A low-offset spinning-current hall plate

Sensors and Actuators, AZI-AU

(1990) 743-W

A Low-offset Sphning~ment

743

Hall Plate

P J A MUNTER Electronic Instrmentairon Laboratory, Department of Eleetncal lihgmeermg, Delft Vnwersrty of Technology, P 0 Box 5031. MO GA DelJ (The Netherlad)

Abstract

An offset-reduction method for Hall plates has been developed which rmmrmzes the mfluence of the stress and the temperature on the offset The new method uses only one single symmetrical Hall plate in wbch the &rectlon of the current is made to spm by contact commutation Hrlth steps of x/6 raQans or smaller The consecutive Hall voltages are averaged over time and the offset cancels out The residual offset 1sabout a factor of 10 less than that spe@ied for commercially avadable silicon Hall plates and 1slmuted by mhomogenelhes m the plate Introdliction

A Hall plate IS a thm sheet of high-mohhty matenal, fitted wth four contacts The Hall effect generates m this plate a transverse Hall voltage proportronal to the bias current and the apphed magnetic field [ 1] However, the Hall plate ~11 exhrblt an unpredictable and unknown output voltage at zero magnetic fields as well, called the offset, when the Hall contacts are not on the same equlpotentlal hne due to, for example, geometrical errors The offset m Hall plates is of parhcular interest when static magnetic fields are measured, an apphcatlon where a snnple coil cannot be used MaJor apphcahons for low-offset Hall plates are m brushless electromotors and non-contact swtches Commercially avmlable Hall plates are hampered by an equivalent offset rangmg from 2 to 100 mT, chefly as a result of stress and geometrical errors [2-61 The offset voltage caused by stress and stram m the package can be rmmrmzed by makmg a proper choice of the crystallograpluc onentatlons of the current flow and of the plane of the chip [7,8], whde the packages themselves can be optmuzed to rmmnnze the stress [3] Sw&mg these Hall plates orthogonally tends to cancel out then asymmetnes, reducmg the offset as well as the thermal offset ft sigmficantly (Fig 1) [5,9] The ever-lmpro@g+i lectromc technology leads us to believe that the electromc Implementation of 092~4247/90/%3 50

FIN I Orthogonally swttched Hall pliitts Hall plates can be newed as a Wbeatstooe bridge The non-mproclty of the matched symmetrical Hall plates IS used to reduce the offset

orthogonally swtched Hall plates has become feasible In our method, a single multlelectrode symmetrical Hall plate is Dverugedover rune by contact commutauon m order to avoid dfferences between both the ‘matched’ plates However, it appears that orthogonal smtchmg 1s not stiaent to make the offset completely package (and thus stress) mdependent, so we need to switch the plate itself orthogonally more than once The spmnmg-current method and its advantages over orthogonal swMung w111be elucidated The mfluence of the crystal plane onentation and the symmetry of the plate reqmred to fully cancel the offset w111be Qscussed, followed by expenmental results on Hall plates Hrlth 16 contacts and the conclusions thereof

The Spinning-nt

Onset-redaction Metbod

The offset in Hall plates is a result of stress, geometrical errors, thermal effects and surface charges [ 1] Stress is one of the mam offset causes which results from the plezorenstivlty of s&on Geometrical errors are the result of mask mtsabgnment and etchmg randomness, and the temperature gra&ents m the plate result m thermovoltages and thermal bridge nnbalance The mlluence of the surface charges can easily be cancelled by using a buned Hall plate [5,6] A Hall plate can be ylewed as a Wheatstone bndge (Fig 1) [ 1,7] The orthogonal couphng offset-reduction method 1s based on the non-

0 Elsevler Sequola/Pnnted m The Netherlands

reclproaty of symmetrrcal Hall plates, 1 e , the bias and the Hall contacts are interchangeable The Hall voltage rotates with the current as it 1s made to spm and the offset does not Therefore, the offset can be cancelled out Calculations on the offset for the normal and the orthogonal current direction m the same Hall plate show that geometrical errors cancel out when both offsets are summed The offset caused by thermovoltages resulting from temperature gradients across the plate cancel out as well when the current 1s switched orthogonally However, orthogonal swtchmg 1s not sufficient to cancel out the stress influence as well and the offset still depends on the stress m the package The homogeneous stress m a Hall plate, wluch results from bending of the die, yields an offset as function of the direction of the current, rp, gven by PI V&e,(P) = @l(V) - %(cp)) cos(2(8 + cp)) x -G/(2&)

(1)

where nl(cp) and x,(p) are the longtudmal and transverse plezoreslstance coefficients, 8 1s the onentatlon of the stress wth respect to the diagonal m the Wheatstone bndge, X is the stress, &is the bias current, and R,, is the input resistance of the plate The piezoreststance coefficients as function of the current direction cp show a x/2 radians perlodlclty m (100) crystal plane onented wafers The stress 1s penodlc over II radians and the offset is, therefore, determined by the product of functions with a n/2 and x spatial penodlclty, a 2/n and l/n spatial frequency respecle, tively Consequently, the offset as function of the current drectlon shows spatial harmomcs of 3/a and l/n Shannon’s frequency sampling theorem states that any signal with a gven maximum frequency needs to be sampled at a rate of at least tmce tts maximum frequency This theorem can be amplemented by sampling the offset at a rate of 6/n, leading to a symmetrical Hall plate with 12 contacts m which the radial distance between the contacts 1s a/6 Another posablhty 1s a symmetncal Hall plate with 16 contacts with a shghtly higher sampling rate of s/8 (Fig 2) Both plates ~11 provide residual offsets which are independent of the (homogeneous) stress m the package Operation of the completed smart sensor will require multiplexers to change the current dlrectlon and an integrator to average out the offset signal (Fig 3) The spmnmg of the current leaves the sensltlvlty unchanged while the final offset VHall IS the average over time of the consecutive output signals V,, , when the current direction spins from 0 to II radians The offset contnbutlon

Fig 2 The splnmng-c-t Hall plate The current Lrect~on 1s made to spm m the symmetrical Hall plate by contact wmmutat~on unth steps given by the r&al dstance between the contacts, I e , n/8 Sunukaneously, the Hall voltage perpendlcular to each current directIon IS measured

Fig 3 The concept of the electromc unplementat~on of the spmnmg-current method Multiplexers commutate the has and the Hall contacts and the offsets V, , are averaged out over a full rotation pmod of the current

of the electronic clrcultry can be cancelled easily by subtracting the output signals of the reversed current dlrechons (I e , ICto 2n radians), usmg the same input stages as m the normal current dlrection (1 e , 0 to 71 ra&ans) It can be concluded that geomettrcal errors and Seebeck potentials cancel out when the Hall plate 1s swtched orthogonally The homogeneous stress can be cancelled out when the offset 1s sampled at a rate of at least 7c/6 radians

Results on Spinning+urrent

Hall Plates

The spmmng-current Hall plates were fabncated m a 10 pm thck epdayer m standard blpolar technology with a 330 pm plate radius and contacts of 10 x 10 pm2 Offset measurements on

the wafer show that the maximum offset m our samples IS below 4 mV, and it IS mainly caused by geometrical errors The Hall plates were diced and attached to an ahnnma substrate urlth Epotex H61 epoxy, increasing the offsets to rnaxlmally 50 mV These offsets result from strains of up to 50 x 10m6 Encapsulation does not increase the offset significantly, only the non-hneanty in the orthogonal offsets and residual offsets after averagmg mcreases The offset after encapsulation in our example of Fig 4(a) IS less thin 15 mV at 5 mA bias 16

-16 0

10 BIRS

(a)

30

40

CURRENT

20

(mfl)

50

‘a

-100 W

0

I

I

I

I

10

20

30

40

BIAS

CURRENT

1

50

CmFl)

FIN 4 (a) The offset (b) The orthogonal offsets and the residual offset (dashed hue) as a fun&on of the supply current for various current dIrectIons us a 16-contact Hall plate The current dxectlon IS Oven by the product of the ID&X at the curve and the radial distance between the contacts, I e .2n/16 The average of the offsets wltb Index 0 to 5 In (aj ccnktbtes the orthogonal offset with Index 0 m (b), etc The residual offset IS the average of all orthogonal offsets

current for any current direction One can see clearly that the orthogonal current du-echons yield approximately opposite offsets Every Hall plate ~11 have a dflerent due&on of the bias current leadmg to its maxunum offset, for the stress onentatlon and magmtude ~111be dflerent m each plate Note that the offset vanes proporuonally to the bias current, as 1s expected for offset resultmg from geometrical errors or stress (see eqn (1)) The offset IS reduced by approxnnately a factor of 100 by orthogonal surltchmg and the improvement IS even larger at small bias currents (Ag 4(b)) However, the bias current cannot be decreased unhmltedly because the sensitivity IS proportional to the bms current Only geometncal errors and thermovoltages cancel out when swtched orthogonally, the orthogonal offset itself remains stress-dependent The offset, after averagmg over SIXcurrent directions m a 12contact Hall plate, results in only a factor of two tmprovement with respect to the orthogonal offset This IS, m part, a result of the fimte contact dimensions and the geometrical errors which cause the sampling pomts not to be m exactly the position reqmred by the samphng theorem It IS, therefore, better to use a shghtly higher samphng rate of n/8 radians m a 16-contact Hall plate The offset, after averagmg over eight current dlrectlons, IS improved m thus case by about a factor of four Hrlth respect to the maxunum orthogonal offset Note that the orthogonal offsets and the residual offsets after averagmg were calculated with the aid of a computer and, therefore, do not contam any offset contrrbutlons such as rmght have been caused by the electronic c1rcultry The errors which remain are hkely to be the offset contnbutlons whch rotate Hrlth the current the Peltier effect and the mhomogeneitles resulting m a bndge imbalance and thermoelectnc potentials [ 1] The non-lmeatrty suggests that thermal effects are involved The influence of mhomogenatles on the offset IS probably determmed by the vanatlon m the local potential and the local temperature m the plate as the current spins The Peltier effect results m a temperature gradient across the plate m the direction of the bias current and this gradient IS also hkely to mduce thermal stress which rotates with the bias current as well Measurements made on the temperature profile of the plate by incorporated thermoplles show such a temperature gradient between the current contacts of up to 0 5 K at 5 mA bias current which vanes wth the due&on of the current Fmally, we observed that the thermal dnft was reduced as well as was expected m accordance with the theory [5,9]

746

conehlslolw

The offset in the spmmng-current Hall plate is smaller wth respect to the offset m orthogonally swtched Hall plates 250 PT (at 5 mA has current and 0 5 V/T sensitlvlty) compared to 2 mT (at 1 mA bias current and 0 25 V/T sensltlvlty) The crystallographx dependence of the plezoreslstance coefficients determmes the mmlmum number of contacts on the Hall plate requxed to cancel out the homogeneous stress The residual offset after averagmg IS probably lmuted by the mhomogeneltles m combmation wth the Peltier effect The ahhty to reduce the offset slgmficantly by spmnmg the current has been proven There are plans to implement the electromc arcultry in the near future

Acknowledgements The author would hke to thank the members of the IC-Ateher at Delft for makmg the clups

and especxally Jan Groeneweg, who spent a lot of time skdfully bondmg the numerous samples

1 H Weiss, Structure and Appltcatron of G&anomagner~c Devices, Pergamon, Oxford, 1969, pp 88-133 2 H P Bal&and R S Popovlc, I&grated semaxnductor magnetic field sensors, Proc IEEE, 74 (1986) 1107-1132 3 J Hausslez Trends and develomnents m Hall-effect m&rated cucmts, Eiecrron Eng, 51 (1$79)37-46 4 J T MauDmandM L Geske.TheHalletTectmshconcucmts. m C L &XI and C R We&ate (eds ), The Hall Effect a&

atsApphcatlons, Proc Commemoratuw Symp , Baltnnore, MD USA, 1979, Plenum, New York, 1980, pp 421-455 5 Improved Hall devxes find new uses, orthogonal couplmg yelds senslhve products unth reduced voltage offsets and low dr~fi, Efectron Weekly, (Apr 29) (1985) 59-61 6 R S Popovq Hall-effect devzes, Semors and Actuators, 17

(1989) 39-53 7 Y Kanda, A grapiucal representation of the p~ezores~stance coe&xnts m siluxm, IEEE Trans Electron Devnces,ED-19 (1982) 64-70 8 Y Kanda et al, Shcon Hall-e&t power ICs for brushless motors, IEEE Trans ElecrronDewes, ED-29( 1982) 15 1- 154 9 G S Randhawa, Monohtluc mtegrated Hall devxcs m ticon cucmts, Mzrcoelectron J , 12 (1981) 24-29