MicroElectroMechanical Systems (MEMS) for applications in

acoustics

Rui Sampaiorui.sampaio@ist.utl.pt

Instituto Superior Tecnico, Lisboa, Portugal

December 2013

Abstract

The success of MicroElectroMechanical systems (MEMS) as small microphones for mobile applicationverified in recent years is expected to be reflected in MEMS loudspeakers. Some advantages includevery low power consumption, low fabrication cost and integrability with CMOS technology.

The aim of this work was to present a new fabrication process based on PECVD amorphous silicon forultra-low power electrostatic MEM loudspeakers together with a consistent theoretical description andinitial experimental characterization. The first approach was carried by extending the well-developedprocess for thin bridges and cantilevers at INESC-MN. Because of the incompatibility of this processwith a loudspeaker application a second generation process was developed. The simplicity of the processis lost but important aspects such as low temperature, CMOS compatibility and the use of typicalmaterials in MEMS processing are retained.

A working prototype for the second generation is presented and the first generation processis revisited for a first study on the mechanical properties of the structures. Resonance frequencymeasurements in a pressure controlled environment are provided together with absolute deflectionmeasurements in the audible-rage. Finally a general discussion is provided setting design rules forfurther development.Keywords: MEMS, Electrostatic, Loudspeaker, Amorphous Silicon

1. Introduction

MEMS microphones are currently being adoptedfor many portable devices such as smartphones,tablets or laptops with a projected revenue of $493.5million for 2012 and $667.0 million by 2015 (IHSiSuppli Research, January 2012) and are replac-ing the conventional electret condenser microphones(ECM) [1]. Advantages of MEMS microphones in-clude immunity to electromagnetic interference andradio frequency radiation (for digital microphones),directionality, noise cancellation by using arrays ofmicrophones, on-chip integration, CMOS compati-bility and better performance and stability metrics[5].

The microphone working principle is the trans-duction of acoustical energy into electrical energyby conversion of mechanical movement to an elec-trical signal. Transduction mechanisms for siliconMEMS include piezoelectric, piezoresistive and con-denser [19]. In piezoelectric transduction the de-flection of the sensing diaphragm is converted intovoltage drop, sensed by a top and bottom electrodeon the diaphragm. Piezoresistive transduction isbased on the change of resistance due to the in-

duced strain on the diaphragm. Sensing is usuallyaccomplished in a Wheatstone bridge. Condensertransduction is based on the change of capacitancebetween the diaphragm and a sensing gate. This ismost widely and most successful implementation ofMEMS microphones nowadays.

MEMS loudspeakers are expected to share thesuccess of their microphones counterpart. Marketcompetitive product are however more difficult tocome by due to the need of large deflection or largeareas of actuation. Possible applications includemobile devices ([4], [9], [10], [14], [3]), hearing aids([7], [8]) and ultrasonic systems ([16], [11]) usingdifferent mechanisms of actuation such as piezo-electric, electrostatic, electrodynamic and thermoa-coustic.

Piezoelectric actuation is based on the contrac-tion of a piezoelectric block in between two elec-trodes by applying an external electric field. Typ-ical materials include ZnO and PZT usually de-posited on top of a silicon nitride layer for mechani-cal control and stability. Piezoelectric loudspeakersenjoy of a robust fabrication process and are easilyscalable for large areas, as far as hundreds of mm2.

1

Also they radiate as a monopole, circumventing theneed for front-side / back-side isolation. Their dis-advantage is the presence of a polarization - electricfield (PE) hysteresis curve and a low first resonancefrequency leading to a very non-linear response inthe audible range ([13], [12], [22], [10]). Electrody-namic actuation is based on the Lorentz force. Inthe presence of a magnetic field a current line expe-riences a force perpendicular to the current line andthe magnetic field. The magnetic field is typicallygenerated by a permanent magnet. Metal tracksare incorporated in the membrane and the deflec-tion is controlled by the current’s magnitude. Softmagnets are usually present to focus the permanentmagnetic field. The electrodynamic transductionmechanism is the most common in the literaturewith several different proposed devices ([21], [17],[3], [8], [2], [20]). Electrostatic actuation uses thereverse principle of capacitive microphones. Themembrane is driven by the electrostatic force im-posed by an external source. The fixed electrode iscalled the gate electrode while the suspended elec-trode is called the membrane or diaphragm. Elec-trostatic actuation is well suited very-low power ap-plication and integrability with CMOS dies. Themain disadvantages of electrostatic driving is a highvoltage cost and low deflection amplitudes ([16], [9],[18]).

Electrostatic MEMS loudspeakers present someadvantages over electrodynamic or piezoelectricdriven loudspeakers — they can be integrated ina CMOS dies, using common materials such as sili-con, aluminium or silicon dioxide, they have no DCpower consumption and require very low alternat-ing current amplitude avoiding local heating andmaterial deterioration. Unfortunately they presentstrong disadvantages such as high driving voltagesand low amplitudes of deflection when compared toelectrodynamic actuation, for example. The devicesproposed here aim for a very low driving voltage of3.3 V, with deflection of the order of 1 µm. The de-sign and choice of materials itself also allows array-ing of single structures, thus proving lower acousticwaveform deformation over large areas of actuationand better control over the membranes mechanicalproperties. For the particular application of hearingaids, low driving voltages with ultra-low power con-sumption and large areas of actuation are required.The purposed devices deliver on all these require-ments. Moreover, the novelty of the fabrication pro-cess in this field, overcoming the large voltage costdrawback, allows the possibility of entering on thevirtually unexplored market of MEMS loudspekersfor hearing aids. Finally, large area MEMS havestrong applications in other areas such as microflu-idics, physical sensors, biosensors or electronic com-ponents. While the process development and struc-

tural characterization and optimization is acousticoriented, valuable know-how is to be retained forsuch other applications.

2. Fabrication

Two fabrication processes were explored — a firstgeneration process resulting from the extension ofa previously well developed process for thin beamsand bulk resonators and a second generation pro-cess developed in view of the incompatibility of theformer for a loudspeaker application.

2.1. First generation

The first approach to the problem was to extendedthe well developed standard process for thin beamsand bulk resonators at INECS-MN to thin plateswith large areas, held by four tethers (Figure 1).The process is summarized in Figure 2.1 —(a) Theprocess starts with the cleaning of a two by oneinch glass substrate; (b) A sputtered TiW layer ispatterned by RIE to define the gate electrode; (c)Sputtered aluminium is used to defined the sacrifi-cial layer by wet etching; (d) the structural doublelayer a-Si:H/TiW is patterned by a single step ofRIE and (e, f) the substrate is diced into individ-ual dies and the sacrificial layer is removed by wetetching, releasing the structure.

2.2. Second generation

The proposed structures for the second genera-tion of loudspeakers are depicted in Figure 4 — aclamped a-Si:H plate (a) and a suspended squareplate (b) held by four tethers. Each membrane isseparated by an air gap from a gate electrode forelectrostatic actuation and the lateral dimensions,membrane side or diameter, are much larger thanthe air gap height or the thickness of the membrane.

The gate electrode and substrate are perforatedfrom side to side to introduce vent holes in order todecrease the compression of air between the mem-brane and substrate and allow the back-wave topropagate. Also, to assure a constant spatial dis-tribution of the electrical potential through out themembrane, a metal layer is present on top of themembrane, with thickness much smaller than themembrane’s. Finally, aluminium oxide (Al2O3) lay-ers are introduce between the gate and substrateand between the gate and membrane in the case ofthe clamped geometries for electrical isolation.

The proposed process is a 7 layer process with onelayer on the back-side of the sample plus 6 layerson the front-side of the sample. A summary of theprocess is depicted in figure 3

Alignment marks are first etched on both sidesof a double side polished, undoped < 100 > siliconwafer and individual rectangular substrates with 2inch by 1 inch are then diced from the silicon wafer.Sputtered alumina (Al2O3) is first patterned with a

2

(a)

(b)

Figure 1: 3D models of the first generation loud-speakers for the (a) perpendicular geometry and (b)parallel geometry.

Figure 2: Process overview of the first generationloudspeakers. a) 2 inch by 1 inch glass substrate;b)Patterning of the TiW gate; c) Patterning of theAl sacrificial layer; d) Patterning of the a-Si:H/TiWstructural layer; e) Dicing and f) structure release.Not to scale.

wet etch on the back-side of the sample. This will beused latter on as the hard mask for the DRIE of thesubstrate. A similar alumina layer is then patternedon the front-side of the sample for electrical isola-tion of the substrate. The gate contacts are thendefined using sputtered aluminium together with awet etch. A silica layer is introduce for passivationof the underling Al layer. Another alumina layer ispatterned on top of the gate layer for electrical iso-lation between the gate and membrane. The SiO2

sacrificial layer is then defined using a PECVD steptogether with a RIE step. The a-Si:H/Al structurallayer is deposited using a PECVD step for the a-Si:H and a sputter deposition for the aluminium.The aluminium is first patterned using a wet etchand the a-Si:H using a RIE step. The substrate isthen perforated from the back-side using a DRIEstep. The sample is diced into individual dies forthe release step with HF vapor finishing the micro-fabrication process. . For the suspended square ge-ometry the process is almost exactly the same withthe difference that the alumina layer for electricalisolation between gate and membrane and the SiO2

passivation layer are not present.Due to the complexity of the process and the re-

quirement for optimization on several steps, a sim-pler process was used for optimization of the deposi-tion of a-Si:H film and provide an initial experimen-tal characterization. The process is here referred asthe amorphous silicon deposition test process. Itreplicates every step of the full process with theexception of the DRIE step (and the back-side alu-mina hard mask). Small perforation are introducedon the membrane instead to allow the etchant toreach the sacrificial layer.

3. Theoretical DescriptionThe general form of the response of a thin plate toan harmonic excitation can be written as the sumof all natural modes for the particular geometry,namely,

w(η, ξ, τ) =

∞∑n=1

Gn(Ω4

n − Ω4) + j2ζΩ2Wn(η, ξ)ejΩ

2τ

(1)where w(η, ξ, τ) is the complex normalized displace-ment of the membrane at the normalized points η =x/a and ξ = y/a at the normalized time τ = t/tp, ais the side or radius of the plate, tp = ρta4/D, ρ isthe density of the material, t is the thickness of theplate, D = Et3/12(1−ν2) is the rigidity of the plate,E is the Young’s modulus, ν is the Poisson coeffi-cient, Ωn is the n’th natural frequency, Wn is then’th natural mode, Gn = (1/Nn)

∫dAFa(η, ξ)Wn

is a weighting factor determining the extent of theexcitation of the n’th mode, Nn =

∫dAW 2

n is anormalization factor, Fa(η, ξ) is the applied load,ζ = ca4/D is the damping parameter, c is the damp-

3

a

b

c

e

f

g

h

i

j

Substrate Al2O3 Al

SiO2 a-Si:H n+

perforation sites

d

via forwirebonding

Figure 3: Second generation loudspeaker processsummary. Image not to scale.

(a)

(b)

Figure 4: 3D models of the rectangular clampedgeometry and the suspended-square geometry. Notto scale.

ing coefficient and Ω =√

2πftp is the normalizeddriving frequency. For thin beams, the deflectiononly depends on one direction, say x, and D shouldbe replaced by EI where I = wt3/12 for rectangularcross-section, w is the width of the beam.

Depending on the case to be analysed, clampedrectangular plates, clamped circular plates or sus-pended squares, the coefficient Gn and the normalmodels Wn will take on different form accordinglyto the specific case. Figure 5 shows the frequencyspectrum for a thin-beam, a clamped rectangularplate and a circular rectangular plate for the caseof no axial stress. It is noted that the frequencyspectrum of the thin-beam does not correspond tothe frequency spectrum of the suspended square ge-ometry but it provides important information sincethe stiffness of the system is essentially determinedby the tethers.

3.1. One degree of freedom approximation

For frequencies bellow the first resonance andaround it the system can be approximated bya driven liner damped spring-mass system usingequivalent lumped parameters — an effective mass(m0), an elastic constant (k0) and a damping coef-ficient (cd). Assuming that the driving force can beseparated into a static component F0 and an har-monic component Fω cos(ωt), and the displacementis much smaller the air gap, the equilibrium solution

4

1 2 5 10 20 50 100

10-7

10-6

10-5

10-4

0.001

0.01

W

Am

pli

tudeof

vib

rati

ono

fth

ece

ntr

alpoin

th

=0.5

(a)

1 2 5 10 20 50 100

10-8

10-7

10-6

10-5

10-4

0.001

W

Am

plitu

de

of

defl

ection

of

the

centr

alpoin

th

=x

=0.5

(b)

1.0 10.05.02.0 20.03.01.5 15.07.0

10-5

0.001

0.1

W

Am

pli

tudeo

fdef

lect

iono

fth

ece

ntr

alpoin

tr=

0

(c)

Figure 5: Normalized frequency spectrum for (a)a thin-beam, (b) a clamped rectangular plates and(c) a clamped circular plate.

t = 0.5 mm

t = 1 mm

t = 1.5 mm

t = 2 mm

300 400 500 600 700 800 900 10000

20

40

60

80

100

Membrane side HaL @umD

Ela

stic

con

stan

tHk

eL@

Nêm

D

(a)

t = 0.5 mm

t = 1 mm

t = 1.5 mm

t = 2 mm

300 400 500 600 700 800 900 10000

20

40

60

80

100

Membrane side HaL @umD

Reson

an

ce

Freq

.Hf

0L@

kH

zD

(b)

Figure 6: Elastic constant (a) and resonance fre-quency (b) as a function of the side and thickness ofa rectangular membrane without axial stress. Thecase for circular plates yields very similar values ascan be seen from table (1).

can be written as

x(t) = x0 +Fω/m0√

(ω20 − ω2)2 − c2dω2/m2

0

cos(ωt+ φ)

(2)where x0 is the equilibrium static displacementcaused by F0, φ is the phase shift relative to theexcitation force and ω0 is the angular resonancefrequency. The elastic constant is taken consider-ing the maximum displacement for a static uniformload, the resonance frequency must match the firstresonance frequency of the thin plate and the ef-fective mass is given by the well known relationm0 = k0/w

20. These parameters are summarized

in Table 1 for the three geometries presented here.Figure 6 illustrates the range of values expectedfor the resonance frequency and elastic constant forthe case of rectangular membranes with axial stressand Figure 7 shows the effect of the axial stress onthe first resonance frequency of circular membraneshighlighting the pronounced effect of this parame-ter.

5

Resonance frequency (f0) Elastic constant (k0) Effective mass (m0)

Square membrane 5.72797√

Dρta4 787.402Da2 0.607904 ρta2

Circular membrane 1.6259√

DρtR4 64π D

R2 0.613243 ρtπR2

Suspended square 4.411√

EIL3

bρt(1.5344wLb+a2)768EIL3 ρt(1.5344wLb + a2)

Table 1: First resonance frequency, elastic constant and effective mass for the square and circular mem-branes and for the suspended square without axial stress. For circular membranes, R is the radius of themembrane.

0.01 0.1 1 10 100

1000

500

200

300

1500

700

Tensile radial stress @MPaD

f 0@k

Hz

D

R = 100 mm

t = 0.5 mm t = 1 mm t = 2 mm

t = 3 mm t = 4 mm

0.01 0.1 1 10 100

100

50

20

200

30

15

150

70

Tensile radial stress @MPaD

f 0@k

Hz

D

R = 400 mm

t = 0.5 mm t = 1 mm t = 2 mm

t = 3 mm t = 4 mm

Figure 7: Effect of radial tensile stress on the firstresonance frequency of circular membranes with 100µm radius (top) and 400 µm radius (bottom).

4. Experimental characterization

Two distinct experimental setups were used — onefor high frequency characterization at low pressureand one for quasi-DC and audible range measure-ments. The former highlights intrinsic mechanicalproperties of the resonators such as resonance fre-quencies and axial stress while the later allows formeasurements of absolute deflection in the audiblerange at room pressure and temperature.

4.1. Quasic-DC and audible range setup

This simple setup comprises an laser, focused onthe membrane, and a quadrant photodiode detec-tor aligned with the reflected beam off the mem-brane. The current generated from the detectoris converted to a potential difference by a tran-simpedance amplifier and fed to a lock-in amplifier,synchronized with the signal generator that is excit-ing the membrane. The displacement of the beam isproportional to the displacement of the membranewith

δ =√

2/2 ζVAB = ζVABout (3)

where δ is the amplitude of vibration of the plate,V outAB is the value read by the lock-in and ζ is the

proportionality constant to be determined experi-mentally for each measurement session.

First generation structures alone were character-ized using the quasi-DC setup. The structures are∼ 2 µm thick with a target air gap of 1.5 µm. Allthe results presented are for the perpendicular ge-ometry with 20 µm wide tethers.

Figure 8 (a) shows the frequency spectrum of a300 µm by 300 µm membrane held by 200 µm longtethers in the audible range.

Figure 8 (b) shows the response of a 500 µm by500 µm membrane held by 100 µm long tethers atconstant frequency (20 Hz) and DC bias (10 V) asa function of the amplitude of the input sinusoidalsignal.

Further characterization on these structures wasnot carried because of their incompatibility with aloudspeaker application (see bellow).

6

10 100 1k 10k0,0

0,4

0,8

1,2

1,6

2,0

2,4

Am

plitu

deao

fade

flec

tiona

(µm

)

Frequencya(Hz)

Measured

VDC = 2 VVAC = 1 V

a = 300 μmL = 200 μm

(a)

0 1 2 3 4 5

0

1

2

3

4

Am

plitu

dezo

fzde

flec

tionz

(µm

)

VAC

(V)

MeasuredLinearzfit

fz=z20zHzV

DC=z10zV

az=z500zµmLz=z100zµm

(b)

Figure 8: (a) Frequency spectrum in the audiblerange of a 300 µm by 300 µm membrane held by200 µm long tethers and (b) amplitude of deflectionat 20 Hz of a 500 µm by 500 µm membrane heldby 100 µm long tethers at constant DC bias as afunction of the input excitation signal.

2 0 0 µ 3 0 0 µ 4 0 0 µ 5 0 0 µ05 0 k

1 0 0 k1 5 0 k2 0 0 k2 5 0 k3 0 0 k3 5 0 k4 0 0 k

First R

esonan

ce Fre

quency

(Hz)

M e m b r a n e s i d e ( m )

t h i c k n e s s = 3 µmV D C = 0 , 5 VV A C = 0 , 2 V

O f f s e t b y t e n s i l e s t r e s s

P r e d i c t e d f i r s tr e s o n a n c e f r e q u e n c yw i t h o u t a x i a l s t r e s s

Figure 10: First resonance frequency as a func-tion of the side of the membrane for the suspendedsquare geometry with in-plane tensile stress.

4.2. High frequency detection setupThe high frequency detection setup also uses anoptical detection method but instead of a quad-rant detector it uses a APD detector (HamamatsuC5331 ) connected to a network analyzer (HP Net-work Analyser 4195A). Because the detector has alow frequency cut around 4 kHz this setup is onlyused for measurement above 50-100 kHz and no in-formation about absolute deflection is provided. In-stead, higher modes of vibration can be detectedin a pressure controlled chamber with informationabout mode shape a quality factor. An externalsource is used to set a DC bias and a the mem-brane is excited harmonically by the network anal-yser. The output of the detector is fed to the net-work analyser. The sample is wire bonded to a chipcarrier and placed on a pressure controlled chamber.The setup is described in detail elsewhere [6].

Suspended square membranes were characterizedfor the first generation process. Membranes 3 µmthick with an air gap height of 1 µm and sides from210 µm up to 710 µm were fabricated. The fre-quency spectrum from 100 kHz to 2 MHz was mea-sured and plotted in Figure 9 for the 210, 410, 610and 710 membranes.

Figure 10 shows the dependence of the first reso-nance mode with the dimensions of the tethers sidehighlighting the offset of the tensile stress on theresonance frequency.

Clamped membranes were fabricated using thea modified version of the glass-aluminium processand using the silicon-silica process for the amor-phous silicon deposition tests. Figure 11 shows thefrequency spectrum of a clamped rectangular mem-brane with 500 µm radius for the glass-aluminiumprocess. The first resonance mode predicted forthese structures is around 155 kHz which suggestsan in-plane stress value between 10 MPa to 100MPa. This is in line with the values expected for

7

0

20µ

40µ

60µ0,0 500,0k 1,0M 1,5M 2,0M

Sign

alqA

mpl

itude

q(a.

u.)

Lq=q210qum

0,0 500,0k 1,0M 1,5M 2,0M

0

20µ

40µ

60µ

Lq=q410qum

0 500k 1M 2M 2M

0

20µ

40µ

60µ

Sign

alqA

mpl

itude

q(a.

u.)

Frequencyq(Hz)

Lq=q610qum

0,0 500,0k 1,0M 1,5M 2,0M

0

20µ

40µ

60µ

Frequencyq(Hz)

Lq=q710qum

Figure 9: Frequency spectrum overview for the suspended square for different membrane dimensions.

0,0 500,0k 1,0M 1,5M 2,0M

0

100µ

200µ

300µ

Sign

alA

mpl

itude

Frequency)(Hz)

450 kHz

987 kHz

VDC = 1.0VAC = 0.7

a = 500 μm

Figure 11: Frequency spectrum of a clamped rect-angular membrane with 500 µm radius using themodified aluminium-glass process.

this fabrication process.

Figure 12 shows the variation of the first reso-nance for the equal membranes across the die indi-cating good reproducibility. The mean calculatedresonance frequency is 420.7 kHz with a standarddeviation of 27.4 Hz corresponding to 6.5 % of themean value. This is an important assessment ifarraying is required to assure that all membranesshow minimal variation in their mechanic charac-teristics.

Finally, Figure 13 shows a SEM micrograph of a800 µm side clamped membrane using the silicon-silica process for the amorphous silicon depositiontests and Figure 14 shows the corresponding fre-quency spectrum The membranes are 3 µm thick.Although these first structures shows some cracksover the border, which probably is the origin of thehigh number of resonances, and there is still someproblems during the structure release to be over-come the realization of the first standing and vi-brating membranes for the newly developed processis definitely a landmark.

1 2 3 4 5 6350,0k

400,0k

450,0k

500,0k1s

t res

onan

ce f

requ

ency

Membrane number

σ = 6.5 %

f0 = 420.7 kHz ± 27.4 kHz

Figure 12: First resonance frequency variationacross a single die of 500 µm clamped membranesshowing a standard deviation of 6.5 %.

Figure 13: Second generation released 800 µclamped membranes fabricated using the amor-phous silicon deposition test process.

8

0 200k 400k 600k 800k 1M

0

100µ

200µ

Vdc

=)0,7)V

Vac

=)0,2)V

Measured

Sign

al)A

mpl

itude

)(V

)

Frequency)(Hz)

Figure 14: Frequency spectrum of a 800 µm clamped membrane for the silicon-silica process.

5. Discussion and ConclusionThe first generation structures were design as an ex-tension of a well developed microfabrication processfor amorphous silicon thin beams and plates. Thisis an attractive process due to its low temperaturecharacteristics, great flexibility on the choice of sub-strate and overall simplicity. Unfortunately this ge-ometry proved to be inconsistent for the realizationof a loudspeaker. A suspended membrane radiateslike a dipole (see for example [15]) meaning that thepressure immediately above a bellow the membraneare equal and opposite or, in other words, the front-wave and back-wave are in complete opposition ofphase.The second generation structures were designconsidering the limitation of the first generationones. The perforation of the substrate proved tobe indispensable based on several numerical simu-lations (results not shown). Due to technology limi-tations the substrate had to be change to crystallinesilicon to allow back-side/front-side alignment, ma-terial compatibility and the etch of the perforations.The necessity for complete physical isolation of theback-side and front-side volumes is not clear and forthis reason both clamped structure and open struc-tures are presented. Open structures have particu-lar advantages over clamped ones such as simplifi-cation in the fabrication process, more tolerance tothe intrinsic stress of the structural layer and moredegrees-of-freedom for performance optimization.

There are several degree-of-freedom such as area,thickness, bias voltage or perforation density thatcan affect the overall behaviour of the system, eachone of which playing a particular role. Throughboth theoretical and experimental data several con-clusions are drawn setting guidelines for furtherinvestigation on the topic. It is clear that sin-gle structures with side or diameter of the orderof millimetres are not straightforwardly realizablewithout fine optimization of the intrinsic stress ofthe a-Si:H structural layer. The same is valid for

the thickness of such layer, where a narrow mar-gin between 1 to 3 µm exists imposed by the tech-nology. Extensive experimental data must be col-lected for different geometries in order to providefaithful information on non-linear parameters suchas squeeze-film damping or electrostatic force in alarge-deflection regime, together with the limitationimposed by the technology available.

5.1. Achievements

The microfabrication process for an amorphous sil-icon electrostatic actuated loudspeaker for ultralow power consumption applications was presented.The proposed process allows different geometriescompatible with a loudspeaker application and alsointroduce new concepts not yet present in the mar-ket or literature. Moreover typical materials inMEMS processing are used facilitating the transi-tion to a possible production scale. The minimal de-pendence on the substrate also shows great promis-ing for new trends such as processing on glass andflexible substrates.

Parallel to the process development a consistenttheoretical description is provided including differ-ent aspects of the problem that will play a funda-mental roll in the design and optimization of theloudspeaker. An initial experimental characteriza-tion is also provided showing the viability of theprocess, validating some presented theoretical ele-ments, such as in-plane stress or voltage controlledresonance frequency, and also providing initial in-formation on orders of magnitude of residual stress,dimensions feasibility or possible actuation voltagerange.

Finally, a general discussion is provided consider-ing both theoretical and experimental results pro-viding general guidelines to further develop and op-timize the loudspeaker performance.

9

5.2. Future workFuture work must be set on fine-optimization of thefabrication thus providing a consistent and robustprocess. Namely, focusing on the amorphous silicondeposition and substrate DRIE is crucial for con-trol of the mechanical properties of the membrane,reproducibility and high yields. Extensive exper-imental characterization on non-linear phenomenasuch as squeeze-film damping is also on the hori-zon, which will provide important data to modelthis crucial effect. The study of squeeze-film damp-ing will certainly yield pertinent information notonly for the particular application of a loudspeakerbut also for many MEMS applications where perfo-rations are present.

Feedback from acoustical measurements will alsoprovide important information for further develop-ment and optimization and comparison of the per-formance of clamped vs suspended geometries.

Finally, double gate structure may also be con-sider which present some advantages such as a widerlinear rage of actuation and lower actuation volt-ages required.

AcknowledgementsThe author would like to thank his adviser Prof.Joo Pedro Conde and Dr. Virgina for their guidingthought the project. Also to Joao Mouro, Alexan-dra Gualdino and Pedro Sousa for all their help andfruitfull discussions on the this work.

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