Technology of anisotropic magneto resistive sensor on silicon substrate
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The need for sensors and transducers increased with many technological applications. Hrisoforou recently Hauser et al., 2000 reviewed the magnetic effects in the physical
sensors in the design and development at the International Workshop on Amorphous and nano structured Magnetic Materials Iasi - Romania 2001.
In the development of Micro Technology Integrated Circuits MTIC studied magnetoresistive sensor developed micro, which is used as a magnetic field sensor such as
the navigation system, servomotors, playback mechanism and other automated equipment. Solid state magnetic field sensors have advantages, such as the size and power compared to
the coil, and a superconducting flux gate Quantum Interference Detectors SQUID. As a physical phenomenon, this sensor is based on the anizotropic magnetoresistive effect of thin
ferromagnetic layer, the deposit on mono crystal silicon substrate Laimer Kolar, 2000; Fulmek Hauser, 1993.
Table 1. Comparison of magnetic sensors. Sensor type:
Min. B Max. B
Frequency range Induction coils
100 fT unlimited
0.1 mHz–1 MHz Hall sensors
10 nT 20 T
0–100 MHz Magnetoresistive Sensors
100 pT 100 mT
0–100 MHz Fluxgates
10 pT 1 mT
0–100 MHz SQUIDs
5 fT 1000 nT
0–100 kHz
2. AMR sensors theory
AMR sensors are based on the theory of ferromagnetic complex process in a very thin film. Some of the effects that affect can be simplified in math. First, that the magnetization
M in ferromagnetic materials always have a magnetic force magnitude saturation magnetization MS but just changed direction. Second, the theory of complex AMR effect
there is also the effect of isotropic MR used in the semiconductor layer can be divided into two, namely, the relationship between the electrical resistivity and the direction of
magnetization magnetic force, and the relationship between the direction of magnetization magnetic force is applied in the an external magnetic field.
Anisotropic magnetoresistive effect
Anisotropic magnetoresistive effect is a distinct shift of energy levels of electrons with spin positive and negative, respectively under the influence of a magnetic field. This causes
a shift in the Fermi level. To calculate this effect satisfactorily, by differentiating with experimental data Dibbern, 1989. Therefore, the most important parameters are
determined experimentally. It has been shown that the electrical resistance R can be derived by a simple theory of the angle Θ is the angle between the electric current density and
magnetic force see Figure 1a:
1 In the above equation, ρ0, n and Δρ is a material constant, l is the length of the resistive
strip, b is the width, and d is, its thickness. In general, l b d. R0, n is perpendicular to the magnetic barriers, and ΔR is the maximum change in resistance due to the magnetic field.
For today in the direction of x, the voltage Ux is as follows:
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2 It should be noted that the voltage Uy perpendicular to the direction of current flow.
Because of the similarity of the Hall effect, this effect is called planar Hall effect. In general the Hall effect, the voltage change because the magnetic field perpendicular to the film,
because the planar Hall effect, the magnetic field is the same as the current flow. Planar Hall effect is rarely used for practical purposes because the voltages involved are very small.
a b
Figure 1. a The geometry of the strip to the magnetization M and the direction of the current I b Geometry of elliptically shaped thin films; axis is assumed to be in a state
parallel to the x axis.
External magnetic field
Magnetization M in the film are in the direction of the total energy minimum. The most important energy involved is the external field energy, material anisotropy energy
magnetocrystalline anisotropy energy, and energy demagnetising shape anisotropy energy. Most of the energy contribution depending on the direction. This means that the
energy required to turn M into a given direction can be visualized by three-dimensional energy region Fasching, 1994.
Spontaneous magnetization MS will be located in the direction of the minimum energy. Magnetocrystalline anisotropy energy region of the iron has six easy axis ie, the
minimum energy towards the edge of the crystal cube. Nickel has eight easy axis in the diagonal of the unit cell volume. In addition, the total energy depends on the mechanical
stress Hauser Fulmek, 1992 and geometry. Energy from permalloy Ni: Fe 81:19 is more complicated. There are 16 easy axis. However, the constant Magnetostriktif near zero in
permalloy, namely, the magnetic force has no effect on the dimensions of the crystal lattice. With a total anisotropy field H0 = 2K μ0MS the anisotropy constant K, the angle φ between
M and the easy axis x-direction results for HX = 0 as:
3 for –1 H
y
H 1.
It should be noted that the voltage U
y
perpendicular to the direction of current flow. Because of the similarity of the Hall effect, this effect is called planar Hall effect. In general
the Hall effect, the voltage change because the magnetic field perpendicular to the film, because the planar Hall effect, the magnetic field is the same as the current flow. Planar Hall
effect is rarely used for practical purposes because the voltages involved are very small.
Technology of anisotropic magneto resistive sensor on silicon substrate
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Magnetoresistive sensors
The calculation of the angle Θ between M and the easy axis and the dependence of the electrical resistance in the direction of M will be combined to evaluate the sensor. Also
introduced a new resistance R , p and R
: 4
5 R
is the average resistance, can be calculated using the AMR sensors simple characterization of new parameters. Figure 2a illustrates the dependence of resistance on
the angle between the current flow and magnetic force. Eqs. 2 and 4 lead to resistance R Θ:
6 Eq. 3 to calculate the resistance in dependence of the measured field H
y
. Figure 2b illustrates this dependence. For real measurement, the magnetic force F changed entirely the
hard axis for a very strong field alone. Therefore, there is a smooth transition to the saturation resistance:
7 8
For |H
y
| ≤ H and for |H
y
| H . Resistance depends non-linearly on the external field.
Furthermore, the sensitivity of dRDHY very small area adjacent to the origin and disappears entirely for H
y
= 0. Further weakness of this setup is that the sign of Hy can not be determined because R is a function of H
y 2
.
a b
c
Figure 2. a Resistance in the x direction as a function of the angle Θ between the current I and the magnetic force M. b Resistance ferromagnetic thin films as a function
of the transverse field H
y
. c The current flows in a barber pole structure, and resistance R ferromagnetic thin films with a barber pole structure as a function of the transverse
field Hy.
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Barber pole
In order to reduce losses, barber-pole structure is shown in the image above. Barber- pole structure consists of a series of strips of high electrical conductivity that forces the flow
of current into a 45 ° angle to the x-axis. Figure 2c shows that the current path is distorted by the barber pole. The layout of the optimum width and spacing poles barber pole is
important Laimer Kolar, 2000. Strip either did reduce the total resistance, they also reduce the active part of the surface where the resistance changes contribute to the sensor
signal. Mathematically, a barber-pole represented by introducing additional angle ψ = 45 °, which is the angle between the axis and currents.
The angle Θ in this case: 9
Barber-pole characteristics of AMR sensor 10 is formulated with the following equation:
10 A graphical representation of a barber-pole characteristics of AMR sensor is shown in
Figure 2c. For H Hy2, is quite linear with the non-linearity of less than 5. This behavior
applies only if the magnetic field spontaneously without outside in the positive x direction. Changes in resistance changes its sign if spontaneous magnetisation is flipped to the negative
x direction. Reversing the spontaneous magnetic force can be used to determine the value of R0 accurate as the arithmetic mean value of the two resistance values before and after
flipping.
In order to change the resistance to voltage changes without dc component, the sensor is realized as a Wheatstone bridge with four individual resistors. This approach shows one
more advantage of the barber pole structure: With using barber pole under 45° and 135°, respectively, resistor with positive and negative ΔR in the linear range can be realized. In
order to obtain the maximum output voltage, the resistor has two diagonally opposite pole barber below 45°, and the other two, below 135° see Figure 3. This setup also compensates
for the temperature dependence of the resistor.
Figure 3. Wheatstone bridge with four magnetoresistive devices. + Indicates a barber pole below 45°, and -, below 135°.
Technology of anisotropic magneto resistive sensor on silicon substrate
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Sensitivity and measurement
The output voltage of the Wheatstone bridge can be explained by:
11 The sensitivity of the sensor measurement results
12 Thus the sensitivity can be improved by using a material that AMR effect with the
characteristics of high and low field H0. Linear behavior of the sensor with an error of less than 5 in the range of a-H0 2 for H0 2. It is possible, to improve the measurement range
by applying a magnetic field compensation ie, with compensation-null bridge. Since the sensor is always operating in the region of zero field, the non-linearity will have no effect.
The maximum resolution in this case depends on the stability of the magnetic film.
In addition, the layout of the magnetoresistive element forming the Wheatstone bridge must be optimized. Demagnetising achieve homogeneous and small field, an elliptical
shape AMR array is proposed [6]. By using the compensation coil integrator output, the sensor can be operated in zero magnetic field. Linear output response V0 voltage versus
applied field Ha is comparable resistor R for the applicable compensation coils. Both compensation flips and coil conductor in the form of a thin layer mean deric, shown in Figure
4.
Figure 4. Electronic circuits with flip Lf and compensation Lc rolls Hauset et al., 2000.
There are two definitions of the sensitivity of AMR sensors in bridge arrangement: 1. S0 = two DHY UB, and 2 × SU = Umax two DHY UB. The advantage of the second
definition is that it also takes into account the maximum energy dissipation Pmax = UB, MAX2 R on the sensor. The supply voltage can not be done suddenly becomes high. For a
comparison of the sensitivity of the sensor, use the first definition in this paper, as is done by most of the literature.
3. Metodology
