**2. Resonant magnetic sensors**

Resonant sensors exploit Lorentz force of resonating micromachined structures. These sensors can detect magnetic fields up 1 mT with a resolution down to 1 nT. Such devices are normally based on MEMS technologies, are small in size (order of millimetres), and promise all the advantages related to the employment of fabrication microtechnologies including multifuntionalities and integration of mechanical and electronic components on a single chip.

Resonant magnetic field sensors use resonant structures that are excited at their resonant frequencies by Lorentz forces. Such devices are able to give an amplified response if excited at frequencies equal to the resonant frequencies or vibrational modes of the structures (Bahreyni, 2008).

These structures commonly consist of clamped-free beams or clamped-clamped beams or torsion/flexion plates. In figure 1 it is shown a schematic diagram of the Lorentz force principle acting on a clamped-clamped beam resonant structure. This device can be designed for example to resonate to its first resonant frequency, associated to its first flexural vibration mode. This beam, exposed to an excitation source with a frequency equal to its first resonant frequency, will have a maximum deflection at its midpoint. In order to excite the device a metallic loop is placed on the clamped-clamped beam surface where an excitation current (I) flows inside it with a frequency equal to the first resonance frequency. When the beam is exposed to an external magnetic field (Bx) in the x-direction, then a Lorentz force (FL) is generated.

Fig. 1. Schematic diagram of the Lorentz force principle acting on a clamped-clamped beam.

This force can be determined as:

104 Magnetic Sensors – Principles and Applications

Magnetic field sensors based on MEMS technology, depending on their operation principle and magnetic range, have a great potential for numerous applications in several fields spanning from vehicle detection and control to mineral prospecting and metal detection as

This paper aims at the description of current research status in magnetic field sensors focusing on devices fabricated by exploiting MEMS technologies. The paper presents advances in the classes of devices that take advantage from these technologies to scale down

Resonant sensors exploit Lorentz force principle on micromachined structures excited at one of their resonating modes. These sensors can detect magnetic fields with sensitivity up to 1 T

Fluxgate sensors are inductively working sensors consisting of excitation and sensing coils around a ferromagnetic core. Such sensors can detect static and low frequency magnetic

Hall sensors are based on Hall effect transduction principle and measure either constant or

Following the introduction, the paper is organized as follows. The second section, is devoted to the resonant sensors, including the Lorentz force operation principle, examples of realized devices reported in the literature with an highlight on the employed technologies for the fabrication. Third section is focused on fluxgate microsensors including operation principle, state of the art and involved fabrication technologies. Fourth section is dedicated to the description of the Hall effect and Hall magnetic sensors employing MEMS technologies are reported. The fifth section describes the possible applications of this new class of compact devices. Finally in the section sixth the paper ends with the conclusion.

Resonant sensors exploit Lorentz force of resonating micromachined structures. These sensors can detect magnetic fields up 1 mT with a resolution down to 1 nT. Such devices are normally based on MEMS technologies, are small in size (order of millimetres), and promise all the advantages related to the employment of fabrication microtechnologies including multifuntionalities and integration of mechanical and electronic components on a

Resonant magnetic field sensors use resonant structures that are excited at their resonant frequencies by Lorentz forces. Such devices are able to give an amplified response if excited at frequencies equal to the resonant frequencies or vibrational modes of the structures

These structures commonly consist of clamped-free beams or clamped-clamped beams or torsion/flexion plates. In figure 1 it is shown a schematic diagram of the Lorentz force principle acting on a clamped-clamped beam resonant structure. This device can be designed for example to resonate to its first resonant frequency, associated to its first flexural vibration mode. This beam, exposed to an excitation source with a frequency equal to its first resonant frequency, will have a maximum deflection at its midpoint. In order to

varying magnetic field. They have a magnetic field sensitivity range from 1T to 1T.

magnetic sensors size, namely resonant sensors, fluxgate sensors and Hall sensors.

fields up to approximately 1 mT with a maximum resolution of 100 pT.

well as to non-distructive testing and medical diagnostics.

and a maximum achievable resolution of 1 nT.

**2. Resonant magnetic sensors** 

single chip.

(Bahreyni, 2008).

$$F\_L = IB\_x L\_y \tag{1}$$

where the flowing current can be expressed as:

$$I = \sqrt{2}I\_{rms}\sin\left(2\pi ft\right)\tag{2}$$

where Ly is the length of the metallic loop perpendicular to the magnetic field, Irms is the root mean square of the current I, f is the frequency and t is the time.

The Lorentz force acts as an excitation source on the clamped-clamped beam, causing an amplified deflection on the midpoint. Thus, the magnitude of the beam deflection depends on the Lorentz force amplitude, which is directly proportional to I and Bx.

The application of an external magnetic field alters deflection/torsion of resonating structures with different shapes that is detected by exploiting different readout techniques.

In fact such deflections/torsions result in strain which is related to the elastic modulus of the structure material, to the geometrical characteristics of the resonating structures and to the quality factor (Herrera-May et al. 2010).

The quality factor is an important parameter of the resonant structures. It defines the bandwidth of the resonator relatively to its central resonant frequency or equivalently it expresses the maximum amplitude of the bending structure taking into account the different damping sources (Elwenspoek & Wiegerink, 2001, Beeby et al., 2004). High quality factors involve better device performance, better resolution and improved insensitivity to the disturbances (Beeby et al., 2004).

Another parameter of interest in resonant structures is the resonance frequency. Its determination can be obtained by using both analytical models and simulation tools and

Magnetic Field Sensors Based on Microelectromechanical Systems (MEMS) Technology 107

Finally, the SOI layer is etched by reactive ion etching (figure 2(f)) to define the plate-beam

Figure 3 shows a schematic design of the resonant magnetic field microsensor reported by Herrera-May et al. (2009) with an highlight on the plate-beam structure and its working

Fig. 3. Schematic design of resonant magnetic field microsensor (left) and highlight on the plate-beam structure and its working principle (right) reported by Herrera-May et al. (2009).

One of the main elements of this sensor is the aluminum rectangular loop deposited on the silicon plate. The Lorentz force causes a seesaw motion on the microplate and the bending of microbeams. Four piezoresistors (p-type) are connected in a Wheatstone bridge and two of these are active piezoresistors located on the microbeams. The Lorentz force originates a longitudinal strain on the two active piezoresistors changing their resistance. The change in the resistance of the active piezoresistors produces an output voltage shift of the Wheatstone

This sensor has a resonant frequency of 136.52 kHz, a quality factor of 842 at ambient pressure, a sensitivity of 0.403 μVμT-1, a resolution of 143 nT with a frequency variation of 1 Hz, and power consumption below 10 mW. However, the sensor registered an offset and

Tapia et al. (2011) reported on a piezoresistive resonant magnetic microsensor with seesaw rectangular loop of beams reinforced with transversal and longitudinal beams. This device was designed to be compact and to have high resolution for neurobiological applications. Characteristics of this microsensor are a resonant frequency of 13.87 kHz with a quality factor of 93, a resolution of 80 nT, a sensitivity of 1.2 VT-1 and a power consumption of 2.05

Other examples of piezoresistive magnetic sensors on the microscale have been reported in

Among the resonant magnetic sensors, there are some of them exploiting the optical

mW at ambient pressure. This sensor requires a simple signal processing circuit.

linearity problems in the low magnetic field range.

the literature (Beroulle et al. (2003), Sunier et al. (2006)).

structure.

principle.

bridge.

detection.

depends on elastic modulus, density, deflection and geometrical features of the resonant structure.

Moreover resonance frequencies are affected by residual stresses on the structure (Weaver et al. 1990). For example thermal stresses inside resonant devices (Hull, 1999) causes strains in the structures which in turn involve (Sabaté et al., 2007) a shift of the resonant frequency of the structures.

Such sensors are typically fabricated in silicon and polysilicon and main disadvantage of this technology is the resonance frequency shift due to temperature changes and environmental pressure which requires compensation electronic circuits and packaging under vacuum respectively.

To detect deflection of resonant structures different readout techniques have been used including the employment of piezoresistive, optical or capacitive techniques.

Piezoresistive sensing exploits changes in the resistance of piezoresistive elements placed in the hinges of the resonant structure, to detect changes in the output voltage signal as effect of strains originating from motions of beams or plates due to the Lorentz force.

Herrera-May et al. (2009) reported on a magnetic field microsensor based on a silicon resonant microplate (400 × 150 × 15 m3) and four bending microbeams (130 × 12 × 15 m3).

Figure 2 shows a schematic diagram of the fabrication process of the device.

The fabrication process is based on bulk micromachining technology on (100) 4" silicon-oninsulator (SOI) wafers. The process starts by growing a thin thermal oxide layer and depositing a silicon nitride layer on a SOI n-type substrate. The nitride layer is removed from the front side of the wafer and is patterned on the backside (figure 2(a)). Using a second mask, boron is implanted to create four p-type piezoresistors (figure 2(b)). A 1 μmthick oxide layer is then grown and patterned. The area contacts (120 × 120 μm2) are opened (figure 3(c)) and then an aluminum layer is deposited and patterned to define metallic lines and pads (figure 4(d)). At this time the silicon substrate is etched from the backside using KOH that stops at the SOI buried oxide (figure 2(e)), which is then removed.

Fig. 2. Schematic diagram of the fabrication process of a piezoresistive resonant magnetic sensor reported by Herrera-May et al. (2009)

depends on elastic modulus, density, deflection and geometrical features of the resonant

Moreover resonance frequencies are affected by residual stresses on the structure (Weaver et al. 1990). For example thermal stresses inside resonant devices (Hull, 1999) causes strains in the structures which in turn involve (Sabaté et al., 2007) a shift of the resonant frequency of

Such sensors are typically fabricated in silicon and polysilicon and main disadvantage of this technology is the resonance frequency shift due to temperature changes and environmental pressure which requires compensation electronic circuits and packaging

To detect deflection of resonant structures different readout techniques have been used

Piezoresistive sensing exploits changes in the resistance of piezoresistive elements placed in the hinges of the resonant structure, to detect changes in the output voltage signal as effect

Herrera-May et al. (2009) reported on a magnetic field microsensor based on a silicon resonant microplate (400 × 150 × 15 m3) and four bending microbeams (130 × 12 × 15 m3).

The fabrication process is based on bulk micromachining technology on (100) 4" silicon-oninsulator (SOI) wafers. The process starts by growing a thin thermal oxide layer and depositing a silicon nitride layer on a SOI n-type substrate. The nitride layer is removed from the front side of the wafer and is patterned on the backside (figure 2(a)). Using a second mask, boron is implanted to create four p-type piezoresistors (figure 2(b)). A 1 μmthick oxide layer is then grown and patterned. The area contacts (120 × 120 μm2) are opened (figure 3(c)) and then an aluminum layer is deposited and patterned to define metallic lines and pads (figure 4(d)). At this time the silicon substrate is etched from the backside using

Fig. 2. Schematic diagram of the fabrication process of a piezoresistive resonant magnetic

sensor reported by Herrera-May et al. (2009)

including the employment of piezoresistive, optical or capacitive techniques.

of strains originating from motions of beams or plates due to the Lorentz force.

Figure 2 shows a schematic diagram of the fabrication process of the device.

KOH that stops at the SOI buried oxide (figure 2(e)), which is then removed.

structure.

the structures.

under vacuum respectively.

Finally, the SOI layer is etched by reactive ion etching (figure 2(f)) to define the plate-beam structure.

Figure 3 shows a schematic design of the resonant magnetic field microsensor reported by Herrera-May et al. (2009) with an highlight on the plate-beam structure and its working principle.

Fig. 3. Schematic design of resonant magnetic field microsensor (left) and highlight on the plate-beam structure and its working principle (right) reported by Herrera-May et al. (2009).

One of the main elements of this sensor is the aluminum rectangular loop deposited on the silicon plate. The Lorentz force causes a seesaw motion on the microplate and the bending of microbeams. Four piezoresistors (p-type) are connected in a Wheatstone bridge and two of these are active piezoresistors located on the microbeams. The Lorentz force originates a longitudinal strain on the two active piezoresistors changing their resistance. The change in the resistance of the active piezoresistors produces an output voltage shift of the Wheatstone bridge.

This sensor has a resonant frequency of 136.52 kHz, a quality factor of 842 at ambient pressure, a sensitivity of 0.403 μVμT-1, a resolution of 143 nT with a frequency variation of 1 Hz, and power consumption below 10 mW. However, the sensor registered an offset and linearity problems in the low magnetic field range.

Tapia et al. (2011) reported on a piezoresistive resonant magnetic microsensor with seesaw rectangular loop of beams reinforced with transversal and longitudinal beams. This device was designed to be compact and to have high resolution for neurobiological applications. Characteristics of this microsensor are a resonant frequency of 13.87 kHz with a quality factor of 93, a resolution of 80 nT, a sensitivity of 1.2 VT-1 and a power consumption of 2.05 mW at ambient pressure. This sensor requires a simple signal processing circuit.

Other examples of piezoresistive magnetic sensors on the microscale have been reported in the literature (Beroulle et al. (2003), Sunier et al. (2006)).

Among the resonant magnetic sensors, there are some of them exploiting the optical detection.

Magnetic Field Sensors Based on Microelectromechanical Systems (MEMS) Technology 109

packaging to increase its performance. For a pressure of 10 Pa and 150 mV driving voltage amplitude, the microsensor has a resolution of 30 nT in the linear range from 3 T to 30 µT, a sensitivity of 481 mVT-1, a resonant frequency close to 1380 Hz, and a quality factor around

Fig. 5. Schematic design of the resonant magnetic sensor exploiting the capacitive sensing

Brugger et al. (2009) reported on a complex magnetic field sensor with a size of 7.5 mm 3.2 mm, consisting of an electrostatically driven silicon resonator characterized by interdigitated combs for electrostatic excitation and capacitive detection, an amorphous magnetic concentrator and a pair of planar coils. It requires a complex fabrication process combining MEMS technology based on a silicon-on-insulator (SOI) substrate, the epoxyresin-based attachment of a thin amorphous magnetic ribbon structured by wet chemical etching, micropatterning of the magnetic concentrator by UV-laser and vacuum packaging.. For a coil current of ±120 mA, the device offers a sensitivity of 1.91 MHzT-1 and a resolution of 1.3 μT. Under a pressure of 10-5 mbar, this microsensor presents a sensitivity of 1 MHzT-1, a resolution of 400 nT, and a quality factor around 2400. It does not need a complex

J. Kyynäräinen et .al. (2008) reported on resonant micromechanical magnetometers based on capacitive detection for 3D electronic compasses. The sensors has been fabricated by exploiting aligned direct bonding of a double side polished silicon wafer and a SOI wafer. Devices operated in vacuum to reach high enough Q values. Magnetometers measuring the field component along the chip surface have a flux density resolution of about 10 nT/√Hz at a coil current of 100 A. Magnetometers measuring the field component perpendicular to the chip surface are currently less sensitive with a flux density resolution of about

There are in the literature other works reporting on capacitive sensing-based resonant

magnetic sensors (Emmerich et al. (2000), Kádár et al. (1998), Tucker et al. (2000)).

2500. Nevertheless, it presented a non-linear response from 0 to 3 µT.

and reported by Ren et al. (2009).

feedback and modulation electronics.

70 nT/√Hz.

Keplinger et al. (2004) reported a resonant magnetic field sensor using U-shaped silicon microbeams and an optical readout system. Figure 4 shows a schematic sketch of the device reported by these authors.

Fig. 4. Schematic sketch of the resonant magnetic sensor with optical readout reported by Keplinger et al. (2004).

Devices are processed by both surface micromachining and bulk micromachining techniques. The etching process has been also used to form the groove for the optical fibers. The microbeams contain a gold loop with a thickness of 500 nm. A magnetic field and an ac electrical current generate a Lorentz force, which bends the microbeams. These deflections are measured by optical sensing using an arrangement consisting of two fibers to avoid interference of reflected light. Figure 4 shows a design, in which the emitted light beam is reflected only once at the microbeam front side. This sensor can measure magnetic fields from 10 mT to 50 T at moderate excitation amplitudes. It can be used in harsh environments under mechanical vibrations and low temperatures. The device has a resonant frequency around 5 kHz, a resolution of 10 mT, and a power consumption of few milliwatts. The device needs high current magnitudes thus increasing the temperature and deformation at the silicon microbeam, with a possible resonant frequency shift.

Another example of magnetic sensor based on MEMS technology and having an optical readout has been reported by Wickenden et al. (2003).

Ren et al. (2009) reported on a resonant device exploiting the capacitive readout. The magnetic field sensor has been fabricated by using conventional MEMS technology and silicon-to-glass anodic bonding process. The device consists of a low-resistivity silicon plate suspended over a glass substrate by two torsional beams, as shown in figure 5. This silicon plate acts as electrode of sensing capacitances. Au capacitance plates are fabricated on the glass substrate and a multi-turn coil (Cr and Au layers) is deposited on silicon-plate surface. The Lorentz force causes an oscillating motion of silicon plate around the torsional beams, which produces a capacitance shift between the Au electrodes and the silicon plate. A capacitance detection circuit measured the capacitance change that depends on the magnitude and the direction of the external magnetic field. This sensor required a vacuum

Keplinger et al. (2004) reported a resonant magnetic field sensor using U-shaped silicon microbeams and an optical readout system. Figure 4 shows a schematic sketch of the device

Fig. 4. Schematic sketch of the resonant magnetic sensor with optical readout reported by

Devices are processed by both surface micromachining and bulk micromachining techniques. The etching process has been also used to form the groove for the optical fibers. The microbeams contain a gold loop with a thickness of 500 nm. A magnetic field and an ac electrical current generate a Lorentz force, which bends the microbeams. These deflections are measured by optical sensing using an arrangement consisting of two fibers to avoid interference of reflected light. Figure 4 shows a design, in which the emitted light beam is reflected only once at the microbeam front side. This sensor can measure magnetic fields from 10 mT to 50 T at moderate excitation amplitudes. It can be used in harsh environments under mechanical vibrations and low temperatures. The device has a resonant frequency around 5 kHz, a resolution of 10 mT, and a power consumption of few milliwatts. The device needs high current magnitudes thus increasing the temperature and deformation

Another example of magnetic sensor based on MEMS technology and having an optical

Ren et al. (2009) reported on a resonant device exploiting the capacitive readout. The magnetic field sensor has been fabricated by using conventional MEMS technology and silicon-to-glass anodic bonding process. The device consists of a low-resistivity silicon plate suspended over a glass substrate by two torsional beams, as shown in figure 5. This silicon plate acts as electrode of sensing capacitances. Au capacitance plates are fabricated on the glass substrate and a multi-turn coil (Cr and Au layers) is deposited on silicon-plate surface. The Lorentz force causes an oscillating motion of silicon plate around the torsional beams, which produces a capacitance shift between the Au electrodes and the silicon plate. A capacitance detection circuit measured the capacitance change that depends on the magnitude and the direction of the external magnetic field. This sensor required a vacuum

at the silicon microbeam, with a possible resonant frequency shift.

readout has been reported by Wickenden et al. (2003).

reported by these authors.

Keplinger et al. (2004).

packaging to increase its performance. For a pressure of 10 Pa and 150 mV driving voltage amplitude, the microsensor has a resolution of 30 nT in the linear range from 3 T to 30 µT, a sensitivity of 481 mVT-1, a resonant frequency close to 1380 Hz, and a quality factor around 2500. Nevertheless, it presented a non-linear response from 0 to 3 µT.

Fig. 5. Schematic design of the resonant magnetic sensor exploiting the capacitive sensing and reported by Ren et al. (2009).

Brugger et al. (2009) reported on a complex magnetic field sensor with a size of 7.5 mm 3.2 mm, consisting of an electrostatically driven silicon resonator characterized by interdigitated combs for electrostatic excitation and capacitive detection, an amorphous magnetic concentrator and a pair of planar coils. It requires a complex fabrication process combining MEMS technology based on a silicon-on-insulator (SOI) substrate, the epoxyresin-based attachment of a thin amorphous magnetic ribbon structured by wet chemical etching, micropatterning of the magnetic concentrator by UV-laser and vacuum packaging.. For a coil current of ±120 mA, the device offers a sensitivity of 1.91 MHzT-1 and a resolution of 1.3 μT. Under a pressure of 10-5 mbar, this microsensor presents a sensitivity of 1 MHzT-1, a resolution of 400 nT, and a quality factor around 2400. It does not need a complex feedback and modulation electronics.

J. Kyynäräinen et .al. (2008) reported on resonant micromechanical magnetometers based on capacitive detection for 3D electronic compasses. The sensors has been fabricated by exploiting aligned direct bonding of a double side polished silicon wafer and a SOI wafer. Devices operated in vacuum to reach high enough Q values. Magnetometers measuring the field component along the chip surface have a flux density resolution of about 10 nT/√Hz at a coil current of 100 A. Magnetometers measuring the field component perpendicular to the chip surface are currently less sensitive with a flux density resolution of about 70 nT/√Hz.

There are in the literature other works reporting on capacitive sensing-based resonant magnetic sensors (Emmerich et al. (2000), Kádár et al. (1998), Tucker et al. (2000)).

Magnetic Field Sensors Based on Microelectromechanical Systems (MEMS) Technology 111

where H is the field in the core material and is lower than the measured field Hex in the open

The first term in the equation (4) is the basic induction effect, and causes interference. Fluxgate operation is based on the second term, due to the variation of the core permeability with the excitation field. By considering the effect of demagnetization, the basic fluxgate

*<sup>D</sup> d t V NA H*

The output voltage is on the second harmonics of the excitation frequency, as permeability

In accordance with the shape of the magnetic core, parallel-type fluxgate sensors fall into the categories of single core, dual core, ring-type core, racetrack type core (Ripka, 2001). The configuration of figure 6 is single core type. In order to eliminate the induction effect, a dual


(1 ( ( ) 1)) *<sup>r</sup> <sup>i</sup> ex*

*r*

1 ( )

*D t dt*

where D is the demagnetising factor, Hex = Bx/µ0 and M is the magnetization.

reaches its minimum and maximum twice in each excitation cycle.

core configuration has been proposed, as showed in figure 7.

Fig. 7. Dual core (left) and ring type (right) configurations of a fluxgate sensor.

induced due to the differential change of the permeability (Primdahl, 1979).

The driving coil is wound in opposite direction around the two cores, thus the induced magnetization fields are opposite in sign. If no external field is applied, the voltage induced in the sensing coil is zero in the ideal case. When an external field is present, a voltage is

High sensitivity can be achieved by increasing the number of turns N (if N is very high coil parasitic capacitance limits the sensitivity), by decreasing the demagnetization factor D or by increasing the excitation frequency, because (dHex/dt) ~ f up to frequency values that

Such devices can be also classified in parallel type and orthogonal type fluxgate sensors depending on the excitation field is parallel or perpendicular to the sensitive axis of


(6)

air due to demagnetization (Bozorth & Chapin (1942)):

equation becomes (Primdahl, 1979):

make eddy currents negligible.

the sensor.
