Lorentz Force Magnetometer Research Articles

Single-structure 3-axis Lorentz force magnetometer based on an AlN-on-Si MEMS resonator

This work presents a single-structure 3-axis Lorentz force magnetometer (LFM) based on an AlN-on-Si MEMS resonator. The operation of the proposed LFM relies on the flexible manipulation of applied excitation currents in different directions and frequencies, enabling the effective actuation of two mechanical vibration modes in a single device for magnetic field measurements in three axes. Specifically, the excited out-of-plane drum-like mode at 277 kHz is used for measuring the x- and y-axis magnetic fields, while the in-plane square-extensional mode at 5.4 MHz is used for measuring the z-axis magnetic field. The different configurations of applied excitation currents ensure good cross-interference immunity among the three axes. Compared to conventional capacitive LFMs, the proposed piezoelectric LFM utilizes strong electromechanical coupling from the AlN layer, which allows it to operate at ambient pressure with a high sensitivity. To understand and analyze the measured results, a novel equivalent circuit model for the proposed LFM is also reported in this work, which serves to separate the effect of Lorentz force from the unwanted capacitive feedthrough. The demonstrated 3-axis LFM exhibits measured magnetic responsivities of 1.74 ppm/mT, 1.83 ppm/mT and 6.75 ppm/mT in the x-, y- and z-axes, respectively, which are comparable to their capacitive counterparts.

Design, fabrication, characterization and reliability study of CMOS-MEMS Lorentz-force magnetometers

This article presents several design techniques to fabricate micro-electro-mechanical systems (MEMS) using standard complementary metal-oxide semiconductor (CMOS) processes. They were applied to fabricate high yield CMOS-MEMS shielded Lorentz-force magnetometers (LFM). The multilayered metals and oxides of the back-end-of-line (BEOL), normally used for electronic routing, comprise the structural part of the MEMS. The most important fabrication challenges, modeling approaches and design solutions are discussed. Equations that predict the Q factor, sensitivity, Brownian noise and resonant frequency as a function of temperature, gas pressure and design parameters are presented and validated in characterization tests. A number of the fabricated magnetometers were packaged into Quad Flat No-leads (QFN) packages. We show this process can achieve yields above 95 % when the proper design techniques are adopted. Despite CMOS not being a process for MEMS manufacturing, estimated performance (sensitivity and noise level) is similar or superior to current commercial magnetometers and others built with MEMS processes. Additionally, typical offsets present in Lorentz-force magnetometers were prevented with a shielding electrode, whose efficiency is quantified. Finally, several reliability test results are presented, which demonstrate the robustness against high temperatures, magnetic fields and acceleration shocks.

A Resonant Lorentz-Force Magnetometer Exploiting Blue Sideband Actuation to Enhance Sensitivity and Resolution

This paper reports a miniaturized resonant Lorentz-force magnetometer that exploits blue-sideband actuation to attain a better sensitivity and resolution. The resonant magnetometer consists of a double-ended tuning fork (DETF) resonator with cavity slots to optimize thermoelastic dissipation, as well as a Lorentz-force generator structure to transduce the magnetic force to the axial of the resonator. The proposed device demonstrates a Lorentz-force sensitivity of 5.5 mV/nN, a noise floor of 1.25 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{V}/\surd $ </tex-math></inline-formula> Hz, and a resolution of 0.23 pN/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula> Hz. In comparison with a conventional drive scheme, the blue-sideband actuation achieves approximately two orders of magnitude improvement regarding sensitivity and resolution than that of the amplitude modulation (AM) readout and 3.6-fold enhancement than that of the frequency modulation (FM) readout. The results affirm the merit of the novel excitation method and provide solid evidence of its effectiveness in practical applications. [2022-0018]

A Resonant Lorentz-Force Magnetometer Featuring Slotted Double-Ended Tuning Fork Capable of Operating in a Bias Magnetic Field

Magnetometers are ubiquitous in applications covering many aspects of modern life, such as navigation, smart devices, biomedical systems, geological surveying and aerospace. This work reports a resonant Lorentz-force magnetometer featuring structural topology, in which cavity slots are incorporated in the device structure to improve the thermoelastic dissipation. Such a device is capable of sensing a small Lorentz-force and can be used as a sensitive magnetic field sensor. The most prominent property of this subject is implementing sensing tasks under a large bias magnetic field. The proposed magnetometer achieves a quality factor of 43000 in a vacuum of 4 mPa, a Lorentz-force sensitivity of 0.2 Hz/nN, and a magnetic field change sensitivity of 3375 Hz/T. The topology of the double-ended tuning fork (DETF) using cavity slots in the tine beams resulted in a 5.9-fold enhancement of the Q-factor compared to a common DETF resonator with the same geometry. Experimental characterization of the proposed magnetometer confirms its feasibility and functionality. Experiments about an application scenario with a large pre-existing bias magnetic field were carried out. The prototype device demonstrated a magnetic field change sensitivity of 2585 Hz/T and a noise-limited resolution of 210 nT/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula> Hz, under a bias magnetic field of 0.13 T. [2021-0162]

Dual-Resonator MEMS Magnetometer Based on Self-Clocking Sigma-Delta Modulation

This paper presents the design and experimental evaluation of a micromachined Lorentz force magnetometer with a dual-resonator structure, interfaced with an electromechanical sigma-delta modulation (EM- $\Sigma \Delta {\text {M}}$ ) force rebalancing control loop. The magnetometer chip comprises a matched pair of resonators on the same silicon die. The closed-loop control circuit relies on a self-oscillating architecture; the frequency of which is determined by first resonator. It is used to generate a drive current injected to the second resonator, and also generates all internal circuit clocks based on a self-clocking scheme. System level simulation indicate a signal-to-noise ratio (SNR) larger than 100dB in a bandwidth of 64Hz with a 10mT, 32Hz magnetic field input ( ${B}$ ). The system was implemented in hardware based on a dual quantization technique, which has the advantage of reduced quantization error of multi-bit quantization in a single sigma-delta modulator. Experimental results demonstrate that proposed dual-resonator magnetometer achieved a 7-fold improvement in bias instability (increasing the averaging time to reach the bias instability from 1s to 8s) and the bandwidth (BW) is increased to ~80Hz, 16-fold higher compared to an open-loop magnetometer with a single resonator. With a 1mA bias current, the output noise is less than $1\mu \text{T}/\surd $ Hz for the z-axis magnetic field.

Piezoelectric-on-Silicon MEMS Lorentz Force Lateral Field Magnetometers.

This paper describes the realization of piezoelectric-on-silicon lateral field Lorentz force magnetometers (LFMs) that target operation in ambient pressure instead of vacuum. Specifically, we describe two device topologies based on the out-of-plane resonant vibration modes. The first is based on a classic cantilever while the other is based on a corner-flapping square plate. In both topologies, piezoelectric transduction is exploited to enhance the sensitivity of the device compared to prevailing approaches to microelectromechanical system (MEMS) LFMs based on capacitive output interfaces. We show that the responsivity of the corner-flapping square plate topology (12026 ppm/T) is 8.5 times higher than a state-of-the-art lateral field LFM based on a capacitive output interface even without relying on vacuum. We here define responsivity as the output sense current per unit magnetic field density normalized over the input excitation current.

Extended Bandwidth Piezoelectric Lorentz Force Magnetometer Based on a Mechanically Coupled Beam Resonator Array

We present a piezoelectric-on-silicon Lorentz force magnetometer (LFM) based on a mechanically coupled array of clamped–clamped beam resonators for the detection of lateral ( $xy$ plane) magnetic fields with an extended operating bandwidth of 1.36 kHz. The proposed device exploits piezoelectric transduction to greatly enhance the electromechanical coupling efficiency, which benefits the device sensitivity. Coupling multiple clamped–clamped beams increases the area for piezoelectric transduction, which further increases the sensitivity. The reported device has the widest operating bandwidth among LFMs reported to date with comparable normalized sensitivity despite the quality factor being limited to 30 when operating at ambient pressure instead of vacuum as in most cases of existing LFMs.

Piezoelectric-on-silicon Lorentz force magnetometers based on radial contour mode disk resonators

In this paper, we realize two unique design topologies for Lorentz force magnetometers (LFMs) based on radial contour (RC) mode piezoelectric-on-silicon disk resonators for the detection of out-of-plane magnetic fields (i.e. normal to the plane of fabrication). The proposed topologies take advantage of the strong electromechanical coupling from the piezoelectric Aluminum Nitride (AlN) layer to enhance the sensitivity of the devices while operating under ambient pressure, thus avoiding the need for vacuum encapsulation. Compared to previously reported modes, we show that RC mode provides a higher coupling efficiency. This ultimately leads to higher responsivity (defined here as the ratio of the pre-amplified output resonant current to the external magnetic field strength, normalized over the excitation current applied) compared to other modes previously reported. Having shown the advantages of the disk LFM, we then extend the advantages of a single disk LFM by mechanically coupling two disk resonators to increase the responsivity. We show that the quality (Q) factor, which determines the responsivity at resonance, does not degrade substantially by mechanically coupling the disks. The responsivity of our coupled disk LFM (21.20 ppm/mT) is 8 times higher compared to a state of art vacuum sealed LFM based on capacitive readout, but without the contraint of requiring vacuum.

Monolithic 3-Axis MEMS Multi-Loop Magnetometer: A Performance Analysis

The work introduces the first MEMS Lorentz-force magnetometer that both includes multiple current recirculation loops and combines in a single, low-footprint ( $\mu \text{A}_{\text {rms}}$ sinewave current delivered from an MEMS-based oscillator, the sensor reaches on all axes noise levels of 100 nT/ $\surd $ Hz over a 50-Hz 3-dB bandwidth, with a full-scale range of ±7 mT and 0.1% nonlinearity. Cross-axis contributions, inherently higher than in separate-axis sensors, are linearly compensated to less than 1.5%. [2018-0056]

Fiber-optic Lorentz force magnetometer based on a gold-graphene composite membrane

Because of its outstanding mechanical and electronic properties and unique transfer flexibility, graphene is ideal for miniature all-in-fiber nanoelectromechanical systems (NEMS) in ultrasensitive sensing applications; however, its application in magnetic detection is limited because of the lack of magnetic-optic response. Here, we demonstrate a high spatial resolution fiber-optic magnetic field sensor based on Lorentz force in a pseudo–magnetic-response quasi-static graphene NEMS. The ultra-compact design of this all-fiber-based sensor is achieved by integrating a hybrid gold-graphene membrane and two gold electrodes onto the hollow endface of a single-mode fiber. An electrical current flowing through the suspended membrane in a perpendicular magnetic field can generate Lorentz force to cause a nanoscale deformation of the membrane. The sensor has a much higher spatial resolution, which is nanometer-scale longitudinally, compared with conventional optical fiber magnetic sensors.

A Lorentz force magnetometer based on a piezoelectric-on-silicon square-extensional mode micromechanical resonator

In this letter, we present a Lorentz force magnetic field sensor based on a thin-film piezoelectric-on-silicon (TPoS) CMOS-compatible resonator for the detection of an out-of-plane (perpendicular to the plane of fabrication) magnetic field. We here exploit the fundamental breathing mode of vibration in a suspended square plate, which is commonly referred to as the square-extensional (SE) mode. The symmetric stress profile of the SE mode avails stresses in the two orthogonal in-plane axes to be effectively coupled into a charge output through the piezoelectric transducers. This in turn enhances the output motional current from the device, which effectively determines the responsivity of the device. In this context, the responsivity has been defined as a ratio of output motional current to the external magnetic field, which has been further normalized against the input reference current of the device. The reported device has recorded a responsivity of 6950 ppm/T (μA/A.T) at a resonant frequency of 5.28 MHz and a reasonable mechanical quality (Q) factor of 1056 in air.

Magnetic field sensor based on coupled photonic crystal nanobeam cavities

We report the design, fabrication, and characterization of a resonant Lorentz force magnetic field sensor based on dual-coupled photonic crystal nanobeam cavities. Compared with microelectromechanical systems (MEMS) Lorentz force magnetometers, the proposed magnetic field sensor has an ultra-small footprint (less than 70 μm × 40 μm) and a wider operation bandwidth (of 160 Hz). The sensing mechanism is based on the resonance wavelength shift of a selected supermode of the coupled cavities, which is caused by the Lorentz force-induced relative displacement of the cavity nanobeams, and thus the optical transmission variation. The sensitivity and resolution of the device demonstrated experimentally are 22.9 mV/T and 48.1 μT/Hz1/2, respectively. The results can be further improved by optimizing the initial offset of the two nanobeams.

Reducing Offset and Bias Instability in Lorentz Force Magnetic Sensors Through Bias Chopping

In this paper, we describe a method for reducing offset and offset-related 1/f (flicker) noise in micromechanical resonator-based Lorentz force magnetometers by chopping the dc bias voltage applied to the resonator. This 1/f noise is shown to determine the stability of the sensor's output at long averaging times. The magnetometer is operated at a 40-Hz frequency offset from its 62.88-kHz resonant frequency. At 4.6-mA bias current, the input referred noise is 70 nT/√Hz limited by white electronic noise. Using the proposed bias chopping method, the sensor's offset is reduced from 310 to 15 μT, and the bias instability is reduced from 27 to 7 nT. The averaging time to reach the bias instability increases from 18 to 290 s as a result of chopping. The root cause of 1/f noise is demonstrated to be 1/f noise on the ac and dc bias voltages applied to the sensor. While the sensor's readout is modulated at the 62.92-kHz excitation frequency and could therefore be expected to be free from 1/f noise, the baseband 1/f noise on these voltage sources is shown to be up-converted to the excitation frequency. Up-conversion occurs through the existence of fabrication imperfections that lead to mismatches in the sensing capacitances, resistances, and parasitic feedthrough capacitances of the sensor. By chopping the bias voltage, the Lorentz force signal is separated from the offset and 1/f noise produced by these error sources. This technique is a generic method to reduce 1/f noise and bias instability in sensors based on micromechanical resonators. [2016-0184].

A Sub-400-nT/&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\sqrt {\text {Hz}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, 775-&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$\mu \text{W}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, Multi-Loop MEMS Magnetometer With Integrated Readout Electronics

This paper presents a novel ${z}$ -axis Lorentz force magnetometer coupled with a low-power readout integrated circuit. The sensor is fabricated using an industrial process, and exploits an Al-on-polysilicon multi-loop architecture that gives a five-fold sensitivity and resolution improvement, useful for off-resonance operation. The integrated readout is based on a differential charge amplifier front-end, and designed to be balanced with the sensor in terms of noise and power consumption. The overall system, including demodulation and filtering stages, shows a programmable full-scale up to ±2.4 mT, limited by the electronics saturation. The bandwidth can be programmed up to 150 Hz for off-resonance operation where a sub-400-nT/ $\sqrt {\text {Hz}}$ resolution at 775- $\mu \text{W}$ power consumption is obtained, including the integrated readout and the Lorentz current. Perspectives on low-consumption driving oscillators for off-resonance mode are finally given. [2015-0139]

Extended Bandwidth Lorentz Force Magnetometer Based on Quadrature Frequency Modulation

In this paper, a Lorentz force magnetometer demonstrates quadrature frequency modulation operation. The Lorentz force magnetometer consists of a conventional 3-port resonator, which is put into oscillation by electrostatic driving and sensing. The bias current flowing through the resonator is proportional to the displacement, and generates Lorentz force in quadrature with the electrostatic force. As a result, the Lorentz force acts as an equivalent spring and the magnetic field can be measured by reading the change in oscillation frequency. The sensor has a sensitivity of 500 Hz/T with a short-term noise floor of 500 nT $\surd $ Hz. The bandwidth of the sensor is increased to 50 Hz, a factor of 12 greater than that of the same resonator operating in amplitude-modulated mode. The short-term noise floor within 50-Hz bandwidth is comparable with CMOS Hall-effect sensors.

Force-rebalanced Lorentz force magnetometer based on a micromachined oscillator

This paper presents a 3-axis Lorentz force magnetometer based on an encapsulated micromechanical silicon resonator having three orthogonal vibration modes, each measuring one vector component of the external magnetic field. One mode, with natural frequency (fn) of 46.973 kHz and quality factor (Q) of 14 918, is operated as a closed-loop electrostatically excited oscillator to provide a frequency reference for 3-axis sensing and Lorentz force generation. Current, modulated at the reference frequency, is injected into the resonator, producing Lorentz force that is centered at the reference frequency. Lorentz force in the first axis is nulled by the oscillator loop, resulting in force-rebalanced operation. The bandwidth and scale-factor of this force-rebalanced axis are independent of resonator Q, improving the sensor's temperature coefficient from 20 841 ppm/ °C to 424 ppm/ °C. The frequencies of the other two modes are closely spaced to the first mode's reference frequency and are demonstrated to track this frequency over temperature within 1 ppm/K. Field measurements in these two axes are conducted open-loop and off-resonance, ensuring that the scale-factor is independent of Q to first order and producing a measurement bandwidth of over 40 Hz.

Frequency-Modulated Lorentz Force Magnetometer With Enhanced Sensitivity via Mechanical Amplification

This letter presents a micromachined silicon Lorentz force magnetometer, which consists of a flexural beam resonator coupled to current-carrying silicon beams via a microleverage mechanism. The flexural beam resonator is a force sensor, which measures the magnetic field through resonant frequency shift induced by the Lorentz force, which acts as an axial load. Previous frequency-modulated Lorentz force magnetometers suffer from low sensitivity, limited by both fabrication restrictions and lack of a force amplification mechanism. In this letter, the microleverage mechanism amplifies the Lorentz force, thereby enhancing the sensitivity of the magnetometer by a factor of 42. The device has a measured sensitivity of 6687 ppm/(mA $\cdot $ T), which is two orders of magnitude larger than the prior state-of-the-art. The measured results agree with an analytical model and finite-element analysis. The frequency stability of the sensor is limited by the quality factor ( ${Q}$ ) of 540, which can be increased through improved vacuum packaging.

Sensitivity Enhancement of Lorentz Force MEMS Resonant Magnetometers via Internal Thermal-Piezoresistive Amplification

This letter presents sensitivity enhancement of MEMS resonant magnetometers using the thermal-piezoresistive internal amplification effect in silicon microstructures. Preliminary results show up to ~15 X improvement in sensitivity per bias current for a resonator operated as a Lorentz force magnetometer. Magnetometer sensitivity figure-of-merit, defined as sensitivity (mV/T) over sensor dc bias current, has increased from 0.29 Ω/T(mV/Tesla/mA) to 4.22 Ω/T via internal thermal-piezoresistive amplification that also led to resonator effective quality factor (Q) increasing from its intrinsic value of 1140 to 16900 (in air). Previous work on the thermal-piezoresistive amplification effect suggests that amplification factors up to 3-4 orders of magnitude can be achieved using optimally designed structures, which can lead to ultra-high sensitivities for the presented sensors. It should be noted that the main focus of this letter is not to demonstrate a highly sensitive magnetometer, but rather to demonstrate the ability to improve magnetometer sensitivity as the resonator internal Q-amplification kicks-in. Although the resonant structure in this letter has not been optimized to operate as a magnetometer, sensitivities as high as 262 mV/T in air (minimum detectable field in the μT range) have been achieved.

Operation of Lorentz-Force MEMS Magnetometers With a Frequency Offset Between Driving Current and Mechanical Resonance

The paper discusses the operation of Lorentz-force-based microelectromechanical magnetometers at a driving-current frequency slightly lower than the device resonance frequency. Among the advantages with respect to operation at resonance, there are a higher achievable signal to noise ratio (thanks to the lower permitted pressure and damping coefficient, which have now no influence on the maximum sensing bandwidth) and the possibility of driving more magnetometers in series through a single current source, enabling the fabrication of low-power 3-axis magnetic field sensors. A partial drawback is represented by a loss in gain-factor. Experimental results obtained on a sample device confirm the trade-off between gain-factor decrease and bandwidth increase. Guidelines for an optimized design of Lorentz force magnetometers are given together with a comparison with other state-of-the-art technologies through the introduction of a figure of merit. In particular, it is shown how Lorentz force devices can reach better performance in terms of minimum detectable magnetic flux density per unit current consumption and bandwidth.

Area-Efficient Three Axis MEMS Lorentz Force Magnetometer

A micro-electromechanical-systems (MEMS) three-axis Lorentz force magnetometer based on a 0.24 × 0.4 mm2 MEMS resonator that is the smallest Lorentz force sensor reported to date is presented in this paper. A magnetic field can be detected in two axes using a single MEMS structure. Placing two structures perpendicular to each other in a single die makes three-axis sensing possible. Sensing is performed by exciting the MEMS resonator at its in-plane and out-of-plane mechanical resonant frequencies of 40.5 and 107.4 kHz, respectively. A modest die-level vacuum packaging results in in-plane and out-of-plane mechanical quality factors of 110 and 310, respectively. The sensor has a bandwidth of 184 Hz for z-axis and 189 Hz for x/y-axis magnetic field. With an excitation power of 2 mW, the sensor resolution is 285 nT/√Hz for z-axis magnetic field inputs and 344 nT/√Hz for x/y-axis magnetic field inputs. The resolution is limited by Brownian noise in the z-axis whereas the x/y-axis resolution is limited by electronic noise. With an averaging time of 288 s, the sensor shows an offset stability of 23 nT.