U.P.B. Sci. Bull., Series A, Vol. 72, Iss.

4, 2010 ISSN 1223-7027

GEOMETRY INFLUENCE ON THE HALL EFFECT DEVICES

PERFORMANCE

Maria-Alexandra PAUN1, Jean-Michel SALLÈSE2, Maher KAYAL3

The influence of the geometry, via the ratio L/W of the Hall cells and the
geometrical correction factor G on several figures of merit regarding Hall sensors
is analyzed, namely the sensitivity, Hall Voltage and power dissipated within the
device. Experimental values for the parameters of interest are given for eight
different geometries integrated in CMOS technology using certain biasing currents.
We discuss how these results compare with an analytical model and we propose a
global optimization analysis for guiding the designer in best Hall cell dimensions
selection.

Keywords: Hall effect sensors, geometrical correction factor, sensitivity, Hall

voltage, power dissipated

1. Introduction. Generalities about the Hall effect sensors

Since more than hundred years, Hall effect devices have been used to
demonstrate the basic laws of physics, to study details of carrier transport
phenomena in solids, to detect the presence of a magnet and as sensing devices for
magnetic fields. Generally, the Hall effect takes place in any solid-state electron
device exposed to a magnetic field. When a bias current is supplied between two
contacts of a Hall plate and a perpendicular magnetic field is applied to the device,
a voltage appears between the sense contacts. This voltage is called Hall voltage
[1].
Microscopic models have recently been developed to simulate self-
consistent electric potentials in Hall devices. Molecular dynamics for the motion
of electrons and electron-electron interactions and conformal mapping were used
to obtain the Hall potentials, by a computational feasibility method [2].
The Hall voltage is proportional to the vector cross product of the current
(I) and the magnetic field (B). It is on the order of few tens of mV in silicon and
thus requires amplification for practical applications. Silicon exhibits the
1
PhD Student, STI-IEL-Electronics Lab (LEG), Ecole Polytechnique Fédérale de Lausanne
(EPFL),CH-1015 Lausanne, Switzerland, Corresponding author: maria-alexandra.paun@epfl.ch
2
Prof., STI-IEL-Electronics Lab (LEG), Ecole Polytechnique Fédérale de Lausanne (EPFL),
CH-1015 Lausanne, Switzerland
3
Prof., STI-IEL-Electronics Lab (LEG), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-
1015 Lausanne, Switzerland
258 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

piezoresistance effect, a change in electrical resistance proportional to strain. This

effect can be minimized by properly orienting the Hall element on the IC and by
using multiple Hall elements. Fig. 1 shows two Hall elements located in close
proximity on an IC. They are positioned in such a way that they experience the
same packaging stress, represented by ΔR. The first Hall element has its
excitation applied along the vertical axis and the second along the horizontal axis.
Summing the two outputs eliminates the signal due to stress. Micro switch Hall
ICs use two or four elements [3].

2. Basic Hall effect sensors

The Hall element is the basic magnetic field sensor. It requires an

amplifier stage and temperature compensation circuitry in order to use it in most
applications. Voltage regulation is needed when operating from an unregulated
supply. Figure 2 illustrates a basic Hall sensor from the Honeywell reference on
Hall sensors. If the Hall voltage is measured when no magnetic field is present,
the output should be zero. However this is never satisfied in practice and there is
always an offset voltage that should be minimized. According to Popovic’s
monography, major causes of offset are imperfections in the device fabrication
process, such as misalignment of contacts, non-uniformity in material resistivity
and thickness. A mechanical stress in combination with the piezoresistance effect
can also generate offset.
Vtotal = Voffset + VH (B ) (1)
On the other hand, the potential of each output terminal measured with
respect to ground will not be zero. This is the common mode voltage (CMV) that
should be equal for both output nodes, therefore the potential difference should
ideally be zero. Figure 2 shows a schematic where only the potential difference,
the Hall voltage, is amplified, thus rejecting the common mode voltage. The Hall
voltage is of the order of 30 mV in the presence of a one gauss magnetic field.
This low-level output requires an amplifier with low noise, high input impedance
and moderate gain. A differential amplifier with these characteristics can be
readily integrated with the Hall element using different technologies on Si, in
general CMOS technology. Temperature compensation is also easily integrated.
Since the Hall voltage is a function of the input current, there is a need for
a regulator that will maintain a constant current.
 Geometry influence on the Hall effect devices performance 259

Fig. 1 Hall element orientation

Fig. 2 Basic Hall effect sensor

Today, due to economical considerations, a new class of Hall microsensors

with minimal design complexity was developed [4].

3. Classical approach for Hall cells

In the classical approach, the Hall cell is shaped as a Greek cross. The
structure has some symmetry and it is invariant by a rotation of π/2. This allows
current-spinning technique to be used for minimizing residual offsets.
The offset depends on many parameters such as technology, temperature
and stress. Practically, it limits the minimum magnetic field that can be measured.
A classical way of reducing offset is to couple two or four identical cells that are
rotated [5]. Hall circuits fabricated in CMOS technology rely on the so-called
spinning current method (periodic supply and output-contacts permutations) to
enhance the sensor sensitivity [6].
The 3D cross presented in Fig. 3 has 4 contacts (in darker grey shades),
among which two used to impose a current (namely A and C) and others are used
 260 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

(B and D) for sensing the Hall voltage. Length and width of the cross are
respectively denoted by L and W, sensing contacts extension is further on denoted
by s, and the thickness of the active region is referred as t.

Ibias Ibias
D B
L VHall

y
B

C
z
x S

Fig. 3 Classical Greek Cross

To summarize, different quantities are used to characterize the Hall device [1].
The Hall Voltage
The Hall voltage follows the well known relation.
Gr (2)
V H ( B ) = H I bias B⊥
nqt
where B is the magnetic field component perpendicular to the plane, G is the
geometrical correction factor, Ibias the biasing current, rH is the scattering factor of
silicon that can be approximated to 1.15, n is the carrier density, q is the magnitude of
the electron charge, t is the thickness of the plate and SI is the current-related
sensitivity.
Equivalently, we have
W
VH ( B) = μ H GVB⊥
L (3)
where is the Hall mobility.
The geometrical correction factor, G
In general, the geometrical correction factor G for a Hall device is given by the
following relationship
πL
16 − ⎛ 8 − 2πWL ⎞⎛ θ H2 ⎞
G = 1− e 2W ⎜1 − e ⎟⎜1 − ⎟⎟ (4)
π 2 ⎜ 9 ⎟⎜ 3
⎝ ⎠⎝ ⎠
This relation is valid for 0.85 ≤L/W≤∞ and 0≤θH≤0.45 radians.
 Geometry influence on the Hall effect devices performance 261

The absolute sensitivity, S

The absolute sensitivity of Hall effect sensors is given by:

VH GrH
S= = I bias = GS I I bias (5)
B⊥ nqt
where SI is the current-related sensitivity.
Further on, we have the relationships:
rH
S = GS I I bias ; S I = S I max = (6)
nqt
where the geometrical factor G models the reduction of VHALL due to the part of the
current which is perturbed from the sensing contacts as well as the short circuit effect
induced by the biasing contacts [7].

The power dissipated, P

The Hall voltage expressed as function of the dissipated power is
1/ 2
⎛ μ ⎞
1/ 2 (7)
⎛W ⎞
VH ( B ) = G⎜ ⎟ rH ⎜ ⎜ ⎟
⎟ ( P )1/ 2
B ⊥
⎝L⎠ ⎝ nqt ⎠
For certain values of the width-to-length ratio, the dissipated power inside the
device can be introduced as:
VH2 (8)
P=
⎛W ⎞ ⎛ μ ⎞ 2
G 2 ⎜ ⎟rH2 ⎜⎜ ⎟⎟ B ⊥
⎝ L ⎠ ⎝ nqt ⎠

4. Hall device configurations

Up to 8 geometries implemented in 0.35 μm CMOS technology have been

measured and analyzed in terms of specific parameters, such as absolute sensitivity,
Hall voltage and power dissipated. All structures are symmetric and invariant to a
rotation with π/2. The classical Greek cross was implemented as the basic cell. Further
on, the variation of the cell dimensions led us to proposing the cells called L, XL. To
avoid piezoresistive effects, the axes of the cells were oriented 45 degrees with respect
to the Si crystallographic directions. Leaving the cross behind, we also implemented
new shapes, such as as borderless and square structures. The borderless cell has the
sensing contacts located inside of the active N-well region in order to minimize as
much as possible errors related to the border. A low doped Hall cell with higher
absolute sensitivity was also integrated
The resistances of the Hall cells, the dimensions of the active N-well, as well as
values for the sensing contacts have been reported in table 1. The narrow contacts,
 262 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

borderless and square cells have small sensing contacts in comparison with the others
in order to satisfy that the condition s/W < 0.18 is fulfilled. The geometrical correction
factor has been computed for each individual geometry. For the first five geometries,
Eq. (4) was used. For the last three structures, because of the small sensing contacts
area, an approximate expression given by Eq. (11) could also be used.
The Hall cells were integrated together with the specific electronics and an
automated measurement system was used to measure the specific parameters of the
proposed geometries.

5. Results and discussion

An analysis at the device level was performed. The following table summarizes
the eight tested geometries and their specific parameters, such as resistance,
dimensions of the active area, geometrical correction factor (G), length-to-width ratio
L/W, etc.
Table 1
Properties of the eight analyzed Hall cells geometries
Geometry Basic Low- L XL 45 Deg Narrow Borderless Square
Type doped Contacts

Shape

R0 (kΩ) at
T=300K 2.3 5.6 2.2 2.2 2.1 2.5 1.3 4.9
and B=0T
W, L (μm)
of the W=11.8 W=11.8 W=17.8 W=22.6 W=11.8 W=9.5 W=49.9 W=20
Active Area
N-well L=21.6 L=21.6 L=32.4 L=43.2 L=21.64 L=21.6 L=49.9 L=20
s (μm) for
Sensing S=11 S=11 S=16 S=20.7 S=11 S=1.5 S=2.3 S=2.3
Contacts
Geometrica
l 0.913 0.913 0.912 0.924 0.913 0.87 0.76 0.73
Correction
Factor (G)
L/W 1.83 1.83 1.82 1.91 1.83 2.27 1 1
W/L 0.54 0.54 0.55 0.52 0.54 0.44 1 1
s/W 0.932 0.932 0.898 0.915 0.932 0.157 0.04 0.115

The absolute sensitivity of the eight cells as a function of the biasing current, between
0-2 mA, is represented in Fig. 4.
 Geometry influence on the Hall effect devices performance 263

Fig. 4 The measured absolute sensitivity (V/T) of the eight cells as a function of the biasing
current (A)

Measurements were made for a perpendicular magnetic field of B=0.497 T and current
sweeping between 0-2 mA. The cells behavior with emphasis at 1 mA is summarized
in Table 2.
Table 2
Measured vs. computed values for certain parameters of the Hall Cell
Geometry Basic Low- L XL 45 Deg Narrow Borderless Square
Type doped Contacts
Absolute
Sensitivity 0.0807 0.3392 0.0804 0.0806 0.0807 0.0822 0.0325 0.0884
(V/T) at
Ibias=1 mA

Measured
VHall (mV) 40.10 168.58 39.95 40.05 40.10 40.85 16.15 43.93
at Ibias=1
mA
Computed
VHall (mV) 39.96 150.29 39.91 40.44 39.96 38.07 33.26 31.95
as a
function of
G
 264 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

Power
Dissipated 2.302 5.606 2.202 2.202 2.102 2.503 1.301 4.905
(mW) at
Ibias=1 mA

Computed
power 1.999 7.288 1.949 2.014 1.999 2.437 1.072 1.072
(mW) as a
function of
VHall and G

Further on, the graph of the estimated versus measured Hall voltage (mV) is
presented, as well as the power dissipated within the device, for Ibias=1 mA and a
perpendicular magnetic field B=0.497 T.

200 8

7
Measured values
Estimated values Measured values
150 Estimated values
6

5
100

3
50

0 1
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
The eight geometries The eight geometries

(a) (b)
Fig. 5 Measured vs. estimated values for VHALL(mV) (a) and power dissipated (mW) within the
device (b) for Ibias=1 mA

For correcting the resistance with the presence of the magnetic field, we used:
R = R0 (1 + μ 2 B 2 ) (9)

After calculations, we obtained an increase of 1.0012 for the resistance in the

presence of magnetic field B=0.497 T.
From [1], it is possible to evaluate the highest Hall voltage that can be obtained
for different situations that will depend on how the device is monitored. For instance,
 Geometry influence on the Hall effect devices performance 265

imposing the bias current (assuming a long device, i.e. L/W>3), imposing the input
voltage (which requires a rather short device, L/W < 0.1), and fixing the power
(requiring L/W≈1.3-1.4).
Analysis of the geometrical correction factor behavior
Using MATHEMATICA 7.0, the geometrical factor G is plotted as a function of
the length to width ratio L/W and Hall angle, θH.
 
 
 
 
 
 
 
 
 
 
 
 
 
 

(b) 
(a)
Fig. 6 Representation of the Geometrical correction factor (G), as a function of L/W and Hall
angle, θH, for 0.85 < L/W < 3 (a) and 0.85 < L/W < 5 (b)

G presented in Eq. (4) will be interpreted in terms of physical meaning, therefore

L/W will be evaluated up to 5. In general, for L/W >3, the Hall plate is considerate
infinitely long, but we decided to see what happens for 3< L/W<5.
As we can see on Figure 6, for 0.85 < L/W < 3, the geometrical correction factor
has a maximum value of 0.98 obtained for L/W=3 and θH=0.45 radians. For 0.85 <
L/W < 5, the maximum of G is 0.99 and is obviously obtained, due to the behavior of
the curve, for the maximum Hall Angle θH=0.45 radians and at maximum ratio L/W=5.
We observed that for 3< L/W<5, the upper limit of G begins to rapidly increase, from
0.98 to 0.99, but it’s only after L/W>5 when G begins to rapidly approach 1.
Indeed, the mathematical limit of G
⎛ 16 − πL ⎛ 8 − πL ⎞⎛ θ 2 ⎞ ⎞
lim G = lim ⎜1 − 2 e 2W ⎜⎜1 − e 2W ⎟⎟⎜⎜1 − H ⎟⎟ ⎟ = 1 (10)
L / W →∞⎜ 3 ⎠ ⎟⎠
⎝ π ⎝ 9
L / W →∞
⎠⎝
If we plot the geometrical correction factor as before, but we take L/W to start
from 0, we obtain a point of inflexion, with a point of minimum at 0.85 and a
decreasing behavior of G with respect to L/W in the range (0, 0.85]. This can be
considered as the limit of validity of relation written in Eq. (10).
 266 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

Fig. 7 The presence of the inflexion point close to L/W=0.85

If we include the length of the sensing contacts, we obtain the following

simplified expression for the geometrical correction factor
πL
⎛ − ⎞
2W ⎟⎛
2 s ⎞
⎜
G = 1− e 1−
⎜ ⎟⎜⎝ π W ⎟⎠ (11)
⎝ ⎠
which is valid if L/W >1.5 and is sensing contacts are relatively small, namely s/W <
0.18.
We shall try to find the maximum of the sensitivity, S.
Analytical calculus of the maximum sensitivity as a function of L, W and of
the sensing contacts length, s
Using Eq. (6), we write further on
dS = S I I bias dG (12)

where dG is the differential of the geometrical factor, written in Eq. (11), more
precisely
∂G ∂G ∂G
G = G ( L, W , s ) , dG = dL + dW + ds (13)
∂L ∂W ∂s
The partial derivatives of G with respect to each variable are the following:
π L
∂G π ⎛ 2 s ⎞ −2W
= ⎜1 − ⎟e
∂L 2W ⎝ π W ⎠
π L
∂G 1 ⎛ Ls 2 s πL ⎞ − 2s
= 2 ⎜ − − ⎟e 2 W + (15)
∂W W ⎝ W π 2 ⎠ πW 2
π L
∂G ⎛ 2 ⎞⎛⎜ − ⎞
⎟
= ⎜− ⎟ 1− e 2W
∂s ⎝ πW ⎠⎜⎝ ⎟
⎠ (16)
 Geometry influence on the Hall effect devices performance 267

For finding an extremum of a function f, we assume a domain A that is open and

that f is of class C2 over A. We consider a point a of A and we denote the Hessian
matrix of f at point a by ∇ 2 f (a ) .
If ∇f (a ) = 0 and if ∇ 2 f (a ) is negatively defined and f has a local maximum point
at a.
Conversely, if ∇f (a ) = 0 and ∇ 2 f (a ) is positively defined, then f has a local
minimum point at a.
Therefore, in our case, G has a point of extremum, a, when

⎧ ∂G
⎪ ∂W (a ) = 0
⎪
⎪ ∂G (17)
⎨ (a ) = 0
⎪ ∂L
⎪ ∂G
⎪ ∂s (a ) = 0
⎩
To decide whether the extremum point is a maximum or a minimum the second
order derivatives should be investigated. The sign of the following determinant must
therefore be evaluated.
∂ 2G ∂ 2G ∂ 2G
(a) (a) (a )
∂L2 ∂L∂W ∂L∂s
∂ 2G ∂ 2G ∂ 2G
( )
det ∇ 2 G (a) =
∂W∂L
(a)
∂W 2
(a)
∂W∂s
(a )
(18)

∂ 2G ∂ 2G ∂ 2G
(a) (a ) (a)
∂s∂L ∂s∂W ∂s 2

Solving by hand the above system for finding the extrema, we find out that G has no
maximum. Therefore, it seems that there is no way to maximize G unless the ratio L/W
goes to infinity. MATHEMATICA 7.0 was used to find the maximum value (in this
case the upper limits) for G for the certain physical intervals investigated, with the best
accepted error by the software.
Numerical values obtained with MATHEMATICA 7.0, for the maximum
absolute sensitivity
 268 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

Fig. 8 Variation of the geometrical correction factor G as a function of L/W and s/W

Using MATHEMATICA 7.0, we find that optimized values for L/W and s/W, over
the interval analyzed giving a geometrical factor close to 1 are.
L s
= 5 and =0 (19)
W W
This is consistent with the fact that the maximum geometrical correction factor
G=1 is obtained for infinitely long Hall devices with point-like sensing contacts.
L s
→ ∞ and →0 (20)
W W
In terms of the eight Hall cells analyzed, seven of them have a carrier
concentration n1, but the lightly-doped cell has a carrier concentration n2 four times
lower than n1. Since the carrier concentration n2 is four times lower than n1, we obtain
an absolute sensitivity four times higher.
Assuming that the biasing current is the same, we can calculate the maximum
sensitivity. Then, using G=1 and the technological parameters we obtain the following
theoretical maximum absolute sensitivities for the different doping concentrations with
Ibias=1 mA.
S max, n1 = 0.088 V / T for n1
(21)
S max, n 2 = 0.33 V / T for n 2
The proposed global optimization methodology could be used to find optimum in
Hall devices where additional parasitic effects could also impact the sensitivity (doping
homogeneity, strain…). The maximization procedure for the geometrical factor and
absolute sensitivity could be applied for finding extrema points of functions with
constraints. For example, if we have a certain available surface of Si at our disposal,
 Geometry influence on the Hall effect devices performance 269

fixing therefore the value of A=LW, and having a smin imposed by the technology for
the sensing contacts, we could be thinking about finding W or L giving us a maximum
sensitivity (by maximizing G) in this context. In this way, we end up with one variable.
This procedure that could guide the designer into tailoring the Hall cell dimensions.
Therefore, Eq. (11) can be rewritten as
πA
⎛ ⎞⎛
⎟⎜1 − 2 s ⎞⎟
−
G = ⎜1 − e 2W
2
(22)
⎜ ⎟⎝ π W ⎠
⎝ ⎠
Keeping constant the contact size provided by the technology (in our case smin
=0.35 μm) and having at our disposal a certain area of Si, meaning fixed A, we proceed
at maximizing G, now a function of only one variable W, imposing these constraints.
Further on, in Figure 9, the variation of L/W with respect to the area A, for different
contact sizes, s, which assures a maximum correction factor G, is plotted.

4.5

3.5

3 s=0.35um
s=0.5um
s=1um
s=1.5um
s=2um
2.5
500 1000 1500 2000 2500
2
A (μm )
Fig. 9 Variation of L/W with respect to the area A, for different contact
sizes s, assuring the maximum correction factor G

Some of the 0.35 μm CMOS Si technology parameters in which the cells were
integrated, are summarized in the table below. The N-well doping concentration is
usually a Gaussian, but the values of n1 and n2 are taken close to the center of the
Gaussian. The value of n2 corresponds to a lightly doped N-well.
 270 Maria-Alexandra Paun, Jean -Michel Sallèse, Maher Kayal

Table 3
Technology parameters of interest
Parameter name Symbol Units Value

Mobility μ m2V-1s-1 0.0715

Carriers Concentration n1 m-3 8.16e22

for N-well
n2 m-3 2.17e22

Thickness of N-well t m 1e-6

5. Conclusions

A series of eight different shapes was integrated in 0.35 μm CMOS Si technology.

A device level analysis of the Hall cell geometries, in terms of sensitivity, VHALL,
power dissipated, etc. was performed. Each structure was geometrically characterized
by the L/W, s/W ratio and geometrical correction factor, G. The impact of the
geometrical parameters and how these affect the device performances was studied.
With the proposed technology, a maximum absolute sensitivity Smax,n1=0.088 V/T
was obtained with the carrier concentration n1 and Smax,n2=0.33 V/T for lightly doped
N-wells, with a carrier concentration n2. As the absolute sensitivity is proportional to
G, cells with G close to unity will assure obtaining the maximum absolute sensitivity.
MATHEMATICA 7.0 was used for evaluating the maximum values of the
geometrical correction factor, for the two expressions, both in terms of L/W, θH and
L/W and s/W respectively, for the intervals imposed by the physical interpretation of
Hall devices.
For 0.85 < L/W < 3, the geometrical correction factor has a maximum value of
0.98 obtained for L/W=3 and θH=0.45 radians. For 0.85 < L/W < 5, G approaches 0.99.
For values of L/W >5, the geometrical factor begins to asymptotically tend to 1. The
geometrical correction factor G begins to asymptotically tend to 1, for infinitely long
devices (L/W > 5) with point-like sensing contacts (s→0).
Measurements versus simulations were investigated, for all eight cells, in terms of
VHALL and power dissipated. Because the cells were measured with an automated
system, the same biasing conditions were applied to all the 8 cells. A biasing current
between 0-2 mA, together with a compliance voltage for the current source of 5 V,
was sufficient for testing the majority of cells, but for the low doped and square,
saturation begins to appear for higher biasing currents. However, for the absolute
sensitivity curves for these two cells, an extrapolation was done between 1 and 2 mA
of biasing current. Due to the high values of the resistances for the low-doped cells
(approximately 5 kΩ) the values for the measured versus estimated power dissipated
 Geometry influence on the Hall effect devices performance 271

show some discrepancies, due to the effective saturation that might appear when
biasing the cells with higher currents.
VHALL has an average value of 40 mV for Ibias=1 mA and B=0.497 T, with a value
four times higher for lightly doped N-wells. For the tested geometries, the highest
Hall voltage was obtained with a given bias current, if a Hall device was long, let’s
say with L/W≈2.
The proposed maximization procedure for the geometrical correction factor and
subsequent sensitivity maximization was used for guiding the designer in finding the
optimum dimensions (W, L) for the Hall cell, subject to some technological
constraints (imposed sensing contact size) and Si surface availability.

Ackowledgements

This work has been supported by Swiss Innovation Promotion Agency CTI
(Project 9591.1) and the company LEM - Geneva, Switzerland.

REFERENCES
[1] R.S Popovic, Hall Effect Devices, Second Edition, Institute of Physics Publishing, 2004
[2] T. Kramer, V. Krueckl, E.J. Heller, R.E. Parrott, Self-consistent calculation of electric
potentials in Hall devices, Physical Review B, Vol. 81, 205306, 2010
[3] Honeywell References, Micro Switch Sensing and Control, Chapter 2, Hall Effect Sensors
[4] S.V. Lozanova, C.S. Roumenin, Parallel-Field Silicon Hall Effect Microsensors with Minimal
Design Complexity, IEEE Sensors Journal, Vol. 9, No. 7, 761, 2009
[5] R.S. Popovic, Z. Randjelovic, D. Manic, Integrated Hall-effect magnetic sensors, Sensors and
Actuators A, Vol. 91, 2001, pp.46-50
[6] M. Kayal, M. Pastre, Automatic calibration of Hall sensor microsystems, Microelectronics
Journal Vol. 37, 2006, pp. 1569–1575
[7] J. Pascal, L. Hébrard, J.-B. Kammerer V. Frick, J.-P. Blondé, First vertical Hall Device in
standard 0.35 μm CMOS technology, Sensors and Actuators A: Physical, Vol. 147, 2008,
pp. 41-46