**1. Introduction**

102 Magnetic Sensors – Principles and Applications

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**6. References** 

In the last decades magnetic field sensors have been developed and realized for analyzing and controlling thousands of functions (Ripka, 2001), and they have become a widespread presence in modern lifestyle. Numerous applications in different fields of science, engineering, and industry rely on the performance, ruggedness, and reliability of magnetic field sensors.

The applications of magnetic sensors depend on magnetic field dynamic range and resolution and include position sensing, speed detection, current detection, non-contact switching, space exploration, vehicle detection, electronic compasses, geophysical prospecting, non-distructive testing, brain function mapping (Lenz & Edelstein, 2006).

Nowdays there is an increasing requirement for magnetic devices with improved sensitivity and resolution, trying to keep as low as possible their cost and power consumption. Additionally there is the need to develop compact devices with several sensors able to measure different parameters including magnetic field, pressure, temperature, acceleration. In this way a multifunctional device could be integrated on the same substrate containing transducers and electronic circuits in a compact configuration without affecting device performances.

In this context microelectromechanical systems (MEMS) technologies play a prominent role for the development of a new class of magnetic sensors.

In general MEMS devices are miniaturized mechanical systems produced using fabrication techniques already explored in the electronics industry. The exploitation of MEMS technology for device fabrication not only makes possible the reduction of the device dimensions on the order of micrometers, but also allows the integration of the mechanical and electronic components on a single chip. In addition to the small device size this involves other important advantages such as light weight, minimum power consumption, low cost, better sensitivity and high resolution. This technology was successfully employed for the realization of portable devices such as gyroscopes (Chang et al., 2008), accelerometers (Li et al., 2011), micromirrors (Singh et al., 2008), and pressure sensors (Mian & Law, 2010).

Magnetic Field Sensors Based on Microelectromechanical Systems (MEMS) Technology 105

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

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

*I I ft* 2 sin 2 *rms*

where Ly is the length of the metallic loop perpendicular to the magnetic field, Irms is the root

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

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

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

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

*F IB L L x <sup>y</sup>* (1)

(2)

Lorentz force (FL) is generated.

This force can be determined as:

where the flowing current can be expressed as:

quality factor (Herrera-May et al. 2010).

disturbances (Beeby et al., 2004).

mean square of the current I, f is the frequency and t is the time.

on the Lorentz force amplitude, which is directly proportional to I and Bx.

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 well as to non-distructive testing and medical diagnostics.

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

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 and a maximum achievable resolution of 1 nT.

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

Hall sensors are based on Hall effect transduction principle and measure either constant or varying magnetic field. They have a magnetic field sensitivity range from 1T to 1T.

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.
