Magnetostrictive microelectromechanical loudspeaker Thorsten S. Albacha) and Reinhard Lerch University of Erlangen-Nuremberg, Chair of Sensor Technology, Paul-Gordan-Strasse 3-5, 91052 Erlangen, Germany

(Received 22 April 2013; revised 2 September 2013; accepted 26 September 2013) A microelectromechnical-loudspeaker based on the magnetostrictive effect is presented. The membrane consists of a comb structure of monomorph bending cantilevers with an area of about 16 mm2 . Prototypes generate a sound pressure level (SPL) of up to 102 dB at 450 Hz with a total harmonic distortion of 2% inside a 2 cm3 measurement volume. The fabrication process of the device as well as a coupled simulation model to calculate its sound pressure is introduced. The model reproduces the measurements and is employed to further optimize the loudspeaker membrane. As a result, a computed maximum SPL of 106 dB has been achieved with a 6 dB C 2013 Acoustical Society of America. frequency range extending from 100 Hz to 2.6 kHz. V [http://dx.doi.org/10.1121/1.4824815] PACS number(s): 43.38.Ct, 43.38.Ja [DDE]

Pages: 4372–4380

I. INTRODUCTION

Microelectromechanical (MEMS) microphones are used in millions of devices from consumer electronics to mobile phones. They are small, robust, and economically priced. MEMS-loudspeakers could have similar advantages. But until now, no commercial integrated MEMS-device for sound generation in the audio range does exist. State-of-the-art miniature loudspeakers in mobile applications are assembled by means of precision mechanics. They behave electrically inductive. Therefore, it will be an advantage for MEMS-devices designed to replace them to show inductive behavior as well. Acoustical requirements for a marketable MEMS-loudspeaker are the generation of a high sound pressure level (SPL) over a broad frequency range and low total harmonic distortion (THD). In general, simple and economical fabrication with low tolerances, low power consumption, mechanical as well as chemical robustness, and small geometric dimensions are further requirements to promote a market entry. Different actuation principles have been investigated in order to develop a MEMS-loudspeaker. The electrostatic principle utilizes the force on electric charges in an electric field.1,2 The setup resembles a plate capacitor, with one plate designed as a flexible membrane. A drawback is the required high electrical voltage. Amplitudes lie in the range of 20 V to 200 V. The same idea can also be realized in a simpler (nonMEMS) setup by applying the electrodes directly on the top and bottom surface of a dielectric polymer.3,4 The polymer is contracted by electrostatic forces when an electric voltage is applied. The required voltages are even higher with amplitudes up to 1 kV. Active materials showing the piezoelectric effect have been utilized as MEMS-loudspeakers.5–9 These materials (mostly PZT, ZnO, or AlN) are deposited and structured upon a passive membrane. An applied electric voltage leads to a geometric deformation which excites a movement a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]

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of the membrane. The fabrication processes are comparatively straightforward. All the above-mentioned actuation principles lead to electrically capacitive loudspeakers. Inductive concepts have also been investigated. There have been attempts to transfer the electromagnetic actuation principle of hearing aid speakers into a MEMS-setup.10 Electrodynamically actuated MEMS-loudspeakers are based on the Lorentz force on a current driven coil in the magnetic field of a permanent magnet.11–14 Either the permanent magnet or the coil is attached to the membrane. So far, the most promising results have been achieved by the piezoelectric5 and the electrodynamic12,14 setups. Still another actuation principle has been used for sound generation as early as 1861 in the invention of the first telephone by Philip Reis:15 the magnetostriction, more precisely, the Joule-magnetostrictive effect. It describes the strain of ferromagnetic materials under the influence of a magnetic field. Some advantageous characteristics make it also suitable for use in MEMS applications: high energy density and contactless operation, as well as the possibility of low driving voltages due to low electrical actuator impedances.16–19 However, this effect has never been considered to develop a MEMS-loudspeaker. In fact, it has rarely been used in micromechanics at all. Among the few examples are optical scanners20 and bio-sensors.21 This paper, which is based on previous work,22–27 extends the research toward a magnetostrictive MEMS-loudspeaker. Contributions of the presented magnetostrictive design to the above given requirements for MEMS-loudspeakers are laid out in the following sections. First, the concept of this loudspeaker is presented. Its electrical impedance is of inductive nature. The special design of the membrane, consisting of separate bending cantilevers, leads to certain improvements over a closed membrane. Its fabrication process is introduced. It is as straightforward as for piezoelectric membranes.5–9 Furthermore, a simulation model is derived from the physical interrelationships. It combines the methods of lumped elements and finite elements. A suitable linear working point for the magnetostrictive material is identified by measuring the

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C 2013 Acoustical Society of America V

membrane deflection. The setup for measuring the generated sound pressure in a standard 2 cm3 measurement volume is illustrated. Acoustic measurement results show a good conformance with simulation output. Finally, possibilities for further optimizations are discussed. An optimized setup, increasing the SPL, and expanding the acoustical bandwidth is presented. II. CONCEPT

The presented MEMS-loudspeaker is designed for inear use. Thus, the sound pressure is measured inside a standard 2 cm3 measurement volume that emulates the human ear. The MEMS-loudspeaker consists of three parts. (i) (ii) (iii)

A silicon chip, which carries a magnetostrictively actuated membrane (membrane-chip), a current driven coil, which provides a magnetic field, and a housing, which carries the generated volume flux into the measurement volume.

A. Membrane-chip

Figure 1 depicts the design of the membrane. It consists of two rows of long and narrow bending cantilevers that are positioned opposite to each other. The membrane is processed micromechanically on a silicon substrate. A cavity is etched through the silicon underneath the membrane to provide an acoustic back volume (see Sec. III). Figure 2 shows a cross section (A-B) along one bending cantilever. The monomorph setup consists of a magnetostrictive layer on top and at least one passive layer underneath. A ~ parallel to the length of the cantilever magnetic field, 6H, causes the magnetostrictive layer to strain by Dlc (positive magnetostriction). Thus, the cantilever bends downward. But, elongation of the magnetostrictive material in one direction leads to contractions in the perpendicular directions. This leads to a transverse bending around the x-axis and an unwanted increased stiffness of the cantilever. A high length to width aspect ratio is chosen to suppress this side effect. The membrane design shown in Fig. 1 offers certain advantages compared to a closed membrane. First, the bending stiffness of the membrane is decreased which allows higher deflections. Second, two additional design parameters provide control over the acoustical frequency response: the width of the airgaps between the cantilevers and the mechanical eigenfrequency of the cantilevers. Processing cantilevers

FIG. 1. Design of the membrane consisting of a comb structure of bending cantilevers. J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013

FIG. 2. Working principle, cross section A-B as in Fig. 1 (not to scale).

of different lengths inside the same membrane lead to different eigenfrequencies. This can add even more parameters to tune the frequency-response of the loudspeaker. An alternative layer setup has also been investigated.25,26 B. MEMS-loudspeaker setup

In an integrated MEMS-loudspeaker setup, the magnetic ~ to drive the cantilever movement can be provided field, H, by flat multilayered microcoils on a separate silicon-chip.24 To demonstrate the performance of the membrane-chip, a cylindrical coil is used in this paper. Due to the highly nonlinear nature of the magnetostrictive effect, an additional offset magnetic field is needed to set up a linear working point. Small permanent magnets can be utilized here. In this paper, an additional direct current (DC) through the cylindrical coil is provided to increase the flexibility of the measurements. Figure 3 depicts the corresponding measurement setup of the MEMS-loudspeaker in an exploded view. The membrane-chip is fixed to a housing (2) and positioned inside the cylindrical coil (1). A standard hearing aid rubber tube (3) leads the sound pressure into the measurement volume (4; RA0038, IEC 126, and ANSI S3.7-1973, G.R.A.S. Sound and Vibration A/S, Holte, Denmark), which emulates the human ear. The microphone (5; 1/2 in. type 4189 with amplifier type 2669, Bruel and Kjaer, Naerum, Denmark) detects the pressure signal. III. FABRICATION PROCESS

This section briefly introduces the micromechanical fabrication process of the membrane-chip. The length of the bending cantilevers, lc , is constant inside one chip. Two different types of membranes, with lc ¼ 1250 lm and lc ¼ 1500 lm, are presented in this paper. Their different mechanical eigenfrequencies lead to different acoustical characteristics. As magnetostrictive material, Vanadium Permendur (Fe49 Co49 V2 ) is used. The passive layer consists of silicon dioxide (SiO2 ). Boron doping reduces its brittleness. Chromium (Cr) serves as adhesion layer. The process

FIG. 3. Setup to demonstrate performance of membrane-chip (exploded view): (1) cylindrical coil, (2) membrane-chip fixed to housing, (3) small hearing aid rubber tube, (4) measurement volume (2 cm3 ), and (5) microphone. T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

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requires three lithography masks. Silicon wafers are processed from both sides. Figure 4 depicts the main process steps (cross section C-D as in Fig. 1): (1) Wet oxidation of a (100)-Si-wafer and boron-doping of SiO2 (0.9 lm); (2) sputter deposition of Cr (0.035 lm)–Fe49 Co49 V2 (1.05 lm)–Cr (0.035 lm) layers on the front; (3) wet etching of the metal layers on the front: definition of the membrane area; (4) wet etching of the SiO2 on the back: definition of the cavity area; (5) wet etching of all layers on the front: definition of the cantilevers; (6) anisotropic wet etching of silicon from the back (KOH, 15%, 40  C); and (7) anisotropic wet etching of silicon from the front (KOH, 15%, 40  C): liberation of the bending cantilevers. For the prototype membrane-chips, the width of the cantilevers is 72 lm and the gap between adjacent cantilevers is 13 lm. The membrane area, including the airgaps, amounts to Am ¼ 16:2 mm2 for both cantilever lengths. This leads to a total number of cantilevers per chip of n ¼ 126 for the longer and n ¼ 152 for the shorter ones. Figure 5 shows an example of a membrane-chip. IV. MODEL SETUP

In order to understand and optimize the performance of the MEMS-loudspeaker, a simulation model is presented in this section. The model assumes linear behavior of the involved physical effects. A MEMS-loudspeaker needs an electrical signal as its input. Its output is the sound-pressure

FIG. 5. Membrane-chip with highlighted membrane area, Am .

in the ear volume. Since these are both scalar quantities, the MEMS-loudspeaker may be represented by a scalar transfer matrix. The different components of the MEMS-loudspeaker, which are the current driven coil, the membrane-chip and the acoustical network, can be modeled independently. Each of these components can also be represented by a scalar transfer matrix, whereas the calculations to achieve these matrices may include more than one spatial dimension. In this paper, the magnetic field is generated by a cylindrical coil. The electrical feedback of the moving membrane into this coil can be neglected. Thus, the simulation model, as depicted in Fig. 6, directly handles the magnetic field (flux density, B^x , and field strength, H^ x ) as its input. This field is assumed to be homogeneous along the cantilevers and to only have a component in x-direction. Here, the nota^ ¼ me ^ ju denotes the complex amplitude of the time tion m ^ cosðxt þ uÞ with its phase u. function mðtÞ ¼ m Nevertheless, for an integrated MEMS-loudspeaker with flat multilayered microcoils,24 the coils have to be modeled accordingly and the electrical source has to be chosen as input quantity. The membrane-chip can be represented by a transfer matrix, AMC , coupling the magnetic field to the mechanic field (force, F^y , and velocity, ^v y ). The acoustical network, represented by AAN , couples these quantities to the acoustic field (sound pressure, p^2 , and volume flux, q^2 ) in the measurement volume. A. Model of the membrane-chip

The model of the membrane-chip describes the movement of the bending cantilevers due to the magnetostrictive effect, as well as their response to the generated sound pressure. This behavior is frequency dependent. Assuming plane strain condition in the x-y-plane, it is sufficient to model a cross section of one bending cantilever,

FIG. 4. Micromechanical fabrication process of the membrane-chip. 4374

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FIG. 6. Simulation model of the MEMS-loudspeaker. T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

according to Fig. 2. The results have to be scaled with the total membrane area. The membrane-chip can thus be represented by a twodimensional coupled field problem, including the magnetic and the mechanic field. The underlying coupling effect can be described by the linear magnetostrictive equations (Voigt’s notation) ~ ~ ¼ eS þ lS H; B H ~ T ¼ c S  et H;

(1)

where tensors of first order are denoted by vector arrows, and those of higher order in bold print. The index “t ” denotes ~ is the magnetic flux density, H ~ is the maga transposition. B netic field strength, S is the mechanical strain, and T is the mechanical stress. The magnetic permeability at constant strain is denoted as lS , the mechanical elasticity at constant magnetic field is cH , and the magnetostrictive coupling tensor is e. All materials are assumed to be isotropic, except for the magnetostrictive layer. Here, transverse isotropic coupling is assumed,16,28 which leads to the coupling tensor 0

0 B e¼@ 0 e31

0

0

0

e15

0 e31

0 e33

e15 0

0 0

0

(2)

where the magnetization lies in 3-direction. Material coordinates are mapped to the geometry as 0 1 0 1 x 3 B C B C (3) @ y A $ @ 2 A: z

B^x H^ x



 ¼ AMC

 F^y : ^v y

Fy ¼ bc nny ;

J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013

(5)

where n is the total number of cantilevers and bc is their individual width. B. Model of the acoustical network

The model of the acoustical network (transfer matrix, AAN ) describes (i)

the coupling between the mechanic and the acoustic field (transfer matrix, AAN;1 ) and the acoustical behavior of the MEMS-loudspeaker (transfer matrix, AAN;2 ).

This leads to AAN ¼ AAN;1 AAN;2 :

(6)

The coupling is described by the gyrator-type equation       p^1 0 Ac F^y ¼ AAN;1 ^ with AAN;1 ¼ ; q1 0 1=Ac ^v y (7)

1

The solution to this problem can be found using the method of finite elements (FE).29 The simulation domain has to be spatially discretized. The underlying coupled partial differential equations can then be transferred to a system of algebraic equations, including appropriate boundary conditions. Losses in the vibrating mechanical structure are included by adding a velocity proportional damping term (Rayleigh damping model). Additionally, two initial conditions are provided along the cantilever: a homogeneous magnetic field in the x-direction, resembling the input magnetic field, and an equally distributed mechanical load, ny , in the y-direction, resembling the sound pressure. The numerical solution yields the distribution of the magnetic and the mechanic field along the finite elements. It is calculated for frequencies in the audio range. For the FE simulations, we use CFSþþ (“coupled field simulation”), which is a numerical simulation tool optimized for coupled field problems.30 By providing adequate values for the initial conditions in different simulation runs, the transfer behavior between the magnetic and the mechanic field can be achieved. The membrane-chip can thus be represented by a frequency dependent, one-dimensional transfer matrix AMC (see Fig. 6) as

(4)

Here, B^x and H^ x are the spatially averaged magnetic field properties along the magnetostrictive layer of the cantilever in the x-direction. ^v y denotes the average velocity of the cantilever in the y-direction (this property determines the acoustic volume flux) and F^y is the total force on all bending cantilevers in the y-direction, calculated from the initial load, ny , as

(ii)

1

C 0 A; 0



where Ac is the total cantilever area (membrane area, Am , without the airgaps) Ac ¼ lc bc n;

(8)

p^1 is the acoustic pressure and q^1 is the volume flux generated by the moving cantilevers. The acoustical behavior of the MEMS-loudspeaker is described by       p^1 p^2 a11 a12 ¼ AAN;2 ^ ; with AAN;2 ¼ : q^1 q2 a21 a22 (9) In the next step, the components a11   a22 of AAN;2 have to be derived. Since the physical dimensions of the MEMSloudspeaker are small compared to audio wavelengths in air, it is possible to model the acoustic network using lumped elements.15,31 In this paper, an electroacoustic analogy is used, which maps the acoustic pressure, p, to the electric voltage and the volume flux, q, to the electric current. The resulting acoustic lumped element model is depicted in Fig. 7. Assuming an ideally closed measurement volume, no volume flux leakage will occur and q^2 can be set to zero. The quantity that is actually of interest is the sound pressure T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

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FIG. 8. Setup for measuring the magnetostrictive bending of the cantilevers: (1) coil on ferromagnetic yoke, (2) magnetic field sensor, (3) membranechip, and (4) confocal measurement microscope.

FIG. 7. Lumped element model of the acoustical network.

in the measurement volume, which is then equal to p^2 . Cavities of the acoustical network are modeled as acoustic compliances, N0;1;2 , the hearing aid rubber tube is represented by a mass element, Mt , and a friction element, Rt . The airgaps between the cantilevers are modeled with a friction element, Ra . The corresponding equations31 are N0;1;2 ¼ ft ¼

V0;1;2 ; qc2

4g ; pqrt2 0

1 1 qlt Mt ¼ B1 þ rffiffiffiC 2 ; pr fA t @ 2 ft 1 Rt ¼ 2

Ra ¼

sffiffiffi0 1 f 1 8glt 1 þ rffiffiffiC 4 ; ft B f A prt @ ft

12gtc : b3a la;tot

(10) (11)

(12)

a21 ¼

ðRa þ Z 2 ÞðZ1 þ Z t þ Z 0 Þ þ Z 1 ðZ t þ Z 0 Þ ; Z 0 Z 1 Ra

(17)

a22 ¼

ðZt þ Z 1 ÞðRa þ Z 2 Þ þ Z 1 Zt ; Z 1 Ra

(18)

with the acoustic impedances Z0 ¼

1 ; jxN0

Z1 ¼

1 ; jxN1

(19)

Z2 ¼

1 ; jxN2

Z t ¼ jxMt þ Rt ;

(20)

where j is the imaginary unit and x is the angular frequency. With Eq. (6), this leads to the transfer matrix, AAN , of the acoustical network

(13)

(14)

Here, V0;1;2 denote the volumes of the corresponding cavities, c ¼ 343 m/s is the sound velocity, q ¼ 1:2 kg=m3 is the air density, and g ¼ 1:8  105 kg/(m s) is the viscosity of air. The characteristic frequency for the hearing aid tube is ft , the length of the hearing aid tube is lt , and rt is its radius. The thickness of one bending cantilever is tc , the width of the airgap between two cantilevers is ba , and la;tot is the total length of all the airgaps between the cantilevers. Deriving the components of the matrix, AAN;2 , from Fig. 7 [see Eq. (9)] leads to the equations a11 ¼

a12

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Z2 ðZ 1 þ Z t þ Z0 Þ þ Z1 ðZ t þ Z0 Þ ; Z0 Z1

Z ðZ þ Z t Þ þ Z1 Z t ¼ 2 1 ; Z1 J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013

(15)

(16)

FIG. 9. Normalized tip deflection of the cantilevers under the influence of a magnetic field. (a) Outer hysteresis loop when driven into saturation at H^ ¼ 135 kA/m, (b) and (c) inner hysteresis loops around a working point at HDC ¼ 12 kA/m with outer hysteresis loop given as reference. T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

TABLE I. Measured key data from the MEMS-loudspeakers as in Figs. 10 and 11; frequencies rounded to 10 Hz. 1250 lm

1500 lm

Sensitivity, SI , at 450 Hz

0.08 Pa  m/kA

0.16 Pa  m/kA

Frequency range (6 dB)

340 Hz–1020 Hz

360 Hz–800 Hz

Cantilever length, lc

Maximum SPL Corresponding THD Corresponding frequency

FIG. 10. Measurements of SPL and THD; cantilever length, lc ¼ 1250 lm; measurement resolution is 20 Hz to 50 Hz below 1.4 kHz and 100 Hz above 1.4 kHz.



F^y ^v y



 ¼ AAN

 p^2 ; q^2

(21)

as defined in Fig. 6. C. Model of the MEMS-loudspeaker

Finally, the sound pressure, p^2 , in the measurement volume can be expressed as     p^2 B^x A A ¼ : (22) MC AN 0 H^ x V. MEASUREMENT SETUP A. Deflection measurements

When excited with large magnetic fields, the magnetostrictive effect shows highly nonlinear behavior including

95 dB 3% 430 Hz

95 dB 6% 890 Hz

102 dB 2% 450 Hz

102 dB 6% 650 Hz

saturation and hysteresis. In order to quantify these nonlinearities, the magnetostrictive deflection of the cantilevers is measured as depicted in Fig. 8. A confocal microscope (lsurf explorer, Nanofocus AG, Oberhausen, Germany) measures the topography of the cantilevers under the influence of a magnetic field, which is provided by a current driven coil on a ferromagnetic yoke. The static magnetic field, which is measured with a Hall effect sensor, is adjusted in small steps after each topography measurement. B. Acoustic measurements

The sound pressure inside the ear volume is measured using the setup depicted in Fig. 3. The SPL is calculated from the root-mean-square (rms)-value of the sound pressure component, pI;rms , which has the same frequency as the exciting magnetic field with respect to 20 lPa,   pI;rms : (23) SPL ¼ 20 log10 20 lPa The total harmonic distortion (THD) is calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p^2II þ p^2III þ    THD ¼ ; p^2I þ p^2II þ p^2III þ   

(24)

where p^I ; p^II ; ::: are the sound pressure amplitudes at one, two,… times the excitation frequency. The sensitivity, SI , of the MEMS-loudspeaker can be calculated from the amplitude of the exciting magnetic field, ^ as H, ^ SI ¼ p^I H:

(25)

VI. MEASUREMENT RESULTS A. Magnetostrictive deflection

Figure 9 shows measurements of the tip deflection of the cantilevers. The deflection is normalized to its maximum and defined as zero at its minimum. The exciting magnetic field as a function of time is varied in a triangular shape TABLE II. Geometric dimensions.

FIG. 11. Measurements of SPL and THD, cantilever length, lc ¼ 1500 lm; measurement resolution is 20 Hz to 50 Hz below 1.4 kHz and 100 Hz above 1.4 kHz. J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013

Length of rubber tube Inner radius of rubber tube Housing volume

lt ¼ 5:2 mm rt ¼ 0:5 mm V1 ¼ 0:03  106 m3

T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

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TABLE III. Mechanic material data: density, q; Young’s modulus, Y; Poisson ratio, ; SiO2 is boron-doped.

Fe49 Co49 V2 Cr SiO2

q in kg/m3

Y in GPa



8100 7100 2500

230 280 60

0.3 0.21 0.17

with constant amplitude. In Fig. 9(a), the field amplitude of H^ ¼ 135 kA/m drives the magnetostrictive material into saturation. This results in the characteristic and essentially nonlinear outer hysteresis loop of the deflection behavior. Nevertheless, the magnetostrictive hysteresis is less distinct compared to piezoelectric materials,32 which is an advantage for audio applications. However, in order to operate a loudspeaker, a linear relationship between magnetic field and deflection is needed. An appropriate working point for the material Fe49 Co49 V2 has been found at an offset magnetic field of HDC ¼ 612 kA/m. With the excitation of small magnetic fields, the magnetostrictive effect can be approximated by a linear function around this working point [see Eq. (1)]. Two examples are given in Figs. 9(b) and 9(c) for field amplitudes of H^ ¼ 11 kA/m and H^ ¼ 19 kA/m. To keep within the linear operating range, maximum field amplitudes of 23 kA/m are allowed (see also Sec. IV B). B. Acoustic properties

Figures 10 and 11 show the measured SPL and THD for membrane-chips with cantilever lengths of 1250 lm ^ and 1500 lm. The amplitude of the magnetic field, H, is varied between 1.6 kA/m and 23.3 kA/m. The DC working point is chosen according to Sec. IV A (HDC ¼12 kA/m). The 6 dB cutoff frequencies are indicated in both figures. The corresponding 6 dBbandwidth is larger for shorter cantilevers where this bandwidth amounts to 680 Hz (Fig. 10). On the contrary, the maximum SPL is higher for longer cantilevers, where a maximum SPL of 102 dB has been measured (Fig. 11). In both cases, the THD is well below 10% for frequencies above 400 Hz inside the 6 dB-bandwidth. Observing Figs. 10 and 11, the relationship between the sound pressure and the magnetic field strength is found to be nearly linear up to an amplitude of 23 kA/m. That means the sensitivity, SI [Eq. (25)], is nearly constant in this field range and also confirms the choice of the working point, HDC . For field amplitudes above 23 kA/m, the sensitivity has been found to decrease due to the nonlinear behavior of the magnetostrictive effect, which becomes more visible at high field amplitudes (Fig. 9). The resulting key data from these measurements is summarized in Table I.

FIG. 12. Cantilever length, lc ¼ 1250 lm; simulation of SPL; tolerance band from simulation runs with 65% tolerance on material properties and layer thicknesses; magnetic field strengths as in Fig. 10; measurement data reproduced from Fig. 10 for comparison.

VII. COMPARISON WITH SIMULATION DATA

Simulation results for the sound pressure, p^2 , in the measurement volume are obtained by evaluating Eq. (22). The geometric dimensions are equal to the measurements and are given in Table II. The mechanic material data given in Table III has been verified by comparison of the mechanical eigenfrequencies of the cantilevers.23 The magnetostrictive coupling tensor, as given in Table IV, has been derived from measurements of the static deflection of the cantilevers (Fig. 9). The saturation magnetostriction of Fe49 Co49 V2 has been measured22 to ks ¼ 62  106 with a tolerance of 613%. For the relative permeability of Fe49 Co49 V2 , a value of lr ¼ 50 has been obtained using a vibrating sample magnetometer. The magnetic field amplitudes in the simulation are chosen equal to the measurements. The simulated SPLs are given in Figs. 12 and 13 for the two different types of the membrane. Table V indicates the resulting key data. Micromechanical processes are always subject to possible tolerances. Thus, it is important to gain knowledge of the influence of these tolerances on the output quantity. Realistic tolerances are assumed to be 65% concerning all material parameters as well as all layer thicknesses. The tolerance of the length of the cantilevers is neglected. The resulting deviations of the SPL are referred to as tolerance band in Figs.

TABLE IV. Magnetostrictive coupling tensor for Fe49 Co49 V2 , as measured in the working point 12 kA/m [see Eq. (2)]; e15 is set to zero. e33 780 Vs/m2

4378

e31

e15

390 Vs/m2

0 Vs/m2

J. Acoust. Soc. Am., Vol. 134, No. 6, December 2013

FIG. 13. Cantilever length, lc ¼ 1500 lm; simulation of SPL; tolerance band from simulation runs with 65% tolerance on material properties and layer thicknesses; magnetic field strengths as in Fig. 11; measurement data reproduced from Fig. 11 for comparison. T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

TABLE V. Simulated key data from the MEMS-loudspeakers as in Figs. 12 and 13; frequencies rounded to 10 Hz. 1250 lm

1500 lm

Sensitivity, SI , at 450 Hz

0.08 Pa  m/kA

0.18 Pa  m/kA

Frequency range (6 dB)

350 Hz–1030 Hz

360 Hz–720 Hz

Cantilever length, lc

Maximum SPL Corresponding frequency

97 dB 440 Hz

97 dB 940 Hz

103 dB 450 Hz

103 dB 630 Hz

12 and 13. The measurement data given in these figures is the same as in Figs. 10 and 11, respectively. From the comparison of measurement and simulation data, the following conclusions can be drawn: (i)

(ii)

(iii)

Measured key data, such as cutoff frequencies, maximum SPL, or sensitivity is closely reproduced by the simulation. Thus, the simulation model is validated by the measurement results. The process tolerances of the membrane-chips lie inside the assumed boundaries. Thus, repeatability of the fabrication process can be presumed. The simulation model assumes purely linear behavior of the involved physical effects. Thus, also the prototypes of the MEMS-loudspeaker are found to exhibit good linearity.

VIII. OPTIMIZATION

TABLE VI. Design of the optimized membrane. Cantilever length, lc Cantilever width, bc Thickness of Fe49 Co49 V2 Thickness of SiO2 Airgap width, ba Number of cantilevers, n Membrane area, Am

1250 lm 72 lm 2.4 lm 3.6 lm 4.5 lm 152 14.57 mm2

closed when the airgaps are smaller than 3 lm. Opening up the airgaps flattens the frequency response of the SPL (in the range ba ¼ 3 lm–13 lm). When the airgaps become too wide, a considerable loss of sound pressure occurs (acoustic short-circuit condition). By performing further geometric variations, several design rules are found for optimizing the membrane. (1) Adequate airgaps between the cantilevers lead to a flat frequency response of the SPL. (2) The upper cut-off frequency is given by the mechanical eigenfrequency of the bending cantilevers. (3) The bending cantilevers should be processed as thick as possible; to adjust a certain upper cut-off frequency, their length has to be chosen accordingly. (4) The optimal layer thickness ratio between the magnetostrictive and the passive layer is about 2:3 for the presented materials; the passive layer is the thicker one.

The aim is to develop an optimized membrane design that shows a higher SPL output and a broader bandwidth. Using the validated simulation model [Eq. (22)], different design parameters can be varied and the effect on the SPL can be examined. As an example, Fig. 14 shows the influence of the airgap width, ba , between the cantilevers. The cantilever length is lc ¼ 1250 lm. The layer thicknesses and the number of cantilevers are chosen as in the corresponding measurements. The amplitude of the magnetic field is H^ ¼ 23:3 kA/m. The airgap width, ba , has direct influence on the acoustic friction element, Ra [Eq. (14)]. From Fig. 14, the following conclusions can be drawn: The membrane operates as acoustically

Following these design rules, an example for an optimized membrane geometry is presented in Table VI. The layer thicknesses present the estimated upper limits for the given fabrication process. The corresponding simulated SPL is depicted in Fig. 15. The magnetic field for the simulation is again set to H^ ¼ 23:3 kA/m. This enables a comparison to the corresponding measurements from Figs. 10 and 11. The acoustic geometry and the material data are chosen as in Tables II–IV. Table VII presents the key data extracted from the simulation (Fig. 15). In comparison to the key data from the measurements (Table I), a significant increase in bandwidth as well as in the SPL has been achieved. This shows the acoustic potential of the presented technology and design. However, a fully integrated MEMS-loudspeaker still needs to incorporate flat microcoils into the setup.

FIG. 14. Influence of the airgap, ba , on the SPL; lc ¼ 1250 lm; H^ ¼ 23:3 kA/m.

FIG. 15. SPL of optimized loudspeaker membrane (as in Table VI) and measurements of prototype membranes (as in Figs. 10 and 11) for comparison; H^ ¼ 23:3 kA/m.

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TABLE VII. Simulated key data from the simulation of the optimized loudspeaker (Fig. 15); frequencies rounded to 10 Hz. Sensitivity, SI , at 450 Hz

0.20 Pa  m/kA

Frequency range (6 dB)

100 Hz–2660 Hz

Maximum SPL (H^ ¼ 23:3 kA/m) Corresponding frequency

106 dB 1400 Hz

IX. CONCLUSION

In this contribution, a concept for a magnetostrictively actuated MEMS-loudspeaker has been presented. The membrane consists of more than a hundred separate bending cantilevers. This design advantageously introduces additional tuning parameters for the acoustic frequency response. Electrical impedances are of inductive nature, which enables the possible replacement of state-of-the-art miniature loudspeakers. The fabrication process for the membrane on a silicon-chip is as straightforward as the process for piezoelectric membranes. Its reproducibility has been verified. Nevertheless, a fully integrated setup of the MEMSloudspeaker will still add another silicon-chip carrying flat microcoils. A coupled simulation model has been developed to calculate the generated SPL inside a 2 cm3 measurement volume. Measurement data validates the model. A maximum SPL of 102 dB has been measured with a THD of 2% at 450 Hz. The membrane has been further optimized by employing the simulation model; a theoretical SPL of 106 dB has been achieved at 1.4 kHz with a 6 dB frequency range extending from 100 Hz to 2.6 kHz. This result shows the potential for acoustical applications of both the magnetostrictive actuation principle as well as the special membrane design. 1

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T. S. Albach and R. Lerch: Magnetostrictive MEMS-loudspeaker

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