The Future of Magnetic Sensors

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E L S E V I E R Senso~ and Actuators A 56 (1996) 39--55A

The future o f m agnet ic sensorsR.S. P opovic, J.A . Flanagan, P.A . Besse

Sw iss Federal Institute o f Teclmology (EPFL). Institute of Microsystems. Lausann e. Switzerland

Abs t rac tThe operation o f magnetic-field sensors is based on m any different physical principles rang ing from induction to magneto-optical effects.

Th is in t u rn leads to a vast range o f poss ib le magnet ic sensor t ypes. Wh at w i l l f i na l l y dec ide the commerc ia l v ia b i l i t y o f a par t i cu la r magneti csensor i s i t s per fo rmance as we l l as i t s comp at ib i l i t y w i th m in ia tur i za t ion and m icroe lec t ron ic c i rcu i t s . The magnet ic sensors w i th t he mostpotent ia l for future ap pl icat ions includ e: H al l devices, magne toresistors, indu ct ive coi ls and fluxgates. The H al l device , w hi le v ery compat iblewi th m icroe lec t ron ics , su f fe rs f rom a l im i ted s ens i t i v i t y i n s i l i con , a h igh leve l o . I I f noise and a relat ively large of fset . Ferromagnet icmagnetores is to rs g enera l l y have a h igh s ens i t i v i t y at a low f ie ld ; assoc ia ted prob lems are the f l i pp ing e f fec t a r ' t hys teres is . I nduct i ve cmlsf ind m any app l i ca t ions in p ro x im i t y and d is tance sensors , bu t t he m in ia tur i za t ion o f co i l s i s d i f f i cu l t . The f l uxgate i s a h igh ly se ns i t i ve ,nagneti csensor. In pr in ciple , i t could be integrated, but the ma in challenges are the three-dimensional st ructure o f the coi ls and the low magne t icperm eab i l i t y o f i n tegra ted fe rromagneti c cores. The per fo rmance o f sensors can be cons iderab ly improve d by incorpora t ing them in to a systemand us ing syn erg is t i c re la t ionsh ips such as feedback and compensat ion . Th e fu ture o f magnet ic sensor m icrosystems looks br ig h t w i th m anypromis ing app l i ca t ion areas.geywords : Magnetic sensors; Miniaturization; Hall devices; Ma gnetoresistors; Proximity detectors; Inductive coils, Fluxgates; Sensor syste ms

1 . I n t r o d u c t i o nA magne t i c s ens o r i s a dev ice capab le o f s ens ing a mag-

ne t i c f i eld and ex t rac t ing in fo rma t ion f rom i t . In mos t p rac -t i c al app l i c a t ions , t he in fo rm a t ion i s r e l a t ed to the magne t i cinduc t ion a long an ax i s and i s t r ans duced by the s ens o r in toan e l ec t r i c a l s igna l . T he re fo re , a m agne t i c s en s o r i s a t r ans -duce r tha t conve r t s a magne t i c f i e ld in to a co r re s pond inge lec t r i c a l s igna l .

T he re i s a wea l th o f phys ica l p r inc ip le s us ed to rea l i z emag ne t i c s ens o rs. T hey inc lude : induc t ion , ga lvano mag nc t i ce f fec t s , nuc lea r p rece s s ion , s upe rconduc t ing quan tum in te r -fe rence , magne tos t r i c t ion and m agne to -op t i ca l e f fec t s [ 1 ,2 ] .In th is r ev iew we s ha l l cons id e r on ly mag ne t i c s ens o rs o f b igp rac t i c a l impor tance and thos e w i th the h igh po ten t i a l t o reachthis status.

Now adays , a s ens o r c an be p rac t i c a l ly impor tan t on ly i f itf e a tu re s a p r i c e -pe r fo rmance ra t io comparab le to tha t o fmic ro e lec t ron ic s c i rcu i t s {3 ] . Us ua l ly th i s c an be a ch ievedon ly i f a magn e t i c s ens o r i t s e l f i s s ma l l enoug h and com pa t -ib l e w i th m ic r~ lecU 'on ic s in t e rms o f ma te r i a l s , t e chno log ie sand ope ra t ing cond i t ions (e . g . , ope ra t ing t empe ra tu re s ) .On ly s o l id - s t a t e mag ne t i c s ens o rs ba s ed on ga lvanomag ne t i ce f fec t s , s uch a s H a l l dev ice s and m agne to re s i s to r s , and induc -t ive s ens o rs ba s ed on s ma l l co i l s , s uch a s f luxga te magne to -Elsevier Science S.A.P il S 0 9 2 4 - 4 2 4 7 ( 9 6 ) 0 1 2 8 5 - X

mete rs and induc t ive p rox imi ty s ens o rs , more o r l e s s fu l f i lt he s e requ i remen t s .In th i s pape r, we s ha l l concen t ra t e ou r a t t en t ion on the s e

mag ne t i c s enso rs . Our a im i s to iden t i fy the mos t im por tan tp rob lems , to po in t ou t s ome p romis ing idea s to s o lve thep rob lems , ind ica te t r ends in the deve lo pm en t , bu t a l s o to wa rnof pos s ib le dead ends .

A m agne t i c s ens o r i s r a re ly us ed a lone . Us ua l ly , i t i s com -b ined wi th o the r s ma l l - s i z e dev ice s in to a s o -ca l l ed mag ne t i cs e n s o r m i c r o s y st e m .

A magne t i c s ens o r mic ros ys tem i s a complex dev ice tha tt rans fo rms a m agne t i c s igna l in to an e l ec t r i c a l s igna l , p roc -e s s e s th i s s igna l, and t rans mi t s the re s u l t t o o the r e l ec t ron ics ys tems . T l le e s sen t i a l ope ra t ing com pone n t s o f s uch a mic ro -s ys tem a re a m agne t i c s ens o r , b i a sing , s igna l -p roces s ing andin te r face c i rcu i ts . In s ome ca s e s , t he mic ros y s tem ma y a l s oincorpora te fu r the r s pec i f i c componen t s , s uch a s magne t i cconcen t ra to rs , pe rm anen t magn e t s and co i l s . A l l t he s e com-ponen t s a re a s s em bled in a s u i t ab le pa~;kagc o f s ma l l d im en-s ions , i n the mi l l ime t re to c en t ime t re range .

T he magne t i c s igna l to be de tec :ed by a magne t i c s ens o rmic ros ys tem may be a s s oc ia t ed wi th an ex te rna l magne t i cf i eld . In th i s c a s e , t he mic ros ys tem w orks a s a s mar t mag ne t i cs ens o r . T yp ica l ly , s uch magne t i c s ens o r mic ros ys tems a reapp l i ed in magne tom e te rs , mag ne t i c compas s e s , cu r ren t s en -

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40 R.S. Popovic et ,zl. ~Sets , rs and Actuawrs A 56 (1996) 39-5.5

s o t s , m a g n e t i c r e a d o u t h e a d s a n d a s r o t o r o o s i l i o n s e n s o r s inb r ush l e s s m o ' ,o r s . A l t e r na t i ve l y , t he s igna l m ay s t em f r om anex t e r na l mo du l a t i on 0~" a mag ne t i c f i e ld ca r r i ed by t he s e nso rmi c r osys t em i t s e l f . The i n t e r na l magne t i c f i e l d i s c r ea t ed bya l oca l sou r ce , such a s a pe r manen t magne t o r a co i l . Them o d u l a t i o n o f t h e m a g n e t i c f i el d c o m e s a b o u t , f o r e x a m p l e ,b y v a r y i n g t h e d i s t a n c e b e t w e e n t h e s e n s o r m i c r o s y s t e m a n dan ex t e r na l f e r r omagne t i c ob j ec t . I n t h i s c a se , t he magne t i cs i g n a l i s u s e d j u s t a s a m e a n s t o m e a s u r e a n o n - m a g n e t i cq u a n t i t y . T y p i c a l a p p l i c a t i o n s o f s u c h s e n s o r m i c r o s y s t e m sa r e s e n s i n g o f p o s i t io n , p r o x i m i t y o f a n o b j e c t , l in e a ra n d a n g u l a r v e l o c i t y , p r e s s u r e ( t h r o u g h d e f l e c ti o n o f am e m b r a n e ) a n d s o o n. T h e m a g n e t i c i n d u c ti o n s e n c o u n t e r e di n t he se app l i ca t i ons a r e i n t he h i gh mi c r o - and mi l l i t e s l ar a n g e s . A r e v i e w o f m a g n e t i c s e n s o r a p p l i c a t io n s i s g i v e n ,f o r e x a m p l e , i n R e f . [ 4 ] .

T h e u l t im a t e g o a l i n t h e d e v e l o p m e n t o f a m i c r o s y s t e m i st o a c h i e v e a h i gh p e r f o r m a n c e - p r i c e r a ti o i n sp i t e o f t h e u s eo f m e d i o c r e c o m p o n e n t s . O u r a i m i n th i s p a p e r w i l l a l s o b et o i den t i f y some bas i c ways t ha t may l e ad t o t h i s end i n t hea r e a o f m a g n e t i c s e n s o r m i c r o s y s t e m s .

E a c h o f t h e f o l l o w i n g s e c t i o n s b e g i n s w i t h a v e r y b a s i ch d r o d u c t i o n t o o n e o f t h e a b o v e - m e n t i o n e d s u b j e c t s . T h e n ,' , c av i ng many de t a i l s a s i de , we sha l l concen t r a t e on a f ewi s s u e s fu n d a m e n t a l t o t h e f u tu r e d e v e l o p m e n t o f t h e m a g n e t i cs e n s o r i n q u e s t i o n .2 . H a l l d e v i c e s

H a l l d e v i c e s a r e b y f a r t h e m o s t w i d e l y u s e d m a g n e t i cs e n s o r s t o d a y . T o g e t h e r w i t h p h o t o d i o d c s , t h e y a r e a l s o p r o b -a b l y t h e m o s t w i d e l y u s e d s e n s o r s i n g e n e r a l. A s p h o t o d i o d e s ,H a i l d e v i c e s o w e t h e ir h i g h d e g r e e o f d e v e l o p m e n t t o a p e r -f e c t c o m p a t i b i l i t y w i t h m i c r o e l e c t r o n i c c i r c u i t s . N e v e r t h e -l e s s , Ha l l dev i ce s a r e no t i r r ep l aceab l e i n magne t i c s ens i ngapp l i ca t i ons . The i r f u t u r e depends i n pa r t i cu l a r on whe t he rmea ns w i l l be f ound i t) i nc r ea se t he i r s ens i t i v i t y and dec r ea seo f f s e t .

A Ha l l dev i ce i s a f ou r - t e r mi na l so l i d - s t a t e e l ec t r on i cd e v i c e , s i m i l a r t o th a t w i t h w h i c h H a l l d i s c o v e r e d h i s e f f e c t[ 5 ] . Usu a l l y , i t ha s t he f o r r a o f a p l a t e , so i t is a l so ca l l ed aH u l l p la t e . O t h e r t e r m s i n c o m m o n u s e f o r a H a l l d e v i c e a r e:Ha i l e l emen t , Ha l l gene r a t o r and Ha l l s enso r .

A n e x a m p l e o f a p l a te - l i k e H a l l d e v i c e i s s h o w n i n F ig . I .Th i s i s a t h i n p l a t e o f cond uc t i ng ma t e r i a l l ~ :t ed wi t h f ou re l ec t r i c a l con t ac t s a t i ts pe r i phe r y . A b i a s cu r r en t i s supp l i edt o t h e d e v i c e v i a t w o o f t h e c o n t a c t s , c a l le d t h e c u r r e n t c o n -t a c ts . T h e o t h e r t w o c o n t a c t s a r e p l a c e d a t t w o e q u i p o t e n ti a lp o i n t s o n t h e p l a t e b o u n d a r y . T h e s e c o n t a c t s a c e c a l l e d t h ev o l t a g e c o n t a c t s o r t h e s e n s e c o n t a c t s . I f a p e r p e n d i c u l a rmagne t i c f i e l d i s app l i ed t o t he dev i ce , a vo l t age appea r sb e t w e e n t h e s e n s e c o n t a c t s . T h i s v o l t a g e i s c a l l e d t h e H a l lv o l t a g e . T h e H a l l v ~ l t a g e c o m e s a b o u t a s a m a n i f e s t a ti o n o ft h e a c t io n o f t h e L o r e n t z f o r c eF = q E + q [ v B ] ( 1 )

on quas i - f r ee cha r ge ca r r i e r s i n t he p l a t e . He r e q deno t e s t hepa r t i c l e cha r ge , E i s the e l ec t r i c f i e l d tha t p r od uces t he cu r r en t ,v is the ca r r i e r ve l oc i t y and B i s t he magn e t i c i nd uc t i on .

The ca r r i e r ve l oc i t y v i n Eq . ( I ) i s due t o t he t he r ma lag i t a t i on and d r i f t . To a f i r s t app r ox i ma t i on , t he i n f l uence o ft he t he r ma l ag i t a t i on ma y be neg l ec t ed , and v in Eq . ( 1 ) c anbe cons i de r ed a s t he d r i f t ve l oc i t y o f t he ca r r i e r s . Fo r a g i vene l ec t r i c a l f i e ld , t he d r i f t ve l oc i t y o f t he c a r r i e r s i s p r opo r t i ona lt o t he i r mob i l i t y . A l so , f o r a g i ven b i a s cu r r en t , t he d r i f tve l oc i t y o f t he ca r r ie r s i s i nve r se l y p r o po r t i ona l t o t he ca r r i e rd e n s i t y an d th e p la t e t h i c k n e s s ( s e e E q s . ( 4 ) a n d ( 1 0 )b e l o w ) . T h e r e f o r e , w e c o n c l u d e t h a t t h e s t r e n g th o f th e H a l le f f ec t i s p r opo r t i ona l t o t he ca r r i e r mob i l i t y and i nve r se l yp r opor t i ona l t o t he p r oduc t o f t he p l a t e t h i cknes s and t hec a r r i e r c o n c e n t r a t i o n . C o n s e q u e n t l y , m o d e r n H a l l p l a t e s f o rm a g n e t i c s e n s o r a p p l i c a t io n s a r e u s u a l l y r e a l i z e d i n th e f o r mo f l o w - d o p e d s e m i c o n d u c t o r t h i n f il m s . T h i s f a c t m a k e s t h e mv e r y c o m p a t i b l e w i t h m i c r o e l e c t r o n i c c i r c u it s .

F i g . 2 s h o w s a s a n e x a n t p l e a H a l l d e v i c e r e a l i z e d a s a p a rto f t he n - l ype l aye r i n a s i l i con b i po l a r i n t eg r a t ed c i r cu i t p r oc -e s s . Th i s i s t he so - ca l l ed bu r i ed Ha l l dev i ce . I t ha s a s t r uc t u r e

i. /vFig. i. Hall device n the form of a rectangular plate. Mod ern Hall plates areusually of microscopic dimensions. For example, the thickness might be

t = l 0 / ~ m , the length ! ,-"2 0 0 / ~ r n and the width w = 1 0 0 / z m . A bias voltageV s applied to the plate via the two current contacts CC~ and CC,. The b iasvoltage creates an electric field E and forces a current I. if the plate isexpos ed to to a perpendicular magnetic i~duction B, the H all electric fieldgives rise to the appearance of the Hall vo ltage V~e betw een the two sensecontacts St and Sz (adap ted from [6] ).

Fig. 2. Buried Flail devic e realized using integrated circuit technology. N isthe n-type active legion, P- the substrate, P the deep -diffused isolationwalls, SP the shallow p-layer, DL the depletion ayer, CC the current contactsand SC the sense contacts. The dev ice senses he m agnetic field compon entperpendicular to the chip surface . The ins et illustrates the shielding e f f e c t o fthe shallow p-layer. In order to be effective, he shallow p-layer must not becompletely depleted (adapted from [6] ).

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R . S . P o p o v i c e t a l . /Sensors a n d A c m a t o r x A 5 6 f 1 9 9 6 ) 3 9 - 5 5 41

r e m in i s c e n t o f a p in c h c o l l e c to r - l a y e r r e s i s to r i n b ip o la r i n t e -g ra t e d c i r c u i t s . T h e s h a l lo w p - l a y e r p l a y s th e ro l e o f a n e l e c -t ro s t a t i c s h i e ld b e tw e e n th e s i l i c o n d io x id e in t e r fa c e a n d th ea c t iv e r e g io n o f th e H a l l d e v ic e . T h e s h ie ld in g g re a t lyi m p r o v e s t h e s t a bi l i ty o f t h e H a l l d e v i c e a n d r e d u c e s i t s I / fn o i s e . T h e in t e re s t e d r e a d e r c a n f in d o th e r b a s i c s a n d d e ta i l si n a m o n o g r a p h o n H a l l - e f f e ct d e v i c e s [ 6 ] .

T o b e u s e f u l a s a m a g n e t i c s e n s o r , a H a l l d e v i c e m u s tfe a tu re a s e t o f c h a ra c te r i s t i c s a d e q u a te fo r t h e in t e n d e d a p p l i -c a t i o n . W e s h a l l n o w d i s c u s s a f e w c h a r a c t e r i st i c s d e c i si v efo r th e a p p l i c a b i l i t y o f H a l l d e v ic e s .2.1. Sensitivity

T h e r e s p o n s i t i v it y o f t h e o u t p u t v o l t a g e o f a H a l l d e v i c e t oa ma g n e t i c f i e ld c a n b e c h a ra c te r i z e d b y th re e f ig u re s o f me r i t ,i . e. , a b s o lu te s e n s i t i v i ty S ^ , s u p p ly -c u r re n t - r e l a t e d s e n s i t i v i tyS , a n d s u p p l y - v o l t a g e - r e l a t e d s e n s i t i v i t y Sv.

T h e a b s o l u t e s e n s i t i v i ty S ^ i s d e f i n e d b y= I v " IS^ IBm_ 'H e re V H i s t h e H a l l v o l t a g e a n d B j_ is t h e n o rma l ( to th e

H a l l p l at e ) c o m p o n e n t o f t h e m a g n e t i c i n d u c t i o n .S u p p ly c u r re n t - r e l a t e d s e n s i t i v i ty ( in s h o r t : s e n s i t i v i ty S t )

i s d e f i n e d b yS , = ~ = l l V " I, V H = S tlB ~1 7 ~ - ~ - ( 3 )w h e r e i i s t h e s u p p ly (o r b i a s ) c u r re n t o f t h e H a l l d e v n c e . F o ra s t ro n g ly e x t r in s i c H a l l p l a t es,=c,-~ (4)q n tw h e re G d e n o te s t l ' . t~ g e o m e t r i c a l c o r r e c t i o n f a c t o r ( G < 1 ) ,rH i s t h e H a l l f a c to r ( r , > I ) , q i s t h e e l e me n ta ry c h a rg e , n i sth e c a r r i e r d e n s i ty a n d t i s t h e th i c k n e s s o f t h e p l a t e .

I n m o s t c u r r e n t l y u s e d H a l l m a g n e t i c s e n s o r s , o n e f i nd sth e v a lu e s o f t h e s e n s i t i v i ty S~ o f th e o rd e r o f 1 0 0 V A - ~ T - * .T o e s t i m a t e t h e i m p r o v e m e n t p o t e n t i a l , w e s h a ll n e 0v d e t e r -min e th e p ra c t i c a l l im i t fo r t h e in c re a s e o f S , a n d S . ,. W e s h a l ld o s o u s i n g a s i m p l i f i e d m o d e l o f t h e b r r i e d H a l l d e v i c es h o w n i n F i g . 2.

T h e s t ru c tu re o f t h e H a l l d e v i c e in F ig . 2 i s h mi l a r ; .o th a to f an N - c h a n n e l j u n c t i o n f i e l d -e f f e c t t r a n s is t u r ( J F E T ) : t h ea c t i v e N - r e g i o n c o r r e s p o n d s t o t h e c h a n n e l , o n e o f t h e c u r r en tc o n ta c t s (C C ) to th e s o u rc e , t b e o th e r c u r r , ;n t c o n ta c t t o th ed ra in , a n d th e p - ty p e r e g io n s u r ro u n d in g th e a c t iv e a - ty p er e g i o n t o t h e g a t e . S u p p o s e w e c o n n e c t t h e ~ ef t c u r r e n t c o n t a c ta n d th e p - ty p e ' g a t e ' t o a z e ro p o te n t i a l , a n d th e o th e r c u r re n tc o n ta c t t o a p o s i t iv e v o l t a g e V . T h e n th e c ro s s s e c t io n o f o u rH a l l d e v ic e lo o k s s c h e ma t i c a l ly a s in F ig . 3 . F ro m th e th e o ryo f J F E T s [ 7 ] w e k n o w t h a t t h e t h i ck n e s s o f t he ch a n n e l td e p e n d s o n th e d ~ s ta n ce f ro m th e s o u rc e . I f w e in c re a s e th ed e v ic e c u r re n t L th e v o l t a g e V w i l l a l s o in c re a s e , th e c h a n n e l

th i c k n e s s t w i l l fu r th e r d e c re a s e , a n d e v e n tu a l ly th e c h a n n e lw i l l p i n c h o f f a t t h e d r a i n . T h e d e v i c e c u r r e n t c a n n o t b ei n c r e a s ed a n y f u r t h e r . W e h a v e n o w r e a c h e d t h e c o n d i t i o n sfo r th e ma x ima l p o s s ib l e v a lu e o f th e a b s o lu te s e n s i t i v i ty S ^o f a g iv e n b u r i e d H a l l d e v ic e .

T h e s a tu ra t io n c u r re n t i s g iv e n b y [ 7 !1 1- c ~ 2 ~ , 3/ , ~ , =

w h e r eV., t~,q'-No'-a ~ WC , V,, + V, . . . " I e . L ( 6 )

Her e Vb, iS the bu i l t - in vo l t age ( V.+ < ! V ), V~t is the sa tu-ra t io n v o l t a g e . / J . , t h e e l e c t ro n mo b i l i t y in th e c h a n n e l , q th ee l e m e n t a r y c h a r g e . N D is t h e d o n o r d e n s i t y i n t h e c h a n n e l , ai s d e f in e d in F ig . 3 . % i s t h e p e rmi t t iv i ty o f t h e ma te r i a l a n dW a n d L a re th e w id th a n d th e l e n g th o f th e c h a n n e l , r e s p e c -t iv e ly . F ig . 4 (a ) g iv e s th e c a l c u la t e d v a lu e s o f t h e s a tu ra t io nc u r re n t o f a s i l i c o n b u r i e d H a l l d e v ic e fo r V ~ ,, = $ V a n dW IL = ! .

I f w e m u l t ip ly th e s a tu ra t io n c u r re n t , E q . (5 ) , b y th e s e n -s i v it y St , E q . ( 4 ) , w e o b t a i n t h e m a x i m u m p o s s i b l e a b so l u t es e n s i t iv i ty :

c h i n n l l O o p l e t l o n' o f l l o n~ . 7 P

G 4 - - x , , p . tLFig. 3. Simplified FET model of the buried Ha l l dev i ce with lhe p.type galeG and the so urce S both connected to ground. The length of the n-typchannel is L and its metallurgical hickness is 2a. The effective thickness ofthe channel at any po int along the channel is t, t < 2a because of the depletionzone. The voltage drop from drain D to S is Vand the current passi~Ig hroughthe current contacts CCI and CC2 is I.1

o . s -0 . 6

~ ) 0 , 40 . 2

o1 4 . 1( a )

i 1 i l

' I1 ' $ 1 5 . 5 1 16 1 6 . 5o u g , o ( N o ) [=~'~

0 " 5 7 7 / 1 a ~

o . ~ , ~ r - + + . i . ~- - " s ' 6 1 - . . . . . . . / ' Ii . // ..............1" S / : . . .. . 1

14.5 l S I,$.S 16 16.$(b } o O g , o ( N o ) [ o 1 1 " ) 1

Fig. 4 (a) Plot of the satutmion current I , .~ for the JRET s ;ruc tute of F ig. 3for d i f ferent leve!s of n-dop ing in the channo l . (b) Plot of the var iation ofthe absolute sens iL iv ity SA of the bur ied H ~! dev ice wi th the doping of thea-c i '~nnel . The graph was calculated f ront the product o f F .q . (7) .

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42 R.S. Popovi c et al. / Sensors and Actuator s A 56 (1996) 39- 55

KNDa~[ 1 / 3 - C v + (2 / 3 ) C ~ / 2 ]SA~ ax= Stl~ 't ~--eV,-2 I ( 7 )

a - V q N o ]K = I x, q W 12e~ L rag (8)

H e re fo r t h e c a l c u la t io n w e u s e th e c h a n n e l t h i c k n e s s a tth e mid d le o f t h e c h a n n e l l e n g th . T h e c a l c u la t e d v a lu e s o fS^ , ,~ , fo r W / L r . G = 1 and V~.. , are shown in Fig. 4(b).

U s i n g t h e c o r r e s p o n d i n g v a l u e s f r o m F ig . 4 ( a ) , ( b ) , w ec a n c a l c u la t e th e ma x imu m p o s s ib l e s e n s i t i v i ty St. F o r e x a m -ple, for/ . .~, = 0,2 m A and V~..,= 5 V , w e ob ta in S tm,~ = 2865V A - ~ T - ~. N o te th a t t h i s r e s u l t d e p e n d s v e ry l i t t le o n th ema te r i a l i n v o lv e d .

I f t h e ju n c t io n f i e ld e f fe c t d o e s n o t e x i s t o r c a n b e n e g le c t e d ,th e n th e a b s o lu te s e n s i t i v i ty o f a H a l l d e v ic e i s l im i t e d b y th ea v a i l a b le s u p p ly v o l t a g e V . T h e r e l e v a n t p a ra m e te r i s t h e nth e s u p p ly -v o l t a g e - re l a t e d s e n s i t i v i ty ( in s h o r t : s e n s i t i v i tySv) , d e f in e d b ys v = = V B , ' V . = S v V B I ( 9 )

T h e v a l u e o f Sv i s p a r t i c u la r ly imp o r t a n t i n lo w -v o l t a g ea p p l i c a t io n s o f H a l l d e v ic e s .

F o r a s t ro n g ly e x t r in s i c H a l l p l a t ewS v = ~ . . ~ G ( I 0 )

w h e re P-N is t h e H a l l mo b i l i t y o f t h e ma jo r i ty c a r r i e rs , w / I isth e w id th - to - l e n g th r a t io o f t h e e q u iv a le n t r e c t a n g le o f t h eH a l l p l a t e , a n d G i s t h e g e o me t r y c o r re c t io n f a c to r , t h e s a mea s in E q . (2 ) .

T h e v a l u e o f t h e t er m ( w / l ) G i s the la rges t in la rge -con tac tH a l l d e v ic e s , t h e l im i t b e in gSvnvax = 0.74 2y.x ( 11 )

T h e s e n s i t iv i ty Sv d e p e n d s s t ro n g ly o n th e ma te r i a l u s e dto f a b r i c a t e a H a l l d e v ic e . W h i l e s i l i c o n , w i th i t s mo d e s tm o b i l i t y , a l l o w s , a t r o o m t e m p e r a t u r e , S V m ~ = O . 12 6 V ( VT ) - ' , G a A s g i v e s 0 . 6 7 V ( V T ) - ~ a n d I n G a A s [ 8 ] 0 . 7 8 V(V T ) - ~. T h e re fo re , o n e c l e a r a n d imp o r t a n t t r e n d in th ed e v e lo p me n t o f H a l l d e v ic e s i s t h e s e a rc h fo r a n d th e a p p l i -c a t i o n o f h i g h - m o b i l i t y m a t e r i a l s . T h e r e c o r d m o b i l i t y o fa b o u t 6 0 0 0 0 a t 3 0 0 K w a s a c h ie v e d in a thin f i lm o f In S b[2 ] . A s e r io u s p ro b le m w i th In S b i s i t s s ma l l b a n d g a p( E g = 0 . 3 6 e V ) a n d , c o n s e q u e n t ly , h i g h t e m p e r a t u r e c r o ss -s e n s i t iv ity . A v e ry h ig h H a l l m o b i l i t y o f 1 6 0 0 0 c m" V - ~s - 'w a s o b t a i n e d i n t h e p s e u d o m o r p h i c l n A I A s / l n G a A s h e t e r -o s t r u c t u r e , o f t h e t y p e c o m m o n l y u s e d f o r h i g h e l e c t r o nm o b i l i t y t r a ns i s to r s ( H E M T S ) [ 9 ] . H o w e v e r , t h e c u r r e n t i ns u c h a H a l l d e v ic e i s u s u a l ly l im i t e d b y th e ju n c t io n f i e lde f fe c t , a n d th e p a ra m e te r S t i s a t l e a st a s r e l e v a n t a s Sv .

I t is i n t e re s t in g to n o te th a t t h e im p o r t a n c e o f a h ig h c a r r i e rmo b i l i t y fo r t h e s e n s i t i v i ty o f a H a l l d e v ic e a p p l i e s o n ly a t

weak b ias e lec tr ica l f ie lds , in such a case , the h igher themo b i l i t y , t h e h ig h e r th e d r i f t v e lo c i ty o f t h e c a r r i e r s , a n dh e n c e th e h ig h e r th e ma g n e t i c p a r t o f t h e L o re n tz fo rc eq [ v j B ] w h ic h i s a t t h e o r ig in o f t h e H a l l e f f e c t . B u t a ts t rong b ias e lec tr ica l f ie lds , the d r i f t ve lo c i ty is sa tu ra ted . T hes a tu ra t e d d r i ft v e lo c i ty d o e s n o t v a ry m u c h f ro m o n e ma te r i a lto a n o th e r : i t is a lw a y s a b o u t 1 07 m s - t . O n e w a y to c i r c u m-v e n t th e p ro b le m o f c a rr i e r mo b i l i t y m ig h t b e to u s e s a tu ra t e dv e l o c it y s t ru c t u re s . W e h a v e d e m o n s t r a t e d a m a g n e t i c s e n s o rs t ru c tu re th a t a p p ro a c h e d th i s g o a l [ 1 0 ] .2.2. Offset

T h e o f f s e t v o l t a g e o f a H a l l d e v ic e i s a q u a s i s t a t i c o u tp u tv o l t a g e th a t e x i s t s i n th e a b s e n c e o f a ma g n e t i c f i e ld . W i thre fe re n c e to F ig . 1 , i n v i r tu e o f t h e s y mme t ry , w e w o u lde x p e c t t h e o u tp u t v o l t a g e o f th e H a l l d e v ic e V x to b e z e ro int h e a b s en c e o f t h e m a g n e t i c f i el d . H o w e v e r , t h e s y m m e t r y o fa H a l l d e v ic e i s n e v e r p e r fe c t : t h e re a re a lw a y s s ma l l e r ro r sin g e o me t ry a n d v a r i a t io n s in d o p in g d e n s i ty , s u r fa c e c o n d i -t io n s , c o n ta c t r e s i s ta n c e , e t c . A l s o a me c h a n ic a l s t r e s s in th eH a l l d e v ic e , i n c o mb in a t io n w i th th e p i e z o re s i s t a n c e e f fe c t ,c a n p ro d u c e a n e l e c t r i c a l n o n -s y mme t ry . T h e re s u l t i s a p a r -a s i t i c c o mp o n e n t in th e H a l l v o l t a g e w h ic h c a n n o t b e d i s t in -g u i s h e d f ro m th e r e a l q u a s i s t a t i c p a r t o f t h e H a l l v o l t a g e .T h e re fo re , t h e o f f s e t s e v e re ly l im i t s t h e a p p l i c a b i l i t y o f H a l ld e v i c e s w h e n n o n - p e r i o d i c o r l o w - f r e q u e n c y m a g n e t i c s i g -n a l s h a v e to b e d e te c t e d .

T h e o f f s e t o f a H a l l d e v ic e i s b e s t c h a ra c te r i z e d b y th eo f f s e t -e q u i v a l en t m a g n e t i c i n d u c t i o n B ow U s i n g E q . ( 9 ) a n dE q . (1 0 ) , w e f in d

V o . 1 1 V,,ffB a = V S v i t , V ( 1 2 )w h e r e w e t a k e ( w / l ) G = ! . T h i s e q u a t io n d e m o n s t r a t e s o n c ea g a in th e imp o r t a n c e o f a h ig h H a l l mo b i l i t y o f t h e ma te r i a lu s e d fo r H a l l d e v ic e s .

W h e n a mic ro e le c t ro n i c s t e c h n o lo g y i s u s e d to f a b ri c a t e aH a l l d e v ic e , t h e o f f s e t v o l t a g e u s u a l ly a mo u n t s to l e s s th a n0 . 1 % o f t h e v o lt a g e ap p l i e d b e t w e e n t h e i n p u t ( c u r r e n t ) c o n -tac ts . Inse r t ing th is va lu e in Eq . ( 12 ) , we f in d Bott_< 10 , 1a n d 0 . 1 m T f o r S i , I n G a A s a n d I n S b H a l l d e v i c e s ,r e s p e c t iv e ly .

I t i s imp o r t a n t t o n o te th a t m e o f f s e t v o l t a g e ~s n o t s t a b le .I t v a r i e s w i th t e mp e ra tu re a n d t ime . E v e n i f a l l o th e r in f lu -e n c e s a re s o m e h o w e l i m i n a t e d , t he r e r e m a i n l o n g - t e r m ( o v e ra p e r io d o f mo re th a n a n h o u r ) f lu c tu a t io n s o f t h e o u tp u tv o l t a g e d u e to 1 I f n o i s e . F r o m o u r e x p e r i e n c e w i t h h i g h -qua l i ty s i l icon Hal l d ev ic es [ 11 ] , these f luc tua t ions corre -s p o n d to a B o rf = 1 0 / s T .

S e v e ra l me th o d s to d e c re a s e th e o f f s e t v o l t a g e h a v e b e e nd e v e l o p e d . T h e y i n c l u d e t r im m i n g , c o m p e n s a t i o n u s i n g t h ei n p u t v o l ta g e [ 1 2 ] , m u t u a l c o m p e n s a t i o n o f t w o o r m o r e H a l ldev ices [ 13 ,1 i 1 , sp in- po la r iza t io n [ 13 ,14 ] , ca l ib ra t ion an dlo o k -u p t a b le s , a n d e l im in a t io n o f me c h a n ic a l s t r a in [ 1 5 ] .T h e s m a l l e st v a l u e o f Borf i n s i l i c o n H a l l d e v ic e s ( l e s s th a n

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R.S. Popov ic et al. / Sensorx aad Actuatorx A 56 (1996) 39-55 430 . 1 roT ) was ob ta ined us ing the s p in -po la r i z a t ion me thod[ 1 4 ]2 .3 . O ther prob lems

T he des t iny o f Ha l l magne t i c s ens o rs a l s o depends on thefu tu re impro vem en t s o f the fo l lowing non- idea l cha rac te r i s -t i c s ( s ee Sec t ions 5 . 2 . 3 -5 . 2 . 6 in R e f , [61 ) :

1 T he long- t e rm s t ab i li t y o f a ll cha rac te r i s ti c s , bu t inpa r t i cu la r o f s ens i t iv i ty and o f f s e t . L ong- t e rm ins t ab i l it y dueto the s u r face e f fec t s and p iezo re s i s t ive and p iezo -Ha l l e f fec t si s ra the r we l l unde rs tood . W e th ink tha t s ome hu lk e f fec t sma y a l s o p lay a ro l e , bu t p rac t i c a l ly no th ing i s pub l i s hed inthe open l i t e ra tu re on the s ub jec t . T he be s t pub l i s hed long-term s tab i l i ty of the sens i t iv i ty St is 1 0 - 4 [ I l ] .

(2 ) No i s e i s a l imi t ing fac to r in low- leve l magne t i c meas -u rem en t s , s uch a s in cu r ren t s ens ing . Us ua l ly , I / fn o i s e i s t hemos t d i s tu rb ing . I / . / 'no i s e may be dec rea s ed by s eve ra l o rde rso f magn i tude i f pe r fec t ma te r i a l s and bur i ed s t ruc tu re s a rcus ed . In a good s i l i con Ha l l s ens o r , t he no i s e equ iva len tm a g n e t i c i n d u c t i o n i n t h e f r e q u e n c y ra n g e 0 . 1 - 1 0 H z i s a b o u tI ~,T [ l l ] .

(3 ) T he t empe ra tu re c ros s - s ens i t iv i ty o f a Ha l l dev ice i san undes i rab le s ens i t iv i ty o f i t s cha rac te r is t i c s , s uch a s m ag-ne t i c s ens i t iv i ty , t o t em pe ra tu re .

In the ca r r i e r -dens i ty s a tu ra t ion rang e o f the s emicon duc to rma te r i a l u s ed fo r the Ha l l dev ice , t he t empe ra tu re c ros s - s en -s i t iv i ty o f the m agne t i c s ens i t iv i ty S~ i s abou t 0 . 1% K - ~. B ya s i m p l e c o m p e n s a t i o n , it c a n e v e n b e r e d u c e d b y a f a c t o r o f10 . B u t ou t s ide o f the s a tu ra t ion range , na me ly in the in t rin s i crange and in the f reeze -ou t range , the t empe ra tu re depende nceof S t becom es exponen t i a l . T h i s rende rs a Ha l l dev ice us e le s sin s ome app l i ca t ions , T o ex tend the ope ra t ing range to h ighe rt empe ra tu re s , w ide band-gap s emiconduc to rs a re us ed ( i . e . ,G aAs up to 175 C [16] ) . Ano the r in t e re s t ing idea i s t oope ra te a Ha l l dev ic e in the minor i ty -ca r r i e r exc lus ion m ode .An ope ra t ing t empe ra tu re o f s i l i con Ha l l dev ice s a s h igh a s350 C has been dem ons t ra t ed in th i s way [ 17 ] .2.4. Outlook

T he m a in v i r tue s o f Ha l l -dev ice magne t i c s ens o rs a re the i rra the r good bas i c cha rac te r i s t i c s, s impl i c i ty o f the ope ra t ingpr inc ip le and o f the s t ruc tu re , and compa t ib i l i t y w i thm i c r o e l e c t r o n i c s .

Due to the good bas i c cha rac te r i s t i c s , Ha l l dev ice s a rea l ready ve ry w ide ly us ed a s m agne t i c s ens o rs . T h i s fa c t p l ace sthem, in tu rn , ve ry h igh on a l e a rn ing cu rve , a p l ace d i f fi cu l tt o a c h i e v e w i t h m o s t o f t h e c o m p e t i n g m a g n e t i c s en s o rs . T h es impl i c i ty o f a Ha l l dev ice a l lows an ea s y op t imiza t ion fo rd i f fe ren t app l i c a t ions . T h i s w i l l he lp , no tab ly , t o adap t thes t ruc tu re to fu tu re low-vo l t age app l i ca t ions . T h i s makes i te a s i e r to s ca le dow n a Ha l l dev ice . Sca l ing down a Ha l l dev icedoes no t a f fec t i t s magne t i c s ens i t iv i ty much , a s i s t he ca s e ,fo r exam ple , w i th ind uc t ive s ens o rs. T h i s mak es a Ha l l dev ice

an in t e re s t ing cand ida te fo r de tec t ing f lux -poor magne t i cs ource s , s uch a s thos e in mag ne t i c mem ory d i s ks .

T hank s to the i r compa t ib i l i t y w i th mic roe lec t ron ic s , t hed e v e l o p m e n t o f H a l l m a g n e t i c s e n s o r s w i l l c o n t i n u e t o t a k eadvan tage o f h igh -qua l i ty ma te r i a l s and eve r - im prov in g fab -r i c a t ion me thod s ava i l ab le in the mic ro e lec t ron ic s indus t ry .In pa r t i cu la r , we expec t tha t t he improvemen t s in the ba s i cma te r i a l s w i l l l e ad to a reduc t ion o f 1 / ] 'no i s e and an impro ve -men t o f the long- t e rm s t ab i li t y o f Ha l l dev ice s . T he inc rea s ein the fab r i ca tion p rec i s ion wi l l be us ed to reduce o f f s e t fu r -the r . T he in t eg ra ted com bina t ion o f Ha l l dev ice s w i th be t t e rin t e r face and s igna l -p roce s s ing e l ec t ron ic c i rcu i t s w i l l l e adt o t h e d e v e l o p m e n t o f n e w m a g n e t i c s e n s o r m i c r o s y s t e m sw i t h a v e r y h i g h p e r f o r m a n c e - p r i c e r a t io .

3 . M a g n e t o r e s i s t o r sM a g n e t o r e s i s t o r s a r e t h e s e c o n d m o s t c o m m o n l y u s e dmag ne t i c s ens o rs. In the i r ba s i c fo rm, they a re ve ry s imple :

re s i sto r s the re s i st ance o f wh ich chang es in the p re s ence o f amagne t i c f i e ld . T he re a rc two d i s t inc t t ypes o f magne to re s -i s to r s : magne to re s i s to r s ba s ed on th in fe r romagne t i c f i lmsa n d s e m i c o n d u c t o r m a g n e t o r es i st o r s .3. i. Ferro ma gnetic magnetoresistors

The se m agne tores is to rs a re based o n ferron~.agnetic me ta lsand a l loys tha t exh ib i t an an i s o t rop ic re s i s t iv i ty in a mag ne t i cf i eld . F rom an e l ec t r i c a l po in t o f v i ew , th i s an i s o t ropy appea rsa s a d i f fe rence o f the re s i st iv i ty P l m eas ured w hen the cu r ren tI i s p a r a ll e l to t h e m a g n e t i c m o m e n t v e c t o r M c o m p a r e d t othe re s is t iv i ty p~ me as ured wi th the cu r ren t pe rpend icu la r tothe m om ent [ 2 , 18 ] . In gene ra l , t he re s i st iv i ty is dependen ton the re l a t ive ang le ~ be twe en the cu r ren t and the magne t i cm o m e n t asp ( 0 ) = p ~ + ( P l - P ~ ) c o s 2 0 = P J- + A ~ s 2 0 ( 1 3 )

Phys ica l ly , t he e f fec t i s r e l a t ed to d i f fe ren t sh i f t s o f ene rg yleve l s fo r e l ec t rons w i th pos i t ive and nega t ive s p ins unde rthe in f luence o f m agne t i c f i e lds .

In fe r romagne t i c ma te r i a l s the in t e rna l magne t i za t ion i sh igh , due to the pa ra l l e l o r ien ta t ion o f the e l ec t ron m agne t i cmoments . T h i s pa ra l l e l i s m i s loca l i z ed in s ma l l doma ins ,s epa ra ted by wa l l s . Wi th no ex te rna l magne t i c f i e ld eve rydom a in i s r andom ly o r i en ted s o tha t t he to ta l magne t i za t ionvan i s hes . In th in f i lms o f s o f t f e r rom agne t i c me ta l , t he f i lmth icknes s i s s ma l l com pared to the dom a in l eng th , s o tha t themagnet iza t ion l ies in the f i lm plane . In the thin f i lm i tse l f , ap re fe r red magn e t i za t ion d i rec t ion appea rs due , fo r exam ple ,to c rys t a l an i s o t ropv , dema~m e t i zat ion fi e lds o r mec han ica ls t re s s re l a t ed to the geom e t r i c a l d imens ions . T h i s re s u l t s i n at o ta l m a g n e t i c m o m e n t v e c t o r M a l i g n e d a l o n g a n a x is o flowes t ene rgy , c a l l ed the ea s y ax i s (e . a . ) . Un de r the in f luenceo f a n e x t e r n a l m a g n e t i c fi e ld H , t h e m a g n e t i c m o m e n t M ( s e eF ig . 5 ) .

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44 R.S . Popov ic e t aL / Sensors and Actuators A 56 (1996) 39-5 5

Hy --

H ~ xFig. 5 . Rota t ion of the magne t ic mom ent M , r ider the inf luence of an exte rna lma gne t i c f i el d H .3. l . 1. Rotat ion o f the magnet i zat ion by an external magnet icf i e l dIn o rde r to c a l cu la t e the in f luence o f an ex te rna l magn e t i cf i e ld H on the mag ne t i c mom ent M con s ide r F ig . 5 . Accord -i n g t o th e S t o n e r - W o h l f a r t h t h e o r y [ 1 8 , 1 9 ] t h e a n g l e Tb e t w e e n t h e e a s y a x is ( e . a . ) a n d t h e m o m e n t M c a n b edes c r ibed a s

H,s i n ( y ) = ( 1 4 )14.,+ H=/cos( y)whe re Hs i s a cha rac te r i s t i c sa tu ra t ion f i e ld depen den t on thefe r romagne t i c f i e ld us ed . T he equa t ion i s va l id fo r

- 1 _ < s in (y ) < 1 o the rw is e s in ( ' , / ) = + 1 .3.1.2 . Magnetoresis t ive sensors base d on ferrom agne t icmaterials

T he bas i c e l emen t in s uch s ens o rs i s a th in f i lm o f mag-ne to re s i s t ive me ta l o r a l loy wi th a rec t angu la r shape a s s how nin F ig . 6 . T he ma gne t i c m om ent M o wi thou t an ex te rna l f i eldi s a long the ea s y ax i s . T wo e lec t rodes a re a t t a ched and acu r ren t i s app l i ed . T he ex te rna l m agne t i c f i e ld is s uppos ed tobe in the y -d i rec t ion . It t ends to ro t a t e the magne t i c mom ent .T ak ing E q . (1 3 ) and E q . (14 ) in to accoun t , t he re s u l t ingre s i s t ance can be expre s s ed a s [ 18 ]R ( H ) = R o ' - A R ( H y lH , ) 2 ( 1 5 )

T he norma l i zed behav iour o f th i s func t ion i s g iven inF ig . 7 . T h i s conf igu ra t ion ha s the d i s advan tage o f hav ing aquadra t i c behav io ur . Fu r the rm ore the s ens i tiv i ty van i s hes fo ra low ex te rna l f i e ld , and the d i rec t ion o f the ex te rna l f i e ldcanno t be m eas ured . D i f fe ren t s o lu t ions have been p ropos edt o o v e r c o m e t h e s e p ro b l e m s .3. ! .3. Linearizat ion o f the sensi t iv i tyB as ica l ly , t he l inea r i za tion can be ob ta ine d by in t roduc inga n a n g l e b e t w e e n t h e m a g n e t i c m o m e n t w i t h o u t a n e x te r n a lf ie ld /14o and the current I . A f i rs t solut ion is to add to the

mlres~five,

x M e u d i z a f i o n H?Fig . 6 . Schem at i c v iew o f a mag netores is t i ve sensor in i t s s imples t geomet ry .The ex tem a] f i e ld H i s supposed Io be in Ihe y -d i rec t ion .

, - , I - . . . . . . - . . " '

- ' , . o ! ~ ; o i = 1 ' ~F i g . 7 . N or ma l i z e d r e s i s t a nce f o r t he s i mp l e s t ge ome t r y o f F i g . 6 , c ompa r e dwi th the solut ion us in g barber po les as in F ig. 8. The s ign o f the s lope of theba r be r po l e s o l u t i ons de pe nds on t he o r i e n t a t i on o f M o i n , he + x o r - xdi rec t ion.

l ~ x Mo ~ HyF i g . 8 . S c he ma t i c v i e w o f a m a gne t o r e s i s ti ve s e ns o r u s i ng b a r be r po l e s . T heexte rna l f ie ld H i s suppo sed to be in the y-di rec t ion. Whi te r egions avemagnetoresistive layer s and hatch ed parts are stripes of mu ch betterconductivity.ex te rna l magne t i c f i e ld H a b ia s f ie ld Hn [20 ] . In th is c a s e ,the re s i s t ance i s ob ta ined by rep lac ing H: in E q . (15 ) by14.,. + H ,~ . Th e need to gen e ra te a b i a s f i e ld inc rea s e s the com -p lex i ty o f the s ys t em. T h i s l imi t s the app l i ca t ion o f s uch al inea r i za tion me thod .

A s econd s o lu t ion i s t o ro t a t e the d i rec t ion o f the cu r ren tcompared to the ea s y ax i s [21 ] . T h i s c an be rea l i z ed byapp ly ing , du r ing the evapora t ion o f the fe r romagne t i c ma te -r i a l, a m agne t i c f i e ld in a w e l l -de f ined d i rec t ion . I t w i l l r e s u l tin a ro t a tion o f the ea s y ax i s in F ig . 6 . Wi th ou t an ex te rna lf i e l d , t h e c u r r e n t a n d t h e m a g n e t i c m o m e n t a r e n o l o n g e rpa ra l l el . An ang le o f 4 -45 i s o f t en us ed . An o the r e l ega n ts o lu t ion cons i s t s o f u s ing s o -ca l l ed ba rbe r po le s [22 ] a ss how n in F ig . 8 . In th is conf igu ra t ion , s l an ted s t r ipe s o f goodc o n d u c t i n g m a t e r ia l a r e p l a c e d b e t w e e n s t r ip e s o f m a g n e t o -re s i s t ive ma te r i a l w i th lower conduc t iv i ty . T he cu r ren t w i l lthen fo l low the pa th w i th the low es t r e s i s tance be tw een thetwo con tac t e l e c t rodes . I t w i l l try to min im ize the pa th in themagne to re s i s t ive ma te r i a l whe re the re s i s t ance i s l a rge r .T he re fo re i t w i l l p ropaga te pe rpend icu la r to the ba rbe r po le sa s d r a w n s c h e m a t i c a ll y in F i g . 8. W h e n t h e a n g l e b e t w e e nthe ea s y ax i s and the cu r ren t i s + 45 , t he f i e ld - re s i s tancere la t ions h ip i s expre s s ed by [ 18 ]R ( H ) = Ro A R ( H , , / H s ) ~ / I L ( H , / H s ) 2) (16 )

T w o s o lu t ions ex i s t , depend ing on the s ign o f /14o . T hes etwo cu rve s a re rep re s en ted in F ig . 7 . Such l inea r i zod s ens o rsw o r k p r o p e r ly o n l y i f t h e m a g n e t i z a ti o n M o r e m a i n s i n o n emag ne t i za t ion s ta t e . A s wi t ch in g o f/14o be tw een the + x andthe - x d i rec t ion can occur wh en the ex te rna l fi e ld excee ds ace r t a in l imi t . T h i s in t roduces a f l i p f rom one cu rve to theo the r , chang ing the s ign o f the s lope . Neve r the le s s , a t l ow

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R.S. Poln~vicet aL /Sensors a nd Actuators A 56 (1996) 39-55 45ex te rna l f i e lds the s ens o r i s to a g ood approx ima t ion l inear .T he f l ip e f fec t ha s to be av o ided by l imi t ing the ex te rna l f ie ld .B y a p p l y i n g f r o m t i m e t o t i m e a s t r o ng w e l l - k n o w n e x t er n a lf i e ld , a r e s e t o f the mag ne t i c o r i en ta t ion o f M o can a l s o beach ieved . T h i s s a fe ty s o lu t ion inc rea s e s the complex i ty o f thes e n s o r m i c r o s y s t e m .3 . i . 4 . M a t e r i a l s , p e r f o r m a n c e a n d a p p l i c a t i o n s

T hin f i lms o f fe r rom agne t i c me ta l s and a l loys a re us ed inthe fab r i ca t ion o f magne to re s i s t ive s ens o rs . T h in f i lms a reus ed to inc rea s e the nomina l r e s i s t ance o f the s ens o r . Fu r -the rmore , t h in f i lms can be made to behave l ike a s ing lemag ne t i c doma in . W i thou t an ex te rna l magne t i c fi e ld , t he i rmag ne t i za t ion fo l lows one we l l -de f ined d i rec tion ( the ea s yax i s ) s e t du r ing manufac tu re .

For s ens o r app l i ca t ions , an i s o t rop ic magne to re s i s t ancesa re com mo nly us ed . In the s e m a te r i a l s the s a tu ra tion f i e ld isv e r y l o w , w h i c h m a k e s t h e m m o s t u s e f u l f o r th e d e t e c t io n o fs ma l l f i e lds. A t roo m tem pe ra tu re a l loys o f N i , Fe l _ ~ a s we l la s N ixC ol -x h ave been us ed w i th a magn e to re s i s t ive e f fec t( a m a x i m a l r e l a t iv e c h a n g e o f t h e r e s i st i v it y ) o f t h e o r d e r o f3~ [21.

W ith an open- loo p in t e r face the magne to re s i s t ive s ens o rsh a v e a s e ns i ti v i ty r a n g e o f 1 0 - : t o 5 0 G w i t h a d y n a m i c r a n g ef r o m d . c . to I G H z [ 1 ] . I m p r o v e d f e e d b a c k r e a d o u t m e t h o d sreduce the m in im um de tec tab le f i e ld to 10 -6 G fo r l imi t edbandw id ths . T he s ens o rs a re l i gh t , s ma l l , ope ra te w i th 0 .1 to0 .5 m W o f p o w e r an d at t em p e r a tu r e s b e t w e e n - 5 0 a n d+ 2 o o C I l l .R e c e n t d e v e l o p m e n t s i n t h e m a t e r i a l t e c h n o l o g y h a v es how n a po ten t i a l t o inc rea s e the s ens i t iv ity by one o rde r o fm a g n i t u d e c o m p a r e d w i t h p e r m a l l o y s b y u s i n g m a g n e t i cm u l t i l a y e r s . T h e s e k i n d o f m a t e r i a l s h a v e a m u c h h i g h e rs a tu ra t ion f i e ld , wh ich can l e ad to p rob lems in rea lapp l i ca t ions .

F i r s t , magne t i ca l ly coup led mul t i l aye rs , s o ca l l ed 'g i an tnega t ive magne to re s i s t ances ' have been s tud ied [2 , 23 , 24] .T h e s e a r e F e / C r o r C o / C u s u p e r la t ti c e s a n d o t h e r m u l t i l ay e r so f a l t e rna t ing mag ne t i c and non -mag ne t i c me ta l s . A t l i qu id -He t emp e ra tu re s magn e to re s i s t ive e f fec t s as h igh as 80% havebeen obs e rved [ 24 ] . T he i r h igh s a tu ra t ion f i e ld (up to 0 . 4 T )and h igh no i s e l eve l ( i . e ., r educed de tec t iv i ty ) l imi t t he app li -ca t ion o f s uch m a te r i a l s in rea l s ens o r s ys t ems .

Nex t , uncoup led fe r romagne t i c mul t i l aye rs , c a l l ed ' s p inva lve ' ( s v ) [2 ] s t ruc tu re s , and g ranu la r f i lms a l s o exh ib i tg i an t magne to re s i s t ive e f fec t s [2 5 , 26] . In pa r t i cu la r the s vs t ruc tu re s a rc in t e re s t ing fo r dev ice app l i ca t ion s ince they a rcs ens i t ive a t l ow m agne t i c f i e lds w i th a ma gne to re s i s t ive e f fec to f t h e o r d e r o f 4 - 1 0 % [ 2 ] .

P e r m a l l o y m a g n e t o r e si s t o rs a s m a g n e t ic s e n s o r s a r e c o m -m e r c i a l l y a v a i l ab l e ( e . g . , P h il i p s K M Z 1 0 ) . T h e m o s t c o m -mo n app l i ca t ions a re in con tac t l e s s pos it ion s ens ing [2 ] . B yu s i n g t h e p o s i t i o n - d e p e n d e n t f i el d o f p e r m a n e n t m a g n e t s o rby m eas ur ing the f i e ld d i s to r t ions gene ra ted by s o f t - iron mov-ing pa r t s , t he l a t e ra l o r angu la r pos i t ion o f d i f fe ren t p i ece sc a n b e d e t e r m i n e d [ 1 8 ].

O the r app l i ca t ions a re in the f ie ld o f meas u rem en t o f cu r -ren t s and e l ec t r i c a l pow er [ 27 ] . T hes e s ens o rs have a l s o beenu s e d a s m a g n e t o m e t e r s , f o r e x a m p l e , a s c o m p a s s e s [ 2 8 ] .M agne to re s i s t ive s ens o rs we re app l i ed a s read ing heads a sea r ly a s 1971 [20 ] .3 . i .5 . D i s c u s s i o n a n d o u t l o o kC ompared to o the r magne t i c s ens o rs , t he fe r romagne t i cmagne to re s i s to r s have in gene ra l a h igh s ens i t iv i ty a t l owf ields . T h i s i s due to an in t r in s i c ga in , s ince the s e ns o r i t s e l fac t s a s a m agne t i c concen t ra to r . T h i s inhe re n t e f fec t s t rong lyinc rea s e s the s ens i tiv i ty o f the dev ice .

F e r r o m a g n e t i c m a g n e t o r e s is t o r s h a v e t w o m a i n d i s a d v an -t ages : t he f l ipp ing e f fec t and hys te re s i s [ 29 l . E s pec ia l ly fo rl inea r i zed sens o rs , w i th a s ens i tiv i ty a s in F ig . 7 , e ach s ens o rhas to be m agne t i zed in one d i rec t ion be fo re us e , i n o rde r tohave w e l l -de f ined cba rac te r i st i c s . B y app ly ing a l a rge d i s -tu rb ing f i e ld in the oppos i t e d i rec t ion , t he s ens o r re s pons ecan be a f fec ted and in the ex t rem e ca s e s the re s pons e can bereve rs ed . In F ig . 7 th i s e f fec t co r re s pon ds to a s udden f l ipf r o m t h e b a rb e r c u r v e " + ' t o t h e b a rb e r c u r v e ' - - ". T o a v o i dth i s dange r a pe r iod ic magne t i za t ion o f the s ens o r c an beapp l i ed , bu t th i s inc rea s e s the complex i ty o f eve ry s ys t embas ed on the s e k inds o f dev ice s .Ne w de ve lopmen t . s a t e s t il l emerg ing . S ign i f i c an t impro ve -men t s a re expec ted in ba s ic ma te r i a l s . T he f reedom in de s ignof fe red by the new m agne t i c mul t i l aye rs ha s to be exp lo redfu r ther . W hi l e , a t p re s en t , the s e m a te r i a l s have a h igh s a tu -ra t ion f i e ld com pared to s t anda rd magne to re s i s to r s , t he deve l -opm en t i s on ly a t t he beg inn ing . T he in t r in s i c no i s e in s uchn e w c o m p o n e n t s h a s t o b e a n a l y s e d a n d u n d e r s t o o d i n d e ta i l.I t may s t rong ly l imi t t he de tec t iv i ty o f s ens o rs us ing the s ema te r i a l s .3 .2 . S e m i c o n d u c t o r m a g n e t o r e s i s t o r s

A s e mic ondu c to r magne to re s i s to r is a th in p la t e o r a f i lmof a h igh -mobi l i ty s emiconduc to r f i t t ed wi th two e l ec t r i c a lcon tac t s . T he re s i s t ance meas ured be tween the con tac t sincreases i f the dev ice is exposed to a perpen dicu lar magnet icf ield. The increase in the resistance is another manifestat iono f t he ac t ion o f t he Lo ren tz f o rce ( Eq . ( I ) ) on the cha rgecarr iers in the f i lm . B r ie f ly , the magnet ic par t o f the Lorentzforce br ings about a def lec t ion o f charge car r iers re la t ive tothe i r pa ths w i th no magne t ic f i e ld . The m ic rodc f l ec t i on o f t hecarr iers" free transits between col l is ions is responsible for agenera l increase in the mater ia l res is t iv i ty . T h is is ca l led thephys ica l magnetores is tance ef fec t. The macroscopic def lec-t ion o f cur rent l ines addi t iona l ly increases the dev ice res is-tance. S ince th is e f fec t depends on the fo rm of the sample, i tis cal led the geometr ical magnetoresistance effect.

T he geome t r i c a l magne to re s i s t ance e f fec t i s be s t seca ins hor t bu t w ide (wi th l a rge con tac t s ) s ample s . On the o the rhand , the magn e to re s i s t ance e f fec t i s l a rge enou gh to be us e -fu l on ly in h igh -mob i l i ty ma te r i a l s . A s hor t s amp le o f a h igh -mobi l i ty m a te r i a l ha s a ve ry low re s i s t ance , wh ich i s d i f f i cu lt

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4 6 R S . P o p o v i c e t al . / S e n s o r s a n d A c t u at o r s A 5 6 ( 1 9 9 6 ) 3 9 - 5 5

t o meas ure w i th a h igh eno ugh p rec i s ion . T he re fo re , t he s em-iconduc to r magne to re s i s to r s us ua l ly have a fo rm o f manyshort res is tor ce l ls conn ected in ser ies . The interes ted readercan f ind more in fo rm a t ion on the phys ic s o f the magne to re s -i s t ance e f fec t in a mo nograp h [ 22 ] and a de ta i l ed accoun t onthe deve lopm en t work in a re cen t rev iew pape r [ 18 ] .

Sem icondu c to r magne to re s i s to r s made o f InSb a re s impleand ve ry s ens i t ive mag ne t i c - f ie ld sens o rs. T h ey a re o f t en us edto de tec t a m agne t i c f i e ld l a rge r than abou t 20 mT . C o mb inedwi th a pe rm anen t mag ne t , t hey f ind app l i ca tion , fo r example ,in p rox imi ty de tec to rs . T he p rob lem w i th s uch magne to re s -i s to r s i s t he ir r a the r s trong t emp e ra tu re dependence ( ln Sb i sa s ma l l -band-gap s emiconduc to r ) and h igh non- l inea r i ty .T he re fo re , t hey a re no t no rm a l ly us ed to meas ure a m agne t i cfield.W e be l i eve tha t s emico nduc to r magne to re s i s to r s w i l l con-t inue fo r s ome t ime to be us ed a s s imple and robus t magne t i cde tec to rs in s ome n iche app l ica t ions . T he i r s ma l l comm erc ia limpor tance can , howeve r , no t ju s t i fy ma jo r re s ea rch anddeve lop men t e f fo r t s and the i r impac t w i l l d imin i s h .

4 . I n d u c t i v e p r o x i m i t y a n d d i s t a n c e s e ns o r sInduc t ive p rox imi ty and d i s t ance s enso rs a re ba s ed on thel a w o f i n d u c t i o n ( F a r a d a y ' s l a w ) : U = - N ( d c k / d t ) . T his

impl i e s tha t a vo l t age U wi l l appea r a t t he ends o f a co i l w i thN turns wh en the m agn et ic f lux ~b in th is coi l i s varying.Induc t ive s ens o r mic ro s ys tems wi l l t he re fo re con ta in the fo l-lowing ba s i c comp onen t s [ 18 , 30 ] : a m agne t i c - f i e ld s ource,a rece ive r e l emen t to de tec t t he magne t i c - f i e ld var i a tions andan e l ec t ron ic in t e r face and s igna l -cond i t ion ing c ircu i t ry toampl i fy the we ak vo l t age comin g f rom the co i l and to ex t rac tf rom i t u se fu l in fo rma t ion .

Of cours e the s ys t em requ i re s a t a rge t , loca ted ou t s ide thes ys tem. T he in f luence o f th i s componen t on the magne t i cf i e ld w i l l depend on the ma te r i a l compos i t ion o f the t a rge tand o n i ts profi le , as we l l as on the ta rge t to sensor dis tance .B as ica l ly bo th fe r romag ne t i c a s we l l a s conduc t ing t a rge t scan be de tec ted by induc t ive s ens o rs . T he in f luence wi l linc rea s e by d ec rea s ing the t a rge t to co i l s epa ra tion .

W i th t e r rom agne t i c ma te r i a ls , t he re luc tance o f the mag-ne t i c c i rcu i t com pos ed o f the co i l and the t a rge t w i ll dec rea s eby app roach ing the t a rge t . T h i s l e ads to an inc rea s e o f theinduc tance L o f the p ickup co i l . On the con t ra ry , fo r con-duc t ing ma te r i a l s eddy cu r ren t s w i l l appea r in the t a rge t .Acco rd ing to L enz ' s p r inc ip le , the eddy cu r ren t s w i l l coun-t e rac t t he p r imary cu r ren t and p roduce a nega t ive change o fthe coi l inductance . In fac t , a mirrored coi l wi th negat ivecout~l in~ to the primary, eoi! wi l l be produced in the con-duc t ing t a rge t [ 30 ] . T he eddy cu r ren t s a l low the magn e t i cf i elds to pene t ra t e conduc to rs on ly to a c e r t a in dep th , c a l l edthe s k in dep th 8 - ~/21aurpop', with o" the cond uct ivi ty andPoP, the pe rmeab i l i ty o f the t a rge t. T he s k in dep th dec rea s e sa s the f requency w inc rea s e s. C ur ren t s w i l l be concen t ra t ednea . 1he s u r face o f the conduc t ing t a rge t , decay ing rap id ly

pas t t he s k in dep th . N o t i ce that , be s ide the indu c tance change ,varia t ions of the ser ies ces is tance of the coi l as a funct ion o fthe t a rget pos i t ion a re a l s o expec ted fo r bo th fe r rom agne t i cand con duct in g materia ls [ 31 ] .4. i. Applications

From the us e r po in t o f v i ew , the mic ros ys tem s hou ld becons ide red a s a b l ack -box , de l ive r ing an e l ec t r i c a l s igna l . T hef i eld o f app l i cat ion wi l l be de te rm ined by the phys ica l i n t e r -pre ta t ion of th is s ignal . In front of a f la t ta rge t of knowncompo s i t ion , t he s igna l w i l l be in t e rp re t ed a s a m eas urem en to f the d i s t ance to the t a rget . B o th s ys t ems w i th ana log ou tpu t ,used as dis tance sensors , and sys tems with a s tep responseus ed a s p rox imi ty de tec to rs a re com mer c ia l ly ava il ab le .Deve lop men t s have been rea l i z ed to make th i s k ind o f p rox-imi ty de tec to r more o r l e s s independen t o f the t a rge t com-pos i tion [32 ] . Fo r o the r app l ica t ions [ 33 ] , t he s ys t em canbe de s igned to g ive the ma te r i a l compos i t ion o r the th i cknes sof a f la t ta rge t a t a kno wn dis tance .

B as ed on the s e s ens ors , s ys t ems fo r l a t e ra l d i s p lacemen tand fo r ro t a tion meas urem en t s have been deve lo ped [ 18 ] .T a rge t s w i th known p ro f i l e , fo r example ro ta t ing impu l s egea rs , a re us ed in f ron t o f the de tec to r . T he m ot ion w i l l beg iven by the num ber o f t e e th s een by the s ens o r . In the sameway , by a l a t e ra l dep lacem en t o f the s ens o r ra i c ros ys tem, as can o f an unkno wn t a rge t p ro f i le fo r imag e ry [34 , 35] andrecogn i t ion o f me ta l l i c p i ece s [ 36 ] c an b e ob ta ined . Fur the r -more , s uch s ens o rs c an de te rm ine and loca l i z e de fec t s in theta rge t ma te r i a l , fo r example mic roc racks in ga s p ipe l ine s[ 3 7 ] .

In a l l t he s e app l ica t ions , t he qua l i ty o f the s ens o r m ic ro -s ys tem wi l l depend on p rope r t i e s l i ke ax ia l and l a te ra l r e so -lu t ion , r ange o f work ing d i s t ance , l i nea r i ty , t empe ra tu redepend ency and s i ze .4.2. Sourc e of magnetic field

T w o k inds o f magn e t i c - f ie ld s ource s can be us ed , name lype rma nen t magne t s [38 ] and co i l s [ 18 ] . As the magne t i cf i eld i s cons tan t, no eddy cu r ren t s a re p roduced s o tha t on lymo ving fe r romagne t i c t arge t s c an be de tec ted . Fur the rmore ,by us ing a pick up coi l tha t is only se ns i t ive to the varia t ionso f the mag ne t i c f lux , on ly rap id chan ges a re de tec ted . No tetha t th i s d i sadvan tage can be ov e rcom e by us ing , fo r example ,a Ha l l s ens o r o r a f lux ga te a s a re ce ive r [ 39 ] .

A l t e rna t ive ly , co i l s a re o f t en us ed a s s o urce s fo r the m ag-ne t i c f ie ld . Accord ing to Am i~r e ' s l aw , ~ H . dl = N . L a cu r-ren t I i n an N- tu rn co i l w i l l p roduce a mag ne t i c f i e ld a roundth is co i l [ 18 ] . T he c ros s s ec t ion o f the w i re s ha s to be l a rgein o rde r to adm i t a l a rge e l ec t r i c a l cu r ren t fo r the p roduc t ionof an in t ens ive mag ne t i c f i e ld . T h i s l imi t s the num ber o f tu rnsin integra ted f ia t coi ls wi th a f ixed aspect ra t io and a givena rea . Fur the rmore , t he ma te r i a l s hou ld have a s h igh a con-duc t iv i ty a s pos s ib le . Us ing co i l s i n s t ead o f a pe rmanen tmagn e t a l lows the magne t i c f i e ld to be m odu la ted . In the nex t

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sec t ion w e sha l l focus on t he se k ind o f source s fo r magne t i cfields.4.3. Pickup coils

Since a t the rece iv er s ide only sm al l s ignals a re expected,i t is preferable to increase the n um ber of turns in the pickupco i l, even a t t he cos t o f a dec rea se o f t he c ross sec t i on o f t hewi re s . Accord ing t o Fa raday ' s l aw, t he number N o f t u rns i nthe coi l i s the re levant fac tor for the induc ed vol tage U. Thisimpl i e s tha t t he op t imu m des igns o f t he source and p i ckupco i l s a re som ewh a t d if f e ren t. M ic rosys t ems wi th two co i l ssepa ra te ly op t im ized w i l l be u sed i n app l i ca t ions whe re h ighprec ision and high sensi t ivi ty are requi red, l ike in prec ised i s t ance measurem ent s . For app l i ca ti ons l i ke l ow-cos t p rox-imi ty de t ec to r s , whe re on ly t he p re sence o f me ta l l ic p i ece shas t o be de t ec t ed , a compro mise i s made i n t he de s ign o f t heco i l. In o rde r t o s im pl i fy t he mic rosys t em, on ly one co i l i sused a s bo th sou rce and rece ive r .W e rem ark t ha t i n t he fu tu re , p rox imi ty and d i s t ance -meas-u rement sensor m ic rosys t ems wi l l a l so be ba sed on o the rk inds o f r e ce ive r s l i ke Ha l l dev i ce s and f l uxga t e sensor s .4.4. Elec tron ic interface an d signal-conditioning circuitry

The in t e r fac ing o f a sens i t i ve e l emen t wi th t he s i gna l -p rocess ing c i r cu i t ry i s a ma jo r p rob l em in sensor sys t ems . Inmost c a se s , t he ove ra l l de t ec t iv i t y o f t he who le sys t em wi l lbe s t rong ly i n f l uenced by t he ch osen so lu t i on . Many in t e rfacec i rcu it s fo r i nduc t i ve p rox imi ty sensor s have b een p re sen t edin the past , som e of whic h are used today in indust r ia l prod-ucts . The main interface pr inc iples a re based on br idge c i r -cu i t s and on osc i l l a to r c ir cu i ts [40] .

Due t o t he d i f f e ren t i a l na tu re o f t he i r m easuremen t p r in -c ip l e, W hea t s tone b r idges a re we l l know n fo r t he ir goodpe r fo rmance ( e .g . , l i nea r i ty , t empe ra tu re compensa t i on , ve r -sa t i l i ty) [41] . In genera l br idge c i rcui t s need severa l e le -men t s and a re t he re fo re compl i ca t ed .

Osc i l l a to r c i r cu it s have l e ss e l emen t s and a re wide ly used[ 421 . The i n fo rma t ion o f i n t e res t i n an osc i ll a t o r c i r cu it m igh tbe i n t he f r equency ra the r t han i n t he amp l i tude , p rov id ingan i nc rea sed immu ni ty to e l ec t romagne t i c n t e r fe rences [41 ] .A f i rst c lass of such c i rcui t s i s harmonic osc i l la tors usedma in ly wi th capac i t ive o r i nduc t i ve sensor s [4 3] . Th i s t ypeof c i rcui t in terface is kn ow n to hav e a very high sensi t ivi ty ,due to i t s resonant na ture . In thes e c i rcui ts var ia t ions in f re-quency and ampl i t ude a re o f t en coup led t oge the r . Moreove rthis c i rcui t has to inc lude ra ther bulky offse t -compensat ionci rcui t ry , which makes c i rcui t in tegra t ion di f f icul t [421.An other type o f osc i l la tor c i rcui t tha t i s ra ther s imple but lesssensi t ive than the h arm onic osc i l la tor i s the re laxat ion osc i l -lator [41 ].

Recen t ly a di f ferent ia l version of the re laxat ion osc i l la torhas been p roposed t ha t l e ads t o a s t rong ly improved sens i ti v -i ty [44 ,45] . Th i s no ve l i n te r face ha s good fea tu re s o f bo thosc i l la tors and br idges: i t i s s imple and has an output s ignal

f r equency and ampl i t ude i ndependen t o f one ano the r, a s i nre laxat ion osc i l la tors . Fur thermore the f requency idea l lyincreases to inf ini ty , s imi lar to the am pl i tude o f the signal ina ha rmo nic osc i l la tor . Therefore i t can be m ade very sensi ,~ive .I t has a di f ferent ia l na ture , a l lowing compcnsat iens simi larto br idge c i rcui t s . The novel interface i s a se l f -osc i l la t inge l ement , de l i ve r ing a s an ou tpu t s i gna l a d ig i t a l- compa t ib l esqua re -wave s igna l a t va ry ing f requency [46] .4.5. Integrated single-coil serLtor microsystem

Th e future o f microsen sors wi l l be in integra, .zd devices ,no t on ly fo r e conom ica l r e a sons , bu t a l so f rom a sys t em po in to f v i ew. Sma l l s i z e wi l l be needed fo r me in t roduc t i on o fsuch i nduc t ive sensor s i n sys t em s v , i th m ore com plex i ty , l i kemagne t i c l ev i t a t i on and bea r ings i n compute r ha rd d i sks[47 ] . F or image ry app l i ca t i ons, t he s i z e o f t he sensor w i l la l so de t e rmine the p ixe l r e so lu t ion o f t he sys t em. W e sha l ld i scuss he re tw o d i f f e ren t ways t o i n t eg ra t e t he co i ls fo r fu tu reprox imi ty and d i s t ance sensor s .

Far ther sensor m icrosys tems could be f i rs t rea l ized usir .gmic roso l eno ids [61 ] ob t a ined by ' advanced s i l icon t e chno l -og i e s (F ig . 9 ( a ) ) . In such dev i ce s a f e r romagne t i c co re canbe i n t roduced ; fu r the rmore , t he num ber o f t u rns i s no t l im i t edby t he c ross sec t i on o f t he co i l. Sm a l l p ixe l s cou ld be ob t a inedwi th a l a rge co i l i nduc t ance . The d i sadvan t age o f t h i sapproach i s t he com plex i ty o f t he t e chno logy requ :aec l [48 ] .

Ano the r approach fo r i n teg ra t i on i s f la t co i l s (F ig . 9 (b ) )[4 8] . In this case , an easier technolog y [4 9] o1" even tual ly a~tandard p rocess [50,5 1] l ike the me. ta ll iza tion steps ofCM OS can be appl ie , ! for the fabr ica t ion of the coi l s .

By sca l i ng down the sensor , d i f f e ren t t r adeof f s shou ld be.made [ 31 ] . D ue t o t he fundam enta l d iv i s i on o f t he magne t i cf ie ld around a coi l , both the la tera l resolut ion and the w orkingd i s t ance o f t he sensor a re p ropor t i ona l t o t he co i l d i am e te r[34 ,52] . The sca l ing down wi l l r e su l t i n a h ighe r p ixe l r e s -o lu t i on bu t a l so i n a dec rea se o f t he w ork ing d i s t ance . Ano the rt radeo ff i s give n by the parasi t ic e ffec ts . Rela t ive to the indue-t ance o f t he co i l , t he pa ra s it i c c apaci t y be tween t he r ams andthe ser ies resistance wi l l increase [ 31 ] . T he ind uct ive behav-iour o f t he dev i ce t ends t o d i sappea r a t ve ry sma l l d imens ions .Neve r the l e ss , p ro to types o f such sensor m ic rc~ys t ems havebeen rea l i z ed and success fu l l y t e s t ed [53 ] us ing a hybr iddi fferent ia l re laxat ion osc i l la tor as an e lec t ronic interface(F ig . 10 ) .

- t( a ) C o )

Fig . 9 . (a) Pr inc ip le o f i n tegra ted mic ros o leno id as d is tance sensor mic ro-system, (b) INinciple f integrated lat coil as distance ensorn,icrosystem.

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48 R .S . Popov ic e t a l. / Sens or s and Ac tuator s A 56 (1996) 39-55

F l a t c o i l ~ a m o l e r 1 0 r n ~

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5 105 ................. :: .. .. .. .. !4 Io ~ , , _ ~ , J . . . . i . . . . i . . . . i . . . . -(b) 0 1 2 3 4 5Distance cc, l to target [mini

Fig. I0. (a) Pro:otypeoCa flat coil distancesensor microsystem ( after [ 531 ).(b) Measured frequt'ncy variation as function of the distance of the targetto the coil (after I53 1)

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(b)Fig. I i. (a ) Principle of a differential trmlsformer. (b ) Picture of the inte-grated differential transformer as deve loped at the CSE M Neuch.~lel (after[54]).

4.6. hztegratcd differential transformer 4. 7. O utlookI n o r de r t o i l l u s t r a t e t he new pos s i b i l i t i e s o f f e r ed by t he

i n t eg r a t i on , we a l so p r e sen t t he p r i nc i p l e o f a d i f f e r en t i a lt r a n s f o r m e r ( F i g . 1 1 ( a ) ) . T h i s d e v i c e is m a d e o f t h r e e c o i l st r ad i t i ona l l y w oun d on t he f e r r om agne t i c co r e i t s e l f [ 18 ] . I nou r F i gu r e , w e s epa r a t e ~ .he exc i t a t i on , t he r ece i v e r and t hem o v i n g c o r e , i n o r d e r t o p r e p a r e f o r t h e d i s c u s s i o n o f t h ei n t eg r a t ed ve r s i on o f such a s enso r . Co i l I i s exc i t ed b y ana . c . cu r r en t . The p i ckup co i l s 2 and 3 a r e magne t i ca l l y cou -p l e d t o c o i l 1 . T h e d e g r e e o f c o u p l i n g i s c o n t r o l l e d b y t h em o v i n g c o r e . F o r a n a s y m m e t r i c a l p o s i t i o n o f th e c o r e a ni n d u c e d v o l t a g e a p p e a r s i n t h e p i c k u p - c o i l c ir c u it . T h i s s e r v e st o meas u r e t he l a t e r a l pos i t i on o f t he co r e .

T h e C S E M a t N e u c h ~ t e l h a s d e v e l o p e d a n e w i n t eg r a t e ds e n s o r m i c r o s y s t e m [ 5 4 ] b a s e d o n an a n a l o g p r i n c ip l e( F i g . 1 1 ( b ) ) . T h e f ir s t c h i p c o n t a i n s t h e f i a t p i c k u p c o i l s 2and 3 , r e a l i z ed i n a s t anda r d a l u mi n i um me t a l l i z a t i on p r oces s .The exc i t a t i on co i l r equ i r e s a l ow se r i e s r e s i s t ance and i st he r e f o r e r ea l i z ed on a s econd ch i p , f l i p - ch i p moun t ed on t hef i r s t , w i t h a t h i ck coppe r l aye r a s a f i a t co i l . Due t o t he t h i ns t r uc t u r e s u sed i n i n t eg r a t ed dev i ce s , t he co i l s 2 and 3 a r es t r ong l y coup l ed t o t he exc i t a t i on co i l . Fu r t he r mor e , a t a r ge twi t h a l a t e r a l p r o f i l e c an ac t a s a mov i ng co r e , t he pos i t i on o fw h i c h i s t o b e d e te c t e d . S o m e o f th e p e r f o r m a n c e o b t a i n e dw i t h t h i s s e n s o r s y s t e m i n c l u d e s s u b - m i c r o n r e s o l u t i o n , af r e q u e n c y r a n g e o f 0 to 4 k H z , a w o r k i n g d i s t a n c e b e t w e e nsenso r and t a r ge t o f O t o 2 mm and h i gh t em pe r a t u r e s t ab i l i t y .

T h e f u t u re o f in t e g r a te d i n d u c t i v e s e n s o r m i c r o s y s t e m sw i l l st r o n g l y d e p e n d o n t h e s c a l in g d o w n o f t h e c o i l d im e n -s i o ns . O n e o f t h e m a i n p r o b l e m s i s t he a p p e a r a n c e o f p a ra s i ti ce f f ec t s l i ke t he r e l a t i ve i nc r ea se o f t he s e r i e s r e s i s t ance[ 31 , 55 ] . An i mpor t an t i s sue wi l l be t he ava i l ab i l i t y o f a l ow -c o s t , h i g h - a s p e c t - r a t i o a n d h i g h - r e s o l u t i o n t e c h n o l o g y t ode f i ne and s t r uc t u r e t he co i l s .

I t s eems t ha t i n t he nea r f u t u r e , i nduc t i ve p r ox i mi t y andd i s t a n c e s e n s o r m i c r o s y s t e m s w i l l h a v e t h e f o r m o f s m a l l b u te s p e c i a l l y o f t h in d i s k s . T w o v e r s i o n s o f t h e s e s e n s o r s w i l lbe deve l ope d . F i r s t, m i c r os enso r s w i l l be f ab r i ca t ed u s i ng f la tco i l s on l ow- cos t subs t r a t e s l i ke p r i n t ed c i r cu i t s o r g l a s swaf e r s . I n t h i s c a se , t he s i gna l - cond i t i on i ng e l ec t r on i c s w i l lbe on a s epa r a t e s i l i con ch i p , i n t e r connec t ed wi t h t he co i l i na hyb r i d i n t eg r a ti on . Th e d i am e t e r o f t he co i l w i l l r ema i nc o m p a r a b l e t o t h a t o f cu r r e n t l y a v a i l a b l e s e n s o r s . A s e c o n dv e r s i o n o f i n d u c ti v e s e n s o r m i c r o s y s t e m s w i l l s c a le d o w n t h es i ze o f t he co i l s by a mono l i t h i c i n t eg r a t i on o f t he co i l andt he e l ec t r on i c s on a s i ng l e s i l i con ch i p u s i ng pos t - p r oces s i ngt echno l og i e s . Due t o t he mi n i a t u r i za t i on , t he i nduc t ance o ft h e c o i l w i ll d e c r e a s e . N e v e r t h e l e s s , w h e n t h e p a r a s it i c e f f e c t sa r e n e g l ig i b l e, t h e s e n s i t i v i ty o f t h e s c a l e d - d o w n m i c r o s y s t e mwi l l r ema i n cons t an t i f, t ogs ! he r w i t h t he l i nea r s ca l i ng dow nof t he co i l d i mens i ons , t he t a r ge t d i s t ance i s a l so l i nea r l ys c a l e d d o w n a n d t h e f r e q u e n c y i s i n c r e a s e d b y t h e i n v e r s esqua r e o f t he mi n i a t u r i za t i on f ac t o r [ 31 ] . The dev e l op me n t

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Rs . Popovic et aL I Sensors and Actuators A 56 I'1996)39-55 49o f h ig h - f r eq u en cy e l ec t ro n i c i n t e r f aces wi l l t h e re fo re b ereq u i r ed fo r t h e m o n o l i t h i c i n t eg ra t i o n o f m in i a tu r i ze d i n d u c-t i v e p ro x im i ty an d d i s t an ce sen so r s .

F ro m th e ap p l i ca t i o n s p o in t o f v i ew, b o th k in d s o f t h in -d i sk i n d u c t i v e sen so r s wi l l h av e i n t e r es t i n g p ro p er t i e s fo rc o m p l e x s y s t e m s w h e r e a r e g u l a t i o n s c h e m e i s a p p li e d . T h ed i s t a n c e t o b e m e a s u r e d w i ll t h e n b e m a i n t a i n e d c o n s t a n t.Th i s wi l l av o id t h e i n t r i n s i c n o n - l i n ea r i t y o f t h e sen so r , t h em a x i m u m o f s e n s i t i v i ty b e i n g s e t a t t h e p o i n t o f i n te r e s t. F o re x a m p l e , m i c r o s o l e n o i d s c a n b e u s e d a s a c t u a t o r s b u t a l s o a ssen so r s i n m ag n e t i c l ev i t a l i o n an d b ear in g sy s t em s . In t eg ra t edf i at co i l s wi l l a l so f i n d ap p l i ca t i o n s i n m e asu r in g t h e d i s t an ceo f m e t a l l i z e d m e m b r a n e s e s p e c ia ! l y in n o n - h e r m e t i c s y s t e m s ,wh e re i n sen s i t i v i t y to h u m id i t y an d d u s t i s r eq u ir ed .

I n t he l o n g t e r m , i n d u c t i w i m a g e r y a n d i m a g e r e c o g n i ti o nw i l l d e p e n d o n t h e i n t e g r a t io n o f l a r g e a r r a y s o f m i c r o c o i l s[ 5 6 ] a n d o n t h e d e v e l o p m e n t o f s i m p l i f ie d e l e c tr o n i c i n t er -f aces . In t h ese ap p l i ca t i o n s t h e n o n - l i n ca r i t y o f t h e sen so rs h o u l d b e u s e d a s a c o n t r a s t e n h a n c e m e n t f a ct o r. A s t r o n gl im i t a t i o n is se t b y t h e r e l a t i o n sh ip b e twee n t h e co i l d i am e te r ,wo rk in g d i s t an ce an d l a t e ra l r e so lu t i o n . L i t tl e wo rk h as b eend o n e t o d ev e lo p fo cu s f i e l d sen so r s , b u t t h e i n t eg ra t i o n o ft h e s e e l e m e n t s s h o u l d s ti ll b e r e a l iz e d [ 5 1 ] . A n o t h e rap p ro ach fo r im ag ery wi l l b e to r ep l ace t h e a r ray o f i n d u c t i v eco i l r ece iv e r s b y an a r r ay o f o th e r m a g n e t i c sen so r s l i k e Ha l ld e v i c e s , k e e p i n g t h e c o i l s a s e x c i t a t i o n e l e m e n t s . A d d r e s s i n go f l a rg e a r r ay s wi l l a l so b e an i s su e . No t i ce t h a t s im p l i f i eds c h e m e s ar e u s e d i n e l e c t r o n s p i n r e s o n a n c e ( E S R ) i m a g e r y[ 5 7 1 , a n d c a n g i v e n e w i d e a s f o r f u rt h e r d e v e l o p m e n t s ini n d u c t i v e i m a g e r y .

5 . F l u x g a t e s e n s o r sT h e f l u xg a t e m a g n e t o m e t e r [ 5 8 - 6 0 ! i s a m a g n e t i c s e n s o r

ty p i ca l l y cap ab l e o f m easu r in g d . c . o r s l o wly v a ry in g f i e l ds t r en g th s o f th e o rd er o f 1 0 " ) t o 1 0 4 T wi th a r eso lu t i o no f a p p r o x i m a t e l y O . 1 - 1 0 n T . I n t e r m s o f r a n g e a n d r e s o l u t io n ,t h e y f a l l i n to t h e c a t e g o r y o f m a g n e t i c s e n s o r s b e t w e e n t h ei n e x p e n s i v e H a l l d e v i c e a n d v e r y e x p e n s i v e s e n s o r s b a s e d o nq u a n t u m e f f e c t s s u c h a s S Q U I D s . T h e y f i n d m a n y a p p l i c a -t i o n s i n d i f f e r e n t e n v i r o n m e n t s ( e . g . , m i n e r a l p r o s p e c t in g ,s u b m a r i n e d e t e c t io n , m e a s u r e m e n t s in o u t e r s p a c e ) . S u c h awid e r an g e o f ap p l i ca t i o n i s d u e t o t h e i r ro b u s tn ess , r e l i ab i l it y ,s t ab i l it y , lo w n o i se l ev e l an d ec o n o m i c o p era t i o n .

Th e b as i c f l u x g a t e i s sh o wn in F ig . 1 2 . I t co n s i s t s o f af e r r o m a g n e t i c c o r e w r a p p e d w i t h t w o c o i l s , th e p r i m a r y o rex c i t a t i o n co i l , an d t h e seco n d ary o r p i ck u p co i l . Du r in go p era t i o n an a . c . ex c i t a t i o n cu r r en t I ~ a t a f r eq u en cy fo i sf o r c e d o n t h e p r i m a r y c o i l. T h e a m p l i t u d e o f t h e e x c i t a ti o ncu r ren t i s su f f i c i en t to sa tu ra t e t h e f e r ro m ag n e t i c co re wi thp erm eab i l i t y / . t . Th e r easo n fo r ca l l i n g t h i s d ev i ce a f lu x g a t et h e n b e c o m e s o b v i o u s . W h e n t h e f e r r o m a g n e t i c c o r e i s n o tsa tu ra t ed , b eca u se o f i ts h ig h r e l a t i v e p e rm eab i l i t y i t o f f e r s ap a th o f l o w m a g n e t i c r es i s t an ce t o t h e f l u x l i n es o f t h e ex te rn a lf i e ld B , (F ig . 1 2 ( a ) ) . W h en t h e co re is sa tu ra t ed t h e m ~ g -

"" \ (a) / "/ / -

I,,==.0 V,~

Fig, 12. The basic fluxga ling principle. (a) The central ferromagn etic corewith permea bil ity /~, surrounded by two coils, the excitat io n coil wh ichdelivers the excitat ion current/~,~ and the seconda ry o r p i c k u p coi l whichhas an induced vol tage V ~ be tw~ n i ts ends. When the exc itation is 7erothe core is non-saturated and thus wit h a high relat ive pe rmeabil i ty. T he f luxof the external magne tic ie ldBo is thus concentrated n the core, which s apath of low mag netic esistance..',b) The core is saturated by/c,~cand itsrelat ive perm eabil i ty (k 'creases. The f lux 8 o is then expulsed from the core.n e t i c r e s i s ta n c e o f t h e c o r e i n c r e a s e s a n d t h e e x c e s s m a g n e t i cf l u x li n e s a r e e x p u l s e d f r o m t h e co r e ( F i g . ] 2 ( b ) ) . T h ea l t e rn a t e g a t i n g o f t h e f lu x c a u s e s a c h a n g e o f f l u x t h r o u g ht h e p i c k u p - c o i l w i n d i n g s . I f w e e x a m i n e t h e r e s u l t a n t v o lt a g eV, ,. , i n t h e p i ck u p co i l we f i n d f ro m F arad ay ' s l aw o f i n d u c t i o nth a t

d B . Av ~.. = N - - ~ - + v ~ , ( 1 7 )w h e r e A i s th e v e c t o r s u r f ac e a r e a o f t h e c o r e p e r p e n d i c u l a rt o t h e co i ls , B i s t h e g a t ed f i e ld an d N th e n u m b er o f t u rn s i nt h e s e c o n d a r y c o i ls . T h e v a l u e o f B. A = KBoA, w h e r e K i st h e co n cen t r a t i o n f ac to r o f th e ex t e rn a l f i e l d b y t h e f e r ro m ag -n e t i c co re . Un fo r tu n a t e ly , i n ad d i t i o n t o t h e u se fu l p a r t o fV, ,~ , n am ely t h e fi r st te rm in t h e su m o fE q . (1 7 ) , t h e re is ap a r a s i t i c c o m p o n e n t V ~ c a u s e d b y t h e c h a n g e o f m a g n e t i cf lux m the core crea ted by the ex ci tat io n curren t Ic ,,~ .

F ro m th i s ex p l an a t i o n o f t h e o p era t i o n o f t h e f l u x g a t e , wesee w h ich f ac to r s i n f l u en ce t h e sen s i t iv i t y o f t h e d ev i ce . Ap ar tf r o m t h e o b v i o u s f a c t or s o f i n c r e a s i n g t h e n u m b e r o f t u r n s Nin t h e p i ck u p co i l an d t h e f e r ro m a g n e t i c q u a l i ti e s o f t h e co re ,o n e way t o i nc rease : : h e sen s i t i v i ty i s t o au g m en t t h e l en g tho f t h e co re i n t h e d i r ec t i o n o f t h e ex t e rn a l f i e l d , wh ichin creases K an d t h e g a t i n g f r eq u en cy fo .

T h e r e e x i s t t h re e m a i n m e t h o d s f o r e x t r a c t in g t h e l e v e l o ft h e ex t e rn a l f i e ld Bo f ro m th e o u tp u t s i g n a l V , ,~ : s e c o n d - h a r m o n i c p r i n c ip l e p u l se -p o s i t i o n p r i n c ip l e p u l se -h e ig h t p r in c ip l e

The secondJmrmonic principle i s b ased o n t h e f ac t t h a tt h e m ag n e t i za t i o n cu rv e o f t h e co re i s an u n e v en fu n c t i o n . I fan a .c . s ignal H( t ) a t f r eq u e n cy fo i s ap p l i ed t o t h e co re , i t

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50 R.S Popovic et al. / Se,txor.~ and Actuators A 5o (1996) 39-5 5

~ ~ Excitationcoll

l P , o , ,o c o i ,Excllalion :oli PickupcollaxFig . 13. (a) A do ub le-co re f l uxgate cons is ting o f tw o co-cs wrapped wi ththe exc i ta t io n co i l s i n opp os ing d i rect ions . The sum o f the two f ie lds B~ . ',ndB2 caused by I== s ze ro i f the t wo cores are per fec t l y matched. Thus thef l u x s e e n b y t h e p i c k u p c o i l t h a t s u r ro u n d s th e t wo c o re s s d u e o n l y t o a ne x t e rn a l f i e ld . ( b ) Th e e x c i l a t i o n a n d p i c k u p c o i l a re o n h o g o n a l t o e ac hother and hence the f lux produced by the exc i ta t ion current w i l l no t be scanb y t h e p i c k u p o il .

c a n b e s h o w n t h a t t h e vo l t a ge V , d c o n t a in s o n l y o d d h a r -m o n i c s o f fo . Ho w ev er , i f t h e ap p l i ed m ag n e t i c s i g n a l co n t a in sad .c . co m p o n e n t ( i . e . , d u e t o t h e ex t e rn a l f ie l d Bo ) t h en ev en -h a r m o n i c c o m p o n e n t s a r e i n t r o d u c e d a n d t h e a m p l i tu d e o ft h e seco n d h arm o n ic a t a f r eq u e n cy 2 fo i s p ro p o r t io n a l t o t h eam pl i tu de of the f ie ld Bo. The s ignal V,, ,~ s then pro cess ed toex t r ac t t h i s seco n d h arm o n ic an d r ec t i fy i t t o o b t a in a d . c .s i g n a l p ro p o r t i o n a l t o B0 . Th ere a r e tw o m ean s o f r em o v in gth e p a ras i t ic c o m p o n en t Vp ~ d u e t o t h e ex c i t a t io n so u rce a tthe f re que ncy fo . On e i s to f i l ter V, ,d elect r ical ly ; the o ther i st o f i l te r th e s i g n a l m ag n e t i ca l l y b y d es ig n in g t h e sen so r su chth a t t h e p a ras i ti c t e rm i s can ce l l ed . Th i s can b e ach i ev e d i ns e v e r al w a y s , t w o o f w h i c h a r e u s i n g t w o c o r e s t h e m a g n e t -i za t i o n s o f wh ich can ce l (F ig . i 3 ( a ) ) , o r p l ac in g t h e p i ck u pco i l o r t h o g o n a l t o t h e ex c i t a t i o n co i l (F ig . 1 3 (b ) ) . I n eachcase t h e o n ly f l u x ch an g e seen b y t h e p i ck u p co il i s th a t cau sedb y t h e g a t ed ex t e rn a l f i el d . By e l im in a t i n g t h e co m p o n e n t a tfo t h e e f fo r t r eq u i r ed t o ex t r ac t t h e u se fu l seco n d h a rm o n ic i sco n s id e rab ly r ed u ced . Go o d o p era t i o n o f a d o u b l e -co ref l u x g a t e r eq u i res t h a t t h e two co res b e p e r f ec t l y m atch ed ( i. e. ,t h e i r m a g n e t i c ch arac t e r i s t ic s an d g eo m et ry ) wh ich i s n o t aneasy task . S im i lar ly for the or lhog .~nal f luxgate, whe re i f thetwo co i l s a r c n o t p e r f ec t l y o n h o g o n a l t o each o th e r a co n t ri -b u t i o n f ro m Vt,~ w i l l appea r in Vi ,d-The pulse-position principle i s b ased o n t h e ch an g e i n t h ep u l se p o s i t i o n o f t h e v o l t ag e i n t h e p i ck u p co i l , wh ere t h i sch an g e i n p o s i t i o n can b e r e l a t ed t o t i l e m ag n i tu d e o f t h eex t e rn a l f i e l d Bo. Th i s a l l o ws fo r easy i n co rp o ra t i o n i n to ad ig i ta l m easu r in g sy s t em , as t h e m a g n i tu d e o f t h e f i e l d Bo i seas i l y t r an s fo rm ed i n to a p u l se -wid th -m o d u la t ed ~ ig n al .The pulse-height principle i s based on th e fact that increas-i n g Bo cau ses t h e p eak s o f ~h e p i ck u p co i l v o l t ag e t o i n c reasein o n e p o l a r i t y an d d ecrease i n t h e o th e r . Th e d i f f e r en ceb e tw een t h e n eg a