieve optimal sensitivity and SNR at the same time for the current-mode cross-like Hall plates.

Micro-Tesla Offset in Thermally Stable AlGaN/GaN 2DEG Hall Plates Using Current Spinning

This article describes the characterization of a low-offset Hall plate using the AlGaN/GaN 2-D electron gas (2DEG). A four-phase current spinning technique was used to reduce the sensor offset voltage to values in the range of ∼20 nV, which corresponds to a low residual offset of ∼3.4 ± 2 μ T when supplied with low voltages (0.25–1 V). These offsets are 30x smaller than the values previously reported for GaN Hall plates, and it is on par with state-of-the-art current-spun silicon (Si) Hall plates. In addition, the offset does not exceed 10 μ T even at a higher supply voltage of 2 V. Current spinning was done with a relay matrix at a switching frequency of 1 Hz to enable an offset reduction. The sensor also shows stable current-scaled sensitivity over a wide temperature range of −100 °C to 200 °C, with a temperature coefficient of ∼100 ppm/°C. This value is at least 3x better than the state-of-the art Si Hall plates. Additionally, the sensor's voltage-related sensitivity (∼57 mV/V/T) is similar to that of the state-of-the-art Si Hall plates. Because of the low offset values enabled by current spinning, the AlGaN/GaN 2DEG Hall plates are viable candidates for low-field current and magnetic sensing in high-temperature environments.

A MAGNETIC DOUBLE INTEGRAL

In a recent study of how the output voltage of a Hall plate is affected by the shape of the plate and the size of its contacts, U. Ausserlechner has come up with a remarkable double integral that can be viewed as a generalisation of the classical elliptic ‘arithmetic–geometric mean (AGM)’ integral. Here we discuss transformation properties of the integral, which were experimentally observed by Ausserlechner, as well as its analytical and arithmetic features including connections with modular forms.

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.