Sensors and Actuators A 237 (2016) 62–71
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical
journal homepage: www.elsevier.com/locate/sna
Design and fabrication of an innovative three-axis Hall sensor
C. Wouters a,c,∗ , V. Vranković a , C. Rössler b , S. Sidorov a , K. Ensslin b , W. Wegscheider b ,
C. Hierold c
a
b
c
Magnet Section, Paul Scherrer Institute, CH-5232 Villigen, Switzerland
Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
Micro and Nanosystems, ETH Zürich, CH-8092 Zürich, Switzerland
a r t i c l e
i n f o
Article history:
Received 24 August 2015
Received in revised form 28 October 2015
Accepted 19 November 2015
Keywords:
3D Hall sensor
High-accuracy Hall sensor
Planar Hall effect
Three-axis magnetic field measurement
Small active volume
a b s t r a c t
The measurement of all three components of a magnetic field, simultaneously to high precision with
Hall sensors, remains a challenge. Given the high precision of state-of-the-art conventional uniaxial Hall
sensors, this is disappointing. Currently, three-axis Hall sensors suffer from either, or a combination, of the
following: large spatial distribution between active areas; high signal noise; cross-sensitivity between
measurement axes due to angular errors or the planar Hall effect; the inability to measure at a single
point in space and time. A new type of three-axis Hall sensor is proposed, consisting of three sets of
uniaxial Hall sensors in a small active volume. The feasibility of the proposed sensor has been proven in a
prototype with an active volume as small as 200 !m × 200 !m × 200 !m. Due to its unique configuration,
the new sensor addresses current three-axis Hall sensor limitations: it provides a high spatial resolution
of 30 !m × 30 !m × 1 !m for each field component; full field vector measurements practically at a single
point in space and time; and a reduction of the planar Hall effect by a factor of 35. Angular errors between
the individual Hall sensors in the prototype lie between 0.1◦ and 0.5◦ , above the tolerable error for
non-corrected measurements. However, once understood they can be taken into account. With proper
calibration, this type of three-axis Hall sensor has great potential for high-accuracy three-axis magnetic
field measurements and is particularly suitable for field mapping of magnets.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Hall effect devices are used in a range of applications, like in
solid-state physics for carrier mobility and concentration measurements, position and motion sensing, current measurements,
switches, and the most obvious application is magnetic field measurements.
Hall sensors are routinely used in magnetic field measurements
and mapping of detector magnets in particle physics experiments
and of beamline magnets for particle accelerators with magnetic
fields in the range from milliTesla to a few Tesla. Typically, measurements are done on-the-fly with voltage-to-field reconstruction
done offline. Conventional uniaxial Hall sensors applied for this
task are essentially plate-like devices, and are often referred to
as Hall plates or 1D Hall sensors. Their sensing part is typically a
four terminal cruciform semiconductor in a plane with dimensions
in the micrometer to submillimeter range. The cruciform is most
∗ Corresponding author at: Magnet Section, Paul Scherrer Institute, CH-5232 Villigen, Switzerland. Fax: +41 563103383.
E-mail address: christina.wouters@psi.ch (C. Wouters).
http://dx.doi.org/10.1016/j.sna.2015.11.022
0924-4247/© 2015 Elsevier B.V. All rights reserved.
prevalent because it has a well-defined small and symmetric active
area, making it ideal for point-like measurements and hence for
field-mapping of magnets. The voltage generated in a Hall sensor
is proportional to the magnetic field component along its surface
normal (Hall effect) and to a tangential magnetic field component
(planar Hall effect). The latter is a much smaller but measurable and
generally unwanted effect. Accurate measurements with such Hall
sensors are therefore constrained to single-component magnetic
field volumes with perpendicular sensor orientation to the magnetic field direction. 1D Hall sensors are thus perfectly suitable for
mapping the midplane of e.g., dipole and quadrupole magnets. With
careful alignment, temperature stabilization or correction, and a
repeated thorough calibration of the Hall sensor, a measurement
precision of under 10−4 at the 1 T level can be consistently achieved.
If the magnetic field to be measured is not a predominantly
single-component field, measuring it with a 1D Hall sensor is cumbersome, complex, slow, and might lead to large errors due to the
planar Hall effect. In those cases, three-axis Hall sensors are necessary.
The most straightforward way to measure all three field components simultaneously, is by combining three individual and
C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
orthogonally arranged 1D Hall sensors. The main intention with
this type of three-axis Hall sensor is that the high sensitivity and
excellent precision of the 1D Hall sensor can simply be extended to
three directions. The major drawback is that measurement errors
due to the planar Hall effect and due to non-orthogonality between
the individual Hall sensors can be high. Another drawback is the
large spatial distribution of the single elements. Although adept
placement of three sensors could reduce the distance to a minimum of 250 !m [1], reduction to zero is not possible, preventing
measurements of all field components at the same point at the same
time.
The second type of 3D Hall sensors is Integrated Circuit (IC) Hall
sensors realized by CMOS technology. They incorporate a three-axis
Hall sensor on a single chip: either monolithic [2], or by integrating two or more vertical and horizontal Hall sensors [3]. Monolithic
devices have potentially smaller active volumes due to the reduced
number of contacts since they have only one active region to
63
measure all three field components. However, the performance of
monolithic devices is lowered by the difference in sensitivity to the
three field components as well as cross-sensitivity among them
[2,4,5]. Vertical Hall sensors have inferior characteristics such as
higher offset and lower sensitivity compared to horizontal Hall sensors [6]. The spinning-current technique [7], which compensates
for planar Hall voltages as well as offset voltages, is less effective
when applied to vertical Hall sensors due to the more complex
current flow in these devices [8]. Attempts to improve the performance of vertical Hall devices, by optimizing their symmetry, have
recently resulted in low offset vertical Hall devices [9,10]. Although
the technology has been applied in a 2D device [11], the achieved
accuracy is of the order of a percent and it is yet to result in a 3D
device. Instead, a different type of sensor was pursued in the form of
a hexagonal prism [12]. Isotropic sensitivity to all three field components was achieved but with a thickness of 525 !m, its active
volume is big and, the obtained accuracy is again of the order of a
Fig. 1. Design of the three-axis Hall sensor.
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C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
percent. Also, the three field components cannot be measured at
the same time.
Striving towards high accuracy room-temperature magnet measurements, this paper demonstrates the design and fabrication of a
new type of three-axis Hall sensor, which consists solely of superior
1D Hall plates. Due to its unique configuration, the sensor provides a small spatial distribution of active areas, equal sensitivity
to all three magnetic field components, full field vector measurements virtually at a single point in space and time, and substantial
compensation of the planar Hall effect.
2. Design
The considerations above have led to a novel design for a threeaxis Hall sensor. It is a combination of six 1D Hall sensors in such
way that each Hall sensor forms one face of a submillimeter-sized
cube. Pairs of sensors from opposite faces are sensitive to the same
component of the magnetic field vector. Such a geometry has several advantages. First, the high sensitivity and precision of 1D Hall
sensors is exploited. The double readings for each field component
by the pairs enhance the precision. Second, the averaged values of
Fig. 2. Flowchart of the fabrication process.
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C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
the pairs for all three field components can be assigned to the same
point in space, at the center of the cube. This allows for measurement of the full field vector at that point at the same time. And last,
with appropriate electrical connections of the 1D Hall sensors from
opposing cube faces, described in Sections 3 and 4, the undesired
planar Hall effect can be practically cancelled out.
Simply assembling six Hall sensors onto a cube is not satisfactory
as it results in a large spatial distribution of the active areas, hardly
below a few millimeters. A special design that reduces the active
volume to 200 !m × 200 !m × 200 !m was proposed [13].
The design of the three-axis Hall sensor is depicted in Fig. 1.
It consists of six 1D Hall sensors, each located on a cuboid support with a 2.1 mm × 2.1 mm base and 1.9 mm height including
the Hall sensor, see Fig. 1a. When assembled, these six building
blocks form an inner hollow cube of 1D Hall sensors with dimensions 200 !m × 200 !m × 200 !m. The six sensors form the faces of
this inner cube, with their active areas at the center of each face. In
Fig. 1b and c, respectively, the 1D Hall sensor and the cuboid support
design are shown. The cruciform sensing part with an active area
of 30 !m × 30 !m is located at the corner of the Hall sensor, in the
center of a 200 !m × 200 !m area. Its metal contacts are extended
outwards to gain a larger pad surface area for easier wire soldering
or bonding. Three sensors are designed as shown in Fig. 1b, and the
other three are their mirror images. Fig. 1d shows the assembly of
two halves with three building blocks, and Fig. 1e the complete 3D
Hall sensor. For clarity, the pairs of Hall sensors that are sensitive
to the same magnetic field component are shown in the same color
(red, green or blue). The channel cutouts in the cuboid supports are
designed to accept the wiring (not shown). The inner volume of
200 !m × 200 !m × 200 !m is formed by the 200 !m difference in
height and width of the building blocks. This is more clearly shown
in a cross section of the 3D Hall sensor in Fig. 1f.
nality between measurement axes is 0.1 mrad or 0.006◦ . This is
technologically extremely hard if not impossible to achieve at this
scale in a three-axis Hall sensor made up of individual Hall plates.
However, this does not invalidate the concept. For example, current
three-axis IC Hall sensors, despite their single chip configuration,
claim the non-orthogonality between the measurement axes to be
no better than <0.5◦ [7]. The remedy to overcome too large angular
errors is to in effect reduce them by a suitable calibration method.
Even if the set criterion of 0.006◦ is out of reach, it is beneficial to
minimize the angular errors because for small angular errors, the
correction will be linear.
3.2. Planar Hall effect compensation with a pair of Hall plates
Cross-sensitivity between the measurement axes also arises
from the planar Hall effect. It is well known that, because of the
double angular dependence of the planar Hall effect (see Eq. (1)),
the generated planar Hall voltage can be compensated for by averaging the output of two Hall plates placed in parallel and rotated
in plane 90◦ to each other [15,16]. The cancellation is complete if
the planar Hall coefficients of the two plates are equal, the in-plane
rotation between the two plates is 90◦ , and the values of the Bp
components in both plates are the same. Consider the realistic case
of two Hall plates with slightly different planar Hall coefficients
PH1 and PH2 and in-plane field components Bp1 and Bp2 . Let ! be the
angle between Bp1 and the Hall current vector of Hall plate 1, and
let ϕ be the in-plane rotation angle between the two plates. The
average of the two planar Hall voltages is then
1
1
(VPH1 + VPH2 ) =
2
2
Vout = VH + VPH =
!R "
H
t
IBn +
!P "
H
t
IB2p sin2!
(1)
where t is the Hall plate’s active layer thickness, RH is the Hall coefficient, and PH , by analogy, is the planar Hall coefficient. Bn is the
magnetic field component normal to the Hall plate, and Bp is the
field component in the plane of the Hall plate and is at an angle !
with the Hall current vector.
3.1. Angular errors between measurement axes
Ideally, in a three-axis Hall sensor there should be no crosssensitivity between the measurement axes. Field component
measurements along one measurement axis should be independent of the value of field components along the other measurement
axes. Ignoring the planar Hall effect for the moment, this only holds
true when the three measurement axes of the three-axis Hall sensor are perfectly orthogonal or, in other words, when the field
vector can be decomposed orthogonally along the three measurement axes. Imposing a target upper limit of 10−4 in cross sensitivity
implies that the maximum allowed angular error in the orthogo-
H1
t
IB2p1 sin(2!) +
# $
# #
$$$
1#
≡
A1 sin 2! + A2 sin 2 ! − ϕ
2
3. Measurement accuracy description
Three-axis Hall sensors made of conventional Hall plates face
three main accuracy-limiting factors: angular errors between their
measurement axes; the planar Hall effect; and the spatial distribution between their sensing areas. In relation to these factors,
what are the requirements for a three-axis Hall sensor as proposed
above?
The measured voltage of a homogeneous and isothermal Hall
plate driven at a constant current I in a magnetic field B is the sum
of the Hall voltage generated by the Hall effect and a planar Hall
voltage generated by the planar Hall effect [14]:
!! P "
=
!P "
H2
t
"
IB2p2 sin(2(! − ϕ))
# $ #
# $$
1
(A1 + A2 cos (2ϕ)) sin 2! + −A2 sin (2ϕ) cos 2!
2
(2)
where A1 = (PH1 /t)IBp1 2 and A2 = (PH2 /t)IBp2 2 are the planar Hall
voltage amplitudes of the individual Hall plates. Eq. (2) can be
rewritten in the form
1
(VPH1 + VPH2 ) = Csin(2! + #)
2
(3)
where C = 1/2 sqrt((A1 + A2 cos(2ϕ))2 + (-A2 sin(2ϕ))2 ) is the amplitude of the average planar Hall voltage of the pair of Hall plates,
and # = arctan((−A2 sin(2ϕ))/(A1 + A2 cos(2ϕ))). Working out the
amplitude C gives
C=
#
$
1
sqrt A21 + A22 + 2A1 A2 cos (2ϕ)
2
(4)
In the ideal case where A1 = A2 ≡ A and ϕ = $/2, the amplitude C is
zero and the planar Hall voltage is fully canceled out by the two
plates.
3.2.1. In-plane rotation angle error
Assume the ideal case except for the angle % which due to misalignment is equal to "/2 + #, where ε is small. Then
C=
≈
#
$ 1
1
sqrt 2A2 (1 + cos ($ + 2ε)) = Asqrt (2 (1 − cos (2ε)))
2
2
# # #
$$$
1
Asqrt 2 1 − 1 − 2ε2
= Aε
2
(5)
Therefore the ratio C/A, between the amplitude of the average planar Hall voltages of two plates, and the amplitude of the planar Hall
voltage of a single plate, is ε. For small angular errors, this means
that per degree angular error in the placement of the two plates,
1.7% of the planar Hall voltage is not cancelled out.
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3.2.2. Unequal planar Hall coefficients
Next, assume the ideal case expect for the planar Hall coefficients of two plates not being exactly equal. This can occur because
no two Hall plates are identical. In this case the amplitude C
becomes
2
C=
IBp
1
1
|A1 − A2 | = |PH1 − PH2 |
2
2
t
(6)
and the ratio C/A, between the amplitude of the average planar
Hall voltages of two plates, and the amplitude of the planar Hall
voltage of a single plate, is (1/2)|PH1 − PH2 |/PH1 . This means that for
1% difference between the two planar Hall coefficients PH1 and PH2 ,
0.5% of the planar Hall voltage is not cancelled out.
3.2.3. Unequal in-plane magnetic field component
Finally, assume the ideal case except that the in-plane magnetic
field component is not equal for both plates. Then the amplitude C
is
1 2
2 IP H
C = |Bp1
− Bp2
|
2
t
(7)
and the ratio C/A, between the amplitude of the average planar Hall
voltages of two plates, and the amplitude of the planar Hall voltage of a single plate, is (1/2)|Bp1 2 − Bp2 2 |/Bp1 2 . For small percentage
differences in the field components, the effect on the planar Hall
voltage compensation is one to one: that same percentage of the
planar Hall voltage is not cancelled out.
There can be two reasons why the in-plane field component is
different for two Hall plates. The first is a non-parallelism between
the plates. If the angle between the plates’ normal vectors is ', then
the largest relative difference in in-plane field components that
occurs is (Bp − Bp cos')/Bp = 1 − cos'. The second cause for a different in-plane field component for two Hall plates is their spacing in
a non-homogeneous field. The larger their spacing d and the higher
the field gradient ▽Bp over this distance, the larger the difference:
|Bp1 − Bp2 | = ▽Bp d.
(8)
3.3. Spatial distribution
The spatial distribution of active areas within a three-axis Hall
sensor would be ideally zero, meaning that the full magnetic field
vector is measured at a point. In the three-axis Hall sensor design
presented in the previous section, the active areas of the three
orthogonal pairs of Hall plates are distributed over a cube of size
200 !m × 200 !m × 200 !m. But, by employing a pair of Hall sensors for each of the three field components, the Hall voltages can
be assigned practically to a single point, making the spatial distribution virtually zero. In reality however, the measurement axes of
the six individual Hall plates will not cross at a single point, due to
alignment errors in the fabrication process. Therefore, the averaged
values of the three pairs of Hall plates are not truly assigned to a
point but rather three proximate points.
In a non-homogenous field, the field vector is different at the
separate locations of the individual Hall plates. The assigned average of the Hall voltages of a pair to the midpoint between them only
deviates from the real field at that midpoint when the field distribution is non-linear. The smaller the distance between the pair of
Hall plates, the smaller the error. In a quadratic field distribution
the maximum error that is made by taking the field between two
plates spaced a distance d apart to be linear is a(d/2)2 , where a is the
quadratic coefficient of the field distribution. For a spacing as small
as 200 !m and a tolerable error of 10−4 , fields up to 10 000 Tm−2
induce less than the tolerable error.
Fig. 3. Optical microscope image of the cruciform mesa plus contact areas (before
metallization) for two mirror image Hall sensors.
4. Device fabrication
The fabrication process involves three main steps. First the individual Hall plates and support cuboids are fabricated. In a second
step, each of the Hall plates is mounted on a cuboid support. Finally,
six Hall cuboids are wired and assembled into the complete device.
In a perfect assembly the inner hollow volume forms a perfect
cube of dimensions 200 !m × 200 !m × 200 !m, in which the three
measurement axes are orthogonal and cross at a single point. To
minimize limitations in measurement accuracy due to angular and
alignment errors, tight dimensional tolerances were striven for in
both the Hall plate and support cuboid dimensions. At this point,
for the prototype, the tolerance was 10 !m. The process flow for
the fabrication of the individual Hall plates is shown in Fig. 2a–h as
a cross-sectional view through the four contact pads. The process
flow for the assembly steps is shown in Fig. 2i–k.
4.1. Hall plate fabrication
The wafer material for the fabrication of the individual Hall
plates is a 1 !m thick Si-doped GaAs layer that was grown on a
500 !m GaAs substrate by molecular beam epitaxy. The carrier density of the layer is in the range of (6.7–9.1) × 1016 cm−3 , and the
electron mobility at 4.2 K is in the range of 1700–2150 cm2 V−1 s−1 .
At room temperature the mobility is estimated from Hall voltage and bias voltage measurements of the fabricated Hall plates,
and was found to be roughly 4300 cm2 V−1 s−1 . The four-terminal
cruciform mesa pattern as shown in Fig. 3 was obtained by photolithography using S1828 photoresist, followed by wet etch in
H2 O:H2 SO4 :H2 O2 (100:3:3) for 10 min.
Ohmic contacts were realized by alloying evaporated Au/Ge/Ni,
which is a well-established and widely used Ohmic contact to
n-GaAs. They have low resistivity [17,18] and are found to be nonmagnetic [19,20]. Before the metallization step, the contact areas on
the mesa are patterned by photolithography using AZ5214 image
reversal photoresist. To obtain an undercut profile, the photoresist
is exposed everywhere, except at the desired contact areas, and is
then image reversal baked followed by flood exposure without a
mask. After patterning, Ohmic contacts were realized by thermal
evaporation of Ge (18 nm)/Au (50 nm)/Ge (18 nm)/Au (50 nm)/Ni
(40 nm)/Au (100 nm), a lift-off process, and annealing under nitrogen flow for 20 s at 450 ◦ C.
Dicing of the wafer material into 2.1 mm by 2.1 mm die was done
with a precision diamond scriber. For this purpose, marker lines
were included in the photomask to define the lines along which the
wafer material is to be scribed under the microscope of the diamond
scriber tool. The error in dimensions of the die that resulted from
C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
67
Fig. 4. Dicing with precision diamond scriber tool.
this dicing method was less than 5 !m deviation from the nominal
value, see Fig. 4.
4.2. Support cuboids.
The material for the support cuboids should be a non-magnetic,
non-conductive (no Eddy currents), rigid material that is machinable to tight tolerances. The material’s coefficient of thermal
expansion should match that of GaAs, 5.75 !m m−1 ◦ C−1 (room
temperature) [21].
Polyether ether ketone (PEEK), sapphire, and MACOR were considered as suitable materials. PEEK is a robust thermoplastic and
cheap compared to MACOR and sapphire. Being a plastic, its linear coefficient of thermal expansion is highest among the three
materials, 30 !m m−1 ◦ C−1 (20–100 ◦ C) [22], and is about five times
higher than the thermal expansion coefficient of GaAs. The linear
expansion coefficient of sapphire is closest to that of GaAs. It lies,
depending on crystal orientation, in the range 5.0–5.8 !m m−1 ◦ C−1
(20–50 ◦ C) [23]. The drawback of sapphire is its extreme hardness
and expensive machining with diamond tools. Due to their transparency to light, a coating would be necessary which is yet another
drawback for sapphire.
MACOR is machinable with standard metal working tools to
tight tolerances—up to 13 !m as listed by the manufacturer (Corning Inc.). According to the manufacturer, the linear coefficient of
thermal expansion is 9.0 !m m−1 ◦ C−1 (25–300 ◦ C), which is close
to that of GaAs. Therefore, MACOR has been chosen as the material
for the cuboid supports.
The support cuboids were fabricated by CNC machining. The
critical overall dimensions of the cuboids were controlled and
lay well within the given tolerances of 10 !m. The batch of 16
cuboids had an average width, length and height of 2.103 mm,
2.101 mm and 1.400 mm (nominal values: 2.1 mm, 2.1 mm and
1.4 mm) respectively, with standard deviations of 5 !m, 0.3 !m and
0.5 !m respectively.
4.3. Assembly
A low error of less than 5 !m was achieved in the nominal
dimensions of the Hall plates as well as the support cuboids. But
for the ultimate angular and alignment errors between the six Hall
plates, the assembly is a decisive and therefore a critical step in
the fabrication process. The assembly of the three-axis Hall sensor
was done in three sub-steps, using alignment tools that were made
especially for each assembly step. First, six individual Hall plates
were each mounted on a MACOR cuboid. Next, two Hall cuboids
were mounted together and finally, the complete assembly of 3 × 2
Hall cuboids was made.
The Hall plates were each mounted on their MACOR support
cuboids using epoxy (without fillers), which added up to 15 !m
to the overall height. The accuracy of the outer dimensions of the
three-axis Hall sensor are irrelevant, and only the inner active volume of 200 !m × 200 !m × 200 !m is important. Therefore, each
cuboid and Hall plate has only two out of four side surfaces that
need to be aligned after assembly, namely those adjacent to the
corner with the cruciform active area. For this task, an alignment
tool was made with which the Hall plate and the MACOR support
cuboid can be held at a right angle and clamped together during
the curing of the epoxy in an oven at 70 ◦ C for several hours.
In the next step, electrical connections were made to three out
of six Hall plates (2, 4 and 6 in Fig. 2j) by soldering 100 !m diameter copper enameled wires to their contact pads. Then, in a second
alignment tool, two cuboids with Hall plates were glued together
with epoxy and cured in an oven at 70 ◦ C for few hours. In this
assembly step, one common side surface needs to be aligned and a
200 !m step in height of the assembled pair needs to be assured.
Therefore, the second alignment tool was made such that each
cuboid with Hall plate can be pushed from top and sides into a right
angle on a horizontal base plate with a 200 !m elevated step, see
Fig. 5a for a schematical drawing. After assembly, the total height
of the three pairs deviated from the nominal value (4000 !m) by
16 !m, 28 !m, and 30 !m, which is ascribed mainly to the glue
thickness.
In the final assembly step, electrical connections were made to
the remaining three Hall plates by soldering 100 !m diameter copper enameled wires to their contact pads. After that, the three pairs
of cuboids plus Hall plates were glued together with epoxy into
the complete device. Since in this step the inner closed volume is
formed, the aligned surfaces are inaccessible, and the three pairs of
cuboids plus Hall plates are aligned to their outside surfaces. This is
done in a third alignment tool where the three pairs are pushed into
a right angle on a flat horizontal base during the curing of epoxy
in an oven at 70 ◦ C for several hours. The final assembly step is
schematically represented in Fig. 5b and the result of the assembled prototype three-axis Hall sensor in its final assembly tool is
shown in Fig. 6.
4.4. Electrical connections
The electrical connections were made carefully, such to counteract two effects. The first is the planar Hall effect. To compensate
for it, the bias current directions in pairs of Hall plates on opposing
cube faces are defined to be 90◦ rotated with respect to each other.
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C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
Fig. 5. Schematical drawing of (parts of) the assembly tools.
In that case, the planar Hall voltages in pairs of Hall plates have
opposite signs and cancel out by averaging.
The second effect is an unwanted induced voltage between the
Hall voltage contacts. Such induced voltages occur in loops during
on-the-fly magnetic measurements due to magnetic flux change.
Loops outside of the Hall plate are avoided by using twisted pair
wires. The loop on the Hall plate itself has an area of about 1 mm2 .
The positive and negative bias current connections on each Hall
plate were chosen such that the induced voltages in two Hall plates
from opposing cube faces have opposite sign, and hence cancel out
by averaging.
5. Results of the prototype three-axis Hall sensor
Preliminary results of the prototype three-axis Hall sensor were
obtained in a 38 mm gap dipole magnet with a magnetic field range
up to 2 T. The field homogeneity decreases with magnetic field
strength, at the maximum field of 2 T the homogeneity is 10−4 in
an area of 10 mm radius. The sensor is placed in the center of the
dipole magnet on a non-magnetic rotary system with two rotation
axes. The system is based on two non-magnetic piezoelectric rotary
positioners (SmarAct SR-2013-S-NM) which have a movement resolution of <3 !rad and a sensor resolution of 25 !rad.
Unless stated otherwise, the forthcoming results of the sensor
were obtained at 1 T, a common field strength for beamline magnets, and at a direct bias current of 0.1 mA which was supplied
to all six Hall plates in series by a Keithley 6221 constant current
source. The Hall voltages were read by 8½-digit Agilent 3458A digital multimeters. A detailed description of the characterization of
the three-axis Hall sensor as well as its calibration, is outside the
scope of this manuscript and will be published independently.
5.1. Basic characteristics of the Hall plates
The Hall plates in the prototype three-axis Hall sensor were fabricated from GaAs whose characteristics are summarized in Table 1.
The measured values of the six individual Hall plates lie within
the ranges given in Table 1. The input resistance was measured
between two current contacts in absence of bias current and magnetic field. The offset values are to be taken into account by the
calibration of the sensors, e.g., as the zeroth coefficient of a polynomial function (constant). The non-linearity was measured over
the full range from 0 to 2 T and is defined as the maximum deviation between the measured Hall voltage and the ideal linear Hall
voltage from a linear fit to the data, given in percentage of the Hall
voltage at the point of maximum deviation.
The basic parameters of the Hall plates depend on the geometry
of the active area and the semiconductor material chosen. It should
therefore be noted that the parameters are not an indicative figure of merit of the proposed three-axis Hall sensor. Semiconductor
material and doping level can be chosen freely to suit best a given
application, without modification of the design presented in Fig. 1.
5.2. Orthogonality error
The orthogonality error among all neighboring Hall plates has
been studied by rotating the three-axis Hall sensor in a 1 T homogeneous field around three main axes. The errors lie in the range
between 0.1◦ and 0.5◦ with two outliers of 0.01◦ and 1.0◦ . The three
pairs of MACOR cuboids and Hall plates assembled in the second
step, see Fig. 2j, have orthogonality errors between 0.2◦ and 0.3◦ .
Thus it is plausible that larger errors are due to the third assembly
step. In the third assembly step, a clamping of the Hall cuboids from
the top was foreseen but omitted to avoid force on the soldered
wires before the epoxy was cured. To be conclusive, one needs to
observe the errors in additional assemblies.
5.3. Planar Hall voltage compensation
Fig. 6. The three-axis Hall sensor in its final assembly tool.
Planar Hall voltage compensation by the pairs of Hall plates in
the three-axis Hall sensor was demonstrated by rotation of a pair of
Hall plates in such a way that the magnetic field and the Hall plates
are coplanar to within a degree. It was found that without compensation, the Hall plates’ sensitivity to the planar Hall effect was
already between 500 and 600 times smaller than the sensitivity to
C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
69
Table 1
Basic characteristics of the GaAs Hall plates in the prototype three-axis Hall sensor.
Sensitivity [V A−1 T−1 ]
100–107
Offset voltage [!V] (B = 0 T)
2–80
Input resistance [(]
650–740
the Hall effect. Therefore, without compensation the expected error
would be about 2 mT in a 1 T field or 0.2%. In Section 3 it was shown
that a successful compensation depends on two things—the deviation from a 90◦ in-plane rotation angle between the two plates,
and the inequality of the planar Hall voltage amplitude between
the two plates. The error in in-plane rotation angle is largest for the
red pair, and is about 1.2◦ . For the green pair it is 0.7◦ but the difference in planar Hall voltage amplitudes between two plates is largest
in this pair due to non-parallelism of the plates. The combination of
both effects makes the compensation method least effective for the
green pair. The result of the planar Hall voltage compensation for
the green pair is shown in Fig. 7, where ! is the angle between the
in-plane magnetic field vector and the bias current vector of one
Hall plate. The dashed curve is the planar Hall voltage extracted
from the measurement with a single Hall plate. The solid curve is
the calculated average of the planar Hall voltages extracted from
the measurement by the two Hall plates. The pairs’ remnant planar
Hall voltage amplitude after compensation is below 0.5 !V ↔ 50 !T
for a 1 T in-plane field (maximum error). Therefore, by using pairs
of Hall plates, the planar Hall voltage could be reduced about 35
times even for the worst aligned pair, and can almost certainly be
reduced further by better alignment.
5.4. Estimate of the lower limit accuracy of the three-axis Hall
sensor
The accuracy of the three-axis Hall sensor can be assessed in
a straightforward way by reconstructing the total magnetic field.
Namely, regardless of the orientation of the three-axis Hall sensor
with respect to any magnetic field vector, the magnitude of this
vector Bmod = sqrt(Bx 2 + By 2 + Bz 2 ), as measured by the combined
output of the individual Hall plates in the three-axis Hall sensor,
has to be constant. Assuming the response of the Hall plates to
the magnetic field is linear, and the planar Hall effect is fully cancelled out, the total signal voltage Vtot is given by the expression
sqrt(Vx 2 + Vy 2 + Vz 2 ) where Vx , Vy and Vz are the average output
voltages of the three pairs of Hall plates. In general, the response
of a Hall plate does not scale linearly with magnetic field, and RH
in Eq. (1) depends on B. Depending on Hall plate properties, this
non-linearity can be up to 1% over the range 0–1 T. The response of
Fig. 7. Planar Hall voltage compensation with a pair of parallel Hall plates rotated
in plane ∼90◦ to each other. The solid green curve is the calculated average of the
planar Hall voltages extracted from the measurement by two individual “green” Hall
plates that form a pair. The dashed green curve, for comparison, is the planar Hall
voltage measured by a single Hall plate. The measurement was performed at 0.1 mA
bias current in a 1 T field. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
Temperature coefficient of VH [% ◦ C−1 ] (T = 25 ± 2.5 ◦ C)
∼−0.03
Non-linearity [%] (0–2 T)
0.02–0.03
Fig. 8. Response of the three-axis Hall sensor at 0.1 mA bias current and for rotation
around an arbitrary axis in a homogeneous field of 1 T. The red, green and blue
curves are the averaged Hall voltages measured by the three pairs of Hall plates
respectively. The black curve is the square root of the sum of squares of the red,
green and blue Hall voltage values.
the three-axis Hall sensor for a rotation in a plane around no specific axis, is shown in Fig. 8. The red, green and blue curves are the
responses of the three pairs of Hall plates as a function of rotation
angle ˛. The black curve is the calculated total Hall voltage Vtot .
The value of Vtot is not constant, showing instead a slight double
˛ angular dependence. This is not due to the planar Hall effect but
is due to the angular errors between the Hall plates, which lead
to small phase shifts among the red, green and blue curves. The
amplitude of Vtot varies by ±2% about its average. That means that
without any correction for angular errors, the expected field measurement accuracy is to be of the order of ±2%. However, once the
angular errors are precisely known, they can be calibrated out. A
comprehensive characterization and calibration scheme is being
developed.
6. Discussion
During the fabrication process, the following problems may
occur and the following improvements in the fabrication process
have been identified.
A thick photoresist S1828 has been chosen to overcome resist
adhesion problems with thin resist during wet etch. Employing a
thin resist such as AZ5214 leads to poor mesa results, from rough
side-walls (insufficient adhesion) to complete degradation of the
mesa (no adhesion). The loss in resolution from a thicker photoresist is not relevant for Hall sensors because, while smooth
side-walls and symmetry are important for their performance (i.e.,
linearity and offset), the exact dimensions of the mesa are not.
Minor adhesion problems, leading to rough mesa side-walls, may
also occur with thick photoresist which is above a certain age.
Before photoresist replacement is necessary, the adhesion can be
sufficiently enhanced by a pre-bake of the wafer material at 100 ◦ C
to remove moisture, and/or by applying a primer such as TI-prime
or HMDS.
The error resulting from the scriber/cleaver dicing method in
Hall plate dimensions is smaller than 5 !m. Although accurate, the
method is slow compared to a dicing saw because every scribed
line is manually adjusted and cleaved. About every tenth die is not
cleaved properly, one or more of its sides being not sharp or not
vertical. This effect is expected to diminish for thinner wafer materials. The three-axis Hall sensor could be fabricated with 200 !m
70
C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
thick Hall plates (instead of 500 !m) and MACOR cuboids of height
1700 !m (instead of 1400 !m).
The yield during assembly is only about 50%, due to detachment of soldered wires during assembly. Dimensions for assembly
are tight, with contact pad dimension of 300 !m × 300 !m, MACOR
channel width of 400 !m and height of 600 !m, and four soldered
wires each of diameter 100 !m. Due to generation of large inductive loops, (non-insulated) wire bonding is not a preferred solution.
The yield may be increased by improving the contact pads, e.g., by
thickening the top gold layer or adding a copper layer. Alternatively,
a slightly larger channel width of the MACOR support cuboids is
feasible.
The thickness of epoxy of up to 15 !m leads to a corresponding maximum misalignment between individual Hall plates within
the 200 !m × 200 !m × 200 !m active volume. Therefore, the magnetic field components cannot truly be assigned to a single point,
but to three points separated in space by up to 15 !m. This separation can obviously be reduced by choosing a thinner glue, provided
there is no loss in mechanical stability. Alternatively, if the added
overall height to a cuboid plus Hall plate from the glue thickness
can be made reproducible, the MACOR cuboids can be fabricated
with a height that is reduced by this amount.
With current assembly tools, all angular errors can be brought
below 0.5◦ . This is more than sufficient to compensate effectively
for the planar Hall voltage, but it is not sufficient to reach below
10−4 in cross sensitivity. With an improvement of tooling, one
might hope to reduce the angular errors induced during assembly
even further. Nevertheless, the maximum tolerable error of 0.006◦
is out of reach on such a small-scale device with such assembly
methods.
7. Conclusion
The three-axis Hall sensor reported on in the present work has
the potential for high-accuracy measurements of the full magnetic
field vector. The sensor was mainly designed for and will be particularly suitable for the application of field measurements of magnets.
The typical accuracy-limiting factors of current three-axis Hall sensors, such as the planar Hall effect, inability to measure at a single
point in space and time, and reduced measurement precision along
certain measurement axes, can be overcome or avoided by the
special sensor configuration. The non-orthogonality between the
individual Hall plates in the prototype of this three-axis Hall sensor
is however not negligible. This can be improved, but probably not to
below the set criterion of 0.006◦ . Therefore it is important to eliminate the measurement errors stemming from non-orthogonality
between plates in a proper 3D characterization and calibration
scheme, which is under development. After all, it is through thorough and periodic calibration that any high-precision Hall sensor,
be it 1D or 3D, becomes a high-accuracy Hall sensor.
tories. This research was co-funded by Kommission für Technologie
und Innovation (KTI) and Metrolab SA.
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Biographies
Acknowledgements
Many thanks to Peter Reimann (University of Basel) for the fabrication of the cuboid supports with incredible accuracy. Thanks
to Muhamet Djelili and Max Müller (Paul Scherrer Institute) for
machining the assembly tools, Stéphane Sanfilippo (Paul Scherrer
Institute) for his support throughout the project, Christian Reichl
(ETH Zürich) for the wafer material, Ivan Shorubalko (Empa Dübendorf) and Roland Deckardt (Paul Scherrer Institute) for advises and
valuable discussions, Jens Gobrecht (Paul Scherrer Institute) for
providing important contacts, John Crawford for English spelling
corrections, and thanks to the Nanophysics Group at ETH Zürich
for the much appreciated full and unlimited access to their labora-
Christina Wouters studied at the University of Groningen where she received her
M.Sc. in Physics. In 2011 she joined the Magnet Section of the Paul Scherrer Institute
for an internship where she worked on the set-up of a vibrating wire measurement
system for quadrupole magnetic axis determination. She then started her Ph.D.
in the same group and under the supervision of Christofer Hierold of the Micro
and Nanosystems group at the ETH Zürich. Her doctoral research focuses on the
development and implementation of a novel three-axis Hall sensor.
Vjeran Vranković studied Electrical Engineering at the University of Zagreb. After
graduation he was with Končar Electrical Industry Inc. for five years where he
worked on the development of MRI systems. In 1990 he joined the Magnet Section of the Paul Scherrer Institute where he started his career in computational
magnet design. He has written numerous software applications including an analytical ray-tracing program and a magnet pole profile optimizer that are used within
the institute. Currently, his major research areas are computational magnet design,
beam tracking calculations and the development of magnetic measurement systems.
C. Wouters et al. / Sensors and Actuators A 237 (2016) 62–71
Clemens Rössler studied Physics in München and Nottingham. In 2008 he received
his Ph.D. in Physics from the Ludwig-Maximilians-Universität in München for
research on suspended nanostructures. Since 2009, he is a postdoc in Klaus Ensslin’s
group at ETH Zürich, conducting transport spectroscopy of low-dimensional electron systems.
Serguei Sidorov studied Mechanical Engineering at the State Technical University of
Volgograd. After graduation, he was with Institute of High Energy Physics (Protvino)
for eight years working on the development and mechanical design of different
equipment for scientific researches. From 1997 to 2003 he worked at CERN on the
LHC project being involved in the design of the interconnections on the main LHC
superconductive magnets and afterwards in the integration and layout of the muon
chambers of the muon spectrometer of the ATLAS project. In 2008 he joined the Magnet Section of the Paul Scherrer Institute where he started to work for the SwissFEL
project as the mechanical engineer designing the magnets as well the equipment
and fixtures to build different magnetic measurement systems.
Klaus Ensslin studied Physics in München and Zürich and obtained his Ph.D. at the
Max-Planck-Institute for Solid State Research in Stuttgart in 1989. After postdoc
stays at the University of California in Santa Barbara and the University of München
he started as a professor at ETH Zürich in 1995. Since 2011 Klaus Ensslin is Director
of the National Center for Competence in Research on “Quantum Science and Technology”. The scientific work of Klaus Ensslin focuses on quantum systems in a solid
state environment, mostly in III-V semiconductors but also in graphene.
71
Werner Wegscheider joined ETH Zürich as Professor for Advanced Semiconductor
Quantum Materials in 1999. Since 2011 he has been Head of the Laboratory for Solid
State Physics. From 1999 until 2009 he was Full Professor for Experimental Physics
at the University of Regensburg, where he also served as Head and Deputy Head of
the Department of Physics from 2003 until 2007. Werner Wegscheider published
more than 650 papers in refereed, international journals. He is a member of the
German Physical Society (DPG), where he was Head of the Semiconductor Physics
Division from 2005 until 2009.
Christofer Hierold has been Professor of Micro and Nanosystems at ETH Zürich
since April 2002. His research is focused on the evaluation of new materials for
MEMS, on advanced microsystems, and on carbon nanotubes for sensors. He published more than 200 papers in journals and conference proceedings. From 2009
until 2014 he was Head and Deputy Head of the Department of Mechanical and
Process Engineering at ETH Zürich. Christofer Hierold is Editor-in-Chief of the IEEE
Journal of Microelectromechanical Systems. He is member of the Swiss Academy of
Engineering Sciences (SATW).