IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-26, NO. 12, DECEMBER 1979
`
`1911
`
`A Batch-Fabricated Silicon Accelerometer
`
`LYNN MICHELLE ROYLANCE, MEMBER, IEEE, AND JAMES B. ANGELL, FELLOW, ffiEE
`
`RESISTORS
`
`-------,
`\
`I
`
`SILICON BEAM
`_.,.O PAOOLE
`
`CAVITY' trCK~O lff
`GLASS COVER
`
`0&.AS.S COVER
`
`(a)
`3 ....
`
`~AIAGAP
`
`l lOOJ'
`
`'
`h a .ASS~
`.. ~: ... --~t"'-"':/~'.,:,~:~~-,:~?~:.:-~ss-,:-~,,.,~/_ )7: n
`"'~=,.=~===t-;;;;f';;l;l!ASrS ~~OO~VE~
`~
`
`CONOUCTIV8: EPOXY
`
`(b)
`Fig. 1. Top and cross-section views of the accelerometer. (a) Top view.
`(b) Centerline cross section.
`
`Abstract-An exuemely smal batch-fabricatable accelerometer has
`been developed using silicon IC technology. The device, 3 mm long and
`weighing 0.02 g, is a simple cantilevered beam and mass structure sealed
`into a silicon and glU1 package. The fabrication of the accelerometer is
`described,and the theo,y behind its operation developed, Experimental
`results on sensitivity, frequency response, and linearity are presented
`and found to agree with theozy. The acceleromete, is capable of mea(cid:173)
`suring accelerations from 0.001 to 50 g over a l 00-Hz bandwidth, while
`readily implemented geometry changes allow these performance char(cid:173)
`acteristics to be varied over a wide range to meet the needs of differing
`applications.
`
`I. INTRODUCTION
`
`I NTEGRATED-CIRCUIT (IC} fabrication technology has
`
`permitted the development of an accelerometer weighing
`Jess than 0.02 g, in a 2 X 3 X 0.6-mm package. The accelerom(cid:173)
`eter will detect accelerations down to 0.01 g over a 100-Hz
`bandwidth, with an upper acceleration limit of 50 g. These
`characteristics make the accelerometer ideal for applications
`requiring a very small and light transducer. Further, the versa(cid:173)
`tile design allows the range to be varied readily over several
`orders of magnitude. The given limits meet the requirements
`of the biomedical applications such as measurement of heart
`wall motion for which the accelerometer was initially developed.
`The goal of this work was to develop a transducer which
`meets the following speciflcations: I) smalJ size and mass;
`2) sensitivity to accelerations as low as one-hundredth of the
`acceleration of gravity; 3) a bandwidth of 100 Hz; 4) an out(cid:173)
`put stable over the limited range of temperatures encountered
`in biological environments; 5) an inert package; 6) an accuracy
`of around 1 percent; and 7) an output which is linear with
`acceleration. The device should be sensitive to only one com(cid:173)
`ponent of acceleration.
`
`II. A CCELEROMETER STRUCTURE
`The accelerometer is a glass-silicon-glass sandwich ; the de(cid:173)
`tails of this three-layer composition are shown in Fig. l . The
`center layer ls the heart of the device, a very thin silicon canti(cid:173)
`levered beam surrounded by a 200-JJm-thick rim . This rim
`provides a rigid support for one end of the beam, a region for
`contact pads, and mounting surfaces parallel to the plane of
`the beam. The beam widens at its free end into a rectangular
`paddle which supports a mass, either of some dense substance
`such as gold or of silicon . Fig. 2, a scanning-electron micro(cid:173)
`graph of the bottom side of the silicon element, clearly shows
`
`Manuscript xecetved May 22, 1979; tevised July 30, 1979.
`L. M. Roylance was with the (Jltegrated Circuits Laboratory, Stan·
`ford University, Stanford, CA 9430S. She is now with Hewlett-Packard
`Laboratories, Palo Alto, CA 94 304.
`J . B. Angell is with the Department of Electrical Engineering, Stan·
`ford University, Stanford, CA 9430S.
`
`Fig. 2. SEM of backside of the accelerometer with a silicon mass after
`KOH etch.
`
`the supporting rim, thin silicon beam, and integral silicon
`mass. A resistive half-bridge composed of two p-type resistors,
`one centered on the top surface of the beam and the other
`placed in an unstressed region of the rim, and three large
`p + contact regions complete the silicon portion of the acceler(cid:173)
`ometer. The beam resistor changes its value with acceleration
`due to the stress induced in the beam, while the second resistor
`is used for temperature compensation.
`The top and bottom layers, both of glass, take the place of
`• the T0-5 can or dual-in-line package used for standard lC's. A
`well etched into each glass cover allows the beam to deflect
`
`00 18-9383/79/ 1200-1911$00.75 © 1979 IEEE
`
`Authorized licensed use limited to: University of Maryland College Par!<. Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0001
`
`

`

`~-:::,-1~\ __ 1lC,\ 1 ;q
`~
`
`SCRIBE ALLEY
`
`BEAM
`
`St MASS
`
`SC!IIBE AU.EV
`
`I
`
`I
`
`I
`
`6 I
`I
`1.0mm
`SCALE FOR CROSS SECTIONS
`(S102 NOT TO SCAU'.)
`
`freely up to a given distance-and hence acceleration- set by
`the depth of the wells. The glass covers are hermetically sealed
`to the thick silicon rim using anodic bonding [I], protecting
`the diffusions and, by creating a sealed cavity enclosing the
`fragile beam and mass, the cantilever. Three narrow fingers
`extending from metal pads on the top glass make contact to
`the resistors through p + diffusions. A cable leading to an
`amplifier and recorder can be attached to these pads where the
`top glass overhangs the silicon. With a nonconductive epoxy
`filling the region between the two glass covers and around the
`leads, the pad region is sealed and lead bond strength improved.
`
`III. FABRICATION
`Fabrication of the accelerometer is a batch process utilizing
`standard IC photolithographic and diffusion techniqu1es in
`addition to the special etching techniques required to shape
`the silicon and glass. The silicon element and the top and
`bottom glass covers are fabricated separately in wafer form and
`then bonded together. The final steps are die separation and
`lead attachment.
`The starting material is n-type (100) silicon, chosen because
`the preferred {I 10) direction for p-type piezoresistors coin(cid:173)
`cides with the pattern orientation of anisotropic etchants such
`as KOH irl silicon. Precise dimensional control can be obtained
`even with a large etch depth sirlce the { 111} planes are etched
`two orders of magnitude more slowly than { 100} and { ll 0}
`surfaces. The first step is to etch half a dozen widely spaced
`alignment holes completely through the wafer to obtain proper
`registration of pattems on the top and bottom surface!:. A
`1.5-µm thermal oxide is. grown and two photolithographies
`and diffusions done to form the 10 U/□ p + contacts and the
`100 U/□ p resistors. The fronfoxide is stripped before drive-ill
`to minimize surface steps, while the back oxide is preserv,~d as
`the final etch mask. The remaining processing steps all con(cid:173)
`cern the shaping of the beam, silicon mass (if present), scribe
`lirles, and the window where the glass overhangs the silicon.
`Using a thick densified layer of deposited silicon dioxide to
`protect the front, windows are opened in the backside oxide
`and the silicon is etched away around the beam and mass and
`irl the region where the beam is to be thirlned. The etch is
`stopped when the beam region is twice the desired firlal thick(cid:173)
`ness. The sequence of operations is sketched in Fig. 3.. A
`photolithography on the top ·surface of the partially etched
`wafer defines the air gap around the beam and the window
`opening. The final KOH etch, which etches the beam from
`the bottom and the air-gap regions from both top and bottom,
`is quenched the moment the silicon disappears from the large
`window openings. This visual endpoint gives very good control
`of the beam thickness provided the front and back surfaces of
`the wafer are parallel. Observed uniformity has been very
`good. The final step is stripping the remaining oxide.
`The glass cover plates are also prepared irl wafer form, from
`200-µm-thick pieces of #7740 Pyrex glass, polished optically
`flat on one side. The type of glass is dictated by the silicon(cid:173)
`glass bondirlg process which requires a glass which is slightly
`conductive at the bonding temperature and whose thermal ex(cid:173)
`pansion coefficient matches that of silicon. Unfortunately,
`this glass is not nearly as easy to etch as is silicon. Wells are
`etched irl the top and bottom glass covers with a 30-percent
`
`1.912
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-26, NO. ll , DECEMBER 1979
`
`3mm
`
`TOP VIEWOF'
`S il. ICON OIE
`
`2mm
`
`RE:GION WHERE:
`Gl.ASS W ILL
`OVERHANG $ 11.ICCf,I
`
`SILICON Rl8S HOLD
`ROWS TOGETHER
`AFTE~ ETCH
`
`CROSS SECTI ON (D
`Si02\
`,,_....,. """"""""=~~~-~-~-- BACKSIDE
`.__ ____ ....,.,,_._s,_L1C_o_N ___ .._.,.,,._... __ ..,...1 Pt<OTOLITHOORAPHY
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`~ ..... .-.....,....,_/\J KOH ETCH
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`\ ~ /\.
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`\.,,.,,,,,,/
`,......,..,......,......,.,.(
`\,,,,,(
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`8EAM 0EFIN1TION
`PHOTOLITHOGRAPHY
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`
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`SUPl',.,:;:;=i\""T"",N""G "'!R1!!!M!!!!!!\~==s,=N=Ass.....,...,.Z2NG ><: ETCH
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`BeAM
`FINAL RESUI.TS, (2) and @
`CROSS SECTION $
`CROSS SECTION @
`
`Fig. 3. Diagram of final etch steps.
`
`Fig. 4. SEM of top glass cover.
`
`HN03 , 70-percent HF mixture at 48°C and a chrome-gold
`etch mask. This procedure was found to give smooth, con(cid:173)
`sistent results with minimal undercuttirlg (Fig. 4). Once the
`masking layer is stripped, aluminum is deposited on the top
`glass and the metal bondirlg pads defined.
`Final assembly of the accelerometer sandwich irlvolves at(cid:173)
`taching gold masses if needed, and aligning and bonding the
`glass covers to the silicon. Only after completion of the bond(cid:173)
`ing process are the individual accelerometers broken apart and
`handled one by one through the final phases- attaching a cable
`suited to the proposed application and applying irlsulation or
`some other protective coating. The heart of the assembly pro(cid:173)
`cedure is the anodic bonding technique which produces a
`hermetic and irreversible seal between silicon and glass. The
`glass and silicon are aligned, the temperature raised to about
`400°C, and 600 V applied between the silicon and the glass.
`An advantage of this technique, in addition to its simplicity
`
`Authorized licensed use limited to: University of Maryland College Par!<. Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0002
`
`

`

`ROYLANCE AND ANGELL: BATCH-FABRICATED Si ACCELEROMETER
`
`1913
`
`symmetrically (c2 << 2c1 + L + b) and to ensure that the
`beam thickness is small compared to its overall length if axial
`accelerations are to be ignored.
`In deriving the foregoing results, a massless beam and perfect
`alignment centering the resistor and orienting it along a 110
`direction were assumed. However, for the alignment tolerances
`and beam dimensions of interest the combined error involved
`is less than 1 percent worst case [3] . In addition, the added
`bending of a deflected beam due to an axial load can produce
`another undesired output term. However, calculations of the
`combined effects of such axial and lateral loads show that the
`error term is less than 0.4 percent for an axial load equal to
`1 percent of the Euler load. For a thin beam and heavy mass
`(worst case), this loading is roughly equal to the safe operating
`range of the device.
`In summary, the conditions necessary to minimize the un(cid:173)
`Fig. 5. Cantilevered beam and mass, with diagram of equivalent loads. desirable responses to ax and Oz are
`
`\
`PADDlE
`
`M,
`
`h<<w
`
`.
`
`<tm << 1 rad
`where am and Zr are the angular and linear misalignments of
`the resistor. Similarly, the criterion for a large response to
`ay can be expressed as
`3M(2c1 +L + b) >> wh2
`Since this condition is compatible with the constraints (3), the
`accelerometer design meets the criteria for a sensitive, uniaxial
`device whose response to a given acceleration can be both
`closely controlled and tailored to a particular task.
`
`(3)
`
`(4)
`
`and lack of filler or "glue," is the visual inspection possible for
`a successful bond. Bonded areas appear dark gray, while un(cid:173)
`bonded regions are much lighter in color and show interference
`fringing. With the top and then bottom covers bonded, a
`dicing saw is used to separate the individual devices and leads
`are attached.
`
`IV. ANALYSIS
`
`Static Response
`A detailed analysis [2] (see Appendix) of the accelerometer
`structure shown in Fig. 5 gives the fractional resistance change
`of the accelerometer due to an acceleration ay
`
`~={[½(Du + Il12 + Il44) - (s12 + ½s44)]
`· [M (c, + L ~ b) c ;zh]} ay = S 0ay
`
`where L and h are the beam length and thickness, ~z the mo·
`ment of inertia of the beam cross section about the z axis, c
`• the distance from the centroid of the cross .section to the
`the mass loading .the beam with its
`bottom of the beam, M
`center of gravity at (L + c1 , c2, c3), and Il1; and s1; the piezo(cid:173)
`resistive and elastic compliance coefficients referred to the
`cubic axes of silicon. The resistor extends from x = 0 to
`x = L - b. The accelerometer's sensitivity shows the desired
`linearity; further, the magnitude of the response can readily
`be controlled by varying the geometry.
`Ideally (l) is the only term present for any acceleration a.
`The structure's effectiveness as a uniaxial accelerometer can
`be assessed by comparing the magnitudes of the responses to
`ax and az with the desired sensitivity S0 . The only noll2.ero
`terms are due to the axial force Fx and the moment Mz pro•
`duced byax
`
`Dynamic Behavior
`The primary purpose of this accelerometer is to measure
`time-varying accelerations, requiring an understanding of the
`variation in its behavior with the frequency of the excitation.
`For very low frequencies, the beam can follow the excitation
`without appreciable delay, so the discussion of the acceler(cid:173)
`ometer's static response is directly applicable. At higher fre(cid:173)
`quencies, however, the dynamic characteristics of the system
`produce phase delays and amplitude variations, depending on
`the natural frequencies of the device. A high-Q resonance (in
`an undamped accelerometer) corresponding to the first mode
`of lateral vibration of the beam dominates the behavior of the
`accelerometer. The other vibrational modes of the beam occur
`at much higher frequencies. Hence, the motion of the canti(cid:173)
`levered beam and mass can be modeled as a simple two-pole
`spring and mass system.
`'
`The deflection of the beam is very nearly the deflection of a
`massless beam with a rigid distributed massM·at its end. For a
`static load Fy acting on the centroid of M, the deflection can
`be written as [4]
`
`(5)
`
`The approximation assumes h << w, where w is the width of
`the beam. Clearly, an effort must be made to place the mass where Eis Young's Modulus. Note that the restoring force
`
`Authorized licensed use limited to: University of Maryland College Pan<. Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0003
`
`

`

`1914
`
`IEEE TRANSACTIONS ON ELECT RON DEVICES, VOL. ED-26, NO. 12 , DECEMBER 1979
`
`• (Fy) on the mass Mis proportional to its displac.ement, giving
`simple harmonic motion. Applying the Rayleigh principle (5]
`to this deflection curve, a very good approximation to the res(cid:173)
`onant frequency Wn is obtained (for M uniformly distributed)
`✓E~z
`2 +6/+/2
`W n :::::, ML 3 2
`21
`- + 4f+-J2 + 14/ 3 + 8/4
`3
`2
`_ where the second factor under the tadical varies from three to
`one-tenth as f= ctfL varies between zero and two. Note that
`the }(ey parameters affecting Wn also play a large role in de(cid:173)
`termining the sensitivity. This interrelationship limits the
`,bandwidth which can be obtained for a given sensitivity: For
`• typical accelerometer desigas, Wn is between 500 Hz and ·
`5 kHz; the analysis of the p1eceding section is, therefore , valid •
`over the 100-Hz bandwidth of interest.
`
`(6)
`
`D, 5geometrlc
`
`0
`
`h (1L ml
`Fig. 6. Sensitivity S, resonant frequency In, and deflection D versus
`beam thickness h. Accelerometer dimensions: w = 0.02 cm, c1 =
`0.06 cm, b"' 0.01 cm, M,. 4.5 X 10-4 g (scale fo1 S must be multi(cid:173)
`plied by Ileff to obtain t:.R/R).
`
`Optimization
`We now have the tools to explore the capabilities and limita(cid:173)
`tions of this miniature accelerometer. Expressions for the
`(Jependence of the sensitivity , resonant fre.quency, and deflec(cid:173)
`tion of the accelerometer on its geometric and materials pa- .
`•• rameters have been ·developed which apply, in fact, to any
`accelerometer design consisting of a uniform cantilev1ned
`beam, a mass, and a stress-sensitive element to detect the·stress
`-in tl1e beam. Therefore, much . of the following discussion
`. applies rather generally to small accelerometers using the canti(cid:173)
`• Jevered structure.
`Three materials parameters, the magnitude of the piezo-
`. resistive coefficients in silicon, the · density of the mass, and
`the fracture stress of silicon, set fundamental limits on the per(cid:173)
`In particular the relationship between the maxi(cid:173)
`formance.
`mum stress in the beam and the applied acceleration places an
`upper limit on the ·sensitivity
`
`• So CALCULATED FROM h GIVEN
`BY MEASURED RESONANT
`FREQUENCY
`
`1• 10 3 •
`
`ll: l g
`cmeuu<ed)
`
`2.4•107
`1.2•107
`S0 I g (calcel• ted) •
`·Fig. 7. Experimental versus .theoretical geometric sensitivity. Slope =
`3.5 X 10-11 ~ni2/dyne = ~ff•
`
`3.6 x1o"
`
`. current package size allows a dynamic range of 1C>4 and ranges
`of Ho 103 g.
`
`•
`_neff
`[2c1+L+b]
`So I max - - ; ; Gfract11re . 2 (L + Ci)
`3.SX 109
`0.1 2
`~n
`~--
`a,
`· a,
`
`eff
`
`-
`
`(7)
`
`where a, is the range in acceleration, Gfractu re the fracture
`stress, n eff the effective piezoresistive coefficient, and where
`2c 1 >> L-t b.
`The geometry of the accelerometer also has a profound ef(cid:173)
`:fect on its performance. The most significant parameter is the
`beam thickness h, whose impact on sensitivity, resonant fre (cid:173)
`quency, and beam deflection is plotted in Fig. 6 for typical
`values of h. The optimal choice for h is the smallest value con-
`• sistent with the bandwidth and deflection constraints (SE•t by
`the glass wells) in the design, since this choice gives both a
`• large gain-bandwidth product and minimal transverse axis re-·
`· ' sponse. The minimum beam thickness, from fabrication and
`, deflection considerations, is S µm. Although w and M a]$O in(cid:173)
`fluence the performance, the beamwidth is set primarily by
`structural considerations, while tlte mass is a convenient way
`of setting the sensitivity. By selecting h and Ma wide variety
`• of accelerometers of differing ranges, sensitivities, and useful
`bandwidths can be built from the same basic structure. The
`
`V . · EXPERIMENTAL RESULTS
`The static. responses of accelerometer:s of varying beam di(cid:173)
`mensions and masses were measured u$1.ng the· acceleration of
`gravity as a reference. By .varying the orientation of the beam
`with respect to gravity, ·and comparing the outputs, the con(cid:173)
`tributions · of each of the three ccmponents of acceleration
`. were determined .. . The observed outputs were linear in ay and
`ax, while no dependence on ai was detected, as predicted by
`(1) and (2). The measured fractional resistance change due to
`ay is . graphed for several accelerometers in Fig. 7 against the
`prediction in (1), omitting the term in the piezoresistive co(cid:173)
`efficients. The points fall beautifully on a straight line through
`the origin with a slope of 3.5 X 10-11 cm2/dyne, very close to
`the 4.5 X 10-11 calculated for Ilen, using published values for
`the piezoresistive and elastic compliance coe-fficients.
`Turning to the most significant transverse or off-axis re.(cid:173)
`sponses, which are plotted in Fig. 8, two of the terms, e 1 and
`e3 , representing the effects of axial stress and of a berun of
`nonzero mass, respectively, are found to be extremely small
`even under worst case conditions. The third, and critical, com(cid:173)
`ponent, e2 ; arises from the momentM2 due to an acceleration
`
`Authorized licensed use limited to: University of Maryland College Par!<. Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0004
`
`

`

`ROYLANCE AND ANGELL: BATCH-FABRICATED Si ACCELEROMETER
`
`1915
`
`SENSITIV ITY TO a, : ERROR TERMS e1, t 2 , • ,
`0 .25,,---'oa;;:.O=O __ lc.m ______ ---'-or"".005~----- --,0.01
`
`0
`
`-?.
`
`0.1
`
`OJ
`
`Q
`
`0
`
`10
`
`• DATA POINTS
`
`e3 mu value
`1.1 • 1 ~.,
`e,
`
`h (,.ml
`Fig. 8. Components of relative sensitivity to ax; e 1 , e3 versus beam
`thickness h ;e2 versus l'z .
`
`20
`
`30
`
`(a)
`
`ax. For a large mass mounted on one side of the paddle, this
`component is a substantial fraction of the y..axis sensitivity
`S0 , although it decreases to zero for a symmetrically mounted
`mass. Data from several accelerometers are plotted in Fig. 8
`and show the trend predicted, although the rather large un(cid:173)
`certainty in the magnitude of c2 prevents assessment of the
`accuracy of the theory to better than about 20 percent.
`To compare the two-pole model with the actual behavior of
`the accelerometer, the impulse responses of several accel~rom(cid:173)
`eters were determined experimentally .1 Oscillograms of a
`typical impulse response can be found in Fig. 9. The damped
`sinusoidal behavior and the clean characteristics of the first
`few cycles indicate that the two-pole model is indeed a good
`choice. Values of the resonant frequency were found to agree
`very well with (6). Despite a factor of eighteen variation in
`sensitivity for the accelerometers tested, all had similar values
`for the damping factor t Q, and the damping force Fd, corre(cid:173)
`sponding to air damping of the beam plus any internal damp(cid:173)
`ing in the silicon. The exponential decay shown corresponds
`tot= 0.0046, Q = 109, and Fd = 0.065 dy/dt (dynes).
`Damping the beam resonance by adding a suitable fluid to
`the accelerometer cavity is a very attractive approach to
`minimize the impact of the resonance and increase the useful
`bandwidth. Four common laboratory fluids of roughly equal
`densities, acetone, methanol, deionized water, and isopropyl
`alcohol, were used to investigate the dependence of the ac(cid:173)
`celerometer damping factor on fluid viscosity. The damping
`factor was found to vary linearly with fluid viscosity, as shown
`for one device in Fig. 10, while the viscosity needed to give 0.7
`critical damping was found, by extrapolating the data points,
`to vary between 3 and 4 centipoise depending on the device . •
`Some of the silicone oils have viscosities of this magnitude, and
`may well prove attractive to damp the accelerometer.
`Damping the accelerometer will make it Jess susceptible to
`small fluctuations in ambient temperature, due to the increase
`in thermal mass, and may also help maintain the two resistors
`at the same temperature, both desirable effects. However, the
`
`(b)
`Fig. 9. Accelerometer impulse response. (a) 1 V/vert. div., 5 rns/horiz.
`div. (b) Same device, 1 V/vert. div., 0.5 rns/horiz. div . .
`
`100 , - - - -- -- - - - - - - ,
`
`ISOPROPYL
`
`ACETONE•
`
`01 Hp
`"ME THANOL
`
`IR
`
`,o·•~ .._.._._......,_...__._~-..__ ....... ~
`10 ·1
`10°
`10'
`VISCOSITY ( <p)
`Fig. 10. Damping factor versus damping fluid viscosity.
`
`beam and mass are totally immersed in the damping fluid , so
`that the buoyant force on the mass must be considered in
`determining the sensitivity of the damped accelerometer. In
`effect, the -mass appearing in (I) is reduced by the mass of an
`equal volume of fluid. Although this change has little effect
`for a device with a gold mass, it can be important for a silicon
`mass device, particularly if the fluid density approaches the
`density of silicon.
`
`1 The accelerometer was mounted on one face of a shon piece of drill
`rod used as the weight for one pendulum of a dual-pendulum arrange(cid:173)
`ment. A steel sphere weighting the other pendulum was released from
`a measwed distance to swing into the opposite face of the rod; the re(cid:173)
`sultini impact is an impulse on the time scale of the accelerometer.
`
`Perfomuznce Limitations
`Perceived accelerometer performance is affected by two in(cid:173)
`escapable properties of real systems, noise and temperature
`sensitivity. Thermal noise ultimately determines the useful
`
`Authorized licensed use limited to: University of Maryland College Pan<. Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0005
`
`

`

`1916
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-26, NO. 12, DECEMBER 1979
`
`EQUIVALENT
`ACCELERATION• 15.2g
`
`"
`
`range of the accelerometer. Measurements made on several
`accelerometers • Indicate that the resistors contribute only
`Johnson noise, so that fairly conventional amplifier noise
`analysis and design techniques are applicable to the accelerom(cid:173)
`eter. Modeling the system as a Wheatstone bridge followed by
`a single amplifier stage, the minimum detectable acceleration
`amin (for signal/noise= 1), assuming a low noise amplifier and
`a 100-Hz bandwidth, is
`
`(8)
`
`,
`1
`a . =
`min 1.5 X 108 vPs /s.R/R
`where Ps is the power supplied to the bridge, t:.R/R is the fac(cid:173)
`tional resistance change per unit acceleration of the accelerom(cid:173)
`eter, and R = 7.5 kn. For the most sensitive designs amin is
`less than 0.001 g.
`The temperature dependence of the accelerometer output
`imposes another limitation on performance. Both the resis(cid:173)
`tance differential between the sensing and temperature com(cid:173)
`pensation resistors and the sensitivity t:.R/R are functions of
`temperature. The drift in the accelerometer output is due
`principally to the combination of the temperature coefficients
`of the diffused resistors and any mismatch between the re(cid:173)
`sistors. However, since drift can be eliminated whenever it is
`not necessary to measure true de acceleration, the thermal
`variation of accelerometer sensitivity is generally more sig(cid:173)
`nificant. This variation is due to the temperature coefficient
`of the piezoresistive effect in silicon, and has been found to be
`between -0.2 and - 0.3 percent per degree Celsius, in agree(cid:173)
`ment with published values. Although this variation is not sig(cid:173)
`nificant for the constant temperature environment of the
`body, for other applications both th.e sensitivity change and
`the drift can be compensated for by using more elaborate tech(cid:173)
`niques on the temperature compensation resistor output.
`The final concern in evaluating limitations on accelerometer
`performance is the linearity of the input-output characteris(cid:173)
`tics. This linearity was verified experimentally by measuring
`outputs over th~ range ±1 g and peak responses to impulses of
`various magnitudes. Results from several accelerometers are
`plotted in Fig. 11 against the magnitude of the applied im(cid:173)
`pulse, with the equivalent peak acceleration given for each de(cid:173)
`vice. The output characteristics are quite linear even though
`the data include points up Jo roughly one-fifth the acceleration
`at which the devices are expected to break. The nonlinearity is
`about ±2 percent of the maximum output, due to the bridge
`configuration and other sources such as the nonlinearity of
`the piezoresistive effect at high stress levels.
`
`VI. CONCLUSION
`The purpose of this section is twofold: to summarize the key
`characteristics of this accelerometer, and to evaluate what has
`been achieved in its fabrication. The characteristjcs of two
`miniature accelerometers, one fabricated with a gold mass and
`the other with silicon mass, are given in Table L They are
`represent ative of the range of devices fabricated during this
`investigation.
`Immediately apparent are the very small size
`and mass of both accelerometers-a major goal. Further, most
`of the remaining device characteristics are more than adequate
`for the proposed applications, and compare favorably with
`
`d
`Fig. 11. Linearity of accelerometer response: impulse ~ 0.37 wnd.
`
`5
`
`10
`
`15
`
`20
`
`TABLE I
`CHARACTERISTICS OF THE MINIAT URE A CCELEROMETERS
`
`Proper t y
`
`Si_ze
`
`Sili con Mass
`
`Gol d Mass
`
`2x3x0.61!11l
`
`Mass ( o f accelerometer)
`
`Range
`
`Ove r r ange
`
`Sens I tivi ty
`~/g
`
`mV/g/V supply
`Resonant Frequency
`
`0. 02 gm
`! 200 g
`! 600 g
`
`2 X 10·
`
`4
`
`0. 05
`2330 Hz
`
`Transverse Sens i ti vity
`
`10 ,:
`
`0.02 gm
`! 40 g
`! 120 g
`
`1 X 10"3
`
`0 .25
`1040 Hz
`
`2 %
`
`Non 1 i near i ty
`
`Thennal Zero Shi ft
`
`• ! 1% Full Scale
`
`°!1 . 4% FS/100°F
`
`Thermal Sensitivity· Shift
`
`! 11%/l00°F
`
`Res! st ance
`
`7.5 kn
`
`simi}ar (though much larger) commercial strain gauge acceler(cid:173)
`ometers. The undesirable t ransverse sensitivity of the silicon
`mass device is due solely to the asymmetric loading of the
`mass, and hence the cost of the miniature accelerometer comes
`in sensitivity and in thermal sensitivity shift. Temperature
`compensation of the response sl).ould reduce the thermal sensi(cid:173)
`tivity shift to close to ±1 percent/100°F in applications where
`thermal variations are important. In addition, the sensitivity
`of the present design can be doubled by going to a full bridge
`configuration with two active elements.
`This investigation has demonstrated the feasibility of an ex-
`. tremely small batch-fabricated accelerometer. The perfor(cid:173)
`mance and limitations of the miniature transducer have been
`thoroughly explored, and an understanding developed of the
`importance of symmetry In the design to minimize cross-axis
`responses. Accelerometers with sensitivities varying from
`AR/R = 5 X 10-s to 2 X 10-3 per g have been fabricated, al-
`
`Autnorized licensed use limited to: University of Maryland College Parle Downloaded on October 07,2023 at 21 :09:18 UTC from IEEE Xplore. Restrictions apply.
`
`Petitioner Samsung Ex-1039, 0006
`
`

`

`ROYLANCE AND ANGELL: BATCH-FABRICATED Si ACCELEROMETER
`
`1917
`
`lowing accelerations less than 0.001 g to be detected. The
`miniature accelerometers compare very well with the small
`strain gauge accelerometers available commercially, while pro(cid:173)
`viding more than an order of magnitude reduction in volume
`and mass. The small size of tbi_s accelerometer, coupled with
`its performance and the low cost potential of batch fabrica.
`tion, makes it extremely attractive for m~y applications.
`
`transition between the beam and paddle where the actual dis(cid:173)
`tribution of shear and nonnal forces due to a load on the mass
`is significant [ 6) . Replacing these forces by their resultants,
`the load on the equivalent cantilever is
`
`Fx = - Max Mx = M (Cgay - C2az)
`
`Fy =-May My = M(ciaz - C3ax)
`
`(A4)
`
`where a;, F;, and M; are the components of the acceleration
`and the resultant forces and moments. Applying the general
`theory of mechanics [7], (8) and the principle of superposi(cid:173)
`tion to the accelerometer's trapezoidal cross section and cubic
`anisotropy, a complete solution for the tensile stress distn1m(cid:173)
`tion and an approximate solution for the shearing stresses is
`obtained [2]. The tensile stress u~ is the only nonzero stress
`term appearing in (A3).
`
`] +
`M Mc2
`Mc3
`- + -
`0 = - a
`- y + - -z Oy
`[
`x A
`x
`fz
`~y
`
`[M(L +c1 -x) ]
`y
`~z
`
`+az
`
`[
`
`M (L + Ci - x) ]
`z
`j
`y
`
`(AS)
`
`where A is the area of the beam cross section and §i are the
`appropriate moments of inertia. The current flow in the re(cid:173)
`sistor can be assumed to be confmed to the surface of the
`beam, y = c - h, because of the doping profile of the diffusion.
`However , the stress in the beam must be averaged over the x
`and z excursions of the resistor to calculate the resulting frac(cid:173)
`tional re,sistance change (1).
`
`RE FERENCES
`{1) G. Wallis and D. I. Pomerantz, " Field-assisted glass-metal sealing,"
`J. Appl. Phys. , vol. 40, no. 10, p. 3946, Oct_ 1969.
`.
`(21 L. M. Roylance, "A miniature integrated circuit accelerometer for
`biomedical applications," Ph.D. dissertation, Department of Elec(cid:173)
`trical Engineering, Stanford University, Stanford, CA, pp. 47-80,
`1971.
`(3) Ibid. , pp. 74-78.
`[41 S. Timoshenko and D. H. Young, Elements of Strength of Ma·
`terials, Sth ed. New York: Van Nostrand Reinhold, 1968, p.
`197ff.
`[SJ W. T. Thomson, Theory of Vibration with Applications. Engle(cid:173)
`wood Cliffs, NJ: Prentice-Hall, 1972, p . 200.
`(61 Adhemar Jean Claude Barre de Saint-Venant, "Memoire sur la
`torsion des prismes," in Memoires des Savants Etrangers, vol. 14,
`1885.
`[7) S. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd. ed.
`New York: McGraw-Hill, 1951.
`(8) S. G. Lekhnitskii, Thea-y of Elasticity of an Anisotropic Elas