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johnnepaleseElectronics - Devices

Oct 10, 2013 (3 years and 10 months ago)

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312
Sensors
and Actuators, A26At3(1990) 312-315
Capacitive Silicon Accelerometer with Highly Symmetrical Design
H SEIDEL, I-I RIEDEL, R KOLBECK, G MOCK, W KUPKE and M KL)NIGER
Messerschmi~t-B~~ow-~~o~ Gm&& P 0 Box 801109, D-8&@ Munzch 80 FR G )
Abstract
The destgn and performance of a capacltrve
~crom~hanlcal accelerometer, as well as an elec-
tromc crrcult for the condlttonmg of the output
signal are described The sensing element consists
of a differential capacitance which 1s formed by a
seismic slhcon mass and two counter electrodes
situated on anodlcally bonded glass plates The
mass IS s~e~~lly suspended on at least eight
cantilever beams located on both sides of the
slhcon wafer For a f 5 g device a typical sensltlv-
lty of 1 pF/g wth a zero capacitance of 10 pF and
a detection hmlt below 1 mg was achieved For
signal condlttonmg a s\krltched capacitor CMOS-
ASIC was developed, yieldmg an analogue voltage
output sIgna
The rapidly advancmg techmques for the
micromachimng of sdicon allow for the fabnca-
&on of a multrtude of mmiatunzed sensors and
actuators Among these, sensors for pressure and
acceleration have attained the highest degree of
mdustnal development
Most s&con accelerometers published to date
use the plezorenstlve prmclple to measure the
mechamcal stram m a cantdever beam, defiected
by a seismic mass under acceleration
[
1,2] The
&stance change IS converted to a
voltage change
by the usual bndge configuration This prmciple,
however, lmphes a relatively large temperature
dnft and long-term dnft, and also restricts the
usable temperature range Furthermore, plezo-
reststive devices are qmte senslhve to mechamcal
strain Induced by the fabncation process or by
packagmg
In capacitive accelerometers, the seismic mass
IS mmultaneously used as one electrode of a van-
able capacitance, moving wrth respect to a counter
electrode situated on a second plate Thus, a
capacltlve sensor measures a vanable &stance due
to the deflection of the movable plate [3,4] Tha
prmclple leads to significant advantages concern-
mg the above-mentioned problems of plezorens-
tlve devices
For the purpose of achlevmg a low cross-ams
~ns~~~ty and a good hnear behavlour of the
sensor output signal, a h@y symmetric suspen-
sion of the ~srmc mass, leading to a parallel
movement of the capacitor plates, 1s desirable
TUB is one of the main design prmclples for the
accelerometer presented m this work
sensor
Deaerlptloll
The pnnclple design of the sensor 1s shown m
Fig 1 The movable plate IS formed by a block
connected to a surrounding frame by at least etght
cantilever beams located on both sides of the
&con wafer The th&ness of tlus block 1s p;lven
by the thickness of the wafer All suspension
beams are aligned with the &agonal axes of the
W
Fig 1 Schematic diagram of the capantrve accelerometer (a) cross xztxx~, (b) top view of seu~~c mass
~2~424~~~~S3 50 0 Elsevler ~uoia~~nted m The Netherlands
313
Rg 2 Scannmg electron mlcrogaph of the seisnuc mass of
the accelerometer
seismic mass, thus leading to a maximum symme-
try m the structure [5] Thus element IS fabncated
by amsotroplc etching techmques, including an
etch stop for the suspension beams A scanning
electron mlcrograph of this selsmlc element 1s
shown m Fig 2
The counter electrodes are located m etched
cavltles on glass substrates, anodlcally bonded to
both sides of the slhcon wafer Gold was chosen
as the electrode matenal The air gap between the
electrodes had a typical dlmenston of 5 pm, lead-
mg to a zero capacitance of 10 pF
In order to provide further posslblhtles for the
compensation of temperature effects, a second
pair of capacitors with ldentlcal dlmenslons to the
sensing element but wlthout the freeing of the
selsmlc mass was included on the same chip The
dlmenslons of the complete sensor element were
3 5 x 3 5 mm2 without and 3 5 x 7 0 nun’ mclud-
mg the reference capacitance pair
Signal Codtioning Circuit
In order to convert the sensor capacitance mto
an easily measurable quantity, a CMOS slgnal
condltlonmg clrcmt wth a voltage output was
designed This circuit uses switched capacitor
techniques It yields an output signal which IS
inversely proportional to the sensor capacitance
and therefore proportional to the acceleration ap-
plied Furthermore, a temperature compensation
1s obtained by formmg the ratio of the above-
mentioned reference capacitance and the vanable
sensor capacitance The circuit contams an ana-
logue section with CMOS operational amphfiers
as well as an integrated oscillator provldmg the
appropnate pulses for a multiple phase clock An
integrated sample and hold function, which IS
internally clocked at a rate of 100 kHz provides
the final output signal which can then be dlgltlzed
by an A/D converter
This clrcult and the sensor are placed m close
proximity by a hybnd integration m order to
mmnmze overall size and stray capacitances with
respect to the small sensor capacitance of 10 pF
Experimental Results
Characterrzatlon of the accelerometers was per-
formed with respect to sensitivity m static and
dynarmc apphcatlons as well as to temperature
behavlour and frequency response Vanous damp-
mg condttlons were applied to the sensor by con-
trollmg the pressure under operatmg condltlons
The sensitivity of the discrete accelerometer
was determmed on a precision turntable by mea-
surmg the sensor capacitance m the earth’s gravl-
tatlonal field, using a capacitance meter Stray
capacitances caused by the measurement set-up
were compensated by a cahbratlon procedure
Sensltlvltles of accelerometers under test were ap
proximately
1
pF/g with good reproduclhhty The
mmlmum detectable acceleration was found to be
below 1 m-g and was limited by the resolution of
the capacitance meter By using an appropnate
detection circuit wtth better resolution, the actual
hmlt can be further improved The output signal
of a sensor m the range of f 1 g 1s shown m Fig
3 Inverting the signal leads to a good hneanza-
tlon with a remaining devlatlon from hneanty of
less than 0 5%
-10 -08 -06 -0L -02 0 02 OL 06 g 10
ACCELERATION
Fig 3 Output signal of the accelerometer for a + 1 g mea-
surement m the earth’s gravitational field The top diagram
shows the capacitance, the bottom diagram shows the Inverse
capacrtance as a function of acceleration
314
-
twOucWCY
Rg 4 Dywmc behavtour of the accelerometer for ditTerent
residual
pressures m
the eavlty
The dynamrc behavtour of the accelerometer
was measured on a shaker at frequenctes rangmg
from 10 Hz
to
10 kIIz At atmosphertc pressure tt
was found to be damped apenodtcally due to the
sttffness of the an cushrons within the narrow
gaps Therefore the sensor has to be operated at
reduced pressure m order to achieve critical damp-
mg Measurements were made Hrlth a set-up that
allowed adJ~tment of the pressure from 1 to
1000 mbar, the results of which are shown m Fig
4 The largest usable frequency bandwtdth of the
sensor was obtamed at a pressure close to
10 mbar The resonance frequency at 1 mbar was
35kHz
For both parts of the dual-sided capacitance
the temperature behavlour of the accelerometer
was mvestigated from -40 “C to + 70 “C Each
indrvrdual capacnance exhibited a temperature
drift of 10 mg/K Usmg the ratio of both capacl-
tances as an output signal leads to a strong reduc-
tion of the temperature dnft down to a value of
approximately 20 PgfK
Discussion
The lughly symmetric design of the sensor
whmh Induces a nearly tilt-free movement of the
setsrmc mass leads to a good hnear behavlour of
the inverse capacrtance
The measured curves of the dynarmc sensor
behavlour do not comcrde with those expected
from a classical damped harmomc oscdlator m
two ways First, the resonance peak slufts towards
higher frequencies when the damping increases,
and secondly, a decrease of the ~nsi~~ty at
medium frequencies can be observed even when a
resonance peak still exists Tlus behavrour can be
understood by a careful analysis of the equation
of mohon for a harmomc oscdlator
Y(r) +2&Y(f) +&Y(r) = a exp(iutf)
Cl)
where Y(f) IS the tlcme-dependent elongatton, (I and
w are amphtude and frequency of the drrvmg
acceleratton, respecttvely, and w, ts the resonant
frequency This equahon is based on the assump-
tron that the dampmg force desertbed by the
parameter E 1s pro~~o~ to the velocsty of the
movmg object In our case, thts frictron arises from
the aerodynamtc drag of the senmuc mass m the
cavrty This force wrll only be proporttonal to the
veloctty if the relaxanon time of the gas 1s small
compared to the period of excttatton When relax-
atron tnne and perrod of excttauon are of compara-
ble magmtude, a tune delay of the f’rrettonal force
agamst the veloctty of the mass anses, due to a
slow relaxation of the ddferentlal pressure between
both au gaps Thus, we propose to introduce a
retardatron time T for the veloctty term Subshtut-
mg Y(f) by Y(t - r) m eqn (1) the new equation
of motion ytelds the fo~o~ng frequency response
L-4 lW3
r=
[(
l+6.n~~~~-~z~+(~~~~~~~ (2)
In order to obtain dunensronless quantrtms, the
following substrtutions were made e: = O/W,,
x = WIT, Q = 0,/2e and
A IS
the amphtude of
mohon By an approprtate choice of the parame-
ters Q and x m eqn (2) a good agreement wrth the
expenmental data can be achieved This is dlus-
trated m Ftg 5
Both the quahty factor Q and retardatton r can
be expected to be funcuons of pressure, tempera-
ture, and molecular mass of the gas, as well as of
the geometrical &menstons of the gap and the
setsmrc mass The precise nature of these func-
ttons remams to be determined For an optmuzed
6
0
0 OL 08
12 16 20
2L 2B
NORMALIfE FREOUENCY
Fxg
5
Calculated frequency response of an oscdiator, accord-
mg to eqa (2) assummg a retardation x = 12
315
frequency response of the sensor, all these
parameters have to be taken mto account
The measured temperature behavlour can be
attnbuted to the nusmatch of the thermal expan-
sion coeffiaents of slhcon and glass, which IS of
the order of 1 x 10P6 Despite the symmetnc
glass-sdicon-glass construction of the sensor,
ths leads to a bendmg effect of the glass plates,
changmg the sue of the air gap Consequently, a
one-matenal sensor construction wdl greatly un-
prove the thermal dnft behavlour
To summarize, a capacltlve &con accelerome-
ter has been reahzed which exhlblts a large sense-
tlvlty and good hnear behavlour, as well as a
relatively Hrlde usable frequency bandHrldth
References
1 L M Roylance and J B Angeli, A batch-fabncated s&on
accelerometer,
IEEE Trm Electron Devuzes.
ED-26 (1979)
. I
1911-1917
2 S Terry. A muuature s&con accelerometer mth budt-m
dampa&
Tech Dtgest, Sohd-State Sensor and Actuator
Workshov, H&on Head Zsland, SC. V S A
,
Jme 6-9. 1988.
pp 114-116
_ ,
3 K E Petersen, A Sharkl and N F Raley, Muxomechamcal
accelerometer mtegrated w&h MOS &e&on nrcwtry,
IEEE Tram Electron Devices, ED-29 (1982) 23-26
4
F Rudolf, A Jomod and P Benae, .%bam micro-
accelerometer,
Pm 4h Znr Conf Sold-State Sensors and
Actuators (Transducers ‘87), Tokyo, Japan, June 2-5, 1987,
pp
395-398
5
H Sexlel, Capantwe accelerometer, Ger
Parent DE
3625411 C2 (1988)