A High-Performance Tunneling Accelerometer

Transcription

1 A Hgh-Performance Tunnelng Accelerometer Edward Boyden Osamah El Rfa Bran Hubert Maurce Karpman Dave Roberts Term Project 6.777, Introducton to Mcroelectromechancal Systems Sprng 1999, Prof. Stephen D. Sentura

2 TABLE OF CONTENTS I. INTRODUCTION... 4 I.1. PROBLEM STATEMENT... 4 I.. SCANNING PROBE MICROSCOPY... 4 I... Tunnelng... 5 I... Current, appled bas, and tp-electrode separaton... 5 II. DESIGN METHODOLOGY... 8 III. PROOF MASS AND MECHANICAL DESIGN... 9 III.1. GENERAL DISCUSSION OF ACCELEROMETER GEOMETRY AND SPECIFICATIONS... 9 III.1.. Accelerometer Senstvty... 9 III.1.. Accelerometer Response Tme III.1.. Cross-axs senstvty III.. OVERVIEW OF CANTILEVERED BEAM DESIGN IV. SYSTEM MODEL IV.1. BEAM FLEXURAL DYNAMICS IV.. SQUEEZE FILM DAMPING...15 IV.3. ELECTROSTATIC ACTUATORS IV.4. MODELS FOR THE FEEDBACK ELECTRONICS IV.5. BEAM DESIGN: DYNAMIC CONSIDERATIONS IV.6. LOCATION OF ELECTROSTATIC PADS IV.7. VACUUM OPERATION IV.8. LINEARIZATION AND TUNNELING SET POINT: IV.9. CONTROLLER DESIGN IV.10. SIMULATION RESULTS... 0 V. ELECTRONICS... 8 V.1. DESIGN PRINCIPLES... 8 V.. SINGLE-CONDUCTOR DESIGN... 8 V.3. INSTRUMENTATION: ELEMENTS... 9 V.4. INSTRUMENTATION: MODEL V.5. INSTRUMENTATION: IMPLEMENTATION VI. PROCESS FLOW VI. 1. OVERVIEW VI.. THE PROCESS FLOW VII. CONCLUSION APPENDIX A A.1. BEHAVIOR OF A CANTILEVERED BEAM A.. CROSS-AXIS SENSITIVITY...46 A.3 TOLERANCE ANALYSIS A.4 DETAILED GEOMETRIC CONSIDERATIONS APPENDIX B... 51

3 B.1. OVERVIEW B.. THE PROCESS FLOW... 5 REFERENCES BIBLIOGRAPHY... 58

4 I. Introducton I.1. Problem Statement The goal of ths project was to desgn an accelerometer based on the operatng prncples of Scannng Probe Mcroscopy (SPM. The process was constraned to form the tp on the same wafer as the proof mass. The performance targets for the devce were as follows: Full range 5g Response tme 10ms Lnearty <1% Cross-axs senstvty <1% Self-test output.5g Shock survvablty 100ms, 100g shock wth 1ms rsetme I.. Scannng Probe Mcroscopy A number of technques have been developed whch allow surfaces to be maged wth subangstrom resoluton. These technques all nvolve a tp on the end of a cantlever whch s brought nto close enough proxmty to a surface to nteract wth the surface. Measurement of the nteracton allows determnaton of the heght of the surface at each pont. The tp s scanned over the surface to create an mage of the surface. These technques are collectvely known as Scannng Probe Mcroscopy (SPM modes (How93. The senstvty of SPM modes to deflecton of the cantlever makes them excellent canddates for the fabrcaton of hgh senstvty accelerometers. The frst decson the team faced was selectng the SPM mode for ths project. The modes can be grouped by the method used to determne the vertcal poston of the tp. Three detecton methods are n use; pezoresstance, optcal and tunnelng current. Poston detecton usng pezoresstance s accomplshed by fabrcatng a pezoresstor at the root of the cantlever and measurng the change n resstance as the cantlever s deflected. Ths method s relatvely poor at measurng small deflectons and therefore yelds relatvely low resoluton. Moreover, pezoresstve elements generally have complex varatons wth temperature. For these reasons, pezoresstve technques are not approprate for constructon of a hgh senstvty accelerometer. The second, and most common, method of determnng the vertcal poston of the tp s optcal. A laser beam s bounced off the back of the cantlever onto a poston senstve photodetector. Deflecton of the cantlever causes the poston of the beam on the detector to shft. The rato of the dstance from the cantlever to the detector to the length of the cantlever amplfes the moton of the beam. As a result, ths method can acheve sub-angstrom resoluton. The optcal method has several advantages; t s extremely senstve, t does not requre a vacuum, t can be used wth conductve and nsulatng samples, and t can be used wth a varety of SPM modes. However, the need for a laser dode and a photodetector, and the sze penalty mposed by the optcal method make t undesrable for an SPM accelerometer.

5 The thrd method used to determne the vertcal poston of the tp s to measure the tunnelng current between the tp and the substrate. Ths was the frst SPM mode developed. Because the tunnelng current s exponentally dependent on the separaton between the tp the substrate, the dstance between the tp the substrate can be measured to wthn 0.01 Angstrom. Despte the senstvty of tunnelng, t has been largely dsplaced by optcal methods because t requres a vacuum for magng oxde formng samples and can only be used wth conductve tps and samples. These drawbacks are not serous mpedments to the constructon of an accelerometer. As a consequence, all of the SPM accelerometer work the team encountered n the lterature reles on tunnelng current as the detecton method. Based on the above logc and the exstence proof of tunnelng accelerometers n the lterature, the team selected tunnelng as the SPM mode for ths project. I... Tunnelng The proposed mcroelectromechancal (MEMS tunnelng accelerometer uses a general prncple of operaton that s commonly used for scannng tunnelng mcroscopy (STM. In STM a bas voltage s appled between a sharp metal tp and a conductng sample. When the tp and sample are brought to wthn a few Angstroms (Å of each other, a tunnelng current can flow due to quantum mechancal tunnelng effects. Because the tunnelng current s exponentally dependent on the separaton between the tp the sample, the dstance between the tp the sample can be measured to wthn 10-3 (Å. Due to ths hgh senstvty to poston, we propose that a MEMS cantlever structure wth a varable gap between an ntegrated tunnelng tp and a conductng electrode can be used n the constructon of a tunnelng accelerometer. Due to the excellent stablty of ts surfaces n vacuum or ambent gases, gold s the tunnelng materal of choce for both the tp and the electrode. Ths prevents drft n the observed tunnelng current over tme. However, platnum-rdum alloys wth low reactvty can also be used to form the tp and the conductng electrode of the proposed tunnelng accelerometer f very hgh fabrcaton temperatures lmt the usefulness of gold. I... Current, appled bas, and tp-electrode separaton For the followng dscusson, we consder only the case of a one-dmensonal metal-vacuummetal tunnelng juncton. Ths s the confguraton for the proposed tunnelng accelerometer when operated wthn a vacuum nstead of ambent gas. If the lateral dmenson of the tp end s much larger than the characterstc wavelength related to the decay constant, π / κ 6 Å, whch s expected for the proposed fabrcaton technques used to create the tp, the one-dmensonal treatment of tunnelng parameters are approxmately accurate (Che93, p. 7 The followng symbols are used n subsequent equatons and wll now be defned: E energy of the electron; typcally measured n electron volts (ev, where 1 ev = J. V the appled voltage bas appled between the tp and the conductng electrode; n classcal mechancs the electron may not penetrate nto any potental barrer wth E < U (z m electron mass = grams

6 ! Planck constant over π ; ev s = J s φ effectve local potental barrer heght; also used nterchangeably wth the work functon of a metal surface; usually refers to the conductve electrode and not the tp; defned as the mnmum energy requred to remove an electron from the bulk to the vacuum energy level; when measured n ev, the work functons of metals range from 4.1, 4.6, 4.8, and 4.8 for Al, Cu, W, and S on the low end to 5.4, 5.6, and 5.7 for Au, Ir, and Pt on the hgh end [HCP]. Θ electron decay rate (n unts of Å -1 ; descrbes a state of the electron decayng n the postve z drecton through the nsulatng barrer z postve z s n a drecton parallel to the "thckness" of the nsulatng barrer; z = 0 s located at the boundary of the metal sample and vacuum; z = s s located at the boundary of vacuum and the metal of the tp s the gap separatng the tp from the conductng electrode; usually measured n the Angstroms; the gap s usually occuped by vacuum or ambent gas Let us frst consder tunnelng between metal tp and the conductng electrode wthn the lowbas regme. Typcally ths means that the voltage between the tp and the conductve electrode s n the mllvolt range. Dependng on surface preparaton, tp geometry, tunnelng medum, and other factors, tunnelng currents can range from nanoamps to mcroamps. In the low-bas regme, the vacuum tunnel juncton exhbts Ohmc behavor so that tunnelng current I s lnearly proportonal to the appled bas V. At the same tme, tunnelng current vares exponentally wth sze of the gap s between the tp and the plug. These relatonshps are llustrated n the followng equatons: ( sθ I V e (a where the electron decay rate Θ n unts of Å -1 s obtaned by Θ = mφ 0.51! φ (b For example, f we assume a typcal surface work functon of 4 ev, the value for the decay rate Θ s about 1 Å -1, and the current decays about e 7.4 tmes per Å of gap. The dependence of the logarthm of the tunnelng current wth respect to dstance s a measure of the work functon, or the tunnelng barrer heght. In fact, at constant appled bas V, As a consequence, we fnd φ [ ev ]! d ln I = 8m ds d ln I ds const d ln I 0.95 ο ds Α (c (d In smlar fashon, at constant tunnelng current,

7 φ [ ev ]! d lnv = 8m ds d lnv 0.95 ο ds Α (e Therefore, n the low-bas (mllvolt lmt, where the tunnel juncton exhbts Ohmc behavor, we smply fnd di I = (f dv V Therefore, equaton (a reduces to I V e (( const ( s because φ const and Θ const. In summary, the appled bas voltage vares wth the tpelectrode separaton f the tunnelng current s kept constant. For a constant tunnelng current I, the quantty di dv therefore dverges lke 1V as V approaches zero. The problem of 1 V dvergence can be solved by operatng at a constant tunnelng conductance σ = I V nstead of constant tunnelng current [We, p. 148]. For standard tunnelng operatons, tp-electrode dstance ranges between 1 Å and 4 Å, whch provdes a correspondng conductance range of 10-6 to 10-8! -1. When taken to the logcal concluson, operaton at constant conductance yelds constant tp-sample separaton dstance s, as shown n the followng dervaton: (g σ = I V = const e (( const ( s (h ln const ( s const s = const ( (j It should be noted that equatons (h, (, and (j only hold n the low-bas regme when voltage and current and lnearly related. For hgher bas (on the order of volts between the tp and the conductng electrode, the bas-dependence of the tunnelng current generally does not exhbt Ohmc behavor. In the hgher bas regme, the electronc states of both the tp and the electrode contrbute to the tunnelng current, and these states are dependent on the appled bas voltage. Tunnelng current s proportonal to a transmsson coeffcent, whch tself s dependent on the bas. In general, the bas-dependence of the transmsson coeffcent at hgh-bas leads to an order-of-magntude ncrease n the tunnelng current for each volt ncrease n appled bas voltage (We94, p. 18. In short, a tunnelng accelerometer can operate wth constant current, constant voltage, or constant conductance. For reasons that are explaned n the sectons on control crcutry, our proposed accelerometer operates at constant voltage n the low-bas mllvolt regme.

8 II. Desgn Methodology The process flow for the desgn of ths accelerometer s shown n Fgure 1 and can be descrbed as follows. The requrement on full-scale acceleraton and the chosen method of sensng dctate the requred z-axs senstvty of the devce. Ths z-axs senstvty then dctates the geometry of the proofmass. For a determned proofmass geometry, basc open-loop performance crtera can be evaluated, such as beam stffnesses, modal frequences, and cross-axs senstvtes. Once ths proofmass geometry satsfes the basc performance crtera, more n-detaled desgn procedures and analyses are carred out to determne the electroncs desgn, the pad layout, the tunnelng tp geometry, the detaled mcrofabrcaton process flow, and characterstcs assocated wth the detaled feedback smulaton. Ths process s an teratve one, and much of the desgn nvolves tradeoffs between varous parameters. Full-scale Acceleraton = 5g Electron-Tunnelng Method Senstvty or k/m rato Beam/Proofmass Geometry Open-loop Behavor Stffness ModalFreqs Cross-axs senstvtes Tunnelng Tp Geometry Devce Fabrcaton Process Flow Electroncs, Pad Layout Feedback Smulaton Response Response Tme Dampng Lnearty Self-Test Shock Survvablty Fgure 1: Desgn Process Flowchart

9 III. Proof Mass and Mechancal Desgn III.1. General Dscusson of Accelerometer Geometry and Specfcatons The sensng means chosen for ths proposed accelerometer s electron-tunnelng current. Ths method of sensng acceleraton requres the ablty to control the moton of the devce s proof mass wthn a dsplacement range of approxmately 1 Angstrom. The bulk of successful accelerometers on the market today use other methods of sensng, such as capactve or pezoresstve, whch requre sgnfcantly larger ranges of moton (on the order of hundreds or thousands of angstroms than that requred by electron-tunnelng sensng. It s ths dsplacement range that dctates the complexty of the proof mass desgn. As wll be dscussed n ths secton, whereas these other sensng types of accelerometers are requred to possess large bulk mcromachned proof masses suspended by ntrcately shaped tethers to successfully satsfy senstvty specfcatons, the electron-tunnelng accelerometer s able to use a much smper surface mcromachned cantlever beam structure. III.1.. Accelerometer Senstvty An accelerometer s senstvty s a functon of the requred magntude of acceleraton to be sensed and the method of sensng. The nverse of ths senstvty can be descrbed by the k/m rato, where k s the stffness of the proof mass sprng and m s the mass of the proof mass. These characterstcs are derved from a smple statc force balance on the proof mass tself, where a s the magntude of acceleraton and z s the proofmass dsplacement: Fsprng = Facceleraton kz = ma k a = m z k " " m rato 1 = senstvty For example, gven an accelerometer full-scale requrement of 5g and an electron-tunnelng range of 1A, an estmate for the k/m rato and senstvty can be derved: k 5g = = 50. x10 11 s m 1A or senstvty = 0. x10 1 s For capactve or pezoresstve accelerometers under the same 5g requrement, snce the dsplacement ranges are on the order of 1000, the requred k/m ratos for these devces are 3 orders of magntude smaller than for the proposed tunnelng current accelerometer. As a result, these types of accelerometers requre a combnaton of larger mass and reduced proof mass stffness. Typcal bulk mcromachned proof mass geometres for capactve or pezoresstve accelerometers are shown n Fgure.

10 Fgure : Typcal Bulk-Mcromachned Proof Mass Geometres (Left:Deb90; Rght:Ash95 These geometres are characterzed by very large proof masses suspended by ntrcately shaped tethers. In comparson, the proposed electron tunnelng accelerometer can use a smple surface mcromachned cantlever beam to satsfy a much larger k/m rato characterzed by reduced mass and ncreased stffness. III.1.. Accelerometer Response Tme The response tme of the devce s dctated prmarly by the natural frequency of the proof mass. In modelng a smple sprng-mass system, the natural frequency s descrbed by the followng relaton: k ω n = m As a result, accelerometers that possess very small senstvtes (or large k/m ratos nherently have hgh natural frequences. For a smple sprng mass second order system (assumng crtcal dampng, the response tme can be estmated by: t response = 4 ζωn In realty, ths expresson s actually the defnton of settlng tme, but for conservatve estmates t s used here for the response tme. Accelerometer s that possess hgh natural frequences therefore exhbt very fast response tmes. Reorganzng ths expresson, and baselnng a requred response tme specfcaton, t response, a lower bound for the requred proof mass natural frequency can be derved: 4 ωn = ζ t response Snce the requrement for ths accelerometer s t response = 10 ms, the lower bound for requred proof mass natural frequency s:

11 4 ω n = = r s x / ( ( s Ths natural frequency puts the followng requrement on the k/m rato for the proof mass structure: k ( 565r/s m k 3.x10 5 s m Based on these smple arguments, t s clear to conclude that f the proof mass structure satsfes the 5g acceleraton requrement above, t wll automatcally satsfy the response tme requrement. Ths s a beneft of usng such a small dsplacement range technque as electrontunnelng current sensng. III.1.. Cross-axs senstvty In any accelerometer, t s crucal that the z-axs senstvty be at least two orders of magntude smaller than any other axs. Otherwse, the desred z-axs output sgnal from the accelerometer wll nclude unwanted cross-axs behavor. A sgnfcant advantage n usng a smple constant thckness surface mcromachned cantlever beam structure rather than a large bulkmcromachned proof mass desgn s the nherent reducton n ths cross-axs exctaton. The problem wth most large bulk-mcromachned proof mass structures s that the center of gravty of the proof mass s sgnfcantly far below the plane comprsng the tethers that form the proof mass sprngs (agan see Fgure. Rockng moton s therefore a challengng ssue to overcome. The cantlever beam desgn elmnates ths problem altogether snce the beam s of constant thckness throughout. The tunnelng tp, located close to the beam free end, does protude below the beam, but because the tp s extremely small n volume compared to the beam dmensons, any transverse full-scale acceleratons n the x or y drectons produce mnmal tp moton n the z-drecton. Consequently, cross-axs behavor s mnmzed wth such a cantlevered beam desgn. Based on these concse arguments concernng z-axs senstvty, response tme, and cross-axs senstvty, a cantlevered beam proof mass geometry s baselned. III.. Overvew of Cantlevered Beam Desgn The proposed electron-tunnelng current accelerometer contans a cantlevered beam, shown n Fgure, wth the followng dmensons, where L s length, W s wdth, t s thckness, gap s the spacng between the substrate and the undersde of the beam, rho s materal densty, and E s the materal Young s modulus: L = 70 um W = 60 um t = um gap = 1.5 um rho = 300 kg/m3 E = 190e9 Pa

12 The tunnelng tp s located at the centerlne of the beam wdth and s spaced 10 um from the free end of the beam. The tp s 1. um n length and um n dameter. An SOI approach was selected for creaton of the beam due to the predctable propertes and low bult-n stress of sngle crystal S (see Fabrcaton dscusson. The base structure supportng the beam s comprsed of SO materal and has dmensons 40 um x 40 um. x 1.5 um thck. 40 um 40 um Z X Y L = 70 um S W = 60 um t = um gap = 1.5 um SO Fgure 3: Fnal Proofmass Beam Geometry Smple analytcal models of the beam were ntally used to estmate z-axs senstvty, x-axs senstvty, y-axs senstvty, the cross-axs senstvty and the beam modal frequences. Usng both analytcal expressons and a detaled ANSYS fnte-element model of the beam, tolerance analyses of the beam length, wdth, thckness, densty, and Young s modulus were performed as well as nvestgatons nto the effect of the base structure dmensons, the base structure materal, thckness varaton along the beam, thckness varatons across the beam, and tunnelng tp placement. These analyses are ncluded n Appendx A. Mode shapes of the fnal beam desgn are shown n Fgure 3. The fnal characterstcs of the cantlever beam structure (open-loop wth no feedback are now summarzed. z-axs senstvty =.41e-11 s (or a k/m rato = 4.145e10 s - y-axs senstvty =.680e-14 s (or a k/m rato = 3.731e13 s - z-axs senstvty = 3.577e-16 s (or a k/m rato =.796e15 s - Cross-axs senstvty = 3.78e-17 s (~0.000% of z-axs senstvty Modal Frequences (based on FEM: f1 = (1 st z-axs bendng f = ( nd z-axs bendng f3 = (1 st torson f4 = (3 rd z-axs bendng For ths baselne fnal desgn, the nd mode frequency s tmes the frst mode frequency and therefore consderaton of only the 1 st mode dynamcs n the full smulaton s justfed.

13 IV. System Model There s a need to develop a fnte-dmensonal lnear dynamc model of the system to be used n desgn analyss and feedback desgn. A more comprehensve model, ncludng real-devces behavor, s requred for better evaluaton of the expected devce performance. In what follows, models for the major system components wll be presented. acceleraton m eff Set pont Control DAC I Amp. V Electrostatc Actuator F a Beam z t I tun Tunnelng Amp. V tun ADC Fgure 4: Block dagram of controller IV.1. Beam Flexural Dynamcs The cantlever s modeled usng elementary beam theory. In elementary beam theory, beams are assumed to have a tall cross-secton,.e. a plane stress condton. However, the beam under consderaton s of a wde cross-secton,.e. a plane stran condton. The elementary beam theory s stll applcable provded that the modulus of elastcty E, be replaced by E/(1- ν, where ν s Posson s rato. Consder the beam of Fgure 5, wth appled electrostatc actuaton and self-test forces, F a and F st, respectvely. The forces are modeled as concentrated loads actng at a dstance x a and x st, respectvely, measured from the fxed end of the beam. Dampng force proportonal to beam velocty relatve to ts base, F d = c z( x, t, s assumed. The effect of tp mass s neglected and justfcaton wll be gven n (some where n Dave s secton??. Usng the prncpal of vrtual work, and assumng a vrtual dsplacement δu(x,t, the governng equaton of moton of the beam s gven by, 4 ( z + zb z E I z ( δu( x, t ρ A δu( x, t + c δu( x, t + dx = F u( x, t F 4 a δ a + t t 1-ν x x L ( 0 st δu( x where, z s the beam deflecton relatve to ts base (fxed end, z b s the moton of the base, ρ mass densty, I s the moment of nerta, and δ(x-x s the Drac delta functon whch s nfnty at x = x and zero elsewhere. st, t

14 W F a L Z Y X F st T p x stxa x t Fgure 5: Schematc of the cantlever beam. Usng the method of assumed modes, the soluton and the vrtual dsplacement can both be expressed as, = = t u x t x u t q x t x z ( (, (, ( (, ( δ ψ δ ψ, where, ψ (x s the mode shape functon, and q (t s the temporal part of the soluton. Substtutng ths form of the soluton nto the governng equaton, and usng orthogonalty propertes of the mode shape functon, the resultng modal dfferental equaton s, = = = = + = + + b L L L L st st a a z a dx x E I k dx x c b dx x A m a dx x A F x F x q k q b q m, 1, (, ( ( ( ( ψ ν ψ ψ ρ ψ ρ ψ ψ Usng the boundary condtons of zero deflecton and slope at the cantlever's fxed end, and zero moment and shear force at the free end, the mode shape functon s found to be, sn( (snh( cosh( (cos( + ( cosh (cos( snh( (sn( ( x x L L x h x L L x λ λ λ λ λ λ λ λ ψ + + = where, λ s the soluton of the followng transcendental equaton, 0 1 cosh( cos( = + L L λ λ. The values for λ 1, L = 1.875, The fundamental moton of the tp can be approxmated usng the frst mode as, ( (, ( ( 1 1 t q x t x z t z t t t ψ = = Ths assumpton was later justfed for the fnal beam desgn. The resultng transfer functon from the appled forces to tp poston s therefore, L t st st t a a t t a dx x x A F x x F x x k b s m s s Z ( ( ( ( ( ( 1 ( ψ ψ ρ ψ ψ ψ ψ **

15 IV.. Squeeze Flm Dampng The dsspaton n the mechancal structure s manly due to squeeze flm flow n the gap formed between the undersde of the beam and the top of the substrate. In addton, squeeze flm flow results n a sprng-lke force actng on the beam due to compressblty of flud n the gap. If the bandwdth of the system s much smaller than a crtcal frequency ω c, (.e. low squeeze number σ, the sprng force can be neglected compared to the dsspaton force. In ths case, the frst mode dampng coeffcent n **, s gven by, 96µ L w b = π 4 3 g o w π g o ω, ω c 1µ w o 1µ σ = = P g 3 P where, µ s the flud vscosty, w s the cantlever wdth, P s the nomnal pressure, g o s the nomnal gap, and ω s the frequency. For the fnal beam desgn, ω c = 460 >> system bandwdth (~ 10, hence the sprng force can be safely neglected. IV.3. Electrostatc Actuators The electrostatc forces are modeled as concentrated loads. To avod pull-n effect, the tp length protrudng below the beam s desgned to be larger than two thrds of the nomnal gap beneath the cantlever. The electrostatc forces are gven by, F a = ( g o ε o Aa Va ψ 1( xa + z ψ ( x ε o Ast Vst Fst = ψ 1( xa ( g o + zt ψ 1( xt where, ε ο s the permttvty, A a/st s the area of the correspondng electrostatc pad, and V a/st s the voltage to the correspondng pad. 1 t t IV.4. Models for the feedback electroncs The tunnelng current s sensed usng a trans-mpedance amplfer. The operatonal amplfer s modeled as sngle domnant pole wth a gan-bandwdth product of A o1 f o1. The effect of parastc capactance C p, at the nput of the amplfer s also modeled. The transfer functon of ths amplfer s gven as,

16 V I tun tun = R C 1 p s π f o1 A 1 + ( π f o1 o1 R 1 + R C 1 p s + ( A o1 + 1 The tunnelng voltage s dgtzed through a DAC wth a samplng frequency of f DAC. The sgnal s processed and a control sgnal s then sent to an ADC wth a samplng frequency of f ADC. The man effect of samplng at a fnte frequency s to ntroduce delays n the feedback loop. These delay wll have lttle effect f the closed loop bandwdth s kept very small compared to the samplng frequency. Two sample-and-hold, (zero-order-hold, were used to model effects of ADC and DAC samplng. In addton, quantzaton effects due to fnte bt-sze were modeled as round-off quantzers. Moreover, manufacturer s data on least sgnfcant bt nose n the ADC was also ncluded n the model random nose wth an approprate varance. Output current from the ADC s sent to a second trans-mpedance amplfer modeled wth a transfer functon of, Va Ao R = I s ADC + (1 + Ao π f o The voltage V a s sent to the electrostatc actuaton pad to compensate for changes n the tunnelng current due to nput acceleraton. IV.5. Beam Desgn: Dynamc Consderatons From the gven desgn requrements, the followng consderatons are desred:! Hgh bendng natural frequency.! Well-damped bendng mode for non-oscllatory transent response and small settlng tme.! Hgh torsonal stffness and natural frequency for low cross-axs senstvty.! Low electrostatc voltage requrement for DC deflecton and self-test. From the prelmnary statc analyss presented prevously, the ntal beam desgn had dmenson of 5 x30x µm. The frst modal frequences are 58 (Q ~ 6, and 450 for the bendng and torsonal modes respectvely. A potental process flow was developed for fabrcaton. Ths process requred havng holes n the cantlever for facltate ts release. Accordngly, the effectve wdth for estmatng squeeze flm dampng becomes the holes spacng (15 µm. Ths ncreases the qualty factor Q ~ 48. In order to actvely provde adequate dampng (Q~1, for such a hghfrequency mode a very hgh bandwdth electroncs wll be requred. However, the ganbandwdth product of the operatonal amplfers and the parastc capactance mpose a practcal lmt on the bandwdth of the electroncs. A bandwdth of 400 can be expected for the sensng trans-mpedance amplfer for an estmated 1 pf parastc capactance. Therefore, t was necessary to change the proposed process to elmnate the release holes. Ths would allow ncreasng the wdth of the cantlever w, hence squeeze flm dampng (~ w 3. The resultng tradeoff s a decrease n torsonal mode frequency (~ w -1, hence cross-axs senstvty. In addton, the bendng frequency was reduced by ncreasng the beam length. The fnal desgn has dmensons

17 that gave a good compromse between the aforementoned trade-offs. The dmensons are 70 x60x µm. The frst modal frequences are 40 (Q ~ 1, and 381 for the bendng and torsonal modes, respectvely. IV.6. Locaton of Electrostatc Pads The locaton and sze of the electrostatc pads were selected to provde a compromse between DC offset voltage and self-test voltage on one hand and avodng nterference of frngng felds between neghborng pads. The self-test pad s 30 µm long along the beam s length and has a 60 µm wdth and centered at 145 µm from the base of the beam. The actuaton pad s 50 µm long along the beam s length and has a 60 µm wdth and centered at 05 µm from the base of the beam. IV.7. Vacuum operaton Vscosty decreases at low pressures. At atmospherc pressure the vscosty of ar s 1.8 x At 300 o K and 10 Torr, the vscosty of ar decreases to 1.6 x From dynamc response consderatons, operaton n vacuum s very dffcult to acheve due the lmted bandwdth of the feedback electroncs. Ntrogen and ar have very smlar values of vscosty at room temperature ( µ ar = 1.84 x 10-5, µ ar = 1.77 x Therefore the model for the devce s nearly dentcal for operaton n ntrogen or ar envronments. IV.8. Lnearzaton and tunnelng set pont: It s a common practce n STM machnes and n some tunnelng accelerometers (Yeh et. al. to use a logarthmc amplfer to lnearze the exponental dependence of the tunnelng current on the tunnelng gap. Ths approach was not adopted here, snce t would ntroduce addtonal dynamcs that may reduce the maxmum achevable bandwdth. Alternatvely, a hgh-bandwdth lnear controller wth a hgh gan-margn wll be desgned to compensate for ths nonlnear tunnelng behavor. The tunnelng current set pont was selected as compromse between good devce senstvty and a large gap sze to avod tp crash durng transents. IV.9. Controller Desgn The controller s expected to mantan the tunnelng current constant n the presence of nput acceleraton. It should provde as fast response as possble wth a well-damped transent to avod tp crashng and long settlng tme. The control problem can be thought of as dsturbance rejecton problem, wth the nput acceleraton actng as a dsturbance. To be able to reject ths dsturbance the closed loop bandwdth has to be large compared to the frequency of the measured acceleraton. In addton, to provde actve dampng of the cantlever dynamcs, one can cancelng the effect of these dynamcs by ntroducng controller zeros wth a frequency that s very close to the cantlever s modal frequency. Ths approach of stable pole-zero cancellaton s however, not practcally robust. Uncertantes n the locaton of the cantlever may result n hgh frequency rngng. Alternatvely, by placng controller zeros close to the real axs, lghtly

18 damped modes can be adequately damped. Ths typcally requres a large bandwdth. However, there s a practcal upper bound on the closed loop bandwdth. The bandwdth s lmted to be consderably lower than feedback amplfers, bendng and torsonal resonances of the beam. The structure of the controller s a PID wth an addtonal hgh-frequency pole. The ntegrator s used to reduce senstvty to op-amps nput voltage drft and offset and other constant or slowly varyng dsturbances. The zeros of the controller provde the requred phase-lead near crossover frequency. The samplng frequency (1 MHz s very large compared to the expected bandwdth (few. Therefore, the controller can be desgned n contnuous tme and then dgtzed to obtan the equvalent dscrete-tme controller wth no degradaton n closed loop performance. Durng transents, large changes n the effectve loop gan are expected due to the exponental dependence of tunnelng current on tp dsplacement. For example, for a tunnelng gap of 8.5 o A, I tun 1 zt, where at a gap of 5 o A, I tun 5 z t. Moreover, the tunnelng barrer heght φ, s a very uncertan parameter. For a gold tp tunnelng n ar, changes as much as a factor of 5 has been reported (Ken. Hence, t s requred to be robust to gan uncertantes by desgnng for a large gan margn. Addtonally, the effect of samplng and hgher order dynamcs requre that the bandwdth be lmted and to have a large phase margn. A system model lnearzed at the operatng pont was used for controller desgn. The root locus plot s shown n Fgure 3. The lnear frequency response s shown n Fgure 4. The closed loop system has a gan margn of 8, a phase margn of 9 o and a crossover frequency of 9. 5 x Im ag A x s Real A xs x 10 6

19 x Im ag A x s Real A xs x 10 5 Fgure 6: (top Root locus plot, (bottom a zoom-n vew. Bode Dagram s Phase (deg; Magntude (db Frequency (rad/sec Bode Dagram s 0 Phase (deg; Magntude (db Frequency (rad/sec Fgure 7: Lnear frequency response, (top open loop, (top closed loop from set pont to tunnelng voltage.

20 IV.10. Smulaton Results The full nonlnear model, ncludng nose and samplng effects was used to smulate the expected devce performance. The man observatons are presented Step response: ± 5g, Fgure 8.! Amplfer offset voltage shfts the operatng pont from 8.5 Å to 8.86 Å.! Intal response s dfferent for postve or negatve acceleraton sgnals due to changes n effectve loop gan durng transents.! Steady state response s repeatable and consstent.! Response tme s 35 µs for postve and negatve acceleraton sgnals g - 5g 13 o Tunnelng Gap, (A Tm e, (µ s g - 5g Tunnelng Current, (na Tm e, (µ s Fgure 8:Step response for 5g acceleraton Full-scale nonlnear response: (Fgure 9

21 ! Wthout any changes to the nomnal desgn, the devce can used n low acceleraton hgh bandwdth or hgh acceleraton low bandwdth applcatons, e.g. 5g upto 10, or 50g upto 1.! Transents des out quckly.! Devce has excellent lnearty (control voltage vs. nput acceleraton.! o Tunnelng Gap, (A Tm e, (µ s 0 Electrostatc AC Voltage, (mv Tm e, (m s Fgure 9:Nonlnear frequency response, 5g 10.

22 o Tunnelng Gap, (A Tm e, (m s 00 Electrostatc AC Voltage, (m V Tm e, (m s Fgure 10:Nonlnear frequency response, 50g 1. Mnmum detectable Acceleraton: 0 mg (Fgure 6! Lmted manly by LSB and amplfers nose (~ 0 µv.! Mnmum detectable acceleraton 0mg, ( 0.1 % for 5g full scale or 0.01% for 50g full scale.

23 mg - 0m g 8.88 o Tunnelng Gap, (A Tm e, (µ s mg - 0m g Tunnelng Current, (na Tm e, (µ s Fgure 11:Step response for 0mg acceleraton Shock test: 100g held for 100 ms wth 1 ms rse tme (Fgure 1! Very small devaton from nomnal poston durng rampng (< 0.5 Å.! Controller mantans the gap at nomnal value durng hold perod, therefore, smulaton s shown for 5 ms hold perod nstead of 100 ms.

24 o Tunnelng Gap, (A Tm e, (m s A c c eleraton, (g Tm e, (m s Fgure 1:Shock test, 100g, 5 ms, 1 ms rse tme. Robustness to parameter uncertanty: Varatons n the tunnelng barrer heght φ: 5g step response, φ = 0.5 ev (Fgure 13, φ = (Fgure 14.! Varatons n the tunnelng barrer heght for a gold tp n ar between ev, form a nomnal value of 0.17 Ev, (Ken.! Excellent feedback stablty robustness to large perturbatons, (-70 % to +300 %.! Moderate changes n the transent behavor wth consstent and steady state response.! Slght ncrease n response tme from 35 to 50 µs for a 70% varaton.! Changes n the nomnal gap from 8.5 Å to 5 Å (0.5 ev, and 16 Å (0.05 ev.! Maxmum expected value of φ has to be consdered n selectng nomnal operatng pont, to avod tp crash durng transent.

25 g - 5g o Tunnelng Gap, (A Tm e, (µ s g - 5g Tunnelng Current, (na Tm e, (µ s Fgure 13:Step response for 5g acceleraton, wth varaton n tunnelng barrer heght, 0.5 ev 4 + 5g - 5g o Tunnelng Gap, (A Tm e, (µ s

26 g - 5g Tunnelng Current, (na Tm e, (µ s Fgure 14:Step response for 5g acceleraton, wth -70 % varaton n tunnelng barrer heght (0.05 ev. Varatons n squeeze flm dampng: 50% reducton n dampng coeffcent (Fgure 15.! Excellent feedback stablty robustness to large perturbatons, despte a 50% reducton n dampng coeffcent.! Moderate changes n the transent behavor wth consstent and steady state response.! Slght ncrease n response tme from 35 to 55 µs g - 5g 14 o Tunnelng Gap, (A Tm e, (µ s Fgure 15:Step response for 5g acceleraton, wth 50 % decrease n squeeze flm dampng.

27 14 13 DC Voltage, (V Resdual Stress, (MPa Fgure 16: Resdual stress, f present Devce senstvty and lnearty: (Fgure 17! Senstvty of 4 mv/g (nose ~ 0 µv, mn. acceleraton 0 mg 80 µv.! Lneraty << 1%, s easlly acheved. Fnal devce lnearty may depend on sgnal condtonng Output Voltage, (mv Input Acceleraton, (g Fgure 17:Input acceleraton vs. output voltage.

28 V. Electroncs V.1. Desgn Prncples Because of the wde varety of parameters upon whch the hgh-senstvty tunnelng current depends, ncludng the CVD oxde thckness (and hence the actuaton capactor dmensons, the length of the tp (whch depends on a tmed oxde etch, the beam dmensons and materal parameters, and the hstory of the tp (a crash, albet unlkely gven the soundness of the control algorthm, mght requre recalbraton, we have chosen a dgtal core for the sgnal chan. Ths permts us to set DC voltages such as the large component of an electrostatc actuaton voltage, for example, wth a certan number of bts n an EEPROM, as opposed to laser-trmmng a resstor n a voltage dvder, or requrng the end-user to compensate wth external crcutry. It also allows us to change the behavor of the devce for dfferent regmes of operaton as noted earler, we can operate the accelerometer n a hgh-bandwdth, low-acceleraton mode, or a lowbandwdth, shock-acceleraton mode. DACs and ADCs are farly cheap, and offer a large degree of control for very lttle nvestment. There are four major voltages that need to be specfed: the frst s the voltage of the beam (and thus the tp, V beam, whch s drectly fed from the power supply. The voltage of the self-test pad, V self, s specfed by an EEPROM value whch s fed nto an 8-bt DAC, whch specfes voltages n the range of 0.63 to 0.77 V (assumng a possble 10% error about the exact value of 0.70 V for a.5-g force, n ncrements of 0.55 mv; ths permts us to specfy the value of the self-test acceleraton to better than 0.08 %. The actuator pad, V act, has a DC offset of 10 V, whch brngs the 1.3 µm-long tp down roughly 00 nm, so that t s only a few Angstroms away; ths V act s precsely found by rampng up the voltage untl a tunnelng current of 1 na appears; the resultant value can be stored n the EEPROM, to be fed out through an 8-bt DAC. For a possble error of 0%, we would specfy voltages n a range roughly spannng 8 V to 1 V, wth a resoluton of 15 mv. (The small control voltage whch s added to the DC component of the actuator voltage, operates roughly between 15 mv and 15 mv n normal crcumstances; we control ths wth a hgh-speed 14-bt DAC whch s operated so that the most sgnfcant bt of the small control voltage s greater than the least sgnfcant bt of the DC component of the actuator voltage. Fnally, the tunnelng-pad voltage V pad s specfed ether by a lnearly voltage-dvded Zener dode, or by some other relatvely constant source, wth respect to V beam. As we wll see n the secton on nstrumentaton, the tunnelng-pad voltage s actually specfed as a vrtual voltage through a transmpedance amplfer, so that the tp-to-pad voltage s held at around 0. V. V.. Sngle-conductor Desgn One key aspect of the electroncs desgn s that we use a sngle conductor for both the tunnelng tp and the part of the beam whch responds to the capactve actuators. Ths s only possble for a well-decoupled system that s, one for whch the varous current paths do not nterfere. Snce we are operatng at low frequences, at frst glance ths seems lke t shouldn t be a problem, but t s worth to consder possble effects of usng a sngle-conductor desgn, snce our sgnal and power currents are phenomenally low. As we wll see, despte the low currents, the resstances and capactances are of approprate scales that we need not worry about couplngs; the beam can be treated much as ground planes are n radofrequency desgn.

29 Why use a sngle conductor? Creatng separate conductors for dfferent current paths would add another mask, complcate the beam model, and possbly exacerbate regstraton ssues snce we would be tryng to ft three separate current paths on a beam that measures a few dozen mcrons wde. The most mportant reason, however, s that t s not necessary, as we ll see from the followng bref arguments. The capactance between the R = 1 µm-radus round tunnelng tp (as specfed n the process flow and a tunnelng pad d 0 = 10 Å below t, s da 0 d π ε = ε 0 θ R rdr d = 0.6 ff R r + d whereas the capactance between the actuaton pad and the beam s ε 0 A d = ( ( ( /( = 11 ff whch s sgnfcantly more. In any case, both of these values present an ncredbly hgh mpedance at the relevant frequences of a few klohertz (1/Cs ~ 50 teraohm, and thus crosscouplng can be neglected, snce the resultant currents would be much smaller than the currents of nterest anyway. Further, the tunnelng current, whch obeys the proportonalty I tun g Ve = 0 α φ x gves a dynamc resstance at 10 Å of over 00 MΩ, whereas the output resstance of the power supples and opamps s a few ohms at most. Fnally, we can estmate the relatve values of the relevant currents, usng results from the smulaton, whch suggests that n a 5-g acceleraton, the control loop changes the voltage of the bottom actuator pad by 13 mv over 0.15 ms: I = C dv dt 13mV = ( 10.6 ff = 0.9 pa << I.15ms act act tun ~ 1 na and so we see that n practce, the capactve current would not affect the tunnelng current sgnal by more than 0.09%, even f the current paths were not well-decoupled. V.3. Instrumentaton: elements Although we would almost certanly choose to create an ASIC for ths MEMS devce, and operate the devce n a two-chp confguraton, for the purposes of modelng we decded to use commercally avalable parts wth exstant specfcatons. The reasons are twofold: frst of all, we need farly senstve components n order to acqure and synthesze sgnals on the tny scales of nanoampere tunnelng currents and angstrom-sze dsplacement, and although the technology for makng these very senstve parts exsts, to meet all of ther specfcatons mght take decades of teraton and sharng of nsght. Secondly, f we were to replcate these parts, the specfcatons

30 would be very smlar to the orgnal parts (wth a few exceptons, lke de sze and power consumpton, snce we don t need the generalty of an end-user IC, gven that we are operatng near some of the fundamental physcal lmts for room-temperature devces, so for modelng purposes there s nothng to be lost by usng exstant parts wth well-defned models. We have chosen four commercally avalable parts wth publshed macromodels, for the sgnal chan of our system. The 1 na-scale current frst flows through a transmpedance amplfer consstng of a 1 MΩ resstor (Johnson nose of 0.19 µv/hz 1/ whch connects the - termnal of an opamp to ts output, wth the + nput at V pad. The negatve termnal, whch s connected to the tunnelng pad, s therefore held at the vrtual voltage V pad. We assume a parastc capactance of 1 pf over ths contact, whch we nclude n the control model. For the macromodel for ths amplfer, we use that of the AD515 opamp (Ana, whch draws a mere 75 fa of nput current due to ts extremely hgh-mpedance JFET front end. The AD515 has a 1 MHz gan bandwdth product, whch we compensate so as to gve an open-loop gan of 1000 and a domnant pole at 1. The nose power spectral densty s 55 nv/hz 1/ across 10 Hz-1, and the opamp has a 0.4 mv offset voltage, whch we dgtally subtract off n the dgtzaton process. The ADC model that we are usng s that of the AD960 (Ana, whch can sample at.5 MHz wth 16-bt resoluton. It has a sgma-delta archtecture wth a flash quantzer, a ppelned A/D wth 5 successve approxmaton stages, and s on the whole very complex. However, ths type of A/D converter s now becomng farly common, spurred onward by the telecommuncatons revoluton, and t s lkely that n the comng years such dgtzaton capabltes wll be common n many devces. In partcular, ths model has about 30.5 uv/hz 1/ of nput nose, for a V full scale sgnal, whch s a useful and reasonable number to ncorporate nto our model. The DAC model for our sophstcated 14-bt DAC s that of the AD9754 (Ana, a 14-bt, 15 MHz DAC, whch can source + 0 ma of current, wth 50 pa/hz 1/ current nose. As before, such DACs are now becomng qute accessble, and wll make dgtal control more accessble for hgh-senstvty, hgh-bandwdth applcatons. The fast converson rates of the ADC and DAC allow mnmal effects from the zero-order hold effects of analog/dgtal nterface crcutry, thus allowng us to preserve fast settlng tmes on the order of tens of mcroseconds. The DAC output s fed nto a 10 ohm resstor (wth neglgble Johnson nose, 0.4 nv/hz 1/, for a fnal transmpedance amplfer stage whch creates the control voltage. The + termnal of the transmpedance stage s held at the actuator DC offset voltage (~10 V, for brngng the beam down 00 nm, as observed n the prevous secton, so that the output of the transmpedance stage provdes 10 V + 00 mv, whch s suffcent to accurately servo all acceleratons on the order of 5 g (+ 15 mv, whle stll havng enough range to compensate for a 100g shock. The amplfer model we used for ths stage was the AD743, a low-nose opamp whch has only an nput nose of 3.5 nv/hz 1/, whle stll preservng a gan bandwdth product of greater than 1 MHz (whch we compensate, agan, as havng a gan of 1000 wth a domnant pole at 1. Also mportant for the system s a swtchng power supply, to provde step-up converson of the nput power to whatever voltages are requred for the actuaton, and possbly a charge pump, f extremely hgh voltages are needed although from the above analyss, and from the smulatons, t appears that ths requrement s superfluous.

31 Schematcs and explanatons of DACs, ADCs, hgh-mpedance and low-nose opamps, Johnson nose, swtchng power supples, and capactor-dode charge pumps can all be found n (Hor89. V.4. Instrumentaton: model On the next page, we now present a schematc for the crcutry, and explan the components as necessary. The model was mplemented n Smulnk, as explaned earler. All of the nose values and bandwdth parameters n the prevous secton, as well as the effects of zero-order-holds, and the parastc capactance were smulated. The p++ beam has resstvty ~ 10-3 Ω-cm, whch corresponds to a 9 Ω resstance between the base of the beam and the pont on the beam opposte the self-test pad, a 10.4 Ω resstance between the self-test pad and the actuator pad, and a.1 Ω resstance between the actuator pad and the gold tp. Snce the current flowng through the beam s order 1 na at all tmes, the voltage drop across the beam s 31.5 nv, whch s far below the nose floor due to the amplfers and resstors, and much less than the actuaton voltages, and so we can completely neglect the resstance of the beam, and treat the system as well-decoupled. A 1 pf parastc capactance was chosen as a reasonable value, gven sources n the lterature. The transmpedance amplfer (AD515 converts the 1 na current nto a ~ 1 mv sgnal, whch s then dgtzed by the ADC at 1 MHz. A dgtal PID controller (whose mplementaton s descrbed n the next secton operates on ths sgnal, whch s then output at 10 MHz through a DAC. The ncreased speed of the output was used to reduce the effects of the zero-order-hold on the output; a smple and perhaps wse alternatve mght be to put a low-pass flter on the output of the DAC, at a reasonably low frequency (say, 50, but ths was not modeled, and ddn t prove necessary gven the very low frequency of the mechancal system compared to the capabltes of modern dgtal/analog nterface crcutry. The DAC output was then nserted nto a transmpedance stage/summer amplfer, whch created the voltage for the actuaton pad. In an EEPROM are stored bts ndcatng the value of the self-test voltage, the DC offset voltage, the varous swtchng power supply tmng parameters, the exact values of the parameters used n the PID controller, the controller setpont, and the values of the varous offset voltages and currents that need to be added or subtracted from the default values n order to run the accelerometer at maxmum performance. We dscuss how to set these values n the next secton.

32 Fgure 18: The Electroncs

33 V.5. Instrumentaton: mplementaton We very brefly speculate on the sze of the resultant package, snce we were asked to keep the mass of the system under 5 grams. We also noted that each of these devces can be made usng a sngle layer of crcutry, and therefore s sutable for SMARTMUMPS style fabrcaton processes. Each of the two opamps requres on the order of 50 transstors, and can be expected to take up an area of 1 mm each. Each DAC requres on the order of 30 resstors, plus 15 transstors to act as current sources, plus 30 transstors to make a smple summng amplfer, and some overhead crcutry; ths can reasonably ft n an area of about 1- mm. The ADC requres several dozen transstors and resstors, and mght take up an area of -3 mm. Fnally, the dgtal logc as syntheszed n Verlog takes up around 400 gates, when explctly optmzed so that that as much as possble, bts are routed so that no computaton s necessary. For example, f our dgtal flter s I o (n = V (n 1.96 V (n V (n I o (n I o (n, whch n fact t s (all gan parameters are external, n the amplfers, then we can mplement, for example, multplcaton by 1.96 as multplcaton by 1.8, plus multplcaton by 0.64, plus multplcaton by 0.004, and so on. Each multplcaton by a power of corresponds smply to a bt-shft operaton, whch can be hardwred (so that t doesn t requre any gates to the nput of a smple adder. A more versatle programmable verson would requre more gates, but would stll probably ft nto a square mm on a sde f the feature sze were 1. µm. The total area s therefore just under 3.5 mm by 3.5 mm on a sde. We may have been overoptmstc on some of these estmatons, but we are probably not far off. And certanly we are far under the 5 g lmt. We also brefly explan the test-and-calbraton method. Frst, apply a 0. V voltage between the tunnelng tp and pad and ncrease V act untl tunnelng appears, at the 1 na level. That s the setpont for the 8-bt DAC that syntheszes the DC-offset component of the actuator pad. Measure the offset voltages of the amplfers for baselne subtracton. Then f necessary (although t s unlkely, tune the controller to nsure a proper settlng tme, fnal value, and transent sgnal. Laser trm the resstors to provde approprate transmpedance gans. Calbrate the readout by adjustng the acceleraton settng on a shaker table and readng out the voltage reported by the accelerometer electroncs snce after the settlng tme passes, F net = k x = 0, ma = F act, and the dgtally syntheszed actuator force drectly reflects the acceleraton, so that a smple lnear ft between actuator force and nput acceleraton should suffce to calbrate the part. Fnally, measure the voltage that must be appled to the self-test pad n order to cause a.5-g acceleraton, as compared to a standard.5 g acceleraton created by the shaker table.

34 VI. Process Flow VI. 1. Overvew We have developed a fve mask process flow for the fabrcaton of the mcroelectromechancal assembly for a tunnelng accelerometer. A cantlever proof mass wth an ntegrated tunnelng tp s created wthn a sngle bonded wafer. The dmensons of the completed proof mass are "m wth a nomnal 1.5 "m gap between the actuaton, self-test, and sense electrodes and the undersde of a conductve p ++ ep-s cantlever. The tunnelng tp protrudes about 1.3 "m from the undersde of the cantlever. The process flow descrbed n ths secton satsfes three major challenges. The frst challenge was set forth n the ntal desgn problem statement. Specfcally, the tunnelng tp and the proof mass must are fabrcated from the same wafer. The squeeze flm dampng requrements of accelerometer dctated the second challenge. Etch release holes n the beam drastcally reduce the squeeze flm dampng effects. Therefore, the cantlever s released wthout the ade of etch release holes. The thrd challenge was self-mposed by the desgn team. Specfcally, every effort has been made to desgn a smple process flow that uses the fewest number of masks or process steps, and does not requre unusual or expensve fabrcaton technologes. The expected benefts of meetng ths thrd challenge nclude less uncertanty n the fabrcaton process, mproved tolerance benchmarks, reduced tme to market, and lower cost per de, among others. A conventonal doped SOI wafer can be fabrcated by bondng a frst slcon wafer wth an oxde layer to a second slcon wafer wth a p ++ ep-s layer so that a bond lne s formed along an oxde-ep nterface. We have mplemented a process flow that s based on a modfed SOI wafer fabrcaton procedure. Before the bond s made, four process steps are carred out. Frst, a ntrde delectrc layer s deposted. Second, gold metal (wth two addtonal adheson promotng metals s deposted and patterned to form the electrodes and contact pads. Thrd, an oxde layer s deposted. Fourth, a cavty s etched nto the oxde layer just below the pont where the cantlever s to be formed. Ths presence of ths cavty sgnfcantly reduces the lateral dmenson of oxde that must be removed durng the fnal cantlever release process. Therefore, etch release holes are not requred and the second challenge s satsfed. Fnally, ths wafer s planarzed and polshed and then bonded to a second commercally prepared wafer wth a.0 "m p ++ ep-s layer on one surface. The two wafers are fused together along an oxde-ep bond lne wthout the use of specal algnment procedures. Ths modfed SOI wafer s then thnned down to the p ++ ep-s layer wth a combnaton of grndng and ansotropc etchng. The tunnelng tp s formed by frst etchng a hole through the p ++ ep-s layer. The hole then acts as an etch mask so that a sphercal depresson can be sotropcally etched nto the underlyng oxde layer under hgh agtaton. The depresson s used as mold for subsequent deposton of gold. Ths forms a gold tunnelng tp wth a sphercal end. Then the lateral dmensons of the cantlever are defned. The wafer s bonded to wafer mountng tape and the de s cut usng a de saw. A tmed oxde etch s used to release the cantlever and to expose the end of the tunnelng tp protrudng from the undersde of the cantlever. Ths s followed by a super crtcal CO release step. Fnally, the cantlever chp and the electroncs chp are mounted sde-by-sde n a two chp package, ball bonded, and sealed under ntrogen.

35 We have also desgned an alternate process flow for the fabrcaton of a tunnelng accelerometer wth a tunnelng tp that has more precse geometry and smaller tp radus. Ths process flow s smlar to the process flow presented here. However, the prmary modfcaton s that the mold for the tunnelng tp s ansotropcally etched n to an undoped ep-slcon layer nstead of sotropcally nto oxde. The resultng mold depresson has a pyramd shape wth predctable and precse geometry and small tp radus. Addtonally, ths ansotropc etch s somewhat selflmtng and s less therefore less senstve to precse tmng of the etchng step. The entre descrpton for ths alternate process flow s presented n Appendx B. VI.. The Process Flow Process 1: Depost Feld Ntrde A feld ntrde layer s deposted onto one sde an undoped double-sde polshed wafer. Ths ntrde delectrc serves as electrcal solaton for the electrode pads. RCA clean 50:1 HF dp DI rnse and dry LPCVD of ntrde (1 "m Ntrde S Process : Mask #1 --- Metal Pads A T-Pt-Au metal tr-layer s deposted and patterned usng a conventonal lftoff process to create the actuaton, self-test, and tunnelng pads. The electrcal contacts and conductve lnes runnng to each pad are also fabrcated. The tr-layer metal deposton s done to enhance adheson of the gold layer to the wafer. The Pt layer s thermodynamcally stable and prevents the mgraton of T through to the tunnelng gold surface. RCA clean 50:1 HF dp DI rnse and dry HMDS, spn coat postve photoresst, and prebake Expose wth Mask #1 ("Electrode Mask" Postbake and develop Depost 50 Å T, and 50 Å Pt, and 400 Å Au

36 Metal and photoresst lftoff by hot (40 C ultrasonc acetone bath Nanostrp to clean off photoresst resdue DI rnse and dry T-Pt-Au Ntrde S Process 3: Oxdaton A sacrfcal feld oxde layer s deposted onto the wafer usng low temperature plasma enhanced CVD. Low temperatures are desrable to mantan stablty of the electrode metal. Depost 3.0 "m oxde by PECVD SO Ntrde T-Pt-Au S Process 4: Mask # --- Oxde Cavty A cavty that s nearly as large as the cantlever s etched nto the oxde layer. Ths cavty s used to speed up the cantlever release process durng the wet oxde etch of the sacrfcal oxde. HMDS, spn coat postve photoresst, and prebake IR algnment of Mask # ("Cavty Mask" and expose Postbake and develop 6:1 BOE etch oxde cavty DI rnse and dry

37 SO Ntrde T-Pt-Au S Process 5: Planarze and Bond The oxde layer s CMP planarzed and polshed to a mrror-smooth fnsh. A second, undoped doped slcon wafer wth a.0 "m layer of hghly doped (> 10 0 cm -3 boron eptaxal slcon on one surface s obtaned from a commercal vendor. The two wafers are then fused together along an oxde-ep bond lne. No fne algnment procedures are requred durng the bondng process because the ep wafer has no patterned features. Polsh (CMP the oxde to 1.5 "m over Au Pranha clean Clamp wafers together and hold at 900 C, 1-4 barr, oxygen ambent Anneal at 800 C S p ++ ep S SO Ntrde T-Pt-Au S Process 6: Thn Down to Etch-stop Gross wafer thnnng of the upper bulk slcon layer s carred out by grndng. Precson thnnng s acheved by an etch n EDP (ethylene damne pyrocatechol down to the p ++ ep-s etch stop. The etch rate of slcon wth boron concentratons above 10 0 cm -3 n EDP etchant s 350 tmes slower than for ntrnsc slcon, so nearly all of the orgnal two mcron thckness of the ep-s layer should be preserved after the thnnng process s complete. At ths pont, the modfed bonded SOI wafer s fnshed and ready for further processng. Backgrnd top of the bonded wafer to 5 "m

38 EDP etch, 66 C Pranha and RCA clean p ++ ep S SO Ntrde T-Pt-Au S Process 7: Mask #3 --- Etch Tp Hole Through ep-s A mold for root of the tunnelng tp s formed by frst plasma etchng a crcular hole through the hghly doped eptaxal layer. RCA clean HMDS, spn coat postve photoresst, and prebake IR algnment of Mask #3 ("Tp Mold Mask" and expose Postbake and develop RIE etch hole through hghly doped eptaxal S Prahna strp photoresst DI rnse and dry p ++ ep S SO Ntrde T-Pt-Au S Process 8: Etch Tp Into Oxde The hole etched through the ep-s layer n the prevous process step s used as an etch mask for a tmed partal etch of the underlyng oxde layer. A sphercal depresson s sotropcally etched nto the oxde layer under hgh agtaton. At ths pont the mold for the tunnelng tp s complete. Tmed BOE Pranha strp photoresst DI rnse and dry

39 p ++ ep S SO Ntrde T-Pt-Au S Process 9: Mask #4 --- Metallze Tp and Contact A conductng tunnelng tp s formed by deposton of gold nto the depresson prevously etched nto the oxde layer. The gold s patterned wth a lftoff process. Ths process also forms the electrcal contact pad to the hghly doped eptaxal layer. HMDS, spn coat postve photoresst, and prebake Expose wth Mask #4 ("Tp Metal Mask" Postbake and develop Depost 10,000 Å Au Metal and photoresst lftoff by hot (40 C ultrasonc acetone bath Nanostrp to clean off photoresst resdue DI rnse and dry Au p ++ ep S SO Ntrde T-Pt-Au S Process 10: Mask #5 --- Defne Cantlever The lateral dmensons of the ep-s cantlever are defned usng an RIE etch step. The tunnelng tp and top contact are protected under photoresst durng the etchng process. The wafer s bonded to wafer mountng tape and the de s cut usng a de saw. Fnally, the photoresst s strpped. HMDS, spn coat postve photoresst, and prebake Expose to Mask #5 ("Cantlever Mask" and expose Postbake and develop RIE etch p ++ ep-s layer

40 Bond wafer to mountng tape Cut de wth de saw Pranha strp photoresst DI rnse and dry Au p ++ ep S SO Ntrde T-Pt-Au S Process 11: Oxde Etch and Release The cantlever s released durng a tmed wet etch of the sacrfcal oxde layer. The tme requred for the wet etch s sgnfcantly reduced by the presence of the cavty prevously etched nto the oxde just below the cantlever. Ths short etch tme also prevents sgnfcant undercuttng of the oxde footng of the cantlever. It should be noted that no etch release holes are requred to free the structure. At ths tme, the gold tunnelng tp and counter electrode become exposed. Due to the long length of the cantlever relatve to the gap, super crtcal CO s employed to prevent adheson of the cantlever to the floor of the gap. Tmed 6:1 BOE etch of the oxde layer Super crtcal CO release Au p ++ ep S SO Ntrde T-Pt-Au S Process 1: Packagng Fnally, the cantlever chp and the electroncs chp are mounted sde-by-sde n a two chp package, ball bonded, and sealed under ntrogen. Due the small sze of both chps, through-hole dp-chp and submnature surface mount confguratons can be used.

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