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Abstruet

SCtl'Ol' ,lIlll Atluator" A 61 ( J9(7) J39-J..t I

A micromachined silicon magnetometer

F. Ayela *, T. Fournier, 1. ChaussyC('IIf/I!(/e R/!l-Il/!rcllt.' \/11 I/!\ "lre\ J!(III/.',\ T('IIIJIf!lCltllrtJ~. CNRS. BP 1M, F·3{I)0.J2 GIf.'lloble CC'(!t'l 9, Fnmel'

seNSORsACTUAfORS

APHYSICAL.

A nowl magnetic !lem.or I~ under invc\tigation. Tlth devIce h a bldll1lcl1~lOnal genclall/ntion of vibrnling reed magnetometers, and b.intended to be~ell!'lltlve to very low magnetic lield!oo (abouIIO- 'IT Hz- 1/2) and to very low magnetic moment!oo. Thi!< !lcl1!loru'\c\the magneticforce which acl!l on a sample of tolal llmgnclwluon M \ubmittcd to a magnetic field grulllcnt gr~ld8. The dcformmioll caused by the lorceapplied to a Ihm Mlicon mClllbnmc can be cap:tcllively detected. Whclllhc lield gradient IS 'Ul alternatlng olle 'It the rc!\onJnce frequency ofthe membrane, the deformation 1\ enhallced by (he Q-f:'lctor. With \uch adeVice, one could perform mugnetlc mCU"lirement~ with ull\urpa~~ed

\ell!tilJVIUe~ over aWide range ortemperaturc. An experlmcntal !\ct-up to perform Qmca\urClI1cnt\ 011 Si mCl11bmnc~ !tubmj(tcd to an allernatlngelectro!tt311C force 1\ uho dC!\CI Ibed

K('\,II(}/(I\. Magncllc \cn"or\. SilIcon IllCmhr,llle\. Eleclro\WIIC lor~'c Q-fac(or"

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1. Introduction

The most sensitive magnelic devices are up to now quan­tum interferometers whose superconductlllg properties Implythe use of a cryoge",c infrastructure. We urc eluborating asensor which can act over a Wide range of temperature,because it IS bu,ed on the mugnetic force which derives from'he magnctic potential E= -MH, where M is the magneticmoment of a sample or of a thin liIm under investigatIOn.When this sample is submitted to an alternating magneticfield gradient, the magnetic force will move it periodIcally.This method has ulready been used wllh cantilevers [1-31.We wunt to upply Il to a thin nllcromachined siliconmembrane, in order to measure capacillvely the magnetiza­tIOn vru the thin membrane deformation, and to increase thesensitivity. We present the sensor concept. an estimation ofthe sensitiVIty and an expelimentul set-up built to mea,urethe Q-factor of silicon diuphragms.

2. Sensor concept

The magnelic force is a consequence of the pocentialE= - MB. When M is ,patially umfonn. the resulting forceF, ulong the direction: IS

uB, aB, uB,F,=M' a: +M,·u: +M'ilz

'" ConC\pOndlOg author, Tel.. +33476889071 F.II(.· +33476885060

0924·-1247/97/$1700 © 1997 EI~cvlcr SCICOlC S A. All nghh rc\ervedPII 50924-424 7 (97) 0 I489-1

M" M, and M, urc the components of the magnetic momentM under invcstigation. uBla: b a magnetic field g-adientcontrolled by the u,er. C1u"ical values of uBli!: range from0.5 to 5 T m-1 II]. An alternating field gradient gives wayto an ulternating force. Fig. I shows the sen'or concept. Thesample is fixed on thc silicon membmnc in front of a fixedelectrode plute. mordcno produce uvariable capucitor [4,5].Coils produce an alternullng magnetIc field gradient A cor­rect orientatIon 01 the'e coils may select un uppropriate com­ponent of dlJlul, und so the rcsulting force F, is proportionalto M" M, or M,. It is obvious that thc frequency ofaBla: husto bc sct to Ihe mechanicu' resonance frequency of the Si

I Sisubslralc2 SI dIaphragm3GIJsselcclrOde4 Sample of magnetic momenll\t5 MagnctlccOlI~

.. Melalhzcdarcas

fig. I Schcm.llh: concept of the magncllc \Cll\Or.

.140 F. Aye/a t!t (II. /St!I/f(}I~ lim! Al.tJlator.!J A(j/ (/997J 339-34/

3. Qmeasurements

membrane with the sample. The maximum deflection of themembrane is

where G is the total gain ofamplification. Afrequency sweepallows the resonance frequency to be determined and C to bemeasured.

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Biasing the capacitor with Ii V= V+vcoswt, where V» ",gives rise to an electrostatic fOlce F= Fo+FJe1ldf +F2e12

/JJt,

where Fu=Fo(V'), F,=F,(V,,), F,=F,(v'). One hasF,« F, «Fo. As a consequence, the 5i diaphragm will onaverage move as

z(t) =zo+z,exp[j(wl+c/>I») +z,exp[j(2wl+q,2)] (5)

The current flowing through the capacitor and the loadresistance of the field-effect transistor assuming the first stageof amplification is

i=C~1i V+!iV~dt dl

because C is a function of time.When the excitation is made at the resonance frequency

w= wo, z, is amplified by Q, and cjJl = -1T12. The capaci­tance is

C",C*(1 + ~;r sin wut+~ cos 2wut-(Q;')' sin'w"t) (7)

with C· = foilld, as long as Q<I «d and z, «d.One finds:

i= woC*( vaf, cos w"t-" sin WoI+"af, cos 2wut

-2vaf, sin 2Wot}

where the relative variations aft and af, are

aft =Qz,d

af,=~+~(QZJ)' ",~(Qz,)'-d2d 2d

The analysis of the in-phase term in coswol allows us tod~termine the Q-value. The amplitude z, is a fU'lction of F,which varies as Vv, so that i(cosWot} = wuC*V must vary asV' for a fixed value of v af, is varying as V',,', so that thequadratic term in sin2wol must be a function of V'v'.

For all the tesled diaphragms, a frequency sweep per­formed under a primary vacuum of 0.3 torr has shown thatthe mechanical resonance frequency is in the audio frequencyrange ( '" 8-10 kHz). The evolution oftlte ullJphfied voltageat Wo allowed the Q-value to be determined. Recent resultsarc reported in Fig. 3. This is the evolutIOn ofthe input voltageV,,(wo) =Ri(wo) as a function of V'. The hnear aspect ofthe plots is well established. The dete'mined Q-valueobtained from the experimental data is around 300. Probablythis low value is caused by the poor vacuun,le,el [6]. Theevoluti'ol1 of the quadratic term at 2wo is plotted in Fig. 4 asa function of V',,'. The linear variation confirms that theabove calculation and the experimental Q-vnlue agree Withthe one found before.

The principle of Q measurement now being well estab­lished, the experimental set-up is being enhanced to reach a

4. Future prospects

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IiC QAF.

c= 16EN

Relative changes IiclC of 10-7 can be easily detected.With classical values such as Q= 5000, A=5 mm', E= 10"N m-', 1=3 f1m and d= 10 f1m, one can detect a value ofF,'" 10-1S N, corresponding to 10- 12 emu OrlO about 10-14T with perfect diam,lgnetism of a superconducting thin film.

H(w)=jGRCw

where E is the Young modulus of silicon, Q, A and I are thequality factor, the area and the thickness of the dltlphragm,respectively. It can easily bc shown that the capacitance ofsuch a system is C=foil/(d-z) where d is the distancebetween the two electrodes of the capacitor and z= z,,/3.

The relative variation of C is

Various silicon diaphragms with relatively large areas( '" 0.5 cm X 0.5 cm) have been made following classicaletching techniques. Their thickness runs from 2 to 8 f1m. Anapproximatly 1000 Athick gold or niobium layer was sput­tered onto the 5i diaphragms to ensure the electrical conduc­tivity ofthe moving electrode. Recesses were etched in piecesof Pyrex and metallized to form an air gap ( '" IS f1m) ?udone of the capacitor pl?tes. The capacitance of such devicesIS about a few picofarad.

We have used the electrical set-up shown in Fig. 2 to studythe d)namic properties of the 5i diaphragms. An alternatingvoltage /lcoswl is applied to an RC series circuit where C isthe capacitance of the sensor and R the load resistance at theinput of the field-effect transistor. The transfer functionH(w) =GV"lv is

Fig 2. Electronic deSign lonpply an electrostatic force onto the Si diaphragm.The 100 nF capacitor and the 10 Mil re~lstor have to prevent the electromccirCUitry from any dnmage caused by the high contmuou.. voltage V. whenthe 51 electrode louche:. the other electrode of the capJcitor C.

F. Aw!la et al /Sell.lor~ wul AclIllIton A 61 (1997) 331)-34/ 341

160- • -v,,'O,5V.. 0-. v",:lV

0- vO#'2V

tion, These preliminary steps are preceding the magnetic­sensor realization itself.

Rderenccs

40

.0

~---~-~-~-~-:~-~-~:--- ~OL.....~--'-~.........~~--"-'~.-1..~---.J

o 2000 4000 6000 8000 10000V 'tV')

Fig. 3. MiI ..illlUlll mea~ured voltage V,: lllea"ureu at the rc'\onanee Ircqucncyu" a functioll f)f V2• for diffcrent .llternllting voltage" I' A\ predicted, theevolution i" linear und allow'\ the Q-value of tile re"onatorlo he dctcrmined

100

( ro=tOOo

)

10:;- .,.:; •,5> •.,

•.'

0.110' 10' 10' 107

v.',V: (Vs)Fig 4, M.lxlmum vollJgc V,n mea"ured at 2~). •1\ II function of V ll'~ ThiSplololgree'\ wIth the expected evolulloll. and 1\ another WolY to determme theQ-valu~ of the dillphragm.

vacuum better than 10-' tOIT. Sr,veral SI membranes withdifferent types of vibratmg mode:; are now under investiga-

1r I W. Rom. KA Hempel. C. Voigt. H Dedench" .md R Schipper. High!'len~ltlvlly vlbratmg reed magnetometer, Rei'. Sci.III.~lrlllll" 51 (1980)612-613.

[21 H. ZijI"tr,l. A vlbr.llln£ reed magnetometer for mlcrm.coplc partlc!e:-.,Rei'. Su Imlmll/,,4/ (1970) 1241-1243.

13 J PJ, Flanden.. An ultemuting-grudlent mllgnetometel.J Appl. Plnf .63(1988) 3940-3945,

[41 P. Roth ilnd E, Gmelin. A colpacitanc.e dh.placement 'oen'oor with cl.l"ticl.haphragm. Rei'. SCI, Imlrlllll" 63 (1992) 2051-2053.

[51 PG Dolrgie ,1111.1 S,T. Hughc". A thick· film C.lpJClllVI; differentialpre\'iure tran\duccr.Mc(j\ SCI. Tee/mol. 5 (1994) 1216-1220.

[61 JC. Greenwood, Etched \dlCOn vibr.lting :-,cl1\or.J, p".l'f E.17 (19K4)650-652

Iliographics

Frederic Aye/a received a Ph.D. degree In solid-state phys­ics from the Universil" Joseph Fourier de Grenoble in 1993.He became an assistant profes<OI at this univerSIty in thesame year and is working on solid-state physics experiments.

711ierry Fomllier is a research engineer. He received aDoctorate ofPhysics from the Institut National Polytechniquede Grenoble in 1986. Since 1988, he has worked for theCentre National de la Recherche Scientifique,

Jacques Clwus.\y is a re~earch director at the CentreNational de la Recherche SClentifique, HIS research team setup very sensitive devices in order to perform fundamentalphysics experiml'nt' at very low temperatures,