Sensors and Actuators A 263 (2017) 159–165
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Sensors and Actuators A: Physical
journal homepage: www.elsevier.com/locate/sna
Multilayer anisotropic magnetoresistive angle sensor
Yue Guo a,∗ , Yong Deng b , Shan X. Wang a,b
a
b
Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
Department of material Science and Engineering, Stanford University, Stanford, CA 94305 USA
a r t i c l e
i n f o
Article history:
Received 23 February 2017
Received in revised form 30 May 2017
Accepted 1 June 2017
Available online 2 June 2017
Keywords:
Magnetic angle sensor
Anisotropic magnetoresistance
Intrinsic sensing error
a b s t r a c t
A multilayer anisotropic magnetoresistive (AMR) sensing stack has been proposed in this paper for high
accuracy angle sensing. A quadruple-layer AMR angle sensor was fabricated and showed smaller detection
errors than traditional single-layer AMR angle sensors. Based on spectral analysis, intrinsic errors in AMR
angle sensors can be attributed to two dominant sources. One is the second harmonic error due to induced
anisotropy, and the other is the eighth harmonic error from shape anisotropy. The fabricated quadruplelayer AMR angle sensor with correction algorithm reduces angular errors by a factor of 5 relative to the
traditional single-layer device. In addition, the quadruple-layer AMR angle sensor can be operated at
low magnetic fields under 100 Oe, enabling the use of weaker, smaller, and cheaper hard magnets for
magnetic field sensing. Therefore, the present quadruple-layer AMR angle sensor shows great potential
for many industrial applications.
© 2017 Elsevier B.V. All rights reserved.
1. Introduction
Magnetic angle sensors are a preferred choice for measuring angular position of a rotating body in harsh environments.
Various kinds of magnetic sensing technologies, including Hall
effect, anisotropic magnetoresistive (AMR), giant magnetoresistive (GMR), and magnetoimpedance (MI), can be used for angle
detection [1–3]. Currently, Hall sensors and AMR sensors are commonly used for angular position detection [4–7]. They both have the
advantages of low cost, noncontact operation, easy maintenance,
and robustness to contamination [8,9]. They are widely needed
in modern industries, like automobiles, collaborative robots, and
even space exploration [10–14]. In automotive applications, for
instance, angle sensors play a vital role in various functions such
as anti-lock braking, transmission control, and fuel level measurement [4,15,16]. In addition, angular sensors are necessary to control
rotating mechanisms in robotics [17,18].
Today, AMR magnetic angle sensors are becoming an increasingly popular choice for angular measurement [19–21]. In
comparison with Hall sensors, AMR angle sensors are advantageous
in power consumption, sensitivity and accuracy [22]. Thus, they
are preferred for systems that require precise angular positioning
and advanced control capability. In order to achieve good sensing
accuracy, however, traditional AMR angle sensors need to be operated under a large magnetic field, typically ranging from 300 Oe
to 500 Oe [23,24]. Hence, expensive rare-earth magnets are usually required to fulfill the strong field requirement [25]. Moreover,
angular detection errors increase abruptly with decreased magnitude of applied magnetic fields.
In this paper, a multilayer AMR sensing stack has been proposed, with a proof-of-concept implementation in the form of a
quadruple-layer angle sensor. Compared with traditional singlelayer AMR angle sensors, the multilayer AMR devices show good
detection accuracy even at low magnetic fields under 100 Oe, which
removes the requirements for strong magnets to generate the driving magnetic fields. Intrinsic errors of AMR angle sensors have also
been studied by the fast Fourier transform (FFT). Based on spectral analysis results, angular errors can be attributed to two main
sources. The first source of error is a second harmonic error due to
induced anisotropy, which is introduced by magnetic fields applied
during deposition. The other is an eighth harmonic error from shape
anisotropy. Identification of these error sources allow for further
implementation of a correction algorithm for improved accuracy.
Taken together, the present quadruple-layer AMR angle sensor proposed is more accurate and cost-effective, and is very promising for
a wide range of applications.
2. Material characterization
∗ Corresponding author Postal address: 476 Lomita Mall, McCullough Building,
Room 208, Stanford, CA 94305.
E-mail address: yueguo@stanford.edu (Y. Guo).
http://dx.doi.org/10.1016/j.sna.2017.06.001
0924-4247/© 2017 Elsevier B.V. All rights reserved.
Permalloy (Ni80 Fe20 at%) is a common material choice for magnetic sensors, due to its favorable soft ferromagnetic property, low
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Y. Guo et al. / Sensors and Actuators A 263 (2017) 159–165
Fig. 1. Schematic view of (a) a single-layer and (b) a quadruple-layer AMR sensing stacks.
hysteresis and small magnetostriction coefficient [26]. The permalloy layer can be deposited by sputtering, and is typically deposited
in the presence of an external magnetic field from a hard magnet
in the chamber. Consequently, an easy axis is induced in a certain direction defined as ␣ = 0◦ , as shown in Fig. 1a. The magnetic
energy density of single-layer AMR materials can be described by
the equation [27]:
EA = Ku · sin2 ˇ
(1)
where ˇ is the angle between the easy axis and magnetization
direction, and Ku is the induced anisotropy. Such uniaxial induced
magnetic anisotropy can result in detection errors and is not preferred in AMR angle sensors. The corresponding errors will be
analyzed in the fourth section. If a magnetic film is sputtered in
the absence of a magnetic field, anisotropy can still develop, but
with a random easy axis orientation, which is similarly unsuitable
for sensor applications [28].
In this work, a multilayer AMR sensing stack has been presented,
with the easy axes of each ferromagnetic thin layer aligned to different directions that are equally distributed from 0 to 180◦ . All layers
are deposited under a continuous vacuum by using an ultra-high
vacuum magnetron sputtering system with a hard magnet installed
in the chamber to generate a magnetic field. cAdditionally, every
two ferromagnetic layers have orthogonal easy axes, and hence, can
form a pair for compensation, leading to a constant energy density,
as described in the following equation:
EA = Ku · sin2 ˇ + Ku · sin2 ˇ + 90◦ + Ku · sin2 ˇ + 45◦
+Ku · sin2 ˇ + 135◦ = Ku
(2)
where ˇ is the angle between the easy axis of the first ferromagnetic layer and magnetization direction, and Ku is the induced
anisotropy. Therefore, the presented quadruple AMR sensing stack
is isotropic in terms of magnetic anisotropy, which is highly favorable for AMR angle sensors.
Fig. 2 demonstrates measurements in a BH curve tracer for all
single, double and quadruple-layer thin films. Insets illustrate the
corresponding material stacks. Permalloy layers are sandwiched by
a Ta buffer layer at the bottom and another protective Ta capping
layer at the top. The single-layer sample comprising only one NiFe
layer is used as a control. In multilayer sensing structures, Ti spacer
layers are employed to separate ferromagnetic layers effectively
[29,30]. For example, the quadruple-layer stack contains four layers of NiFe and three Ti spacer layers. When choosing the spacer
material, three major factors were considered. Firstly, a Ti buffer
layer can improve <111> texture and induce larger grain sizes in
NiFe thin films [31–33]. Secondly, it is favorable to have similar
or larger resistivity in the spacer layer than the permalloy, so that
ferromagnetic layers can work as major conducting layers. Thirdly,
thickness of spacer layers is also very critical. A thinner layer is not
enough to magnetically decouple ferromagnetic layers, whereas a
thicker layer shows a side effect of current shunting. Thus, the Ti
spacer layers are optimized to 3 nm in our multilayer AMR sensing
stacks.
The BH curves are scanned along 4 directions, where angle 0◦
corresponds to the direction aligned with easy axis of the first MR
layer. As shown in Fig. 2(a), the single-layer AMR sample shows
an obvious uniaxial anisotropy, with the easy and hard axis of BH
curves aligning along 0◦ and 90◦ , respectively. Next, the doublelayer sample in Fig. 2(b) depicts an improved performance. BH
curves overlap along either 0◦ and 90◦ or 45◦ and 135◦ . Finally,
the quadruple-layer sample in Fig. 2(c) gives almost identical BH
loops along all four measured directions, demonstrating a preferred
magnetically isotropic behavior.
3. Sensor design and fabrication
Magnetic angle sensors can be used to measure a rotating magnetic field that is typically generated by a hard magnet installed at
the end of a rotor. Fig. 3a gives a schematic view of an AMR sensing
pair. There are two Wheatstone bridges, one of which is tilted at
45◦ relative to the other one. As described by the governing equations 3 and 4, two bridges in the AMR angle sensor show different
responses to magnetic fields.
V1 =
1
VB · MR · sin(2)
2
(3)
V2 =
1
VB · MR · cos(2)
2
(4)
In our layout, bridge 1 gives a sine wave signal, whereas bridge 2
exhibits a cosine one. The detected angle can be computationally
extracted from outputs of the two bridges by using the arctangent
relationship, as given in equation 5.
=
1
· arctan
2
V 1
V2
(5)
Y. Guo et al. / Sensors and Actuators A 263 (2017) 159–165
161
Fig. 2. BH curves of (a) single-layer (b) double-layer (c) quadruple-layer samples with magnetic fields scanned along 4 different directions. Insets are illustrations of material
stacks.
(a)
Fig. 3. (a) Schematic view of an AMR sensing pair with two Wheatstone bridges, and the governing equations. (b) Microscopic view of a fabricated AMR angle sensor.
Fig. 3b provides a microscope image of a fabricated AMR angle sensor, and the two Wheatstone bridges are highlighted by two red
squares.
Fig. 4 gives a process flow for fabricating AMR angle sensors.
The device fabrication starts with thermally growing an oxide layer
with a thickness of 200 nm on a silicon substrate. Then, AMR sensing
stacks can be deposited in a sputtering chamber under ultra-high
vacuum. In order to compare performance, both single-layer and
quadruple-layer samples were prepared. In step (c), a layer of
photoresist was coated and lithographically patterned. Sensing elements were then etched by ion milling. Next, a second lithographic
step was performed, followed by sputtering of a layer of aluminum.
Finally, electrodes were subsequently formed by a lift-off process.
4. Experimental test and analysis
In our measurement, the device under test is located in the
center of a Helmholtz coil, which can supply a rotating in-plane
magnetic field. In order to achieve uniform and accurate magnetic
fields, a 16-bit multifunction data acquisition board from National
Instruments was used to control the driving current. Fig. 5a shows
typical outputs from a single-layer AMR angle sensor. The supply
voltage is 1 V to both Wheatstone bridges, as labeled in Fig. 3a.
The black solid line and red dashed line correspond to outputs
from bridge 1 and bridge 2 respectively. According to the measurements, fabricated sensors have a peak-to-peak output voltage of
about 21 mV/V. Also, output offsets are 1.26 mV/V and 0.36 mV/V
for bridge 1 and 2 respectively. After conducting output normal-
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Y. Guo et al. / Sensors and Actuators A 263 (2017) 159–165
Fig. 4. Process flow of the presented AMR angle sensors.
(a) 15
(b)
Bridge1
1.0
Normalized Outputs
10
Outputs [mV]
Bridge 1
Bridge 2
Bridge2
5
0
-5
-10
0
90
180
270
360
Ideal Sine
Ideal Cosine
0.5
0.0
-0.5
-1.0
0
Angle [degree]
50
100
150
Angle [degree]
Fig. 5. (a) Outputs from the two bridges in the single-layer AMR angle sensor. (b) Normalized bridge outputs are compared with ideal sine and cosine functions of period
half.
ization and offset correction, bridge outputs are compared with
ideal sine and cosine functions of half period, as shown in Fig. 5b.
Based on Equation 5, angles of the rotating magnetic field can be
extracted from the ratio of these two voltage outputs, while any
difference between the actual applied magnetic field and the value
calculated hence is the angular detection error. Although actual
outputs from experiments almost overlap with the ideal ones, there
are still small deviations between curves, indicating the presence
of angular detection errors in these sensors.
By subtracting predetermined angles of input magnetic field
(␪Field ) from measured results (␪Measured ) by angle sensors, we can
calculate angular errors for our devices across one full rotation.
Angular detection errors from single-layer AMR sensors are plotted in Fig. 6a. Angular errors can also be analyzed in the frequency
domain by means of the fast fourier transform (FFT). As shown in
Fig 6b, the error spectrum of single-layer AMR angle sensors can
be calculated based on the collected data. The majority of spectral
errors reside in two dominant parts: the 2nd harmonic component
and the 8th harmonic component. Specifically, the 2nd harmonic
error can be attributed to the induced anisotropy in AMR sensing
materials, whereas the 8th harmonic error arises from the shape
anisotropy due to our sensor geometry.
A quadruple-layer AMR angle sensor was also fabricated and
measured for comparison. Fig. 7 gives angular errors of quadruplelayer AMR sensors from 0◦ to 360◦ , and their corresponding error
spectrum. A much smaller 2nd harmonic error can be observed
in the quadruple-layer AMR angle sensors, compared with the
traditional single-layer AMR angle sensors, which have only one
ferromagnetic layer. Due to isotropic magnetic anisotropy in the
quadruple AMR thin films, uniform magnetization in all rotational
directions can be achieved, leading to the reduction of angular
errors. Therefore, the proposed quadruple-layer sensing stack is
beneficial for lowering the intrinsic 2nd harmonic error in AMR
angle sensors.
On the other hand, the 8th harmonic error, which is another
dominant error source, can be attributed to sensor shape and layout. Fabricated quadruple AMR angle sensors that have identical
geometry to the single-layer sensors show a similar 8th harmonic
error. The error can be estimated from theoretical calculation,
according to the Stoner-Wohlfahrt model as follows [34]:
E = Ku +
1
0 NM 2 sin2 (MR − ω) − 0 MH cos ϕH cos MR − 0
2
MH sin ϕH sin MR
(6)
where Ku is the induced anisotropy, M is the total saturation magnetization, H is the applied external magnetic field, and N is the
demagnetizing factor, which can be estimated by utilizing an equation for rectangular ferromagnetic prisms [35]. Also, angles in the
equation indicate the magnetization angle ␪MR , field angle ␸H , and
sensing element angle ␻. All three angles have 0◦ aligned with the
easy axis of the first ferromagnetic layer. Since the quadruple-layer
AMR sensor has an isotropic induced anisotropy, the Ku term is
independent of angle. However, the sensing element angle ␻ can
be pointing at four different directions within the two Wheatstone
Y. Guo et al. / Sensors and Actuators A 263 (2017) 159–165
(b)
(a)
Amplitude [degree]
Angular error [degree]
0.8
0.4
0.0
-0.4
-0.8
0
163
90
180
270
0.4
0.2
0.0
0
360
2
Angle [degree]
4
6
8
10
Harmonic Number
Fig. 6. (a) Angular error of single-layer AMR sensors between 0◦ and 360◦ . (b) Angle error spectral analysis of single-layer AMR sensors.
(a)
(b)
0.4
0.4
Amplitude [degree]
Angular error [degree]
0.8
0.0
-0.4
-0.8
0
90
180
270
360
Angle [degree]
0.2
0.0
0
2
4
6
8
10
Harmonic Number
Angular error [degree]
Fig. 7. (a) Angular error of quadruple-layer AMR sensors between 0◦ and 360◦ . (b) Angle error spectral analysis of quadruple-layer AMR sensors.
0.8
0.4
0.0
-0.4
-0.8
0
90
180
270
360
Angle [degree]
Fig. 8. Therotical estimation of the 8th harmonic error in patterned quadruple-layer
AMR angle sensors.
bridges, thus leading to an 8th harmonic error that arises out of
shape anisotropy. Fig. 8 demonstrates a therotical estimation of the
8th harmonic error in patterned quadruple-layer AMR angle sensors. The calculated error pattern is very similar to the experimental
result that is shown in Fig. 7a. In order to further reduce angular
errors in the quadruple-layer angle sensors, the 8th harmonic error
can be corrected by subtracting theoretically calculated values from
the measured ones.
Fig. 9a gives a comparison of angular errors between 0◦ and 360◦ .
The quadruple-layer AMR angle sensor with 8th harmonic correction algorithm illustrates much smaller angular errors than the
conventional single-layer sensor. The average angular error is only
∼20% of its original value. Fig. 9b shows the resultant error spectra.
In comparison with a traditional single-layer angle sensor, which
is influenced by both the 2nd and 8th intrinsic harmonic errors, the
quadruple-layer AMR angle sensor with correction algorithm illustrates a flat error spectrum. Therefore, this sensor demonstrates
better performance, and is promising in applications requiring high
accuracy angle detection.
Fig. 10 gives the relationship between the magnetic fields and
the average of the absolute values of angular errors over one rotation; dashed lines are the corresponding nonlinear fitting curves.
Magnetic field dependence of errors is studied for both single and
quadruple-layer AMR sensors. The quadruple-layer AMR angle sensor illustrates smaller angular errors than does the single-layer one
for diverse applied magnetic fields. In addition, use of the quadruple AMR sensing stack can lower requirements for hard magnets.
Due to magnetic anisotropies in soft ferromagnetic thin films, AMR
angle sensors will have large output deviations, if a relatively low
magnetic driving field is applied. So, a strong hard magnet is usually
used to lower detection errors. In quadruple-layer angle sensors,
however, the same angle detection accuracy can still be achieved
for relatively small magnetic field magnitudes, allowing the use
of weaker and cheaper magnets. With an applied magnetic field of
150 Oe, our single-layer AMR angle sensor demonstrates an average
angular error of about 0.3◦ , whereas the proposed quadruple-layer
angle sensor with correction algorithm achieves a better angle
detection accuracy even at a weaker applied field of 80 Oe. Therefore, the quadruple AMR sensors show lower detection errors even
Y. Guo et al. / Sensors and Actuators A 263 (2017) 159–165
0.8
0.5
1 layer
4 layers w/ correction
(a)
(b)
0.4
0.0
-0.4
-0.8
0
90
180
270
360
1 layer
4 layers w/ correction
0.4
Amplitude [degree]
Angular error [degree]
164
0.3
0.2
0.1
0.0
0
Angle [degree]
2
4
6
8
10
Harmonic Number
Fig. 9. (a) Comparison of angular errors between 0◦ and 360◦ . (b) Spectral analysis of angle errors in different AMR angle sensors.
Angular Error [degree]
1.2
References
1 layer
4 layers w/ correction
1.0
Fitting 1 layer
0.8
Fitting 4 layers w/ correction
0.6
0.4
0.2
0.0
60
90
120
150
Field [Oe]
Fig. 10. Relationship between applied magnetic field and mean magnitude of angular errors over one rotation for both single and quadruple-layer AMR sensors. Dashed
lines are the corresponding nonlinear fitting curves.
at smaller magnetic fields, hence allowing for more economical
AMR angle sensors, while maintaining high performance.
5. Conclusion
A multilayer AMR sensing structure has been presented for angle
sensing and is compared with conventional single-layer AMR thin
film. Intrinsic errors of AMR angle sensors have been studied. Based
on spectral analysis, angular errors are dominated by the second
harmonic component caused by induced anisotropy, and the eighth
harmonic component from shape anisotropy. Angular detection
errors can be effectively eliminated by a quadruple-layer AMR angle
sensor with a correction algorithm. In addition, the quadruple-layer
sensor demonstrates good accuracy even when operating at a low
magnetic field, which relaxes the requirement for expensive, rareearth permanent magnets. Therefore, the proposed multilayer AMR
angle sensor, with its enhanced accuracy and cost-effectiveness,
can be a very promising candidate in a wide range of industrial
applications.
Acknowledgements
The authors thank Chin Chun Ooi for critical reading of the
manuscript. Part of this work was performed using the Stanford
Nanofabrication Facility and the Stanford Nano Shared Facilities at
Stanford University.
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Biographies
Yue Guo obtained his Ph.D. in Electrical Engineering from Stanford University in
January 2017. His research includes advanced piezoresistive and magnetoresistive
sensors for different industrial applications.
Yong Deng received his B.S. degree in chemistry from University of Science and
Technology of China in 2015. He is currently a PhD candidate in the Department
of Materials Science and Engineering at Stanford University. His research includes
magnetoresistive and magnetostrictive materials.
Shan X. Wang obtained his Ph.D. in Electrical and Computer Engineering from CMU
in 1993. He is a Professor and Associate Chair of Materials Science & Engineering and
jointly Professor of Electrical Engineering at Stanford University, and by courtesy,
a Professor of Radiology at Stanford School of Medicine. He directs the Center for
Magnetic Nanotechnology, and is a co-Principal Investigator of the Center for Cancer Nanotechnology Excellence for Translational Diagnostics (CCNE-TD) at Stanford
University. He has over 250 publications, and holds 54 issued or pending patents
in the area of magnetic nanotechnology, biosensors, nanofabrication, spintronics,
power management and information storage. He is a scientific founder of MagArray
Inc. and serves on the advisory boards of Nvigen Inc. and several other companies.
He is elected a Fellow of the Institute of Electrical and Electronics Engineers (IEEE)
and a Fellow of American Physical Society (APS) for his seminal contributions to
magnetic materials and nanosensors. He has been recognized by numerous other
honors and awards, including an Inaugural Frederick Terman Fellowship, a Distinguished Award in Nokia Sensing XCHALLENGE, and a finalist in Qualcomm Tricorder
XPrize competition.