Journal of Vibration and Control-2016-Hadj Said-1077546316637298

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Article

A MEMS-based shifted membraneelectrodynamic microsensorfor microphone applications

M Hadj Said1, F Tounsi1, SG Surya2, B Mezghani1,

M Masmoudi1 and VR Rao2

Abstract

In this paper we present a multidisciplinary modeling of a MEMS-based electrodynamic microsensor, when an additionalvertical offset is defined, aiming acoustic applications field. The principle is based on the use of two planar inductors, fixedouter and suspended inner. When a DC current is made to flow through the outer inductor, a magnetic field is producedwithin the suspended inner one, located on a membrane top. In our modeling, the magnetic field curve, as a function of

the vertical fluctuation magnitude, shows that the radial component was maximum and stationary for a specific verticallocation. We demonstrate in this paper that the dynamic response of the electrodynamic microsensor was very appro-priate for acting as a microphone when the membrane is shifted to a certain vertical position, which represents animprovement of the microsensors basic design. Thus, a proposed technological method to ensure this offset of the innerinductor, by using wafer bonding method, is discussed. On this basis, the mechanical and electrical modeling for the newmicrophone design was performed using both analytic and Finite Element Method. Firstly, the resonance frequency wasset around 1.6 kHz, in the middle of the acoustic band (20 Hz 20 kHz), then the optimal location of the inner averagespiral was evaluated to be around 200mm away from the diaphragm edge. The overall dynamic sensitivity was evaluatedby coupling the lumped elements from different domains interfering during the microphone function. Dynamic sensitivitywas found to be 6.3V/Pa when using 100 mm for both gap and vertical offset. In conclusion, a bandwidth of 37.6 Hz to26.5 kHz has been found which is wider compared to some conventional microphones.

Keywords

MEMS-based sensors, electrodynamic transducer, microphone modeling, FEM simulation, diaphragm design andoptimization, magnetic and electric modeling

1. Introduction

The major advancements in the field of microsensors

have undoubtedly taken place within the past 20 years

with emerging microelectronic features, and there are

cogent reasons to consider these achievements as a

giant leap towards maturity. This trend is consistent

with reduction in unit cost and with the diversity of

functions made available to public while maintaining

low tolerance and high sensitivities (Madou, 1997). A

diversion of microelectronics has led to Microsystems

(or MEMS, Micro-Electro-Mechanical Systems) which

combines semiconductor microelectronic processes and

micromachining techniques, allowing the realization of

complete systems on a chip (Ma, 2015). The main

advantages of the introduction of MEMS technology

are (i) the miniaturization of devices, (ii) a high degree

of dimensional control and (iii) the reduction of man-

ufacturing cost. The microphone can be considered as

one of the mature and successful MEMS applications

1Electronics, Microtechnology and Communication (EMC) research

Group, National Engineering School of Sfax, Sfax University, Route

Soukra, Tunisia2Centre for Research in Nanotechnology and Science, Indian Institute of

Technology, IIT-Bombay, Mumbai, India

Corresponding author:

F Tounsi, Electronics, Microtechnology and Communication (EMC)

research Group, National Engineering School of Sfax, Sfax University,

Route Soukra, BP 1173, 3038 Sfax, Tunisia.

Email: [email protected]

Received: 18 June 2015; accepted: 8 February 2016

Journal of Vibration and Control

115

! The Author(s) 2016

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(Hohm and Gerhard-Multhaupt, 1984; Sprenkels et al.,

1989). It is a transducer that converts the pressure input

into electrical signal and is mostly used in communica-

tion, hearing-aid devices and vibration control systems

(Ma and Man, 2002). Most microphone sensors are

developed for audio applications, with frequency

ranges from 20 Hz to 20 kHz and pressure level rangefrom 20Pa to 60 Pa. Sound pressure can be detected

using many techniques such as piezoelectric (Horowitz

et al., 2007), piezoresistive (Schellin and Hess, 1992),

optic (Bilaniuk, 1997) and capacitive (Mohamad

et al., 2010). The latter is considered to be the most

common type among silicon microphone schemes

because of its high sensitivity (mV/Pa), large band-

width and low noise level (Ganji and Majlis, 2009;

Huang et al., 2011). On the other hand, piezoresistive

microphones are robust nevertheless generate a low

sensitivity (Sheplak et al., 1998) and the piezoresistive

material can suffer from thermal degradation due to

Joule heating effect. Finally, the piezoelectric micro-

phone is very common in aeroacoustic applications

but also with low sensitivity and low bandwidth

(Horowitz et al., 2007). The drawbacks of optic

microphones reside in the requirement of stable optical

reference and encapsulation of all system components,

such as light sources, optical sensor and photodetector,

which should be properly aligned and positioned. To

overcome defects encountered in each transductions

type, a totally recent integrated transduction technique

will be proposed and studied in order to detect the

acoustic waves. This technique is based on the electro-

dynamic theory and is known to be commonly used intraditional microphones but never in micromachined

counterparts. Nevertheless, the traditional dynamic

microphone still suffers from low sensitivity due to

the slow vibration velocity as a result of the heavy dia-

phragm (16mm thick and 25 mm in diameter) and the

non-integrated spiral moving coil vertically attached to

the diaphragm, which makes the whole device quite

bulky (Horng et al., 2010). To address this problem,

we will introduce the MEMS electrodynamic (or

inductive) microphone in order to increase the perform-

ances by increasing the vibrations velocity, since the

electrodynamic microphone should be a velocity

conversion and not displacement like the condenser

transducer (Merhaut, 1981). Moreover, the design

aims to reduce the unit cost and decrease physical

dimensions. An attempt to manufacture a miniaturized

electrodynamic microphone has been reported, but it

combines a diaphragm with coils manufactured in

MEMS technology and a macro-magnet embedded in

the external package (Horng et al., 2010). Through this

paper, we will present the basic design and the oper-

ation principle of this new transducer. We will also

demonstrate how the bandwidth can be enlarged

while keeping a high dynamic performance on the

acoustic band. This was done by modifying the micro-

phones basic design by providing a vertical offset to the

vibrating diaphragm.

This paper is organized as follows: the first section

presents a mechanical modeling of the suspension

design using both analytical and FEM analysis accom-plished using Comsol. The section objective is to

determine the mechanical properties such as the reson-

ance frequency and the membrane displacement mag-

nitude. This modeling will include the optimization of

the membrane dimensions as well, to achieve the tar-

geted microphone dynamics performance in accordance

with the manufacturing technology available. In the

second section, we will present the magnetic modeling

of the outer square inductor and we were interested in

seeking the B-field distribution produced by this latter.

This result will be validated by FEM analysis. Then, the

technological method for manufacturing the micro-

phone will be proposed. In addition, we will investigate

theoretically the induced voltage. Finally, we will evalu-

ate the global sensitivity of the microphone by deter-

mining the coupling schemes between the domains

involved (acousticmechanicalelectric). The design

parameters were determined using a mixed modeling

method from analytic and numeric FEM study.

2. Basic principle of the electrodynamic

design

When a conductor (or wire), carrying current, is

moving inward in a magnetic field, a voltage is inducedat its ends which is proportional to the strength of this

magnetic field, the movement velocity and the con-

ductor length that is immersed in the magnetic field

(see Figure 1a). The equation governing the generated

induced voltage, known as Faradays law of induction,

is given by:

e

Iloop

v!

^ B!

dl!

1

wheree [V] is the instantaneous output voltage, B [T] is

the magnetic flux density, l[m] is the length of the con-

ductor and v [m/s] is the instantaneous movement vel-

ocity of the conductor. When B is constant, the output

voltage is directly proportional to the conductor

velocity.

Based on this electromagnetic induction principle,

referred to by Lorentz force law, a MEMS-based

microphone is proposed and analyzed. The primary

implementation of this technique is ensured by the

use of two coaxial planar square inductors, which

occupy separate regions (see Figure 1b). The basic

2 Journal of Vibration and Control



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idea consists of placing a fixed outer inductorB1on top

of the substrate, and an inner inductor B2implemented

on a suspended membrane over a micromachined

cavity. By biasing the primary inductance B1, a per-

manent magnetic field will be produced within B2.

Vibration of the suspended membrane, including B2,

in the magnetic field will generate at its ends an induced

output voltage, which is proportional to the fluctuation

amplitude caused by the incident acoustic wave. In a

previous work, the inductor section and the spacing in

between were optimized to increase the magnetic field

(Hadj et al., 2014). In the next section, the resonant

frequency and the displacement of the membrane are

deduced based on dimensions imposed by the targeted

technology in IIT Bombay.

3. Mechanical modeling of the structure

3.1. Resonant frequency evaluation

To achieve a suspended diaphragm on top of a cavity,

generally two methods are possible based on the etch-

ing attack: a surface micromachining, wherein a sand-

wiched sacrificial layer is etched from the front side, or

a bulk micromachining wherein the substrate is etched

from the back side. In the present design, since the

membrane is attached to the substrate at its peripherals,

the back side bulk micromachining technique is the

most suitable. In fact, this technique permits to avoid

not only the use of attachment arms, which implies the

existence of apertures around, but also holes which

should serve for etching the sacrificial layers. In prac-

tical terms, the existence of openings around the dia-

phragm can lead to an acoustic short path in the

dynamic range, especially in the vicinity of low frequen-

cies, between the surrounding air above and the cavity

underneath the diaphragm (Hurst et al., 2014). This

acoustic short path occurs given that any modification

in the pressure of the ambient air will propagate rapidly

into the cavity under the sensing diaphragm through

openings around arms and/or etching holes (Jusoe ,

2013). As a consequence, pressure equilibrium is

obtained and the membrane will be blocked; these

effects reduce significantly the dynamic performance

of the microphone (Jusoe , 2013).

For an electrodynamic microphone targeting audio

applications, the natural frequency of the membrane

must be defined at the geometric mean distance

(GMD) of the acoustic wave band [20 Hz20 kHz], con-

trary to the electrostatic microphone whose resonant

frequency is defined above the useful band (Merhaut,

1981). So, in our modeling we firstly had to adjust

the membrane length based on the feasible thicknessto achieve a resonance frequency around 1.6 kHz.

Thereby, by neglecting the axial stress caused during

the fabrication process, the first mode resonant fre-

quency of an attached square membrane can be

expressed as (Dominiguez, 2005):

f1 35:99

2L2

ffiffiffiffiffiffiffiD

th

s 2

whereL is the membrane side length, is the equivalent

stacked material density, th

is the diaphragms elastic

thickness and D is the flexural rigidity given by:

D Et3h

12 1 2 3

where E is the Youngs modulus of the equivalent

stacked materials, and its equivalent Poissons ratio.

According to the available manufacturing process in

IIT Bombay, the membrane will be composed of a

superposition of two layers: silicon dioxide and nitride.

Thus, to obtain a resonant frequency in the Geometric

Figure 1. (a) Magnetic induction principle illustration and (b) 3D representation of the electrodynamic microphone structure.

Hadj Said et al. 3



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Mean Distance of the acoustic band, we draw the mem-

brane resonance frequency curve as a function of the

membrane side length, L, for different possible mem-

brane thicknesses (see Figure 2). In fact, when the

thickness increases, we need to increase the membranes

length in order to reach the targeted resonant fre-

quency. For a membrane of 1500 mm side length and

0.3 mm thickness (0.2 mm oxide and 0.1 mm of silicon

nitride), we obtain a resonance frequency around

1.6 kHz. Its mechanical effective mass and stiffness

are, respectively, given by (Sampaio, 2013):

Mmedia 0:607904thL2 4

Kmedia 787:402D

L2 5

For validation purpose, a modal analysis was

performed using the Solid mechanics module in

Comsol multiphysics software. The previously men-

tioned suspended membrane was simulated for both

analytical thickness and length, and results are sum-

marized in Table 1. The slight difference in values is

primarily due to the used mesh size in FEM

simulations.

3.2. Harmonic membrane displacement

evaluation

The membrane displacement is related to the frequency

of the incident sound wave. In the present study, we

consider the simplest case where the acoustic wave is

purely sinusoidal with an amplitude equals to 0.1 Pa,

corresponding to people conversation magnitude

(70dB). So, the harmonic displacement of the

diaphragms center was simulated and evaluated

using Shell module in Comsol Multiphysics

when applying a dynamic pressure of 0.1 Pa. The max-

imum simulated displacement around the resonance

frequency was found to be around 13mm, as shown in

Figure 3a. We note that the displacement is maximal

around the already set resonant frequency. The curve

showing the membrane behavior for each point on its

midline is drawn on Figure 3b using the same frequency

of 1.6 kHz.

4. Magnetic and electric modeling

of the electrodynamic microphone

4.1. Magnetic field induced by the outer

inductor using DC bias

Planar integrated inductors have a square shape made

by a juxtaposition of several conductors together.

Hence, according to the principle of superposition,

the resulting magnetic field B created at any point

M(x, y, z) inside the inductor, is the sum of magneticfield vectors generated by the contribution of each con-

ductor segment. In a previous work, we did demon-

strate theoretically that the magnetic field produced

by a planar square inductor, constituted by n spirals,

is equal to a superposition ofn single spirals having the

inductors average diameter (see Figure 4a) (Francis

and Krzysztof, 2013). When denoting " as the distance

separating both inductances, so "a designates the aver-

age distance separating their average diameters, and a

as the average outer inductor diameter (see Figure 4b).

The inductor spirals width and pitch are referenced

respectively by w and s. Due to technological limita-

tions, the inner diameter of the external inductor sur-

rounding the membrane is chosen to be slightly higher

than the membrane side, i.e. 1504 mm.

The 3 magnetic field component expressions (Bx, ByandBz) produced by the average diameter of the exter-

nal inductor are calculated in a Cartesian coordinate

system by an analytical approach determined in a pre-

vious work (Francis and Krzysztof, 2013). Since the

inductances fluctuation is out of plane, the radial mag-

netic field components Bx and By are the key param-

eters in the microsensors sensitivity evaluation, and

0 0.5 1 1.5 2 2.5

103

104

105

X: 0.001509

Y: 1600

Membrane Length [mm]

Frequen

cy[Hz]

t=0.3m

t=0.5m

t=1m

t=2m

Figure 2. Evaluation of the analytical resonance frequency of

the membrane as a function of its side length, L.

Table 1. Analytic and FEM evaluation of the mechanical

properties of the square diaphragm.

Diaphragm properties Analytic FEM

Resonance frequency (fr) 1.619 (kHz) 1.632 (kHz)

Effective mecanical

mass (Mdia)

1.025 109 (g) 1.048 109 (g)

Mecanical spring

constant (Kdia)

0.106 (N/m) 0.110 (N/m)




5/15

103

104

0

2

4

6

8

10

12

14

Frequency [Hz]

Spectrumdisplacement[m]

-750 -500 -250 0 250 500 750-14

-12

-10

-8

-6

-4

-2

0

Membrane side, L [m]

Deflection[

m]

(a) (b)

Figure 3. Representation of the diaphragms (a) center displacement over frequency and (b) midline deflection for the resonancefrequency of 1.6 kHz.

Figure 4. (a) In plane considered equivalent scheme of the two inductors, (b) 3D geometrical arrangement of the two simplified

spirals and (c) Contour of the magnetic field around a vertical cutting xz plane of one turn inductor polarized with I 1 100mA.

Hadj Said et al. 5



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then they are responsible for the generation of the

induced voltage. The radial component, Bx, generated

by the outer inductor is given by:

BxM n10I1 z

4

1

a2

x2 z2

a2

y

c1

a2

y

c2 "

1

a2

x2 z2

a2

y

c3

a2

y

c4

# 6

Where constants c1 to c4 are given by:

c1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia

2 x2 a

2y2 z2

q ,

c2


2 x2 a

2y2 z2

q ,

c3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

x2 a2

y2 z2q ,c4


2 x2 a

2y2 z2

qwhere I1 is the current flowing through the external

inductor (see Figure 4a) and m0 is the vacuum perme-

ability. The optimal number of turns in both inner and

outer inductances was found to be equal to 50. Indeed,

increasing further this latter parameter will have no

significant influence on the produced magnetic fields,

as its average spiral will be far removed from the dia-

phragm. Due to the inductors symmetric square shape,

the By radial component can be found using the same

equation by substituting x by y (and vice versa). The

two radial components are equal and they increase

when approaching the outer inductor. In addition,

from the analytic equation 6 we can note that they

are null on the substrate plane (z 0). In order to val-

idate the B-field expressions given by the theoretical

model, we used FEM simulation with Comsol soft-

ware via magnetic and electric module library. In

the simulation Graphical User Interface (GUI), thespiral should be surrounded by air and biased using a

DC current at one terminal while grounding the second.

In Figure 4c, the magnetic field density contour sur-

rounding one spiral is evaluated, along anx-z sectional

plane, showing a rapid decrease when moving away

from the conductor cross section.

Using analytical approach, the curve of Bx inside a

spiral, as a function of the fluctuation magnitude, was

plotted in Figure 5a for different average spirals spacing

"a, while setting y 0. It is worth noticing that the

radial component curve increases linearly reaching a

variable maximum value, referenced byBx-max, in a cer-

tain critical position z0, then decreases smoothly (see

Figure 5a). Almost, the same curves were found using

FEM simulations, confirming the analytic approach

already detailed in (Hadj et al., 2014).

The maximum value of the radial magnetic field

component as well as the critical position can be eval-

uated theoretically using these expressions (Francis and

Krzysztof, 2013):

Bx-max n10

4

a

"a ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8 "2a a

2

p

!I1 7

-250 -200 -150 -100 -50 0 50 100 150 200 250-6

-4

-2

0

2

4

6

Vertical positi on z [m]

MagneticfieldcomponentBx[mT]

Analytic a=104m

Analytic a=144m

Analytic a=184m

FEM a=104m

FEM a=144m

FEM a=184m

100 120 140 160 180 200 2202

2.5

3

3.5

4

4.5

5

5.5

Average spiral spacing a[m]

MaximummagneticfieldB

x,max

[mT]

Analytic

FEM

(a) (b)

Figure 5. (a) Analytic approach and FEM simulation of the radial component Bxcurve while keeping y 0 for different spiral spacing

"a and (b) Maximum magnetic field Bx-max as a function of the distance between inner and outer spiral.




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z0 1

4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12"2a a

2 2

4"aa 2

q 4"2a a

2 r

"a

8

In order to investigate the variation of Bx-max,

Figure 5b shows the decrement of this maximum as a

function of the distance between the internal and exter-

nal average spirals when using different calculation

methods (direct method given by equation 7 and point

by point plot resulting from FEM simulation). Since

Bxmax is inversely proportional to "a2

as shown inboth equation 7 and Figure 5b, it can be deduced that

the inner inductor should be placed as close as possible to

the outer one to take advantage of the greatest possible

magnetic field magnitude, and then optimize the gener-

ated induced voltage as stipulated by Faradays law.

To confirm the developed theory, equation 8 is

drawn in Figure 6 and validated numerically using

FEM, we noted that when moving away from the

outer inductor toward the diaphragm center, the critical

vertical position increases, as clearly shown. Therefore,

we can deduce that the optimum offset position should

be ideally equal to the average spirals spacing. Based on

these observations, we can come out with the idea to

establish a vertical offset between the primary and sec-

ondary inductors in order to take advantage of the

maximum and locally stagnant magnetic fields in the

vicinity of the new fluctuation position. In the next sec-

tion, we will demonstrate that for a given critical pos-

itionz0, the generated induced voltage will depend only

on inductors geometrical parameters and membrane

velocity but not on displacement, which is very import-

ant to broaden the sensitivity curve of the proposed

electrodynamic microsensor.

4.2. Induced voltage evaluation

when the inner inductor is shifted

Based on previous observations, we will assume that the

inner inductor was shifted by z0 (see Figure 7a). As a

consequence, the surrounding magnetic field, expressed

by equation 7, will be constant and maximized, so thecorresponding induced voltage is given by:

eoff

Iloop

v!

^ B!

dl!

4 a 2"a Bx-maxv 9

Moreover, the equation ruling the membrane displace-

ment, , associated to a harmonic motion around the

new rest offset zobecomes hz.sin(!pt) zo, where!pis the angular velocity of the incident acoustic pressure,

hz is the membrane displacement maximum magnitude

and t is time. Thus the corresponding induced voltage,

eoff, can be expressed by (Francis and Krzysztof, 2013):

eoff n1n20

a a 2"a

"affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

8"2a a2

p !

I1v K Bx-maxv 10

where K is a purely geometric constant parameter.

Based on equation 10, the electromotive force eoff is

inversely proportional to the distance between the two

inductors "a, i.e., in the same way the inner inductor

location should be implemented as close as possible to

the outer one. In the other hand, it should be placed the

nearest possible to the membrane center since its deflec-

tion will be higher (as shown in Figure 3b). So, in orderto find the optimal inner inductors position, we need to

calculate the resulting induced voltage for different pos-

sible location on the membrane.

Given that the induced voltage is found by the prod-

uct of the magnetic field and velocity (integral of dis-

placement), thus when placing the inductance close to

the membrane edge, the membranes velocity is min-

imal, however the magnetic field is maximal and vice

versa. Then, to maximize the induced voltage given by

equation 10, an optimal location of the internal induct-

ance must be evaluated based on a compromise

between either maximizing magnetic field or membrane

velocity. Figure 7b shows the evaluated induced volt-

age, given by equation 10, for different inner average

spiral locations, under an actuating pressure of 0.1 Pa

at the resonance frequency. We notice that the optimal

induced voltage is obtained when the inner inductor

average diameter is located around 200mm away from

the diaphragm edge (which leads to "a 200mm

(w s).n/2 250mm). This same value should be con-

sidered as a vertical offset to induce a maximize voltage.

However, damping effect is a key parameter for setting

operation bandwidth as will be explained later. A

100 120 140 160 180 200 220100

120

140

160

180

200

220

Average spiral spacinga[m]

Verticaloffset

z0[m]

Analytic

FEM

Figure 6. Evaluation of the vertical position, zo, over the aver-

age spirals spacing.

Hadj Said et al. 7



8/15

technical method to achieve the vertical shift of the

inner inductor will be discussed in the next section.

4.3. Technological method for membrane shifting

After designing each inductor on a separate substrate, a

wafer bonding method should be added in the micro-

phones process flow to ensure a vertical offset of the

membrane and consequently the inner inductor design.Nowadays, wafer bonding is one of the most promising

techniques for MEMS microphones fabrication and

packaging (Bergqvist et al., 1991; Pang et al., 2008).

Many bonding approaches are suitable for MEMS

applications as anodic bonding, fusion bonding, eutec-

tic bonding and adhesive bonding (Dragoi et al., 2003).

In our case, the latter technique will be used since it has

simple process properties in addition to the ability to

form high aspect ratio micro structures with low cost.

The adhesive bonding consists of introducing an inter-

mediate layer between both wafers, such as SU-8 epoxy

based negative photoresist. The main advantage of

using this approach is the low temperature processing

(maximum temperatures below 450C), the thickness of

the SU-8 which can reach hundreds ofmm, the absence

of electric voltage usage and the ability of using differ-

ent substrate types (Silicon, Glass, Metal, etc).

Figure 8 shows the proposed process to obtain a

vertical position of the inner inductor with the mem-

brane. Firstly, each wafer is fabricated separately,

shown in Figure 8a and Figure 8b, then they are

bonded together as shown in Figure 8c. A back side

bulk micromachining post process should be applied

to the chip #1 in order to release the diaphragm and

access connection pads of the inner inductor. Other

techniques are under study to get the same offset pos-

ition without modifying the original standard sensor

design. Ideas include the use of Lorentz force, which

is embedded in the inner inductor, and/or the residual

stress occurred during the fabrication process, etc.

Finally in the last section, the overall microphones sen-

sitivity will be deduced after including the acousticeffect of the pressure wave as well as the air gap

under the membrane.

4.4. Sensitivity evaluation with shifted membrane

The overall sensitivity depends on domains involved in

the microphone operation principle which are acousti-

cal-mechanical-magnetic. The acoustic domain effect is

present when the incident pressure hits the membrane

surface which produces an acoustic wave radiating out-

ward. In fact, when the diaphragm vibrates in response

to a sound pressure, a sound wave is generated in con-

tact with the air particles and radiates outward, it acts

as a speaker (Baltes et al., 2005). This effect can be

modeled using radiation impedance represented by an

acoustical resistance and a mass given by (Jusoe , 2013):

Zacrad1

8

air

cair!2 j

4

3

air

L ! Rrad j!Mrad 11

whereairis the air density, Cairis the sound velocity in

the air. On the other hand, the diaphragm represents a

mechanical resonator, which is a key element in the

Figure 7. (a) Vertical offset illustration between inner and outer spirals and (b) Induced voltage evaluation for different inner average

spiral locations, under an actuating pressure of 0.1 Pa at the resonance frequency.




9/15

acoustic-mechanical transduction scheme. This can be

explained by the fact that when an incident pressure Pinphysically hits the diaphragm top surface, a fluctuation

of this same surface occurs. This fluctuation is modeled

by mechanical impedance composed by a mass and an

ideal compliance Cdia which is inversely proportional

to the mechanical stiffness, Kdia. Therefore, membrane

mechanical behavior can be modeled by a stiffness and

mass given by:

Zmedia j!Mdia Kdia

j!12

The membrane fluctuation, due to the acoustic pres-

sure, will transmit pressure, Pcav, to the gap under-

neath. When the air volume contained in the closed

gap under the diaphragm is compressed, it can be

assimilated to a damping force. In fact, a viscous damp-

ing will be produced via the air film compression

trapped between the diaphragm and the cavity base.

This viscous squeeze film damping arises from the inter-

action of the air with a mechanical structure in motion

(Bao and Yang, 2007). Like all surface phenomena, it

has a much greater influence on the microscopic scale

than in the macroscopic scale. The damping force in the

gap can be modeled by a damping coefficient referred to

an acoustic resistance Rair and by a compressibility

effect modeled by a stiffness coefficient Kair (Zandi,

2013). Concerning the damping coefficient, it depends

on both gap thickness and diaphragm dimensions. To

find out this damping coefficient, we performed firstly a

FEM simulation using the squeeze film damping

Figure 8. 3D Microphone structure process flow using adhesive wafer bonding.

Hadj Said et al. 9



10/15

module in Comsol, which solves Reynolds equation

between two parallel plates. This study was performed

under a specific multiphysics boundary conditions set,

such that mechanical boundary (fixed constraint, pres-

sure load), and film boundary conditions (the film pres-

sure is zero at edges). Moreover, in simulation, we may

need to include some effects in the air gap, such as therarefaction effects. This effect can influence the damp-

ing coefficient especially for narrow bands, as men-

tioned in (Rocha et al. 2006). In our case, the

Knudsen number Kn that relates the gas specific mean

free path, l,and the gap thicknessG (Kn l/G) is lower

than 0.01 for different studied gaps (see Table 2), so we

can neglect this effect in the simulation.

In Figure 9a, a harmonic analysis was performed

and the pressure distribution in the cavity under the

membrane has been plotted at a frequency of 1.6 kHz.

We can note that pressure near plate edges is almost

equal to the atmospheric pressure, whereas the highest

pressure was around 18 108Pa, which appears

around the middle regions. In addition, we also note

that during fluctuation, air is flowing from the center to

the closest edges, and seems to be extremely weak

around membrane corners. To quantify the damping

coefficient, we integrated the pressure distribution

under the membrane that induces the damping force.

This latter gathers both real and imaginary parts, so the

damping coefficient was deduced by dividing the

imaginary part of the corresponding damping force

by the structure velocity Rmecair Im(Fdam)/V, where

Rmecair denotes the mechanical damping coefficient

(Zandi, 2013; Nigro et al., 2012). Figure 9b shows the

simulated damping coefficient for different air gaps

thicknesses. We noted that this coefficient increases

when the air gap decreases.

Moreover, we need to check the compressibility

effect in the air gap. Indeed, when the air is considered

as compressible, it leads to certain rigidity in the gap, so

we need to introduce another corrective coefficient that

models the stiffness or compliance of the air inside the

gap. To verify the air compressibility, we need to find

the Squeeze number , which is defined by (Bao and

Yang, 2007):

12L2!p

PaG 13

where is the air viscosity, Pa is the ambient pressure

and !p is the frequency of the audible sound. If the

number s is >>1, then the air can be considered as

compressible. In our case, and based on Figure 10,

the squeeze number increases with frequency and is

always


11/15

describing the air gap in acoustical domain can be writ-

ten as:

Zacair RmeairS2

14

The final effect that we have to study concerns the

mechanical-magnetic conversion. The diaphragm fluctu-

ation will generate an induced voltage at the inner induc-

tor ends. This electrodynamic phenomenon is modeled

by a magnetic induction link reflected by equation 4.

Since the microphones dimensions are small com-

pared to the smallest wavelength of interest (lat 20 kHz

is around 17 mm), the different parameters introduced

above can be gathered in a lumped element model rep-

resenting all the previously explained effects (see

Figure 11). When applying analogy between different

energy fields, a lumped element model of the

microphone can be built. The analogy requires a

series connection of all elements crossed by the same

acoustic flow and in parallel elements corresponding to

a flow addition. The lumped model consists of a sus-

pended diaphragm, which separates the back chamber

from the front space, playing a role of mechanical

springs. We consider, as the only possible movement,a vertical harmonic oscillation around its rest position,

which will progressively damp until it stops. This damp-

ing comes, on one hand, from the acoustic radiation

and the reaction forces of the environment opposing

to the movement, and, on the other hand, from the

energy losses by internal friction in the suspension.

The electro-acoustic lumped equivalent model, shown

in Figure 11, essentially consists of four components:

{1} the radiation impedance, Mradand Rrad, generated

by the diaphragm movement, {2} the diaphragm

impedance itself, Mdia and Cdia (the compliance is

equal to the inverse of the resistance, Kdia), {3} the acous-

tic resistance of the cavity beneath the diaphragm, Rair. In

our electro-acoustic model, the voltage is represented by

the sound pressure acting on the diaphragm, pin(t), and

the current is represented through the acoustic flow, w(t).

The developed circuit links the different domains together

through transformers and gyrators, with an appropriate

coupling coefficient (Blackstock, 2000). The coupling

coefficient between mechanical and acoustical domains

is S, which represents the membrane surface (Rossi,

2007; Tounsi et al., 2015). This coefficient relates the

acoustic pressure that hits the membrane with the mech-

anical force F. In the same context, it also relates the

acoustic flow ratew and the velocity of the membranevas given by the following system:

P FS

w S v

15

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25

Frequency [Hz]

Squeezenumber

Gap=250m

Gap=100m

Gap=80m

Gap=50m

Figure 10. Squeeze number evolution as a function of the

diaphgram fluctuation frequency.

Figure 11. Lumped elements model of the microphone coupling different involved domains.

Hadj Said et al. 11



12/15

Moreover,K Bx,max, coefficient deduced from equation

10, represents the coupling coefficient between the mech-

anical and the electric domain. This coefficient relates,

through a gyrator, the electromagnetic force (or Laplace

force) and the current across the inner inductor ends. In

addition, it relates the induced voltage with themechanical

velocity of themembrane as showninthefollowing system:

FLor K Bxmaxi

eoff K Bxmaxv

16

Subsequently, the lumped model scheme was simpli-

fied by transferring elements from the mechanical

domain to the acoustical domain as shown in

Figure 12. This simplification was obtained using cou-

pling coefficients between mechanical and acoustic

impedance deduced from this equivalence:

Zmec F

v

P:SwS

S2Zac 17

From our model, we assume that the forceFdue to the

incident pressure is higher compared to the electromag-

netic force shown in equation 16, so the acoustical flow

was determined and can be written as:

w Pin

Zacray Zacdia Z

acair

18

After simplification, the total sensitivity, Sen, was deduced

by combining equations 15, 16 and 18 and is given by:

Sen eoff

Pin

K:Bx-max

S

1

Zacray Zacdia Z

acair

19

Based on equation 19, we can notice that the sensi-

tivity is proportional to the coefficient K Bx-max(which mainly depends on the current I1, the inner

inductor length and the spiral numbers as shown

in equation 10). The sensitivity was drawn in

Figure 13.a as a function of the frequency, for different

air gap thicknesses. We can note the broadening ofthe bandwidth when the air gap is narrower in the

detriment of the sensitivity magnitude. So, unlike the

electrostatic microphone, dynamic performance in

the electrodynamic microphone is proportional to the

membranes velocity since fluctuation is controlled by a

resistance and not by compliance (Tounsi et al., 2015).

In fact, the microphone sensitivity is proportional to

the diaphragm displacement when the electrical field

is used for electromechanical transduction (capacitive

or piezoelectric principle); the term displacement

microphone is often used to name this family. If the

microphone transduction effect is based on magnetic

field (electromagnetic or electrodynamic), then its sen-

sitivity will be proportional to its diaphragm velocity.

Usually, the corresponding family is named as velocity

microphone (Tounsi et al., 2009). In the case of cap-

acitive microphones, the resonant frequency coincides

with the high cutoff frequency. The electrostatic micro-

phone is designed to operate at a frequency range lower

than the resonant frequency where its constant

frequency response is controlled by the rigidity. For

microphones using a magnetic field, the resonant fre-

quency is located at the center of the useful frequency

range of the microphone. From the same Figure 13a we

note that, for 100mm-gap thickness, the microphone hasquite large bandwidth (from 37.6 Hz to 26.5kHz),

which is suitable for audio applications, and has a fre-

quency response broader than some microphones in

bibliography, such as the one designed by Horng

Figure 12. Simplified lumped model of the microphone after transformation to the acoustic domain.




13/15

et al. (2010) (50Hz20 kHz). The theoretical sensitiv-

ity value, before amplification, is found to be equal

6.3 mV/Pa (104 dBV/Pa), which is in the same

range as piezoresistive and piezoelectric microphones

(Sheplak et al., 1998; Horowitz et al., 2007). Those per-

formances make our new proposed electrodynamic

technique competent with traditional transducers.

In the case where the inner inductor was in-plane, as

shown in the sensor basic design of Figure 1, the radial

magnetic field component will depend on the mem-

brane displacement, and will not be constant as in the

case of the shifted membrane. This dependence on the

displacement is due to the fact that the radial magnetic

field is linearly proportional to z, for low amplitude

fluctuation value. The final optimized microsensors

dimensions for acting as a microphone are summarized

in Table 3. The proposed design of the Figure 8 requires

a vertical offset almost equals to the gap thickness and

to the separation between the averages spirals, to be

placed wherein the magnetic field is maximum and

stationary (see Figure 5a). On the contrary, the basic

design of the electrodynamic microphone, shown in

Figure 1, allows only a designing of a displacement

conversion microphone (Hadj et al., 2015). Applying

the same developed theory on the initial design (copla-

nar inductors), results in a sensitivity which is max-

imum around the membrane resonant frequency, with

a tiny bandwidth as shown in Figure 13b. Theses per-

formances make the basic design more useful in appli-

cations like frequency detector or ultrasonic testing

sensors which require a high sensitivity within a

narrow bandwidth (resonance model). Finally, the pro-

posed microphone represents the advantage of being

the first micromachined electrodynamic microphone

which allows a standard monolithic integration with

its electronic circuitry while offering a competitive per-

formance to the mostly used capacitive counterpart.

Moreover, its standard structure design leads to a con-

siderable reduction not only in the occupied surface but

also in the unit cost.

101

102

103

104

105

-120

-115

-110

-105

-100

-95

-90

-85

-80

Frequency [Hz]

Sensitivity[dB

.V/Pa]

Gap=250m

Gap=100m

Gap=80m

Gap=50m

101

102

103

104

105

-250

-200

-150

-100

-50

0

Frequency [Hz]

Sensitivity[dB.V

/Pa]

Gap=250m

Gap=100m

Gap=80m

Gap=50m

(a) (b)

Figure 13. Microphone sensitivity (a) with vertical offset for the inner inductor and (b) without vertical offset of the inner inductor.

Table 3. Final optimized dimensions and main used parameters for microphone sensitivity evaluation.

Microphone dimension Value Acoustic and Magnetic parameters Value

Number of turnsn1 and n2 50 turns Current flowing in external coil (I1) 100 mA

Distance between average inductances ("a) 104 mm Air viscosity () 1,6.105 Ns.m2

Outer inductor average side (a) 1604 mm Sound velocity (Cair) 331 ms1

Inductor width (w) and pitch (s) 1 mm Electric conductivity (A) 37,7.106 sm1

Membrane side (L) 1500 mm Mean free path () 69 nm

Membrane thikness (th) 0.3 mm Ambient pressure (Pa) 1,01.105Pa

Gap height (G) and offset position (zo) 100 mm Air density (air) 1,21 kg/m3

Hadj Said et al. 13



14/15

5. Conclusion

In this paper, the basic electrodynamic microsensor

design has been adjusted by shifting the inner inductor

position to be used in acoustic microphone applica-

tions. In fact, the magnetic field evaluation shows that

for a given offset position, the B-field is maximum and

constant. Based on this observation, a complete studyof the microsensor has been performed using both ana-

lytic equations and FEM simulations. The microphone

study consists, firstly, in the determination of the mem-

brane mechanical properties such us dynamic behavior,

resonant frequency and displacement. In the second

part, the optimum location for the inner inductor has

been deduced thought the induced voltage examination

when using an incident pressure of 0.1 Pa. This was

done for different distances between inner and outer

inductors. Thereafter, the overall dynamic sensitivity

was determined by coupling all involved domains in

the microphone. Damping effect is a key parameter

which has been considered in the electrodynamic micro-

phone since it affects deeply the bandwidth of the

sensor. In fact, two kinds of microphones can be dis-

tinguished, namely: (i) velocity type (resistive con-

trolled) or (ii) displacement type (compliance

controlled). So, the presented electrodynamic design is

unlike electrostatic microphones which dynamic per-

formance is controlled through the membrane stiffness,

which means that their resonance peak is just above the

useful frequency band. The proposed MEMS-based

microsensor design improves performances, especially

the bandwidth, by designing a velocity conversion elec-

trodynamic microphone controlled by resistance (ordamping). For an air gap of 100mm, the bandwidth

was found to be around (37.6 Hz to 26.5 kHz) with a

dynamic sensitivity of 6.30 mV/Pa, which is considered

acceptable compared to MEMS-based conventional

microphones.

Acknowledgments

The authors would like to thank Mrs Nidhi Maheshwari from

department of Electrical Engineering at IIT Bombay for dis-

cussing technology issues. In addition, authors are indebted

to Prof. Libor Rufer from TIMA Laboratory at University of

Grenoble Alpes in France for his kind help, discussions andadvice.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with

respect to the research, authorship, and/or publication of this

article.

Funding

The author(s) disclosed receipt of the following financial sup-

port for the research, authorship, and/or publication of this

article: This work was carried out with support from the

Tunisian Ministry of Higher Education and Scientific

Research and the Department of Science & Technology,

India in the framework of the Tunisian-Indian joint research

cooperation in the field of scientific and technological

research.

References

Baltes H, Brand O, Fedder GK, et al. (2005) CMOS-MEMS:

Advanced Micro and Nanosystems, 1st edition, Germany:

Wiley-VCH.

Bao M and Yang H (2007) Squeeze film air damping in

MEMS. Journal of Sensors and Actuators A 136: 327.

Bergqvist J, Rudolf F, Maisano J, et al. (1991) A silicon con-

denser microphone with a highly perforated backplate.In:

Proceedings of International Conference on Solid-State

Sensors and Actuators, Piscataway, pp. 266269.

Bilaniuk N (1997) Optical microphone transduction tech-

niques. Applied Acoustics 50: 3563.

Blackstock DT (2000) Fundamentals of Physical Acoustics.

Hoboken, USA: Wiley.

Dominiguez C (2005)Conception de transducteurs acoustiques

micro-usine. PhD Thesis, University of Grenoble, France.

Dragoi V, Glinsner T, Mittendorfer G, et al. (2003) Adhesive

wafer bonding for MEMS applicationsIn: Proceedings of

SPIEThe International Society for Optical Engineering

5116: 160167.

Francis L and Krzysztof I (2013) Novel Advances in

Microsystems Technologies and Their Applications. USA:

CRC Press (Taylor & Francis).

Ganji BA and Majlis BY (2009) Design and fabrication of a

new MEMS capacitive microphone using a perforated alu-

minum diaphragm. Journal of Sensors and Actuators A

149: 2937.Hadj SM, Surya S, Tounsi F, et al. (2014) Numerical

Magnetic Analysis for a Monolithic Micromachined

Electrodynamic Microphone, In: International

Conference on MEMS and Sensors ICMEMSS14,

Chennai, India, 1820 December 2014, pp. 1016.

Hadj SM, Tounsi F, Surya S, et al. (2015) Mechanical

Modeling and Sensitivity Evaluation of an

Electrodynamic MEMS Microsensor. In: 12th

International Multi-Conference on Systems, Signals and

Devices, Mehdia, Tunisia, 1619 March 2015, pp. 16.

Hohm D and Gerhard-Multhaupt R (1984) Silicon-Dioxide

Electret Transducers. Journal of the Acoustical Society of

America 75: 12971298.

Horng RH, Chen KF, Tsai YC, et al. (2010) Fabrication of a

dual-planar-coil dynamic microphone by MEMS tech-

niques. Journal of Micromechanical and Microengeneering

20: 17.

Horowitz S, Nishida T, Cattafesta L, et al. (2007)

Development of a micromachined piezoelectric micro-

phone for aeroacoustics applications. Journal of

Acoustical Society of America 122: 34283436.

Huang CH, Lee CH, Hsieh TM, et al. (2011) Implementation

of the CMOS MEMS Condenser Microphone with

Corrugated Metal Diaphragm and Silicon Back-Plate.

Sensors 11: 62576269.




15/15

Hurst AM, Goodman S, Hilton JP, et al. (2014) Miniature

low-pass mechanical filter for improved frequency

response with MEMS microphones & low-pressure trans-

ducers.Journal of Sensors and Actuators A 210: 5158.

Jusoe E (2013) La technologie CMOS MEMS pour des appli-

cations acoustiques. PhD Thesis, University of Grenoble,

France..

Ma T and Man TY (2002) Design and fabrication of anintegrated programmable floating gate microphone.

In: 15th International Conference on Micro Electro

Mechanical Systems, pp. 288-291.

Ma J (2015) Advanced MEMS-based technologies and dis-

plays. Displays journal37: 210.

Madou M (1997) Fundamentals of Microfabrication.

Boca Raton: CRC Press.

Merhaut J (1981)Theory of Electroacoustics. USA: McGraw-

Hill Inc.

Mohamad N, Iovenitti P and Vinay T (2010) Modelling

and Optimisation of a Spring-Supported Diaphragm

Capacitive MEMS Microphone. Engineering 2: 762770.

Nigro S, Pagnotta L and Pantano MF (2012) Analytical andnumerical modeling of squeeze-film damping in perforated

microstructures. Journal of Microfluid Nanofluid 12:

971979.

Pang C, Zhao Z, Du L, et al. (2008) Adhesive bonding with

SU-8 in a vacuum for capacitive pressure sensors. Journal

of Sensors and Actuators A 147: 672676.

Sampaio R (2013) MicroElectroMechanical Systems

(MEMS) for applications in acoustics. Master Thesis,

University of Lisbon, Spain.

Schellin R and Hess G (1992) A silicon subminiature micro-

phone based on piezoresistive polysilicon strain gauges.

Sensors and Actuators A: Physical32: 555559.

Sheplak M, Breuer KS and Schmidt MA (1998) A wafer-

bonded, silicon-nitride membrane microphone with dielec-

trically-isolated single-crystal silicon piezoresistors. In:

Technical Digest Solid-State Sensor and Actuator

Workshop Transducer Res, Cleveland, OH, USA, pp. 23

26.

Sprenkels AJ, Groothengel RA, Verloop AJ, et al. (1989)

Development of an Electret Microphone in Silicon.

Sensors and Actuators 17: 509512.

Rocha LA, Mol L, Cretu E, et al. (2006) Experimental veri-

fication of squeezed-film damping models for MEMS.In:

International Mechanical Engineering Congress and

Exposition, Chicago, USA, November, pp. 510.

Rossi M (2007) Audio. Italy: Presses polytechniques et uni-

versitaires Romande.

Tounsi F, Rufer L, Mezghani B, et al. (2009) Highly Flexible

Membrane Systems for Micromachined Microphones

Modeling and Simulation, In: 3rd Int. Conf. on Signals,Circuits and Systems, Tunisia, 6 November 2009, pp.16.

Tounsi F, Mezghani B, Rufer L, et al. (2015) Electroacoustic

Analysis of a Controlled Damping Planar CMOS-MEMS

Electrodynamic Microphone. Archives of Acoustics 40:

527537.

Zandi K (2013) Integrated Microphotonic-MEMS Inertial

Sensors. PhD Thesis, University of Montreal, Canada.

Hadj Said et al. 15

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