In this work we describe a MEMS instrument that resonates at audible frequencies, and with which music can be made. The sounds are generated by mechanical resonators and capacitive displacement sensors. Damping by air scales unfavourably for generating audible frequencies with small devices. Therefore a vacuum of 1.5 mbar is used to increase the quality factor and consequently the duration of the sounds to around 0.25 s. The instrument will be demonstrated during the MME 2010 conference opening, in a musical composition especially made for the occasion

Abelmann, L.

Beekman, J.G.

Been, A.J.

Boer, H. de

Elwenspoek, M.C.

Engelen, J.B.C.

Folkertsma, G.A.

Fortgens, L.

Graaf, D. de

Vocke, S.

Woldering, L.A.

English

de Boer, H.

Fortgens, L.C.

de Graaf, D.B.

University of Twente Research Information

Back to the ProgrammeA MUSICAL INSTRUMENT IN MEMSJ. B. C. Engelen1, H. de Boer1, J. G. Beekman1, A. J. Been1, G. A. Folkertsma1, L. C. Fortgens1,D. B. de Graaf1, S. Vocke1, L. A. Woldering1, L. Abelmann1, and M. C. Elwenspoek1,21Transducer Science and Technology, MESA+ Institute for Nanotechnology, University of Twente, Enschede, the Netherlands2Freiburg Institute for Advanced Studies (FRIAS), Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, GermanyAbstract — In this work we describe a MEMSinstrument that resonates at audible frequencies,and with which music can be made. The sounds aregenerated by mechanical resonators and capacitivedisplacement sensors. Damping by air scales un-favourably for generating audible frequencies withsmall devices. Therefore a vacuum of 1.5 mbar isused to increase the quality factor and consequentlythe duration of the sounds to around 0.25 s. Theinstrument will be demonstrated during the MME2010 conference opening, in a musical compositionespecially made for the occasion.Keywords — Musical instrument, capacitive sen-sor, comb driveI – IntroductionIn 1997, researchers at Cornell University fabricated theworld’s smallest guitar, about the size of a human bloodcell [1]. Two years later, a micro harp was made [2].In 2003, laser light was used to strum the ‘strings’ of ananoguitar [3]. However, no human has heard the soundof these instruments; the strings vibrate at frequencieson the order of tenths of megahertz. With the adventof a microphone for MEMS structures [4], there seemsto be a growing interest in the field of MEMS musicalinstruments.In this work we describe a MEMS instrument, consist-ing of micromechanical mass-spring resonators that canbe ‘plucked’ using electrostatic comb-drive actuators.The instrument’s vibrations are sensed by capacitivedisplacement sensors using comb structures as sensingelements. The measured capacitance is used as the audiosignal.In the following, first the design of the instrument willbe explained, after which measurements of the MEMSinstrument’s tone will be discussed.II – Theory and designOur instrument consists of individual resonators for eachnote, similar to a harp. The resonators are (relativelylarge) masses suspended by folded flexures. Each res-onator is actuated by a comb drive. A resonator behavesaccording to the well known differential equationmd2xdt2+ γdxdt+ kx = Fcomb, (1)where m is the mass of the resonator, x the displace-ment, γ the coefficient of viscous damping by air, k thecombdrivemovingbody (m)foldedflexures (k)200 µmFigure 1: Scanning electron micrograph of one of the res-onators of the MEMS instrument. The perforated structure isthe moving body (mass m), suspended by folded flexures onboth sides. The mass is ‘plucked’ by a comb drive on one side,and the mass’s displacement is measured by a comb drive onthe other side.suspension spring constant, and Fcomb the comb-driveforce. The solution of (1) is the expected comb-drivedisplacement after it has been excited,x(t) = e−αt sin(2π f0t), (2)with α = γ/2m. The free resonance frequency for anunderdamped system isf1 =12π√km−α2 ≈ f0(1− 18Q2), (3)with f0 = 2π√k/m, and Q = π f0/α . The approxima-tion is correct for low damping. Tailoring the mass andspring constant, resonators with different resonance fre-quencies are made. In order to obtain resonance frequen-cies in a range from 400Hz to 1000Hz, large structuresare needed compared with common MEMS structuresizes.A. Scaling issues — Q-factorFor our mass-spring-damper system resonators, the qual-ity factor equalsQ =√mkγ. (4)The duration of a note after being excited/struck, is pro-portional to the Q-factor and inversely proportional tothe resonance frequency.Scaling the dimensions of the mass with factor l, themass scales cubically, m ∝ l3. The spring constant shouldscale proportionally to the mass in order to maintain thesame resonance frequency, hence k ∝ m. The viscousMME2010 Workshop 193Back to the Programme     Amplitude (a.u.)Frequency (Hz)straight fingerstapered fingers0 f0 2f0 3f0 4f0Figure 2: The Fourier transform of the simulated capacitanceof comb drives with straight and tapered fingers for an ex-ponentially decaying sinusoid displacement. The non-linearcapacitance versus displacement of tapered fingers gives riseto higher harmonics besides the fundamental (first harmonic).damping is proportional to the area of the mass, γ ∝ l2.Consequently, the Q-factor scales with l; reducing thedimensions of the system results in a proportionally re-duced Q-factor. In general, at equal resonance frequen-cies, a smaller mass-spring oscillator will experiencemore damping and will sound a shorter note than a largeroscillator. To solve this issue of small MEMS instru-ments, we decrease γ by placing the instrument in avacuum chamber.B. Capacitive read-outWe use a comb drive together with capacitance mea-surement circuitry to generate the audio signal. Besidesease of fabrication, the use of a comb drive allows us toadjust the timbre of the note, by modifying the comb-drive finger shape. For straight comb drive fingers, thecapacitance is linearly proportional to the displacement.However, the capacitance of a comb drive with taperedfingers depends non-linearly on the displacement x [5],Ctapered = 2ε0hx+ x0g− (x+ x0) tanα, (5)where x0 and g are the initial overlap and gap betweenfingers respectively, h is the comb-drive height, and αthe angle of the tapering. This non-linearity gives riseto higher harmonics in the audio signal, resulting in amore interesting tone. The upper bound on the angle αis set by fabrication limits; α = 0.72◦ for our designs.Figure 2 shows the Fourier transform of the simulated ca-pacitance for both straight and tapered fingers using (2)for displacement x. Besides the fundamental, the secondharmonic is clearly present. However, the relative am-plitude of the second harmonic is small due to the smallangle α .C. Instrument designThe designed instrument contains six resonators at dif-ferent frequencies. The instrument is designed such thatthe notes form part of a major diatonic scale. We chosesix notes with n = {0,2,4,5,7,12}, where n indicatesthe number of semitones above a ‘C’ [6]: Do, Re, Mi,Fa, So, and (high) Do. The instrument is not tuned toa particular existing instrument. A frequency for our‘C’ is chosen at 396Hz, from which the subsequent notefrequencies follow from [6],fn = 2n12 ×396Hz. (6)The general layout of our instrument chip is shownin Figure 3. Both the suspension spring stiffness k andthe moving body mass m of the resonators are adjustedto obtain the desired resonance frequencies. The springstiffness of the folded flexure suspension equals [7]k =2Ehb3L3, (7)where E is the effective Young’s modulus of silicon, hthe spring height, b = 3µm the spring width, and L thespring length. The effective mass of the resonator meff isequal to the moving body mass plus the folded flexuretruss mass. Because the folded flexure trusses moveonly half the distance, only half their mass contributesto the effective mass. The moving body and trussesneed to be perforated because of the used fabricationprocess. The perforation consists of 5µm×5µm squarewith 3µm silicon beams in between. This results in anarea reduction Rperf of approximatelyRperf ≈82−5282. (8)Only one dimension of the moving body is adjusted. Re-ferring to Figure 3, B = 1.2mm is fixed, W is adjusted.The area of the perforated trusses Atruss is the productof the width and length, 32µm and W +333µm, respec-tively. The total area Afingers of the comb-drive fingers onboth sides of the resonator equals 3.84×10−8 m2. Wefind for the effective mass,meff = ρSi h ·[Afingers +Rperf (WB+Atruss)]. (9)First L is chosen such that the resonators fit on the chip,according to the layout shown in Figure 3. Subsequently,W is adjusted. The dimensions are listed in Table 1.III – Experimental Details and ResultsThe MEMS instrument is fabricated from a (100) single-crystal highly boron-doped silicon-on-insulator wafer,with a 50µm thick device layer (determining height hof the comb drive and springs) and an oxide thicknessof 3µm. The structures are made by deep reactive-ionetching (DRIE) [8, 9], after which the (movable) struc-tures are released by HF vapour phase etching [10] ofthe oxide layer. Large structures, like the moving bodyof the resonator, need to be perforated to allow etchingof the underlying silicon oxide. The result is shown inFigure 1.MME2010 Workshop 194Back to the ProgrammeDOREMIFA SODOL WBFigure 3: Layout of the 7mm×7mm instrument chip. Sixresonators fit on the chip. The comb drives and length B areequal for all resonators, only the spring length L and masswidth W are varied to obtain the correct resonance frequencies.Table 1: Frequencies of the instrument notes and the resultingdesign parameters for the spring length L and moving bodysize W. The measured frequencies and the relative deviationfrom the design are listed on the right.f0 (Hz) L W f0 (Hz) out-of-Note design (µm) (µm) meas. tuneDo 396 1050 670 475 20%Re 445 950 718 592 33%Mi 499 890 693 -Fa 530 840 735 695 31%So 595 770 758 778 31%Do 2 788 690 589 1031 31%The measurement setup, shown in Figure 4, consistsof a charge amplifier, lock-in amplifier and an additionalamplifier with band-pass filter. The resulting audio signalcan either be played through a loudspeaker or recordedusing the soundcard of a PC.The resonators are actuated by a programmable mi-crocontroller with a D/A-converter and a high-voltageamplifier. At rest, the applied voltage is 0V. A noteis ‘plucked’ by ramping the applied voltage in about8ms up to the actuation voltage Vact, and subsequentlyrapidly reducing the applied voltage back to 0V. Theramp prevents sounding a note upon both the increaseand decrease of the applied voltage. This simulates man-ually pulling back the resonator and releasing it, similarto plucking a string. The height of the actuation voltageVact is determined from the velocity parameter receivedin the MIDI messages from the MIDI keyboard.Figures 5 shows the recorded audio signal of the lowDo resonator, for two pressures of respectively 1.5mbarand 20mbar. The audio signal is a decaying sine wave,lock-inamplifier1 MHzMIDI interfaceband-passcharge amplifiercircuitaudiosignalFigure 4: Simplified drawing of the used measurement setup.The displacement of a resonator is measured from the comb-drive capacitance, using a charge amplifier circuit and lock-inamplifier. In total, six resonators are connected in parallel toone charge amplifier circuit (only two resonators are drawn).The resonators are actuated by high-voltage amplifiers that arecontrolled through a MIDI interface. 0  0.01  0.02  0.03  0.04  0.05  0.06Audio signal (a.u.)Time t (s)p = 1.5 mbarp = 20 mbarFigure 5: The recorded tone of the low Do note at two differentvacuum pressures. The sine frequency equals 475Hz. Thedashed curves are equal to ±e−αt , with α equal to 13s−1 at1.5mbar and 40s−1 at 20mbar.that is slightly asymmetric due to the non-linearity ofthe sensing comb drive. The damping α is estimatedby fitting an exponential curve to the decaying sine; Qequals 115 and 37 at 1.5mbar and 20mbar, respectively.Clearly, the duration of the note is greatly increased at areduced pressure. At ambient pressure, only a very briefoscillation was measured.The Fourier transform of the audio signal at 1.5mbaris shown in Figure 6. The fundamental frequency equals475Hz. As expected from the non-linear capacitanceversus displacement curve of the tapered comb-drive fin-gers, a second peak at double the resonance frequency(951Hz) is visible, compare with Figure 2. The mea-sured resonance frequencies of the other resonators arelisted in Table 1. There is no measurement of the Miresonator as it broke before it was measured. All notesMME2010 Workshop 195Back to the Programme 0  500  1000  1500  2000Amplitude (a.u.)Frequency (Hz)Figure 6: Fourier transform of the audio signal of the lowDo note, showing a large peak at 475.1Hz. A second peak at951Hz is visible, caused by the non-linear capacitance versusdisplacement curve of the tapered comb-drive fingers.resonate at a much higher frequency than the design pre-dicted. However, the instrument is still largely in-tunewith itself, because the frequency increased with an al-most equal factor for Re, Fa, So and the high Do. Theinstrument is pitched close to a C5 major scale (exceptfor the low Do, that is closest to A]4). It should be notedhowever, that a second chip was more out of tune. Thelarge increase in frequency may be explained by a strongincrease in spring stiffness, because their thickness waslarger than originally designed.IV – DiscussionBecause of intrinsic uncertainties in fabrication, there isa large uncertainty in the resonance frequencies after fab-rication. Clearly, tuning of the instrument is necessary.There are several methods of tuning. Because the comb-drive finger shape is tapered, applying an offset voltageto both the actuating and sensing comb drives wouldresult in a lower spring stiffness [11]. Another methodto lower the spring constant is heating the springs, whichlowers the Young’s modulus of the silicon [12], for exam-ple by flowing an electrical current through the springs.Large frequency adjustments can be realised throughsubsequential mass fine-tuning performed by manuallydepositing additional material on the moving body.V – ConclusionIn this work we show that it is possible to make a mu-sical instrument in MEMS. Viscous damping by air isrelatively large for micro resonators at audible frequen-cies, resulting in a short tone. A vacuum of 1.5mbar wasrequired for a short note around 0.25s. The frequenciesof the fabricated notes are 20% to 33% higher than ex-pected, however, the instrument is still mostly in-tunewith itself. Improvement of the fabrication method isnecessary to correctly tune the device by design, withoutthe need for tuning after fabrication.References[1] Cornell University Science News, “World’ssmallest silicon mechanical devices are made atCornell,” 1997. [Online]. Available: http://www.news.cornell.edu/releases/july97/guitar.ltb.html[2] D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead,and J. M. Parpia, “Measurement of mechanicalresonance and losses in nanometer scale siliconwires,” Appl. Phys. Lett., vol. 75, no. 7, pp.920–922, 1999, doi:10.1063/1.124554.[3] B. Steele, “New nanoguitar offers promiseof applications in electronics, sensing,” 2003.[Online]. Available: http://www.news.cornell.edu/Chronicle/03/11.20.03/new nanoguitar.html[4] D. R. Yntema, J. Haneveld, J. B. C. Engelen, R. A.Brookhuis, R. G. P. Sanders, R. J. Wiegerink,and M. Elwenspoek, “Listening to MEMS: Anacoustic vibrometer,” in Proc. IEEE MEMS 2010,Hong Kong, China, Jan. 24-28 2010, pp. 663–666,doi:10.1109/MEMSYS.2010.5442319.[5] J. Mohr, P. Bley, M. Strohrmann, and U. Wallrabe,“Microactuators fabricated by the LIGA process,” J.Micromech. Microeng., vol. 2, no. 4, pp. 234–241,1992, doi:10.1088/0960-1317/2/4/003.[6] R. W. Young, “Terminology for logarithmicfrequency units,” J. Acoust. Soc. Am., vol. 11,no. 1, pp. 134–139, 1939, doi:10.1121/1.1916017.[7] R. Legtenberg, A. W. Groeneveld, and M. C.Elwenspoek, “Comb-drive actuators for largedisplacements,” J. Micromech. Microeng., vol. 6,no. 3, pp. 320–329, 1996, doi:10.1088/0960-1317/6/3/004.[8] F. Laermer and A. Schilp, “Method of an-isotropically etching silicon,” German PatentDE 4 241 045, 1994.[9] H. V. Jansen, M. J. De Boer, S. Unnikrishnan,M. C. Louwerse, and M. C. Elwenspoek, “Blacksilicon method X,” J. Micromech. Microeng.,vol. 19, no. 3, p. 033001, 2009, doi:10.1088/0960-1317/19/3/033001.[10] P. J. Holmes and J. E. Snell, “A vapour etchingtechnique for the photolithography of silicondioxide,” Microelectron. Reliab., vol. 5, no. 4, pp.337–341, 1966, doi:10.1016/0026-2714(66)90162-4.[11] B. D. Jensen, S. Mutlu, S. Miller, K. Kurabayashi,and J. J. Allen, “Shaped comb fingers for tailoredelectromechanical restoring force,” J. Microelec-tromech. Syst., vol. 12, no. 3, pp. 373–383, 2003,doi:10.1109/JMEMS.2003.809948.[12] C.-H. Cho, “Characterization of Young’s modulusof silicon versus temperature using a “beamdeflection” method with a four-point bendingfixture,” Curr. Appl. Phys., vol. 9, no. 2, pp.538–545, 2009, doi:10.1016/j.cap.2008.03.024.MME2010 Workshop 196

A Musical instrument in MEMS

A vapour etching technique for the photolithography of silicon dioxide,”

Black silicon method

Characterization of Young’s modulus of silicon versus temperature using a “beam deﬂection” method with a four-point bending ﬁxture,”

Comb-drive actuators for large displacements,”

Listening to MEMS: An acoustic vibrometer,” in

Measurement of mechanical resonance and losses in nanometer scale silicon wires,”

Method of anisotropically etching silicon,”

Microactuators fabricated by the LIGA process,”

New nanoguitar offers promise of applications in electronics, sensing,”

Science News, “World’s smallest silicon mechanical devices are made at Cornell,”

Shaped comb ﬁngers for tailored electromechanical restoring force,”

Terminology for logarithmic frequency units,”

http://purl.utwente.nl/publications/74825

A Musical instrument in MEMS

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