Anal. Chem. 1003, 65, 352-362
352
Interdigital Capacitance and Surface Acoustic Wave Sensors David C. Stone and Michael Thompson' Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 1A1,Canada
The affects of the water content of sample vapors and the dlelectrlc constant of a surface fllm on surface acoustk wave sensor performanceare examlned wlth respect to dgnal n o h and the eMrlcal propetilesof the Interdlgltaltransducer( IDT) electrodes. The different mechanisms by whlch a surface fllm can affect SAW sensor response are reviewed before conslderlnghow the fllm dlelectrlc constant may be Important. ThetotalstatkcapacttanceotanIDTkdeocrlbedtheoretlcalty, and the effect of dkrepancles In publlshedequations for tMs discussed. The effect of dlelectrlc constant for a angle IDT with a contactlng surface medium Is estlmated Wing the equlvalent electrlc clrcult, and the results are applled to a SAW delay-line. The value of capacltatlve componentsIn the electrlcal clrcult of a SAW delay llne oscillator Is also demonstrated to have a profound effect on SAW senor response.
interaction of its dipole (or induced dipole) with the electric potential wave accompanying the acoustic wave through the piezoelectric substrate. It was thought that this latter effect would be negligible in comparison to mass, viscoelastic, and conductance effects. A second mechanism exists, however, through which the dielectric constant of an adsorbed species or coating may affect sensor response, namely by changing the static capacitance of the interdigital transducers and hence the response of the sensor circuit as a whole. We present here the results of further studies made in an attempt to clarifyour earlier observations. Experiments were performed to investigate the role of the water content of the sample vapor on noise and stability. These were followed by experiments to determine the effect of the dielectric constant of a contacting film on the IDTs as well as the influence of electrical circuit properties. In order to provide the necessary theoretical background, we first review the effects of different types of layers on SAW devices before discussing the role of the electrical properties of the IDTs.
INTRODUCTION
THEORY
Surface acoustic wave (SAW) devices have been employed as chemical-sensingdevices since the original work of Wohltjen and Dessy demonstrated their utility for this type of application.'-3 Since then, SAW sensors have been applied to a variety of measurements, both chemical and A great deal of work has been directed toward determining the mechanisms of sensor response for different conditions such as conducting surface films or viscoelastic polymeric coatings. The results have shown the complexity of the interactions between the acoustic wave, the surface coating, and the analyte of interest. A study of the literature together with anecdotal evidence, however, suggests that our understanding of these mechanisms is still incomplete. Different groups have obtained apparently contradictory results,Bsgwhile theoretical sensitivities are not always obtained in practice and experimental resulta are not always as predicted. In an earlier publication10 we reported that anomalous frequency shifts may sometimes be observed followinginitial exposure of a SAW device to sample vapor. It has also been found that baseline noise may sometimes be worse following an adsorption cycle. These results were attributed to the sample vapor affecting the interdigital transducers (IDTs) of the SAW devices since, in the experiments where such shifts were observed, the IDTs were uncoated and fully exposed to the gas stream. It was not clear, however,what the mechanism for this might be. Initial discussion suggested that finite surface conductance effects could be responsible, together with the dielectric constant of the adsorbed species through
Background. More detailed reviews of the theory and application of SAW chemical sensors can be found elsewhere.*-'Jl For our current purpose, it is sufficient to note that surface acoustic waves may be generated by applying an alternating electric potential across a pattern of interlaced metal electrodes (the interdigital transducer or IDT) fabricated on a suitable piezoelectric substrate such as quartz or lithium niobate. SAW chemical sensors work by virtue of the fact that there are a number of physical parameters that can cause a perturbation of SAW propagation velocity ( v ) which in turn can be monitored by velocity measurements or changes in frequency, phase, or amplitude of an electrical circuit containing a SAW device. This perturbation can be expressed after Ricco et al.12 as
(1) Wohltjen, H.; Dessy, R. Anal. Chem. 1979, 51, 1458-1464. (2) Wohltjen, H.; Dessy, R. Anal. Chem. 1979, 51, 1465-1470. (3) Wohltjen, H.; Dessy, R. Anal. Chem. 1979, 51, 1470-1475. (4) Bastianns, G. J. In Chemical Sensors; Edmonds, T. E., Ed.; Blackie: Glasgow, UK, 1988; pp 295-319. (5) Ballantine, D. S.;Wohltjen, H. Anal. Chem. 1989,61,704A-715A. (6) Fox, C. G.; Alder, J. F. AnaZyst 1989, 114, 997-1004. (7) Nieuwenhuizen, M. S.; Venema, A. Sem. Mater. 1989,5,261-300. (8)Martin, S. G.; Frye, G. C. Appl. Phys. Lett. 1990,57, 1867-1869. (9) Bartley, D. L.; Dominguez, D. D. Anal. Chem. 1990,62,1649-1656. (10) Thompson, M.; Stone, D. C.; Nisman, R. Anal. Chim. Acta 1991, 248, 143-153. 0003-2700/93/0365-0352$04.00/0
A ~- -[-Am 1 - av v0
v0 am
+ -Ac av + -A€ av + -A0 av + ac
ae
aa
a+
T+
where vo is the unperturbed wave velocity, m is the mass, c is the stiffness, e is the dielectric constant, a is the conductivity, T is the temperature, and p is the pressure. Under normal operating conditions, it has in the past been assumed that the contributions from such parameters as stiffness, conductivity, and relative permittivity are negligible in comparison to the effect of changes in surface mass, while the effects of temperature and pressure have been reduced by operating under conditions of constant T and p and/or use of a reference SAW device to provide compensation. It is possible, however, to exploit any or all of these parameters to produce a SAW chemical sensor. In the followingsections, we review the effect of different types of surface film on the frequency of SAW delay line oscillators. This is followed by a discussion of the electrical properties of the IDTs, particularly with respect to capacitance. (11) Wohltjen, H. Sens. Actuators 1984,5, 307-325. (12) Ricco, A. J.; Martin, S.J.; Zipperian, T. E. S e a . Actuators 1985, 8, 319-333. 0 1993 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65, NO. 4, FEBRUARY 15, 1993
Organic Coatings. Wohltjenll after Auld13 has given an equation for the frequency shift produced by the deposition of a soft organic polymeric film onto a SAW device:
where Af is the frequency shift,f o is the unperturbed oscillation frequency, kl and k2 are material constants, h is the film thickness, p' is the film density and 1.1' and A' are the film shear modulus and first Lam6 constant, respectively. For ST-cut, X-propagating quartz devices, kl and k2 are -8.7 X 10-8 and -3.9 X 10-8m%/kg,respectively.14J5 Wohltjen" has pointed out that for certain types of polymers the second term on the right-hand side of eq 2 becomes negligible when the ratio 4p'/vo2 is less than 100, yielding the simplified expression Af = (k, + k2)f,,%p' (3) which predicts a linear decrease in Af with increasing mass per unit area. It should be noted that the derivation of eqs 2 and 3 assumes that the film is lossless, nonconducting, nonpiezoelectric, isotropic, and thin relative to the acoustic wavelength X (h < 0.2% A). The validity of these equations has been demonstrated for poly(methacry1ate) films up to 2.1 pm thick," Langmuir-Blodgett (LB) films of tetrakis(cumy1phenoxy)phthalocyaninesup to 65 1ayem,16and various other LB films up to 70 layers.17J8 Other films,however, have not shown agreement over the same ranges," while for some films that showed a linear decrease in Af with increasing thickness, the mass sensitivity was systematicallylower than predicted.14 Other workers have also found deviation from eqs 2 and 3, including frequency shifts in the wrong direction.8JQ-22 These results may be attributed to changes in film viscoelastic properties, acoustic loss into the film, and sheet conductivity effects. In addition, it is important that the film properties should conform to the conditions assumed in the derivation of eqs 2 and 3; the properties of the films used in the experiments reported above have not always been known. The effect of vapor sorption into the film is obviously important since the majority of SAW sensing applications described to date exploit this process. Vapor absorption will result in both film volume and modulus changes. Frye et al.23 have suggestedthat positive frequency shifts at low vapor concentrations for a methanol/polyimide system may be due to either film stiffening or changes in film thickness on swelling. They further suggested that at higher methanol vapor concentrations plasticizing effects could make a significant contribution to the observed response. Martin and Fry@subsequently employed a Maxwellian model to describe (13) Auld, B. A. Acoustic Fields and Waves in Solids; Wiley Interscience: New York, 1973; Vols. 1 and 2. (14) Wohltjen, H.; Ballantine, D. S.; Jarvis, N. L. In Chemical Sensors and Microinstrumentation. Murray, R. W., et al., Eds.; ACS Symp. - - Ser. 1989,403,157-175. (15) Grate, J. W.; Snow, A.; Ballantine, D. S.; Wohltjen, H.; Abraham, M. H.; McGill, R. A.; Sasson, P. Anal. Chem. 1988,60,869-875. (16) Snow, A. W.; Barger, W. R.; Klusty, M.; Wohltjen, H.; Jarvis, N. L. Langmuir 1986,2,513-519. (17) Wohltjen, H.; Snow, A. W.; Barger, W. R.; Ballantine, D. S. IEEE Trans. Ultrason. Ferroelec. Freq. Control 1987, UFFC-34, 172-178. (18) Grate, J. W.; Klusty, M. Anal. Chem. 1991, 63, 1719-1727. (19) Dickert, F. L.; Bertlein, G.; Mages, G.; Bulst, W. E. Adu. Mater. 1990,2,420-422. (20) Ballantine, D. S.; Wohltjen, H. IEEE Ultrasonics Symp. Proc. 1988, IEEE Cat. No. 88CH2578-3 559-562. (21) Roberta, G. G.; Holcroft, B.; Barraud. A.; Richard, J. Thin Solid Films 1988,160,5340. (22) Grate, J. W.; Klusty, M.; McGill, R. A.;Abraham,M. H.; Whiting, G.; Andonian-Haftvan, J. Anal. Chem. 1992,64,610-624. (23) Frye, G. C.; Martin, S. J.; Ricco, A. J. Sens. Mater. 1989,1,335357.
353
the effects of temperature and plasticization on response for such systems. Bartley and Dominguezgdeveloped expressions for examining the effects of film stiffness on sensor response. Their results indicated that positive frequency shifts were unlikely to be caused by film stiffening effects since these should be considerably smaller than the mass loading effect. Most recently Grate et al.22 described a model based on partition coefficients as a measure of polymer mass loading and thermal expansion as a measure of polymer swelling. Their results indicate that swellingeffects can be significantly greater than mass-loading effects when the polymer and vapor densitiesare similar,and that this can be explained by polymer modulus changes. Other factors affecting SAW sensor response have been acknowledged but little investigated since the effects are believed to be minor in comparison with those already mentioned. Among these latter effects is the influence of the dielectric constant of the contacting medium.23-25 This can readily be seen since the dielectric constant is related to both the dipole moment and the polarizability (ease with which a dipole may be induced by an external field or other dipole) through the Debye equation (4)
where Nu = number of molecules per unit volume, a! = polarizability, p~ = dipole moment, cg = permittivity of free space, k = Boltzmann constant, T = absolute temperature, and cr = relative permittivity (dielectric constant). There is the possibility of coupling between a dielectric medium on the SAW device surface and the electric potential wave accompanying the SAW through the piezoelectric substrate through realignment of dipoles and/or induced dipoles with the changing electric field. This is feasible since the time scale for molecular reorientations and polarization effects is on the picosecond time scale, well within the frequencyranges typically used for SAW sensors. This is illustrated by the recent observation of Baer and F1o1-y~~ that liquids with a high dielectric constant show significant attenuation of leaky SAW waves through electrical dissipation. This will produce some perturbation of the SAW velocity, although the size of this effect is probably very small in comparison to the effects described above. Conducting Surface Layers. A SAW propagating through a piezoelectricmedium is accompanied by an electric potential wave, which can be affected by an applied electric field or the properties of a conducting or semiconducting surface layer. Alder2Idescribed the effect of such a layer and showed that both amplification and attenuation of the SAW could result, depending on the charge carrier drift velocity in the conducting layer: If this is less than the phase velocity of the acoustic wave then attenuation occurs; if it is greater, amplification occurs. This effect was further discussed by DattaZ8and Lec et al.29and exploited by Ricco et al.l293o to form a SAW chemical sensor using a semiconducting phth(24) Nieuwenhuizen, M. S.;Barendsz, A. W.; Nieuwkoop,E.; Vellekoop, M. J.; Venema, A. Electron. Lett. 1986, 22, 184-185. (25) Martin, S. J.; Ricco, A. J.; Ginley, D. S.; Zipperian, T. E. IEEE Trans. Ultrason. Ferroelec. Freq. Control 1987, UFFC-34, 142-147. (26) Baer, R. L. and Flory, C. A. Some Limitations on the use of Leaky SAW Mode Sensors in Liquids. Presented at the IEEE Ultrasonics Symposium, Lake Buena Vista, FL, December 1991. (27) Alder, R. IEEE Trans. Sonics Ultrason. 1971, SU-18, 115-118. (28) Datta, S. Surface Acoustic Waue Deuices; Prentice-Hak Englewood Cliffs, NJ, 1986. (29) Lec, R.; Vetelina, J. F.; Falconer, R. S.; Xu, Z. IEEE Ultrason. Symp. h o c . 1988, IEEE Cat. No. 88CH2578-3, 585-589. (30) Martin, S. J.; Ricco, A. J.; Ginley, D. S.; Zipperian, T. E. IEEE Trans. Ultrason. Ferroelec. Freq. Control 1987, UFFC-34, 142-147.
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ANALYTICAL CHEMISTRY. VOL. 65. NO. 4, FEBRUARY 15, I993
alocyanine fh. Conductivity effects have also been noted by Nieuwenhuizen et al.31 Rigid, Nonconducting Films. Sensors have been reported that employ insulating metal oxide and silica films. The latter were formed theSAW sensor being used as a microbalance to obtain nitrogen adsorption isothermsfor the processedgel.32-36 In this case, the response of the device was given as Af/fo = K A V I U =~-KCJ&
(5)
where 6 is the number of adsorbed molecules per unit area, c. is the mass sensitivity of the device (= 1.3 X 1o-B cm2s/g for quartz13), m is the mass of one molecule of the adsorbing species, and I = 1 if the entire surface area of the device is covered. Thin equation assumes that only the mass term in eq 1is significantunder the conditions used. Equation 5 can he extended to the case of a rigid, thin nonpiezoelectric nonconducting film by noting that the term rn6 is the added mass per unit area and can be replaced by hp' where h and p' are the film thickness and density respectively, i.e.
(6) Contact withaLiquid Layer. Roedererand Bastiaans37 first described the use of a SAW sensor in contact with a liquid for a microgravimetric immunosensor, although the type of the acoustic wave propagating under the conditions used has heen disputed by Calabrese et al." The nature of the interaction between the acousticwave and the liquid layer willdependonthethicknessofthelayerrelativetotheacoustic wavelength. The attenuation of Rayleigh waves by liquid helium has beenstudied by CheekeandMorisseau." Rayleigh waves have both longitudinal and transverse components. For the case of a liquid in contact with the surface, the longitudinal component couples to the liquid through the liquid viscosity while the transverse component couples through an acoustic mismatch (partial transmission due to adifferenceinacousticimpedancebetween thesubstrateand the liquid). The new mode of propagation is known as a leaky Rayleigh wave. The relative contrihutions of these two mechanisms depend on the liquid viscosity and the thickness of the liquid layer. If the layer is very thin the attenuation can he quite moderate and a Rayleighwave can still propagate, but for fluid layers thicker than a few acoustic wavelength the losses are large and can result in total attenuation of the Rayleigh wave.38 This can be seen clearly in the adsorption isotherms reported by Cheeke et al." for helium where the measured attenuation at 720 MHz was less than 0.1 dB/cm up to near the saturation vapour pressure, where there was a sharp increase due to multilayer build-up, i.e. the presence of a liquid layer on the surface of thickness approaching the acoustic wavelength. When the layer is thin (as in the case of adsorbed vapour molecules on the device surface) eq 5 or
Fbwa 1. Construction of an lnterdlgltaltransducer. S y m W e b w prameurS used In eqs 7-13.
Af = -IcJ:hp'
.
"" . (39)Cheeke, J. D.N.; Morisseau. P. J. Lou Temp. Phya. 1982,46, 319-330. (40) Cheeke, J. D. N.: Moriaeeau, P.; Poirier, M. Phys. Lett. A 1982, &SA. 359-362. l "
+FIwm 2. Eqdvalsnt electrical ckcm fa an interdigital banaducsr actlng as an awustlc transmmer.
6 can be applied since perturbation of the SAW velocity is then largely through the mass-loading effect." Characterization of a n ID". The key to the operation of SAW devices is the IDT (Figure 1). This can act as both a transmitter (convertingelectrical energy into acoustic)and a receiver. In characterizing the electrical properties and operation of IDTs we therefore have to consider both the electrical and acoustic properties. These can be descrihed either in terms of the impedance (2) or the admittance (Y= l/a,both of which are functions of frequency. Although it is normal to measure impedance, it is often more convenient toconsidertheadmittamein anydiscussion. Thisadmittance is due to the ordinary capacitance of the IDT, which is independent of the acoustic properties, and an acoustic admittance Y. where the subscript "a" denotes ita acoustic origin. This results from the interaction of the IDT with the acoustic waves generated by it; an ac potential applied across the fingers of the IDT results in the generation of acoustic waves which, as they propagate away from the IDT, induce currents in the other electrodes. If the substrate on which the IDT was manufactured was nonpiezoelectric, it would act solely as a capacitor. The electrical circit representation of the IDT of Figure 1when acting as a transmitter is shown in Figure 2. The acoustic admittance is complex, the real part being the radiation conductance G. and the imaginary part being the radiation susceptance B. V and R. are the source voltage and resistance, respectively, and C , is the capacitance of the IDT which gives rise to the electrical admittance j2.rfC.~. Calculation of Interdigital Capacitance. The calculation of the capacitance of an interdigital electrode array in of general importance in the field of micmelectronic device fabrication as well as in the design of interdigital capacitative gas sensors. This can be achieved by considering the contributionsfromthesurfacechargeon theeleetrodesurface against (a) the crystal, (b) the medium in contact with the device surface, and (c) any second medium present between the electrode fmgers. In general for two pardel plate electrodes separated by a dielectric medium, capacitance
ANALYTICAL CHEMISTRY. VOL. 65. NO. 4, FEBRUARY 15, 1993
-5
increases with increasing dielectric constant and plate area and decreases with increasing separation; more polar substances have higher dielectric constants. This simple expression for capacitance has to be modified to take into account the elliptical field lines resulting for the case of the parallel, coplanar electrodes forming an IDT. S c a ~ p l described e~~ the calculation of the capacitance of an interdigital array based on the capacitance per unit length for two identical infinite coplanar parallel strips42 with nearedge distance 2a and far-edge distance 26 (in MKS units)
c, = t K[(1-P)”2] K[rl
(7)
where if the substrate has a dielectric constant tl and the medium above it has dielectric constant €2 then t = (el + t2)/2, K[m] is a complete elliptical integral of the first kind43 and r = alb. It is assumed for an interdigitated pattern that the far-edge distance lies in the center of the conductor strips (see Figure 1for the definition of these geometrical parameters). In this case the total capacitance (neglectingthe ‘end effect” arising from the lower potential distribution on the outermost fingers) is given by C T = (N-l)C,W (8) where N is the number of finger pairs and W is the finger overlap. When N is large this can he further simplified by writing (N-1)IN. Similar calculationshave been given by Auld13 based upon the earlier work of Engan.a This leads to a different form of eq 7, however:
c, = (to+ tp’)
K[kl K[(1- k*)“2]
(9)
where
is the permittivity of free space, tpT is the zero-stress permittivity, and a = d/26 (d is the finger width and r = 1 - a). Auld and Kino45 later gave eq 9 with k expressed as eo
k = sin (us) (11) whereB=d/L=al(l+a). If,however,thesameassumption is made regarding the far-edge distance then 5 = d/26 = a, and it can be shown that eq 11 is then identical to eq 10 except that the sine term differs by a factor of We have been unable to determine the origins of these differences, but their effects can he calculated for various values of r (Figure 3). Equations 7 and 9 give values of C. thatarethesameforr= 1andr-0. Themaximumdifference with a = 7.5 pm occurs for r I 0.73,the value from eq 7 being 18%larger. The use of eq 11for k in eq 9 results in much lower values of C., with C. increasing with increasing r unlike the expressions of Scapple and Engan. If eq 11is used with 5 = a,the value of C. passes through a maximum at r I 0.5. The three different expressions for C. give similar results only for r t 0.85, and only then if the far-edge distance assumption is made. Since the capacitance of a parallel plate capacitor is proportional to the areaover theseparation, Auld (41) Scapple, R.Y. IEEE 1974 Electronics Components Conference, 1974, IEEE Cat. No.74CH0853-2PHP,203-207.
(42)Gray, D. E.. Ed. American Imtitute of Physics Handbook, 2nd ed.; MeGraw-Hill, New York, 1963: pp 5-15. (43)Arfiren, G. Mothematical Methods For Physicists, 3rd ed.; Academic Press: Orlando, FL, 1985: p 322. (44)Engan, H. IEEE Tram. Electron. Deuices 1969, ED-16, 1014-
0.0
02
0.4
0.6
0.8
1.0
12
I.&%
nourn 9. Ette* 01 using Merent expressions on calculatedvalue ot G. 0 = Scnpple (eqs 7,8); 0 = Engan (eqs 8-10); A = Auld and Kino (eqs 9-1 1 with 8): = Auld and Kino (eqs 9-11 w h a).
+
Model for thecapacitanceofa mid lnterdlgitaltransducar (after Endres and DrosP). Fbur.4.
and Kino’s expression with 5 = a probably gives the most realistic values. Recently Endres and Drost46 have used eq 7 with a modification of eq 8 to account for a third medium between the fingers of an interdigital capacitor (Figure 4) with capacitance 3‘
= ‘Of3(;)
h
where t3 is the relative dielectric constant of the medium and h is the f i g e r height so that CT = (N - l)(C3+ C,) W
(13)
Combining eq 13with eqs 9.11, and 12 allows us to calculate the capacitance of a single IDT for the devices used in this study with various different coatings of known dielectric constant; these results are given in Table I. In the c m of a semiinfiite medium contacting the IDT and fdling the gaps between the fingers the effect on CTcan be large. The effect is obviously much smaller when the medium only fills the region between the fingers (with gas or a vacuum above this) but can still be significant, especially for highly polar substances. Effect of Transducer Capacitanceon Circuit Behavior. Knowing the range of variation for CT it is possible to calculate the effect of this on the oscillator performance by making use of the equivalent circuit shown in Figure 2. The acousticadmittance Y.canhe replaced byaseriesRLCcircuit with component values R,, L,, and C. representing the motional properties of the quartz.28 This results in the same equivalent circuit as that used to represent simple disk or plate thickness shear mode resonators, which are commonly referred to as bulk acoustic wave (BAW) devices. The impedance characteristics of this circuit can be derived by considering first the total admittance of the circuit (ref 47
1017.
(45)Auld, B. A,; Kino, G . S. ZEEE Tram. Eleetrnn. Devices 1971, ED-18,898-908.
(46) Endres, H.-E.: Dmt, S. Sem. Actuators B 1991,4,9.5+8. (47) Kipling, A.; Thompson. M. A w l . Chem. 1990.62, 1614-1519.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 4, FEBRUARY 15, 1993
Table I. Effect of Different Dielectric Media on Total Static Capacitance of an IDTa material argon Teflon acetone propan-2-01 ethanol methanol diethyl ether n-pentane chloroform water acetone methanol n-pentane chloroform water
€2
€3
CdPF
1.0005 2.1 20.7 18.3 24.3 32.63 4.34 1.844 4.806 80.37 1.0005 1.0005 1.0005 1.0005 1.0005
1.0005 2.1 20.7 18.3 24.3 32.63 4.34 1.844 4.806 80.37 2.1 32.63 1.844 4.806 80.37
6.543 7.919 31.20 28.19 35.70 46.13 10.72 7.599 11.31 105.9 6.566 7.211 6.561 6.623 8.218
44
40
52 56 f/Mk
40
60
64
68
72
Figwe 5. Typical plot of the magnltude(l4)and phase (0)characterkks of the equivalent clrcult for a SAW resonator. For condltlonssee text. 80
used in this study). €1 for ST-cut quartz was taken as 4.3. €2 is the relative permittivity of the medium above the electrodes, €3 is that for the medium between the electrodes (see Figure 4).
2-
/ i E
and references cited therein)
'O
Y = Ym+ YT = G + j B
(14) Substituting for the motional and capacitative admittances and collecting the real and imaginary terms together gives
Rm
100
n
ItlIR
-100
36
32
a Calculations for 50 finger pair IDT with a = 7.5 pm, b = 15 pm, W =4.8 mm, and h = 760 A (these are the dimensions for the devices
G=
-
loo0
U
60
(15) 50
10
0
20
40
30 CTlpF
50
Flgure 6. Effect of varying Gr on differentcharacterlstlc frequencles for the IDT equhralent electrlcal clrcult. For condltlons see text.
and since
V,!, I
lzl=
la=
arg 2 = -arg Y
tan 0 = X / R = -BIG
= ,I-)(
which leads to expressions for the real and imaginary parta of the impedance 2
RE-
G G~ + B~
SOURCE
mivor
!LOAD
Flgure 7. Equhralent elecblcel clrcult for a SAW delay llne osclHator. V, f, / = source voltage, frequency, and current. R,, = source, load
resistance. The equations best fitting the data for I q m i n , were
lqmax,
and Om=
lamin = 50.17 - 0.037 14CT- 0.012 32CT2+ 0.001 41CT3
X=- -B
Iq,,
G2 + B2 Examples of the impedance and phase characteristics calculated for this circuit with R, = 50.0 52, L m = 1.90 pH, C m = 4.90pF, and CT= 12.0 pF are shown in Figure 5. The effect of varying CTon the frequencies of minimum and maximum impedance (fmin, f,,), the low and high frequencies of zero phase Cf8o and f p o ) and the frequency of maximum phase cf(O), for the circuit are shown in Figure 6. These were calculated for R m 50.0 a, L, = 1.90 pH, C, = 4.90 pF, and 4.00ICTI40.0 pF. The effect of varying CTon the minimum and maximum impedances (IZlmin, Mma.) and the maximum phase angle (Om-) was also calculated. As can be seen from Figure 6, increasing CT drives fmin, f m m , and f(O),, to lower frequencies. The values of IZlmin, Mm-9 and Omax also decrease while fd and f p o converge on fW,, until the point is reached beyond which the phase angle is negative at all frequencies.
generator
e,,
= (49.78 X 103)CT-'.600
= 87.52 - 4.229CT
+ 0.0478CT' - o.c@o 1 8 c ~ ~
The theoretical equivalent circuit for a SAW oscillator having two identical IDTs is shown in Figure 7.2S It is clear from this that, from an electrical point of view, changing the capacitance of the IDTs will clearly influence the resonant frequency of the circuit. One important difference between the SAW and BAW devices, however, is that the resonant frequency of the BAW devices is inversely proportional to the thicknesswhile the SAW reaonant frequencyis determined by the IDT finger spacing (and r ) and the acoustic wave velocity, i.e. for Rayleigh wave propagation and r = 0.5
fo = v d X = vd4d (19) Thus changing the effective value of CT will not change the
ANALYTICAL CHEMISTRY, VOL. 65, NO. 4, FEBRUARY 15, 1993
resonant frequency of the SAW device as such. What it will do, however, is "pull" the resonant frequency of the circuit a~ a whole to either a higher or lower value. Any additional components (whether real or parasitic components due to connections, etc.) between the IDTs and the rest of the electrical circuit (amplifierand other circuitry) will also have an effect. Indeed, this can be used to "tune" SAW oscillators to the desired frequency, shifts in f o of up to 200 ppm being achieved through use of the appropriate ~alues.~a
EXPERIMENTAL SECTION Apparatus. The SAW devices used in this study were 52MHz ST-cut quartz dual delay-lines from Microsensor Systems, Inc. (BowlingGreen, KY). The necessary electrical circuitry was provided by a CEM-52 module from the same source. This unit contains two oscillator circuits with individual outputs, a frequency mixer, and a TTL-compatible difference frequency output. The resulting two delay line oscillators can therefore be usedeither individuallyor as a sampleand reference combination. Frequency measurements were made using a Hewlett-Packard (Palo Alto, CA) HP5328A counter connected to an Apple Macintosh I1 computer (Cupertino, CA) via a National Instruments GPIB interface bus (Austin, TX). All the software necessary to collect, display, and analyze the frequency data was written and compiled in-house using the Think C programming environment (Symantec,Cupertino, CAI. Samplevapor streams were generated using a simple flow system described previously.10 Electrical characterization of the IDTs was performed using a Hewlett-Packard HP4159A network/spectrum analyzer with an HP41951A impedance test kit. Since the devices used are dual delay-line devices, we have adopted the convention of using f to refer to the frequency of a single delay-line, and F to the beat or difference frequency between two delay lines (reference mode). Chemicals. All chemicals were used as received. Acetone and propan-2-01 were ACS analytical reagent grade. Ethanol and n-pentane were reagent grade. Water was distilled from a deionizedsupply. Gascarrier streamswere either argon or helium and were passed through hydrocarbon and moisture traps. Effect of Water Content. Steady-state adsorption measurements were made on a plain SAW device (SAW no. 6) using acetone, ethanol, n-pentane, and water vapor. The frequency of only one delay line was recorded with time. This was followed by replicate experiments with a Teflon (PTFE) film (Fisons Instruments, Mississauga, Ont.) sprayed across both the generating (G)and receiving (R) IDTs. This was done in an attempt to determine whether the effects observed with a completely uncoated device were related in some way to exposure of the IDTs to the sample stream. The approximate gas-phase concentrations of the different analytes used were acetone, 900 ppm; ethanol, 200 ppm; pentane, 670 ppm. These were measured by passing the sample stream through a cold trap and weighing. Initial adsorption measurements were performed using 5 min 'onn and "off" times. Further measurements were made using longer "off" times, and the effect of flow rate on gas-phase concentration and observed Af values studied. Following these experiments, one device (SAW no. 9) was sputter-coated with silica to an initial thickness of =300 A. After performing some adsorption experiments, this was increased to -800 A. Effect of Added Capacitance on SAW Performance. Capacitors (3,10,15 and 20 pF) were connected directly across the screw terminals for the electrical connections to (1) the generating and (2) the receiving IDT of one delay line. The operating frequency was monitored using the HP5328A counter. The signal amplitude for one delay line was monitored by connecting an HP1740A oscilloscope to the appropriate port provided on the CEM-52 unit. This provides a direct measurement of the oscillator frequency for that delay line. Since the SAW devices used have two delay lines manufactured on to the same quartz substrate there is somedegree of "cross-talk" between the two delay lines. When the values of fo for each oscillator (48) Parker, T. E. IEEE Ultrason. Symp. h o c . 1982, IEEE Cat. No. 82CH1823-4,26&274.
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Table 11. Effect of PTFE Film on Sensitivity to Various VaDors (AfllHzwithout ( W H zwith sample vapor polymer film polymer film acetone 212 5073 129 ethanol 6582 133 n-pentane 849 2892 75% EtOH/25% H20 (v/vP N/A 1241 231 75% EtOH/25% H20 (v/v)A 1766 187 ethanol A 836 75% EtOH/25% H20 (v/v) B 352 1579 207 ethanol B water A 272 434 191 499 water B a Following entries are for subsequent experimenta with the SAW device orientated differently in the cell holder. A and B refer to the two different delay lines on a single device.
circuit are close (
