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This paper reports a MEMS gradiometer consisting of two independent, laterally oscillating masses on a single chip with integrated optical readout featuring a responsitivity of 35V/T at resonant operation. The symmetrical design of the two masses offers high accuracy and low cost by using conventional MEMS batch fabrication technology. The sensing principle is based on lateral displacement of the masses actuated by Lorentz forces which modulates a light flux passing through a stationary mask and the moving mask integrated in the masses. Phase and intensity detected by photodiodes reveal information about the uniformity of an external applied magnetic field, hence, enables the measurement of gradient-, homogeneous- and offset gradient magnetic fields.

This paper reports on a novel, miniaturized magnetomechanical transducer/sensor made of borosilicate glass with wide dynamic range. The prototype is manufactured with laser micromachining and ablation techniques. Compared to state of the art, borosilicate glass substrate offers the highest thermal shock resistance and is best suited for MEMS magnetometers, for aerospace and space applications or magnetic monitoring systems for diagnostics and plasma stability control of nuclear fusion experiments, where thermal shock resistance is a critical requirement.

This paper reports on a MEMS gradiometer consisting of two independent laterally oscillating masses on a single chip with integrated optical readout. The symmetrical design of the two masses offers high accuracy and low cost by using conventional MEMS batch fabrication technology. The sensing principle is based on laterally displacement of the masses actuated by Lorentz forces which modulates a light flux passing through a stationary mask and the moving mask integrated in the masses. Phase and intensity detected by photodiodes reveals information about the uniformity of an external applied magnetic field, hence, enables the measurement of gradient-, homogeneous-and offset zradient maanetic fields. A quadrupol magnetic field created from four identical neodymium bar magnets had been characterised to demonstrate the sensor's working principle.

This contribution describes a novel magnetic field transducer based on a MOEMS (micro-opto-electo-mechanical-system) readout. The silicon structure is deflected in a static magnetic field due to the Lorentz force This deflection is measured with the mechano-optical transducer [1] . The transduction method is based on the modulation of a perpendicularly introduced light flux. The modulation is achieved by one movable optical grating on a suspended structure and a second grating that is fixed to the foundation of the system. The proof-of-concept device was characterized at ambient pressure exhibiting a sensitivity of 200 mV/T. The noise equivalent magnetic resolution limit is 1.5 μT/√Hz which results mainly from the opto-electrical evaluation circuit. By introducing advanced opto-electronics and using improved MEMS devices it is feasible to reduce this value down to 1 nT/√Hz which is equivalent to the fundamental mechanical Brownian noise limit.

Accurate knowledge of the spatial magnetic field distribution is necessary when measuring field gradients. Therefore, a MEMS magnetic field gradiometer is reported, consisting of two identical, but independent laterally oscillating masses on a single chip. The sensor is actuated by Lorentz force and read out by modulation of the light flux passing through stationary and moving arrays of the chip. This optical readout decouples the transducer from the electronic components. Both phase and intensity are recorded which reveals information about the uniformity of the magnetic field. The magnetic flux density is measured simultaneously at two points in space and the field gradient is evaluated locally. The sensor was characterised at ambient pressure by performing frequency and magnitude response measurements with coil and various different permanent magnet arrangements, resulting in a responsivity of 35.67 V/T and detection limit of 3.07 &micro, T/ Hz (@ 83 Hz ENBW). The sensor is compact, offers a large dynamic measurement range and can be of low-cost by using conventional MEMS batch fabrication technology.

This paper presents a magnetic field sensor with capacitive read-out, whose active element is a micromachined mechanical resonator. The MEMS magnetic field sensor exploits the Lorentz force to detect external magnetic flux density through the displacement of the resonant structure, which can be measured with optical and capacitive sensing techniques. The micromachined U-shaped cantilever features a length of 2 mm, a base width of 90 μm and a thickness of 20 μm, and is manufactured in SOI technology. The designed sensor has a measured resonant frequency of 4.359 kHz for the fundamental mode and a calculated mass of the flexible structure of 24.5 ng. A quality factor in the order of 104 at an ambient pressure of 0.3 Pa has been measured where a magnetic field resolution of 15 nT can be achieved. Although these arrangements are well suited to capacitively sense the vibrations caused by the Lorentz force on the current lead on the silicon part, care has to be taken to avoid undesired mutual interferences. A serious interference was observed in case of a DC bias voltage at the readout capacitance and a significant voltage drop caused by the current needed for the generation of the Lorentz force. This work investigates in detail this phenomenon as well as the complete physical transduction chain and improves the understanding of such microelectromechanical systems significantly. An analytical model of the electrostatic system is established including all relevant components and their interactions as well as the motion of the MEMS part. The importance of electrostatic back-action for a feasible detection limit for magnetic fields was recognized for the first time.

We present a novel design of a resonant magnetic field sensor with capacitive read-out permitting wafer level production. The device consists of a single-crystal silicon cantilever manufactured from the device layer of an SOI wafer. Cantilevers represent a very simple structure with respect to manufacturing and function. On the top of the structure, a gold lead carries AC currents that generate alternating Lorentz forces in an external magnetic field. The free end oscillation of the actuated cantilever depends on the eigenfrequencies of the structure. Particularly, the specific design of a U-shaped structure provides a larger force-to-stiffness-ratio than standard cantilevers. The electrodes for detecting cantilever deflections are separately fabricated on a Pyrex glass-wafer. They form the counterpart to the lead on the freely vibrating planar structure. Both wafers are mounted on top of each other. A custom SU-8 bonding process on wafer level creates a gap which defines the equilibrium distance between sensing electrodes and the vibrating structure. Additionally to the capacitive read-out, the cantilever oscillation was simultaneously measured with laser Doppler vibrometry through proper windows in the SOI handle wafer. Advantages and disadvantages of the asynchronous capacitive measurement configuration are discussed quantitatively and presented by a comprehensive experimental characterization of the device under test.

A Lorentz-force actuated cantilever used as a magnetometer detecting alternating magnetic fields (AMF) is described. The device consists of a U-shaped single-crystal silicon cantilever manufactured in SOI technology. This micromachined cantilever features a length of 2mm, a base width of 90μm, and a thickness of 20μm, whereat the two 2mm cantilevers are hold together by a 1.5mm long bar at the free moving ends. The cantilever is placed in a vacuum chamber surrounded by a pair of coils configured as Helmholtz coil which generates the alternating magnetic field. The test structures are harmonically excited by the Lorentz force acting on the gold lead at the top surface of the cantilever carrying an alternating current. In the presence of a sinusoidal magnetic flux density, the resulting Lorentz force contains two alternating terms including the sum and difference of current and field frequencies. Therefore, the resonating cantilever is used as mixer in a heterodyne detector for alternating magnetic fields with variable frequency. Resonant excitation only occurs if one of these frequencies is close to a mechanical resonance that satisfies the selection rule imposed by the field configuration. In the experiments, emphasis is laid on the investigation of the first symmetric and first antisymmetric vibration mode, where the amplitude of the vibration is proportional to the exciting vector component of the magnetic field. For this work the harmonic deflection of the cantilever was measured with a capacitive readout system and additionally, with a laser-Doppler vibrometer. By changing the drive current, the operating range of the magnetometer can be varied from a few μT up to 1mT, whereas the sensitivity remains constant with an uncertainty of less than one percent, valid for both vibration modes. This operation principle of the prototype allows a further miniaturization leading to a spatial resolution of the magnetic field detection determined by the size of the cantilever.

We present a study of the damping behavior of monocrystalline silicon cantilevers in different rarefied gas regimes. Mechanical quality factors Q were analyzed at controlled ambient pressures in the range of 0.01 Pa to 100 Pa. Emphasis was laid on the investigation of the fundamental vibration mode. Hence, the test structures were harmonically excited by the Lorentz force acting on the current carrying lead attached to the top surface of the cantilever. The micromachined clamped-free cantilevers featuring a length of 2 mm, a width of 1.5 mm and a thickness of 20 μm, were manufactured in SOI technology. The experimental results were compared with existing theories revealing an underestimate of the damping parameter for the Knudsen range Kn = 0.1 to 10. So far, squeeze-film damping by free molecular flow and kinetic damping were taken into account in damping models for the quasi-molecular regime. However, our measurements indicate that also the ongoing molecular flow around the test structures has to be considered. Hence the damping coefficient has to be calculated with methods of the free molecular aerodynamics. Thus, we used an algorithm based on the random walk model that allows the usage of already available knowledge in the field of Direct Simulation Monte Carlo. With this approach the quality factor of a squeezed-film damped cantilever in the quasi-molecular regime was derived. The results were compared with the most recent stochastic model, where the theoretical predictions and the experimental investigations indicate significant squeezing up to a Knudsen number of 10. In a superposition of both damping mechanisms, kinetic and squeeze-film damping, a satisfactory characterization of the damping behavior of an oscillating cantilever in the quasi-molecular regime with Knudsen numbers in the range of 10 down to 0.02 was achieved.