Analysis and optimization of Love wave liquid sensors

Analysis and Optimization of Love Wave

Liquid Sensors

Bernhard Jakoby, Member, IEEE, and Michael J. Vellekoop

Abstract—Love wave sensors are highly sensitive microa-coustic devices, which are well suited for liquid sensing applications thanks to the shear polarization of the wave. The sensing mechanism thereby relies on the mechanical (or acoustic) interaction of the device with the liquid. The successful utilization of Love wave devices for this purpose requires proper shielding to avoid unwanted electric inter-action of the liquid with the wave and the transducers. In this work we describe the effects of this electric interaction and the proper design of a shield to prevent it. We present analysis methods, which illustrate the impact of the inter-action and which help to obtain an optimized design of the proposed shield. We also present experimental results for devices that have been fabricated according to these design rules.

I. Introduction

M

icroacoustic sensor deviceshave proved to be suitable for sensing physical quantities like mass den-sity, viscoden-sity, and acoustic properties of liquids. By us-ing so-called chemical interfaces, they can furthermore be used for determining the concentration of a certain target compound in a liquid or gaseous environment. A compre-hensive overview on the state-of-the-art in microacoustic sensing can be found in [1].

Among the commonly used devices, Rayleigh wave sen-sors have proved to show high sensitivities, which is related to the concentration of the acoustic energy at the sensitive surface. However, for liquid sensing applications they pose a serious disadvantage: Due to the particle displacement component normal to the sensing surface, compressional waves are excited in the liquid leading to a large damp-ing of the wave. A suitable alternative is the utilization of shear polarized wave modes where Love waves have been theoretically shown to be the most sensitive ones [2], which has been confirmed by experiments [3]–[5].

To obtain optimum performance of a Love wave liquid sensor, it is an absolute necessity to provide proper elec-trical shielding of the delay line from the liquid in order to avoid electric interaction between device and liquid, which would interfere with the desired sensing effect. In [6] a thin gold layer has been applied on the acoustic propaga-tion path to provide a basis for the attachment of lipid layers for biochemical sensing applications. Such a layer

Manuscript received September 8, 1997; accepted April 8, 1998. This work was supported by the Brite-Euram project BE-95-1745:MIMICS.

The authors are with the Electronic Instrumentation Labora-tory/DIMES, Delft University of Technology, 2628 CD Delft, The Netherlands (e-mail:jakoby@ei.et.tudelft.nl).

prevents electric interaction of the liquid with the propa-gating wave; however, it is a crucial point to also shield the acousto-electric inter-digital transducers (IDTs) of the device because the IDT admittances are strongly influ-enced by the liquid’s (di)electric properties, especially for liquids containing ions or for polar liquids (e.g., natural water in biosensing applications). Because the IDT admit-tances represent the load and source admitadmit-tances for the electronic sensor circuitry, this influence would lead to an undesirable sensing effect. This undesirable influence on the IDT admittance generally even predominates the (also unwanted) electric interaction with the propagating wave itself, which is often negligible (especially for low coupling piezoelectric substrates such as quartz).

The operation principle and configuration of a Love wave sensor is briefly outlined in Section II. In Section III we discuss the effects of the above mentioned electric liq-uid/device interaction on the electric parameters of a non-shielded device, which are compared to those of a non-shielded device. Furthermore, we outline the influence of acoustic and electric losses on the device parameters. In Section IV we show analysis results allowing the evaluation of the im-pact of these unwanted effects on the device performance. Furthermore, they enable us to determine the properties of shielded devices. In Section V we present experimental results illustrating the device behavior.

II. Operation Principle of a Love Wave Sensor

Commonly a Love wave device for sensor applications is used in a delay line configuration. Love waves are acoustic shear modes that propagate in a thin guiding layer that is deposited on a substrate. To allow for electric excitation of the wave, we used a piezoelectric substrate that was chosen to be ST-cut quartz. For efficient shear wave exci-tation, the chosen propagation direction is orthogonal to the crystalline X axis. The wave is excited and received by means of interdigital transducers being embedded on the substrate/layer interface (see Fig. 1). In the co-ordinate system drawn, the shear movement associated with the Love wave would be in y direction. As guiding layer mate-rial, we used SiO2, which is deposited by plasma enhanced

chemical vapor deposition (PECVD). Fig. 1 also shows an optional metalization covering the entire guiding layer, the purpose of which is the aforementioned prevention of elec-tric interactions between Love wave device and liquid. The top surface of the entire structure represents the sensing surface, which is brought in contact with the liquid to be

Fig. 1. Love wave delay line.

analyzed. We note that, although we consider an SiO2

/ST-quartz structure in this work, the presented methods and conclusions can be applied to other configurations in a similar manner.

For biochemical sensing applications, a special film that selectively adsorbs molecules out of the liquid environ-ment is attached on the sensing surface. The corresponding change in mass loading on the surface causes a change in the wave velocity that leads to a change in delay time. For viscosity sensing applications, we use the effect that the shear movement sensing surface leads to an entrainment of a thin liquid layer with the acoustic shear vibration [7]. This effect also leads to a change in wave velocity and, moreover, causes a damping of the wave [8], where both effects can be used to determine the viscosity of the sample liquid.

To measure the change in wave velocity accurately and with high resolution, the delay line is used as feedback el-ement for an automatic gain controlled amplifier, which represents an oscillator setup. The dependence of the os-cillation frequency on mass loading at the sensing surface is the quantity that essentially determines the sensitivity for both, biochemical and viscosity sensing. It has been shown that the optimum sensitivity for an SiO2/ST-quartz

waveguide can be obtained at a layer-thickness of about h = 0.18λ, where λ denotes the wavelength of the Love wave [3], [9].

III. Electrical Properties of the Delay Line

To allow for the design of the electronic sensor circuitry, we have to describe the delay line in terms of electric net-work parameters. The input admittance of an IDT can be characterized by the equivalent circuit shown in Fig. 2 [10]. Each of the circuit components can be attributed to a par-ticular physical effect. The static transducer capacitance is represented by Ct, which typically is the dominating reactive (imaginary) part of the input admittance. The admittance Ya = Ga+ jBa corresponds to the effect of the acoustically induced charges on the transducers due to

Fig. 2. Equivalent circuit for the IDT admittance. TABLE I

Change of the Equivalent Circuit Parameters for Liquid Loading and Shielding.

Parameter Case (a) Case (b) Case (c) no shield, no shield, shielded1

unloaded liquid loading

Ct Ct,0 > Ct,02 > Ct,01

Ga Ga,0 < Ga,02 < Ga,01

Gl = 0 6= 02 = 01

1_{Value does not depend on the electric properties of}

the liquid.

2 _{Value depends on the electric properties of the}

liquid.

the piezoelectricity of the substrate material. Its real part, Ga is related to the power radiated into surface wave, it is hence referred to as radiation conductance. Ba can be obtained from Ga directly by subjecting it to a Hilbert transform [11]. The series resistance Rs accounts for the ohmic losses in the transducer metalization. These compo-nents are in full analogy to those of the equivalent circuit for Rayleigh surface acoustic wave (SAW) transducers [10]. Apart from these components, there is a further conduc-tance Gl; it represents the electric losses in the adjacent liquid (if any).

Table I gives an overview on how the values of the com-ponents in the equivalent circuit change if (a) the structure is not shielded and no liquid is present, (b) the structure is not shielded but liquid is present, and (c) the structure is shielded. Rs is not listed as it is about the same for all three cases, Ba is directly related to Ga as has been men-tioned above. The values for case (a) are provided with a subscript 0, and the typical change of these values in the other cases is given. The capacitance Ct increases in both cases where its increase depends on the kind of liq-uid for case (b). The latter also holds for the radiation conductance, which is reduced in both cases. This reduc-tion can be explained by the fact that the (electrically grounded) shield tends to concentrate the electric field in the guiding layer, which is not piezoelectric and, hence, the efficiency of electro-acoustic power conversion is reduced.

The loss conductance Glis present only in case (b); it also depends on the liquid’s electric properties. It can be re-lated to the loss tangent of the liquid’s permittivity (see Section IV-A). Thus, in order to avoid the influence of the electric properties of the liquid on the circuit param-eters of the IDT, shielding is a proper measure. However, one has to realize that the above mentioned reduced ef-ficiency in electro-acoustic power conversion induced by the shielding generally leads to an increase of the insertion loss of the delay line compared to the nonshielded case. This, in turn, can reduce the stability of the oscillator cir-cuit. Hence, it is of major interest to know the degree of these changes and their relation to other design parame-ters (such as the height h of the guiding layer) in order to design a stable sensor system. Note that we are here refer-ring to the insertion loss in terms of signal transfer instead of power transfer. For an acoustically lossless device the power insertion loss can in principle always be reduced to 6 dB regardless of the value of the radiation conductance by using proper matching networks. In the contrary the damping in terms signal transfer generally crucially de-pends on Ga as matching networks, due to their intrinsic temperature coefficients, are not desirable for sensing ap-plications. For instance, for voltage steering at the input and current sensing at the output of the delay line, the sig-nal transfer function is directly given by the short circuit transfer admittance that directly depends on Ga [see also (1)]. Moreover, for the practical case of finite source and load impedances the increase of Ct also can considerably reduce the signal transfer efficiency.

We also note that instead of shielding the top of the guiding layer, one also can try to make the influence of the liquid’s electric properties negligible by sufficiently increas-ing the layer thickness h. These issues will be discussed in the following section.

So far we only discussed the properties of a single IDT. In theory, the input characteristics of one IDT also are determined by the electric load at the other IDT. How-ever, if the second IDT is short circuited, reflections due to piezoelectric charge regeneration on the second IDT are suppressed. This means that the above given equivalent circuit can be interpreted as a description for the short circuit driving point admittance Y11, which gives the

in-put admittance into IDT number 1 if IDT number 2 is short circuited (vice versa for Y22). We mention that we

did not consider mechanical reflections from the IDT struc-tures; however, they can be avoided by using split finger IDTs [10]. In case of a substrate with weak acousto-electric coupling (such as quartz) the influence of the other IDT’s termination often can be neglected so that the input ad-mittance into IDT number i is approximately given by Yii for arbitrary load at the other transducer1.

To complete the two-port description in terms of short circuit admittances Yij [12], we need the short circuit transfer admittance Y12(= Y21because of reciprocity)

giv-1_{In terms of short circuit parameters this is the case if|Y}

ii|  |Y12|. Y12 is closely related to the radiation conductances, which, in turn,

depend on the acoustoelectric coupling efficiency.

ing the short circuit current at one transducer due to an applied unit voltage at the other transducer. It also can be shown [10] that the magnitude of Y12 can be directly

obtained from:

|Y12|2= Ga,1Ga,2, (1) where the Ga,1and Ga,2denote the radiation conductances of the transducers. Here diffraction effects are neglected, and we assumed that both IDTs have the same acoustic aperture. We note that this equation holds only in the loss-less case, i.e., when there are no acoustic damping mecha-nisms and no ohmic losses in the metallic transducer struc-tures. Acoustic losses (e.g., due to the viscosity of the liq-uid [8]) can be approximately accounted for by multiplying the right-hand side with a loss factor exp(−2αd) where α characterizes the damping of the propagating Love wave, which is given by the imaginary part of the propagation constant. d denotes the center-to-center distance between the IDTs. Ohmic losses in the IDT metalization simply can be taken into account by formally extracting the resistors Rsout of the two port and considering the Yij parameters for the so obtained two port.

IV. Numerical Analysis

We have noted that the evaluation of the input admit-tance provides valuable information about the electrical characteristics of the delay line. Of primary importance are thereby the static capacitance Ct, because it is the major part of the load seen by the driving electronic circuitry, and the radiation conductance Ga, as it contains information about the acousto-electric conversion efficiency, which, in turn, determines the insertion loss of the delay line. For the calculation of both quantities, it is essential to know the charge distribution on the IDT fingers. The numerical method that we used to determine the charge distribution is briefly outlined in the appendix. The results in this sec-tion are all calculated for an ST-quartz substrate where the IDTs are oriented such that the propagation direction (x in Fig. 1) is oriented orthogonal to the crystalline X direction. For the SiO2 layer we assume the material

pa-rameters for fused quartz. All the material data has been taken from [13]. The results have been obtained for split finger transducers, the metalization ratio was 50%, i.e., the finger width equals the width of the gap between the fin-gers. The major design parameter is the thickness of the guiding layer, h (see also Fig. 1). A lot of the following re-sults will be given for layer thicknesses scaled as h/λ where λ denotes the wavelength of the Love wave at the center frequency, which is identical to the electrical period of the IDT. Note that the geometrical finger period equals λ/4 as we are considering a split finger transducer.

A. Static Capacitance Ct

Once the charge distribution is known, we can evaluate directly the capacitance Ctby calculating the total charge

Fig. 3. Capacitance Ct0= Ct/(Nλa) (in pF/mm) versus relative layer

height h/λ for a split finger IDT with 50% metalization ratio for different environment permittivities.

on the transducer and dividing it by the driving voltage. Fig. 3 shows the scaled capacitance C_t0 being defined as C_t0= Ct/(Nλa) where Nλis the number of electric periods (Nλ = l/λ, l = length of the transducer) and a denotes the aperture (= length of finger overlap) of the transducer. Curves are shown for an unshielded device in air (εr,2 = 1), for devices in environments with relative permittivities εr,2= 10 and εr,2= 80 (≈ permittivity of water at room temperature), and for a shielded device. Here and in the following subscripts “2” indicate quantities associated with the environment being sensed in while subscripts “1” refer to parameters of the guiding layer.

For the nonshielded device with air loading, we observe an increase in capacitance with increasing h because the layer permittivity εr,1 is larger than that of air. At about

h = 0.4λ, an asymptotic value is reached. This means that the layer is thick enough such that all the electric field is concentrated in guiding layer and substrate. This saturation also is reached in the other cases. For higher environment permittivities ε2, the curves more and more

approach that of the shielded case. Generally a high capac-itance is not desired as it loads the amplifier and causes an increased noise level in the oscillator. In that respect, the shielded device represents the worst case; however, the value of the capacitance is not depending on the permit-tivity ε2 of the adjacent liquid, which avoids the above

mentioned unwanted sensing effect. It might appear that, in order to achieve that independence, one also could de-sign a device with sufficiently large h such that we are close to the asymptotic value. Large layer thicknesses, however, generally constitute technological problems and, more im-portantly, we are then far away from the optimum height h/λ ≈ 0.18 for maximum mass sensitivity [3], [9]. The acousto-electric coupling efficiency also decreases for large h (see below) which would lead to a large insertion loss of the device.

Next let us consider the influence of electric losses (e.g., due to ionic conductivity) in the liquid. Analytically this can be considered by introducing an imaginary part in the liquid’s permittivity ε2= ε02− jε002, where the relation

with its specific conductivity σ2 is given by ε002 = σ2/ω.

Here ω = 2πf denotes the angular frequency. We re-mark also, that nonconductive liquids show losses at higher frequencies due to polarization losses. The losses gener-ally can be characterized by a loss tangent being defined as tan δ2 = ε002/ε02. By introducing an imaginary part in

ε2, we can numerically calculate the resulting complex

transducer capacitance to obtain a loss tangent for Ct as tan δ =|Im{Ct}/Re{Ct}|. This loss tangent is related to the conductance Gl in the equivalent circuit (Fig. 2): tan δ = Gl/(ωCt).

Fig. 4 shows the resulting loss tangent associated with Ct due to a loss tangent tan δ2 in the liquid, where we

assumed a relative permittivity of ε0r,2 = 80 as real part. Generally tan δ decreases strongly with increasing h. In the limit h→ 0 the tan δ almost approaches tan δ2, which

indicates that, due to the high ε0_r,2, almost the entire elec-tric field would be concentrated in the liquid and not in the substrate. Note that even a moderate loss tangent of Ct could already mean that the conductance Gl reaches the order of the radiation conductance Ga. For exam-ple, for a transducer with Nλ = 50 at around 100 MHz, we typically have radiation conductances in the order of 1 mS (= 10−3Ω−1). For a typical transducer capacitance of 10 pF and a loss tangent of tan δ≈ 0.1, we already would have Gl≈ 0.6 mS. We again note that, with a shielding, this influence of (di)electric losses in the liquid on the IDT admittance is completely eliminated.

B. Radiation Conductance

The radiation conductance Ga also depends on the charge distribution. It is given by [10]:

Ga = ωaΓs|˜σ(β

0)|2

V2

t

, (2)

where Vt denotes the voltage applied to the transducer and ˜σ denotes the two dimensional approximation of the resulting charge distribution in the spectral domain, which can be approximated by the static charge distribution ne-glecting the piezoelectric effect (see appendix). β0 is the

wavenumber of the Love wave at the considered frequency ω: β0= v/ω, where v stands for the phase velocity of the

Love wave. Γsis given by the negative residue of the spec-tral electric Green’s function ˜G(β) at the pole β = β0:

Γs = −Resβ0G(β). ˜˜ G describes the potential due to a

point charge in the substrate/layer interface, and it cor-responds to the nonperiodic, static Green’s function ˜Gs introduced in the appendix; but, it also takes the piezo-electric interaction into account (for further details on the Green’s function concept see, e.g., [14], [10]). Γs as well as the wavenumber β0 have been numerically determined

by methods similar to those described in [15], [16]. One of the major differences in (2) compared to Rayleigh SAWs is

Fig. 4. Influence of the liquid’s loss factor tan δ2 (ε0_r,2 = 80) on

the loss tangent tan δ of the transducer capacitance Ct of a split

finger IDT (metalization ratio = 50%) for different relative layer thicknesses h/λ.

that β0 is frequency dependent corresponding to the fact

that Love waves are dispersive.

To evaluate Γs, one can adapt Ingebrigtsen’s approxi-mation [17] to the Love wave case:

Γs≈ β0G˜s(β0)

κ2

2 . (3)

Here κ2 is the electro-mechanical coupling factor being defined as:

κ2= 2v− vs

v (4)

where v and vs denote the wave phase velocities of the propagating Love wave when the substrate/layer interface is free and metalized (electrically short circuited), respec-tively. Considering (2) and (3), we find that, as in the case of Rayleigh waves, κ2 _{is directly related to the radiation}

conductance. However, if we want to compare the radi-ation conductances for the shielded and the nonshielded case, we must not consider κ2_{, only. Actually, ˜G}s_(β

0) as

well as |˜σ(β0)|2/Vt2 can be quite different for these two cases.

In Fig. 5 we show the dependence of κ2 on the relative layer thickness h/λ for different environment permittivities εr,2. It suggests that the optimum thicknesses for acousto-electric power conversion lies in the range from about h/λ = 0.08 (nonshielded, air-loaded case) to h/λ = 0.14 (shielded case). The maximum value of κ2 _{is about 35%}

lower in the shielded case compared to the nonshielded, air-loaded case. However, if we calculate Ga at the center frequency ωcof the transducer (Ga,c= Ga(ωc)), we obtain the result shown in Fig. 6. The axes scaling considers the fact that Ga,c depends on the ratio h/λ but also linearly increases with frequency [see also (2)]. The optimum values of h/λ are now lying closer to each other, and the reduction

Fig. 5. Coupling factor κ2 _{versus relative layer thickness h/λ for}

different environment permittivities.

Fig. 6. Scaled radiation conductance at center frequency G0a,c = Ga,c× λ/(N_λ2a) versus relative layer thickness h/λ for a split finger

IDT with 50% metalization ratio for different environment permit-tivities.

of the optimum value for the shielded case is only about 15% compared to the nonshielded, air-loaded case. This difference compared to the result of κ2 _{essentially can be}

explained by the increased charge density in the shielded case (corresponding to the increased capacitance).

Finally we remark that, for the calculations of Ga, we assumed the adjacent liquids feature negligible viscosity. If that is not the case, the Love wave becomes damped, yielding an additional reduction of the radiation conduc-tance. This phenomenon is the same for the shielded and the nonshielded case; hence, it is not stressed at this point (its impact is discussed with experimental results in Sec-tion V). In the calculaSec-tions, a nonzero viscosity would lead

to a complex propagation constant β0, and the associated

Γswould be complex-valued, in general, which means that we would have to take its real part in (2).

C. Summary of Resulting Design Criteria for h/λ

There are three main objectives that have to be consid-ered in the choice of the ratio h/λ for a shielded device:

•The mass sensitivity determining the sensitivity of the sensor, which has an optimum at about h/λ = 0.18 as it has been shown elsewhere [3], [9]. This value is prac-tically independent from the fact whether the device is shielded or not.

•The acousto-electric coupling efficiency should be op-timally chosen in order to minimize the insertion loss (Fig. 6).

•The capacity Ctmust not be too high in order to min-imize the load for the electronic circuitry (Fig. 3). The optimum choice of h/λ considering the last two items depends to a large extent on characteristics of the electronic amplifier such as input and output impedances, maximum output current that can be driven, noise char-acteristics, and achievable gain [18].

V. Experimental Results

To evaluate the validity of the analysis and the resulting design rules, devices featuring split finger transducers with 50% metalization ratio and an electric period of λ = 52 µm have been fabricated. The number of electric periods and the aperture were chosen to be Nλ= 50 and a = 2.6 mm, respectively. The goal for the thickness h of the PECVD SiO2 layer was to obtain about 6 µm; for the fabricated

devices it has been measured to be h = 5.7 µm. Hence, the resulting ratio h/λ is about 0.11. Regarding the radiation admittance (Fig. 6) we are thus slightly above the opti-mum thickness for the shielded as well as the nonshielded case, but we are still below the optimum for maximum sen-sitivity h/λ = 0.18 [3], [9]. In that respect, this thickness represents a trade off between these two criteria. Some of the devices have been provided with an aluminum shield-ing metalization with a thickness of about 0.6 µm. This allowed the comparison of (otherwise identical) shielded and nonshielded devices. For the measurements with the shielded devices, the shield has been grounded and the ap-plied voltage has been taken symmetrical with respect to ground (as it has been assumed for the analysis results presented above).

According to Fig. 3, the expected scaled transducer ca-pacitance for h/λ = 0.11 varies between C_t0= 0.08 pF/mm for the nonshielded, air-loaded case to C_t0= 0.113 pF/mm for the shielded case. For Nλ = 50 and a = 2.6 mm this transforms into capacitances Ct= 10.4 pF and Ct= 14.56 pF, respectively, leading to an increase of about 40% for the shielded case compared to the nonshielded, air-loaded case. The measurements below will indicate an even higher increase because the IDT bus bars connecting the

fingers on each side of the transducer also are covered by the shield and/or the liquid (if any) which further increase the input capacitance of the transducer (this also holds for the lines connecting the bus bars with the bonding pads be-cause they also are partially covered by the shield/liquid). For our devices these additional increases amount to val-ues in the order of the “pure” transducer capacitance Ct because the bus bars and the connection lines are fairly wide (400 µm in our case) compared to the IDT fingers in order to keep the series resistance Rssmall. The resulting increase of the input capacitance for the shielded device (compared to that of the nonshielded, air-loaded device) is about 140%.

Fig. 7 shows the measured input admittances of the IDTs for the shielded and nonshielded devices around the center frequency. To illustrate the effects of liquid loading on the device, we measured them air-loaded, water-loaded, and loaded with a highly viscous 95% glycerol-water solu-tion (solid, dashed, and dotted lines, respectively).

In the imaginary parts we see essentially the change in the input capacitance and, around the resonance, the con-tributions from Ba. Note that, apart from the choice of the zero position, the scaling for the abscissae is equal to allow for a fair comparison between the shielded and the non-shielded case. It can be seen that the input capacitance shows large variations according to the different permit-tivities of the loading substances while it stays the same in the shielded case. The imaginary part is the dominat-ing part in the input admittance, so changes in the input capacitance would lead to an unwanted sensitivity of the sensor system with respect to the permittivity of the liq-uid. The observed changes in Ba are related to the changes in the radiation conductance Ga, which will be discussed below.

Considering the real parts, we first observe a global shift between the curves for air and liquid loading for the nonshielded device. Outside the frequency region where acoustic waves are excited, Re{Yin} should be mainly de-termined by the loss resistance Rs(assuming that the loss conductance Gl can be neglected). Because we are con-sidering the real part of the input admittance, being ap-proximately given by ω2_C2

tRs (neglecting all components except Rsand Ct, and assuming Rs 1/ωCt, see Fig. 2), we find that this shift is essentially due to the change in the capacitance Ct. However, we note that even Rs itself de-pends on the permittivity of the adjacent substance. This is due to the fact that Rs is only a lumped element rep-resentation of the resistive electrode losses, which can be more accurately described by resistances in a distributed RC network (see also [19]) that represents the IDT fingers as well as the bus bars and the connection lines to the bonding pads of the device. Even though the distributed resistance (characterizing the electrode losses) in this RC network is constant, the real part of the input impedance (corresponding to Rsin our equivalent circuit) will depend on changes in the distributed capacitances.

The relative height of the peak at the center frequency corresponds to Ga,c; this value changes only slightly under

Fig. 7. Input admittances Yinof the IDTs for the shielded (right) and nonshielded (left) devices around the center frequency for air-loading

(solid lines), water-loading (dashed lines), and loaded by a 95% glycerol-water solution (dotted lines).

water loading. This is in accordance with Fig. 6 (note that we have h/λ = 0.11). Previous experiments with devices featuring h/λ < 0.05 showed more serious reductions in Ga, which also is confirmed by Fig. 6. For the shielded device, we would expect no influence due to the water’s permittivity (as confirmed by the constant capacitance). However, the measured curves indicate a small difference between the curves for water and air loading also for the shielded device. This difference can be attributed to the effects of the water’s viscosity. Viscous substances show a mechanical coupling with the Love wave causing a change in the propagation constant and introducing damping [8]. These effects lead to a corresponding change in the radi-ation conductance. When using the Love wave device as a viscosity sensor, these are, of course, wanted effects. For the nonshielded device, both the water’s permittivity as well as its viscosity lead to a change in Ga. To demonstrate this effect of the viscosity, we also loaded the devices with a 95% glycerol-water mixture featuring a very high viscos-ity (347.5 cP) compared to that of water (0.89 cP, both values are valid at a temperature of 25◦C). The associated high damping of the wave leads to serious reduction of Ga. Eventually we remark that the center frequency is dif-ferent for the shielded and the nonshielded device. This is due to the mass loading by the Al-film used for shield-ing (after all, the intended sensshield-ing effect relies on the fact that the phase velocity of the Love wave is sensitive to mass loadings). As mentioned above, viscous loading, apart from introducing a damping, also changes the propagation

con-stant (and hence the phase velocity) which also leads to a shift of the center frequency. Indeed it can be observed that, in the shielded as well as in the nonshielded case, the peaks in Re{Yin} for water loading and loading with the 95% glycerol-water solution are shifted to lower frequencies where the effect is more pronounced for the latter solution (according to its higher viscosity).

To illustrate the capabilities of the analysis more in de-tail, let us compare the calculated frequency characteris-tics for the radiation admittance with the measured ones. A crucial point in the calculation is the usage of the proper material constants. Although the substrate (bulk) param-eters are well known, the relevant paramparam-eters for thin films (PECVD SiO2in our case) are less well known. In the

cal-culation of the results shown in Section IV, we used the material parameters for fused quartz, that can be expected to represent a reasonable approximation for PECVD SiO2.

The film parameters relevant for pure Love wave propaga-tion are the permittivity ε, the mass density ρ and the shear modulus µ. To obtain more accurate parameters for the fabricated PECVD SiO2 thin film, we used a fitting

procedure (similar to that described in [3]) to determine µ while ρ and ε were taken to be the values for fused quartz (ρ = 2200 kg/m3 _{and ε = 3.74 ε}

0). For the fitting

we used measured values of the phase velocity for differ-ent frequencies, which have been obtained by determin-ing the center frequency and the neighbordetermin-ing transmission zeros of the transducer and relating them to the corre-sponding wavelength [3]. The resulting fitted value for µ

Fig. 8. Calculated and measured frequency characteristics Ga(f )

around the center frequency for a nonshielded device and a device shielded by an aluminum layer (in both cases split finger IDT with 50% metalization ratio). The latter also leads to a shift in the center frequency (see text).

was 2.505× 1010 _N/m2 _{(in contrast to the value for fused}

quartz: 3.12× 1010 _N/m2_).

Fig. 8 shows the measured and calculated frequency de-pendence of Ga where the measured characteristics have been obtained from the measured input impedance after subtracting a constant value Rs (which has been deter-mined from the real part of the input impedance at fre-quencies with zero transmission, i.e., where Ga = 0). To account for the nonvanishing thickness of the aluminum layer on the shielded device, it had to be considered as an additional layer in the calculation. Because the mechani-cal thin film parameters of the aluminum layer also were unknown, we used the parameters of bulk aluminum and fitted the aluminum layer thickness until the proper shift of the center frequency had been reached. The resulting fitted thickness for the Al-layer was 0.56 µm compared to the measured value of 0.7 µm. We note that the peak val-ues for Ga,c taken from Fig. 6 still predict the measured values for Ga,c with an accuracy of about 5%, although Fig. 6 has been calculated for the parameters of fused quartz and the mass loading of the aluminum has been ignored in the shielded case. The obtained results show very good agreement confirming that the presented anal-ysis methods provide valuable tools in the design of Love wave sensors.

VI. Conclusions

Thanks to their shear polarization and high sensitivity, Love wave devices are highly suited for liquid sensing ap-plications. To enable optimum sensor performance, electric interaction of the device with the liquid being sensed has to be avoided. It has been shown that this can be done

most efficiently by applying a shielding metalization on the device-liquid interface. The impact of this shield on the device characteristics has been outlined, and design guidelines deduced from numerical results have been pro-vided. The suitability of the shield and the validity of the provided design rules have been demonstrated by experi-mental results.

Acknowledgments

The authors thank Dr. A. Venema for the provided in-spiration and useful discussions. Furthermore the fabri-cation of the test devices by the ICP group of DIMES (especially thanks to Dr. P. M. Sarro, C. de Boer, and J. Groeneweg) is gratefully acknowledged. We also thank Dr. J. F. L. Goosen for discussions on some aspects of this work.

Appendix Charge Distribution

For the calculation of the charge distribution, the piezo-electricity can be neglected, especially as we are consider-ing a low couplconsider-ing substrate. Furthermore, we used a two-dimensional approximation by assuming that the charge density on a finger does not significantly vary along co-ordinate y (see Fig. 1). To improve the efficiency of the method, we adopt the infinite array approximation and calculate the charge distribution for an infinite periodic array of fingers. The related approximate charge distribu-tion for the finite structure is then obtained by windowing the infinite array solution. For Rayleigh SAW IDTs, closed form solutions for the charge distribution on infinite peri-odic finger arrays can be found [20]; however, this is not possible for the more general structure considered here. To determine the periodic charge distribution numerically, we use the “Method of Moments” [21], which has been intro-duced into the analysis of microacoustic waves about two decades ago [14], [22]. Summarizing the approach is as fol-lows.

We expand the charge distribution on one IDT finger in a finite sum of N rectangular pulse functions P (x):

σf(x) = N X k=1 αkP (x− xk), where P (x) = ( N/w, |x| < w/(2N) 0, else . (5)

Here w denotes the finger width, xk = −w/2 + (k − 1/2)(w/N ) stands for the center position of the kth pulse function [see Fig. 9(b)], and αk are the expansion coeffi-cients to be determined.

Next we write the electric potential φ(x) in the finger plane z = 0 as a convolution of a so-called periodic Green’s function Gs

Fig. 9. (a) Finger configuration and connection to voltage source. (b) Real charge distribution σ(x), its approximation on a single fin-ger σf(x), and point charge array δp(x) generating Green’s function Gp(x). (c) Potential φ(x) and periodic Green’s function Gsp(x).

finger, σf, given above [see also (6)]. Gsp(x) is defined as the potential (in z = 0) due to a periodic array of alternating point charges δp(x) =Pk(−1)

k_{δ(x− kp) in the plane z =} 0 (see Fig. 9). The superscript s indicates that we are considering a static quantity neglecting piezoelectricity.

We enforce the boundary condition for the potential on the finger metalization: φ(x) = Vt/2 (Vt denotes the applied transducer voltage). Note that it is sufficient to enforce this condition on a single finger (in this case one lying on a positive potential Vt/2) since the boundary con-ditions on the other fingers will be fulfilled automatically thanks to the application of the periodic Green’s function.

Due to the approximation (5) for the charge distribu-tion, this boundary condition can be fulfilled only in a weighted sense. This means that we multiply φ(x) = Vt/2 on both sides by a set of linearly independent testing functions and integrate over x. We employ the so-called Galerkin approach in which the set of testing functions is chosen to be equal to the set of charge expansion functions

P (x− xk). This yields: +_∞ Z −∞ dxP (x− xk) × +_∞ Z −∞ dx0Gs_p(x− x0) N X l=1 αlP (x0− xl) | {z } φ(x) = Vt 2, (6)

where k = 1, . . . , N . Interchanging summation and inte-gration, it can be seen that this represents a linear system of equations for the expansion coefficients, which can be written in compact form:

N X l=1 Aklαl= Vt 2, k = 1, . . . , N. (7) To determine the matrix elements Akl, we have to calculate a double integral as it appears in (6). This can be done in a very efficient manner in the Fourier (spectral) domain being defined by (spectral domain quantities are indicated by a tilde) FT{f(x)} = ˜f (β) = +∞ Z −∞ f (x)ejβxdx. (8)

Taking into account that the spectral periodic Green’s function ˜Gs

p is given by the spectral nonperiodic Green’s function ˜Gs_{being sampled with a train of Dirac delta} func-tions located at βm= π/p+m2π/p(m =−∞, . . . , ∞) [23], [24], the interaction elements Akl can be written as:

Akl= 1 p +_∞ X m=−∞ ˜ P (−βm) ˜Gs(βm) ˜P (βm)e−jβm(xk−xl). (9) This infinite series can be truncated, then efficiently eval-uated using the fast Fourier transform (FFT) algorithm, which provides all required Akl elements as the result of a single FFT run [25]. To perform this calculation we need the spectral (nonperiodic) Green’s function ˜Gs_{(β) giving} the potential (in the plane z = 0) due to a point charge at x = 0. With these methods that also have been used for Rayleigh wave structures [10], we obtain the following closed form expressions:

˜ Gs(β) =    1 |β| εp+ε21+ε1/ε2 tanh |β|h_{1+ε2/ε1 tanh |β|h}
, no shield 1 |β|(εp+ε1coth|β|h), shielded . (10) Here ε1and ε2 denote the permittivities of the layer

ma-terial and the medium above the sensing surface, respec-tively. εp can be obtained by εp =

p

ε11ε33− ε213 where

the εij denote elements from the permittivity tensor of the anisotropic substrate.

Once the solution for the expansion coefficients αk has been obtained, an approximation for the charge distribu-tion on a finite number of fingers can easily be set up. We

also note that the approach works in the same manner for split fingers; in this case the expansion and testing func-tions are chosen such that they cover only that part of the range [−w/2, +w/2] (see Fig. 9) that is metalized.

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Bernhard Jakoby (S’91–A’95) was born in

Neuss, Germany, in 1966. He obtained the Dipl.-Ing. (M.Sc.) degree in communication engineering and the Ph.D. degree in electri-cal engineering from the Vienna University of Technology, Austria, in 1991 and 1994, respec-tively.

From 1988 to 1990 he worked as a tu-tor (teaching assistant) at the Institute of Communication- and Radio-Frequency Engi-neering and from 1991 to 1994 he worked as a research assistant at the Institute of General Electrical Engineering and Electronics at the Vienna University of Technology. In the sequel he obtained an Erwin Schr¨odinger grant from the Austrian Fund for Scientific Research (FWF) for perform-ing research on the electrodynamics of complex media at the Depart-ment of Information Technology at the University of Ghent, Belgium. In 1996 he joined the Electronic Instrumentation Laboratory at the Delft University of Technology, Delft, The Netherlands, to work on the development of micro-acoustic biosensors in the course of a Euro-pean research project. Dr. Jakoby is a member of IEEE. His research interests are focused on numerical and analytical methods, complex media in electromagnetics and acoustics, and microacoustics and its applications in general.

Michael J. Vellekoop was born in

Amster-dam in 1960. He received the B.Sc. degree in physics from the HTS Dordrecht, The Nether-lands, and the Ph.D. degree in electrical en-gineering from the Delft University of Tech-nology, Delft, The Netherlands, in 1982 and 1994, repsectively.

From 1982 to 1984 he stayed with the Royal Netherlands Naval College as a reserve officer, after which he joined the Electronic Instrumentation Laboratory at the Delft Uni-versity of Technology to work in the field of acoustic wave sensors. In addition, from 1988 to 1996 he was man-aging director of Xensor Integration B.V. being involved in the de-velopment and the production of silicon sensors and actuators. Cur-rently he leads the Physical Chemosensors and Microacoustic Devices Group of the Electronic Instrumentation Laboratory, where he holds the position of an associate professor. His recent research activities have been in the areas of microacoustic sensor systems for gas and liquid sensing applications, solid state sensor technology, and physi-cal chemosensors.