Dichromatic reflectance model

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Introduction

Magnetic field sensing can be categorized into four general types[1] depending on the magnitude of the measured field. If the targeted B-field is larger than the earth magnetic field (maximum value around 60 μT), the requirement on the sensitivity of the sensor is not aggressive. To measure the earth field larger than the geomagnetic noise(around 0.1 nT), better sensors are required. For the application of magnetic anomaly detection, sensors at different spots have to be used to cancel the spatial-correlated noise in order to achieve a better spatial resolution. To measure the field below the geomagnetic noise, much more sensitive magnetic field sensors have to be employed. These sensors are mainly used in medical and biomedical applications, such as MRI, molecule tagging and etc.

There are many approaches for magnetic sensing, including Hall effect sensor, magneto-diode, magneto-transistor, AMR magnetometer, GMR magnetometer, magnetic tunnel junction magnetometer, magneto-optical sensor, Lorentz force based MEMS sensor, Electron Tunneling based MEMS sensor, MEMS compass, Nuclear precession magnetic field sensor, optically pumped magnetic field sensor, fluxgate magnetometer, search coil magnetic field sensor and SQUID magnetometer. MEMS-based magnetic field sensor can offer small-size solution for magnetic field sensing. Smaller device can be placed closer to the measurement spots and thereby achieving higher spatial resolution. Additionally, MEMS magnetic field sensor does not involve the microfabrication of magnetic material. Therefore, the cost of the sensor can be largely reduced. Integration of MEMS sensor and microelectronics can further reduce the size of the entire magnetic field sensing system.

Lorentz-force-based MEMS sensor

This type sensor relies on the mechanical motion of the MEMS structure due to the Lorentz force acting on the current-carrying conductor in the magnetic field. The mechanical motion of the micro-structure is sensed either electronically or optically. The mechanical structure is often driven to its resonance in order to obtain the maximum output signal. Piezoresistive and electrostatic transduction method can be used in the electronic detection. Displacement measurement with laser source or LED source can also be used in the optical detection. Several sensors will be discussed in the following subsections in terms of different output for the sensor.

Voltage sensing

Beroulle et al.[2] have fabricated a U-shape cantilever beam on silicon substrate. Two piezo-resistors are laid on the support ends. There are 80-turns Al coil passing current along the U-shape beam. Wheatstone bridge is formed by connecting two "active" resistor with another two "passive" resistor free of strain. When there is an external magnetic field applying to the current carry conductor, motion of the U-shape beam will induce strain in two "active" piezo-resistors and thereby generating an output voltage across the Wheatstone bridge which is proportional to the magnetic field flux density. The reported sensitivity for this sensor is 530 m Vrms/T with a resolution 2 µT. Note that the frequency of the exciting current is set to be equal to the resonant frequency of the U-shape beam in order to maximize the sensitivity.

Herrera-May et al.[3] fabricate a sensor with similar piezoresitive read-out approach but with different mechanical motion. Their sensor relies on the torsional motion of a micro-plate fabricated from silicon substrate. The exciting current loop contains 8 turns of aluminum coil. The location of the current loop enables a more uniform Lorentz force distribution compared with the aforementioned U-shape cantilever beam. The reported sensitivity is 403 mVrms/T with a resolution 143 nT.

Kádár et al.[4] also chose the micro-torsional beam as the mechanical structure. Their read-out approach is different. Instead of using piezoresitive transduction, their sensor relies on electrostatic transduction. They patterned several electrodes on the surface of the micro-plate and another external glass wafer. The glass wafer is then boned with the silicon substrate to form a variable capacitor array. Lorentz force generated by the external magnetic field will results in the change of capacitor array. The reported sensitivity is 500 Vrms/T with a resolution of a few mT. The resolution can reach 1 nT with vacuum operation.

Emmerich et al.[5] fabricated the variable capacitor array on a single silicon substrate with comb-figure structure. The reported sensitivity is 820 Vrms/T with a resolution 200 nT at the pressure level of 1mbar.

Frequency shift sensing

Another type of Lorentz force based MEMS magnetic field sensor utilize the shift of mechanical resonance due to the Lorentz force applying to certain mechanical structures.

Sunier et al.[6] change the structure of aforementioned U-shape cantilever beam by adding a curved-in support. The piezoresistive sensing bridge is laid between two heating actuation resistors. Frequency response of the output voltage of the sensing bridge is measured to determine the resonant frequency of the structure. Note that in this sensor, the current flowing through the Aluminum coil is dc current. The mechanical structure is actually driven by the heating resistor at its resonance. Lorentz force applying at the U-shape beam will change the resonant frequency of the beam and thereby change the frequency response of the output voltage. The reported sensitivity is 60 kHz/T with a resolution of 1 µT.

Bahreyni et al.[7] fabricated a comb figure structure on top of the silicon substrate. The center shuttle are connected to two clamped-clamped conductors used to change the internal stress of the moving structure when external magnetic field is applied. This will induce the change of the resonant frequency of the comb finger structure. This sensor use electrostatic transduction to measure the output signal. The reported sensitivity is improved to 69.6 Hz/T thanks to the high mechanical quality factor (Q = 15000 @ 2 Pa) structure in the vacuum environment. The reported resolution is 217 nT.

Optical sensing

The optical sensing is to directly measure the mechanical displacement of the MEMS structure to find the external magnetic field.

Zanetti et al.[8] fabricated a Xylophone beam. Current is flowing through the center conductor and the Xylophone beam will be deflected as the Lorentz force is induced. Direct mechanical displacement is measured by an external laser source and a detector. The resolution of 1 nT can be reached. Wickenden[9] had tried to shrink the footprint of this type of device by 100 times. But a much lower resolution of 150 µT was reported.

Keplinger et al.[10][11] were trying to use an LED source for optical sensing instead of using an external laser source. Optical fibers were aligned on the silicon substrate with different arrangements for the displacement sensing. A resolution 10 mT is reported.

== When the temperature increases, the Young’s modulus of the material used to fabricate the moving structure decreases. This will leads to the softening of the moving structure. Meanwhile, thermal expansion and thermal conductivity will increase with the temperature inducing an internal stress in the moving structure. These effects can result in the shift of the resonant frequency of the moving structure which is equivalent noise for resonant frequency shift sensing and the voltage sensing as well. In addition, temperature rise will generate larger Johnson noise (affect the piezoresitive transduction) and also large mechanical fluctuation noise (affect the optical sensing). Therefore, advanced electronics for temperature effect compensation have to be used to improve the sensitivity.

References

  1. ↑ Lenz, J., Edelstein, A.S., "Magnetic sensors and their applications." IEEE Sensors J. 2006, 6, 631-649.
  2. ↑ Beroulle, V.; Bertrand, Y.; Latorre, L.; Nouet, P. Monolithic Piezoresistive CMOS magnetic field sensors. Sens. Actuators A 2003, 103, 23-32
  3. ↑ Herrera-May, A.L.; García-Ramírez, P.J.; Aguilera-Cortés, L.A.; Martínez-Castillo, J.; Sauceda-Carvajal, A.; García-González, L.; Figueras-Costa, E. A resonant magnetic field microsensor with high quality factor at atmospheric pressure. J. Micromech. Microeng. 2009, 19, 015016.
  4. ↑ Kádár, Z.; Bossche, A.; Sarro, P.M.; Mollinger, J.R. Magnetic-field measurements using an integrated resonant magnetic-field sensor. Sens. Actuators A 1998, 70, 225-232.
  5. ↑ Emmerich, H.; Schöfthaler, M. Magnetic field measurements with a novel surface micromachined magnetic-field sensor. IEEE Tans. Electron Dev. 2000, 47, 972-977.
  6. ↑ Sunier, R.; Vancura, T.; Li, Y.; Kay-Uwe, K.; Baltes, H.; Brand, O. Resonant magnetic field sensor with frequency output. J. Microelectromech. Syst. 2006, 15, 1098-1107.
  7. ↑ Bahreyni, B.; Shafai, C. A resonant micromachined magnetic field sensor. IEEE Sensor J. 2007, 7, 1326-1334.
  8. ↑ Zanetti, L.J.; Potemra, T.A.; Oursler, D.A.; Lohr, D.A.; Anderson, B.J.; Givens, R.B.; Wickenden, D.K.; Osiander, R.; Kistenmacher, T.J.; Jenkins, R.E. Miniature magnetic field sensors based on xylophone resonators. In Science Closure and Enabling Technologies for Constellation Class Missions; Angelopoulos, V., Panetta, P.V., Eds.; University of California: Berkeley, CA, USA, 1998; pp. 149-151.
  9. ↑ Wickenden, D.K.; Champion, J.L.; Osiander, R.; Givens, R.B.; Lamb, J.L.; Miragliotta, J.A.; Oursler, D.A.; Kistenmacher, T.J. Micromachined polysilicon resonating xylophone bar magnetometer. Acta Astronautica 2003, 52, 421-425.
  10. ↑ Keplinger, F.; Kvasnica, S.; Hauser, H.; Grössinger, R. Optical readouts of cantilever bending designed for high magnetic field application. IEEE Trans. Magn. 2003, 39, 3304-3306.
  11. ↑ Keplinger, F.; Kvasnica, S.; Jachimowicz, A.; Kohl, F.; Steurer, J.; Hauser, H. Lorentz force based magnetic field sensor with optical readout. Sens. Actuators A 2004, 110, 12-118.
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