MEMS Electrostatic Acoustic Pixel

Arpys Arevalo*1, David Conchouso1, David Castro1, and Ian G. Foulds1,31Computer, Electrical and Mathematical Sciences and Engineering (CEMSE), King Abdullah University ofScience and Technology (KAUST), 2The University of British Columbia (UBC), School of Engineering,Okanagan Campus.*Corresponding author: 4700 KAUST, Kingdom of Saudi Arabia, arpys.arevalo@kaust.edu.sa

Abstract: This paper reports the simulation of anhexagonal membrane structure using COMSOLMultiphysics 5.0. The structure is a 5µm thickpolyimide layer with an integrated metal layeron top, to apply a bias voltage. The hexagonalmembrane is separated by a 3µm air gap and5µm thick polyimide structural layer from thebottom electrode and a 3µm and 5µm thickpolyimide structural layer from the top electrode.The AC/DC Module was used to extract thecapacitance and pull-in voltage needed to displacethe membrane toward the active electrode. Amodal analysis was performed using the Struc-tural Mechanics Module to extract the structure’sresonance frequency and frequency modes.

Keywords: MEMS, electrostatic speaker,digital sound reconstruction, Acoustic Pixel,polyimide.

1. Introduction

The growth of the electronics industry demandsbetter components for improved electronic sys-tems [1, 2]. Such components need to be moreadvanced in order to keep up with the evolutionof the digital era. The loudspeaker design mech-anism has not been changed for almost a century[3–5]. In an era were almost every component isdigital, the loudspeaker driver design still is thelast analog component that needs to evolve to itsdigital form, to achieve a true digital audio repro-duction cycle.

Efforts to develop a direct digital method ofsound reconstruction has been reported elsewhere[6, 7]. In [4], authors reported a micro-speaker ina single chip using CMOS-MEMS membrane ar-rays and described their method behind the dig-ital sound reconstruction concept. They fabri-cated a 3-bit electrostatic array (seven transducer

element) where they demonstrated the sound re-construction. Due to their fabrication methodseach transducer in the array has a fixed electrodewith a dome shape membrane. Therefore, there isan asymmetry in their system while actuating themembranes.

In previous work, we have tackled this problemby using a piezoelectric layer [7–9]. Using the lat-ter method for the driving mechanism help us toavoid the asymmetry in the system, but adds somecomplexity to the fabrication process. Our workdiffers from other reports [10–14], specifically inthe dimensions of the actuator, the combination ofmaterials used, the micro fabrications process andthe method of sound reconstruction.

In this work we propose an electrostatic ap-proach using Polyimide as the structural layer.Polyimide is a very attractive polymer for MEMSfabrication due to its low coefficient of thermal ex-pansion, low film stress, lower cost than metalsand semiconductors and high temperature stabilitycompared to other polymers [15–17]. Polyimidehas been previously used in the microelectronicsindustry for module packaging, flexible circuitsand as a dielectric for multi-level interconnectiontechnology [18, 19]. Polyimide has demonstratedgreat performance in Micro Electro MechanicalSystems (MEMS) devices [15, 20–34] and in themicroelectronics industry. The polymer can han-dle temperatures of up to 350◦C and can be easilyprocessed and integrated with metal layers to de-velop devices with low complexity.

2. Computational Methods

COMSOL Multiphysics provides the Electro-static Interface, which is available for 3D, 2D in-plane and 2D axisymmetric components. In ourparticular application we have a capacitor whichwill use relatively high voltage (up to 150 Volts).

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The electrostatic equations are not to be takenliterally as ”statics”, but as the observation ortime scale at which the applied excitation changesare in comparison to the charge relaxation time,and that the electromagnetic wavelength and skindepth are very large compared to the size of thedomain of interest [35].

For our device, we need to use the quasi-staticelectric fields and currents that are included inthe MEMS module, together with the AC/DCModule, which do not include the wave propa-gation effects. The physics interfaces takes onlythe scalar electric potential, which can be inter-preted in terms of the charge relaxation process.The three equations used for this physic are: TheOhm’s Law, the equation of continuity and theGauss’ law. COMSOL combines this equationand uses the following differential equation for thespace charge density in a homogeneous medium:

δρ

δt+

σ

ερ = 0 (1)

with solution:

ρ(t) = ρ0e−tτ (2)

where

τ =ε

σ(3)

which is the charge relaxation time. When us-ing a good conductor material such as gold, τ is ofthe order of 10−19s whereas for a good insulatorlike silicon oxide, its of the order of 103s. It is therelation between the external time scale and thecharge relaxation time that determines the physicsinterface and study that we will use.

2.1 Electrostatic Equations

Under static condition the potential, V, is de-fined as the following relationship:

E =−∇V (4)

When combined with the constitutive relation-ship D= εE+P bettwen the electric displacementD and the electric field E, the Gauss’ law is repre-sented as:

−∇ · (ε0∇V −P) = ρ (5)

The equation describes the electrostatic field indielectric materials, the physical constant ε0 is thepermittivity of vacuum with units [F/m], P is theelectric polarization vector in [C/m2], and ρ is thespace charge density given in [C/m3].

For models in 2D, the interface assumes a sym-metry where the electric potential varies only inthe x and y directions and is constant in the z di-rection. Which implies that the electric field E istangential to the xy-plane. The same equation issolved in the case of a 3D model. The interfacesovles the following equation where d is the thic-ness int eh z direction:

−∇ · (ε0∇V −P) = ρ (6)

The axisymmetric version of the physics inter-face considers the situation where the fields andgeometry are axially symmetric. For this case theelectric potential is constant in the φ direction, im-plying that the electric field is tangential to the rz-plane [35].

3. Design and Simulation Setup

The main membrane of our device can be di-vided in three sections: outer hexagonal ring, teth-ers and hexagonal membrane (see Fig. 1).

Figure 1: Top view of the simulated membrane,showing its three different sections.

The device was evaluated with several differ-ent tether designs and the present work is done us-ing the final chosen design for fabrication. The de-sign shows 5 tethers in each side of the hexagonal

Excerpt from the Proceedings of the 2015 COMSOL Conference in Grenoble

membrane. The standard structure has the follow-ing dimensions: 250µm membrane hexagon side,the hexagon was inscribed in a 500µm diametercircumference and tether have a width of 8µm foreach of them.

The structure can be fabricated using twostructural layers and two sacrificial layers. Thestructural layers are made of polyimide and havea thickness of 5µm. To be able to attract and re-pel the membrane we need a set of electrodes. Inour simulations we use the bottom electrode madeof gold, because of its good conductivity, which islocated right on the silicon substrate. Also a mid-dle electrode which is on top of the membrane anda top electrode that is all the way to the top of thestructure. Fig. 2 shows a conceptual view of anindividual membrane.

Figure 2: Conceptual view of the simulated de-vice. The image shows an exploded view on theright, and an assembled view on the left.

To create the 3D model in COMSOL, we firstexported the 2D layout from Tanner L-edit soft-ware, which is the tool we use to design ourdevices for micro-fabrication. The CAD importmodule was used, and the correct scale was set toimport the DXF file into COMSOL environment.The import was done in two different work-planesto be able to extrude the needed features. The fi-nal component was set to form composite faces toeliminate unnecessary features and a union opera-tion.

The selected materials for the electrodes wasgold, as depicted in Fig. 2 in yellow color. Thestructural layer was set to be polyimide, shown inred color in Fig. 2. Also, all the gaps were set to beair. Table 1 contains the material properties usedin the simulation.

Table 1: Materials PropertiesProperty Polyimide GoldRelative permittiv-ity (εr)

2.9 6.9

Young’s modulus(E)

3.1e9 [Pa] 70e9 [Pa]

Poisson’s ratio (ν) 0.34 0.44Density (ρ) 1300 [kg/m3] 19300[kg/m3]

The Electromechanics physics module wassetup with the following constraints: Fixed con-straint for all the six outer sides (faces bound-aries) of the full structure, Bottom Electrode asthe ground and Middle Electrode as a Terminal.The setup will allow the interaction between theelectrodes, and the capacitance will be calculatedby the software.

An interesting feature of our design is that therewill not be an electric short when pull-in occurs,because all the electrodes are completely isolatedfrom each other with structural layer.

To see the behavior of the membrane we used aStationary Study with an auxiliary sweep to applyvoltages between a pair of electrodes ranging from10V - 150V in steps of 10V. The boundary thatwas set to be a terminal was given the declaredparameter ”Vin”.

4. Results

The simulation results give us an insight of the de-formation of the membrane. It is known that thepull-in voltage when the system is unstable, whichhappens at approximately 1/3 of the distance be-tween the electrodes. Therefore, the pull-in willoccur when the membrane moves approximately2.6µm towards the active electrode. In Fig. 3 agraph of the simulated displacement vs the appliedvoltage is shown. Fig. 5 shows the graph of thecapacitance between the electrodes vs the appliedvoltage.

From these results we were able to deduct thatthe pull-in voltage is between 140V and 150V, ap-plying more than this voltage wont let the simu-lation to converge. Fig. shows the result of thedisplacement in the 3D model.

The resonance frequency and mode frequencieswere calculated using the Solid Mechanics Mod-ule to study the behavior of the structure. An

Excerpt from the Proceedings of the 2015 COMSOL Conference in Grenoble

Figure 3: Total displacement on the ”z-axis” vsthe applied voltage.

Eigenfrequency study was setup to find the first6 modes of the structure, shown in Fig. 6.

From this simulation we can see that the modeof interest is the first one at 9.4175kHz, as this willdisplace the air in a uniform mode with only onedeformation node. Since the transducer will be ac-tuated at an expected sample frequency of 40kHz,the closest mode is the sixth at 3.9267kHaz.Mode 6, has one radial node and one central node,but it will not have an impact in the performanceof the membrane because it will be out of therange of the frequency.

If the membrane will be actuated at 40kHz, thismeans that the input signal will behave as a pulsewith a width of 25µm. Therefore, we performeda new simulation with at Time Dependent Studyfrom t = 0 to t = 625µs in steps of 25µs to observethe response time of the structure to a 150V con-stant electric potential applied to one of the elec-trode. Fig. 7, shows the response time of the mem-brane. From this graph we can see that it takes themembrane approximately 125µs to reach the max-imum displacement of about 1.5µm. Also, it canbe seen that it the membrane reaches a stable posi-tion in approximately 500µs at 1µm displacementfrom its original position. Nevertheless, the pulseswill only be 25µs long and this means that thestructure will only displace approximately 0.5µm.

Figure 4: Capacitance vs applied voltage.

Figure 5: (Top Left) Isometric view of the sim-ulation results for displacement, (Top Right) Topview of deformed structure, (Bottom) Side viewof the deformed structure at 150V.

5. Conclusions

The proposed membrane design was simulatedwith the intended operation voltages for the realdevice. The results shows that the membrane issuitable for the intended acoustic transducer ele-ment for the final transducer array. The membranegeometry can be adjusted to change the structureresonance frequency, so that the element has theoptimal acoustic response. The next simulationsteps will be the acoustic response. Now that wehave found the total displacement of the structureat an applied voltage, we can simulate the dis-placement and calculate the sound pressure gen-erated by this change.

Full arrays have already been designed and fab-ricated. The processed chips are diced from a fourinch wafer using our in house dicing method [36].

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Figure 6: Frequency modes of the simulated struc-tures

The chips are currently being tested and the nextsteps include the validation of the presented modeland the experimental results.

6. References

1. J P Rojas, A Arevalo, I G Foulds, and M MHussain. Design and characterization of ultra-stretchable monolithic silicon fabric. AppliedPhysics Letters, 105(15):154101, (2014).

2. J P Rojas, Hussain A M, A Arevalo, I GFoulds, Sevilla GAT, JM Nassar, and M MHussain. Transformational electronics arenow reconfiguring. SPIE Defense+ Security,9467:946709–946709–7, (2015).

3. Carl B Boyer and Uta C Merzbach. A Historyof Mathematics. Wiley (2011).

4. Brett M Diamond, John J Neumann, Jr, andKaigham J Gabriel. Digital sound reconstruc-tion using arrays of CMOS-MEMS micros-peakers. In Micro Electro Mechanical Sys-tems, 2002. The Fifteenth IEEE InternationalConference on, pages 292–295, (2002).

Figure 7: Response time of the structure to an in-put signal of 150V

5. Baron John William Strutt Rayleigh andRobert Bruce Lindsay. The theory of sound(1945).

6. B.M Diamond, J.J. Jr Neumann, and K.JGabriel. Digital sound reconstruction usingarrays of CMOS-MEMS microspeakers. InMicro Electro Mechanical Systems, 2002. TheFifteenth IEEE International Conference on,pages 292–295, (2002).

7. A Arevalo, D Conchouso, D Castro, N Jaber,M I Younis, and I G Foulds. Towards a DigitalSound Reconstruction MEMS Device: Char-acterization of a Single PZT Based Piezo-electric Actuator. In 10th IEEE Interna-tional Conference on Nano/Micro Engineeredand Molecular Systems NEMS2015, Xia’an(2015).

8. A Arevalo and I G Foulds. MEMS Acous-tic Pixel. 2014 COMSOL Conference, Cam-bridge, England, (2014).

9. A Arevalo and I G Foulds. Parametric Studyof Polyimide-Lead Zirconate Titanate ThinFilm Cantilevers for Transducer Applications.In 2013 COMSOL Conference, Rotterdam,Holland, (2013).

10. Zhihong Wang, Jianmin Miao, and Chee WeeTan. Acoustic transducers with a perforateddamping backplate based on PZT/siliconwafer bonding technique. Sensors and Actu-ators A: Physical, 149(2):277–283 (2009).

Excerpt from the Proceedings of the 2015 COMSOL Conference in Grenoble

11. Youngki Choe, S Chen, and Eun Sok Kim.High fidelity loud microspeaker based onPZT bimorph diaphragm. In NSTI-Nanotech2010, pages 316–319, (2010).

12. Sang-Soo Je and Junseok Chae. A Compact,Low-Power, and Electromagnetically Actu-ated Microspeaker for Hearing Aids. ElectronDevice Letters, IEEE, 29(8):856–858, (2008).

13. P Valousek. A digital loudspeaker: ex-perimental construction. Acta polytechnica,46:40–42, (2006).

14. Nicolas-Alexander Tatlas and John N Mour-jopoulos. Digital Loudspeaker Arrays drivenby 1-bit signals. In Audio Engineering SocietyConvention 116, (2004).

15. A Arevalo, E Byas, D Conchouso, D Cas-tro, S Ilyas, and I G Foulds. A Ver-satile Multi-User Polyimide Surface Micro-machining Process for MEMS Applications.In 10th IEEE International Conference onNano/Micro Engineered and Molecular Sys-tems NEMS2015, Xia’an (2015).

16. A A A Carreno, D Conchouso, A Zaher,I Foulds, and J Kosel. Simulation of aLow Frequency Z-Axis SU-8 Accelerome-ter in CoventorWare and MEMS+. In Com-puter Modelling and Simulation (UKSim),2013 UKSim 15th International Conferenceon, pages 792–797, (2013).

17. D Conchouso, A Arevalo, D Castro,E Rawashdeh, M Valencia, A Zaher, J Kosel,and I Foulds. Simulation of SU-8 Frequency-Driven Scratch Drive Actuators. In ComputerModelling and Simulation (UKSim), 2013UKSim 15th International Conference on,pages 803–808, (2013).

18. A Bruno Frazier. Recent applications of poly-imide to micromachining technology. In-dustrial Electronics, IEEE Transactions on,42(5):442–448, (1995).

19. A B Frazier. Uses of polyimide for micro-machining applications. In Industrial Elec-tronics, Control and Instrumentation, 1994.IECON ’94., 20th International Conferenceon, pages 1483–1487, (1994).

20. S.Y. Xiao, L.F. Che, X.X. Li, and Y.L. Wang.A novel fabrication process of {MEMS} de-vices on polyimide flexible substrates. Mi-croelectronic Engineering, 85(2):452 – 457,(2008).

21. Steve Tung, Scott R Witherspoon, Larry ARoe, Al Silano, David P Maynard, andNed Ferraro. A mems-based flexible sen-sor and actuator system for space inflatablestructures. Smart Materials and Structures,10(6):1230, (2001).

22. J. Courbat, M.D. Canonica, D. Briand, N.F.de Rooij, Damien Teyssieux, Laurent Thiery,and Bernard Cretin. Thermal simulation andcharacterization for the design of ultra-lowpower micro-hotplates on flexible substrate.In Sensors, 2008 IEEE, pages 74–77 (2008).

23. A Arevalo, E Byas, and I G Foulds. µHeateron a Buckled Cantilever Plate for Gas SensorApplications. 2012 COMSOL Conference,Milan, Italy, (2012).

24. A Arevalo, D Conchouso, and I G Fould.Optimized Cantilever-to-Anchor Configura-tion of Buckled Cantilever Plate Structuresfor Transducer Applications. 2012 COMSOLConference, Milan, Italy, (2012).

25. A Arevalo, S Ilyas, D Conchouso, and I GFoulds. Simulation of a Polyimide BasedMicromirror. 2014 COMSOL Conference,(2014).

26. A Arevalo and I G Foulds. Polyimide Ther-mal Micro Actuator. 2014 COMSOL Confer-ence, Cambridge, England, (2014).

27. S Ilyas, A Ramini, A Arevalo, and M I You-nis. An Experimental and Theoretical In-vestigation of a Micromirror Under Mixed-Frequency Excitation. Journal of Microelec-tromechanical Systems, (2015).

28. D Conchouso, A Arevalo, D Castro, , andI G Foulds. Out-of-plane Platforms with Bi-directional Thermal Bimorph Actuation forTransducer Applications. In 10th IEEE In-ternational Conference on Nano/Micro Engi-neered and Molecular Systems NEMS2015,Xia’an (2015).

Excerpt from the Proceedings of the 2015 COMSOL Conference in Grenoble

29. Loı̈c Marnat, A Arevalo Carreno, D Conc-houso, M Galicia Martinez, I Foulds, and AtifShamim. New Movable Plate for EfficientMillimeter Wave Vertical on-Chip Antenna.IEEE Transactions on Antennas and Propa-gation, 61(4):1608–1615, (2013).

30. A Alfadhel and Arpys Arevalo. Three-AxisMagnetic Field Induction Sensor Realized onBuckled Cantilever Plate. . . . IEEE Transac-tions on, (2013).

31. D Castro, A Arevalo, E Rawashdeh, andN Dechev. Simulation of a Micro-Scale Out-of-plane Compliant Mechanism. In 2014COMSOL Cambridge, England, (2014).

32. A Arevalo, D Conchouso, D Castro, M Diaz,and I G Foulds. Out-of-plane buckled can-tilever microstructures with adjustable angu-lar positions using thermal bimorph actuationfor transducer applications. Micro and NanoLetters, (2015).

33. A Arevalo, D Conchouso, E Rawashdeh,D Castro, and I G fould. Platform IsolationUsing Out-of-Plane Compliant Mechanisms.In 2014 COMSOL Conference, Boston, USA(2014).

34. N Jaber, A Ramini, A Carreno, and MI You-nis. Higher Order Modes Excitation of Mi-cro Clamped-Clamped Beams. NANOTECHDubai 2015, (2015).

35. COMOSL. Comsol multiphysics referencemanual. (2015).

36. Y Fan, A Arevalo, H Li, and I G Foulds. Low-cost silicon wafer dicing using a craft cutter.Microsystem Technologies, (2014).

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