Hall eect sensors integrated in standard technology and ... · mainsa problem.A solution is proposedin Section 4 where a Hall sensors network is substituted for the multi-strips Hall

Eur. Phys. J. Appl. Phys. 36, 49–64 (2006)DOI: 10.1051/epjap:2006100 THE EUROPEAN

PHYSICAL JOURNALAPPLIED PHYSICS

Hall effect sensors integrated in standard technologyand optimized with on-chip circuitry

J.-B. Kammerer1,a, L. Hebrard1, V. Frick1, P. Poure2,b, and F. Braun1

1 Institut d’Electronique, du Solide et des Systemes (InESS), 23 rue du Lœss, BP 20, 67037 Strasbourg Cedex 2, France

2 Laboratoire d’Instrumentation Electronique de Nancy (LIEN), Faculte des Sciences et Techniques, BP 239,54506 Vandœuvre-les-Nancy Cedex, France

Received: 9 March 2005 / Received in final form: 23 December 2005 / Accepted: 24 March 2006Published online: 6 October 2006 – c© EDP Sciences

Abstract. While silicon is not the best semi-conductor material to design Hall effect sensors, it is widelyused because Hall devices are fully compatible with standard processes such as CMOS or Bi-CMOS. Halleffect sensors can thus take advantage of on-chip circuitry to counterbalance the poor intrinsic metrologicalcharacteristics of silicon Hall devices, and low cost integrated smart magnetometers can be designed usingstandard technologies. Conventional Hall plate as well as the spinning-current method, which is the presentstate of the art technique to improve performances of integrated Hall devices, are reviewed in this paper.Then a new multi-strips Hall device and its specific biasing circuit are introduced. This new device allows tomultiply by n the absolute sensitivity of the Hall sensor where n is the number of strips, but it suffers fromoffset. To overcome this drawback, a Hall sensors network which also allows to increase the sensitivitywhile reducing the offset is proposed. Finally a comparison between the Hall sensors network and thespinning-current is done, showing that both techniques are complementary and should be combined todesign high resolution Hall sensor systems.

PACS. 07.07.Df Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing – 85.30.FgBulk semiconductor and conductivity oscillation devices (including Hall effect devices, space-charge-limiteddevices, and Gunn effect devices) – 85.40.Qx Microcircuit quality, noise, performance, and failure analysis

1 Introduction

Nowadays, Hall effect magnetometers are probably themost widely used magnetic sensors [1]. They find appli-cations in the fields of automotive [2], angular positionsensors [3,4], contact-less current sensing [5,6], compasssystems [7], magnetic tracking [8,9], . . . However, due toa low carrier mobility, silicon is not the most appropriatesemiconductor material to design Hall effect sensors anddiscrete Hall devices are generally produced using high-mobility materials such as GaAs [10]. On the other hand,Hall devices are fully compatible with microelectronics’manufacturing process such as CMOS or Bi-CMOS, andthus can be easily integrated with electronics on the samedie [1]. This new degree of freedom offered by on-chip cir-cuitry can be used to counterbalance the poor characteris-tics of the silicon Hall device thru the use of specific bias-ing circuits [11], smart offset reduction techniques [12–14],

This paper has been presented at “3e colloque inter-disciplinaire en instrumentation (C2I 2004)”, Ecole NormaleSuperieure de Cachan, 29–30 janvier 2004.

a e-mail: [email protected] e-mail: [email protected]

temperature compensation [15], self-calibration [16], andso on. The design of low cost integrated smart magne-tometers is thus possible.

The spinning-current method is now recognized as thestate of the art technique to reduce the offset and 1/f noisein Hall devices [10]. Nevertheless, it suffers from switchingnoise [1] and from any parasitic mechanical vibration aris-ing at frequencies close to the spinning-frequency [11]. Toincrease the sensitivity which is limited by the low carriermobility in silicon and also by the short-circuit effect [17],the present trend is to add ferromagnetic flux concentra-tors [18]. While the sensitivity improvement can be veryhigh, this technique gives rise to non-linearity and hystere-sis in the magnetometer response. Furthermore, it asks fora specific post-processing which increases the cost of thesensor.

In this paper, we introduce new shapes of Hall plateassociated to a new on-chip biasing circuit to improve themetrological performances of Hall effect sensors. While ourwork was focused on horizontal Hall effect sensors, i.e. Halldevices sensitive to the magnetic field perpendicular to theplane of the chip, it could be adapted to vertical Hall sen-sors as well, i.e. sensors sensitive to an in-plane magnetic

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50 The European Physical Journal Applied Physics

− − − − − − − − −

+ + ++

+ ++ + +

t

W

FL

FE

e−

I y

z

x

Vz

Vy

v

B

E

Fig. 1. The Hall effect comes from the equilibrium betweenthe Lorentz force and the transversal electric force.

field [19,20]. The next section reviews the working princi-ple of conventional horizontal Hall devices and highlightstheir main limitations thru the short-circuit effect and thestress-induced offset. In addition, a basic biasing circuitusing the spinning-current method is presented with someexperimental results. In Section 3 a new shape of Halldevice is presented with its specific biasing circuit. Freefrom short circuit effect, the new multi-strips Hall plateexhibits a high absolute sensitivity but its offset still re-mains a problem. A solution is proposed in Section 4 wherea Hall sensors network is substituted for the multi-stripsHall device while keeping the specific biasing circuit. Ex-perimental results show that the resulting magnetometerhas small offset, is insensitive to any mechanical parasiticsignal, and can exhibit high absolute sensitivity. Finally, amulti-strips sensor compatible with the spinning-currenttechnique is proposed as a solution to get high resolutionHall effect magnetometers.

2 Conventional horizontal Hall effect sensors

2.1 Hall effect

The Hall effect is due to the Lorentz force that acts on themoving carriers inside a conducting material as shown inFigure 1. When a current I is flowing thru a conductingelement, in our example a N-type semiconductor, electronsare moving in the opposite direction:

I = −Wt · qnv (1)

where W and t are the width and the thickness of the con-ducting element, q 1.6 × 10−19 C the elemental charge,n the electrons density, and v the speed of the electrons.If such a structure is subjected to a magnetic field B, thetrajectories of the electrons are modified by the Lorentzforce FL = −q · v × B. Electric charges are thus accu-mulated on the sides of the conducting element so thata transversal electric field E establishes. Finally, an equi-librium is reached when both electric (FE = −q · E) andLorentz forces counterbalance each others:

qv × B = −q ·E. (2)

VH VH

B

I I

Fig. 2. Voltage inside a rectangular (left) and a cross-shaped(right) Hall effect sensors. The current flows vertically from thetop contact to the bottom contact. The red color represents thehighest potential while the blue color represents the lowest one.The magnitude of the magnetic field is 3T.

In the particular case of our example, i.e. when the cur-rent is flowing along the x direction (Fig. 1), the previousequation is equivalent to:

Ey = vx · Bz

Ez = −vx · By. (3)

Consequently, voltages proportional to the y and z com-ponents of the magnetic field appears between the lateralsides of the conducting element (Fig. 1):

Vy = vx · Bz · WVz = −vx · By · t. (4)

By inserting equation (1) into the previous formulae, onefinally obtain the following equations:

Vy =−Ix

qnt· Bz

Vz =Ix

qnW· By (5)

where Vy and Vz are the so called Hall voltages. Theequipotentials inside the sensor are thus tilted when amagnetic field is applied (Fig. 2). Nevertheless, these for-mulae are exact only if all the electrons are moving at thesame speed, which is not the case in semi-conductors. Inorder to take the distribution of speeds into account, theconcept of scattering factor r is used [17,21]:

Vy =−Ix · r

qnt· Bz

Vz =Ix · rqnW

· By. (6)

The value of the scattering factor is generally close to 1and depends on the sensor material as well as on the typeof the carriers (electrons or holes).

2.2 Integrated horizontal Hall plates

When the component of the magnetic field perpendicularto the chip plane has to be measured, horizontal Hall ef-fect sensors are generally used. These sensors may have

J.-B. Kammerer et al.: Hall sensors optimized with on-chip circuitry 51

N++

P Substrate Poly−silicon

Silicon oxide

N well

Depleted zone

Fig. 3. Integrated rectangular Hall effect sensor. The sensor isrealized thanks to a N well on a P-type substrate. The biasingand sensing contacts are realized with highly doped ohmic con-tacts. A poly-silicon gate is added in order to create a depletedzone just below the silicon oxide layer.

various shapes but the two most commonly used are therectangle and the cross as shown in Figure 2. Such sensorscan be very easily integrated by using the N well layer ofa CMOS technology on a P-type substrate, the contactsbeing realized with N++ ohmic contacts (Fig. 3). However,whatever the shape of the sensor is, its absolute sensitivitySB is given by the following formula:

SB =VH

Bz= G

rn

qntI (7)

where VH is the Hall voltage which can be measured be-tween the two sensing contacts (Fig. 2), Bz is the compo-nent of the magnetic field perpendicular to the chip plane,G 1 is a geometry dependent correction factor (moredetails about this factor are given in Sect. 2.4), rn is thescattering factor of electrons in silicon and I is the bias-ing current. The scattering factor depends on the sensormaterial and on the carriers type (rn 1.15 for electronsin low-doped silicon), n is the effective doping level of theN well and t is its effective thickness. The factor G rn

qnt isthus a constant and equation (7) clearly shows that a Halleffect sensor should be ideally biased thanks to a perfectcurrent source.

2.3 Gated horizontal Hall effect sensors

Although the thickness twell (Fig. 4) of the N well dependson the chosen technology, the effective thickness t can beslightly reduced by an electrical mean. By adding a poly-silicon gate over the sensor and biasing it properly, theregion just below the oxide can be depleted (Figs. 3, 4)so that the current is forced to flow in the buried partof the N well. The thickness of the depleted region (tdep)depends on the difference of potentials between the buriedpart of the N well (Vwell) and the SiO2/Si interface (VS):

tdep(VG, VS) =√

2εSi

qND· (Vwell − VS

)(8)

where εSi is the silicon permittivity, and ND is the donordensity of the N well. The more, the surface potential de-

Sensing contacts

Biasing contacts

W

t

L

S

twell

tox

x

y

x

z

y

z

Fig. 4. Dimensions of a gated horizontal Hall plate.

pends on both gate (VG) and N well potentials:

VS(V G, Vwell) = V

G − VΦ

2

(1 −

√1 + 4

Vwell − V G

VΦ

)

VΦ =2εSiqND

C2ox

V G = VG − VFB

Cox =εoxtox

(9)

where VFB is the flat-band voltage of the MOS structure,Cox is the capacitance per square meter of the silicon oxidelayer, εox is its permittivity and tox is its thickness (Fig. 4).These relations are only valid when the MOS structure isin the depletion regime, i.e. when Vth ≤ V

G − Vwell ≤ 0,Vth being the threshold voltage of the MOS structure:

Vth = −(

2Φf +√

4qNDεSiΦf

Cox

)

Φf =kT

qln(

ND

ni

)(10)

where ni is the intrinsic carrier density of silicon. Indeed,when V

G−Vwell > 0 the MOS structure is in accumulationregime, i.e. electrons are accumulated at the SiO2/Si inter-face, and the effective carrier density inside the N well (n)is thus larger than ND. Consequently, since the current re-lated sensitivity of a Hall effect sensor is inversely propor-tional to n (Eq. (7)), one should prevent to bias the MOSstructure in accumulation regime. When V

G−Vwell ≤ Vth,an inversion layer (holes) is created just below the siliconoxide layer and the surface potential (VS) remains moreor less constant:

VS(V G ≤ Vth + Vwell, Vwell) VS(Vth + Vwell, Vwell). (11)

Consequently, when V G −Vwell ≤ Vth, the thickness of the

depleted zone below the silicon oxide increases very slowlywhen the gate voltage is pulled down below Vth + Vwell. Fi-nally, the effective thickness (t) of the buried part of the


−4 −3 −2 −1 0 1 22200

2400

2600

2800

3000

3200

3400

3600

Gate to N well voltage (V)

R (

Ω)

inversion

depletion

accumulation

Fig. 5. Input resistance of a rectangular (L = 50 µm, W =20 µm) Hall effect sensor integrated in standard 0.6 µm CMOStechnology as a function of its gate to N well voltage. For thismeasurement, the biasing voltage has been set to 10 mV. Thesolid line is the measured characteristic while the dashed linerepresents the theoretical one.

N well can be simply evaluated from the previous equa-tions:

t = twell − tdep(VG, Vwell) (12)

where twell is the thickness of the N well (Fig. 4). Sincethe input resistance (the resistance which can be measuredbetween the biasing contacts of the sensor) is inversely to1nt , this resistance (Rin) is also proportional to the currentrelated sensitivity, SI , of the sensor:⎧⎨

⎩Rin = L

Wt · 1qnµn

SI = SBI = Grn

qnt

⇒ SI =W

L· Grnµn · Rin (13)

where µn is the mobility of electrons.In order to visualize the effect of the gate voltage on the

current related sensitivity of the sensor, we thus measuredits input resistance as a function of its gate to N well volt-age thanks to a parameters analyzer (Agilent 4156C). TheHall effect sensor prototype was rectangular (L = 50 µm,W = 20 µm) and integrated in a standard 0.6 µm CMOStechnology (twell 1.53 µm, n = ND 2.75× 1022 m−3).The experimental and the theoretical curves are shownin Figure 5 and clearly validate the previous theoreticalanalysis. Compared to a conventional integrated horizon-tal Hall plate with the same dimensions and integrated inthe same technology, such a gated Hall plate allows to in-crease the current related sensitivity up to 35% (depend-ing on the chosen technology and on the biasing condi-tions) which helps in reducing the power consumption [22].

In the following, all the sensors which will be pre-sented are gated and are realized in the same standard0.6 µm CMOS technology in which the ratio rn

qnt is closeto 120 V/AT when the gate is connected to the substrate,i.e. when the gate to N well voltage equals −2.5 V (moredetails about the biasing conditions will be given later).

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120

L/W

Cu

rren

t re

late

d s

ensi

tivi

ty (

V/A

T)

Fig. 6. Influence of the ratio LW

on the current related sensi-tivity of a rectangular Hall effect sensor. The circles are val-ues obtained from finite elements simulations. The dotted linerepresents the theoretical geometrical correction factor givenin (14).

2.4 Geometrical correction factor

The sensitivity of an actual Hall effect sensor is alwayssmaller than the theoretical sensitivity given by (6). In-deed, some short circuit effects take place near the bias-ing and sensing contacts: a part of the current lines aredeflected near the sensing contacts and the Hall voltage isstrongly reduced near the highly doped (n large) biasingcontacts [17]. In order to take these parasitic effects thatreduce the sensitivity of actual sensors into account, theconcept of geometrical correction factor is used as intro-duced in equation (7). Many studies about the geometricalcorrection have been done and the literal expression of Gis well known for most of the commonly used shaped [23].In the case of a rectangular Hall effect sensor, the geomet-rical correction factor is given by [21]:

G [

1 − 16π2 exp

(−π2

LW

)] · f ( SW

)LW > 1.5

0.74 LW · f ( S

W

)LW < 1

(14)

where L is the length of the Hall plate, i.e. the distancebetween the biasing contacts (Fig. 4). f

(SW

)is a function

that is close to one when S, the size of the sensing con-tacts, is less than 0.18 · W [21]. Equations (14) clearlydemonstrate that a “good” rectangular Hall plate shouldbe longer than wide, i.e. L

W should be large (Fig. 6). On theother hand, the larger the ratio L

W , the larger the input re-sistance is (Eq. (13)). Since the biasing current I is directlylimited by Rin (Rin · I ≤ Vsup, where Vsup is the voltageprovided by the power supply of the system), in order tomaximize the sensitivity of the sensor one should minimizeits input resistance, i.e. one should minimize the ratio L

W .However, the geometrical correction factor depends lin-early on L

W when this ratio is lower than 1 (Eq. (14)), andthus one can estimate the maximum absolute sensitivity


R

R

R

R

F

F

R

R

R

R

Fig. 7. When a semiconductor is subjected to mechanicalstress, its conductance changes and the material becomesanisotropic.

of a rectangular Hall effect sensor [17]:

SB ≤SBmax

≤Grn

qntImax

≤0.74 · rnµn · Vsup. (15)

Finally, for a good compromise between power consump-tion and sensitivity, the aspect ratio L

W is generally chosenlarger than 1.5 and smaller than 3. Generally speaking, theabsolute sensitivity of a Hall effect sensor is always lim-ited by its input resistance. Nevertheless, it is possible toovercome this limitation with a specific circuit intendedto bias a multi-strips Hall plate (Sect. 3) or a network ofHall plates (Sect. 4).

2.5 Offset and mechanical sensitivity

In order to understand the relevance of a cross-shapedHall effect sensor, one must notice that a silicon four ter-minal device is also a good shear stress sensor [21,24,25].Indeed, when a silicon crystal is subjected to mechani-cal stress, the distance between crystallographic planesis modified. Since the way electrons are moving inside acrystal directly depends on its elemental mesh size, thematerial conductance is modified when a stress is applied:in the case of a N-type silicon crystal, when the distancebetween crystallographic planes is reduced, the resistanceincreases and conversely (Fig. 7). Furthermore, from anelectrical point of view, a Hall effect sensor can be consid-ered as a Wheatstone bridge as shown in Figure 8. Such abridge model allows to understand the effect of mechani-cal stress on the behavior of the sensor. If a stress is ap-plied along one of the main crystallographic axes (normalstress), all the resistances are identically modified and thebridge remains symmetrical. On the other hand, if the sen-sor is subjected to shear stress, the vertical and horizontalsymmetries are lost: the distances S1-B1 and S2-B2 are re-duced (or increased) while the distances S1-B2 and S2-B1

S2

B2

B1

Ra

Rc

S1 S2

B2

B1

S1 S2

B2

B1

S1 S2

B2

B1

Rd

Rb

S1

Ra Rb

RdRc

F

F

Fig. 8. A Hall effect sensor can be modeled by a Wheatstonebridge. This bridge becomes unbalanced when the sensor issubjected to shear stress.

are increased (respectively reduced) (Fig. 8). The bridge isthus no longer symmetrical and a differential voltage VM

proportional to the shear stress σ is added to the Hallvoltage VH:

VM = Vbias · KM

(0 σσ 0

)(Ix

Iy

)· u (16)

where u is a vector pointing from the negative sensing con-tact (S1) to the positive one (S2), KM is a constant whichdepends on the material, and Vbias is the biasing voltageapplied between contacts B1 and B2. Even if the offsetmay come from masks misalignments or doping gradientinside the sensor, the stress induced voltage is the mainsource of offset in Hall plate. Indeed, because of packaging,integrated systems are generally subjected to large shearstress which cannot be removed.

Since the shear stress induced voltage is due to thechanges in the conductance of the semiconductor material,the sign of the mechanical sensitivity SM = VM

σ dependson the orientation of the sensor relative to the crystal-lographic planes as it can be seen in Figure 8. On thecontrary the magnetic sensitivity does not depends at allon the orientation of the sensor. As a consequence, whenthe sensor is rotated by π

2 rad, the sign of VM is invertedwhile the sign of VH remains constant [26]. Since the rolesof the biasing and sensing contacts of a cross-shaped sen-sor can be inverted, this particular shape allows to takeadvantage of these properties to remove the parasitic me-chanical signal. One just needs to measure the magneticfield in two steps: first the biasing current flows verticallyand the total voltage VT is measured horizontally, and inthe second step, the current flows horizontally and thevoltage is measured vertically as shown in Figure 9 [27].By simply summing or averaging the two resulting


VT

VTB

I

I

Step 1 Step 2

Fig. 9. The spinning current technique: the roles of the bi-asing and sensing contacts are periodically inverted and themeasurement is performed in two steps. The colors have thesame meaning than in Figure 2. The magnitude of the magneticfield equals 3 T.

voltages, one can thus remove the parasitic mechanicalsignal:

VT1 = VH + VM

VT2 = VH − VM

⇒ VT1 + VT2

2= VH. (17)

Since in practical design, step 1 and step 2 are periodicallyreiterated (the so called spinning current technique), thismethod is very efficient to remove quasi-static mechani-cal signal such as packaging stress but may fail when al-ternative mechanical signals have to be removed. Indeed,when the roles of the biasing and sensing contacts areperiodically inverted, the mechanical signal becomes themodulating signal of a square carrier. Consequently, whenthe sensor is subjected to vibrations which frequencies areclose to the spinning frequency, a parasitic signal arisesin the base band. One should also note that since flickernoise in Hall plates is due to conductance random fluc-tuations inside the device, the spinning current techniqueis also very efficient to remove the 1/f component of thetotal output noise of the sensor [12,27].

2.6 Biasing circuits

2.6.1 Basic biasing circuit

In order to make use of a Hall effect sensor, as it has beensuggested in Section 2.2, it should be biased by a per-fect current source. A circuit similar to the one presentedin Figure 10 is thus generally used. The current sourceis used to set the biasing current of the sensor while theoperational amplifier maintains the potential of the leftsensing contact to a reference potential Vref. Consequentlythe potential (Vout) of the right sensing contact is equal toVref + VH and can be easily processed (amplification, fil-tering, analog to digital conversion, . . . ). The more, whensymmetrical power supply is used, Vref is generally chosenequal to 0 so that Vout = VH.

outV

refV

I

−

+HV

Fig. 10. Simple biasing circuit suitable for a conventional Halleffect sensor. The output voltage Vout is equal to Vref + VH.

I bias Vout

VDD

VSS

Fig. 11. Integrated biasing circuit suitable for Hall effect sen-sors. The Hall effect sensor is inserted inside the output stageof an operational transconductance amplifier.

2.6.2 CMOS biasing circuit

When the circuit shown in Figure 10 is integrated thanksto a standard technology such as CMOS or Bi-CMOS tech-nologies, one has the opportunity to optimize the biasingamplifier to fit all requirements in terms of accuracy, noiselevel, power consumption, . . . The inner structure of theamplifier can also be adapted to this specific application.In order to reduce the power consumption of an integratedmagnetometer, we proposed to insert the sensor inside theoutput stage of an operational transconductance amplifier(Fig. 11). In such a circuit, the biasing current of the out-put stage is used to bias the sensor at the same time [22].The PMOS transistor of the output stage behaves as a cur-rent source with high output resistance, and thus set thebiasing current of the sensor. The NMOS transistor of thisstage is controlled by the output voltage of the differen-tial stage and its drain-to-source current is thus automat-ically adjusted in order to sink this biasing current and tomaintain the left sensing contact of the Hall effect deviceto the ground potential (or any other voltage reference).Since the input referred noise of the biasing amplifier isdirectly added to the intrinsic noise of the sensor, the dif-ferential stage must essentially be optimized in terms ofnoise. In particular, when low frequency fields has to be


ClkClk

Clk

Clk

Clk

I bias

Vout

VDD

VSS

Fig. 12. Biasing circuit suitable for the spinning current tech-nique.

measured, the 1/f component of the total input referrednoise must be minimized. More details about the designof such a front-end circuit can be found in reference [22].

2.6.3 The spinning-current technique

As discussed in Section 2.5, in order to remove the 1/fnoise of the sensor and to reduce its offset, the spinningcurrent technique is generally used when low-frequencyfields have to be measured. The integrated circuit de-scribed in the previous subsection (Fig. 11) can be slightlymodified to be adapted to the spinning current technique.The structure of this circuit is shown in Figure 12. Twodifferential pairs (one made of PMOS transistors and onemade of NMOS transistors) are inserted between eachtransistor of the output stage and the cross-shaped Halleffect sensor. These differential pairs are driven by twocomplementary clock signals so that the biasing currentof the output stage is alternatively injected horizontallyor vertically in the sensor. Moreover, the inverting inputof the biasing amplifier as well as the output of the circuitare connected to the adequate contacts thanks to four T-gates (one PMOS and one NMOS in parallel) driven bythe same complementary clock signals than the differentialpairs. Synchronous sampling (switched capacitors circuit)or simple analog low-pass filtering can thus be used to re-move the mechanical signal which is shifted around thespinning frequency, the magnetic signal (the Hall voltage)being in the base-band.

I bias

VSS

VDD

Fig. 13. Low noise – high speed input differential stage forthe biasing amplifier.

To ensure the stability of the system between clockedges, the gain × bandwidth product of such a biasingamplifier must be larger than the clock frequency. How-ever, since the input differential stage is designed so thatits flicker noise level is low, the areas of the transistors aregenerally large and consequently their gate capacitancesare also large1. In particular, the gate capacitances of thetransistors in the current mirror of the input differentialstage are responsible for the presence of a very low fre-quency pole in the transfer function of the amplifier. Thegain × bandwidth product of such an amplifier is thusnecessary small and, consequently, the maximum clock fre-quency is very low (few kHz). In order to overcome thislimitation, the input stage of the circuit in Figure 12 hasbeen slightly modified: a differential stage made only ofPMOS transistors is added before the conventional differ-ential stage with a NMOS current mirror as active load(Fig. 13). This first pre-amplifying stage adds a small gain(∼30), but since a PMOS transistor is less noisy (in termsof flicker noise) than a NMOS transistor of the same di-mensions, the required areas of the PMOS loads, and thustheir gate capacitances, are smaller than the areas thatwould be needed in the case of a NMOS current mirror toreach the expected noise level. The more the PMOS loadsare connected as diodes and thus present high conduc-tances: the bandwidth of this stage is consequently quitehigh compared to the needed gain × bandwidth prod-uct of the whole amplifier. Finally, since the signal is pre-amplified by this first differential stage, the constraints onthe noise level of the second differential stage are relaxed.Consequently, the areas of the NMOS transistors can bestrongly reduced, and thus, the bandwidth of the amplifiercan be increased in the same proportions.

2.7 Experimental results

A magnetometer using a cross shaped Hall effect sensorsimilar to the one of Figure 12 with the input differential

1 The flicker noise power spectral density of a MOS transistoris inversely proportional to the area of its channel.


Clock

small stressLarge stress

Fig. 14. Output signal of the spinning current magnetometer.In order to visualize the effect of the direction of the bias-ing current on the mechanical sensitivity, the clock frequencyis chosen small (110 Hz) compared to the cut-off frequency(−1 dB at 1 kHz) of the low-pass output filter.

stage of Figure 13 has been designed. The biasing currentof the sensor was set to 1 mA and its dimensions are thefollowing: the distance between opposite contacts is 50 µmand the width of each contact is 20 µm. The output sig-nal obtained with this magnetometer was pre-amplified(×100) and filtered thanks to a fourth order low-pass fil-ter (−1 dB at 1 kHz) implemented on a Printed CircuitBoard (PCB). First of all, to visualize the effect of thedirection of the biasing current on the mechanical sen-sitivity, we used a very slow clock signal (110 Hz), wellbelow the cut-off frequency of the low-pass filter, in or-der to switch the biasing current in the sensor. We werethus able to monitor the periodic change of the sign of themechanical sensitivity. During this experiment, the stresswas simply applied manually on the PCB. As expected, weobserved a square wave modulated by the applied stress(Fig. 14). The more, its average value remains constantwhatever the strength of the stress is. Secondly, we mea-sured the magnetic response of the sensor with the clockmaintained to its high level (clk = ’1’ in Fig. 15) and to itslow level (clk = ’0’). In the first case the current flows hor-izontally (see Fig. 12) while it flows vertically when clk =’0’. Consequently, because of the shear stress to which thesensor is subjected (package stress + external stress), op-posite offsets are observed. As explained in Section 2.5, thestress induced offset can be removed by averaging thesetwo responses as shown in Figure 15. Finally, during athird experiment we applied a square wave on the clockinput of our magnetometer. The frequency of the clocksignal (100 kHz) was chosen high compared to the cut-offfrequency of the low-pass filter (−1 dB at 1 kHz) so thatthe averaging process is performed by the filter. The re-sponse obtained during this last experiment (solid line inFig. 15) is very close to the calculated average response.

−6 −4 −2 0 2 4 6−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

B (mT)

Out

put v

olta

ge (

V)

clk=’0’

clk=’1’

average

spinning current

−6 −4 −2 0 2 4 6−0.06

−0.04

−0.02

0

0.02

0.04

0.06

B (mT)

Out

put v

olta

ge (

V)

average

spinning current

Fig. 15. Responses of the spinning current magnetometer.

3 Multi-strips Hall effect sensor

3.1 n-strips Hall device

As explained in Section 2.4, whatever the shape of the Hallplate is, rectangular or cross shape (a cross can be seen astwo rectangles perpendicularly laid out), in order to maxi-mize the geometrical correction factor G the device lengthL should be larger than its width W . A ratio L/W closeto 3 is necessary to have G 1. By using such a ratio,the input resistance Rin is necessary high (Eq. (13)) whichlimits the biasing current I to Imax = Vsup/Rin where Vsup

is the supply voltage. Since the supply voltage is gener-ally limited to some volts, the absolute sensitivity of inte-grated Hall devices is thus generally small. For a typical5 V−0.6 µm CMOS technology with a N well square resis-tance of roughly 1 kΩ and a current-relative sensitivityof 120 V/AT, the input resistance is close to 3 kΩ and themaximal current is limited to 1.5 mA. These data lead toan absolute sensitivity of only 180 mV/T. The only wayto increase this sensitivity is to decrease Rin by reduc-ing the length of the device while keeping G close to one.The biasing current can thus be increased, so the absolute


S1 S2

B2b B2c B2dB2a

B1b B1c B1dB1a

S

l

w

W

L

Fig. 16. 4-strips Hall device.

S1 S2

B2b B2c B2dB2a

B1b B1c B1dB1a

Fig. 17. Multi-strips Hall device biasing principle.

sensitivity. The small value of G in a short Hall device(L < W ) is due to the wide highly doped biasing contactswhere the Hall effect is strongly reduced (the so calledshort-circuit effect). To minimize this short-circuit effect,we simply split the wide contacts into elemental ones asshown in Figure 16, leading to the multi-strips Hall device.The idea is based on a principle first proposed by Popovicfor magnetic field effect transistor (MagFET) [28]. In or-der to let the Hall voltage to establish, each elementalbiasing contact (B1a-d and B2a-d in Fig. 16) has to betotally independent from the others. This is possible ifthe new n-strips device is supplied thanks to two ranks ofn matched and independent current sources as shown inFigure 17. The output impedances of these current sourcesbeing high, the multi-strips device behaves as if it were in-finitely long while it is kept short. Such a biasing methodalso ensures an homogeneous current density inside thewhole Hall plate. Since a multi-strips device can be seenas the merging of minimum size rectangular Hall devices,the biasing contacts B1a-d and B2a-d (Fig. 16) of theseelemental rectangular devices are responsible for a resid-ual short-circuit effect. The geometrical correction factor

Ibias

VDD

VSS

vout

Mp1 Mp2 Mp3 Mp4

Mn1 Mn2 Mn3 Mn4

Fig. 18. Multi-strips Hall device biasing circuit.

of the multi-strips sensor is thus given by the geometricalcorrection factor exhibited by one elemental strip. Look-ing at Figure 16, equation (14) can be adapted for the newmulti-strips device as:

Gnew [1 − 16

π2exp

(−π

22l + L

w

)]. (18)

This equation is valid for (2l + L)/w > 1.5 and S/W <0.18, which is generally the case even when using the min-imum size rules of the technology. The average input re-sistance of a n-strips Hall device is now given by:

Rnew R

(1n

l

w+

L

W+

1n

l

w

)= R

(L

W+

2n

l

w

).

(19)Since W n · w, Rnew is over-valued by:

Rnew R1n

2l + L

w. (20)

As a consequence, the average input resistance of an-strips Hall device is about n times smaller than the in-put resistance of a rectangular device with the same geo-metrical correction factor. The maximal biasing current aswell as the maximal absolute sensitivity are thus n timesgreater than for a conventional rectangular device.

3.2 Specific biasing circuit

The basic circuit in Figure 11 can be adapted as presentedin Figure 18 in order to implement the biasing principleshown in Figure 17. A set of n independent and matchedoutput stages is substituted for the single output stageof the circuit in Figure 11. Since all transistors are main-tained into saturation, they behave as current sources. Thevoltage of each small biasing contact of the multi-strips de-vice can thus establish freely, allowing the elemental Hallvoltages vh across the strips to add up. If we assume aninfinite output resistance for transistors Mn1 to Mn4 andMp1 to Mp4, the voltage at the output of the circuit inFigure 18 is clearly given by (see Fig. 19):

v(r=∞)out = 4 · vh. (21)


VDD

VSS

vout

Mp1 Mp2 Mp3 Mp4

Mn1 Mn2 Mn3 Mn4

vh2

vh2

vh2

vh2

vh2

vh2

vh2

vh2

Vir

tual

grou

nd

Fig. 19. Output stage of a 4-strips Hall device biasing circuit.Each strip is modeled by a Wheatstone bridge.

r r r r

rrrr

R R R R R R R R

RRRRRRRR vh2

vh2 vh vh vh

Virtual ground (high impedance node) Output (high impedance node)

Fig. 20. Small signal equivalent circuit of a 4-strips Hall devicebiased with the circuit of Figure 18.

r2

r2

r2

r2

r2

r2

r2

r2

R2

R2

R2

R2

R2

R2

R2

R2

R2

R2

RRRvh2

vh2

vh2

vh2

vh2

vh2

vh2

vh2

vh2

vh vh vh

v1

v1

v2

v2

v3

v3

v4

v4

1

2

3

4

vout

vout

Fig. 21. Simplified equivalent circuits of the small signal cir-cuit shown in Figure 20.

Nevertheless, in actual circuits, transistors exhibit a finiteoutput resistance which acts as a resistive load, loweringthe effective output voltage. To evaluate this resistive ef-fect, let us consider the small signal equivalent circuit ofthe output stage in Figure 19. This equivalent circuit ispresented in Figure 20 where r is the output resistanceof the matched transistors Mn1 to Mn4 and Mp1 to Mp4,and R is the nominal resistance of the Wheatstone bridgewhich models one strip. Using a star-to-triangle transfor-mation followed by a triangle-to-star transformation, orsimply by considering the symmetry of the Wheatstonebridge connected to the two output resistances r of itsbiasing transistors, this equivalent circuit is easily trans-formed to the circuit in Figure 21. Writing the Kirchhoff’scurrent law for nodes

1 ,

2 ,

3 and

4 , we get the fol-

lowing set of equations:

1 0 + v1−v2+vh

R = − v1r/2

2 v2−v1−vh

R + v2−v3+vhR = − v2

r/2

3 v3−v2−vh

R + v3−v4+vhR = − v3

r/2

4 v4−v3

R + 0 = − v4r/2

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

.

The solution of this equations set gives for v1 and v4:

v1 = −v4 = − 3 + 2 · R/r

2 + 8 · R/r + 4 · (R/r)2· vh.

Thus, the effective output voltage of the circuit in Fig-ure 18 is:

vout = vh + v4 − v1 =4 + 6 · R/r + 2 · (R/r)2

1 + 4 · R/r + 2 · (R/r)2· vh. (22)

As expected, for R/r → 0, i.e. for an infinite output re-sistance of the current sources which bias the multi-stripsdevice, equation (22) reduces to equation (21). On thecontrary, when r is small, i.e. R/r → ∞, then vout → vh

and the multi-strips device behaves like a single strip Hallplate. A deep analysis of the circuit in Figure 18, whichcan be used to bias a cascade of any kind of Wheat-stone bridges, shows that the effective output voltage fora n-strips Hall device biased with such a circuit is givenby [29]:

v(n)out =

q + 1q − 1

· tanh(n

2ln(q)

)· vh (23)

where:

q = 1 +R

r+

√2R

r+(

R

r

)2

. (24)

Since q > 1 and lim [tanh(x)] = 1 for x → ∞, vout reachesa limit for n → ∞ given by:

S(∞) =q + 1q − 1

· vh. (25)

As a consequence, for a given ratio of the nominal Halldevice resistance R to the output resistance of the biasingtransistors r, the number of efficient strips is limited (seeFig. 22). The larger the ratio R/r, the larger the numberof efficient strips can be. In actual design, using singlesaturated transistors as current sources allows to easilyhave n = 10 strips (see Sect. 4.2), while this number ofstrips can be increased when more complex high-output-resistance current sources, like cascode sources [30], areused.

3.3 Chopper stabilized biasing circuit

Thanks to the gain of the differential input stage, the noisedue to the output stage is generally neglected in a two-stage amplifier like the one in Figure 11 [31]. Neverthe-less, in the circuit of Figure 18, a pernicious coupling ef-fect arises between the n strips leading to the main noise


0 50 100 1500

10

20

30

40

50

60

70

v(n

)ou

t/v h

:fr

omeq

uat

ion

(3.2

)

n: number of bridges

: R/r = 0.1

×: R/r = 0.01

: R/r = 0.001

Fig. 22. Normalized sensitivity v(n)out/vh versus n.

virt

ual g

roun

d

vodiff

i3

i34

2.i34i34

i34

i34

i34

i34

VDD

VSS

Mp1 Mp2 Mp3 Mp4

Mn1 Mn2 Mn3 Mn4

Fig. 23. Noise due to the output stages.

component of the system, especially at low-frequency. Inorder to understand this phenomenon, let us assume thatonly one transistor, for example Mp3 in Figure 19 exhibitsnoise. The circuit of Figure 19 is repeated for conveniencein Figure 23 without the Hall voltage sources which are ofno concern for noise calculation. The noise produced byMp3 is represented by the noise current source i3. In orderto maintain the virtual ground on the fed-back node of then-strips Hall device, the differential stage (not shown inFig. 23) adjusts its output, vodiff , so that the noise cur-rent i3 is sunk through Mn1, Mn2, Mn3, and Mn4. As aconsequence, each of the four NMOS transistors sinks aquarter of i3 leading to a current flowing between twoconsecutive strips as indicated in Figure 23. Applying theKirchhoff’s laws for each strip and summing the resultingvoltage drops across the bridges, as shown in Figure 24a,the noise voltage due to i3 can be calculated as:

vout = 2Ri316

+ 2R3i316

+ R

(9i316

− 7i316

)− 2R

i316

vout = Ri32

(26)

which, in terms of power spectral density (psd), reads:

v2out =

14R2i23 (27)

(a)

Vir

tual

gro

und

(b)

Vir

tual

gro

und

vout

vout

i3

i3

i34

i342 i3

4

2 i34

i34

i34

i34

i34

i34

i34

i34

i34

i34

i34

i316

i316

3i316

3i316

3i316

3i316

i316

i316

5i316

5i316

9i316

9i316

7i316

7i316

i316

i316

3i316

3i316

i316

i316

3i316

3i316

vout = Ri32

vout = −Ri32

Fig. 24. Noise current through the 4-strips Hall device.

where i23 is the psd of the noise current generated by Mp3.Using the same approach for each transistor which biasesthe n-strips Hall device, and summing the resulting powerspectral densities, we find for the noise coming from thesetransistors:

v2out =

14R2(i2n2 + i2p2 + i2n3 + i2p3

)+

94R2(i2n1 + i2p1 + i2n4 + i2p4

)(28)

where i2nj and i2pj are the noise current psd generated bytransistors Mnj and Mpj which bias the jth strip. Sinceall the NMOS transistors (respectively the PMOS transis-tors) have the same dimensions and are in the same biasingconditions, they exhibit the same current noise, i2n (respec-tively i2p), and the previous equation can be rewritten:

v2out = 2

(14

+94

)R2(i2n + i2p

). (29)

Finally, this equation can be generalized for a circuit ded-icated to the biasing of a n-strips Hall device [32]:

v2out =

n3 − n

12R2(i2n + i2p

)(30)

where i2n and i2p include thermal and 1/f noise compo-nents. We also have to mention that equation (30) givesa pessimistic noise level because we have neglected thefinite output resistance of the transistor for noise calcu-lation. Actually, the noise voltage drops due to the noisecurrents flowing between the strips are reduced by the re-sistive load effect as for the useful Hall signal. One must


also note from equation (30) that, as expected, when thereis only one strip (n = 1), i.e. in the case of a conventionalHall plate, the output stage does not contribute to the to-tal output noise. Since the Hall voltage exhibited by onestrip is proportional to its biasing current, the quiescentcurrent of the biasing transistors is generally maximized,leading to a high 1/f noise component in the current noisepsd i2n and i2p. The noise due to these transistors being alsoproportional to n3 (see Eq. (30)), it generally prevails overthe noise coming from the input differential stage and fromthe Hall device, and eventually can annihilate the benefitof the increased sensitivity the n-strips Hall device pro-vides. However, if the NMOS and PMOS biasing transis-tors are permuted around the middle point of the n-stripsHall device, the noise voltage they generate is opposite (seeFig. 24b). As a consequence, switching the output stagesof the circuit in Figure 18 around this point of symme-try, at a frequency higher than the useful bandwidth ofthe magnetic signal to be measured, fu, allows to rejectthis excess noise to high frequencies. In fact, the switchingfrequency, fs, has to be higher than 2 · fu (Shannon theo-rem) and a simple low-pass filter can be used to suppressthe 1/f noise which is rejected around fs by the switchingmechanism. This technique is nothing else but a chopperstabilization [33] applied to the output stage of the circuitin Figure 18. It is worth to note that the chopping mech-anism does not modify the thermal noise coming from theoutput stages [33] which remains given by equation (30).


Two multi-strips Hall effect devices with their biasing cir-cuits were integrated. The first one, with 4 strips (W =31.6, w = 3.1, L = 9.6, l = 2.2, and S = 3.1 µm – seeFig. 16), was biased with the basic circuit of Figure 18,without chopping stabilization. On the contrary, the sec-ond one, which was drawn with 5 strips (W = 39, w = 3,L = 9, l = 0.2, and S = 3 µm), was implemented with thechopper stabilized biasing circuit and a 45-kHz oscillatorwhich generates the chopping control signals. Note thatthe NMOS and PMOS transistors which bias the mid-dle strip do not contribute to noise and are not switched.The switches were designed using differential pairs like forthe spinning-current circuit presented in Figure 12. Forthis first version of our chopper-stabilized biasing circuit,we chose to use a smooth switching scheme (see Fig. 25)in order to prevent any switching noise. The way it wasimplemented is explained elsewhere [32]. During the ex-periment, the integrated circuits were mounted on a PCBfeaturing a pre-amplifier and a fourth order low-pass filtersimilar to the ones used for the spinning current experi-ment (see Sect. 2.7). Figure 26 presents the current relatedresponses, i.e. the sensor response divided by the biasingcurrent, of both 4-strips and 5-strips Hall devices. Thegreat dispersion in the data points we measured with the4-strips device is explained by the high 1/f noise levelexhibited by the system and coming mainly from the bi-asing transistors as explained in the previous section. Thechopping stabilization clearly suppresses this noise as it

Time

Chopping control signal

Switching time

VAVAVB

VBT

Fig. 25. Switching scheme used for chopper stabilization. Dur-ing the switching time, both switches transmit current.

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

MAGNETIC FIELD (mT)

HA

LL V

OLT

AG

E (

V/A

)

4−STRIPS SENSOR

5−STRIPS SENSOR

Fig. 26. Responses of the 4-strips and 5-strips Hall devices.The offset is removed for easy comparison.

can be observed on the response of the 5-strips devicewhere the data remain aligned. The absolute sensitivitieswere measured to be 119 mV/T and 195 mV/T for the4-strips and the 5-strips devices respectively. The biasingcurrent being 0.97 mA and 2.07 mA, the current-relatedsensitivities are calculated to be 123 V/AT and 94 V/ATrespectively. The difference between both current-relatedsensitivities is explained by the smooth switching we used.During the switching time, which corresponds to 20% ofthe clock signal period, the strips of the device are short-circuited by the differential pairs and the Hall effect isannihilated. Dividing 94 V/AT by the correction factor0.8 leads to a current-related sensitivity of 117 V/AT. Itis also worth to note that the resistive load effect is higherfor the 5-strips Hall device than for the 4-strips one. Thusthe actual current-related sensitivity is close to 120 V/ATas expected for the used technology. However, accordingto subsequent experimental results (see next section), us-ing a deep-front-edge switching does not lead to significantswitching noise at the output of the system. As a conse-quence, in order to take full benefit of the multi-stripsdevice, this smooth switching scheme should be avoided.

These results show that integrated magnetometersbased on the multi-strips device can exhibit high absolutesensitivities: one has to use a high number of strips with bi-asing current sources having a high output-resistance (byimplementing cascode current sources for example [30]).This is an important advantage since for a given resolutionof the magnetometer, this allows to relax the noise level of


VM

Ib

IbVM

VH

VH

Fig. 27. The elemental differential signals of rectangular Halleffect sensors can be added by simply connecting them by theirsensing contacts. Ib is the biasing current, VH is the Hall volt-age, and VM is the shear stress induced voltage.

the pre-amplifier and the biasing amplifier. Furthermore,the higher the number of strips is, the better the resolu-tion of the n-strips Hall device itself is [32]. However, themulti-strips device exhibits a drawback we did not dis-cuss yet. Each strip exhibits an offset, and these offsetsadd up each others leading to high offset which preventsa straightforward amplification of the signal. While smartcircuitry can be used to solve the problem, the next sectionproposes a simple solution resulting in a high-sensitivitylow offset magnetometer.

4 Sensors network

4.1 Building the network

As explained in Section 2.5, an integrated Hall plate isalso a good shear stress sensor. We pointed out that thespinning current technique was very efficient to removethis cross-sensitivity since the sign of the mechanical sen-sitivity (SM) depends on the orientation of the sensor:if the sensor is rotated by π

2 rad, the sign of SM is in-verted while the sign of the magnetic sensitivity remainsconstant. However, the spinning current technique fails ifthe sensor is subjected to vibrations which frequencies areclose to the spinning frequency. In that case, the alter-native mechanical signal is shifted in the base band andcannot be discriminated from the useful magnetic signal.In order to overcome this problem, we proposed to use anetwork made of an even number of orthogonal rectan-gular Hall effect sensors [34]. Since such sensors generateidentical Hall voltages and opposite shear stress inducedvoltages when they are in the same biasing conditions, onejust needs to sum their elemental contributions to removethe parasitic mechanical signal. The simplest way to sumthe elemental differential voltages of n Hall effect sensorsconsists in connecting them by their sensing contacts asshown in Figure 27. By adding the contributions of aneven number of orthogonal Hall sensors, one can thus ob-tain a signal proportional to the magnetic field and notperturbed at all by mechanical stress. The more, from an

I bias

V SS

V DD

V out

Fig. 28. The same circuit than the one designed for then-strips Hall effect sensor can be used to bias the sensorsnetwork.

Loudspeaker

Magnetic shield Printed circuit board

Fig. 29. A loudspeaker is used to generate vibrations.

electrical point of view, the resulting n-sensors network isvery similar to the n-strips Hall effect sensor described inSection 3. Consequently, the same circuit can be used tobias such a sensors network (Fig. 28).


Three microsystems have been designed. Two of them arebased on a Hall effect sensors network, the first one be-ing made of ten parallel sensors and the second one beingmade of ten orthogonal sensors. The third microsystem isbased on the spinning current method and has been inte-grated to make the comparison. All these three microsys-tems were tuned (their biasing currents were adjusted) sothat they have exactly the same magnetic sensitivities.In order to generate some vibrations in a reproducibleway, we used a loudspeaker mechanically coupled to theprinted circuit board on which the integrated circuit isplaced (Fig. 29). The more, to prevent the magnetic fieldproduced by the moving coil of the loudspeaker from be-ing seen by the magnetic sensors, we added a magneticshield made of soft iron between the loudspeaker and theprinted circuit board. Nevertheless, since we made a holein this magnetic shield to place the alumina axle whichlinks the moving coil to the printed circuit board, the sen-sors may be subjected to a residual magnetic field. Theloudspeaker was driven by an AC power source and thefrequency was tuned to the mechanical resonance (800 Hz)


Output signal

Loudspeaker voltage

Output signal

Loudspeaker voltage

Output signal

Loudspeaker voltage

spinning current

orthogonal network

parallel network

Fig. 30. Experimental results: output signals.

in order to generate mechanical vibrations of a large am-plitude. Since all the microsystems use a dynamic biasingtechnique (clock frequency is 100 kHz), a forth order But-terworth low-pass filter (−1 dB @1 kHz) has been used toget the useful magnetic signal which is in the base band.The results are presented in Figure 30. As one can see, thefirst microsystem is very sensitive to vibrations. Indeed,since all the sensors of the network are parallel this firstmicrosystem just sums ten times the same signal. On thecontrary, the second microsystem which uses an orthog-onal network is quite less sensitive to mechanical stress.However, there is a residual signal which is also measuredwith the third microsystem based on the spinning currenttechnique. This fact seems to indicate that this residualsignal corresponds to the part of the magnetic field pro-duced by the moving coils which is not canalized by themagnetic shield. The more, one can notice that the phaseof the signal observed in the case of an orthogonal networkand in the case of the spinning current is different thanthe phase observed in the case of the parallel network.Subsequently, we made a second experiment in which thealumina axle was removed. The mechanical coupling be-tween the loudspeaker and the printed circuit board wasthus suppressed. During this experiment, we observed thesame responses with the three integrated magnetometers.This proves that the residual signals observed with theorthogonal network and with the spinning current comefrom the leakage through the magnetic shield. Unfortu-nately, because of this residual magnetic field we were notable to quantify the rejection of the mechanical signal.However, by manually applying static stress on the printedcircuit board we were not able to observe any output volt-age fluctuation neither with the orthogonal network norwith the spinning current based magnetometer.

0.97 0.98 0.99 1 1.01 1.02 1.03

x 105

−10

0

10

20

30

40

50

60

70

Frequency (Hz)

Nor

mal

ized

sig

nal (

dB)

Sensors network

0.97 0.98 0.99 1 1.01 1.02 1.03

x 105

−10

0

10

20

30

40

50

60

70

Frequency (Hz)

Nor

mal

ized

sig

nal (

dB)

Spinning current

mechanical signal

shifted flicker noise

Fig. 31. Experimental results: spectrums around the clockfrequency. The spectrums are normalized with respect to thethermal noise level.

Finally, we made a third experiment in which the low-pass filter was removed. The 100 kHz chopping/spinningcarrier was thus kept in the output signal. We then an-alyzed the spectrum of the signal around the clock fre-quency in the case of an orthogonal network and in thecase of the spinning current based microsystem. As it isclearly shown in Figure 31, the spinning current techniquerejects the mechanical signal (800 Hz and its harmonics)around the spinning frequency. On the contrary, in thecase of the Hall effect sensors network the mechanical sig-nal is totally removed but the flicker noise of the out-put stages is rejected around the chopping frequency [32].Since the corner frequency of a transistor can be eval-uated by simulation, one can ensure that all the flickernoise of output stages will be shifted outside of the use-ful bandwidth by choosing a sufficiently high choppingfrequency. On the contrary, in the case of the spinningcurrent technique one cannot forecast the frequency ofthe mechanical excitation which may perturb the magne-tometer. If a mechanical signal of frequency in the range[fclk−flp; fclk+flp] (fclk is the clock frequency and flp thecutoff frequency of the low-pass filter) is applied to such amagnetometer, there will be a parasitic signal in the baseband which will be indiscernible from the magnetic signal.


4.3 Spinning-current versus sensors network

The spinning current technique and the Hall sensors net-work share the same goal, namely the improvement of themagnetometer metrological performances. In some extent,they also share similar aspects like the use of a switchingmechanism to be functional. Nevertheless they are differ-ent. The spinning current method requires symmetricalHall devices which are invariant by a rotation of π

2 rad,while the sensors network can be built from any kind ofelemental Hall device, the only requirement being to drawthese devices two and two perpendicular (see Fig. 28).A symmetrical Hall device to be used with the spinning-current can be seen as two Hall devices which are drawnperpendicular and superimposed (see the cross Hall de-vice in Fig. 2), and the sensitivity of the magnetometeris the same than the sensitivity of one Hall device. Onthe contrary, a network of n Hall sensors exhibits a sen-sitivity which is n times the sensitivity of the elementalHall sensor (here we assume that the output resistanceof the transistors which bias the sensors is high, see dis-cussion in Sect. 3.2). As mentioned at the end of Sec-tion 3.4, this is advantageous since it allows to relax thenoise level of the biasing amplifier and the pre-amplifierfor a given resolution of the magnetometer. The designof both amplifiers is then easier. Finally, both techniquesallow to reduce drastically the offset due to mechanicalstress. Since the spinning-current method shifts by modu-lation the low-frequency noise (an offset can be seen as avery low-frequency noise) around the spinning frequency,it also allows to reduce the 1/f noise due to the Halldevice. Nevertheless in the case of mechanical vibrationsat frequencies close to the spinning frequency, a stress-induced mechanical signal is shifted into the base bandand cannot be discriminated from the useful Hall signal.On the contrary, the sensors network performs a direct off-set cancellation and thus removes any parasitic mechanicalsignal as discussed in the previous section. Furthermoresince the output of a network with n sensors is the sumof the signal coming from each elemental sensor, the noisedue to these sensors is averaged. Thus, the 1/f noise of amagnetometer based on a n-sensors network is 1/

√n less

important than for a magnetometer with only one Hallsensor, but it is not removed as with the spinning-currentmethod.

From this last discussion, it cannot be said that thespinning-current method is definitely better than the sen-sors network and vice versa. Depending on the application,one has to choose the most adapted technique. For exam-ple, using a Bipolar technology where the transistors aregenerally low noise, the spinning-current method shouldbe the best one since it is easy to design low-noise bias-ing amplifiers and pre-amplifiers, while taking advantageof the Hall device 1/f noise suppression provided by thismethod. On the other hand, if a CMOS technology has tobe used where the transistors are well known to be noisy,or if the magnetometer has to be used in a robust systemwhere high frequencies mechanical vibrations may arise, asensors network should be a better choice.

Phase 1

Phase 2

Phase 3

Phase 4

v1 = 2vH + 2v1/fplate + vNP MOS

v2 = 2vH − 2v1/fplate + vNNMOS

v3 = 2vH + 2v1/fplate − vNP MOS

v4 = 2vH − 2v1/fplate − vNNMOS

Fig. 32. Spinning-current compatible multi-strips Hall device.Between phase 1 and 2, or 3 and 4, the 1/f noise coming fromthe squared plates is reversed. Between phase 1 and 3, the noisecoming from the PMOS transistors is reversed, while betweenphase 2 and 4 the noise coming from the NMOS transistorsis reversed. Averaging (low-pass filtering) over the four phasesallows to remove the 1/f noise coming from the Hall deviceand the biasing transistors.

5 Spinning-current compatible multi-stripssensor

The multi-strips principle allows to improve the sensitiv-ity of a Hall device while the spinning-current allows tosuppress the offset and 1/f noise of the device. As a con-sequence, both principles are complementary and the bestsolution to design a good Hall effect magnetometer is prob-ably to combine the two principles. For example cross-shape plates operated by spinning-current can be used inthe circuit of Figure 28 instead of rectangular Hall devices.But each time the current is spun in the cross-shape de-vices, their serial connection has to be changed, leadingto a complicated switching scheme and circuit layout. Amore compact solution is presented in Figure 32 where themulti-strips sensor is drawn as a serie of joined squaredHall plates.

Using such a combination with a chopping stabiliza-tion of the input differential stages of the biasing amplifierand the preamplifier should allow to design high resolutionmagnetometers by suppressing all sources of 1/f noise.

6 Conclusion

A review of the Hall effect and the way it is usually im-plemented in CMOS technologies has been given. The fullcompatibility of Hall devices with CMOS technologies al-lows to take advantage of on-chip circuitry. In particu-lar, the well known spinning-current method has been de-scribed and experimental results were given. While this


method allows to reduce the intrinsic 1/f noise of theHall device as well as the stress-induced offset, it fails inremoving vibration induced parasitic signals which mayarise close to the spinning frequency. Furthermore, the ab-solute sensitivity of a spinning-current Hall device is thesame than the sensitivity of a conventional rectangularHall device, and it is generally small because of the lowcarrier mobility in silicon. This drawback asks for verylow noise biasing amplifier and pre-amplifier in order toobtain a good signal to noise ratio. On the contrary, thenew multi-strips Hall device we proposed allows to dras-tically increase the absolute sensitivity of the sensor. Inorder to be functional, this new device requires a spe-cific chopper-stabilized biasing amplifier which has beenalso presented. While having a high sensitivity, this multi-strips sensor suffers from high offset. Then, a Hall sensorsnetwork, made of conventional rectangular Hall devicestwo and two perpendicular, has been proposed. It requiresthe same chopper-stabilized biasing amplifier to work, andexhibits all the advantages of the multi-strips Hall device.It also suppresses the offset and vibration induced para-sitic signals but it is not able to reduce the intrinsic 1/fnoise of the Hall device as the spinning-current princi-ple does. A comparison between the spinning-current andthe Hall sensors network techniques shows that both tech-niques provide their own advantages and can be advan-tageously combined to design high resolution Hall effectmagnetometers on silicon.

References

1. R. Popovic, Z. Randjelovic, D. Manic, Sensor. Actuat. A97, 98, 39 (2002)

2. A. Frazier, Z. Liub, L. Tianc, J. Parhamd, in Proceedingsof IEEE Sensors, Orlando, Florida, USA, 2002, pp. 1565–1570

3. M. Metz, A. Haberli, M. Schneider, R. Steiner, C. Maier,H. Baltes, in Proceedings of TRANSDUCERS’97, Chicago,USA, 1997, pp. 385–388

4. M. Demierre, E. Schurig, C. Schott, P.-A. Besse,R. Popovic, Sensor. Actuat. A 116, 39 (2004)

5. A. Xin, B. Hai, S. Jiahua, Y. Yihan, in Proceedings ofPOWERCON’98, Beijing, China, 1998, pp. 1015–1020

6. V. Frick, L. Hebrard, P. Poure, F. Anstotz, F. Braun, IEEESensors J. 3, 752 (2003)

7. M.J. Caruso, in Proceedings of IEEE Position Location andNavigation Symposium, San Diego, USA, 2000, pp. 177–184

8. V. Schlageter, P.-A. Besse, R. Popovic, P. Kucera, Sensor.Actuat. A 92, 37 (2001)

9. E. Paperno, P. Keisar, IEEE T. Magn. 40, 1530 (2004)10. R. Popovic, J. Flanagan, P.-A. Besse, Sensor. Actuat. A

56, 39 (1996)11. J.-B. Kammerer, Capteurs integres pour la mesure a haute

resolution de champs magnetiques, Ph.D. thesis, UniversiteLouis Pasteur, Strasbourg, 2004

12. A. Bilotti, G. Monreal, R. Vig, IEEE J. Solid St. Circ. 32,829 (1997)

13. A. Bakker, A.A. Bellekom, S.M. Middelhoek, J.H.Huijsing, in Proceedings of EUROSENSORS XIII, 1999,pp. 543–544

14. R. Steiner, C. Maier, A. Haberli, F.-P. Steiner, H. Baltes,Sensor. Actuat. A 66, 167 (1998)

15. N. Kordas, S. Derksen, H.-L. Fiedler, M. Schmidt,A. Yasujima, M. Matsui, S. Nagano, K. Ishibashi, inProceedings of ISSCC99, 1999, pp. 134–135

16. M. Demierre, S. Pesenti, J. Frounchi, P.-A. Besse,R. Popovic, Sensor. Actuat. A 97, 98, 39 (2002)

17. H. Baltes, R. Popovic, Proc. IEEE 74, 1107 (1986)18. P.M. Drljaca, F. Vincent, P.-A. Besse, R.S. Popovic,

Sensor. Actuat. A 97, 98, 10 (2002)19. R.S. Popovic, Sensor. Actuat. A 85, 9 (2000)20. E. Schurig, M. Demierre, C. Schott, R.S. Popovic, Sensor.

Actuat. A 97, 98, 47 (2002)21. S. Sze, Semiconductor Sensors (Wiley-Interscience, 1994)22. V. Frick, L. Hebrard, P. Poure, F. Braun, Analog Integr.

Circ. S. 36, 165 (2003)23. W. Versnel, J. Appl. Phys. 52, 4659 (1981)24. S. Middelhoek, S. Audet, Silicon sensors (Academic Press,

1989)25. C. Muller-Schwanneke, F. Jost, K. Marx, S. Lindenkreuz,

K. von Klitzing, Sensor. Actuat. A 81, 18 (2000)26. A. Sutor, R. Lerch, H.-P. Hohe, M. Gavesi, IEEE Sensors

J. 1, 345 (2001)27. P. Munter, in Proceedings of the 5th International

Conference on Solid-State Sensors and Actuactors,Montreux, Switzerland, 1989, pp. 430–434

28. R. Popovic, Sensor. Actuat. A 5, 253 (1984)29. L. Hebrard, J.-B. Kammerer, F. Braun, IEEE T. Circuits

I: Regular Papers 52, 1653 (2005)30. E. Sackinger, W. Guggenbuhl, IEEE J. Solid-St. Circ. 25,

289 (1990)31. G. Palmisano, G. Palumbo, S. Pennisi, Analog Integr. Circ.

S. 27, 177 (2001)32. J.-B. Kammerer, L. Hebrard, V. Frick, P. Poure, F. Braun,

IEEE Sensors J. 3, 700 (2003)33. C. Enz, G. Temes, Proc. IEEE 84, 1584 (1996)34. J.-B. Kammerer, L. Hebrard, F. Braun, in Proceedings

of the 3rd IEEE conference on sensors, Vienna, Austria,2004, pp. 1071–1074

Hall eect sensors integrated in standard technology and ... · mainsa problem.A solution is proposedin Section 4 where a Hall sensors network is substituted for the multi-strips Hall

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