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

Transcription

1 Eu. Phys. J. Appl. Phys. 36, (006) DOI: /epjap: THE EUOPEAN PHYSICAL JOUNAL APPLIED PHYSICS Hall effect sensos integated in standad technology and optimized with on-chip cicuity J.-B. Kammee 1,a,L.Hébad 1,V.Fick 1,P.Poue,b,andF.Baun 1 1 Institut d Électonique, du Solide et des Systèmes (InESS), 3 ue du Lœss, BP 0, Stasboug Cedex, Fance Laboatoie d Instumentation Électonique de Nancy (LIEN), Faculté des Sciences et Techniques, BP 39, Vandœuve-les-Nancy Cedex, Fance eceived: 9 Mach 005 / eceived in final fom: 3 Decembe 005 / Accepted: 4 Mach 006 Published online: 6 Octobe 006 c EDP Sciences Abstact. While silicon is not the best semi-conducto mateial to design Hall effect sensos, it is widely used because Hall devices ae fully compatible with standad pocesses such as CMOS o Bi-CMOS. Hall effect sensos can thus take advantage of on-chip cicuity to countebalance the poo intinsic metological chaacteistics of silicon Hall devices, and low cost integated smat magnetometes can be designed using standad technologies. Conventional Hall plate as well as the spinning-cuent method, which is the pesent state of the at technique to impove pefomances of integated Hall devices, ae eviewed in this pape. Then a new multi-stips Hall device and its specific biasing cicuit ae intoduced. This new device allows to multiply by n the absolute sensitivity of the Hall senso whee n is the numbe of stips, but it suffes fom offset. To ovecome this dawback, a Hall sensos netwok which also allows to incease the sensitivity while educing the offset is poposed. Finally a compaison between the Hall sensos netwok and the spinning-cuent is done, showing that both techniques ae complementay and should be combined to design high esolution Hall senso systems. PACS Df Sensos (chemical, optical, electical, movement, gas, etc.); emote sensing Fg Bulk semiconducto and conductivity oscillation devices (including Hall effect devices, space-chage-limited devices, and Gunn effect devices) Qx Micocicuit quality, noise, pefomance, and failue analysis 1 Intoduction Nowadays, Hall effect magnetometes ae pobably the most widely used magnetic sensos [1]. They find applications in the fields of automotive [], angula position sensos [3,4], contact-less cuent sensing [5,6], compass systems [7], magnetic tacking [8,9],... Howeve, due to a low caie mobility, silicon is not the most appopiate semiconducto mateial to design Hall effect sensos and discete Hall devices ae geneally poduced using highmobility mateials such as GaAs [10]. On the othe hand, Hall devices ae fully compatible with micoelectonics manufactuing pocess such as CMOS o Bi-CMOS, and thus can be easily integated with electonics on the same die [1]. This new degee of feedom offeed by on-chip cicuity can be used to countebalance the poo chaacteistics of the silicon Hall device thu the use of specific biasing cicuits [11], smat offset eduction techniques [1 14], This pape has been pesented at 3 e colloque intedisciplinaie en instumentation (CI 004), École Nomale Supéieue de Cachan, 9 30 janvie 004. a jean-baptiste.kammee@iness.c-stasboug.f b philippe.poue@lien.uhp-nancy.f tempeatue compensation [15], self-calibation [], and so on. The design of low cost integated smat magnetometes is thus possible. The spinning-cuent method is now ecognized as the state of the at technique to educe the offset and 1/f noise in Hall devices [10]. Nevetheless, it suffes fom switching noise [1] and fom any paasitic mechanical vibation aising at fequencies close to the spinning-fequency [11]. To incease the sensitivity which is limited by the low caie mobility in silicon and also by the shot-cicuit effect [17], the pesent tend is to add feomagnetic flux concentatos [18]. While the sensitivity impovement can be vey high, this technique gives ise to non-lineaity and hysteesis in the magnetomete esponse. Futhemoe, it asks fo a specific post-pocessing which inceases the cost of the senso. In this pape, we intoduce new shapes of Hall plate associated to a new on-chip biasing cicuit to impove the metological pefomances of Hall effect sensos. While ou wok was focused on hoizontal Hall effect sensos, i.e. Hall devices sensitive to the magnetic field pependicula to the plane of the chip, it could be adapted to vetical Hall sensos as well, i.e. sensos sensitive to an in-plane magnetic Aticle published by EDP Sciences and available at o

2 50 The Euopean Physical Jounal Applied Physics t V z W I F L v + + y + B x + + Fig. 1. The Hall effect comes fom the equilibium between the Loentz foce and the tansvesal electic foce. e E V y F E z I V H B Fig.. Voltage inside a ectangula (left) and a coss-shaped (ight) Hall effect sensos. The cuent flows vetically fom the top contact to the bottom contact. The ed colo epesents the highest potential while the blue colo epesents the lowest one. The magnitude of the magnetic field is 3 T. I V H field [19, 0]. The next section eviews the woking pinciple of conventional hoizontal Hall devices and highlights thei main limitations thu the shot-cicuit effect and the stess-induced offset. In addition, a basic biasing cicuit using the spinning-cuent method is pesented with some expeimental esults. In Section 3 a new shape of Hall device is pesented with its specific biasing cicuit. Fee fom shot cicuit effect, the new multi-stips Hall plate exhibits a high absolute sensitivity but its offset still emains a poblem. A solution is poposed in Section 4 whee a Hall sensos netwok is substituted fo the multi-stips Hall device while keeping the specific biasing cicuit. Expeimental esults show that the esulting magnetomete has small offset, is insensitive to any mechanical paasitic signal, and can exhibit high absolute sensitivity. Finally, a multi-stips senso compatible with the spinning-cuent technique is poposed as a solution to get high esolution Hall effect magnetometes. Conventional hoizontal Hall effect sensos.1 Hall effect The Hall effect is due to the Loentz foce that acts on the moving caies inside a conducting mateial as shown in Figue 1. When a cuent I is flowing thu a conducting element, in ou example a N-type semiconducto, electons ae moving in the opposite diection: I = Wt qnv (1) whee W and t ae the width and the thickness of the conducting element, q C the elemental chage, n the electons density, and v the speed of the electons. If such a stuctue is subjected to a magnetic field B, the tajectoies of the electons ae modified by the Loentz foce F L = q v B. Electic chages ae thus accumulated on the sides of the conducting element so that a tansvesal electic field E establishes. Finally, an equilibium is eached when both electic (F E = q E) and Loentz foces countebalance each othes: qv B = q E. () In the paticula case of ou example, i.e. when the cuent is flowing along the x diection (Fig. 1), the pevious equation is equivalent to: E y = v x B z E z = v x B y. (3) Consequently, voltages popotional to the y and z components of the magnetic field appeas between the lateal sides of the conducting element (Fig. 1): V y = v x B z W V z = v x B y t. (4) By inseting equation (1) into the pevious fomulae, one finally obtain the following equations: V y = I x qnt B z V z = I x qnw B y (5) whee V y and V z ae the so called Hall voltages. The equipotentials inside the senso ae thus tilted when a magnetic field is applied (Fig. ). Nevetheless, these fomulae ae exact only if all the electons ae moving at the same speed, which is not the case in semi-conductos. In ode to take the distibution of speeds into account, the concept of scatteing facto is used [17,1]: V y = I x qnt B z V z = I x qnw B y. (6) The value of the scatteing facto is geneally close to 1 and depends on the senso mateial as well as on the type of the caies (electons o holes).. Integated hoizontal Hall plates When the component of the magnetic field pependicula to the chip plane has to be measued, hoizontal Hall effect sensos ae geneally used. These sensos may have

3 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 51 L P Substate Poly silicon t ox z t t well Silicon oxide N ++ Depleted zone y x Biasing contacts N well Fig. 3. Integated ectangula Hall effect senso. The senso is ealized thanks to a N well on a P-type substate. The biasing and sensing contacts ae ealized with highly doped ohmic contacts. A poly-silicon gate is added in ode to ceate a depleted zone just below the silicon oxide laye. y W vaious shapes but the two most commonly used ae the ectangle and the coss as shown in Figue. Such sensos can be vey easily integated by using the N well laye of a CMOS technology on a P-type substate, the contacts being ealized with N ++ ohmic contacts (Fig. 3). Howeve, whateve the shape of the senso is, its absolute sensitivity S B is given by the following fomula: S B = V H B z = G n qnt I (7) whee V H is the Hall voltage which can be measued between the two sensing contacts (Fig. ), B z is the component of the magnetic field pependicula to the chip plane, G 1 is a geomety dependent coection facto (moe details about this facto ae given in Sect..4), n is the scatteing facto of electons in silicon and I is the biasing cuent. The scatteing facto depends on the senso mateial and on the caies type ( n 1.15 fo electons in low-doped silicon), n is the effective doping level of the Nwellandt is its effective thickness. The facto G n qnt is thus a constant and equation (7) clealy shows that a Hall effect senso should be ideally biased thanks to a pefect cuent souce..3 Gated hoizontal Hall effect sensos Although the thickness t well (Fig. 4) of the N well depends on the chosen technology, the effective thickness t can be slightly educed by an electical mean. By adding a polysilicon gate ove the senso and biasing it popely, the egion just below the oxide can be depleted (Figs. 3, 4) so that the cuent is foced to flow in the buied pat of the N well. The thickness of the depleted egion (t dep ) depends on the diffeence of potentials between the buied pat of the N well (V well )andthesio /Si inteface (V S ): t dep (V G,V S )= ɛsi qn D (V well V S ) (8) whee ɛ Si is the silicon pemittivity, and N D is the dono density of the N well. The moe, the suface potential de- z x S Sensing contacts Fig. 4. Dimensions of a gated hoizontal Hall plate. pends on both gate (V G ) and N well potentials: ( V S (VG,V well )=VG V ) Φ V well VG V Φ V Φ = ɛ SiqN D Cox VG = V G V FB C ox = ɛ ox (9) t ox whee V FB is the flat-band voltage of the MOS stuctue, C ox is the capacitance pe squae mete of the silicon oxide laye, ɛ ox is its pemittivity and t ox is its thickness (Fig. 4). These elations ae only valid when the MOS stuctue is in the depletion egime, i.e. when V th VG V well 0, V th being the theshold voltage of the MOS stuctue: ( ) 4qND ɛ Si Φ f V th = Φ f + C ox Φ f = kt ( ) q ln ND (10) n i whee n i is the intinsic caie density of silicon. Indeed, when VG V well > 0 the MOS stuctue is in accumulation egime, i.e. electons ae accumulated at the SiO /Si inteface, and the effective caie density inside the N well (n) is thus lage than N D. Consequently, since the cuent elated sensitivity of a Hall effect senso is invesely popotional to n (Eq. (7)), one should pevent to bias the MOS stuctue in accumulation egime. When VG V well V th, an invesion laye (holes) is ceated just below the silicon oxide laye and the suface potential (V S )emainsmoe o less constant: V S (V G V th + V well,v well ) V S (V th + V well,v well ). (11) Consequently, when V G V well V th, the thickness of the depleted zone below the silicon oxide inceases vey slowly when the gate voltage is pulled down below V th + V well.finally, the effective thickness (t) of the buied pat of the

4 5 The Euopean Physical Jounal Applied Physics (Ω) invesion depletion accumulation Gate to N well voltage (V) Fig. 5. Input esistance of a ectangula (L =50µm, W = 0 µm) Hall effect senso integated in standad 0.6 µm CMOS technology as a function of its gate to N well voltage. Fo this measuement, the biasing voltage has been set to 10 mv. The solid line is the measued chaacteistic while the dashed line epesents the theoetical one. Cuent elated sensitivity (V/AT) L/W Fig. 6. Influence of the atio L on the cuent elated sensitivity of a ectangula Hall effect senso. The cicles ae val- W ues obtained fom finite elements simulations. The dotted line epesents the theoetical geometical coection facto given in (14). N well can be simply evaluated fom the pevious equations: t = t well t dep (V G,V well ) (1) whee t well is the thickness of the N well (Fig. 4). Since the input esistance (the esistance which can be measued between the biasing contacts of the senso) is invesely to 1 nt, this esistance ( in) is also popotional to the cuent elated sensitivity, S I, of the senso: in = L Wt 1 S I = SB I qnµ n = Gn qnt S I = W L G nµ n in (13) whee µ n is the mobility of electons. In ode to visualize the effect of the gate voltage on the cuent elated sensitivity of the senso, we thus measued its input esistance as a function of its gate to N well voltage thanks to a paametes analyze (Agilent 4156C). The Hall effect senso pototype was ectangula (L =50µm, W =0µm)andintegatedinastandad0.6 µm CMOS technology (t well 1.53 µm, n = N D m 3 ). The expeimental and the theoetical cuves ae shown in Figue 5 and clealy validate the pevious theoetical analysis. Compaed to a conventional integated hoizontal Hall plate with the same dimensions and integated in the same technology, such a gated Hall plate allows to incease the cuent elated sensitivity up to 35% (depending on the chosen technology and on the biasing conditions) which helps in educing the powe consumption []. In the following, all the sensos which will be pesented ae gated and ae ealized in the same standad 0.6 µm CMOS technology in which the atio n qnt is close to 10 V/AT when the gate is connected to the substate, i.e. when the gate to N well voltage equals.5v (moe details about the biasing conditions will be given late)..4 Geometical coection facto The sensitivity of an actual Hall effect senso is always smalle than the theoetical sensitivity given by (6). Indeed, some shot cicuit effects take place nea the biasing and sensing contacts: a pat of the cuent lines ae deflected nea the sensing contacts and the Hall voltage is stongly educed nea the highly doped (n lage) biasing contacts [17]. In ode to take these paasitic effects that educe the sensitivity of actual sensos into account, the concept of geometical coection facto is used as intoduced in equation (7). Many studies about the geometical coection have been done and the liteal expession of G is well known fo most of the commonly used shaped [3]. In the case of a ectangula Hall effect senso, the geometical coection facto is given by [1]: {[ 1 π exp ( )] ( π L G W f S ) W 0.74 L W f ( ) S W L W > 1.5 L W < 1 (14) whee L is the length of the Hall plate, i.e. the distance between the biasing contacts (Fig. 4). f ( ) S W is a function that is close to one when S, the size of the sensing contacts, is less than 0.18 W [1]. Equations (14) clealy demonstate that a good ectangula Hall plate should be longe than wide, i.e. L W should be lage (Fig. 6). On the othe hand, the lage the atio L W, the lage the input esistance is (Eq. (13)). Since the biasing cuent I is diectly limited by in ( in I V sup,wheev sup is the voltage povided by the powe supply of the system), in ode to maximize the sensitivity of the senso one should minimize its input esistance, i.e. one should minimize the atio L W. Howeve, the geometical coection facto depends linealy on L W when this atio is lowe than 1 (Eq. (14)), and thus one can estimate the maximum absolute sensitivity

5 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 53 F B 1 B 1 F S 1 S S 1 S B F B B 1 B 1 F a b a b S 1 S S 1 S Fig. 7. When a semiconducto is subjected to mechanical stess, its conductance changes and the mateial becomes anisotopic. c B d Fig. 8. A Hall effect senso can be modeled by a Wheatstone bidge. This bidge becomes unbalanced when the senso is subjected to shea stess. c B d of a ectangula Hall effect senso [17]: S B S Bmax G n qnt I max 0.74 n µ n V sup. (15) Finally, fo a good compomise between powe consumption and sensitivity, the aspect atio L W is geneally chosen lage than 1.5 and smalle than 3. Geneally speaking, the absolute sensitivity of a Hall effect senso is always limited by its input esistance. Nevetheless, it is possible to ovecome this limitation with a specific cicuit intended to bias a multi-stips Hall plate (Sect. 3) o a netwok of Hall plates (Sect. 4)..5 Offset and mechanical sensitivity In ode to undestand the elevance of a coss-shaped Hall effect senso, one must notice that a silicon fou teminal device is also a good shea stess senso [1,4,5]. Indeed, when a silicon cystal is subjected to mechanical stess, the distance between cystallogaphic planes is modified. Since the way electons ae moving inside a cystal diectly depends on its elemental mesh size, the mateial conductance is modified when a stess is applied: in the case of a N-type silicon cystal, when the distance between cystallogaphic planes is educed, the esistance inceases and convesely (Fig. 7). Futhemoe, fom an electical point of view, a Hall effect senso can be consideed as a Wheatstone bidge as shown in Figue 8. Such a bidge model allows to undestand the effect of mechanical stess on the behavio of the senso. If a stess is applied along one of the main cystallogaphic axes (nomal stess), all the esistances ae identically modified and the bidge emains symmetical. On the othe hand, if the senso is subjected to shea stess, the vetical and hoizontal symmeties ae lost: the distances S1-B1 and S-B ae educed (o inceased) while the distances S1-B and S-B1 ae inceased (espectively educed) (Fig. 8). The bidge is thus no longe symmetical and a diffeential voltage V M popotional to the shea stess σ is added to the Hall voltage V H : ( )( ) 0 σ Ix V M = V bias K M u () σ 0 I y whee u is a vecto pointing fom the negative sensing contact (S1) tothepositiveone(s), K M is a constant which depends on the mateial, and V bias is the biasing voltage applied between contacts B1 and B. Eveniftheoffset may come fom masks misalignments o doping gadient inside the senso, the stess induced voltage is the main souce of offset in Hall plate. Indeed, because of packaging, integated systems ae geneally subjected to lage shea stess which cannot be emoved. Since the shea stess induced voltage is due to the changes in the conductance of the semiconducto mateial, the sign of the mechanical sensitivity S M = VM σ depends on the oientation of the senso elative to the cystallogaphic planes as it can be seen in Figue 8. On the contay the magnetic sensitivity does not depends at all on the oientation of the senso. As a consequence, when the senso is otated by π ad, the sign of V M is inveted while the sign of V H emains constant [6]. Since the oles of the biasing and sensing contacts of a coss-shaped senso can be inveted, this paticula shape allows to take advantage of these popeties to emove the paasitic mechanical signal. One just needs to measue the magnetic field in two steps: fist the biasing cuent flows vetically and the total voltage V T is measued hoizontally, and in the second step, the cuent flows hoizontally and the voltage is measued vetically as shown in Figue 9 [7]. By simply summing o aveaging the two esulting

6 54 The Euopean Physical Jounal Applied Physics B V T I V T I + V ef V H V out Step 1 Step Fig. 9. The spinning cuent technique: the oles of the biasing and sensing contacts ae peiodically inveted and the measuement is pefomed in two steps. The colos have the same meaning than in Figue. The magnitude of the magnetic field equals 3 T. Fig. 10. Simple biasing cicuit suitable fo a conventional Hall effect senso. The output voltage V out is equal to V ef + V H. I voltages, one can thus emove the paasitic mechanical signal: { V T1 = V H + V M V T = V H V M V DD V T 1 + V T = V H. (17) I bias Vout Sinceinpacticaldesign,step1andstepaepeiodically eiteated (the so called spinning cuent technique), this method is vey efficient to emove quasi-static mechanical signal such as packaging stess but may fail when altenative mechanical signals have to be emoved. Indeed, when the oles of the biasing and sensing contacts ae peiodically inveted, the mechanical signal becomes the modulating signal of a squae caie. Consequently, when the senso is subjected to vibations which fequencies ae close to the spinning fequency, a paasitic signal aises in the base band. One should also note that since flicke noise in Hall plates is due to conductance andom fluctuations inside the device, the spinning cuent technique is also vey efficient to emove the 1/f component of the total output noise of the senso [1,7]..6 Biasing cicuits.6.1 Basic biasing cicuit In ode to make use of a Hall effect senso, as it has been suggested in Section., it should be biased by a pefect cuent souce. A cicuit simila to the one pesented in Figue 10 is thus geneally used. The cuent souce is used to set the biasing cuent of the senso while the opeational amplifie maintains the potential of the left sensing contact to a efeence potential V ef.consequently the potential (V out ) of the ight sensing contact is equal to V ef + V H and can be easily pocessed (amplification, filteing, analogto digital convesion,...). The moe,when symmetical powe supply is used, V ef is geneally chosen equal to 0 so that V out = V H. Fig. 11. Integated biasing cicuit suitable fo Hall effect sensos. The Hall effect senso is inseted inside the output stage of an opeational tansconductance amplifie..6. CMOS biasing cicuit V SS When the cicuit shown in Figue 10 is integated thanks to a standad technology such as CMOS o Bi-CMOS technologies, one has the oppotunity to optimize the biasing amplifie to fit all equiements in tems of accuacy, noise level, powe consumption,... The inne stuctue of the amplifie can also be adapted to this specific application. In ode to educe the powe consumption of an integated magnetomete, we poposed to inset the senso inside the output stage of an opeational tansconductance amplifie (Fig. 11). In such a cicuit, the biasing cuent of the output stage is used to bias the senso at the same time []. The PMOS tansisto of the output stage behaves as a cuent souce with high output esistance, and thus set the biasing cuent of the senso. The NMOS tansisto of this stage is contolled by the output voltage of the diffeential stage and its dain-to-souce cuent is thus automatically adjusted in ode to sink this biasing cuent and to maintain the left sensing contact of the Hall effect device to the gound potential (o any othe voltage efeence). Since the input efeed noise of the biasing amplifie is diectly added to the intinsic noise of the senso, the diffeential stage must essentially be optimized in tems of noise. In paticula, when low fequency fields has to be

7 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 55 Clk V DD Clk Clk Clk Clk V DD I bias V SS I bias Fig. 13. Low noise high speed input diffeential stage fo the biasing amplifie. V SS Fig. 1. Biasing cicuit suitable fo the spinning cuent technique. measued, the 1/f component of the total input efeed noise must be minimized. Moe details about the design of such a font-end cicuit can be found in efeence []..6.3 The spinning-cuent technique AsdiscussedinSection.5,inodetoemovethe1/f noise of the senso and to educe its offset, the spinning cuent technique is geneally used when low-fequency fields have to be measued. The integated cicuit descibed in the pevious subsection (Fig. 11) can be slightly modified to be adapted to the spinning cuent technique. The stuctue of this cicuit is shown in Figue 1. Two diffeential pais (one made of PMOS tansistos and one made of NMOS tansistos) ae inseted between each tansisto of the output stage and the coss-shaped Hall effect senso. These diffeential pais ae diven by two complementay clock signals so that the biasing cuent of the output stage is altenatively injected hoizontally o vetically in the senso. Moeove, the inveting input of the biasing amplifie as well as the output of the cicuit ae connected to the adequate contacts thanks to fou T- gates (one PMOS and one NMOS in paallel) diven by the same complementayclock signals than the diffeential pais. Synchonous sampling (switched capacitos cicuit) o simple analog low-pass filteing can thus be used to emove the mechanical signal which is shifted aound the spinning fequency, the magnetic signal (the Hall voltage) being in the base-band. V out To ensue the stability of the system between clock edges, the gain bandwidth poduct of such a biasing amplifie must be lage than the clock fequency. Howeve, since the input diffeential stage is designed so that its flicke noise level is low, the aeas of the tansistos ae geneally lage and consequently thei gate capacitances ae also lage 1. In paticula, the gate capacitances of the tansistos in the cuent mio of the input diffeential stage ae esponsible fo the pesence of a vey low fequency pole in the tansfe function of the amplifie. The gain bandwidth poduct of such an amplifie is thus necessay small and, consequently, the maximum clock fequency is vey low (few khz). In ode to ovecome this limitation, the input stage of the cicuit in Figue 1 has been slightly modified: a diffeential stage made only of PMOS tansistos is added befoe the conventional diffeential stage with a NMOS cuent mio as active load (Fig. 13). This fist pe-amplifying stage adds a small gain ( 30), but since a PMOS tansisto is less noisy (in tems of flicke noise) than a NMOS tansisto of the same dimensions, the equied aeas of the PMOS loads, and thus thei gate capacitances, ae smalle than the aeas that would be needed in the case of a NMOS cuent mio to each the expected noise level. The moe the PMOS loads ae connected as diodes and thus pesent high conductances: the bandwidth of this stage is consequently quite high compaed to the needed gain bandwidth poduct of the whole amplifie. Finally, since the signal is peamplified by this fist diffeential stage, the constaints on the noise level of the second diffeential stage ae elaxed. Consequently, the aeas of the NMOS tansistos can be stongly educed, and thus, the bandwidth of the amplifie can be inceased in the same popotions..7 Expeimental esults A magnetomete using a coss shaped Hall effect senso simila to the one of Figue 1 with the input diffeential 1 The flicke noise powe spectal density of a MOS tansisto is invesely popotional to the aea of its channel.

8 56 The Euopean Physical Jounal Applied Physics Lage stess small stess clk= Output voltage (V) aveage spinning cuent 0.6 clk= 1 Clock Fig. 14. Output signal of the spinning cuent magnetomete. In ode to visualize the effect of the diection of the biasing cuent on the mechanical sensitivity, the clock fequency is chosen small (110 Hz) compaed to the cut-off fequency ( 1 db at 1 khz) of the low-pass output filte. stage of Figue 13 has been designed. The biasing cuent of the senso was set to 1 ma and its dimensions ae the following: the distance between opposite contacts is 50 µm and the width of each contact is 0 µm. The output signal obtained with this magnetomete was pe-amplified ( 100) and filteed thanks to a fouth ode low-pass filte ( 1 db at 1 khz) implemented on a Pinted Cicuit Boad (PCB). Fist of all, to visualize the effect of the diection of the biasing cuent on the mechanical sensitivity, we used a vey slow clock signal (110 Hz), well below the cut-off fequency of the low-pass filte, in ode to switch the biasing cuent in the senso. We wee thus able to monito the peiodic change of the sign of the mechanical sensitivity. Duing this expeiment, the stess was simply applied manually on the PCB. As expected, we obseved a squae wave modulated by the applied stess (Fig. 14). The moe, its aveage value emains constant whateve the stength of the stess is. Secondly, we measued the magnetic esponse of the senso with the clock maintained to its high level (clk = 1 in Fig. 15) and to its low level (clk = 0 ). In the fist case the cuent flows hoizontally (see Fig. 1) while it flows vetically when clk = 0. Consequently, because of the shea stess to which the senso is subjected (package stess + extenal stess), opposite offsets ae obseved. As explained in Section.5, the stess induced offset can be emoved by aveaging these two esponses as shown in Figue 15. Finally, duing a thid expeiment we applied a squae wave on the clock input of ou magnetomete. The fequency of the clock signal (100 khz) was chosen high compaed to the cut-off fequency of the low-pass filte ( 1 db at 1 khz)so that the aveaging pocess is pefomed by the filte. The esponse obtained duing this last expeiment (solid line in Fig. 15) is vey close to the calculated aveage esponse. Output voltage (V) B (mt) aveage spinning cuent B (mt) Fig. 15. esponses of the spinning cuent magnetomete. 3 Multi-stips Hall effect senso 3.1 n-stips Hall device As explained in Section.4, whateve the shape of the Hall plate is, ectangula o coss shape (a coss can be seen as two ectangles pependiculaly laid out), in ode to maximize the geometical coection facto G thedevicelength L should be lage than its width W.AatioL/W close to3isnecessaytohaveg 1. By using such a atio, the input esistance in is necessay high (Eq. (13)) which limits the biasing cuent I to I max = V sup / in whee V sup is the supply voltage. Since the supply voltage is geneally limited to some volts, the absolute sensitivity of integated Hall devices is thus geneally small. Fo a typical 5 V 0.6 µm CMOS technology with a N well squae esistance of oughly 1 kω and a cuent-elative sensitivity of 10 V/AT, the input esistance is close to 3 kω and the maximal cuent is limited to 1.5 ma.these data lead to an absolute sensitivity of only 180 mv/t. The only way to incease this sensitivity is to decease in by educing the length of the device while keeping G close to one. The biasing cuent can thus be inceased, so the absolute

9 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 57 B1a B1b B1c B1d l V DD M p1 M p M p3 M p4 S S1 S L v out Ba Bb Bc Bd I bias w W Fig.. 4-stips Hall device. V SS M n1 M n M n3 M n4 Fig. 18. Multi-stips Hall device biasing cicuit. B1a B1b B1c B1d of the multi-stips senso is thus given by the geometical coection facto exhibited by one elemental stip. Looking at Figue, equation (14) can be adapted fo the new multi-stips device as: G new [ 1 π exp ( π )] l + L. (18) w S1 Ba Bb Bc Bd S This equation is valid fo (l + L)/w > 1.5 ands/w < 0.18, which is geneally the case even when using the minimum size ules of the technology. The aveage input esistance of a n-stips Hall device is now given by: ( 1 l new n w + L W + 1 ) ( l L = n w W + ) l. n w (19) Since W n w, new is ove-valued by: Fig. 17. Multi-stips Hall device biasing pinciple. sensitivity. The small value of G in a shot Hall device (L <W) is due to the wide highly doped biasing contacts whee the Hall effect is stongly educed (the so called shot-cicuit effect). To minimize this shot-cicuit effect, we simply split the wide contacts into elemental ones as shown in Figue, leading to the multi-stips Hall device. The idea is based on a pinciple fist poposed by Popović fo magnetic field effect tansisto (MagFET) [8]. In ode to let the Hall voltage to establish, each elemental biasing contact (B1a-d and Ba-d in Fig. ) has to be totally independent fom the othes. This is possible if the new n-stips device is supplied thanks to two anks of n matched and independent cuent souces as shown in Figue 17. The output impedances of these cuent souces being high, the multi-stips device behaves as if it wee infinitely long while it is kept shot. Such a biasing method also ensues an homogeneous cuent density inside the whole Hall plate. Since a multi-stips device can be seen as the meging of minimum size ectangula Hall devices, the biasing contacts B1a-d and Ba-d (Fig. ) of these elemental ectangula devices ae esponsible fo a esidual shot-cicuit effect. The geometical coection facto 1 l + L new n w. (0) As a consequence, the aveage input esistance of a n-stips Hall device is about n times smalle than the input esistance of a ectangula device with the same geometical coection facto. The maximal biasing cuent as well as the maximal absolute sensitivity ae thus n times geate than fo a conventional ectangula device. 3. Specific biasing cicuit The basic cicuit in Figue 11 can be adapted as pesented in Figue 18 in ode to implement the biasing pinciple shown in Figue 17. A set of n independent and matched output stages is substituted fo the single output stage of the cicuit in Figue 11. Since all tansistos ae maintained into satuation, they behave as cuent souces. The voltage of each small biasing contact of the multi-stips device can thus establish feely, allowing the elemental Hall voltages v h acoss the stips to add up. If we assume an infinite output esistance fo tansistos M n1 to M n4 and M p1 to M p4, the voltage at the output of the cicuit in Figue 18 is clealy given by (see Fig. 19): v (= ) out =4 v h. (1)

10 58 The Euopean Physical Jounal Applied Physics Vitual gound v h V DD M p1 M p M p3 M p4 v h v h M n1 M n M n3 M n4 V SS v h Fig. 19. Output stage of a 4-stips Hall device biasing cicuit. Each stip is modeled by a Wheatstone bidge. v h v h v h v out v h Nevetheless, in actual cicuits, tansistos exhibit a finite output esistance which acts as a esistive load, loweing the effective output voltage. To evaluate this esistive effect, let us conside the small signal equivalent cicuit of the output stage in Figue 19. This equivalent cicuit is pesented in Figue 0 whee is the output esistance of the matched tansistos M n1 to M n4 and M p1 to M p4, and is the nominal esistance of the Wheatstone bidge which models one stip. Using a sta-to-tiangle tansfomation followed by a tiangle-to-sta tansfomation, o simply by consideing the symmety of the Wheatstone bidge connected to the two output esistances of its biasing tansistos, this equivalent cicuit is easily tansfomed to the cicuit in Figue 1. Witing the Kichhoff s cuent law fo nodes 1,, 3 and 4,wegetthefol- lowing set of equations: v1 v+v h v v 1 v h + v v3+v h v 3 3 v v h + v3 v4+v h 4 = v1 / = v / = v3 / v 4 v = v4 /. The solution of this equations set gives fo v 1 and v 4 : 3+ / v 1 = v 4 = +8 / +4 (/) v h. Thus, the effective output voltage of the cicuit in Figue 18 is: v h v h v h v h v h v out = v h + v 4 v 1 = 4+6 / + (/) 1+4 / + (/) v h. () Vitual gound (high impedance node) Output (high impedance node) Fig. 0. Small signal equivalent cicuit of a 4-stips Hall device biased with the cicuit of Figue 18. v h v h 1 v 1 v 1 v h v h v h v h v h v v v out v out v h v h 3 v 3 v 3 v h v h 4 Fig. 1. Simplified equivalent cicuits of the small signal cicuit shown in Figue 0. v 4 v 4 v h As expected, fo / 0, i.e. fo an infinite output esistance of the cuent souces which bias the multi-stips device, equation () educes to equation (1). On the contay, when is small, i.e. /,thenv out v h and the multi-stips device behaves like a single stip Hall plate. A deep analysis of the cicuit in Figue 18, which can be used to bias a cascade of any kind of Wheatstone bidges, shows that the effective output voltage fo a n-stips Hall device biased with such a cicuit is given by [9]: v (n) out = q +1 ( n ) q 1 tanh ln(q) v h (3) whee: q =1+ + ( ) +. (4) Since q>1and lim [tanh(x)] = 1 fo x, v out eaches a limit fo n given by: S ( ) = q +1 q 1 v h. (5) As a consequence, fo a given atio of the nominal Hall device esistance to the output esistance of the biasing tansistos, the numbe of efficient stips is limited (see Fig. ). The lage the atio /, the lage the numbe of efficient stips can be. In actual design, using single satuated tansistos as cuent souces allows to easily have n = 10 stips (see Sect. 4.), while this numbe of stips can be inceased when moe complex high-outputesistance cuent souces, like cascode souces [30], ae used. 3.3 Choppe stabilized biasing cicuit Thanks to the gain of the diffeential input stage, the noise due to the output stage is geneally neglected in a twostage amplifie like the one in Figue 11 [31]. Nevetheless, in the cicuit of Figue 18, a penicious coupling effect aises between the n stips leading to the main noise

11 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 59 v out/vh (n) : fom equation (3.) : / =0.001 : / =0.01 : / =0.1 Vitual gound (a) 9 7 i 3 4 v out = 3 3 v out V DD n: numbe of bidges Fig.. Nomalized sensitivity v (n) out/v h vesus n. Vitual gound v out M p1 M p M p3 M p4 v out = vitual gound. 4 (b) Fig. 4. Noise cuent though the 4-stips Hall device. v odiff V SS i i M n1 M n M n3 M n4 Fig. 3. Noise due to the output stages. component of the system, especially at low-fequency. In ode to undestand this phenomenon, let us assume that only one tansisto, fo example M p3 in Figue 19 exhibits noise. The cicuit of Figue 19 is epeated fo convenience in Figue 3 without the Hall voltage souces which ae of no concen fo noise calculation. The noise poduced by M p3 is epesented by the noise cuent souce.inode to maintain the vitual gound on the fed-back node of the n-stips Hall device, the diffeential stage (not shown in Fig. 3) adjusts its output, v odiff, so that the noise cuent is sunk though M n1, M n, M n3,andm n4.asa consequence, each of the fou NMOS tansistos sinks a quate of leading to a cuent flowing between two consecutive stips as indicated in Figue 3. Applying the Kichhoff s laws fo each stip and summing the esulting voltage dops acoss the bidges, as shown in Figue 4a, the noise voltage due to can be calculated as: v out = + 3i ( 3 + 9i3 7i ) 3 v out = (6) which, in tems of powe spectal density (psd), eads: v out = 1 4 i 3 (7) whee i 3 is the psd of the noise cuent geneated by M p3. Using the same appoach fo each tansisto which biases the n-stips Hall device, and summing the esulting powe spectal densities, we find fo the noise coming fom these tansistos: v out = 1 4 ( i n + i p + i n3 + i p3 ) ( i n1 + i p1 + i n4 + i p4 ) (8) whee i nj and i pj ae the noise cuent psd geneated by tansistos M nj and M pj which bias the jth stip. Since all the NMOS tansistos (espectively the PMOS tansistos) have the same dimensions and ae in the same biasing conditions, they exhibit the same cuent noise, i n (espectively i p), and the pevious equation can be ewitten: ( 1 vout = ) ( ) i 4 n + i p. (9) Finally, this equation can be genealized fo a cicuit dedicated to the biasing of a n-stips Hall device [3]: vout = n3 n ( ) i 1 n + i p (30) whee i n and i p include themal and 1/f noise components. We also have to mention that equation (30) gives a pessimistic noise level because we have neglected the finite output esistance of the tansisto fo noise calculation. Actually, the noise voltage dops due to the noise cuents flowing between the stips ae educed by the esistive load effect as fo the useful Hall signal. One must

12 60 The Euopean Physical Jounal Applied Physics also note fom equation (30) that, as expected, when thee is only one stip (n = 1), i.e. in the case of a conventional Hall plate, the output stage does not contibute to the total output noise. Since the Hall voltage exhibited by one stip is popotional to its biasing cuent, the quiescent cuent of the biasing tansistos is geneally maximized, leading to a high 1/f noise component in the cuent noise psd i n and i p. The noise due to these tansistos being also popotional to n 3 (see Eq. (30)), it geneally pevails ove the noise coming fom the input diffeential stage and fom the Hall device, and eventually can annihilate the benefit of the inceased sensitivity the n-stips Hall device povides. Howeve, if the NMOS and PMOS biasing tansistos ae pemuted aound the middle point of the n-stips Hall device, the noise voltage they geneate is opposite (see Fig. 4b). As a consequence, switching the output stages of the cicuit in Figue 18 aound this point of symmety, at a fequency highe than the useful bandwidth of the magnetic signal to be measued, f u, allows to eject this excess noise to high fequencies. In fact, the switching fequency, f s, has to be highe than f u (Shannon theoem) and a simple low-pass filte can be used to suppess the 1/f noise which is ejected aound f s by the switching mechanism. This technique is nothing else but a choppe stabilization [33] applied to the output stage of the cicuit in Figue 18. It is woth to note that the chopping mechanism does not modify the themal noise coming fom the output stages [33] which emains given by equation (30). 3.4 Expeimental esults Two multi-stips Hall effect devices with thei biasing cicuits wee integated. The fist one, with 4 stips (W = 31.6, w =3.1, L =9.6, l =., and S =3.1 µm see Fig. ), was biased with the basic cicuit of Figue 18, without chopping stabilization. On the contay, the second one, which was dawn with 5 stips (W = 39, w =3, L =9,l =0., and S =3µm), was implemented with the choppe stabilized biasing cicuit and a 45-kHz oscillato which geneates the chopping contol signals. Note that the NMOS and PMOS tansistos which bias the middle stip do not contibute to noise and ae not switched. The switches wee designed using diffeential pais like fo the spinning-cuent cicuit pesented in Figue 1. Fo this fist vesion of ou choppe-stabilized biasing cicuit, we chose to use a smooth switching scheme (see Fig. 5) in ode to pevent any switching noise. The way it was implemented is explained elsewhee [3]. Duing the expeiment, the integated cicuits wee mounted on a PCB featuing a pe-amplifie and a fouth ode low-pass filte simila to the ones used fo the spinning cuent expeiment (see Sect..7). Figue 6 pesents the cuent elated esponses, i.e. the senso esponse divided by the biasing cuent, of both 4-stips and 5-stips Hall devices. The geat dispesion in the data points we measued with the 4-stips device is explained by the high 1/f noise level exhibited by the system and coming mainly fom the biasing tansistos as explained in the pevious section. The chopping stabilization clealy suppesses this noise as it V A V B Switching time V A V B Chopping contol signal T Time Fig. 5. Switching scheme used fo choppe stabilization. Duing the switching time, both switches tansmit cuent. HALL VOLTAGE (V/A) STIPS SENSO 5 STIPS SENSO MAGNETIC FIELD (mt) Fig. 6. esponses of the 4-stips and 5-stips Hall devices. The offset is emoved fo easy compaison. canbeobsevedontheesponseofthe5-stipsdevice whee the data emain aligned. The absolute sensitivities wee measued to be 119 mv/t and 195 mv/t fo the 4-stips and the 5-stips devices espectively. The biasing cuent being 0.97 ma and.07 ma, the cuent-elated sensitivities ae calculated to be 13 V/AT and 94 V/AT espectively. The diffeence between both cuent-elated sensitivities is explained by the smooth switching we used. Duing the switching time, which coesponds to 0% of the clock signal peiod, the stips of the device ae shotcicuited by the diffeential pais and the Hall effect is annihilated. Dividing 94 V/AT by the coection facto 0.8 leads to a cuent-elated sensitivity of 117 V/AT. It is also woth to note that the esistive load effect is highe fo the 5-stips Hall device than fo the 4-stips one. Thus the actual cuent-elated sensitivity is close to 10 V/AT as expected fo the used technology. Howeve, accoding to subsequent expeimental esults (see next section), using a deep-font-edge switching does not lead to significant switching noise at the output of the system. As a consequence, in ode to take full benefit of the multi-stips device, this smooth switching scheme should be avoided. These esults show that integated magnetometes based on the multi-stips device can exhibit high absolute sensitivities: one has to use a high numbe of stips with biasing cuent souces having a high output-esistance (by implementing cascode cuent souces fo example [30]). This is an impotant advantage since fo a given esolution of the magnetomete, this allows to elax the noise level of

13 J.-B. Kammee et al.: Hall sensos optimized with on-chip cicuity 61 V DD I b I b V M V H V out V M I bias V H Fig. 7. The elemental diffeential signals of ectangula Hall effect sensos can be added by simply connecting them by thei sensing contacts. I b is the biasing cuent, V H is the Hall voltage, and V M is the shea stess induced voltage. V SS Fig. 8. The same cicuit than the one designed fo the n-stips Hall effect senso can be used to bias the sensos netwok. Magnetic shield Pinted cicuit boad the pe-amplifie and the biasing amplifie. Futhemoe, the highe the numbe of stips is, the bette the esolution of the n-stips Hall device itself is [3]. Howeve, the multi-stips device exhibits a dawback we did not discuss yet. Each stip exhibits an offset, and these offsets add up each othes leading to high offset which pevents a staightfowad amplification of the signal. While smat cicuity can be used to solve the poblem, the next section poposes a simple solution esulting in a high-sensitivity low offset magnetomete. 4Sensosnetwok 4.1 Building the netwok As explained in Section.5, an integated Hall plate is also a good shea stess senso. We pointed out that the spinning cuent technique was vey efficient to emove this coss-sensitivity since the sign of the mechanical sensitivity (S M ) depends on the oientation of the senso: if the senso is otated by π ad, the sign of S M is inveted while the sign of the magnetic sensitivity emains constant. Howeve, the spinning cuent technique fails if the senso is subjected to vibations which fequencies ae close to the spinning fequency. In that case, the altenative mechanical signal is shifted in the base band and cannot be disciminated fom the useful magnetic signal. In ode to ovecome this poblem, we poposed to use a netwok made of an even numbe of othogonal ectangula Hall effect sensos [34]. Since such sensos geneate identical Hall voltages and opposite shea stess induced voltages when they ae in the same biasing conditions, one just needs to sum thei elemental contibutions to emove the paasitic mechanical signal. The simplest way to sum the elemental diffeential voltages of n Hall effect sensos consists in connecting them by thei sensing contacts as shown in Figue 7. By adding the contibutions of an even numbe of othogonal Hall sensos, one can thus obtain a signal popotional to the magnetic field and not petubed at all by mechanical stess. The moe, fom an Loudspeake Fig. 9. A loudspeake is used to geneate vibations. electical point of view, the esulting n-sensos netwok is vey simila to the n-stips Hall effect senso descibed in Section 3. Consequently, the same cicuit can be used to bias such a sensos netwok (Fig. 8). 4. Expeimental esults Thee micosystems have been designed. Two of them ae based on a Hall effect sensos netwok, the fist one being made of ten paallel sensos and the second one being made of ten othogonal sensos. The thid micosystem is based on the spinning cuent method and has been integated to make the compaison. All these thee micosystems wee tuned (thei biasing cuents wee adjusted) so that they have exactly the same magnetic sensitivities. In ode to geneate some vibations in a epoducible way, we used a loudspeake mechanically coupled to the pinted cicuit boad on which the integated cicuit is placed (Fig. 9). The moe, to pevent the magnetic field poduced by the moving coil of the loudspeake fom being seen by the magnetic sensos, we added a magnetic shield made of soft ion between the loudspeake and the pinted cicuit boad. Nevetheless, since we made a hole in this magnetic shield to place the alumina axle which links the moving coil to the pinted cicuit boad, the sensos may be subjected to a esidual magnetic field. The loudspeake was diven by an AC powe souce and the fequency was tuned to the mechanical esonance (800 Hz)

14 6 The Euopean Physical Jounal Applied Physics 70 Loudspeake voltage 60 paallel netwok Output signal Loudspeake voltage Nomalized signal (db) shifted flicke noise othogonal netwok Output signal 0 Sensos netwok Fequency (Hz) x Loudspeake voltage Output signal spinning cuent Fig. 30. Expeimental esults: output signals. Nomalized signal (db) mechanical signal in ode to geneate mechanical vibations of a lage amplitude. Since all the micosystems use a dynamic biasing technique (clock fequency is 100 khz), a foth ode Buttewoth low-pass filte ( 1 1 khz) has been used to get the useful magnetic signal which is in the base band. The esults ae pesented in Figue 30. As one can see, the fist micosystem is vey sensitive to vibations. Indeed, since all the sensos of the netwok ae paallel this fist micosystem just sums ten times the same signal. On the contay, the second micosystem which uses an othogonal netwok is quite less sensitive to mechanical stess. Howeve, thee is a esidual signal which is also measued with the thid micosystem based on the spinning cuent technique. This fact seems to indicate that this esidual signal coesponds to the pat of the magnetic field poduced by the moving coils which is not canalized by the magnetic shield. The moe, one can notice that the phase of the signal obseved in the case of an othogonal netwok and in the case of the spinning cuent is diffeent than the phase obseved in the case of the paallel netwok. Subsequently, we made a second expeiment in which the alumina axle was emoved. The mechanical coupling between the loudspeake and the pinted cicuit boad was thus suppessed. Duing this expeiment, we obseved the same esponses with the thee integated magnetometes. This poves that the esidual signals obseved with the othogonal netwok and with the spinning cuent come fom the leakage though the magnetic shield. Unfotunately, because of this esidual magnetic field we wee not able to quantify the ejection of the mechanical signal. Howeve, by manually applying static stess on the pinted cicuit boad we wee not able to obseve any output voltage fluctuation neithe with the othogonal netwok no with the spinning cuent based magnetomete. 0 Spinning cuent Fequency (Hz) x 10 5 Fig. 31. Expeimental esults: spectums aound the clock fequency. The spectums ae nomalized with espect to the themal noise level. Finally, we made a thid expeiment in which the lowpass filte was emoved. The 100 khz chopping/spinning caie was thus kept in the output signal. We then analyzed the spectum of the signal aound the clock fequency in the case of an othogonal netwok and in the case of the spinning cuent based micosystem. As it is clealy shown in Figue 31, the spinning cuent technique ejects the mechanical signal (800 Hz and its hamonics) aound the spinning fequency. On the contay, in the case of the Hall effect sensos netwok the mechanical signal is totally emoved but the flicke noise of the output stages is ejected aound the chopping fequency [3]. Since the cone fequency of a tansisto can be evaluated by simulation, one can ensue that all the flicke noise of output stages will be shifted outside of the useful bandwidth by choosing a sufficiently high chopping fequency. On the contay, in the case of the spinning cuent technique one cannot foecast the fequency of the mechanical excitation which may petub the magnetomete. If a mechanical signal of fequency in the ange [f clk f lp ; f clk +f lp ](f clk is the clock fequency and f lp the cutoff fequency of the low-pass filte) is applied to such a magnetomete, thee will be a paasitic signal in the base band which will be indiscenible fom the magnetic signal.