Two-dimensional electron gas based actuation of piezoelectric AlGaN/GaNmicroelectromechanical resonatorsK. Brueckner, F. Niebelschuetz, K. Tonisch, S. Michael, A. Dadgar, A. Krost, V. Cimalla, O. Ambacher, R.Stephan, and M. A. Hein Citation: Applied Physics Letters 93, 173504 (2008); doi: 10.1063/1.3002296 View online: http://dx.doi.org/10.1063/1.3002296 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/93/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Electroreflectance of the AlGaN/GaN heterostructure and two-dimensional electron gas Appl. Phys. Lett. 80, 4549 (2002); 10.1063/1.1487447 Residual strain effects on the two-dimensional electron gas concentration of AlGaN/GaN heterostructures J. Appl. Phys. 90, 4735 (2001); 10.1063/1.1408268 Scattering times in AlGaN/GaN two-dimensional electron gas from magnetoresistance measurements J. Appl. Phys. 88, 932 (2000); 10.1063/1.373758 Persistent photoconductivity in a two-dimensional electron gas system formed by an AlGaN/GaNheterostructure J. Appl. Phys. 82, 1227 (1997); 10.1063/1.365893 Two-dimensional electron gas in AlGaN/GaN heterostructures J. Vac. Sci. Technol. B 15, 1117 (1997); 10.1116/1.589424

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Two-dimensional electron gas based actuation of piezoelectric AlGaN/GaNmicroelectromechanical resonators

K. Brueckner,1,a� F. Niebelschuetz,1 K. Tonisch,1 S. Michael,2 A. Dadgar,3 A. Krost,3

V. Cimalla,4 O. Ambacher,4 R. Stephan,1 and M. A. Hein1

1Institute of Micro- and Nanotechnologies, Ilmenau University of Technology, 98693 Ilmenau, Germany2Institute for Microelectronic and Mechatronic Systems, 98693 Ilmenau, Germany3Institute of Experimental Physics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg, Germany4Fraunhofer Institute for Applied Solid-State Physics, 79108 Freiburg, Germany

�Received 22 September 2008; accepted 25 September 2008; published online 29 October 2008�

Free-standing piezoelectric AlGaN/GaN beam resonators have been prepared on silicon substrates.The two-dimensional electron gas at the interface of the III/V heterostructure has been employed toact as back electrode for the piezoelectric active layer. The fundamental mode as well as higherorder resonant modes of flexural vibration has been excited piezoelectrically and analyzed usingoptical laser–Doppler vibrometry. The experimental investigations were carried out under normalambient conditions. The specific piezoelectric actuation scheme is described and the dependence ofthe measured resonant frequencies between 0.2 and 8.1 MHz on geometry and material parametersis investigated. © 2008 American Institute of Physics. �DOI: 10.1063/1.3002296�

The rapidly progressing research of resonant microelec-tromechanical systems �MEMS� is directed toward thedevelopment of advantageous sensor concepts and radio fre-quency �rf� devices.1,2 Manufactured by appropriate semi-conductor fabrication processes, they consist of free-standingstructures with geometrical dimensions on the micrometerscale or even in the nanometer range in the case of nano-electromechanical systems �NEMS�. Hence, the structuresexhibit mechanical eigenfrequencies in a range where theoscillations can be excited and detected by electrical rf sig-nals. Based on such devices, sensors not only for the detec-tion of chemical3,4 and biological5,6 species but also for themeasurement of environmental parameters7–9 have been re-ported, as the resonant deflection is sensitive to variousphysical parameters. Monolithic oscillators10 and filters11 in-corporating resonant MEMS rival conventional quartz crys-tal or surface acoustic wave solutions in rf circuit technology.A major challenge for all of these applications is an efficientelectromechanical transduction, especially if, in pursuit ofhigher resonant frequencies and increased sensitivity, the de-vice dimensions are scaled down into the NEMS domain.12

Various schemes for the electrical actuation and sensing ofthe resonant mechanical motion have been reported, includ-ing electrostatic,10 magnetomotive,13 and piezoelectric11,14

transduction. However, as device dimensions and, conse-quently, actuation areas are reduced, electrostatic and mag-netomotive couplings become less effective. The need forsmall gap sizes imposes additional technological efforts,10 orexpensive experimental setups become necessary where veryhigh magnetic field strengths are required.15,16 As an alterna-tive, the coupling strength can be enhanced in miniature de-vices by involving piezoelectrically coupled resonators.14

Other mechanisms such as optical, piezoresistive, or thermalcoupling are only suitable either for excitation or forreadout.12 Hence, the piezoelectric transduction scheme,which is in the focus of this paper, offers an elegant solution

to achieve both downscaling and an integrated all-electricalactuation.

Piezoelectric MEMS resonators usually consist of a re-leased structural bottom layer that dominates the elasticproperties of the device. Actuation is provided by a thinpiezoelectric top layer, which is enclosed between two me-tallic layers that serve as top and back electrodes. Differentpiezoelectric materials have been applied, e.g., ZnO, AlN,AlGaAs, and PbZrTiO3 �PZT�, while mainly silicon has beenused for the structural layer. Recently, a piezoelectrically ac-tuated NEMS cantilever has been reported where the piezo-electric layer formed also the structural layer.17

The AlGaN/GaN heterostructures presented here com-bine the pyroelectric and piezoelectric properties of thegroup III nitrides.18 The structural quality and the intrinsicproperties of the material are suitable for size reduction toachieve high frequencies at low intrinsic losses.19 At theAlGaN/GaN interface, a two-dimensional electron gas�2DEG� is confined, for which Hall measurements revealedan electron density and mobility of 1013 cm−2 and1000 cm2 /V s, respectively. Thus, the 2DEG provides suffi-cient conductivity to form the back electrode in a piezoelec-tric transducer configuration.20 Such application of 2DEGelectrodes was demonstrated previously as interdigital trans-ducers for a surface acoustic wave device21 as well as for thepiezoelectric actuation of a mesa heterostructure.20 Whereaspiezoelectricity enables the realization of an integrated cou-pling mechanism, the 2DEG additionally delivers a pro-nounced sensitivity to mechanical stress and other environ-mental parameters, which will allow the beneficialimplementation of sensor principles that utilize these pyro-electric effects.18,19

We demonstrate here the integration of a 2DEG channelinto free-standing doubly clamped beam resonators, wherethe AlGaN/GaN heterostructure supplies both the structurallayer and the piezoelectric layer. The 2DEG forms the backelectrode for the actuation of the active AlGaN layer. Theelectrical excitation of the fundamental mode and higher or-a�Electronic mail: klemens.brueckner@tu-ilmenau.de.

APPLIED PHYSICS LETTERS 93, 173504 �2008�

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der flexural mechanical resonances has been confirmed opti-cally by scanning laser–Doppler vibrometry.

The design scheme of the beam resonators analyzed issketched in Fig. 1. The lower GaN layer and the upperAl0.31Ga0.69N layer with thicknesses of 650 and 30 nm, re-spectively, were deposited epitaxially on silicon substrates bymetal-organic chemical vapor deposition.22 The free-standingstructures were realized by a combination of dry anisotropicand isotropic etching processes, which conserve the 2DEGalong the entire length of the beam.23 By these processes,resonators were prepared with lengths l varying from 10 to1000 �m and widths w between 2 and 10 �m, as illustratedby Fig. 2. 50 nm thick Au top electrodes with a thin adhesiveTi layer underneath were deposited at both ends of thebeams, each extending along the beams by one quarter of thetotal length. This configuration optimizes the electrome-chanical coupling for the fundamental flexural resonantmode.14 The electrical contact to the 2DEG back electrode isprovided by the alloyed Ti/Al/Ti/Au ground contact areas �cf.Figs. 1 and 2�a��. The undercut lu results from the etchingprocess, leading to typical values lu�w /2. The undercut af-fects the residual strain of the resonator beams, as these re-gions can relax during the release process and thus increasethe strain and, as a consequence, the resonant frequenciesslightly.

The inverse piezoelectric effect is utilized for the elec-trical excitation of the mechanical out-of-plane oscillationsof the suspended structures. Therefore, a vertically orientedelectric field is applied between the drive electrode and theconductive 2DEG sheet charge of the beam under test.20

Caused by the piezoelectric modulus d31�2 pm /V, thehorizontal elongation of the upper AlGaN layer and its offsetfrom the neutral axis generate a bending moment that leadsto an out-of-plane deflection. For the fundamental resonantfrequency f1, the expected maximum vertical displacementumax at the center of the beam can be related to the driving

voltage VD by combining the modal force-displacementtransfer function umax�j�� /F�j�� and the electromechanicalcoupling coefficient �1=F�j�� /VD�j�� to the expression14

�umax�j��VD�j��

��=2�f1

� 0.09�Qd31EAlGaN

�GaN f12l2 . �1�

Here, EAlGaN is the Young’s modulus of the active layer and�GaN the mass density of the beam, which essentially consistsof GaN. The loss of mechanical vibration energy, which lim-its the resonance amplitude, is represented by the finite qual-ity factor Q. The additional empirical factor � describes theinfluence of the structural and electronic properties of theelectrodes and thus also accounts for the effect from the fi-nite conductance of the 2DEG on transduction. After releas-ing the beam, the sheet resistance of the 2DEG back elec-trode was measured to be about Rsh�1000 �.20 Theresulting Ohmic impedance of the back electrode Rbe�Rsh l / �4w� appears in series with the capacitance of the drivingport. Comparing the results of Eq. �1� with the measured data�cf. Fig. 3�, we find ��0.02.

To achieve piezoelectric excitation of flexural oscilla-tions of a selected resonator beam, frequency-swept har-monic driving voltages with peak values VD varying between500 mV and 1.5 V were applied to the appropriate contactareas through coplanar wafer-prober contact probes�650 �m pitch�. The time-dependent out-of-plane deflectionwas analyzed by a scanning laser–Doppler vibrometer �Poly-tec MSA-400�, which enables a dynamic characterization upto 10 MHz with a sufficient spatial resolution in lateral�1 �m� and vertical �0.1 pm /Hz1/2� dimensions. Themaximum deflection amplitudes umax and typical modeshapes from scanning along the length of a 500 �m longbeam are shown in Fig. 3 for the fundamental mode and itseighth harmonic. Although the electromechanical couplingcoefficients �n decrease for increasing mode numbers n dueto a progressing mismatch of the vibration sections to thelengths of the top electrodes, all resonant frequencies fn ofeach probed resonator were detected up to the frequencylimit of the vibrometry measurement system. Typical reso-nant peaks for the flexural out-of-plane vibration modes areshown in the spectra of Fig. 4 for two resonator beams ofdifferent length. The measurement was performed under nor-mal ambient conditions, resulting in Q-factors about 100,which were limited by the viscous damping in air.

MEMS chips with 5 and 10 �m wide doubly clampedbeams having lengths l between 80 and 1000 �m were fur-ther investigated systematically. The results for the lowesteight resonant modes �1�n�8� with resonant frequenciesup to 8.1 MHz are compiled in Fig. 5. Double-logarithmic

Ti/Au (60 nm)

Si-substrate

GaN

AlGaN (30 nm)

(650 nm)

ground

drivel

w

lu

ground

sense

2DEGTi/Al/Ti/Au

(230 nm)

FIG. 1. �Color online� Scheme of the analyzed doubly clamped beam reso-nators that vary in length l, undercut length lu, and width w. The layerthicknesses are given in brackets. The drive, sense, and ground contact areasare provided for electrical excitation and detection. The direction of theexcited out-of-plane deflection is indicated by the bold arrows.

FIG. 2. �Color online� �a� Optical microscope image showing part of aprocessed chip. The beam resonators in the right column vary in length from275 to 350 �m. �b� Scanning electron microscope image of one of theshortest realized AlGaN/GaN beams of 20 �m in length.

FIG. 3. �Color online� Exemplary mode shapes of the first �a� and the 8th�b� out-of-plane flexural resonances of a 500 �m long and 5 �m wideAlGaN/GaN beam resonator under piezoelectric actuation �VD=0.5 V�monitored by laser–Doppler vibrometry.

173504-2 Brueckner et al. Appl. Phys. Lett. 93, 173504 �2008�

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scaling was chosen for this figure to emphasize the power-law dependence of the resonant frequency on the beamlength l : f � lb with a characteristic exponent b.

For the fundamental flexural mode �n=1�, the resonantfrequency f1 can be approximated analytically by24

f1 � 1.03�EGaN

�GaN

t

l2�1 + �1� �l2

t2 . �2�

Here, EGaN denotes the Young’s modulus of the dominatingbeam material GaN, is the axial strain, and 0.22��1� ��0.29 is a strain-dependent coefficient. Equation �2� impliesthat the slope b increases from −2 for =0 to a maximum of−1 for →�. According to Fig. 5, the slopes of the f�l�curves fell slightly below −1, e.g., b1=−1.034 for n=1. Thevalues close to −1 indicate a high residual strain within theAlGaN/GaN layer, yielding the highest possible fn values.Multilayer effects on f1 resulting from the AlGaN layer andthe top metallization ��10%�, as well as the additional stiff-ening from the undercut lu ��5%�, are neglected in Eq. �2�.Finite element models including these peculiarities havebeen evaluated using the commercial computer code AN-

SYS®. By this approach, the tensile strain within the AlGaN/GaN layer could be determined as =2.810−3. This resultis in good agreement with the value of 2.210−3 obtained

from x-ray diffraction measurements performed before theetching.

We have demonstrated piezoelectrically actuated doublyclamped AlGaN/GaN MEMS resonators employing an inte-grated 2DEG as back electrode. Under ambient conditions,i.e., at normal pressure and room temperature, the flexuralvibration modes were consistently characterized by scanninglaser–Doppler vibrometry. The measured resonant frequen-cies between 0.2 and 8.1 MHz and their vibration amplitudescould be consistently related to geometry and material pa-rameters of the MEMS resonators. Further improvement ofthe actuation and readout schemes will be in the focus offuture research.

This work has been funded by the German ResearchFoundation �DFG�, Priority Program 1157 “Integrated elec-troceramic functional structures” �Contract Nos. HE3642/2and AM105/2�. The authors would like to thank PolytecGmbH for providing the vibrometry measurement system.

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FIG. 4. �Color online� Spectra of the average out-of-plane displacementof two different resonator beams with lengths of �a� 1000 �m and�b� 500 �m, respectively. The beam width w is 5 �m for both samples.

FIG. 5. �Color online� Resonant frequency fn of the nth flexural vibrationmode �1�n�8� vs beam length l on double-logarithmic scales. The mea-surement was carried out for a set of 5 �m �filled symbols� and 10 �mwide �open symbols� doubly clamped beams with lengths l between 80 and1000 �m. The lines represent power-law fits, yielding slopes slightly below−1 for all data sets.

173504-3 Brueckner et al. Appl. Phys. Lett. 93, 173504 �2008�

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