Two-dimensional phononic crystal sensor based on a cavity mode

Sensors and Actuators B 171–172 (2012) 271–277

Contents lists available at SciVerse ScienceDirect

Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb

Two-dimensional phononic crystal sensor based on a cavity mode Ralf Lucklum a,∗ , Manzhu Ke a,b , Mikhail Zubtsov a a b

Institute of Micro and Sensor Systems (IMOS), Otto-von-Guericke-University Magdeburg, Germany Department of Physics, Wuhan University, China

a r t i c l e

i n f o

Article history: Received 14 October 2011 Received in revised form 21 March 2012 Accepted 23 March 2012 Available online 3 April 2012 Keywords: Phononic crystal sensor Ultrasonic sensor Liquid sensor

a b s t r a c t Phononic crystals offer an innovative platform for acoustic liquid sensors. Based on a longitudinal cavity mode, we introduce an acoustic sensor system using a two dimensional phononic crystal with in-plane wave incidence. The phononic crystal is made up of a steel plate having two regular arrays of holes and a cavity in-between. The holes and the cavity are filled with the liquid of interest. We both theoretically and experimentally demonstrate that the transmission peak caused by the cavity mode can be used for sensor purpose. Theoretical simulation and experimental measurement show good consistency in the response of the transmission peak frequency. This frequency is primarily sensitive to the speed of sound thereby sensitive to the composition of the liquid mixture. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Acoustic waves are currently being used in a wide range including physical sensing, chemical sensing and biosensing [1–5]. A phononic crystal (PnC) is a kind of new artificial structure developed in the last three decades designed to control and manipulate the propagation of acoustic and elastic waves [6,7]. The reported advances in PnCs implementation and fabrication promise both their efficient and beneficial integration into existing technologies and a wide variety of applications [8], including phononic crystal sensors [9], the acoustic counterpart to photonic crystal sensors [10–15]. Although phononic crystals have been intensively modeled and fabricated for further insights to their special and unusual acoustic properties, their application in the sensor field is still in the early stages [9,16–18]. Phononic crystal sensors are expected to satisfy the high demand on ultrasensitive devices which require only an ultra-low analyte volume. When applied as (bio)chemical sensor, the material of interest constitutes one component of the phononic crystal. This can be a liquid in the holes of a regular phononic crystal or in selected holes of a phononic crystal having a defect. To introduce selectivity sensitive materials as known specifically from acoustic microsensors like quartz crystal microbalance [19] can be immobilized on the surface of the holes. In both cases changes in the composition of the analyte alter the properties of the phononic crystal either directly due to a variation in the acoustic properties of the analyte or due to modifications in the sensitive

film as a result of the interaction with the analyte. In this sense phononic crystal sensors recover some major features of acoustic microsensors. Recently we have reported a specific version of liquid sensors by using the extraordinary resonant transmission through a phononic crystal at normal incidence of sound [17,20,21]. Here we report on a phononic crystal sensor with the common in-plane incidence and propagation of sound. The sensing effect is based on a longitudinal cavity mode. The structure consists of liquid holes and a liquid cavity. The holes and the cavity in this system serve as analyte container. Since the geometric parameters of a phononic crystal can be scaled in a large range, the phononic crystal sensor can be integrated into a micro or even nanofluidic system. This specifically applies to the slit cavity we have incorporated as defect and as analyte container. In future developments the holes will be filled with a reference material. Cavity modes in phononic crystals have been greatly used for transmission coupling, filtering and highly directional radiation [22–24]. A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference of many reflections off the cavity’s surfaces. These modes can have a very high quality factor. The frequency can be controled by adjusting the cavity width.

2. Theoretical simulation and experimental measurement ∗ Corresponding author. Tel.: +49 391 671 8310; fax: +49 391 671 2609. E-mail address: [email protected] (R. Lucklum). 0925-4005/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2012.03.063

The structure employed here (Sossna, Germany) and shown in Fig. 1(a) consists of a steel plate with liquid-filled holes in square

272

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277

Fig. 1. Photo of the sample structure (a) and the experimental setup (b).

array and a liquid-filled slit cavity in the centre of the structure parallel to the orientation of the holes and perpendicular to the propagation direction of the incident wave. This is a conceptual change; comparable photonic crystal sensors use waveguides in direction of wave propagation. It targets a short acoustic path length through the analyte to deal with viscous losses. The lattice constant, denoted as a, is 3.0 mm, the thickness, t of the plate is 15 mm, the diameter, d of the hole is 1.8 mm and the width of the cavity, wc , is 1.5 mm. We again apply this phononic crystal as liquid property sensor of a binary mixture. Similar to [9,17,20] different properties are obtained by gradually changing the liquid in the holes and the cavity from pure distilled water (DI-water) through a series of liquid mixture with different molar ratios, x2 , of 1-propanol to pure 1-propanol (Roth, Germany). We first have calculated transmission spectra for a set of parameters a, d, and wc by using the two-dimensional finite-difference time-domain (FDTD) method [25–28] for achieving optimal sensor features. In contrast to the real device the 2D computational model consists of infinitely long cylinders parallel to the z-axis; the material parameters are independent of the coordinate z. The propagation of elastic wave is assumed to be only in the x-y-plane. The calculations are based on the elastic wave equation in homogeneous media, assuming the initial stress and the speed at any point is zero. The relation equations of stress and velocity are obtained by discretization of the equations in both the space and the time domains. In the FDTD calculations, we have chosen a computational cell with dimension 100 × 2000 grid points, corresponding to 100 grid points per lattice constant a. A spatial grid with mesh size x = y = 0.03 mm has been used. In x-direction we have used Bloch boundary conditions, while we have applied Mur’s absorbing boundary conditions in y-direction. For transmission spectrum calculations, a broad band wave packet has been launched to expose the plate to an in-plane incidence perpendicular to the orientation of the holes. The transmitted signal has been recorded as a function of time. The transmission coefficient has been calculated by dividing the transmitted energy flux by the energy flux of the incident wave. A one-dimensional approximation based on the 1D transmission line model as used in [9] has been developed to analyze the sensor sensitivity. Numerical procedures like FDTD are by far too timeconsuming for this purpose. The two 4-row pices of the phononic crystal sensor and the cavity slit have been modeled in a 17-layer

arrangement. Each of the two semi-PnC’s have been replaced by a 4 × 2 layers, where one layer is steel, the other a metamaterial having a density and speed of sound averaged from the steel and liquid values based on the volumetric contributions to this layer. In this way we avoid any free parameter to fit the data. For the experimental measurements, the transmission curves have been obtained using a network analyzer (Agilent 4395A) together with an S-parameter test set (Agilent 87511A). A small in-house developed sample holder has been used. The liquids have been filled in the holes and the slit cavity by three injectors in different directions. In this way one can easily wipe off air bubbles inside the holes and the cavity. The sample has been placed between two contact piezoelectric transducers (V153, Olympus) having a central frequency of 1.0 MHz and a half bandwidth of 1 MHz. A coupling agent has been added between the sample and the solid transducers. The illustration of the experimental setup is shown in Fig. 1(b). Transmission S21 has been measured with and without sample in place respectively. The transmission amplitude has been obtained by normalizing with the amplitude of the equivalent setup without the sample in place. In this way the transfer functions of transmitter and receiver cancel out.

3. Results and discussions First we show in Fig. 2 the calculated transmission spectrum of the regular phononic crystal, i.e. with 8 rows of air (a) and liquid (b)-filled holes and without the slit in between. With air the band gap edge crosses the −3 dB-level at 590 kHz. The maximum slope is about −0.2 kHz−1 . Transmission of acoustic waves is suppressed until the upper edge at 944 kHz. The periodic variation of transmission at lower frequencies is caused by Bragg resonances. With liquid-filled holes the band gap edges move to 586 kHz and 928 kHz (taking the first −3 dB crossing). The second transmission band extends to about 1 MHz. More important, a single peak arises 793 kHz, which can be attributed to the fact that the holes are liquid-filled now. The 1D-approximation reproduces major features of Fig. 2 although we have to consider that the Bragg resonances as well as the lower band gap edge appear at lower frequencies (−40 kHz the latter, the difference can be easily adjusted when using a metamaterial desity 20% higher than geometrically justified, however, fitting has not been our intention here).

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277

a

1.0

0.9

Simulation

(c)

x2=0.021

0.6

0.6

0.3

0.4

transmission

transmission

Simulation

(a)

x2=0 (water)

0.8

0.2 0.0 0.0

273

0.3

0.6

0.9

0.0 0.3

(b)

Experiment

(d)

Experiment

0.2

1.2

f / MHz 0.1

b

0.0 0.6

1.0

transmission

0.6 0.4 0.2

0.3

0.6

0.9

1.2

f / MHz Fig. 2. Transmission spectra of the regular phononic crystal, i.e. without the slit, having the same dimensions as the sample in Fig. 1a, in air (a) and with liquid-filled holes (b).

The approximation especially does not show the peak within the band gap in Fig. 2b. This is just a consequence of the definition of the metamaterial by frequency independent material properties. The transmission through our sample, Fig. 1a, in air is zero since an air-filled gap completely decouples the two 4-row phononic crystals at ultrasonic frequencies. Fig. 3 shows sample transmission spectra of the system filled with DI-water and the liquid mixture with a molar ratio of 0.021 of 1-propanol, where the solid lines in the upper diagrams denote the theoretical simulations and the dashed lines in the lower diagrams represent the experimental results. The band gap seems to appear above 600 kHz, however, several peaks make identification problematically. The second transmission band above 1 MHz is drastically reduced. This is a consequence of the ‘series’ design of our sensor. We further recognize a tiny peak at about 794 kHz, presumably the same as the one at 793 kHz in Fig. 2b. This peak does not significantly move when changing the liquid mixture. We concentrate on the single transmission peak at 1 MHz. According to the longitudinal cavity mode condition,  = wc , 2

1.5

0.6

0.9

1.2

1.5

Fig. 3. Transmission spectrum of the sensor system with water (a, b) and water–propanol mixture having a molar ratio of x2 = 0.021 (c, d), where the solid red lines indicate the FDTD simulation results (a, c) and the dashed lines experimental measurements (b, d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

0.0

n

1.2

f / MHz

0.8

0.0

0.9

(1)

we can calculate the frequency of the cavity mode and estimate the position of the transmission peak. With the overtone number n being 1, the first order cavity mode would be at 496 kHz; the respective transmission peak lies in the first pass-band range of the

phononic crystal. As obvious in Fig. 3 this position is not suitable for our sensor purpose. With n = 2, the second order cavity mode has a frequency of 997 kHz (water) or 1030 kHz (water–propanol). The transmission peak should now appear at a frequency close to the upper band gap edge within the second transmission band of the regular 8 row liquid-filled hole array. The respective values calculated with FDTD are 1018 kHz for water and 1044 kHz for the water–propanol mixture. The reason for the difference to the values of eq 1 can be found in the boundary conditions of the gap. The liquid-solid interface does not act like a reflector in the semiinfinite case. There is always acoustic wave transmission through the boundary opposite to the wave propagating direction of the incident wave introducing a phase shift which ‘detunes’ the resonator frequency. However, this effect does not influence the basic resonant sensing scheme and will be discussed later. Meeting the conditions of resonance requires a shift in the probing frequency to account for changes in speed of sound of the water–propanol mixture as a result of changes in the composition of the mixture. Fig. 3 also reveals that the resonant peak is very sharp and narrow; it is therefore an ideal choice for sensor purposes. The calculated half band width is 4 kHz. This is less than the respective value of a liquid cavity between two semi-infinite steel blocks (12 kHz) and a strong argument pro phononic crystal sensors. Almost perfect match between experiment and simulation can be observed for the cavity transmission peak position (1018/1032 kHz and 1044/1062 kHz theory/experiment). The transmission peak is affected by the properties of the liquid in the cavity as predicted by simulation. We, however, have to consider that the transmission peak has a lower amplitude and larger half band width in the experimental result than in FDTD simulation for both DI-water and liquid mixtures. This finding must be attributed to the experimental limitations. On one hand, the structure of the fabricated sample is not perfect. Complete symmetry across the whole sample is difficult to realize. The hole diameter accuracy is better than the resolution of the microscope scale. On the other hand we have noticed a slight misalignment of the holes between upper and lower surface caused by buckling of the driller during

274

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277

1100

1.2

speed of sound / km s

1.60 1.55

0.3

1.0

1.50

0.2

1.45

0.00

0.05 0.10 0.15 0.20 molar ratio of 1-propanol

0.1

0.25

R

1.40

0.8 0.6

0.0

1000

-0.1

0.4 Experiment Simulation 950

0.00

0.05

0.15

0.20

0.25

0.0

molar ratio of 1-propanol

0

Fig. 4. Resonant frequency vs. molar ratio of 1-propanol in the liquid mixture from FDTD simulation (䊉) and experiment (). The maximum frequency position of the resonant transmission peak corresponds to the highest speed of sound at molar ratio x2 = 0.056. The inset shows the speed of sound vs. molar ratio of 1-propanol in the liquid mixtures.

manufacturing. Variation in the signal response and absorption are further reasons for losses inevitably caused by the experimental circumstances, such as finite thickness of the device and viscosity of the liquid although one should note that pure bulk viscosity is negligible for the longitudinal wave cavity resonator at the given experimental conditions. Fig. 4 summarizes the frequency responses of the cavity transmission peak and the properties of the liquid in the cavity for molar ratios of 1-propanol of 0.021, 0.035, 0.056, 0.102, 0.158, and 0.230. Prior to each measurement, we have made sure the former solution is entirely replaced by the new one. Both the theoretical and the experimental curves demonstrate a strong relation between material properties of the liquid mixture and the position of the transmission peak similar to our previous experiments with a one-dimensional phononic crystal and with transmission through a phononic crystal plate at normal incidence of sound. Fig. 4 again reveals the highest peak frequency at x2 = 0.056 which coincides with the maximum in speed of sound of the mixture (v = 1588 m s−1 ) [29]. The inset in Fig. 4 demonstrates the dominating influence of the speed of sound of the mixture. The density decreases monotonously with the molar ratio and has a far smaller influence on the peak position. Since speed of sound of the liquid is a function of the molar ratio of 1-propanol in the mixture with water and governs the transmission peak frequency, the phononic crystal can serve as a sensor for both the concentration of 1-propanol in the liquid mixture and the speed of sound of a liquid. Due to the appearance of a maximum in Fig. 4, the measurement is not unambiguously in the range between x2 = 0· · ·0.15, however, this fact is a specific feature of the selected test mixture, not a specific feature of the sensor principle. For the same reason care must be taken as well when evaluating the sensitivity of the sensor, Sf , which has been taken as ratio of frequency shift, f, to the change of input parameter, the 1-propanol concentration change in the mixture, x2 : Sf =

f . x2

(2)

The sensitivity is highest in the range x2 = 0· · ·0.035. It reaches 1340 kHz. The sensitivity decreases to zero when approaching the maximum and is −500 kHz at higher propanol concentrations. The sensitivity is higher than that recently found for the onedimensional phononic crystal sensor (1190 kHz [9]) and slightly smaller than the sensitivity of extraordinary transmission through

-0.2

1,450 1,500 cZ fcav

0.2 0.10

cZ

f / kHz

1050

0.4

300

600

-0.3 -0.4 900

1200

1500

1800

f / kHz Fig. 5. Reflection coefficient, R (left axis, solid line, green for vanalyte = 1450 ms−1 and dashed line, red for vanalyte = 1500 ms−1 ) and correction parameter, cZ (right axis, , blue), calculated for a 3-layer one-dimensional phononic crystal with an analyte layer between two metal plates. The respective cavity mode frequencies are marked on the abscissa. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

a phononic crystal plate (1430 [17,20]). The estimation of the sensing capabilities of the different concepts requires taking two more values into account: the probing frequency and the peak half band width. The characteristics of a phononic crystal, including the cavity mode, do not change when plotting the transmission vs. the reduced frequency fa/c. Since f/f = const holds (as long as c is frequency independent), the sensitivity increases linearly with f. When normalizing the above sensitivities in the appropriate manner using S/f0 , where f0 is the probing frequency at some reference point (here the cavity peak frequency for water) one finds 1,5, 1,7, and 1,2 for the one-dimensional, the 2D extraordinary transmission, and the 2D-slit cavity (based on FDTD calculations), respectively. The values are close to or smaller than that of the cavity mode. Further investigations have been performed using the one-dimensional approximation. In a symmetric arrangement with respect to the cavity maximum acoustic wave transmission due to a cavity mode is achieved if Z- Ax = Z- ∗x

(3)

holds, where Z- Ax is the (complex) effective acoustic impedance at the lower analyte interface whereas Z- ∗x is the effective acoustic impedance generated from the analyte layer and an arbitrary number of layers above, * indicates the conjugate. With some approximations which can be applied close to resonance of the analyte layer one finds:



fmax Tr = nfcav n +



2 ZcA Im{Yx } 

= nfcav (1 + cZ (f )) = cF (f )nfcav

(4)

where fmaxTr being the peak frequency, fcav the frequency of the cavity mode, ZcA = A .vA is the characteristic acoustic impedance of the analyte and Y- x = 1/Z- x . The second summand, cZ , moves the peak frequency to lower or higher values since Im{Z- x } can be positive or negative, i.e., the correction factor, cF , can be smaller or larger than 1. For the sensitivity of the sensor it is essential, that Z- x is frequency dependent, i.e., the correction factor changes with frequency as well. Fig. 5 summarizes the results for the 3-layer case. The correction factor is periodic, has negative slope except a small frequency range close to the minimum of Re{Z- x }. At a frequency close to the cavity mode of the two sample cases vanalyte = 1450/1550 ms−1 , respectively, its value is smaller than 1. In consequence fmaxTr is lower than fcav for both n = 1 and n = 2. fmaxTr is smaller than fcav ,

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277

275

Table 1 Peak frequencies, correction parameter and corrected peak frequencies of a 1-dimensional 3 layer PnC sensor determined with the transmission line model for two analytes having v = 1450(1500) ms−1 (see index) and the respective sensitivity, here with respect to the change in speed of sound (Sv = f/v). 3-layer PnC sensor

f1450 f1500 Hz

Sv Hzm−1 s

cZ1450 cZ1500

fcorr1450 fcorr1500 Hz

Sv

corr

Hzm−1 s

fcav

1450 fcav 1500

Hz

Scav Hzm−1 s

n=1

757,106 776,561

389

−0.050 −0.058

796,781 824,302

550

796,703 824,176

549

n=2

1,587,397 1,634,855

949

−0.008 −0.016

1,593,406 1,648,354

1099

1,593,407 1,648,352

1099

more pronounced for n = 1 due to the larger slope of cZ . The resulting sensitivity is always smaller than that of the cavity mode in the whole usable range. For illustration the simulated data are summarized in Table 1. Designing the cavity in a way that fcav falls in the range of the positive slope of the correction factor is not appropriate since the cavity mode vanishes due to the disappearance of boundaries confining the mode. In a more complex structure like the one used as 1D approximation of the slit geometry cZ (f) is more involved. Fig. 6 shows this example for pure water and the water – 1-propanol mixture with highest speed of sound. The small variation between both curves results from filling the holes with the analyte instead of a reference liquid. Within the measurement range cZ (f) (gray) is close to zero (0 . . . −1.5%) and consequently the normalized sensitivity of the slit geometry approaches the theoretical value of the cavity mode. However, although the remaining correction factor is small and the parameters of the metamaterial layer have not been fitted, the corrected values indicate a better agreement with the experimentally determined frequencies than the cavity mode frequencies and the FDTD calculations except at x2 = 0.23. We finally consider the experimentally achievable frequency resolution accounting for inevitable noise in the experiment or limited peak amplitude resolution. The peak half band width can act as an indicator for this purpose. Since this value scales with frequency we redefine our recent definition [20] of the reduced sensitivity to Sred =

f x2 fHBW

(5)

for comparison, fHBW is the half value full band width frequency. The respective numbers are recalculated to 0.17, 0.03, and 0.4, respectively, i.e., the new 2D phononic crystal sensor with the slit cavity has theoretically the highest sensing capability. We however have to consider that the peak half bandwidth is about 5 times

larger in the experiment. We have therefore taken a conservative estimate of the frequency resolution of 1 kHz from experiment for the estimation of the limit of detection (LOD) x2min of the phononic crystal sensor which is better than 0.001 (55 mmol l−1 ). We further have to note that the transmission amplitude is smaller than theoretically predicted as shown in Fig. 7 for water, x2 = 0.021, 0.056, and 0.102. The maximum amplitudes of the cavity transmission peak for the four liquid samples are 10%, 18%, 30% and 18%, respectively. One can note that the closer the resonant transmission peak position to the upper band gap edge, the higher the amplitude whereas the mixture viscosity, which has a maximum at x2 = 0.13, does not have a direct influence [30]. We apply once more the 1D approximation to estimate the influence of losses on the peak amplitude. We consider losses in a complex sound velocity of the analyte and take this value 1000 times larger than that from the attenuation of water reported in [31]. The peak amplitude values are 0.63, 0.68 and 0.42 for water, x2 = 0.056 and x2 = 0.230, respectively and agree in tendency with the experimental findings. Viscous losses have also consequences for miniaturization. The characteristic dimensions of the sensor and hence the probing frequency of a phononic crystal sensor can be varied in a large range, i.e., can be rescaled to smaller wavelength giving access to higher sensitivity and smaller analytes volume which should be favourable e.g. for biosensor applications. This scaling is fundamentally limited by sound attenuation in the liquid. Just recently Holmes et al. have analyzed Millipore water by an acoustic spectroscopy (Ultrasizer MSV, Malvern) [31]. Their experiments confirm theoretical predictions: ω2 ˛= 2v3



4 ( − 1)

+ + 3 cp

0.2



(6)

(a)

10%

water

(b)

18%

x2=0.021

(c)

30%

x2=0.056

(d)

18%

x2=0.102

0.150 corr param water corr param 0.056

0.0

0.100

transmission

0.2

cZ

0.050

0.000

-0.050

-0.100 500

0.0 0.2 0.0 0.2

700

900

1,100

1,300

1,500

1,700

f / kHz

0.0 0.6

Fig. 6. Correction parameter, cZ (, blue for water and solid red line for a water-1-propanol mixture with the molar ratio of 0.056), calculated with the one-dimensional approximation of the slit geometry. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

0.9

1.2

1.5

f / MHz Fig. 7. Experimental transmission results for different molar ratios of 1-propanol in the liquid mixtures: (a) DI-water (x2 = 0); (b) x2 = 0.021; (c) x2 = 0.056; (d) x2 = 0.102.

276

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277

Table 2 Predicted scaling limitations due to sound attenuation in water taking ˛ = 0.0216 Np MHz−2 m−1 from [31] in an extended frequency range. Fundamental frequency

Im {vanalyte } ms−1

Rmin

f

f/f Hz/kHz

fHBW

Sred

1 MHz 10 MHz 100 MHz 500 MHz 1 GHz 1 GHz, without losses

0.008 0.08 0.8 3.86 7.73

0.007 0.01 0.06 0.24 0.39 0

9.6 97 960 4850 9800 9650

9.6 9.7 9.6 9.6 9.8 9.7

9 92 1040 0 21,400 9000

1.07 1.05 0.92 0.64 0.46 1.07

where ˛ describes the dissipative term in the longitudinal wave number,  is the bulk and  is the shear viscosity, is the ratio of specific heats, is the thermal conductivity and  the density of the fluid. In a frequency range between 1 and 100 MHz the attenuation (displayed in Np m−1 ) can be fit by a single polynominal in frequency of the form afb with a = 0.0215 and b = 2.0012. Attenuation arising from thermal conductivity gives only a negligible contribution to the overall attenuation as expected for fluids having low compressibility like most liquids. Therefore at the same frequency overtone modes are less favorable than fundamental modes since attenuation of the latter goes with f only because cavity size goes with f−1 . Some example data obtained with the 1D-model are summarized in Table 2. The frequency range has been extended to 1 GHz although a and b have not yet been experimentally verified. One can conclude that probing frequencies up to 1 GHz, the respective cavity size would be 1.5 ␮m, are useful if other loss mechanisms like those caused by fabrication inaccuracies, excitation of unwanted modes in the real phononic crystal (finite size) and from coupling to the transducers and waveguides are sufficiently low. The sensitivity increases (almost) linear with frequency, the normalized sensitivity is of course constant. The reduced sensitivity, however decreases due to the significant increase in the half band width caused by viscous losses. 4. Conclusion The phenomenon of acoustic longitudinal wave transmission through a phononic crystal structure having a liquid-filled cavity inside can be beneficially utilized for liquid sensor purposes. We have both theoretically and experimentally demonstrated the sensing capabilities by using the resonant transmission peak as a favorable measure. The position of the transmission peak has been proven to be highly sensitive to the speed of sound of the liquid filling the cavity. Since speed of sound is a function of the molar ratio of the liquid mixture the phononic crystal sensor can be exploited as sensor to determine the concentration of a component in a liquid mixture. The results show that the slit cavity design utilizing the classical concept of in-plane excitation is feasible. The acoustic properties of the phononic crystal surrounding the cavity used for measurement should show weak frequency dependence in the range used as output span of the sensor. Higher probing frequencies are recommended to decrease the probing volume or to increase sensitivity, however, a drastic decrease in frequency resolution must be considered as well. Fabrication needs to be further optimized to reduce insertion losses of the sensor. Acknowledgements This work has been supported by FET-Open Project TAILPHOX (grant no. 233883) and the German Research Foundation (Lu 605/12-1). The authors wish to thank Bernhard Penzlin and Carsten Kralapp for experimental support. References [1] P. Hauptmann, N. Hoppe, A. Puettmer, Application of ultrasonic sensors in the process industry, Meas. Sci. Technol. 13 (2002) R73–R83.

[2] K.K. Park, H.J. Lee, G.G. Yaralioglu, Ö. Oralkan, M. Kupnik, C.F. Quate, B.T. KhuriYakub, T. Braun, H.P. Lang, M. Hegner, C. Gerber, J. Gimzewski, Capacitive micromachined ultrasonic transducers for chemical detection in nitrogen, Appl. Phys. Lett. 91 (2007) 094102. [3] G. Lindner, Sensors and actuators based on surface acoustic waves propagating along solid–liquid interfaces, J. Phys. D: Appl. Phys. 41 (2008) 123002. [4] B. Godber, M. Frogley, M. Rehak, A. Sleptsova, K.S.J. Thompson, Y. Uludag, M.A. Cooper, Profiling of molecular interactions in real time using acoustic detection, Biosens. Bioelectron. 22 (2007) 2382–2386. [5] R. Lucklum, C. Behling, R.W. Cernosek, S.J. Martin, Determination of complex shear modulus with thickness shear mode resonators, J. Phys. D: Appl. Phys. 30 (1997) 346–356. [6] M.M. Sigalas, E.N. Economou, Elastic and acoustic wave band structure, J. Sound Vibr. 158 (1992) 377–382. [7] M.S. Kushwaha, P. Halevi, L. Dobrzynski, B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71 (1993) 2022–2025. [8] R.H. Olsson III, I. El-Kady, Microfabricated phononic crystal devices and applications, Meas. Sci. Technol. 20 (2009) 012002. [9] R. Lucklum, J. Li, Phononic crystals for liquid sensor applications, Meas. Sci. Technol. 20 (2009) 124014. [10] H. Kurt, D.S. Citrin, Photonic crystals for biochemical sensing in the Terahertz region, Appl. Phys. Lett. 87 (2005) 041108. [11] X. Wang, Z. Xu, N. Lu, J. Zhu, G. Jin, Ultracompact refractive index sensor based on microcavity in the sandwiched photonic crystal waveguide structure, Opt. Commun. 281 (2008) 1725–1731. [12] M.A. Dündar, E.C.I. Ryckebosch, R. Nötzel, F. Karouta, L.J. van, I. Jzendoorn, R.W. van der Heijden, Sensitivities of InGaAsP photonic crystal membrane nanocavities to hole refractive index, Opt. Express 18 (2010) 4049–4056. [13] I.D. Block, L.L. Chan, B.T. Cunningham, Photonic crystal optical biosensor incorporating structured low-index porous dielectric, Sens. Actuators B 120 (2006) 187–193. [14] P.J. Rodriguez-Canto, M. Martinez-Marco, F.J. Rodriguez-Fortuno, B. TomasNavarro, R. Ortuno, S. Peransi-Llopis, A. Martinez, Demonstration of near infrared gas sensing using gold nanodisks on functionalized silicon, Opt. Express 19 (2011) 7664–7672. [15] M. Huang, A. Yanik, T. Chang, H. Altug, Sub-wavelength nanofluidics in photonic crystal sensors, Opt. Express 17 (2009) 24224. [16] R. Lucklum, J. Li, M. Zubtsov, 1D and 2D phononic crystal sensors, Proc. Eng. 5 (2010) 436–439. [17] M. Ke, M. Zubtzov, R. Lucklum, Sub-wavelength phononic crystal liquid sensor, J. Appl. Phys. 110 (2011) 026101. [18] M.M. Sigalas, N. Aravantinos-Zafiris, Phononic crystal sensors, in: Proc. First Int. Conf. Phon. Cryst., Metamat. and Optomech., Phononics (2011) 66–67. [19] R. Lucklum, P. Hauptmann, Acoustic microsensors-the challenge behind microgravimetry, Anal. Bioanal. Chem. 384 (2006) 667–682. [20] R. Lucklum, M., Zubtsov, M. Ke, Liquid sensor utilizing a regular phononic crystal with normal incidence of sound, Transact. Ultrason., Ferroel., Freq. Contr., in press. [21] M. Zubtsov, R., Lucklum, M., Ke, A., Oseev, R., Grundmann, B., Henning, U. Hempel, 2D phononic crystal sensor with normal incidence of sound, Sens. Acta, B, http://dx.doi.org/10.1016/j.sna.2012.03.017, in press. [22] X. Li, Z. Liu, Coupling of cavity modes and guiding modes in two-dimensional phononic crystals, Solid State Commun. 133 (2005) 397–402. [23] X. Li, Z. Liu, Bending and branching of acoustic waves in two dimensional phononic crystals with linear defects, Phys. Lett. A 338 (2005) 413–419. [24] M.Z. Ke, Z.Y. Liu, P. Pang, C.Y. Qiu, W.G. Wang, Z.G. Cheng, J. Shi, X.Z. Zhao, W.J. Wen, Experimental demonstration of directional acoustic radiation based on two-dimensional phononic crystal band edge states, Appl. Phys. Lett. 88 (2006) 263505. [25] D. Garcia-Pablos, M.M. Sigalas, F.R. Montero de Espinosa, M. Torres, M. Kafesaki, N. Garcia, Theory and experiments on elastic band gaps, Phys. Rev. Lett. 84 (2000) 4349. [26] M. Kafesaki, M.M. Sigalas, N. Garcia, Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials, Phys. Rev. Lett. 85 (2000) 4044. [27] J.O. Vasseur, P.A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost, Method for retrieving effective properties of locally resonant acoustic metamaterials, Phys. Rev. Lett. 86 (2001) 3012. [28] T.T. Wu, Z.G. Huang, S. Lin, Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy, Phys. Rev. B 69 (2004) 094301.

R. Lucklum et al. / Sensors and Actuators B 171–172 (2012) 271–277 [29] W. Schaaffs, Landolt-Boernstein NS5, Springer, Berlin-Heidelberg-New York, 1967, p. 100. [30] W. Schaaffs, Landolt-Boernstein NS5, Springer, Berlin-Heidelberg-New York, 1967, p. 210. [31] M.J. Holmes, N.G. Parker, W.J.W. Povey, Temperature dependence of bulk viscosity in water using acoustic spectroscopy, J. Phys: Conf. Series 269 (2011) 012011.

Biographies Ralf Lucklum has been employed at the Otto-von-Guericke University, Magdeburg (Germany) at the Department of Electrical Engineering since 1986. In 1977 he received his Ph.D. degree; in 2002 he habilitated at the Institute of Micro and Sensor Systems and is currently chairing the Sensor and Measurement Science group. He has been involved in several national and international sensor research projects. His present research activities include the development of ultrasonic sensor systems for process monitoring in fluidic systems based on phononic crystals, acoustic

277

microsensors for chemical analysis and material science as well as application orientated sensor projects. Manzhu Ke is an Associated Professor in Department of Physics, Wuhan University (China). She received her Ph.D degree from Wuhan University in 2006. In 2010–2011 she was employed as a visiting scientist at the Otto-von-GuerickeUniversity Magdeburg for one year. During this period she worked on the design and experiment of phononic crystal sensors. Her research field mainly focuses on artificial-structure material and phononic crystals. Mikhail Zubtsov has been employed as Research Associate at the Otto-vonGuericke-University Magdeburg, Institute for Micro and Sensor Systems since 2010. He received his Diploma degree in physics, with specialization on electron–phonon interaction in disordered alloys, from Moscow State University, Moscow (Soviet Union) in 1979 and the Ph.D. degree in physics of magnetic phenomena, with specialization on the quantum theory of non-local and non-linear exchange interactions in metals, from the same university in 1985. He currently works on phononic crystal sensors.