Overview of Magnetic Field Sensor

This article summarizes the commonly used in magnetic sensors Hall sensors, Anisotropic magnetoresistive sensor (AMR), Giant magnetoresistance effect sensor (GMR) and Tunneling magnetoresistance sensor (TMR). The structure and working principle of each sensor are introduced. In addition, some error sources of magnetic sensors and the calibration techniques used are introduced, and some typical application examples of each sensor are introduced.


Introduction
The development of magnetic field sensors has always been the pursuit of mankind.Today, magnetic sensors are used in a wide range of applications, from commercial machinery to complex aerospace and military applications.[1] [2] .There are two commonly used types of magnetic field sensors: one is a scalar sensor that only measures the size of the magnetic field, and the other is a vector sensor that also measures the direction of the magnetic field [3] .Magnetic sensors can also be classified using other criteria, such as induced power consumption, noise characteristics, and field strength [4] .These magnetic sensors have their own advantages and disadvantages: The fluxgate sensor is a relatively old and simple design, but it is still widely used.Its miniaturization potential, as well as low power consumption, and portable applications can be applied.Fluxgate sensors can be used for trajectory tracking, accurate navigation and metal damage detection of electronic devices.They are also used for archaeological and other expeditionsn [5]; On the other hand, Hall sensors, Anisotropic magnetoresistive sensor(AMR), Giant magnetoresistance effect sensor(GMR) and Tunneling magnetoresistance sensor (TMR) are manufactured using a planar micromachining process, which can provide high sensitivity in a relatively compact volume.which has great attraction for Internet of Things applications.

Hall Effect Sensor
The Hall effect originates from the Lorentz force (or electromagnetic force), where charged particles moving in a magnetic field are subjected to a force perpendicular to their direction of motion.When the current flows through the semiconductor perpendicular to the applied magnetic field, the carrier will deflect [6] ，As shown in Fig 1 .Therefore, the semiconductor carries opposite charges at both ends, resulting in a potential difference at both ends, known as a Hall voltage.This phenomenon of measurable voltage arising from the applied magnetic field is called the Hall effect.Although the mobility of electrons in semiconductors is lower than that of metals and the mobility of holes is lower, the Hall effect is stronger.In semiconductors, this effect is very common.The lower the mobility of semiconductor sensor electrons indicates that in the sensing element, the carrier will stay longer, which will cause greater trajectory deviation, so that the sensor element has a higher gain.Because Hall sensors have a relatively simple hardware structure and are compatible with standard integration technologies, semiconductor devices can be mass-produced at a very low cost without any additional ferromagnetic materials.The biggest advantage of Hall sensors over other low-cost solutions such as inductive sensors is the ability to detect static magnetic fields [7] [8] .However, in sensor design, there are some more important aspects to consider: 1) In the layout of the sensor, special precautions must be taken to avoid interfering with the effect of electric fields on the sensing element.
2) Compared to conductors, semiconductors have higher white noise levels due to their high resistance, and are therefore also subject to more noise sources such as shooting noise, flicker (1/f) noise, and other noise sources.
3) Unbalanced resistance paths in semiconductor materials can lead to offsets.4) Because of the different thermal expansion coefficients of its constituent materials, semiconductor sensors are easy to cause greater mechanical stress, which is more likely to lead to errors.
The sensitivity of common silicon Hall sensors can only reach a feedback signal of 1mv/mT at a current of 1mA.Hall sensors made of thin film indium antimonide (InSb) also have a sensitivity of only 5 times higher, which is not conducive to measuring weak magnetic fields [9] .To solve these problems, researchers have found that using chopper technology and AC bias current can reduce bias, minimize the impact of 1/f noise and shooting noise sources, and improve the sensitivity of Hall sensors.Most hall effect sensors in life are manufactured using complex electronic circuits, adding a DC amplifier inside the sensor, adding a voltage regulator circuit at the back end to provide a stable current, and can compensate for drift, amplify the output voltage, and also digitize the analog signal, and then optimize the processing through the upper computer.
The extremely low production cost and easy manufacturing process are the main advantages of Hall effect sensors.They are often used in life for position detection and mechanical movement counting.One of their common applications in industry is the closed-loop feedback of brushless motors..

Anisotropic magnetoresistive sensor
Magnetoresistance is a property of certain materials, usually ferromagnetic, whose resistance changes with an external magnetic field.In 1856, Lord Kelvin first discovered ferromagnetic metals, whose resistance varies by the Angle between the direction of the current passing through the metal and the direction of the magnetization of the ferromagnetic metal itself.This phenomenon of magnetoresistance change is called anisotropic magnetoresistance.His report pointed out that when the direction of magnetization of the ferromagnetic metal itself is parallel to the current flowing through the conductor, the resistance value will increase, and when the direction of magnetization is perpendicular to the current flowing through the conductor, the resistance value will change to the least [10] .
The AMR sensor piece is usually placed in a very small flat structure, which means that the device has two magnetized axes: the easy axis and the hard axis.The size of its resistance is related to the polarity of the magnetic field, so a single magnetoresistance is not sufficient to determine the polarity of the magnetic field.In order to solve such a defect, AMR magnetic sensors generally use a Wheatstone bridge structure, which is composed of four magnetic sensor components.The magnetoresistance is made of Ni-Fe thin films, and its structure is shown in Fig 2 .Arranging metal electrodes such as copper bars and aluminum bars on a permalloy bar with an angle of 45°between the magnetic moment of the metal electrode and the ferromagnetic layer will result in a 45°current direction and magnetic moment of adjacent metal electrodes, thereby improving the sensitivity of the AMR sensor and expanding the linear working area of the sensor [11] .The best AMR sensors have a noise of 200 pT/Hz 1/2 @1Hz.AMR sensors were originally developed for reading heads in hard disks, but were later replaced by GMR and TMR sensors in this application because of their smaller size and higher storage density.It is also widely used in daily life, and has a huge range of applications in the field of aerospace and public transportation [12] .At the same time, because of the rise of nano-satellites and micro-satellites (artificial satellites with a very small volume compared with traditional satellites), AMR sensors have gradually begun to replace their role in the application range of many fluxgate sensors, and become the first choice for magnetic field sensors in the space field.The gradual rise of the smart grid is also a huge new blue ocean that can provide many application scenarios for AMR sensors.Currently, linear AMR sensors are mainly produced by Philips, Honeywell, and Celes.They have higher sensitivity than Hall sensors and can measure at a resolution of 10 nt [13] .

Giant magnetoresistance effect sensor
In 1988, French scientist Albert Fell discovered the giant magnetoresistance (GMR) effect.About the GMR sensor that the working principle is based on a quantum theory of spin interactions between the free and fixed magnetosphere.
The GMR effect is in a structure similar to a "sandwich", consisting of two ferromagnetic metal layers separated by a nonmagnetic layer, one of which is a free layer made of soft magnetic material.Under the influence of an external magnetic field, the magnetization direction of the layer will change; The other layer is a reference layer, and the resistance change of this mechanism depends on the relative direction of magnetization of two ferromagnetic metal layers.Since the magnetoresistance effect generated is far greater than that of a single layer of anisotropic magnetoresistance, it is called a giant magnetoresistance, or GMR for short [14] .Its structure is shown in Fig 3.
In such magnetic multilayer metal films, where the thickness of each layer is maintained at a nanometer level, continuous metal films have a spontaneous opposite magnetization orientation, so their resistance is high in environments where the magnetic field intensity is low.When the external magnetic field intensity is high, the magnetization direction of each metal film is the same, the resistance will significantly decrease compared to the previous one.For low intensity external magnetic field, the resistance value of the sensor is affected by the linear change of the intensity of the external magnetic field, so the signal output of the sensor tends to be linear with the external magnetic field [15] .Fig. 3 Giant magnetoresistance structure The structure of GMR magnetic sensors utilizes a combination of spin valves and nonmagnetic layers, the interlayer coupling between two ferromagnetic layers can be effectively avoided, improving the measurement range of the sensor [16] .Moreover, the application of spin valves has improved the sensitivity of GMR sensors under weak magnetic detection, which is the reason why they can replace previous types of magnetic sensors.Magnetoresistance sensors are also assisted by various structural designs to improve sensor performance.The push-pull Wheatstone bridge structure is a common design for linear magnetic sensors, which can significantly improve sensitivity and effectively compensate for sensor temperature drift [17] .There are four GMR resistors inside the bridge.When measuring the magnetic field, The output voltage signal can be linearly related to the applied electric field.The measurement direction of the magnetic field is parallel to the magnetization direction of the reference layer.The free layer direction of the GMR element is related to the positive and negative output voltage.The common signal output curve is shown in Fig 4 [18] .
Proper bridge bias and signal conditioning are very important for precision magnetic field measurements.The GMR sensor has the same characteristics as the AMR sensor, that is, feedback can be used to stabilize its sensitivity and suppress static nonlinearity.In addition, using an AC current biased GMR sensor bridge can significantly reduce the effects of hysteresis, nonlinearity, bias, and noise [19] .
By adjusting different parameters, the output of the GMR magnetic sensor can achieve a linear relationship with the applied electric field in the range of 5 to 100Oe, but its measurement range and sensitivity are negatively correlated.Nowadays, in the measurement of low-frequency magnetic fields, the magnetic noise index of GMR magnetic sensors can reach several pT/Hz 1/2 [20] [21] .With the development of modern technology in fine processing technology, GMR magnetic sensors can now be extremely miniaturized and can be used in 10μ The GMR sensor can be integrated within an area of m2 and fabricated on a large scale on a wafer.At the same time, the sensitivity of the GMR sensor can reach more than 1mV/(VmA), which enables it to be integrated into CMOS chips and adapt to different application environments.This is also one of the advantages that GMR magnetic sensors can outperform traditional magnetic sensors [22] .Fig. 4 Voltage output versus field for GMR

Tunneling magnetoresistance sensor
Common TMR sensors are composed of three main structures: a fixed ferromagnetic layer, a tunnel barrier layer and a free ferromagnetic layer, against which magnetic tunnel junction (MJT) devices can be formed.The bottom ferromagnetic layer is a composite layer composed of the antiferromagnetic pinning layer and the ferromagnetic layer.At the top is a ferromagnetic layer called a "free" magnetic domain, the direction of magnetization can be easily rotated in a weak magnetic field, and the hysteresis is very small.In contrast, in the presence of a moderate magnetic field, the magnetization direction of the pinned layer is relatively fixed, but it may be interfered with in a strong magnetic field.5. Relative to the direction of magnetization, the resistance of MTJ varies with the Angle between the free layer and the reference layer.The pinned and free layers are typically between 0.1 nm and 100 nm thick [23] .When two ferromagnetic layers are magnetized in parallel, the probability of electrons passing through the tunnel barrier layer is higher than when two layers of magnetization are antiparallel.Therefore, parallel structures produce minimum resistance and antiparallel structures produce maximum resistance.
Compared with GMR sensors, TMR sensors have a more sensitive magnetoresistance response, so at the same operating voltage, TMR sensors have lower energy consumption than GMR sensors.However, they are affected by higher noise.For TMR sensors often used for detecting weak magnetic field environments, having high sensitivity is crucial.For this reason, noise interference from the sensor must be minimized.Because TMR sensors are a type of resistive sensors, they have multiple sources [24] , Such as low frequency noise, thermal noise, flicker noise and so on.At the same time, because of the artificial construction of TMR sensors, there must be technological defects in the internal structure, which can also cause noise from the TMR sensor [25] .Most resistive sensors are used to measure DC or low frequency signals, so in TMR sensors, low frequency noise sources are the most important influence [26] .In the TMR sensors ,the 1/f noise largely depends on the shape and size of the sensor.Currently, methods for reducing 1/f noise include integrated magnetic flux concentrators and external circuit processing.Fig. 6 The concept of the MEMS flflux concentrator Figure 6 is a MEMS vertically moving magnetic flux concentrator based on a cantilever beam structure [27] , The flux is changed by changing the distance between the flux modulating membranes and the gap between the two flux concentrators.When the distance between the magnetic flux modulation film and the gap increases, as the magnetic flux in the air gap increases, so does the magnetic field; When the distance between the magnetic flux modulation film and the gap decreases, the magnetic flux decreases, and the magnetic field decreases accordingly.Therefore, maintaining a fixed change in the distance between the magnetic flux modulation film and the gap can allow the magnetic field to change in accordance with the desired law, thereby reducing the 1/f noise of the TMR sensor.
Secondly, as shown in Fig 7, it is possible to connect a TMR sensor with an AC bias circuit using phase sensitive detection technology [28] .By reducing the cutoff frequency of the low pass filter (LPF), it can further reduce the accompanying noise in the signal near the excitation frequency.In addition to signals close to the excitation frequency, it can integrate and suppress noise at different frequencies.The disadvantage is that reducing the cutoff frequency can lead to a reduction in the measurement bandwidth of the sensor.

Conclusion
Among magnetoresistive sensors, TMR sensors ultimately have the best performance, and correspondingly, TMR sensors also have the highest cost.At the same time, compared with AMR sensors, GMR sensors have better performance.Secondly, the performance of Hall sensors is the worst in terms of sensitivity and resolution.However, the advantage of Hall sensors is that they can provide a high dynamic range at a low cost, which allows Hall sensors to have a lower cost, while having better performance and high universality, making them the most widely used magnetic field sensors on the market.At present, the magnetic measurement sensing method has been studied more mature.Advanced electronics and continuously optimized composition materials are gradually improving the performance, size and power consumption of sensors.The increased demand for sensitivity in household applications is gradually replacing some Hall effect sensors with magnetoresistive sensors, which in turn requires these sensors to become more affordable.Future innovations in sensor manufacturing and integration are expected to bring new technological changes.

Fig. 1
Fig. 1 Hall effect ExampleThe first generation of Hall sensors was made of thin metal strips and excited by an electric current, the new generation of Hall effect sensors use semiconductor materials instead of thin metal strips.Although the mobility of electrons in semiconductors is lower than that of metals and the mobility of holes is lower, the Hall effect is stronger.In semiconductors, this effect is very common.The lower the mobility of semiconductor sensor electrons indicates that in the sensing element, the carrier will stay longer, which will cause greater trajectory deviation, so that the sensor element has a higher gain.Because Hall sensors have a relatively simple hardware structure and are compatible with standard integration technologies, semiconductor devices can be mass-produced at a very low cost without any additional ferromagnetic materials.The biggest advantage of Hall sensors over other low-cost solutions such as inductive sensors is the ability to detect static magnetic fields[7] [8] .However, in sensor design, there are some more important aspects to consider:1) In the layout of the sensor, special precautions must be taken to avoid interfering with the effect of electric fields on the sensing element.2) Compared to conductors, semiconductors have higher white noise levels due to their high resistance, and are therefore also subject to more noise sources such as shooting noise, flicker (1/f) noise, and other noise sources.3)Unbalanced resistance paths in semiconductor materials can lead to offsets.4) Because of the different thermal expansion coefficients of its constituent materials, semiconductor sensors are easy to cause greater mechanical stress, which is more likely to lead to errors.The sensitivity of common silicon Hall sensors can only reach a feedback signal of 1mv/mT at a current of 1mA.Hall sensors made of thin film indium antimonide (InSb) also have a sensitivity of only 5 times higher, which is not conducive to measuring weak magnetic fields[9] .To solve these problems, researchers have found that using chopper technology and AC bias current can reduce bias, minimize the impact of 1/f noise and shooting noise sources, and improve the sensitivity of Hall sensors.Most hall effect sensors in life are manufactured using complex electronic circuits, adding a DC amplifier inside the sensor, adding a voltage regulator circuit at the back end to provide a stable current, and can compensate for drift, amplify the output voltage, and also digitize the analog signal, and then optimize the processing through the upper computer.The extremely low production cost and easy manufacturing process are the main advantages of Hall effect sensors.They are often used in life for position detection and mechanical movement counting.One of their common applications in industry is the closed-loop feedback of brushless motors..

Fig. 2
Fig.2AMR magnetoresistance fabricated from Ni-Fe thin films AMR sensors can be manufactured on a large scale on integrated chips.AMR sensors are much more sensitive than Hall sensors.Due to the absence of piezoelectric effects, they have stronger resistance to mechanical stress and stronger anti-interference ability.Because they can measure low intensity magnetic fields, such as the Earth's magnetic field, they are very popular and widely used.The best AMR sensors have a noise of 200 pT/Hz 1/2 @1Hz.AMR sensors were originally developed for reading heads in hard disks, but were later replaced by GMR and TMR sensors in this application because of their smaller size and higher storage density.It is also widely used in daily life, and has a huge range of applications in the field of aerospace and public transportation[12] .At the same time, because of the rise of nano-satellites and micro-satellites (artificial satellites with a very small volume compared with traditional satellites), AMR sensors have gradually begun to replace their role in the application range of many fluxgate sensors, and become the first choice for magnetic field sensors in the space field.The gradual rise of the smart grid is also a huge new blue ocean that can provide many application scenarios for AMR sensors.Currently, linear AMR sensors are mainly produced by Philips, Honeywell, and Celes.They have higher sensitivity than Hall sensors and can measure at a resolution of 10 nt[13] .

Fig. 5
Fig. 5 Structure and magnetoresistance curve of MTJ The structure diagram of MTJ is shown in Figure5.Relative to the direction of magnetization, the resistance of MTJ varies with the Angle between the free layer and the reference layer.The pinned and free layers are typically between 0.1 nm and 100 nm thick[23] .When two ferromagnetic layers are magnetized in parallel, the probability of electrons passing through the tunnel barrier layer is higher than when two layers of magnetization are antiparallel.Therefore, parallel structures produce minimum resistance and antiparallel structures produce maximum resistance.Compared with GMR sensors, TMR sensors have a more sensitive magnetoresistance response, so at the same operating voltage, TMR sensors have lower energy consumption than GMR sensors.However, they are affected by higher noise.For TMR sensors often used for detecting weak magnetic field environments, having high sensitivity is crucial.For this reason, noise interference from the sensor must be minimized.Because TMR sensors are a type of resistive sensors, they have multiple sources[24] , Such as low frequency noise, thermal noise, flicker noise and so on.At the same time,

Fig. 7
Fig. 7 AC bias circuit for phase sensitive detection technology