A silicon condenser microphone with structured back plate and silicon nitride membrane

Sensors and Actuators A, 30 ( 1992) 251-258

251

A silicon condenser microphone with structured back plate and silicon nitride membrane Wolfgang Kuhnel and Glsela Hess lnsrrtulfur Uhrrtragungstechmk md Elrkmmkusltk, (Recewed

March

29, 1991, accepted

November

Technache Horhschule Durms~odt, A4ercks~ruv.w 25, 61&I Dorms~ud~ (FRG)

12 1991)

Abstract The fabrlcatlon process of a s~hcon condenser mlcrophone and experimental results of the acoustic measurements are described The mlcrophone consists of two chips One chip carries the 150 nm thick slhcon mtnde membrane, which has an area of 0 8 mm x 0 8 mm The second chip contams the back electrode, the spacer and the contact pads of the mlcrophone In order to reduce the streaming resistances m the air gap, the back-electrode area IS either structured with grooves by a plasma etchmg technique or with holes by an amsotroplc etchmg techmque A frequency-independent sensitivity of IO mV/Pa (open circuit, 1 8 mV/Pa measured) up to 30 kHz IS obtamed as a result of this structuring of the back-electrode area Since the air-gap height 1s only 2 pm, the capacitance of the transducers ranges from I to I 3 pF The total size of the srhcon microphone IS I 6 mm x 2 mm x 0 56 mm

1. Introduction The fabncatlon of mechanical structures such as sensors on slhcon substrates became possible with the employment of mlcromachmmg methods based on semiconductor technology [ 1,2] In slhcon, sensors can be built with much smaller physlcal dlmenslons than 1s possible with conventional fabncatlon methods The mechanical constants of slhcon, oxide and nitride layers are well known, so an accurate modelhng of the mechanical behavlour IS possible Several kmds of sensors for the detection of pressure, acceleration, temperature, gas and liquid composltlon and other apphcations have been realized or are commercially available m a variety of configurations [3-81 One apphcatlon of mlcromachmmg techmques 1s the fabrication of microphones m &con Mlcrophones are basically pressure sensors that are constructed for the detection of airborne sound pressure Pressure levels rangmg from a few PPa up to 100 Pa and more have to be detected Airborne sound pressure levels can be 10 orders of magnitude lower than the barometric pressure, hence acoustic transducers need extremely thm membranes as compared with the diaphragms of barometnc pressure sensors The sensitivity of the microphones depends, among other thmgs, on the 0924-4247/92/$5

00

comphance of the membrane material, which 1s a constructional parameter that can be varied Normally an upper cut-off frequency of 20 kHz 1s obtained In the case of capacitive or plezoelectrlc microphones this value depends on the resonance frequency of the mechanical system Thm membranes yield high resonance frequency values, smce they have low mass terms During the past few years, mlcromachmmg techniques have been used to design and fabricate several microphones m slhcon [9] Plezoelectnc microphones are normally constructed as a onechip design and plezoelectrlc layers are made of zinc oxide (ZnO) or alummmm mtrlde (AlN) [lo121 In the field of condenser microphones, some different concepts have been presented [ 13- 161 In all cases condenser microphones consist of two parts One part carries the membrane of the transducer and the other part carries the back plate In some cases, the diaphragms of the microphones are made of polymer foils and the back plates are made of silicon These sensors are hybrid because of the different materials and fabrication processes Thm layers of slhcon mtrlde can be used as membrane materials so that the membrane chips can be built completely m slhcon technology Condenser microphones have an air gap between the membrane and back electrode The acoustic @ 1992

-

Elsewer

Sequoia

All nghts

reserved

252

behavlour of the air gap due to streaming reastances and comphances determmes the frequency behavlour of the transducers A structuring of the back-electrode area of the microphones 1s necessary to yield low streaming resistance values m the air gap In this paper a mlcrophone 1s described which has a diaphragm of sIllcon nitride and which represents the advanced implementation of d condenser mlcrophone prmclple previously described [ 171 Two tmplementatlons are presented, which have differently structured back-electrode areas Experimental results of the acoustic behavlour are given and are compared with results obtained with smooth and unstructured back electrodes Due to the structuring of the back-electrode area, the sensltlvlty values of the microphones were mcreased and the frequency response curves became nearly flat m the audio frequency range

2. Fabrication process The slhcon mlcrophone consists of two chips, a membrane chip and a back-plate chip Both parts are completely made of (lOO)-oriented n-type slhcon wafers The chips are exclusively fabricated by mlcromachmmg methods using semiconductor technology A cross-sectional view of the slhcon condenser microphone 1s shown m Fig 1 The fabrlcatlon of the membrane chip 1s described elsewhere [ 13, 171 Oxldatlon of the wafers with 100 nm SIOZ prevents bending during the successive procedures A 150 nm thick &con mtrade layer 1s deposited m a CVD process and subsequently implanted with Ions to reduce Its

Fig 1 Cross-sectmnal wew of the s~hcon condenser mcrophone smooth back-electrode area

wth

thermal tensions Imtlally, the lmplantatlon was carried out with nitrogen ions as 1s suggested m ref 5 Nitrogen IS unsmtable since it IS not normally employed m semiconductor fabrication processes The sIllcon nitride lmplantatlon IS preferably carried out with boron ions, since boron IS always available m technology lines An implantation energy of 60 keV leads to an average penetration depth of 150 nm of the boron ions m the nitride layer The dlstrlbutlon of lmplanted Ions m a sohd 1s approximately Gaussian The implantation dose IS varied between 1 and 9 x lOI cm-* The tensde stress m the slhcon mtrade layer 1s determmed by this dose A low dose of 1 x lOI cm-* generates little stress compensation and thus strongly stretched membranes, while a hrgh dose of 9 x lOI cmm2 leads to stressfree membranes A square 1 2 mm x 1 2 mm aperture 1s etched mto the slhcon mtrlde at the ummplanted side of the wafer Wet KOH etchmg 1s applied, which etches completely through the wafer The amsotropy of the KOH etching results m an angle of 54 7” between the surface of the wafer and the walls of the recess The borondoped slhcon nitride layer at the bottom of the recess acts as an etching stop After the KOH etching, a 0 8 mm x 0 8 mm membrane remains As a last step the membranes are metalhzed with 100 nm alummmm As a first step for the fabrication of the backplate chip, the back-volume shts of the transducer are amsotroplcally etched from the back side of the wafer The back volume of the microphone 1s formed by these slits Between the slits a bridge 1s placed, which carries the back electrode of the transducer In the followmg step the back-electrode area 1s structured with grooves or holes (see Fig 3(a) and (b)) m order to reduce streaming resistances m the an- gap of the microphone An oxide base 1s produced at the margin of the backplate chip, which determines the spacer between the membrane and back plate The oxide base, coated with alummmm, 1s guided to a connecting pad on the rear of the chip This provides the contactmg of the membrane metalhzatlon The back electode and a second pad are connected with a conductor made out of evaporated alummmm, which IS led to the rear side of the chip through a small hole m the oxide base This hole 1s also used for the static pressure compensation of the microphone

253

(b)

(d)

(e) Fig 2 Fabrlcatlon process of the bdck-plate chip (a), back-volume shts, (c), structunng of bdck electrode, (d), spacer, (e), msulatmg layer and metalhzatlon

A schematlc representation of the fabrication process of the back-electrode chip IS shown m Rg 2 The fabncatlon steps of the chip are described below m the sequence shown m the Figure (a) The base material IS (lOO)-oriented nslhcon with a reslstlvlty of 9- 11 R cm and a thlckness of 280 pm A thermal oxldatlon (dry, 1000 “C) produces a 100 nm thick oxide layer A sillcon nitride layer with a thickness of 150 nm ISdeposited m a CVD process The slhcon mtnde and oxide layers are opened at the back side of the wafer The two masking windows are 1 4 mm x 0 6 mm m size (b) An onentatlon-dependent etching produces the back-volume slits of the microphone The etchant IS 10% KOH wrth a temperature of 47 “C and an etching time of 23 5 h, correspondmg to an etching rate of about 12 pm/h As a result of the etching, two rectangular slits remam at the top side of the wafer having an area of 1 mm x 0 2 mm The slits connect the au=gap of the transducer with the back volume (c) The back-electrode area IS structured with grooves or holes Nitride and oxide layers are

opened and a plasma etching process 1s used m the case of the fabncatlon of grooves, while for the fabrication of holes amsotroplc KOH etching IS applied Two different plasma etching processes can be applied to the wafer either m a SF,/02 (50/20) plasma or m a CHFJO* (20/2) plasma, which both show similar etching rates m s&on The etching times are 3 and 3 5 mm, resulting m a groove depth of lo- 12 p A groove width of about 30 pm IS obtained Holes m the back electrode are produced by KOH etching m a solution as described m (b) The edge length of the square holes 1s 80 pm and the depth amounts to 3540 pm The natural etch stop of the (111) planes at the bottom of the holes IS not used, it would generate a hole depth of 57 pm (d) The mtrrde and oxide masking layers are removed, and a thermal oxldatlon (wet, 1100 “C) produces a 2 pm thick oxide layer This IS structured m such a way that the spacer of the mlcrophone and the capillary for the static pressure compensation are formed The height of the oxide spacer determines the air-gap height of the mlcrophone (e) A second oxldatlon (CVD, PSG-pyrox) produces a 2 pm thick insulating layer m order to reduce the stray capacitances between the back electrode and the slhcon substrate Finally, a 500 nm thick alummmm layer IS evaporated and structured to form the back-electrode area with the connecting line, the contact metalhzatlon for the membrane and the connecting pads of the transducer The back electrode has an area of 0 5 mm x 0 6 mm, while the connecting lme IS only 10 pm wide SEM photographs of the back-plate chips with grooves and holes m the back-electrode area are shown m Fig 3(a) and (b) The structures m the back electrode reduce streaming resistances m the microphone’s air gap and increase the air-gap compliance Slits for the connection of the air gap and the back volume are beside the back-electrode area To form the spacer of the microphone, the 2 pm thick oxide base IS placed at the margin of the back-plate chips The entire dlmenslons of the chips are 1 6 mm x 2 mm x 0 28 mm For the purpose of assembling the transducer, the back-plate chip IS first glued onto a small epoxy plate, which possesses connectors for the bonding wires and the slgnalhng lines Then the membrane chip 1s put onto the back-plate chip

254

ducer with a polanzatlon voltage, so that the charge on the condenser plates 1s kept approxlmately constant The input resistance of the preamphfier, which transforms the output srgnal of the microphone, forms a high-pass filter with the transducer’s capacitance A microphone capacitance of 1 pF reqmres an input resistance of 8 GR to yield a lower cut-off frequency of 20 Hz The mput capacitance of the preamphfier, together with stray capacitances, forms a capacmve voltage divider with the microphone The open-circuit output voltage of the microphone 1s reduced due to the ratio of the capacitances The mechanical equivalent cu-cult of the s&con condenser microphone consists of three parts the radiation impedance m front of the membrane, the mechanical elements of the membrane itself and the elements that describe the behavlour of the air gap and the back volume The radlatlon impedance m front of the membrane corresponds to that of a circular membrane with the same area The real part I&,,) and the mass term M, of the radiation impedance for wR/c + 1 [ 181 are npoR4

PG4

R T(W)___._~*~~(~~=225x

10-‘6kgsm2

2c

(1) (b) Fig 3 SEM photographs of the back plate chip with (a) pldsmdetched grooves and (b) dmsotroplcally etched holes m the backelectrode drea

and IS adjusted under a microscope, so that the centre of the membrane 1s placed above the backelectrode area Glue IS put around the edges of the two chips, so that these are Joined in an alrtlght manner, except the capillary for static pressure compensation Finally, the bonds from the slhcon condenser mlcrophone to the contacts on the epoxy plate are fabncated

M,=;p,&

=;poL

= 3 x lo- ‘Okg

nfi

(2)

where p. 1s the density of air, c IS the sound velocity, R IS the radius of a circular membrane and a IS the edge length of a square membrane with the same area In the case of the silicon condenser microphone the edge length of the square membrane 1s a = 0 8 mm The mass of the membrane A4, and its comphante C, are derived from the solution of the fundamental mode of vibration of a square membrane n4

hfn,=spda2=75

x lo-“kg

3. Theoretical results Condenser microphones usually operate m a low-frequency circuit If no electret material is used’ to generate the electrical field m the air gap, an external polarlzatlon voltage IS necessary A high ohmic resistor IS used to supply the trans-

where p IS the density of the membrane material, d IS the thickness of the membrane and T IS its tensile stress For the calculation of the total density per unit area, pd, the densities per unit area of the s&con nitride and the alummmm layer have to

255

be taken mto account, smce both materials contribute to the total mass of the membrane The density of the slhcon mtnde 1s 3 3 x lo3 kg/m3, while its thickness 1s 150 nm The alummmm has a density of 2 7 x 10” kg/m-’ and a thickness of 100 nm Therefore the total mass per unit area amounts to pd = 0 76 x 10e3 kg/m* The tensile stress T arlses during the fabrlcatlon of the membrane The maximum value of the tensile stress 1s given by the different thermal coefficients of slhcon, s&con oxide and sIllcon mtnde With the elasticity moduh of the layers and the differences between the process temperatures during the fabrication of the layers and room temperature, the maximum tensile stress can be calculated to be T,,, = 200 N/m (The tensile stress of a layer (L), placed on a substrate (S) 1s given by E,(aL - a,) ATd,, where E IS the elastlclty modulus, ~11sthe thermal coefficient, AT 1s the temperature difference and d IS the thickness ) Implantmg boron ions mto the slhcon mtnde reduces this value as a function of the implanted dose At a certain dose the tensile stress inverts mto compressive stress dnd the membranes become corrugated The behavlour of the air gap of the transducer 1s represented by the streaming resistance R, and the compliance C, A rectangular slit, the height of which 1s small compared to its width and length, has a streaming resistance given by [ 19,201 I 3 R,=12/~~0 i

0

where p = 1 86 x lo-’ kg/m s is the viscosity coefficient of air, w 1s the width, h 1s the height and 11s the length of the slit In the case that the air in the gap streams concentncally towards holes m the back electrode, the expresslon for the streaming resistance 1s given m ref 21 The resistance of one hole 1s (6) where X, = 1 13& and 24, 1s the distance between two holes R IS the radius of one hole and da IS the height of the air gap The compliance C, of a closed volume V 1s given by [ 191 V c, = poc2A:

(7)

A, represents the effective cross-sectional area that 1s traversed by the volume velocity Comphances

Fig 4 Equwalent mechantcal ctrcutt of the mwophone mg to eqn (8)

correspond-

appear m the air gap and m the back volume of the transducer The air-gap compliance C, of the s&con microphone has a low value due to the small air-gap height of only 2 pm In order to mmlmlze its influence on the acoustic behavlour of the transducer, the compliance of the back volume, C,, should be as large as possible The mechanical impedance Z,,, of the mlcrophone follows from the equivalent mechanical c1rcult of the transducer, which 1s shown m Fig 4 1

zm= &co,,+ JW@'fr+ Mm) + J@Gil 1 + iJWC, + JOC& 1+ JwR,C,)I

(8)

The structure of the last fraction m eqn (8) depends strongly on the constructional features of the back electrode m the microphone If the volume velocity IS divided mto different streaming paths m the air gap, the expression becomes more complicated The open-arcult output voltage U, of a condenser microphone under the assumption of constant charge on the condenser plates 1s given by EF v,=E~=Ev,=-_JO

JOZ,

EPAH Jlc.‘Z,

(9)

where E IS the electrical field m the arr gap, x 1s the membrane deflection, II, = JOX is the velocity of the membrane, F =pA, 1s the force on the membrane and p 1s the sound pressure Equation (9) gves the sensltlvlty M, of the microphone

,=c’,=%!z P

JOZ,

(10)

Calculations with numerical values of the transducer’s mechanical elements yield predlctlons on the sensltlvltles and the frequency ranges of the microphones The polarization voltage was assumed to be 28 V This value takes into account three facts (1) due to electrostatic forces, the

256

membrane of the microphone 1s statically deflected, (2) the electrical field m the air gap may not exceed the value where an electrical puncture may occur, and (3) a polarlzatlon voltage of 28 V 1s directly available at the Bruel + KJzr measuring equipment Tensile stresses in the membrane material were varied between 10 and 200 N/m The calculated sensltlvltles are m the range l-10 mV/Pa, which corresponds to -60-40 dB (re 1 V/Pa) In the case of smooth and unstructured back-electrode areas, the upper cut-off frequency 1s hmlted to the region 500-5000 Hz, dependmg on the stress In the membrane The value of the upper cut-off frequency IS mainly determined by the resistance of the au gap Transducers with lower membrane tenslons yield higher sensltlvltles and lower cut-off frequencies A high value of streaming resistance m the air gap is responsible for the absence of a recogmzable membrane resonance These results are m good agreement with the measured behavlour [ 131 If the back-electrode area 1s structured with holes or grooves, the cut-off frequencies are shifted into the range 100-300 kHz These structures have lower streaming resistance of the air gap, while the correspondmg compliance 1s increased

4. Experimental results Measurements of the membrane deflections were reahzed with a Michelson interferometer The membrane chips were glued onto circular metal plates with a hole m the middle, such that the hole was centred opposite the membrane area The metal plates could be screwed onto a cyhndrlcal tube having a volume of 18 cm3, which m addltlon had a connectlon facility for a mu-uature loudspeaker Thus the membranes could be excited mto vibration by the loudspeaker from one side and were accessible to the laser beam from the other side The speaker was placed at the opposite side of the tube and radiated mto the tube volume A sound pressure level of some 10 Pa could be generated mslde the volume The pressure level m the tube was measured with a $’ Bruel + KJar microphone, which was plugged into an additional connector at the tube The measurmg frequency was 600 Hz The tube was installed m a Michelson interferometer where the laser beam was focused onto the middle of the membranes and the centre deflectlon was measured

Pa

Fig 5 Centre deflectmn of the Acon mtrlde membranes as a functmn of sound pressure Parameter LSthe boron Implant&Ion dose (see text)

Figure 5 shows the results of the measurements The effective (rms) value of the sound pressure for the excitation of the membranes was m the range O-4 Pa Figure 5 shows the effective (rms) deflection values of the membrane centre The parameter of the measured curves 1s the boron implantation dose of the membranes The membranes of curve (a) have low lmplantatlon doses of 1 x lOI cm -’ and thus high mechanical tensions, which resulted m small deflection values Curve (e) represents membranes with implantation doses of 9 x lOI cm-‘, the stresses of which are largely compensated Implantation doses of the membranes of the mtermedlate curves are curve (b), 3 x lOI cmm2, curve (c), 5 x lOI cme2, curve (d), 7 x lOI cme2 The relation between deflection per unit pressure and the implantation dose 1s not linear, but increases with ascending implantation dose This result 1s In a good agreement with previous results [ 22,231 The sensltlvlty, frequency range and the noise of the microphones were measured The transducers were mounted onto small epoxy sheet bars with metal plates on the lower sides The metal plates have a y hole with female thread and can be screwed onto a p Bruel + KJar 2633 preamplifier A small brass pm provides the signal contact, whereby one end of the pm 1s connected to the preamphfier mput contact while the other one IS bonded to the back-electrode contact of the mlcrophone The membrane contact of the transducer IS connected to ground The Bruel + KJser preamplifier has a resistive input of 25 GR parallel to a capacitance of 0 25 pF A d c polarlzatlon voltage of 28 V was taken to supply the transducers, since this voltage 1s directly available at the Bruel + KJaer 2610 measuring amplifier

251 -LO

dl3

-50 -50 -70 -60 -90

-100 kHz

(a) -LO

-M -60 dEJ

-70

-90 -100 01 02

05

1 2 kHz

5

10 20

(W Fig 6 Measured frequency response curves of the s~hcon microphones with (a) plasma-etched grooves and (b) amsotroplcally etched holes m the back-electrode area (dB re 1 V/Pa) Parameter IS the boron lmplantatlon dose of the membrane (see text)

A sound pressure level of 94 dB ( z 1 Pa) wlthm a frequency range 100 Hz-20 kHz was used for measuring the frequency-response curves A highpass filter for the suppression of 50 Hz hum was necessary because the microphones were unshielded on their epoxy plates The measured frequency response curves are shown m Fig 6(a) for backelectrode chips with plasma-etched grooves (see also Fig 3(a)) and m Fig 6(b) for back-electrode chips with amsotroplcally etched holes (see also Fig 3(b)) The measured curves were obtamed for systems with different boron Implantation doses of the nitride membranes The curves denoted (a) are recorded for membranes that have lmplantatlon doses of 9 x lOI cm-* and are thus essentially free of tensile stress Curves (b) and (c) are for membranes with lmplantatlon doses of 5 x 1Ol4cmd2 and 1 x lOI cm-* The lower implantation doses yield a smaller reduction m the tensile stresses and therefore result m lower sensltlvlty values The measured sensltlvltles for microphones havmg grooves m the back electrode (Figs 3(a), 6(a)) are between 0 12 and 1 8 mV/Pa If instead back electrodes with holes are used (Figs 3(b), 6(b)), sensltlvltles between 0 09 and 0 56 mV/Pa are obtamed The measured sensltlvlty values are about 12-15 dB lower than the calculated ones Stray capacitances, which reduce the microphones’ out-

put voltages, are responsible for this Stray capaatances normally exist between bonding and connectmg wu-es and the substrate, the backelectrode area and the substrate, border regons of the membrane metalhzatlon and the substrate and also between the substrate and ground The total value of all the stray capacitances mcludmg the mput capacitance of the Bruel + IQer preamplifier 1s m the region of 4 6 pF Microphones with grooves m the back plate have a sensor capacltance of 1 pF, while those with holes tn the back plate have a sensor capacitance of 1 2 pF Signal attenuation caused by stray capacitances 1s m the first case - 15 dB and m the second - 13 7 dB The open-circuit sensitivity of microphones with grooves m the back electrode and stress-free membranes (Fig 6(a), curve (a)) 1s then -40 dB, which corresponds to 10 mV/Pa The results of sensltlvltv measurements on slhcon microphones with smooth back-electrode areas are described elsewhere [ 13, 171 The sensltlvltw here were m the range 0 05-l mV/Pa, depending on the Implantation doses Highly implanted membranes yielded higher sensitivity values, but had lower cut-off frequencies that those with low lmplantatlon doses Due to streaming losses m the air gap, microphones wth a sensltlvlty of 1 mV/Pa showed a cut-off frequency of 2 kHz An attempt to measure the noise of the transducers with the Bruel+ KJaer equipment ylelded no reliable results The Bruel + KJaer 2633 preamplifier and the 2610 measuring amplifier generate an A-weighted noise voltage of 5 PV Since the noise voltages of the microphone, UNm,and of the amplifiers are statlstlcally independent, the total measured noise, UNt, amounts to uNt = [u$, + (5 pvp] ‘I2 Assuming a measuring error of less than l%, the noise voltage of the mlcrophone alone is then UN,,,< 0 7 pV The equivalent soundpressure level for microphones with a sensitivity of 1 8 mV/Pa (Fig 6(a), curve (a)) would then be ~25 dB A-weighted if measured with a noise-free amplifier

Acknowledgements

The authors are indebted to Professor G M Sessler for giving the incentive to this work and for stlmulatmg discussions Thanks also to Dr K Haberle for his helpful advice, and to

2%

I Kopermck, G Tschockel, R Heller and W Geyer for technical support This work was carried out m cooperation with the Instltut fur Halbleltertechmk of the Techmsche Hochschule Darmstadt and was sponsored by the Deutsche Forschungsgememschaft

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9 G M Sessler, Acoustic sensors, Sensors and Actuators A, 25-27 (1991) 323-330 10 M Royer J 0 Holmen, M A Wurm and 0 S Aadland, ZnO on Sl Integrated acoustx sensor, Sensors and Actuators, 4 (1983) 351-362 II J Franz, Plezoelektnsche Sensoren auf Sdlzmmbasrs fur akustlsthe Anwendungen, Fortschrrtt-Berrche VDI, Vol IO, No 87, Darmstadt, 1988 R S Muller IC processed plezoelectrlc microphone, US Patent No 4 783 821 (Nov 1988) D Hohm, Kapantlve Bhzmm-Sensoren fur Horschallanwendungen, Fortschntt-Berrchte VDI, Vol IO No 60, Darmstadt, 1986 A J Sprenkels A slhcon submmlature electret nncrophone. Them, Enschede, 1988 P Murphy and K Hubschl, Submmlature &con Integrated electret capacitor mlcrophones, IEEE Tram Electr lmul, E/-24 (1989) 495-498 I6 K Suzuki, K Hlguchl and H Tamgawa, A slhcon electrostatic ultrasomc transducer IEEE Tram Ultrason , Ferroelectr Frey Control, UFFC-36 (1989) 620-627 17 D Hohm and G Hess, A submmlature condenser microphone with slhcon-mtrlde membrane and silicon backplate, J Acowt Sot Am, (Jan 1989) 476-480 18 P M Morse, Vtbratton and Sound, Acoust Sot Am , CambrIdge MA. 1981 19 H F Olson, Acoustrcal Engmeemg, Van Nostrand, New York, 1957 20 J K Wood and G B Thurston, Acoustic Impedance of rectangular tubes, J Acoust Sot Am, 25 (1953) 858-860 losses m the 21 Z Skvor, On the acoustical resistance due to VISCOUS an gap of electrostatic transducers, Acusfrca, 19 ( 1968) 292-299 22 E P EerNlsse, Stress m Ion-implanted CVD-slhcon-mtnde-films, J Appl Phys, 48 (1977) 3337-3341 23 W Kuhnel, Grundlegende Verfahren der Mlkrostrukurtechmk, Tech Rep, Sennheiser, June 1987