Electrostatic all silicon MEMS speakers for in-ear audio applications –acoustic measurements and modelling approachLutz EHRIG(1) , Franziska WALL(1) , Herman SCHENK(1) , Sergiu LANGA(1,2) , Anton MELNIKOV(1) , Michael STOLZ(1) ,Bert KAISER(1) , Holger CONRAD(1) , Harald SCHENK(1,2)(1) Fraunhofer Institute for Photonic Microsystems IPMS, Dresden, Germany, Lutz.Ehrig@ipms.fraunhofer.de(2) Brandenburg University of Technology Cottbus - Senftenberg, Cottbus, Germany

Abstract
This paper presents the acoustic properties of an electroacoustic MEMS transducer. The transducer is based onelectrostatic bending actuators with lateral deflection. A large number of actuators is arranged in pairs and movein opposite phase between a cover and a handle wafer. By means of an appropriate sound guidance, areas of
opposite phase pressure changes are separated and audible sound is emitted. In this paper, the results of acoustic
measurements with a standard ear simulator are discussed. A linear lumped parameter model is presented andthe results of the simulations are compared with the measurements.
Keywords: MEMS, Speaker, Electrostatic, Headphone, Hearable

1INTRODUCTION

Common macroscopic electrostatic transducers need high voltages due to the comparatively large gap between
the electrodes. The voltage can be reduced by reducing the gap, but this in turn limits the maximum excursionof the diaphragm and consequently the maximum achievable sound pressure level.
Using micro-electro-mechanical systems (MEMS) this limitation can be overcomed by designing electrostatic
actuators with very small electrode gaps. By using a force-transforming mechanism, sufficient mechanicaldeflection and volume displacement can be provided.
The scale of MEMS and the techniques used for fabrication lead to further distinct features: predominantly
the batch fabrication and the usability of common CMOS processes resulting in low costs per unit in mass
production. The small size and light weight of the devices are obvious advantages as are the high energy
efficiency – at least regarding electrostatic and piezoelectric devices –, the enhanced performance and reliability
and the tight tolerances that can be obtained.
A challenge in the development of MEMS devices and the testing of different designs is the long production
time. It is therefore necessary to use models and simulations to identify critical properties and to optimize theMEMS design in advance.

2"NANOSCOPIC ELECTROSTATIC DRIVE"-TECHNOLOGY (NED) FOR IN EAR
AUDIO APPLICATIONSIn order to solve the contradiction between small electrode gap/low voltage and a large deflection, an electrostaticbimorph bending actuator has been developed at Fraunhofer IPMS. A particular design of the electrodes enables
a transformation of the electrostatic force, which, in conjunction with a lever mechanism, allows deflections tobe generated that are significantly larger than the gap itself.
The actuator consists of two non-planar electrodes separated by insulating spacers as depicted in Fig. 1a. In
case of an electrical potential V between the top (green) and the bottom (gray) electrodes an electrostatic field E
is generated, which leads to the attraction of the electrodes due to the Coulomb force. Because of the roof-like
topography of the top electrode, the attraction results in a lateral strain and a force F leading to a downward

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(a)

(b)

(c)

Figure 1. (a) Electrostatic bending actuator “Nano Electrostatic Drive” (NED): An electric potential V between
two electrodes results in a force F, which – due to the topology of the electrodes – results in a bending of thebeam. (b) Clamped-clamped NED-actuators in rest position (upper beam) and with a S-shaped deflection curve(lower beam). (c) NED audio transducer chip with multiple clamped-clamped actuators and a top and a handle
wafer with vents. The beams are shown in the deflected state.
bending of the cantilever tip. Shifting the spacers to the top of the roof-like-structured electrodes, an upwardbending can be achieved. The actuator mechanism is described in detail in [1].
The NED actuators are clamped on both sides and structured in a way that an S-shaped deformation occurs, seeFig. 1b. Beams with opposite deflection curves are arranged in pairs, so that the volume between them changes
according to the applied signal voltage. Multiple pairs of actuators are arranged on a chip, see Fig. 1c. The
device layer is between a top and a handle wafer each of them having vents to release the air. Separating thefront and the back side of the chip, the acoustic short circuit is avoided and the chip emits audible sound.

3

ACOUSTICAL MEASUREMENTS

3.1 Test Structure
A test structure – optimized for the audible frequency range – is depicted in Fig. 2a. It contains three sub-chips
with a size of approx. 6.2 × 2.4 mm2 each and an active area of 5.5 × 1.7 mm2 respectively. The bond wires tothe printed circuit board are visible and on top of each sub-chip, the cover with the air vents can be seen.
A microscopic image of the beams of one sub-chip is shown in Fig. 3. The sub-chip consists of 14 pairs ofbeams with a length of 2200 µm and seven pairs of short beams with a length of 1100 µm as a fill-in. The
mechanical behavior of both types of beams is different, but due to the ratio of 4:1 regarding the total lengthof long beams and total length of short beams, it is safe to assume that the long beams dominate the acoustic
characteristics.
The sub-chip is subdivided into three actuator groups. Group 1 and 3 have the same number of actuators: sixpairs of long beams and three pairs of short beams. Group 2 has two pairs of long beams and one pair of shortbeams.
In Fig. 2b an illustration of the cross section of the chip with one pair of beams is shown. The height ofthe beams is 75 µm, the height of the top wafer and the handle wafer is 400 µm. The clearance, i.e. the gap
between the beams and the handle wafer and the top wafer, is 1 µm respectively.

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(a)

(b)

Figure 2. (a) Test structure of a NED audio transducer with three sub-chips, each having an active area of
5.5 × 1.7 mm2 . (b) Cross section of the chip showing one pair of beams and the vents for the air in the top andin the handle wafer. The arrow direction for the movement of the beams and the air flow shows the first halfof a vibration period.

Figure 3. Stitched microscopic image of one sub-chip of the test structure (without a top cover and with ahandle wafer without vents). The sub-chip is composed of 14 pairs of beams with a length of 2200 µm andseven pairs of beams with a length of 1100 µm. The sub-chip is split in 3 groups.

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Measurement
LPM simulation

100THD in %SPL in dB

120

8060

Measurement
LPM simulation

40

2000.1

1Frequency in kHz(a)

100.1

1

10Frequency in kHz(b)Figure 4. Sound pressure level (a) and total harmonic distortion (b) measured (solid line) and simulated (dottedline) of a test structure with three sub-chips.
3.2 Measurement Setup
The rear side of the test structure was measured through a hole in the printed circuit board (PCB) with anear simulator (GRAS RA0045, in accordance to IEC 60318-4, with a Microtech Gefell MV210 preamplifer)directly attached to the PCB. The front side of the chip remained free. Measurement signals were generated
and analyzed by an audio analyzer system (NTI Audio Flexus FX100). The amplification of the generator signal
and the bias voltage were provided with an amplifier (Krohn-Hite 7602M).
3.3 Measurement Results
The results of the sound pressure level and total harmonic distortion measurements are shown in Fig. 4. All
three sub-chips were measured simultanously with a bias voltage of 40 V and a signal voltage of 10 Vpp.
The frequency response of the sound pressure level in Fig. 4a is dominated by the transfer function of the ear
simulator showing a steady rise of the curve above 1 kHz and the λ2 -resonance of the main coupler volume at
11.3 kHz. The SPL at the almost flat low frequency region is between 77 dB and 80 dB at 20 Hz and 1 kHz
respectively. The slight bump around 8 kHz is due to the mechanical resonance of the NED transducer.
The total harmonic distortion, shown in Fig. 4b, is dominated by the 2nd harmonic due to the quadratic relation
between signal voltage and displacement.

4MODELINGIn Fig. 5 the equivalent electrical circuit of our model is shown, with the electrical domain on the left, themechanical domain in the center and the acoustical domain on the right. All domains are connected through atransduction element representing the eneregy transfer between them. The device behavior is thereby describedat a working point, defined by the DC-voltage, for small periodic oscillations caused by the AC-voltage. Inorder to keep the logic of two-port theory forces are linearized around this working point. Further, a timeindependent energy-transfer is assumed. The electric domain represents the outer electric circuit. Here, theseries resistor takes the voltage source’s internal resistance into account. Leakage currents are summed up in
the parallel resistor.
The transduction element describes the energy transfer from the electric towards the mechanical domain and istherefore derived from the following equation of motion,m7342

d2 x(t)dx(t)1U2+r+k(x+x(t))=εεA.
r000dt 2dt2(g0 − (x0 + x(t)))2(1)Figure 5. Equivalent electrical circuit of the model for our electrostatic transducer.
Here, we assume a damped mass-spring-system combined with a parallel plate capacitor with one movable
electrode. This movement of a mass m is described in the displacement x(t) around the equilibrium position x0
caused by the applied DC-voltage. The elastic force is described with a spring constant k0 . On the other side,
the Coulomb force of a plate capacitor is defined by the vacuum permeability ε0 , the relative permeability εr ,the electrodes area A, the gapsize g0 and the voltage U with an DC-part UDC and a AC-part UAC cos(ωt) withthe electric oscillation frequency ω. For the equivalent network each force is linearized around the working
point x0 ,FSpring = k0 x0 + k0 x(t),
(2)


2x(t)
11+.
(3)
FCoulomb ≈ ε0 εr AU 22(g0 − x0 )2 (g0 − x0 )3The static equilibrium leads to a cancellation of the constant offset by the Coulomb as well as spring force. The
remaining amplitude of the electrostatic force due to the AC-voltage defines the energy transduction coefficient
TEM which depends on the initial transducer capacity C0 scaled with the additional DC-offset of the displacement,
c2C0g0
TEM = UDC 0 with c0 =.
g0
g0 − x0(4)Further, the second harmonic is generated by the squared AC-voltage with its own transduction coefficient. The
conversion of current into velocity v results in an additional parallel capacitor on the electric side through thetime derivative of the voltage.
I ≈ UDC

dU(t)
dC
dC(t)
+ c0C0= UDC v + iωc0C0UAC .
dt
dtdx

(5)

In the mechanical domain forces are equivalent to voltages and thereby a mass to a inductance, damping toa resistance and a spring to a capacitor. In our system the electrostatic force is opponent to the elastic force
leading to a softening for the effective spring constant keff of the complete system. The linear part of theCoulomb force determines keff and makes it thereby depending on the working point,
212TEM
2keff = k0 − ∆kCoulomb = k0 − ε0 εr AUDC=k−.
02(g0 − x0 )3c0C0(6)This effect is accomplished in the negative series capacitance within the electric domain in order to get apurely mechanical domain. The complete transducer system is modeled by parallel connected damped springmass systems.
The force within the mechanical domain is transfered into a pressure scaled with the swept area. Here, we
approximate this area by the beam with a triangular shape. The two ports on the right of the mechano-acoustical7343

coupling transformer represent the front and the back side of the NED beams in the chip. The clearance of
1 µm, which is a fluidic connection between the front and the back side of the beams (see Fig. 3), is modeledby a parallel branch of the coupling transformer consisting of an inductance LCL in series with a resistor RCL
with the impedance given in [2]. It has to be taken into account that the clearance occurs twice, once above
and once below the beams. In order to compare this model to presented experiments the system’s equivalentcircuit is extended at the acoustic domain with an ear simulator according to IEC 60318-4 [3]. The measured
SPL corresponds to the pressure generated by the fundamental mode p1 . The conversion between voltage andpressure is calculated with the equivalent network. This pressure is used to determine the corresponding soundpressure level,p1).
(7)
SPL = 20log10 (prefFor THD the second harmonic’s pressure p2 is compared to the sum of the fundamental and the second mode,
sp22.
(8)
T HD = 100
2p1 + p22

5

CONCLUSION AND FUTURE WORK

The presented micro speaker is based on a multitude of bimorph-like electrostatic bending actuators. Theactuators are arranged between a vented handle and cover wafer and are designed to emit sound in the audible
frequency range.
Measurement results of a test structure were presented proving audio reproduction capabilities for in-ear audio
applications. Below resonance sound pressure levels between 77 dB and 80 dB were measured in an IEC 603184 ear simulator with a THD of 5 %. Harmonic distortions are dominated by second-order products.
A simple lumped parameter model based on a mass-spring-system combined with a parallel plate capacitor waspresented. The simulation results of the model for SPL and THD were presented and are in good agreementwith the measurements.
Further development focuses on increasing sound pressure level and linearity by optimizing the actuator design.
To make efficient use of the long production times in the clean room developing and refining the models of thetransducer is an ongoing task combining the results of analytical calculations, FEM simulations and knowledge
gained from electrical, optical and acoustical measurements.

ACKNOWLEDGEMENT
The work shown here was funded in the project MEMSound by the German Federal Ministry of Education andResearch (BMBF) in the funding measure "Validation of the technological and social innovation potential ofscientific research - VIP +" under the grant number 03VP01800.

REFERENCES[1] Conrad, H.; et al. A small-gap electrostatic micro-actuator for large deflections. Nature Communications,2015, doi:10.1038/ncomms10078.
[2] Beranek, L. Acoustics. Acoustical Society of America, 1993 (1954).
[3] Brüel& Kjær, Application Note Ear Simulator for Telephonometry, Denmark, 2012.

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