Anal. Chem. 1998, 70, 2908-2913
Individually Addressable, Submicrometer Band Electrode Arrays. 2. Electrochemical Characterization Milind P. Nagale and Ingrid Fritsch*
Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701
We report extensive cyclic voltammetric evaluation of gold submicrometer edge band electrodes with different widths, from 25.3 to 143.5 nm. Fabrication of these band electrodes from layers of gold and silicon nitride using conventional microfabrication techniques, was reported in the preceding companion paper. Gold film thicknesses and, thus, the electrode widths were measured by surface profilometry, X-ray interferometry, and atomic force microscopy. The electrodes exhibit typical sigmoidal-shaped cyclic voltammograms at slow scan rates ( 25 V/s). Capacitance of the edge band electrodes is high (187-0.206 mF/cm2 for 71.2-nm edge band electrodes for scan rates of 0.010-204 V/s) and scan rate dependent. Values approach those of macroelectrodes at fast scan rates, indicating imperfect seals at the gold/ silicon nitride, gold/Cr/glass, or gold/epoxy interfaces. A method for fabricating arrays of individually addressable submicrometer band electrodes has been described in the preceding companion paper.1 Electrodes with nanometer dimensions are of great interest not only for small-scale electroanalytical applications and studies involving fast time response and highly resistive media but also for their potential in obtaining fundamental understanding of transport, kinetics, and double-layer structure at an electrode when dimensions approach those of molecules. Thus, it is necessary to thoroughly investigate the electrochemical behavior of the submicrometer band electrodes that we have described previously in order to determine their utility and limitations in addressing some of these issues. Here, we report a detailed characterization of the submicrometer band electrodes by cyclic voltammetry in KNO3 solutions with and without Ru(NH3)63+. The limiting faradaic and charging currents are compared to those expected from theory for band electrodes of different widths, at a series of scan rates, in both the radial and linear diffusion regimes. These studies reveal the quality of the insulator/electrode seal and other features of the electrode structure and geometry that cannot be detected by (1) Nagale, M. P.; Fritsch, I. Anal. Chem. 1998, 70, 2902.
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spectroscopic techniques. To quantitatively compare experimental current to theoretical predictions, it was necessary to determine the widths of the electrodes. Thus, X-ray interferometry, profilometry, and atomic force microscopy (AFM) techniques are compared for measuring metal film thickness. EXPERIMENTAL SECTION Reagents. All chemicals (Aldrich) were reagent grade and used without further purification, unless otherwise specified. Deionized (DI) water was prepared using an ultrapure water system (Millipore, France model Milli Q RG). Sulfuric acid (concentrated) and hydrogen peroxide (30%) were electronic grade (J. T. Baker). Electrode Fabrication. Electrode array microfabrication is described in the preceding companion paper.1 Electrode arrays with different electrode widths were constructed using the same procedure. Gold macroelectrodes were prepared by vapor depositing chromium and gold on 1 in. × 1 in. glass slides. Scanning electron microscopy (SEM) was used to visualize the quality of fabrication. Film Thickness Measurements. Metal film thicknesses were determined by surface profilometry (Sloan Dektak 3030), X-ray interferometry (Phillips XRD X′pert System) and AFM. Measurements with X-ray interferometry were performed on samples from the same batch of gold deposition as the arrays. The measurements were performed using a fixed angle of incidence and a narrow divergence slit, changing the angle of the detector to get diffraction fringes and then measuring the position of diffraction fringes, to calculate the film thickness. Profilometry measurements were performed across the edge of the contact pads or on samples from the same batch of gold deposition as the arrays. Contact AFM (Digital Instruments, CA Model Nanoscope III) measurements were performed across the edge of the contact pads of electrode arrays. The scan rate for film thickness measurements was 0.2 Hz. Measurements were performed on at least two pads on a given array and on two different arrays in some cases. The errors reported are one standard deviation from the mean. Electrochemical Characterization. Cyclic voltammetry (CV) was performed using a computer-interfaced potentiostat (Bioanalytical Systems, model 100B, with BAS 100W software). In all experiments, a low-current amplifier and a faraday cage (Bioanalytical Systems, model PA1 and model C2, respectively) were used. The reference was an aqueous Ag/AgCl (saturated KCl) electrode. S0003-2700(97)01041-X CCC: $15.00
© 1998 American Chemical Society Published on Web 06/05/1998
Table 1. Film Thickness Measurements for Gold/ Chromium on Glass piezoelectric crystal, nma 10 25 35 50 75 100
profilometry, nm
X-ray interferometry, nm 25.7 ( 2.3b 50.2 ( 6.0b,d 71.7 ( 6.0b,d
122.4 ( 2.5b 142.5 ( 3.5c
AFM, nm 25.3 ( 3.3c 37.0 ( 2.0c 71.2 ( 2.5c 77.7 ( 5.3c 125.7 ( 5.3c 143.5 ( 9.6c
a Nominal thickness. b Unpatterned gold samples from same batch as arrays. c Thickness at contact pads of an array. d Measurements with pooled standard deviations.
A platinum foil was used as an auxiliary electrode. Cyclic voltammograms were obtained in pure electrolyte 0.5 M KNO3, and electrolyte with 5 mM hexaammineruthenium(III) chloride. All electrochemical experiments were performed in a closed cell. The solution was purged with high-purity Ar (Zero grade/UHP, Air Products) prior to performing experiments, and an Ar atmosphere was maintained during the experiments to minimize O2 concentration in the solution. RESULTS AND DISCUSSION Film Thickness Measurements. Various measurement techniques were used to measure the gold layer thickness. Knowledge of the thicknesses is necessary to determine the width of the edge band electrodes. Metal film thicknesses were initially estimated during vapor deposition by a piezoelectric thickness monitor. The film thickness varies over the total sample area in the thermal evaporator, and the piezoelectric crystal monitors only a small fraction of it. Therefore, the thickness monitor readings cannot be representative for all of the samples in one deposition. Thus, it is important to measure the actual thickness of the metal film for each sample that is used to make an array. Table 1 shows the actual thicknesses as measured by surface profilometry, X-ray interferometry, and contact AFM obtained for Au/Cr films with different piezoelectric crystal readings (nominal thickness). The actual thicknesses of Au/Cr layers as measured by these techniques are about 1.4-2.5 times higher than the piezoelectric crystal measurements on the evaporator, demonstrating the importance of making independent thickness measurements. AFM is more suitable than profilometry and X-ray interferometry, because it can be used to obtain the thicknesses over the entire range used (25.3-143.5 nm). Another advantage is that AFM can make the measurement directly on the array sample. The AFM was calibrated using only a 180-nm standard (Digital Instruments, CA). Ideally, the vertical calibration of the scanner is performed with standards throughout the same range as that of actual samples, but standards of different thicknesses were not available. Therefore, profilometry and X-ray interferometry were used to verify the AFM-determined thicknesses. The Profilometer and X-ray diffractometer were calibrated using 920- (Sloan Inc.) and 35-nm- (Phillips Inc.) thickness standards, respectively. Surface profilometry and X-ray interferometry are limited in the range of thicknesses that they can measure. Profilometry precisely measures films of ∼50 nm and greater, where a welldefined step is created at the film’s edge. We were only able to
obtain reproducible measurements for film thicknesses greater than 100 nm. We found that X-ray interferometry would determine thicknesses less than 90 nm. The upper limit is presumably caused by surface roughness.2 Another complication is that X-ray interferometry measurements cannot be carried out on an electrode array but on parallel, unpatterned samples coated in the same batch as those that were used to make arrays. The different locations of these parallel samples on the sample holder in the evaporator will result in different thicknesses, and this is evident by a large standard deviation. The data in Table 1 show that thicknesses measured by AFM agree well with those measured by profilometry and X-ray interferometry. The measurements from the different techniques are within one standard deviation of one another except for the 25-nm nominal thickness. This discrepancy may be explained by the fact that the measurements by X-ray interferometry were performed on parallel samples, which were not located close to the array samples in the evaporator during deposition. For measurements where more than one sample was used, pooled standard deviations were calculated. Measurements with profilometry for 100-nm nominal thickness were performed on two array pads, as they were with AFM. All other measurements by profilometry were performed on samples from the same batch of gold deposition as the arrays. Also, repeated measurements with the same samples on different days were in excellent agreement with one another. Thicknesses measured by AFM are used as the band electrode width for all data analyses in this paper, since these measurements were performed on the contact pads of the same array samples that were evaluated electrochemically. Electrochemical Characterization. The current at a band electrode at long time scales (Dt/r02 > 10) can be modeled by that at a hemicylindrical electrode, as derived by Wightman and co-workers3 (eq 1). Equation 1 is based on diffusion to a
i(t) ) 2nFDlC*π/ln[4Dt/ro2]
(1)
hemicylindrical surface, as described by Jaeger,4 where the parameters and the substitution of w/4 (w is the width of the band) for ro were described previously.1 Faradaic Current. General voltammetric behavior of band electrodes is described in the preceding paper.1 Here, additional band electrode widths are characterized and compared to theory. Edge band electrodes with different widths exhibit wellbehaved sigmoidal electrochemical response, as is expected in the case of microelectrodes. The limiting current does not decrease linearly as electrode width decreases. This is a useful trend, in that even smaller electrode widths should provide current that is measurable with conventional electrochemical equipment. Scan rate studies were performed for all electrode widths from 0.010 to 327 V/s. Figure 1 illustrates a scan rate study for a 77.7nm (actual thickness) edge band electrode, in 5 mM Ru(NH3)63+. At higher scan rates (>1 V/s), cyclic voltammograms become more peak shaped, presumably due to an increasing contribution (2) Thin Film System Project Manual, 2nd ed.; N. V. Phillips-The Netherlands, 1991; Chapter 1. (3) Kovach, P. M.; Caudill, W. L.; Peters, D. G.; Wightman, R. M. J. Electroanal. Chem. 1985, 185, 285. (4) Jeager, J. C. Proc. R. Soc. Edinburgh 1942, A61, 223.
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Figure 1. Scan rate study for a 77.7-nm (actual) band electrode in 5 mM Ru(NH3)63+ and 0.50 M KNO3 at different scan rates.
Figure 2. Limiting current vs (scan rate)1/2 for different widths of edge band electrodes. The dotted line is from eq 1, the solid line is from eq 2, and the solid line with circles represents the experimental current.
from linear diffusion. However, the flux appears to be dominated by radial diffusion, even at the fastest scan rate (327 V/s). Figure 2 is one way to represent the changes in faradaic response for different edge bandwidths as a function of scan rate. Plots are shown for limiting current (pseudo-steady-state or peak current, whichever was higher) vs (scan rate)1/2 for 37.0-, 77.7-, and 143.5-nm band electrodes. Each plot also contains theoretical curves for radial diffusion (for long time scales, where we define t as |E of max current - E1/2|/ν, eq 1) and linear diffusion (for short time scales, eq 2 for T ) 25 °C), where A is the area of the
ip ) 2.69 × 105n3/2AD1/2C*ν1/2
(2)
edge band electrodes calculated using actual metal film thickness (AFM) and actual length (SEM) and ν is the scan rate. The current predicted by eq 1 is higher than that by eq 2 for the entire range of scan rates that were studied. This is expected because (5) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley & Sons: New York, 1980.
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radial diffusion should dominate the flux even at the largest bandwidth and highest scan rate, where the diffusion layer, δ, is ∼1 µm (δ ) (2Dt)1/2). The experimental current is consistent with this description, in that it is much greater than that predicted for linear diffusion. The experimental current does not coincide over the entire scan rate range to predictions based on eq 1. This can be attributed to several inadequacies of the model. First, our geometry actually consists of “dual” edge electrodes separated by ∼4.7 µm of insulator (0.35 µm thick at the two edges and 4 µm wide), which results in overlapping diffusion layers that diminish current at long time scales. Second, it does not take into consideration surface roughness and either recessed or protruding edge band geometry, which will change the effective electroactive area. Third, the time parameter in eq 1 is defined for a chronoamperometric step experiment, but it must be estimated here because slow scan rate cyclic voltammetry was performed, instead. Fourth, our electrode geometry places a band electrode perpendicular and adjacent to the substrate plane, instead of in-plane like the model, so that diffusion is blocked from one side. Finally, eq 1 assumes a continuum fluid and nondiscrete diffusion behavior, which might not apply to electrodes having nanometer dimensions. These inadequacies are further discussed below in comparisons with experimental data. At the faster scan rates in Figure 2, the experimental values for all edge bandwidths are much higher than the model and vary approximately linearly with electrode width. This may be explained in two ways, although the exact reason for this behavior is not known at this time. First, because the deviation from the theoretical current increases with electrode width, the actual surface area of band electrodes may be higher than assumed. This may be caused by surface roughness and/or recessed or protruding edge band geometry. If this is the case, then at faster scan rates, where diffusion layer thicknesses may get as small as the surface roughness, higher currents should be observed. Second, the seal between the conductor and insulator may not be perfect, containing cracks. In this case, higher current will be observed at faster scan rates where the diffusion layer thickness is smaller than the cracks (semi-infinite diffusion case). Thus the electrode portions inside the cracks would experience a flux of redox species that leads to higher currents which are proportional to ν1/2. However, the contribution from this to the total current may be very small, even at the highest scan rate, because cracks larger than 1 µm were not observed by SEM. In addition, high iR drop (where R is uncompensated resistance) at higher scan rates would diminish this effect. The evaluation of the conductor and insulator interface is discussed in further detail below. The current at slower scan rates (0.010-1 V/s) deviates more negatively from the theoretical current as electrode width decreases. The experimental current is in best agreement with the theoretical current for 77.7- and 143.5-nm edge-band electrodes. However, at 37.0 nm, the experimental current at 5 V/s matches the theoretical current and dips to lower values with slower scan rates. Unusually low current for slow scan rates (0.020 V/s) at nanoband electrodes was previously reported by White and coworkers.6,7 They attributed this effect to the breakdown of the theory when the electrode dimensions approach the size of the (6) Morris, R. B.; Franta, D. J.; White, H. S. J. Phys. Chem. 1987, 91, 3559.
Figure 3. Comparison of theoretical (based on eq 1) and experimental limiting current (taken from CV at 0.1 V/s) for band electrodes of different widths (37.0, 71.2, 77.7, 125.7, and 143.5 nm) for Ru(NH3)63+. The solid line corresponds to the “in-plane” and the dotted line corresponds to the “perpendicular-to-substrate” band electrode models.
redox species. It was proposed that this happens for two possible reasons. One is that as the electrode width decreases, the finite size of the redox species limits its distance of approach to the electrode surface. The second reason is that reactant concentration varies significantly near the electrode surface due to a noncontinuum fluid structure. Although, in our case, the deviation in limiting current at slower scan rates may also be partly due to electrochemical shielding. Since each 4-µm-wide line has two electrode edges on both sides, the diffusion layers from two sides will overlap at long time scales, yielding lower total limiting current than expected for a single band of twice the length. Concentration profiles obtained from digital simulations and calculations of diffusion layer thickness at different time scales confirm the overlap. However, if the deviation in experimental current is only because of shielding due to overlapping diffusion layers, that factor should influence the current similarly at all the electrode widths studied. Therefore, this factor is unlikely to be the cause of the dependence of the negative deviation of current from theory with decreasing electrode width. If we graph our results and theory obtained at a single slow scan rate (0.10 V/s) in the format described by White and coworkers, which is a simple rearrangement of eq 1, Figure 3 is obtained. The ordinate is the limiting current, normalized to 2nFDlC*π. The abscissa is the normalized natural log term from eq 1 for the width of the edge band electrodes. This figure clearly shows the deviation from theory as a function of electrode width. The solid line is from eq 1 where ro ) w/4 and, thus, is termed the “in-plane” band electrode model where molecules diffuse from a hemicylindrical volume of solution around the electrode. The dotted line is termed the “perpendicular-to-substrate” band electrode model, where molecules diffuse from a quarter-cylinder volume of solution around the electrode. In this case, the limiting current for twice the actual bandwidth is calculated using eq 1 and the total limiting current is divided by 2, to take into account shielding by the substrate plane. Figure 3 shows that, at long times, such shielding of the diffusion layer by the substrate is significant. However, this is compensated for by the additional (7) Seibold, J. D.; Scott, E. R.; White, H. S. J. Electroanal. Chem. 1989, 264, 281.
Figure 4. Dependence of capacitance (normalized) on scan rate for (a) a 71.2-nm edge band electrode, and (b) a gold macroelectrode. Capacitances were calculated by measuring the charging current from a CV response in 0.50 M KNO3 at 0.0 V and dividing by scan rate and electrode area.
flux from underneath the plane of the finite insulator on the other side of the electrode. This is in agreement with Nylander and co-workers.8 They have reported for an edge band geometry similar to ours that eq 1 holds for a plane electrode perpendicular to the substrate and with a finite insulator on top. The experimental points in Figure 3 for the larger electrode widths lie slightly below the solid line, presumably due to the effect of the overlapping diffusion layers. By increasing the value of the time parameter in eq 1, those points could be made to fall on the line. In a chronoamperometry experiment, the parameter t is welldefined. However, when one fits the current of the plateau of a cyclic voltammogram, t is defined both by scan rate and by the potential range on the side of E1/2 where electron transfer occurs. Yet, any error in t would result in a constant offset along the abscissa for all the experimental points. Consequently, assuming that the better model for the edge band electrode behavior is that of the “in-plane” model, and that the time parameter and overlapping diffusion layers affect current similarly for all electrode widths, then another factor must be responsible for the extensive deviation of current from theory at the smallest widths. This factor possibly involves the limitations described by White and coworkers.6,7 The smallest electrode width fabricated was 25.3 nm, but the electrochemical response did not have a well-defined sigmoidal shape. This was observed for two different fabrication batches and may be caused by passivation of the electrode surface due to diffusion of the chromium adhesion layer to the gold band surface. Most of the electrodes showed good shelf life, and the electrochemical response was the same after several months of storage under ambient air conditions. Charging Current and Capacitance. Careful evaluation of the capacitance of electrodes as a function of scan rate can reveal information about the nature of the electrode area and seal with the insulator. Figure 4 shows a plot of the log of the normalized capacitance for a 71.2-nm edge band electrode and a gold macroelectrode in 0.5 M KNO3 vs the log of scan rate. The areanormalized capacitance (Cd ) ic/Aν) for the edge band was calculated by dividing the charging current measured at 0.0 V, by the electrode area (measured length × measured metal (8) Samuelson, M.; Armgarth, M.; Nylander, C. Anal. Chem. 1991, 63, 931.
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Table 2. Capacitances As Determined by CV for Edge Band Electrodes, Lateral Electrodes, and a Gold Macroelectrode at Different Scan Ratesa capacitance (mF/cm2)
b c
Figure 5. Dependence of charging current on scan rate for different widths (37.0-143.5 nm) of edge band electrodes and a 4-µm lateral band electrode. Here, charging currents were measured from CV responses in 5 mM Ru(NH3)63+ and 0.50 M KNO3. Measurements were made at the beginning of the scans where contribution from the faradaic current is minimal.
thickness) and scan rate. The Cd value for a gold macroelectrode was determined in the same way, except the area was equal to the length × width of the region that was immersed in the electrolyte solution. The Cd value of the macroelectrode has little dependence on scan rate, as expected. The Cd value for the edgeband electrode decreases as the scan rate increases and approaches that of the macroelectrode. This is consistent with loglog plots reported by Wehmeyer and Wightman.9 They suggested that, as electrodes get smaller, the effect of an imperfect seal between the conductor and the insulator is more apparent at slower scan rates. At faster scan rates, a higher iR drop will reduce the voltage change in the cracks, thereby decreasing the charging current there. The net effect is that the electrode area in the cracks no longer contributes significantly to the total capacitance. Thus it appears as though the total electrode area is smaller. It should be noted that electrodes are covered by a thin insulating material with a certain dielectric constant, forming a capacitor with conductor on one side and electrolyte solution on the other. This will add some capacitance to all electrodes which will be a constant factor and should be independent of scan rate. The value calculated based on the dielectric constant of silicon nitride reported in the literature10 is very small (18 nF/cm2) compared to the area-normalized capacitance values obtained for all electrode widths even at faster scan rates. Figure 5 is an alternative representation of the data, which more clearly shows how different the dependence of capacitance is between the low and high scan rate regimes.11 It must be noted that although the charging currents were evaluated from scan rate (9) Wehmeyer, K. R.; Wightman, R. M. J. Electroanal. Chem. 1985, 196, 417. (10) Sze, S. M. Semiconductor Devices, Physics and Technology; John Wiley & Sons: New York, 1985.
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electrode type
0.010 V/s
204 V/s
37.0 nmb 71.2 nmb 71.2 nmc 77.7 nmb 125.7 nmb 143.5 nmb 4000-nm lateral electrodeb a macroelectrodec (area 3.24 cm2)c
238 ( 78 146 ( 14 187 86.6 ( 20 54.6 ( 26 30.5 ( 14 10.0 ( 2.5 0.135
0.723 ( 0.036 0.573 ( 0.049 0.206 0.438 ( 0.015 0.582 ( 0.020 0.631 ( 0.094 0.081 ( 0.0012 0.00919
a The values are normalized to the electrode area in each case. Capacitance determined in 5.00 mM Ru(NH3)63+ and 0.5 M KNO3. Capacitance determined in 0.5 M KNO3.
studies in solutions where redox species were present, comparison with the simulated response from Digisim of Bioanalytical Systems (where experimentally determined capacitance was used) compares well with the experimental response at various scan rates. Although the method used to evaluate the electrode capacitance is not ideal, it still serves as a reasonable estimate. A typical electrode should yield a linear plot of ic vs ν, with a slope equal to CdA. Figure 5 shows two distinct regions in the plots, with at least two different slopes, that are most pronounced at the smallest edge band electrodes. As the width increases from 37.0 to 143.7 nm, the plots appear more linear. The most linear plot is for a 4-µm-wide lateral electrode, which is expected behavior, because there is only one seal involved (between glass and the conductor layer). In addition, the electrode area is large, in comparison. Yet, the area-normalized capacitance for the 4-µm lateral electrode is 1-2 orders of magnitude greater than that for a macroelectrode. Perhaps the glass/metal seal or the epoxy overcoat is responsible for this difference. The calculated Cd values for different electrode widths and a gold macroelectrode at two different scan rates are summarized in Table 2. The best comparison for the edge band electrodes is with the lateral electrodes to establish the effect of the overlying silicon nitride layer. The largest area-normalized capacitance in Table 2 is for the smallest edge band electrode (37.0 nm) at the slowest scan rate (0.010 V/s). It is only 20 times greater than that for the lateral electrode, which implies a similar factor of error in the electroactive area. The silicon nitride insulator layer must still have a large effect, otherwise the capacitance would be 100 times greater. At 204 V/s, where charging current in cracks is lower, the capacitance of the 37.0-nm edge band is even closer in value (only 10 times greater) to that of the 4-µm lateral band. Also, the larger the edge bandwidth, the closer the Cd is to the 4-µm lateral values. These results are consistent with the conclusion that an imperfect seal between the conductor and insulator must be present. It can also be seen from Table 2 that all of the widths of the edge band electrodes have similar Cd values at 204 V/s. (The (11) The charging current for Figure 5 was obtained for all electrode widths at different scan rates from CV responses. In this case, the charging current was measured at the beginning of the scan where the contribution from the faradaic current is minimal. Also, an overlay of data in this region for the 71.2-nm edge band electrode with and without redox species was the same.
small differences from one electrode width to another are in some cases within error of the measurement and in other cases could be due to minor variations in surface contamination.) If we assume that at this high scan rate there is no contribution to capacitance from cracks around the electrode, then these data suggest that electrode areas calculated from the measured thickness (by AFM) of the conductor and length of the edge (by SEM) are close to actual areas. CONCLUSIONS Cyclic voltammetry in electrolyte, with and without a reversible redox couple, was used to characterize the edge band electrodes. A hemicylindrical diffusion model (as opposed to a quarter-cylinder diffusion model) seems to best fit the faradaic data, although there are several limitations. The measurement of film thickness is very important in determining the band electrode width, so that the experimental response may be compared more accurately to theory. AFM on the same arrays used for electrochemical experiments was found to be the preferred technique for the range of film thicknesses studied. The shapes of the cyclic voltammograms indicate that even at higher scan rates contribution from radial diffusion dominates the limiting current and is consistent with expected behavior. However, the maximum current at high scan rates is directly proportional to electrode width and much higher than the predicted current for radial diffusion. At the slowest scan rates, the greatest deviations from theory occur for the smallest electrode widths. At those scan rates, overlap of diffusion layers from both sides of the 4-µm feature should be significant. However, this effect, which should be independent of width, cannot explain the width-dependent deviation from theory. The choice of scan rate and other experimental measurements such as the potential at which the current is measured and
the calculation of time would also shift experimental points relative to theory, but equally for all widths. Thus, the trend as shown in Figure 3 appears to be consistent with that described by White and co-workers.6,7 Capacitance studies indicate that the seal at any one of several interfaces may be defective. However, these cracks should not contribute significantly to faradaic current, especially at slow scan rates. Further investigation of the “true” surface area, use of different adhesion materials, and increased separation of the “dual” edge band electrodes, would aid in understanding the correlation of limiting currents and capacitance from experiment to those from different models. ACKNOWLEDGMENT Financial support of this work was provided by the University of Arkansas (Research Excellence Fund) and the National Science Foundation (Grants CHE-9308946, EHR-9180762, and CHE9624114). We express our appreciation to the Department of Electrical Engineering for providing the microfabrication facilities and the High Density Electronics Center for access to AFM, SEM, and XRD facilities. We also thank Prof. Simon Ang for use of the RIE equipment and Prof. Hameed Naseem for use of the thermal evaporator. Dr. G. Sreenivas, Mr. Lim Beng Kooi, and Dr. John Shultz are gratefully acknowledged for their helpful assistance and useful discussions. We also express our gratitude to Dr. Stephen W. Feldberg for valuable discussions and to Bioanalytical Systems for providing us with the evaluation copy of cyclic voltammetric digital simulator software (Digisim).
Received for review September 22, 1997. Accepted April 7, 1998. AC971041P
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