Phononic crystals operating in the gigahertz range with extremely wideband gaps

Y. M. Soliman,1 M. F. Su,1 Z. C. Leseman,2 C. M. Reinke,3 I. El-Kady,3 andR. H. Olsson III4,a�

1Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque,New Mexico 87131, USA2Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA3Department of Photonics Microsystems Technologies, Sandia National Laboratories, Albuquerque,New Mexico 87185, USA4Department of Advanced MEMS, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

�Received 5 May 2010; accepted 1 October 2010; published online 8 November 2010�

Phononic crystals have numerous potential applications including use as filters and oscillators incommunications systems and as acoustic isolators for resonant sensors such as gyroscopes. Theseapplications are based on the ability of phononic crystals to exhibit elastic band gaps, frequencybands where the propagation of acoustic waves is forbidden. Here, we focus on solid-solid phononiccrystals �solid inclusions in a solid matrix�, since they typically exhibit wider band gaps than thoseobserved with air-solid phononic crystals �air inclusions in a solid matrix�. We present amicromachined solid-solid phononic crystal operating at 1.4 GHz center frequency with anultrawide 800 MHz band gap. © 2010 American Institute of Physics. �doi:10.1063/1.3504701�

Phononic crystals �PnCs� are inhomogeneous mediawhere inclusions composed of one material are periodicallyplaced in another material. The periodic variations in elasticproperties can lead to the existence of phononic band gaps�PnBG� where devices such as waveguides1 and filters2 canbe formed. Integration of PnC devices can lead to compactcomponents with high performance for wireless communica-tions and sensing.

Solid-solid �solid inclusions in a solid medium� PnCsexhibit band gaps over a wider range of topological param-eters, and thus generally have a larger minimum feature sizefor easier fabrication,3 than air-solid PnCs.4 With a band gapdesired in the frequency bands used for consumer wirelesscommunication, 400 MHz to 2.4 GHz, the lattice pitch, a,and the radius of the inclusions, r, must be micron scale.Solid elastic materials have higher acoustic velocity andlower acoustic damping than liquids or gases, which is ben-eficial when scaling to higher frequency. Recently, PnCs inthe consumer wireless communication frequency band werereported5 using W rods in a SiO2 medium. However, utiliz-ing Si as the host medium for PnCs offers several advan-tages. First, Si exhibits lower material loss than SiO2. Sec-ond, the elastic speed in Si is higher than in SiO2, whichresults in higher frequency devices for the same lattice con-stant. The elastic speed mismatch between W and Si of �2allows for the maximum band gap to appear at a near opti-mum, for ease of fabrication, r /a ratio of 0.26, as comparedto that of W–SiO2 �0.32� or air-Si ��0.45�. This allows forhigher frequency scaling with less stringent lithography re-quirements. Third, among the previously published PnCsimplemented in low loss materials suitable for microelec-tronic devices, the W–Si PnCs reported here exhibit the high-est frequencies and widest band gaps. Finally, recent researchhas shown that under certain conditions solid-solid PnCs can

be less sensitive to the thickness of the PnC membrane thanair-Si PnCs.3

In this paper, we show the existence of a PnBG in asolid-solid PnC made of W cylindrical inclusions embeddedin a Si membrane operating at a center frequency of 1.4GHz. To investigate the band gap properties of the W–SiPnC plate, the following complementary metal-oxide semi-conductor compatible fabrication process was developed.The process starts with a high-resistivity Si wafer on which a2.5 �m thick sacrificial oxide is thermally grown, followedby the deposition of the 1.2 �m thick poly-Si device layer�Fig. 1�a��. A silicon-on-insulator wafer could also be used aslong as the device layer thickness uniformity is acceptable.Cylindrical trenches are then etched in the Si film followedby a chemical vapor deposition of W to fill the trenches. Thewafer is then polished using chemical mechanical polishingto ensure that W only remains in the trenches and is removedfrom elsewhere on the wafer �Fig. 1�b��. A bottom electrodeis then deposited and patterned �Fig. 1�c��, followed by thedeposition and patterning of an aluminum nitride �AlN� film�Fig. 1�d��. The devices were patterned in a standard photo-lithography process using an optical stepper and reactive-ionetching. The piezoelectric characteristics of AlN are used tolaunch and receive elastic waves through the PnC. A topelectrode, which serves to electrically actuate the AlN film, is

a�Author to whom correspondence should be addressed. Electronic mail:rholsso@sandia.gov. FIG. 1. �Color online� Fabrication process for the W–Si PnC.

APPLIED PHYSICS LETTERS 97, 193502 �2010�

0003-6951/2010/97�19�/193502/3/$30.00 © 2010 American Institute of Physics97, 193502-1

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

then deposited and patterned �Fig. 1�e��. In our case, wedesigned broadband couplers to excite and detect the elasticwaves using interdigitated transducers �IDTs� with differentfinger widths and spacings, known as chirped couplers. Fi-nally, the sacrificial oxide layer under the PnC membrane isremoved using vapor phase hydrofluoric acid �HF� �Fig.1�f��. A scanning electron microscope �SEM� image of thefabricated PnC is shown in Fig. 2, where the lattice pitch aand the radius r of the W inclusions are 2.5 �m and0.65 �m, respectively. The thickness of the Si layer, t, is1.15 �m with a thickness-to-lattice-pitch ratio, t /a, of 0.46,since it has been shown that the PnBG is minimally compro-mised for t�a, or t�10a.5

To measure the PnBG of our fabricated PnC, we moni-tored the transmission in the �X direction through a structurewith 17 layers of W rods between launching and receivingcouplers. We used a network analyzer to excite the structureby applying an electric signal over the frequency range forwhich a PnBG is predicted by finite-difference time-domain�FDTD� simulations.5 The electric field between the top andbottom electrodes induces a displacement in the AlN film,which in turn causes longitudinal and flexural displacementsin the Si membrane. The displacement field propagatesthrough the PnC, where it induces an electric field betweenthe electrodes placed above and below the AlN film on theopposite side of the device. The received signal is comparedwith the launched signal to determine the effect of the PnCon propagating elastic waves.

A single IDT, although chirped for broadband transduc-tion, cannot cover the entire PnBG frequency range. Thus 24couplers were used to cover the frequency range of 0.8–2.2GHz, which spans the location of the PnBG as predicted byFDTD. The 24 PnC structures were identical except that eachIDT was designed to operate at a unique frequency intervalsuch that the overall frequency range of interest is covered.To isolate the effect of the PnC, we also fabricate an unpat-terned matrix, which is the same as Fig. 2 but without the Wrods. Normalizing the transmission through the crystal to thatthrough a matrix isolates the effects of the PnC at the outputport.6

Figure 3�a� shows a comparison between our FDTDmodel and experimental data for elastic wave transmissionthrough the PnC device. A band gap appears between 1–1.8GHz in the experimental results which is well predicted by

the FDTD modeling. The measured gap to midgap ratio of57% is extremely high when compared to previously re-ported values of 25% �Ref. 4� and 44%,5 and is wide enoughto cover a large variety of communications devices. Note thatit appears that a mode can be observed in the experimentaltransmission plot, Fig. 3�a�, at around 1.4 GHz. The modecan be seen in Fig. 3�b� for the matrix response as a dip intransmission at 1.4 GHz but without a corresponding featurein the PnC response. This indicates that such behavior in thenormalized transmission plot is artificial, occurring only be-cause of a sharp dip in transmission through the matrix atthat specific frequency. The sharp dip in transmission at 1.4GHz is present for all 24 matrix couplers and corresponds tothe thickness mode through the Si/Al/AlN/Al transducer. Thenoise floor was also measured and plotted in Fig. 3�b� �“iso-lation” curve�, confirming that, although the measured matrixand PnC signals become small, they are well within the dy-namic range of the characterization system and the featuresin the plot are indicative of the actual acoustic behavior ofthe samples. This isolation measurement was performed bymeasuring the signal across the same frequency range for aset of input and detection IDTs that were identical, in both

FIG. 2. �Color online� An SEM image showing the PnC and AlNtransducers.

FIG. 3. �Color online� �a� Normalized results for transmission through aPnC comparing FDTD and experimental results, �b� the un-normalized ex-perimental crystal and matrix responses.

193502-2 Soliman et al. Appl. Phys. Lett. 97, 193502 �2010�

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

size and spacing, to the ones used in PnC and matrix mea-surements but acoustically isolated from each other.

To better understand the modal behavior of this PnC thatgives rise to the PnBG, the structure was simulated using thetwo-dimensional plane-wave expansion technique.7 The re-sulting dispersion diagram is plotted in Fig. 4�a� for the op-timal r /a of 0.26, where a small PnBG for all modes can beobserved at a center frequency of 880 MHz. However, to

compare these data with the experimental results, two factorsmust be considered. First, the IDTs fabricated on the samplesare unable to excite or detect in-plane transverse modes �thiseffect was also included in the FDTD simulations�, thusthose corresponding modes in Fig. 4�a� can be ignored. Sec-ond, the out-of-plane transverse �i.e., flexural� modes withinthe range of 1.2–1.7 GHz exhibit either negatively sloped orvery flat dispersion behavior, making it extremely difficult tocouple energy into them and highly unlikely that they willtransmit energy to the output IDTs. This, combined with thefact that the inherent coupling of the AlN transducers for thisgeometry is about three times smaller for flexural modes thanfor longitudinal modes, indicates that the out-of-plane trans-verse modes shown in Fig. 4�a� can be ignored as well. Thus,both the complete and longitudinal-only band gaps normal-ized to the center frequency were calculated for r /a valuesranging from 0.1 to 0.48, as shown in Fig. 4�b�. This plotagrees well with the FDTD and experimental results, indicat-ing the same optimal r /a value of 0.26, corresponding to anormalized band gap of 56%. Considering that the measure-ments were performed for only the �X direction, it can beobserved from Fig. 4�a� that the indicated longitudinal bandgap for �X is 0.84–1.73 GHz �indicated by the black arrowat the X point�, again showing good agreement with the ex-perimental results and FDTD.

In conclusion, a PnC exhibiting a band gap between 1and 1.8 GHz has been fabricated and demonstrated. Further-more, the width of the band gap of 800 MHz is one of thelargest absolute band gap widths reported to date, and thegap to midgap ratio of 57% is also among the highestreported.

This work was supported by the Laboratory DirectedResearch and Development program at Sandia NationalLaboratories. Sandia National Laboratories is a multipro-gram laboratory operated by the Sandia Corporation, Lock-heed Martin Co., for the United States Department of Ener-gy’s National Nuclear Security Administration underContract No. DE-AC04-94AL85000.

1T. Miyashita, Meas. Sci. Technol. 16, R47 �2005�.2A. Khelif, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Do-brzynski, J. Appl. Phys. 94, 1308 �2003�.

3C. M. Reinke, M. Su, M. Ziaei-Moayyed, R. H. Olsson III, and I. El-Kady,IEEE Ultrasonics Symposium, San Diego, CA, October 2010 �in press�.

4S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi,Appl. Phys. Lett. 92, 221905 �2008�.

5M. F. Su, R. H. Olsson III, Z. C. Leseman, and I. El-Kady, Appl. Phys.Lett. 96, 053111 �2010�.

6R. H. Olsson and I. El-Kady, Meas. Sci. Technol. 20, 012002 �2009�.7T.-T. Wu, Z.-G. Huang, and S. Lin, Phys. Rev. B 69, 094301 �2004�.

FIG. 4. �Color online� �a� Dispersion diagram for the W–Si PnC, indicatingthe longitudinal, in-plane transverse, and out-of-plane transverse modes. Thecomplete band gap is shown by the solid blue region, the band gap forlongitudinal modes only by the shaded green region, and the measured bandgap ��X only� by the black arrow. �b� Band gap map for the complete �solidblue� and longitudinal-only �dashed green� band gap; lines represent curvefits to the data points.

193502-3 Soliman et al. Appl. Phys. Lett. 97, 193502 �2010�

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp