1199
Anal. Chem. 1993, 65, 1199-1202
Electrical Conductivity Measurements Using Microfabricated Interdigitated Electrodes Norman F. Sheppard, Jr.,' Robert C. Tucker, and Christine Wu Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21218
Microfabricated interdigitated electrode arrays were constructed and evaluated for use as miniature conductivity cells. The arrays were 2 X 3 mm in size and had digits ranging in size from 10 to 80 Nm. The complex electrical impedance of the devices was measured at frequencies spanning from 100 to 100 kHz in solutions with resistivities ranging from 10 to 67 000 Q/cm. An electromagnetic field model of the interdigitated electrode geometrywas used to calculate cell constants.The resulting values ranged from 0.07 to 0.55 cm-l, and they agreed well with the experimental data. The frequency dependence of the complex electrical impedance could be represented by an equivalent circuit incorporating an interfacial impedance consisting of a double-layer capacitance in series with a Warburg-type diffusion impedance.
INTRODUCTION Planar interdigitated electrode arrays are a commonlyused electrode configuration for conductimetric sensing applications. The microfabrication technology used to manufacture integrated circuits can produce arrays with areas on the order of a few square millimeters and digit widths of 5 pm or less. By coating the electrodes with a thin film responsive to the gas of interest, sensors have been constructed for humidityl82 and toxic gases such as NO21.3 and SO2.4 A number of conductimetric biosensors have also been reported, in which biomolecules, such as enzymes or receptor proteins, are coupled to the surface of the device. Enzyme-based conductimetric sensors rely on an increase in the conductivity of the products when the substrate is turned over. Examples include urea sensors5$6and a penicillin enso or.^ Senors for the detection of neurotoxins have been fabricated by incorporating acetylcholine receptors into lipid or polymer membranes.8~9 Some specialized conductimetric sensing applications of interdigitated electrodes include their utility to measure the dielectric properties of thermoset polymers during cure,I0 their use with plasma-polymerized films to determine water content in transformer oil," their use as a
* Corresponding author.
(1)Hammann, C.;Kampfrath,G.;Mueller,M.Sens. Actuators,B 1990,
tool to monitor Langmuir-Blodgett deposited films,'* and their utility to measure the electrical conductivity of tracheal fluid.13 The calibration of conductimetric sensors based on planar interdigitated electrodes has been largely empirical. In most cases, the relationship between the concentration of the analyte of interest and the measured complex electrical impedance of the interdigitated electrodes was determined experimentally. However, there have been reports where solutions to Laplace's equation have been used to relate the properties of the material under test to the interdigitated electrode's impedance. Examples of the use of finitedifference methods include the studies of Fouke13 and Lee.14 The analytical treatments of Endres4 and Zhoul* derive relationships for the capacitance of an interdigitated electrode array coated with a thin film. The model of Zaretsky15J6 is a more general solution to Laplace's equation, permitting the calculation of the complex impedance of a device coated with multiple layers of material. These models enable researchers to examine the tradeoffs in sensor design and performance. In this work, we have constructed and evaluated planar interdigitated electrodes for eventual use in conductimetric biosensors. Electrodes of differing geometries were designed, fabricated, and tested by measuring the complex electrical impedance versus frequency in solutions of differing conductivities. The Zaretsky field model15was used to calculate the cell constants, which were incorporated into an equivalent circuit for the device. These calculations provide a set of design rules for fabricating planar conductivity cells based upon interdigitated electrodes and estimates of the interfacial impedance.
EXPERIMENTAL SECTION Electrode Design. The design of the interdigitated electrode structure is illustrated schematically in Figure la. At one end of the structure is a set of interdigitated electrodes which occupy an area approximately 2 X 3 mm. The width of the digits and the spaces between them are equal, and they range from 5 to 80 km. Bonding pads are located at the opposite end of the chip. There are two bonding pads on each of the interdigitated electrodes so that a four-point conductance measurement can be implemented. There is also a platinum serpentine resistor for use as a resistance temperature detector (RTD)and for determining the sheet resistance of the metallization. Two of the bonding pads are unused in this application.
B1,142-147.
(2)Bolthauser, T.;Bakes, H. Sens. Actuators 1991,A26, 509-512. (3)Kolesar, E. S.,Jr.; Wiseman, J. M. Anal. Chem. 1989,61,23552361. (4)Endres, H.R.;Drost, S. Sens. Actuators, B 1991,B4,95-98. (5)Watson, L. D.; Maynard, P.; Cullen, D. C.; Sethi, R. S.; Brettle, J.; Lowe, C. R. Biosensors 1988,3,101-115. (6)Cullen, D. C.; Sethi, R. S.; Lowe, C. R. Anal. Chim. Acta 1990,231 (l), 33-40. (7) Nishizawa, M.; Matsue, T.; Uchida, I. Anal. Chem. 1992,64,26422644. (8) Valdeq, J. J.; Wall, J. G., Jr.; Chambers, J. P.; Eldefrawi, M. E. Johns Hopkrns APL Tech. Dig. 1988,9, 4-10. (9)Taylor, R. F.;Marenchic, I. G.; Cook, E. J. Anal. Chim. Acta 1988, 213,131-138. 0003-2700/93/0365-1199$04.00/0
(10)Sheppard, N. F.; Day, D. R.; Lee, H. L.; Senturia, S. D. Sens. Actuators 1982,2,263-274. (11)Zaretsky, M. C.; Melcher, J. R.; Cooke, C. M. IEEE Trans. Electr. Insul. 1989,24, 1167-1176. (12)Zhou, G.;Kowel, S. T.; Srinivasan, M. P. IEEE Trans. Compon., Hybrids, Manuf. Technol. 1988,II,184-190. (13)Fouke, J. M.; Wolin, A. D.; Saunders, K. G.; Neumm, M. R.; McFadden, E. R.,Jr. IEEE Trans. Biomed. Eng. 1988,35, 877-881. (14)Lee, H.L. Master's Thesis, Massachusetts Institute of Technology, 1982. (15)Zaretsky, M. C.; Mouyad, L.; Melcher, J. R. IEEE Trans. Electr. Insul. 1988,23,897-917. (16)Zaretsky, M. C.; Li, P.; Melcher, J. R. IEEE Trans. Electr. Insul. 1989,24,1159-1166. 0 1993 American Chemical Society
1200
ANALYTICAL CHEMISTRY, VOL. 65. NO. 9, MAY 1. 1993 Table I. Cell Constant Calculations
electrode
a.
-25mm
A
electrode spacing,a
(urn)
40
1 2 3
160
4
320
80
meander length,M
cell constant
(urn)
Icm)
(ern-’)
10 20 40 80
14.51 7.20 3.54 1.80
0.069
0.138
0.276 0.552
was used to independently measure the conductivity of the solutions in the test cell.
RESULTS A N D D I S C U S S I O N
b.
...
.
A
hi2
w
Substrate
II
C.
J\N”4d lead
Cdl
zw
RL? fbun 1. (a)Design of the interdigitated electrode arrays used in this study. Electrodeswerepanemedlnp!atlnum(witha chomiumadheslon layer) on a borosilicate glass substrate. (b) Interdigitated electrode array geometry used in the Impedance mcdeling analysis of Zaretsky. Aner ref 11. (c)Equivalent circuh used to fit the data in Figures 4 and 5.
Fabrication. The devices were constructed using standard integrated circuit fabrication methods. Borosilicate glass substrates, 100 mm in diameter by 0.040 in. thick (Corning 7740, Mooney Precision Glass,Huntington, WV) were first cleaned etch. Next, a negative image using a‘piranha” (31, H~SOI:H~OZ) of the desired electrode patterns was printed on the substrate in photoresist. Threecoatsofphotoresist (KTI820,KTI Chemicals, Sunnyvale, CAI. each prebaked at 90 “C for 20 min before application of the next coat, were used to produce a relatively thick layer for the lift-off process. The photoresist was then exposed, developed, rinsed in deionized water, and dried. Electron-beam evaporation was used to deposit a 100 nm thick chromium adhesion layer, followed by a 350 nm thick platinum layer. Acetone was used to dissolve the photoresist and lift-off the metal. The substrates were then cut, and the individual devices were packaged in a Kapton “ribbon cahle” package (MicrometInstruments, Inc., Newton, MA). Theelectrodes were platinized prior to testing. The packaged device was cleaned by rinsing with hexane, 2-propanol, and distilled water. Before platinization, both electrodes were shorted together and connected as the working electrode to an EG&G PAR 273 potentiostat. The electrode structure was cycled from -1 to -2 V with respect to an AgiAgCl reference for 3 min in phosphate-buffered saline. Platinization was done in a solution of platinic chloride and lead acetate.I7 A current correspondingto a current density of 13.3 mAlcmZwas passed for 100 s to produce a deposit that was clearly visible under an optical microscope. Testing. The test solutions used were commercial conductivity standard solutions (Fisher Scientific, Curtin Matheson Scientific). The text cell was a 200-mL three-neck pear-shaped flask immersed in a water bath. Temperature was maintained at 25 i 0.1 “C. A Hewlett-Packard 4192A impedance analyzer was used to measure the impedance ofthe devices at frequencies between 100 Hz and 100 kHz. The amplitude of the applied signal was 100 mV rms. A conductivity cell (YSI Model 3417) (17) Encyclopedia of Electrochemistry of the Elements; Marcel Dekker: New York, 1916.
Cell Constant of Interdigitated Conductivity Electrodes. The interelectrode resistance for the devices constructed in this study were estimated using the analytical solution of the electromagnetic field equations for the interdigitated electrode geometry developed by Za~etaky.‘~ This model treats the interdigitated electrode array as a periodic structure, infinite in extent, and solves Laplace’s equation using collocation methods to match the mixed boundary conditions in the plane of the electrodes. The analytical solution enables computation of the impedance of an electrode array, given the geometry of the electrodes and the electrical properties of the half-spaces above and below the electrodes. The half-spaces are represented as one or more layers with a specified thickness, conductivity, and permittivity, and transfer relations are used to solve for the potentialdistribution ineach layer. Though the present work is concerned with the response of interdigitated electrodes covered by an effectively infinite fluid layer, the analysis of conductimetric sensors formed by coating electrode arrays with thin films is possible using this model. The geometry is pictured in Figure lb. The spatial periodicity of the interdigitated electrode array, that is, the distance betweenonedigitandthenextonthesameelectrode, is A. The interelectrode spacing is ‘a’. Following the convention used by Zaretsky, the meander length of the array, M,is equal to the length of a digit times the number of digits on one electrode. (Note that this is one-half the length of the serpentinepathformed between the two electrodes.) In their analysis, the electrodes are assumed to be infinitely thin. This is a reasonable assumption for the electrodes constructed here, since the ratio of electrode width to height is, in the worst case (10 pm wide lineshpaces), greater than 20 to 1. Effects such as the resistance of the finite thickness electrode or the impedance of the platinized layer are best incorporated into the equivalent circuit model discussed below. The halfspaces above and below the electrodes, solution and substrate, respectively, have a specified electrical permittivity and conductivity. In the analysis performed here, the relative permittivity of the borosilicate glass substrate was taken as 3.9, and its conductivity was zero. The surface conductivity at the glass/solution interface was also assumed to be zero. The geometries of the four different electrodes fabricated and tested in this study are summarized in Table I. These arrays are equivalent with respect to the model, since the physical dimensions can be normalized to the underlying periodicity of the electrode structure. The electromagnetic field model calculations yield an admittance per unit length from which the actual admittance can be calculated by multiplying by the meander length. The results of these calculations are also summarized in Table I. For the 2 X 3 mm interdigitated electrode array devices constructed here, the meander length, M,ranged from 14.5 cm (10 pm wide lines/spaces) to 1.8 cm (80 pm wide lines/spaces). The computed conductance of these arrays (equallines and spaces) is 9.66 X l W 3 S/cm of meander length M in a 1W2 (! em-’) I
ANALYTICAL CHEMISTRY, VOL. 65, NO. 9, MAY 1, 1993
N
4
0 v)
101 10
....
1
.
1
.
(
100
.
.
1
.
1
.
1
.
(
.
.
.
1000
.
1
.
1
.
(
.
.
.
.
.
10000
I
Flgure 2. Series equivalent resistance of the interdigitated electrode arrays, measured at 50 kHr, versus solution resistivity. (m) 10 pm llneslspaces (N = 4); (0)20 pm lineslspaces (N = 2); (A)40-pm iineslspaces (N = 4); (+) 80-pm iineslspaces (N = 3). Solid lines represent the calculations based on the electromagneticfield model of the electrodes and lead resistance.
solution. Defining a cell constant K such that u =K/R
(1) where u is the conductivity in S/cm and R is the measured resistance in ohms. The resulting values range from 0.0690 cm-1 for the 10-pm structures to 0.5519 cm-' for the 80-pm structures. Figure 2 is a plot of the 50-kHz series equivalent resistance of the interdigitated electrode arrays as a function of the resistivity of the test solution for devices with lo-, 20-, 40-, and 80-pm lines and spaces. For a given electrode spacing, there is a range of conductivity, indicated by a slope of 1on the log-log plot, where the series equivalent resistance is inversely proportional to the conducitivity. At lower resistivities, the resistance approaches 100 Q,independent of the electrode geometry. The solid lines in the figure represent the expected behavior based on the cell constant calculations and a series resistance (Rlead in Figure IC)of 35 Q to account for on-chip lead resistance. The agreement is very good for resistivities above loo0 Q/cm,while at lower resistivities, the interfacial impedance begins to dominate. In this study, the width of the digits was equal to the electrode spacing; that is, a/X = 0.25. To illustrate the effect the a/X ratio has on the admittance, a dimensionless conductance parameter, G*,can be defined as
C* = G/uM = 1/KM (2) where G is the conductance of an interdigitated electrode array of meander length M in a solution of conductivity u. This quantity is equivalent to the inverse of the cell constant times the meander length. Figure 3 illustrates the behavior of G* as the interelectrode spacing, a, is varied from 0 to X/2. As expected, the conductance rises rapidly as the electrode spacing decreases toward zero, and it correspondingly decreases as the electrode width approaches zero. Not surprisingly, the functional dependence on electrode spacing is identical to that shown in Figure 3 of Endres? which is a plot of electrode capacitance versus electrode spacing, and in Figure 6 of Aoki's treatment of diffusion-controlled redox currents in interdigitated electrode arrays.18 The curve (18)Aoki, K.; Morita, M.; Niwa, 0.;Tabei, H. J. Electroanal. Chem. 1988, 256, 269-282.
0 20
0
100000
Solution Resistivity (ohm-cm)
1201
40 60 2allarnbda (%)
80
1 IO
Flgure 3. Dimensionless interdigitated electrode array conductance, @, versus dimensionless electrode spacing, 2a/X.
u,
100000
t c
L
0
v
8
Ei
10000~
c)
.-v) v)
cr" c a, -
1000,
c)
.-F
= E
100:
v)
.-a, L;
1
1
10 10
100
1000
10000 100000 100 000
Frequency (Hz) Flgurr 4. Series equivalent resistance as a function of frequency,for 10 pm iineslspaces (squares)and 40 pm iineslspaces (circles)arrays In 100 Q-cm(open symbols)and 20 000 Qlcm(filled symbols)soiutions.
exhibits an inflection point a t a value of 2a/ X of approximately 70%; at this point, the sensitivity of the cell constant with respect to variations in electrodespacing (asmight arise during manufacture of the devices)would be minimized. The values in Figure 3 can be used with eq 2 to estimate the cell constant of a proposed array design. For a given choice of electrode width and spacing (or equivalently, 2a/X), the cell constant of the array will simply be the inverse of the product of G* times the meander length. Varying the width of the electrode will produce, a t most, a 5-fold change in K, and so, meander length will be the most effective way to achieve a given cell constant. Equivalent Circuit. Figures 4 and 5 illustrate selected results from the complex impedance measurements. Series equivalent resistance and capacitance are plotted as a function of frequency, over the range of 100 Hz to 100 kHz, for devices with 10 and 40 pm wide features (N= 4)in solutions having resistivities of 100 and 67 OOO Wcm. In the higher resistivity solution, the resistance decreases with increasing frequency, approaching a constant value. At frequencies above 5 kHz, the ratio of the resistances for the devices with 10 and 40 fim wide features are 4,as expected from the cell constant ratios. The capacitance rolls off rapidly at frequencies greater than 10kHz. In the lower resistivity solution, there is considerably more frequency dispersion in the resistive component and less in the capacitance.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 9, MAY 1,
1202
1993 Table 11. Warburg Impedance Parameter, &, Values (LQ)
1000
G c
Y
8
.s=
resistivity (Ricm) 10 100 lo00 10 OOO 20 OOO
100
%
2 is c
10
cn
aJ
i%
0.1
IO
'
""i'fi0
'
"'1;OO'
"i'Ob00
iOob00 IOGVVOO
Flguro 5. Series equlvalent capacitance as function of frequency,for 10-pm iineslspaces(squares)and40-pm iines/spaces(circles)arrays in 100Q/cm(opensymbols)and 20 000 Q/cm(flHedsymbols)solutbns.
The frequency response(s) shown in Figures 4 and 5 were modeled using the equivalent circuit shown in Figure IC.The circuit consists of a series combination of a double-layer capacitance,diffusion impedance, and solution resistance, in parallel with the geometrical capacitance of the electrodes. The on-chip lead resistance, Rlead, is estimated to be 35 0, based on the electrode design and the sheet resistance of the metallization determined from the RTD (see below). A single measured value, obtained by coating an interdigitated electrode array with silver paint, was 40 Q. The choice of this circuit is based on Barker's treatment of the frequency dispersion of the double layer at a perfectly polarizable electrode.19 The analysis indicates that a diffusional impedance, functionally equivalent to a Warburg impedance, can arise at nonzero frequency, which appears as being in series with the double-layer capacitance. The element R, in Figure IC represents the geometrical, or bulk resistance, while C, is the corresponding geometrical capacitance. Values for R, and C, can be estimated using the fields model described above. The double-layer impedance is represented by the capacitance, Cdl, and a Warburg impedance, Zw,described by
where Zois a parameter having dimension of ohms, w is the angular frequency of the applied voltage, and j = 4-1. A nonlinear least-squaresanalysis computer programz0was used to estimate the values of the equivalent circuit elements. The solid lines in Figures 4 and 5 represent the fits obtained for these measurements. The values for the double-layer capacitance ranged from approximately 50 to 500 pFlcm2 of electrode area. There was, however, no discernible trend with solution resistivity or electrode geometry. Values of the parameter 20are summarized in Table 11. These values are relatively independent of the electrode structure's geometry, and they increase with increasing solution conductivity. At 100 Hz, these values correspond to a series capacitance of approximately lo00 pF/cm2 in the 10 Wcm solution and (19)Barker, G.C. J. Electroanal Chem. 1966, 12, 495-503. (20) Boukamp, B. A. Solid State Ionics 1986,20, 31-43.
10
6.3 17.5 8.3 65.8 145.8
electrode spacing (pm) 20 40 80 3.6 4.3 2.7 14.7 25.0 12.7 21.8 33.3 18.3 105.9 114.8 82.0 167.5 186.2 371.7
decrease to 20 pF/cm2in the 67 OOO Q/cm solution, the same order of magnitude as that of the double-layer capacitance. The fact that the interfacial impedance elements do not depend on the type of electrode is not surprising, since the current density will be the same in each case, due to the fact that the alh ratio is the same for each device. The resistance R, extracted by the model was, in most cases (i.e., at higher resistivities), within 10%of the 50-kHz value plotted in Figure 2, indicating that the interfacial impedance is relatively unimportant at this frequency. Values for the geometrical capacitance were obtained only in the higher resistivity solutions and, in the worst case, differed from that calculated using the electromagnetic field model by a factor of 4. The product R,C, is the dielectric relaxation time of the solution, and in the 67 OOO Wcm solution, the inverse of the relaxation time corresponds to a frequency of 2 MHz, so at 100 kHz, the contribution of C, to the measured impedance was small. ResistanceTemperatureDetector. Sixteen RTDs were tested by measuring their resistance over the temperature range of 25-55 "C. Linear regressionsyielded a slope of 0.140 f 0.005%/ O C , considerably less than the temperature coefficient for platinum alone, which is 0.38%. This is due to the relatively thick chromium adhesion layer on these devices. Device-to-devicereproducibility was moderate, the absolute value of the 25 "C resistance was 373 f 37 Q (N= 16). Based on the photomask design, the corresponding sheet resistance was 1.78 f 0.18 Wsquare.
CONCLUSION Miniature conductivity cells were constructed using microfabricated planar interdigitated electrodes. The frequency dependence of the complex electrical impedance could be adequately described by an equivalent circuit incorporating an interfacial impedance consisting of a Warburg-type diffusion impedance in series with the double-layer capacitance. Cell constants calculated from an electromagnetic field model were in good agreement with experimental data. The calculation of a dimensionless conductance, presented in Figure 3, can be used to estimate the cell constant of a planar interdigitated electrode array of specified electrode width, electrode spacing, and meander length.
ACKNOWLEDGMENT This work was supported by the Whitaker Foundation and an NSF Presidential Young Investigator Award to N.F.S. (ECS-9058419). The interdigitated electrodeswere fabricated in the Microsystems Technology Laboratory at the Massachusetts Institute of Technology under the MTL Outreach Program. Thanks to David Mears and Anthony GuiseppiElie for technical discussions. RECEIVED for review October 20, 1992. Accepted January 22, 1993.
