Graphene Metallization of High-Stress Silicon Nitride Resonators for

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Graphene Metallization of High-Stress Silicon Nitride Resonators for Electrical Integration Sunwoo Lee,†,# Vivekananda P. Adiga,‡,# Robert A. Barton,‡,§,# Arend M. van der Zande,§ Gwan-Hyoung Lee,∥,⊥,∇ B. Rob Ilic,¶ Alexander Gondarenko,∥ Jeevak M. Parpia,‡ Harold G. Craighead,‡ and James Hone*,∥ †

Department of Electrical Engineering, Columbia University, New York, New York 10027, United States School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, United States § Energy Frontier Research Center and ∥Department of Mechanical Engineering, Columbia University, New York, New York 10027, United States ⊥ Samsung-SKKU Graphene Center (SSGC), Suwon, Gyeonggi 440-746, Korea ¶ The Cornell NanoScale Science and Technology Facility (CNF), Ithaca, New York 14853, United States ∇ School of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro., Jangan-gu, Suwon, Gyeonggi 440-746, Korea ‡

S Supporting Information *

ABSTRACT: High stress stoichiometric silicon nitride resonators, whose quality factors exceed one million, have shown promise for applications in sensing, signal processing, and optomechanics. Yet, electrical integration of the insulating silicon nitride resonators has been challenging, as depositing even a thin layer of metal degrades the quality factor significantly. In this work, we show that graphene used as a conductive coating for Si3N4 membranes reduces the quality factor by less than 30% on average, which is minimal when compared to the effect of conventional metallization layers such as chromium or aluminum. The electrical integration of Si3N4Graphene (SiNG) heterostructure resonators is demonstrated with electrical readout and electrostatic tuning of the frequency by up to 0.3% per volt. These studies demonstrate the feasibility of hybrid graphene/nitride mechanical resonators in which the electrical properties of graphene are combined with the superior mechanical performance of silicon nitride. KEYWORDS: Silicon nitride resonators, graphene, quality factor, NEMS, optomechanics

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source/drain electrode sizes are then limited. Although actuation and detection schemes based on dielectric forces12,13 have recently been demonstrated for insulating resonators, they suffer from increased fabrication complexity and estimated displacement sensitivities14 that do not reach the levels of capacitively coupled systems.15 Therefore, there is a strong motivation to identify conducting materials that do not impact the quality factor. In order for the dissipation to be dominated by the silicon nitride itself, the metallic coating needs to be much thinner than the Si3N4 film, which is less than 20 nm for the highest quality factor demonstrated to date.6 In this work, we show that graphene can be used as an ideal conductive coating for Si3N4 membranes. Chemical vapor deposition (CVD) graphene16 is directly transferred on top of the suspended Si3N4 resonators using a dry polydimethyl siloxane (PDMS)−poly(methyl methacrylate) (PMMA) transfer technique.17 We have found that the addition of graphene reduces the quality factor of the Si3N4 resonators by less than

esonators are essential components in modern electronics and are often used as filters or oscillators. A key feature of a good resonator is a high quality factor, which conventional electronic filters have failed to meet. Nanoelectromechanical systems (NEMS) are of interest for sensing and signal processing applications because they can have the required high Q in addition to tunability and the potential for integration with silicon electronics.1−4 Recently, stoichiometric silicon nitride resonators have been studied for their extremely high quality factor that can exceed one million, which originates from the high tensile stress they possess.5−7 However, the insulating nature of the material has hindered its broader implementation. As electrical integration is typically accomplished by capacitive coupling to conducting resonators, efforts to metallize silicon nitride resonators by deposition of conventional metals have been demonstrated.8−10 However, it was discovered that such metallization schemes degrade their quality factor by more than a factor of 4 for only 5 nm of chromium8 and even more severely for thicker layers.11 Avoiding the metallization near the clamping area has also been shown to decrease the added dissipation from the metal layer,9 however, at the cost of increased integration difficulty as © XXXX American Chemical Society

Received: June 4, 2013 Revised: July 22, 2013

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wet-etch of the copper with ammonium persulfate (Transene, APS100, 20 Wt%), the graphene/PMMA/PDMS stack is gently pressed against the aforementioned substrate with suspended Si3N4 drums, which is plasma treated to promote adhesion between the graphene and the nitride (Plasma Etch PE-50). Upon heating the stamped substrate at 170 °C for one minute, the PDMS is slowly peeled off. Finally, in order to remove the capping PMMA without collapsing the suspended drum, the sample is annealed at 345 °C for 6 h in forming gas (5% hydrogen and 95% argon by volume).24 Figure 1, panels e and f respectively, shows an optical image and a false-color SEM image of the fabricated SiNG. The colored areas of panel f denote the circular array of the nanoholes that define the size of the suspended SiNG drum resonators, and it was found by SEM analysis that the graphene does not always cover the nanoholes completely due to the occasional rips over the holes. In this study, we used two different schemes to measure mechanical resonance. First, as shown in Figure 2a, is a piezo-

30% on average, in contrast with more than a factor of 4 reported previously using chromium.8 Furthermore, the graphene coating allows electrical actuation and detection of Si3N4 resonators. In this article, capacitive readout is used to demonstrate electrical integration. In addition, electrostatic tuning of the resonant frequency up to 0.3% per volt is observed at the cost of increased dissipation at high gate bias due to displacement current as reported previously,18 suggesting the trade-off between the frequency tuning and the quality factor degradation. These studies pave the way for capacitively coupled circuit cavity optomechanical elements15 and mechanically resonant filters and oscillators with quality factor approaching one million at room temperature. Figure 1 shows a schematic of the fabrication process, which begins with silicon substrates (5−10 Ω-cm). After standard

Figure 2. (a) Inertial drive and optical detection measurement scheme. (b) Electrical measurement scheme with source and drain electrodes patterned by shadow mask. Figure 1. (a−d) Schematic of fabrication processes of Si3N4- graphene resonator: (a) Si3N4 deposition, (b) Si3N4 etch, (c) SiO2 etch (d) graphene transfer. (e) Optical image of graphene-coated resonator with 182 μm diameter. Scale bar: 100 μm. (f) false-color SEM image of a typical device. Scale bar: 50 μm.

drive/optical detection scheme. A 633 nm HeNe laser with power ∼60 μW is used to probe the motion of the resonators; variations in the reflected light intensity are used to transduce mechanical motion into an optical signal, while the mechanical drive is accomplished using a piezoelectric element. The second method is an electrical-drive/electrical detection scheme as shown in Figure 2b. In this method, the resonant motion is electrically actuated by the silicon back-gate, while the induced vibration is translated into the change in gate-to-membrane capacitance, generating a radio frequency (RF) signal out to source. All the measurements are done under vacuum (∼10−6 Torr) to minimize air damping, and the devices were kept under vacuum for several hours prior to measurements to remove moisture and chemical residues.25 In order to examine the change in dissipation for Si3N4 drums with and without graphene on top, we have measured the first few modes of Si3N4 drums before and after the graphene transfer, using the piezoelectric drive/optical detection scheme. Figure 3a shows the change in dissipation before and after the graphene transfer for the first five modes of a single 206 μm diameter drum. We observe that the dissipation (Q−1) significantly decreases for higher order azimuthal modes to reach a dissipation minimum while this reduction in dissipation has been attributed to the destructive interference of elastic waves.26,27 We also find that the increase in dissipation due to graphene addition is small compared to previous metallization schemes.8,9 To establish more robust statistics, Figure 3b demonstrates the quality factor degradation

RCA clean19 on the substrate, ∼660 nm of SiO2 is thermally grown. On top of the oxide, ∼110 nm of high-stress stoichiometric Si3N4 is grown via low-pressure chemical vapor deposition (LPCVD). Following the deposition, PMMA is spun on the substrate to pattern a circular array of holes6 with diameter close to 500 nm using electron beam lithography (EBL, JEOL 6300). The PMMA pattern is then transferred onto the underlying nitride using CF4 plasma etching (OXFORD 80) as shown in Figure 1b. The etched structure is then immersed in 49% hydrofluoric acid (HF) for 75 s to etch away the underlying SiO2 to suspend the Si3N4 drum as shown in Figure 1c. After the HF etching, the sample is dried using critical point dryer (CPD, Tousimis) in order to avoid stiction due to capillary forces from phase transition.20 To further demonstrate the applicability of this technique for wafer scale integration we use CVD graphene with vastly different grain sizes,16,21 whose electrical and mechanical properties can be close to those of mechanically exfoliated graphene.22,23 Detailed growth conditions can be found in the Supporting Information. Following the graphene growth, a layer of PMMA is spin-coated on top of the graphene/copper stack, then a PDMS stamp is pressed on top to support the PMMA/graphene stack during etching and transfer.17 After B

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Figure 3. (a) Dissipation comparison for 206 μm Si3N4 drum resonator before (black) and after (red) graphene transfer. (b) Quality factor degradation measured on first five modes of 12 different SiNG drums with average (green line) ∼26%. (c) Change in dissipation for higher order azimuthal modes before (filled circles) and after the graphene deposition (unfilled circles) for SiNG drums with six different sizes. (d) Change in damping rate for higher order modes due to graphene as a function of device dimensions.

in the first five modes of 12 different devices. The average quality factor degradation due to the graphene metallization of Si3N4 resonator is less than 30%. Figure 3c summarizes the change in dissipation for resonators of different sizes; the quality factor degradation due to graphene appears to be relatively size-independent, suggesting that the added dissipation due to graphene for higher order modes seems to be consistently low even for different size devices. In addition, we have found that the degradation does not depend on graphene quality in terms of grain size as both large grain and small grain graphene caused a similar amount of dissipation. On a few occasions, the quality factors have increased after the graphene deposition, which is possibly due to the removal of polymer impurity during forming gas annealing or an optomechanical effect due to the bimorphic nature of the SiNG resonator.28 However, since the quality factor does not change for different detection laser power, the optomechanical justification is unlikely. Our finding that graphene does not significantly degrade the quality factor of the underlying resonator is surprising, given that mechanical devices made from graphene alone have for the most part shown poor quality factors at room temperature.24,29 To further examine the added dissipation due to graphene, by subtracting dissipation (1/Q) of the bare Si3N4 resonator from the dissipation of SiNG, we can isolate the dissipation from the graphene and calculate the damping rate (γ = f/Q) for higher order azimuthal modes (where bare silicon nitride resonators show minimum dissipation) of different device sizes. Figure 3d represents the damping rate of graphene as a function of device dimension and shows that the damping caused by graphene decreases monotonically with device size. If we assume that the graphene is not slipping against the nitride,30 the grapheneinduced dissipation is not due to the graphene-nitride interaction and is likely due to a mechanism of dissipation intrinsic to the graphene material itself. This suggests that the material dissipation in graphene mechanical systems can be studied by this technique. While further investigation is needed to accurately model the cause of the dissipation due to graphene in this experiment, there are several possible explanations why graphene is superior to other metals as a coating, such as graphene’s extremely low thickness and large grain size compared to that of evaporated metals. However, the fact that we have not seen noticeable differences in graphene-induced dissipation for large and small grain graphene indicates graphene’s low thickness and low loss tangent might be the main attributes responsible for low added dissipation. This measurement also sheds light on previous studies of quality factors in bare graphene.31 In comparison to

resonators made solely from graphene, heterostructure devices such as these are useful as a means to raise the total energy stored in a device while maintaining the beneficial properties of graphene. Having found that graphene does not significantly degrade the performance of the nitride resonators, electrical measurements are performed to further study the electrical characteristics of the SiNG heterostructure as shown in Figure 2b. Source and drain electrodes are deposited using a shadow mask, and the actuation method is changed from piezoelectric drive to capacitive drive. Vector network analyzer (VNA) output and DC biasing source (Yokogawa, GS200) are combined through a bias tee (Mini-circuits, ZFBT-4GW+) and connected to the silicon global back-gate through wire bonding. In order to examine the power handling of the SiNG resonator, we have swept input power until the resonance becomes nonlinear. Figure 4a shows that as the input RF power increases above

Figure 4. (a) Power handling of Si3N4-graphene resonator. As the input power is increased, the resonance becomes nonlinear. (b) Gate tunability of Si3N4-graphene resonator. The resonance downshifts with increasing gate bias due to capacitive softening. The quality factor also degrades with gate bias due to the increase in displacement current as previously reported18.

−40 dBm at Vg = 0 V the SiNG drum starts to resonate, and at 0 dBm the resonance becomes nonlinear, exhibiting the bistability defining the dynamic range of the resonator. Another important characteristic of a NEMS resonator is its frequency. Figure 4b shows how the resonant frequency of the fundamental mode in a 124 μm SiNG drum changes as a function of gate bias. As expected from the high-stress nature of the silicon nitride film, the tunability is small compared to that of graphene resonators (on the order of a few hundred percent),32 and spring constant softening due to nonlinear electrostatic interaction33 is observed. As the gate voltage is swept up to 30 V, the resonant frequency of SiNG drum drops C

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design trade-offs between device size, quality factor, and frequency tuning range. Lastly, the demonstrated ability to capacitively couple to a silicon nitride membrane without diminishing the quality factor is promising for circuit cavity optomechanical devices.35 Further improvement for the direct electrical readout scheme should enable on-chip high quality factor resonators that are capable of replacing off-chip frequency references such as quartz crystals.

from 2.77 MHz down to 2.50 MHz with tunability of about 0.3% per volt. In addition to the frequency tuning from applied electrostatic force, Figure 4b also shows how the quality factor decreases as a function of gate bias. Over the change of 30 V in gate bias, the quality factor decreased by more than an order of magnitude, even though the input power was adjusted at each bias point to keep the resonant response Lorentzian. Such a drop in the quality factor with increasing gate bias has been reported,18 but not in such extreme magnitude. The reason is that for SiNG drums studied here, the suspended device area is much larger (by more than a factor of hundred) compared to the reference, while the suspension height is rather comparable (larger only by about factor of 2), making SiNG drums suffer from much larger displacement current for the same electrostatic force from the gate. With such differences taken into account, we were able to fit the data into the model given by ref 18 that is shown in Figure 4b as a red dashed line. More details for the model and the fit can be found in the Supporting Information. Furthermore, to achieve full electrical integration we have both actuated and detected the SiNG resonators electrically. The optical detection used above is replaced by electrical detection which takes advantage of the capacitance modulation during resonance. Figure 5 shows how the resonance of the 91

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ASSOCIATED CONTENT

S Supporting Information *

Further details of graphene growth, Raman spectra on SiNG resonators, the effect of source-drain bias, and modeling of the gate-bias dependence of quality factor. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions #

S.L., V.P.A., and R.A.B. contributed equally to this work

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Changyao Chen, Vikram Deshpande, Nicholas Petrone, Adam Hurst, Michael Lekas, and Victor Abramsky for critical discussions. Fabrication was performed at the Cornell Nano-Scale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765), and Center for Engineering and Physical Science Research (CEPSR) Clean Room at Columbia University. The authors acknowledge the support by Qualcomm Innovation Fellowship (QInF) 2012, AFOSR MURI FA9550-09-1-0705, the Cornell Center for Materials Research and NSF Grants DMR-0908634, ECCS-1001742, and DMR 1120296.

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Figure 5. Fully electrically integrated 91 μm SiNG drum resonator with 0 dBm source power using capactive detection scheme. A tunability of ∼0.3% per volt is demonstrated, and the line width broadening with increasing gate bias is again observed.

REFERENCES

(1) Craighead, H. G. Science 2000, 290 (5496), 1532−1535. (2) Huang, X. M. H.; Zorman, C. A.; Mehregany, M.; Roukes, M. L. Nature 2003, 421 (6922), 496−496. (3) Nguyen, C. T.-C. Dig. of Tech. Papers TRANSDUCERS 2005, 1, 243−246. (4) Yang, Y. T.; Callegari, C.; Feng, X. L.; Ekinci, K. L.; Roukes, M. L. Nano Lett. 2006, 6 (4), 583−586. (5) Verbridge, S. S.; Craighead, H. G.; Parpia, J. M. Appl. Phys. Lett. 2008, 92 (1), 013112−3. (6) Adiga, V. P.; Ilic, B.; Barton, R. A.; Wilson-Rae, I.; Craighead, H. G.; Parpia, J. M. J. Appl. Phys. 2012, 112 (6), 064323−6. (7) Verbridge, S. S.; Parpia, J. M.; Reichenbach, R. B.; Bellan, L. M.; Craighead, H. G. J. Appl. Phys. 2006, 99 (12), 124304−8. (8) Sekaric, L.; Carr, D. W.; Evoy, S.; Parpia, J. M.; Craighead, H. G. Sensor. Actuat. A-Phys. 2002, 101 (1−2), 215−219. (9) Yu, P. L.; Purdy, T. P.; Regal, C. A. Phys. Rev. Lett. 2012, 108 (8), 083603. (10) Biswas, T. S.; Suhel, A.; Hauer, B. D.; Palomino, A.; Beach, K. S. D.; Davis, J. P. Appl. Phys. Lett. 2012, 101 (9), 093105−5. (11) Waggoner, P. S.; Tan, C. P.; Craighead, H. G. J. Appl. Phys. 2010, 107 (11), 114505−5. (12) Rieger, J.; Faust, T.; Seitner, M. J.; Kotthaus, J. P.; Weig, E. M. Appl. Phys. Lett. 2012, 101 (10), 4. (13) Unterreithmeier, Q. P.; Weig, E. M.; Kotthaus, J. P. Nature 2009, 458 (7241), 4.

μm diameter SiNG drum changes with applied gate bias. We have attempted the direct detection technique25 by applying 9 V across the source and drain electrodes, however, due to insufficient mobility and large gate-to-membrane distance of the device, the change in signal level was insignificant (shown in the Supporting Information). With reduced graphene-to-gate distance as well as improved graphene quality in terms of mobility, it is expected that the resonant signal will be even further amplified owing to the graphene’s transconducting nature.34 In summary, we demonstrated a novel fabrication process for metallizing high-stress stoichiometric Si3N4 resonators using graphene. We showed that the low added mass from graphene on a Si3N4 drum resonator does not significantly degrade the quality factor of Si3N4, and we used the high-quality factor Si3N4 resonators to sensitively measure the material dissipation in the graphene layer. In addition, the graphene layer allowed the resonance to be actuated electrically as well as tuned with applied electrostatic force. Lastly, displacement current induced quality factor degradation has been confirmed, suggesting D

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(14) Faust, T.; Krenn, P.; Manus, S.; Kotthaus, J. P.; Weig, E. M. Nat Commun 2012, 3, 728. (15) Teufel, J. D.; Donner, T.; Li, D.; Harlow, J. W.; Allman, M. S.; Cicak, K.; Sirois, A. J.; Whittaker, J. D.; Lehnert, K. W.; Simmonds, R. W. Nature 2011, 475 (7356), 359−363. (16) Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.; Ruoff, R. S. Science 2009, 324 (5932), 1312−1314. (17) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Nature 2009, 457 (7230), 706−710. (18) Song, X.; Oksanen, M.; Sillanpäa,̈ M. A.; Craighead, H. G.; Parpia, J. M.; Hakonen, P. J. Nano Lett. 2011, 12 (1), 198−202. (19) Kern, W.; Puotinen, D. A. RCA Rev. 1970, 31, 187−206. (20) Mulhern, G. T.; Soane, D. S.; Howe, R. T. Proc. TRANSDUCERS 1993, 1, 7−10. (21) Li, X.; Magnuson, C. W.; Venugopal, A.; Tromp, R. M.; Hannon, J. B.; Vogel, E. M.; Colombo, L.; Ruoff, R. S. J. Am. Chem. Soc. 2011, 133 (9), 2816−2819. (22) Lee, G.-H.; Cooper, R.; An, S. J.; Lee, S.; Zande, A. v. d.; Petrone, N.; Hammerberg, A. G.; Lee, C.; Crawford, B.; Oliver, W.; Kysar, J. W.; Hone, J. Science 2013, 340 (6136), 1073−1076. (23) Petrone, N.; Dean, C. R.; Meric, I.; van der Zande, A. M.; Huang, P. Y.; Wang, L.; Muller, D.; Shepard, K. L.; Hone, J. Nano Lett. 2012, 12 (6), 2751−2756. (24) van der Zande, A. M.; Barton, R. A.; Alden, J. S.; Ruiz-Vargas, C. S.; Whitney, W. S.; Pham, P. H. Q.; Park, J.; Parpia, J. M.; Craighead, H. G.; McEuen, P. L. Nano Lett. 2010, 10 (12), 4869−4873. (25) Xu, Y.; Chen, C.; Deshpande, V. V.; DiRenno, F. A.; Gondarenko, A.; Heinz, D. B.; Liu, S.; Kim, P.; Hone, J. Appl. Phys. Lett. 2010, 97 (24), 243111. (26) Wilson-Rae, I.; Barton, R. A.; Verbridge, S. S.; Southworth, D. R.; Ilic, B.; Craighead, H. G.; Parpia, J. M. Phys. Rev. Lett. 2011, 106 (4), 047205. (27) Adiga, V. P.; Ilic, B.; Barton, R. A.; Wilson-Rae, I.; Craighead, H. G.; Parpia, J. M. Appl. Phys. Lett. 2011, 99 (25), 253103−3. (28) Adiga, V. P.; De Alba, R.; Storch, I. R.; Yu, P. A.; Ilic, B.; Barton, R. A.; Lee, S.; Hone, J.; McEuen, P. L.; Parpia, J. M.; Craighead, H. G. arXiv:1307.2525 2013. (29) Bunch, J. S.; van der Zande, A. M.; Verbridge, S. S.; Frank, I. W.; Tanenbaum, D. M.; Parpia, J. M.; Craighead, H. G.; McEuen, P. L. Science 2007, 315 (5811), 490−493. (30) Conley, H.; Lavrik, N. V.; Prasai, D.; Bolotin, K. I. Nano Lett. 2011, 11 (11), 4748−4752. (31) Barton, R. A.; Ilic, B.; van der Zande, A. M.; Whitney, W. S.; McEuen, P. L.; Parpia, J. M.; Craighead, H. G. Nano Lett. 2011, 11 (3), 1232−1236. (32) Chen, C.; Rosenblatt, S.; Bolotin, K. I.; Kalb, W.; Kim, P.; Kymissis, I.; Stormer, H. L.; Heinz, T. F.; Hone, J. Nature Nanotech. 2009, 4 (12), 861−867. (33) Solanki, H. S.; Sengupta, S.; Dhara, S.; Singh, V.; Patil, S.; Dhall, R.; Parpia, J.; Bhattacharya, A.; Deshmukh, M. M. Phys. Rev. B 2010, 81 (11), 115459. (34) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (35) Rocheleau, T.; Ndukum, T.; Macklin, C.; Hertzberg, J. B.; Clerk, A. A.; Schwab, K. C. Nature 2010, 463 (7277), 72−75.

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NOTE ADDED IN PROOF During preparation of this manuscript, we became aware of an article that takes a similar approach; see arXiv:1305.5890 by Schmid at al.

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