JOURNAL OF APPLIED PHYSICS

VOLUME 95, NUMBER 12

15 JUNE 2004

Ionic and electronic impedance imaging using atomic force microscopy Ryan O’Hayre Department of Materials Science and Engineering, Stanford University. Rapid Prototyping Laboratory, Building 530, Room 226, Stanford, California 94305-303

Minhwan Lee Department of Mechanical Engineering, Stanford University, Stanford, California 94305

Fritz B. Prinz Department of Mechanical Engineering, and Department of Materials Science and Engineering, Stanford University, Stanford, California 94305

共Received 21 October 2003; accepted 12 March 2004兲 Localized alternating current 共ac兲 impedance measurements are acquired directly through a conductive atomic force microscope 共AFM兲 tip. Both a spectroscopy mode 共where full impedance spectra are obtained at fixed locations on a sample surface兲 and an imaging mode 共where single frequency impedance maps are acquired across a sample兲 are used to characterize Au/Si3 N4 test structures, ZnO varistors, and Nafion membrane 共an ion conductor兲. Both modulus and phase information are acquired simultaneously. The use of an ac technique permits the study of electrochemical systems and ion conductors in addition to electronic systems. The capabilities and limitations of the AFM impedance imaging technique are discussed in detail. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1737047兴

I. INTRODUCTION

this paper leverages the capabilities of an AFM to acquire impedance images with sub 100 nm resolution. Furthermore, the technique is designed to measure all solid-state materials systems. The system is constructed from a commercially available AFM coupled to impedance measurement hardware 关Fig. 1共a兲兴. The AFM tip, which must be conductive, serves as the probe electrode for the IS measurements. Successive measurements across a sample surface are obtained by moving the AFM tip. Due to the time requirements for impedance acquisition, measurements are currently obtained in a pointby-point fashion rather than in a continuous scanning manner. Single frequency or complete impedance spectra can be obtained during the scans. Custom developed software automates the communication and synchronization between the hardware systems. AFM electrical property measurements are not new. Scanning spreading resistance microscopy7–9 共SSRM兲, conductive or current sensing AFM,10–12 and 13,14 tunneling-AFM allow dc characterization of materials. Other techniques make use of the long-range electrostatic forces between a sample and a conductive noncontact AFM tip to extract surface potential images15,16 共scanning surface potential microscopy, SSPM兲 or capacitive information on semiconductor oxide surfaces17–19 共scanning capacitance microscopy, SCM兲. Layson et al.20 have obtained ac impedance data on poly共ethylene兲 oxide films directly through a conductive AFM tip at individual points on the film surface, but do not report impedance imaging. Recently, Kalinin and Bonnell21,22 have reported a scanning impedance microscopy technique 共SIM兲 that detects the phase change in a conductive noncontact cantilever as a lateral bias is applied to a sample of interest. This technique in combination with SSPM, is shown to be useful for the determination of ac transport properties across lateral interfaces. In the SIM tech-

In this contribution, we disclose the development of an impedance microscopy system that allows highly localized alternating current 共ac兲 measurements to be acquired at the submicron length scale. Nanometer scale visualization and measurement of impedance is valuable for a wide variety of materials investigations, including solid electrolytes, semiconductors, electroceramics, coatings and corrosion research, and Li-ion battery and fuel cell systems. Impedance spectroscopy 共IS兲 is a key characterization tool in the research and development of diverse materials systems. In fuel cell and battery research, it has been used to distinguish between various sources of cell loss; for example, ohmic losses in the electrodes and electrolyte, activation overpotentials due to reaction kinetics, and mass transport effects. While these measurements resolve electrochemical phenomena mechanistically, they cannot resolve the phenomena spatially. In other words, standard IS measurements produce bulk, or system averaged results. Recently, several spatially resolved impedance techniques have been developed. Fleig et al.1,2 have used patterned arrays of microelectrodes to acquire spatially resolved impedance data from polycrystalline ceramics with a lateral resolution of 15–20 ␮m. Issacs et al. and others3–5 have demonstrated localized electrochemical impedance spectroscopy methods 共now commercialized兲 that function in an aqueous electrolyte and are capable of acquiring impedance data with a resolution of about 30 ␮m. Most recently, Pilaski et al.6 have developed a scanned technique based on a capillary liquid-electrolyte droplet cell with an apparent resolution of around 100 ␮m. In contrast to these methods, the atomic force microscope 共AFM兲 impedance imaging technique introduced in 0021-8979/2004/95(12)/8382/11/$22.00

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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004

O’Hayre, Lee, and Prinz

FIG. 1. Schematics of the experimental configurations used in this study for AFM impedance imaging. 共a兲 General concept of AFM impedance imaging. Impedance is measured between a local probe 共the AFM tip兲 and a bulk electrode. A significant spreading resistance contribution at the AFM tip/ sample contact point ensures local characterization 共shown schematically by the hemispherical lines兲. 共b兲 Experimental configuration for the Au/Si3 N4 test structures. The gold lines 共black兲 are connected to the bulk electrode. If the AFM tip scans over the gold regions, an ohmic response should be obtained. 共c兲 Configuration for the Nafion characterization experiment. The impedance is measured between an AFM tip on the Nafion top surface and a bulk bottom electrode 共a reversible hydrogen electrode兲 which is hermetically sealed and supplied with hydrogen gas.

nique, the voltage perturbation is not applied through the tip, but rather between macroscopic electrodes on the substrate. Shao, Kalinin, and Bonnell23 have even more recently reported a contact version of SIM, using essentially the same technique to acquire localized impedance that we report here.24 Thus, we are not the first to report of contact-mode submicron impedance imaging. Nonetheless, this contribution represents a significant elaboration on the details, capabilities, and limitations of the AFM impedance imaging technique, as well as an extension of the technique to the electrochemical and ionic domain. II. EXPERIMENTAL A. Impedance characterization

Impedance Z is the ratio between an applied sinusoidal voltage perturbation, E(t)⫽E 0 expi␻t, and a system’s resultant current response, I(t)⫽I 0 expi(␻t⫺␾). Laplace transformations of E and I from the time domain to the frequency do˜ ( ␻ ) and I(t)→I˜ ( ␻ )] yield Z as a function of main 关 E(t)→E the frequency ␻: ˜E 共 ␻ 兲 Z共 ␻ 兲⫽ ˜ . I共 ␻ 兲

共1兲

By measuring a system’s impedance over a range of frequencies, an impedance spectrum can be constructed. The frequency-resolved modulus (Z 0 ) and phase 共␾兲 information obtained from an impedance measurement allow characteristic relaxation times of a system to be identified. These relaxation times can be associated with various physicochemical processes including ionic transport, charge transfer, and diffusion. Typical measurement frequencies span from 1 MHz to 1 mHz, thus electronic relaxation processes 共which have much higher relaxation times兲 are usually not resolved. B. Localized impedance

Because AFM impedance measurements are conducted in contact mode, the resolution of the method is governed by the size of the conductive AFM tip. Typical AFM tip dimensions are much smaller than typical sample dimensions, thus

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FIG. 2. Frequency-bandwidth limitations of the current AFM-impedance system. Chart shows the envelope of available impedance/frequency space over which accurate measurements can be made. The characteristic impedance moduli of several sample materials are shown on the chart for reference.

the spreading resistance associated with a small volume of material near the tip/sample contact point often dominates the total impedance response of the system 关see Fig. 1共a兲兴. This localized response may be approximated by the spreading resistance formula for a circular point contact of radius r between the tip and sample: R SR⫽

␳ . 4r

共2兲

Where ␳ is the resistivity of the sample. In nonhomogeneous samples, additional nonlocal contributions to the impedance response can arise from high-impedance elements 共such as blocking grain boundaries兲. In certain cases, these nonlocal contributions can overshadow the localized impedance response. The localized impedance response originates from a small volume of material, roughly equivalent in size to the radius of the tip/sample point contact. Typical conductive AFM tip contact radii are on the order of 10–100 nm 共at the high forces used in this technique兲, thus setting the absolute lower limit for AFM impedance imaging resolution. Small contact points permit high resolution, but also lead to high impedances. The ability to measure extremely high impedance therefore becomes a chief limitation of the AFM impedance technique. For metals, this is not a constraint; assuming an AFM tip contact radius of 10 nm and a typical metal resistivity value ␳ metal⫽10⫺4 ⍀ cm, R SR⫽25 ⍀. However, the resistivities of typical ionic conductors are many orders of magnitude larger. For ␳ ionic conductor⫽104 ⍀ cm, R SR ⫽2.5 G⍀. These large resistances, when combined with unavoidable stray capacitances present in a measuring system, can lead to RC-time constants that may obscure meaningful processes. This can restrict the available frequency bandwidth over which reliable impedance data can be extracted. Figure 2 gives an example of the approximate frequency measurement range for various sample materials ranging from metals to ceramic ion conductors. This figure is based on the typical stray capacitance value in our AFM impedance imaging system 共measured to be around 10–100 pF兲.

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Quantitative AFM impedance measurement depends critically on the nature of the tip/sample contact. The impedance of the tip/sample contact can be modeled with a parallel RC element. R, the tip/sample contact resistance, is a function of the contact force, contact area, and might also be a function of any dc bias between the tip and the sample 共i.e., the tip/sample contact may exhibit Schottky behavior兲 C, the tip/sample capacitance, is a function of the tip/sample contact area. C also contains a nonlinear contribution from stray capacitive coupling to the extended tip area, as well as any contributions from charging due to nonohmic behavior or an electrochemical double layer. Crude estimations of the tip/ sample capacitance 共⬃1 pF兲 are considerably less than the total measured system capacitance 共10–100 pF兲, indicating that the tip/sample capacitance is not the bottleneck in the current system. Further exploration of the tip/sample impedance model is intended for future publication.

C. Experimental configuration

The AFM impedance-imaging hardware consists of a Molecular Imaging PicoPlus AFM in combination with a computer-controlled Gamry PC4/750 potentiostat/impedance measurement system. Optical access for alignment and feature location is provided by a large working distance lens system coupled to a charge-coupled device 共CCD兲 camera output. The available impedance measurement frequency range of the system spans from 100 kHz–1 mHz. Coordination between the impedance measurement system and the AFM system is accomplished via a file interchange communication. The AFM hardware is enclosed in a vibration isolation chamber to limit acoustic noise, and is placed inside a Faraday cage to limit electronic noise. Measurement cables are shielded and cable lengths are balanced and minimized to limit stray capacitance. Impedance measurements are conducted with ac excitation signals ranging from 10–100 mV, and dc bias ranges from 0– 8 V. To ensure quality AFM impedance imaging results, appropriate AFM tip selection is crucial. As will be shown later, reproducible impedance measurements require large tip/sample contact forces 共in the ␮N range兲. Therefore, cantilevers with high spring constants (k⬎10 N/m) must be used. Many researchers have noted that large tip/sample contact forces can lead to rapid wear of both the conductive coating and the Si probe tip.25,26 This problem is mitigated by the use of boron-doped diamond coated probes. The diamond coating is extremely wear resistant and the high-dose boron doping gives degenerate conductivity. Typical probe lifetime is extended from minutes/hours for a metal-coated probe, to days/months for a doped diamond coated probe. Several additional advantages are conferred by the choice of diamond-coated probes over metal-coated probes. Diamond probes exhibit extremely low voltammetric background currents and double-layer capacitances.27 Diamond probes are also highly stable, exhibiting a remarkably wide electrochemical potential window.28 These are all highly desirable traits for an electrochemical impedance probe. For all of these reasons, the data in this paper were acquired with conductive diamond coated noncontact AFM cantilevers

O’Hayre, Lee, and Prinz

FIG. 3. Impedance modulus vs tip/sample contact force for a conductive diamond AFM tip in contact with a gold-coated silicon sample. The measured impedance quickly drops with increasing tip/sample contact force, then stabilizes, suggesting that measurements at high force values are more repeatable.

共Nanosensors GmbH CDT-NCHR兲; the typical force constant was approximately 50 N/m and typical tip resistance was around 3000 ⍀. During impedance measurement a constant tip/sample force of 1.25 ␮N was maintained; during topographic scans this force was reduced by a factor of 20 to limit wear and minimize surface damage. D. Measurement speed and resolution

The absolute resolution limit of the AFM impedance technique is set by the extent of the tip-sample contact spreading resistance. In practice, however, measurement time often constrains the achievable detail of impedance images. To reduce measurement time and limit drift, it is currently necessary to acquire two-dimensional 共2D兲 impedance maps at a single measurement frequency 共for example 100 Hz兲. Generally, full impedance spectra are first taken at several points across the surface to determine the chief frequencies of interest. 共i.e., characteristic frequencies that correspond to spectral peaks or valleys in the impedance spectra.兲 Then, single-frequency impedance images are acquired at these characteristic frequencies of interest. It is assumed that the critical frequencies do not shift significantly across the sample or in time. Measurement speed is currently 1–3 sec per point for frequencies greater than 10 Hz. 共At lower frequencies, the measurement time increases commensurately.兲 This measurement time includes a settling period to allow the tip 共which is stepping from pixel to pixel across the surface兲 to establish good contact with the sample. An automatic cycle integration algorithm is used during the impedance measurement to establish a consistent and repeatable impedance value before the system steps to the next pixel. 2D impedance images consist of impedance measurements from a pixel grid of tens to thousands of points, therefore acquisition of a complete impedance image can take minutes or hours. Location imprecision can be estimated from knowledge of the directed drift rate of the AFM system and the impedance measurement time. Modern AFM system drift rates are quite low, typically less than 2 nm/min—nevertheless, drift

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FIG. 4. The variability of single-point AFM impedance measurements for two different force set points between a conductive-diamond AFM tip and a gold-coated silicon sample. 共a兲 Impedance measurements are acquired while the tip is held at a fixed position in contact with the gold film. 共b兲 Impedance measurements are acquired while the tip is stepped in 10 nm increments across the gold surface. In both cases, the variability of the impedance data decreases substantially at the higher force set point, indicating that measurements at highforce values are more repeatable.

can accumulate during a long measurement. For example, the total time to acquire a 100⫻100 pixel image of a 10⫻10 ␮m area is about 5.5 h. Although the image pixel size in this case is 100 nm, the accumulated drift by the end of the measurement is 330 nm 共based on a 1 nm/min directed drift rate兲. The implementation of a closed-loop scanner control or software-based drift correction may be of tremendous help here. All 2D impedance images presented in this contribution are constructed from single-frequency impedance scans taken in 50⫻50 pixel arrays. The 50⫻50 pixel array size is chosen as a compromise between image detail and measurement time. Typical measurement times for 50⫻50 pixel arrays are 1– 4 h. The raw impedance modulus (Z 0 ) versus position and phase angle 共␾兲 versus position data are postprocessed in MATLAB 共color range, contrast, pixel smoothing, interpolation兲 to produce 2D images. III. RESULTSÕDISCUSSION A. Impedance repeatability

The ability of the AFM impedance imaging system to produce reliable, repeatable, single-point results was evaluated in a series of simple experiments. Because the AFM impedance technique is performed in contact mode, the measured impedance is sensitive to the tip-sample contact force. Figures 3 and 4 summarize the results of impedance repeat-

ability versus force experiments conducted on a simple goldcoated silicon sample 共single point impedance measurements at 100 Hz兲. The sharp bend of the curve in Fig. 3 suggests that impedance measurements made at sufficiently high contact forces 共e.g., ⬍1 ␮N兲 should be relatively insensitive to small errors or inaccuracies in tip/sample contact. In other words, at high contact forces, the measured impedance values change little with small force variations. This hypothesis is further reinforced by the results in Fig. 4. In Fig. 4共a兲, 150 impedance measurements were collected while the AFM tip was held with a constant contact force on the gold film for approximately 0.5 h. The experiment was conducted at two different force set points: 0.50 ␮N and 1.25 ␮N. It is clear that the use of a high force set point dramatically improves data consistency. During AFM impedance imaging, the tip is continually retracted and then extended point by point across a sample of interest. Under these conditions, although a constant force set point is maintained at each measurement point, the repeated establishment of new surface contacts combined with slight variations in the AFM Z-scanner control and tip/ surface interaction could affect the tip/sample contact and thus the measured impedance. The results of Fig. 4共b兲 show that at least for a smooth gold surface, these fears are not warranted. These data were acquired for a stepwise scan 共10 nm steps兲 on the same gold film as in Fig. 4共a兲. Both the

TABLE I. Summary of the single point impedance repeatability data on gold. Higher tip/sample contact force reduces the standard deviation of the impedance measurement. There is little difference between a scanned-tip mode and a fixed tip mode on the variability or absolute magnitude of the impedance data. Trial Scanned tip, 0.5 ␮N Force Scanned tip, 1.25 ␮N Force Fixed contact, 0.5 ␮N Force Fixed contact, 1.25 ␮N Force

Measurements

Average

Standard deviation

Standard deviation 共%兲

150 150 150 150

3243 2633 3254 2635

⫾97.0 ⫾28.2 ⫾127.1 ⫾25.0

2.99 1.07 3.90 0.95

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FIG. 5. Topographic deflection 共top row兲, impedance modulus 共middle row兲, and impedance phase 共bottom row兲 images from a gold/silicon nitride test pattern. Images increase in magnification from left to right. Images acquired according to the experimental configuration from Fig. 1共b兲. Topographic deflection at 2 Hz scan speed, 512⫻512 resolution. Impedance modulus and phase acquired at 1000 Hz, with a 10 mV excitation signal and 0 V dc bias.

absolute values and statistical variability of the scanned-tip data 关Fig. 4共b兲兴 are comparable to those of the fixed-tip data 关Fig. 4共a兲兴, indicating that variations due to tip/sample contact fall within the experimental noise of the impedance measurement 共see Table I兲. Of course, a smooth gold film provides the almost ideal case for repeatable tip/surface contact. Repeatability on rough samples or sharp topographical features will certainly be worse. In addition, dramatically softer or harder samples will likely exhibit very different forceimpedance behavior, obligating larger or smaller force set points to acquire optimal AFM impedance data. B. Impedance imaging of test structures

2D AFM impedance imaging capabilities were validated using specially developed microscale gold test patterns. 共Experimental configuration follows Fig. 1共b兲.兲 Representative Z 0 and ␪ images obtained from the test patterns are compared to their topographic counterparts 共topography deflection images兲 in Fig. 5. Note that the phase angle for the gold region is close to zero, indicative of ohmic transport, while the phase of nitride is close to ⫺90°, indicative of capacitive

FIG. 6. Bode impedance modulus spectra 共a兲 and impedance phase spectra 共b兲 acquired at specific locations (A – E) on the gold/nitride test pattern. The measurement locations (A – E) are denoted on the 10 ␮m impedance modulus image in Fig. 5. Spectra from the gold film show ohmic behavior, while spectra from the nitride region show a capacitive response. The impedance spectra were acquired from 100 kHz–100 mHz with a 10 mV excitation signal and 0 V dc bias.

behavior. 共Mean phase values for the gold and nitride regions are—0.09° and ⫺88°, respectively.兲 Note that at the 1 ␮m scale, the boundary between the nitride film and the gold is more clearly resolved by the impedance image than the topography image. Full impedance spectra taken at several points on the sample 共points A – E in Fig. 5兲 confirm the ohmic response of the gold and the capacitive behavior of the nitride 共Fig. 6兲. As indicated by the color-scale, the impedance images in Fig. 5 show an apparent binary contrast between the gold and the nitride. The mean impedance of the gold is around 5000 ⍀, while the mean impedance of the nitride is (4⫻106 ) ⍀. If the image contrast is adjusted so that variations at the low-

FIG. 7. 共a兲 Impedance modulus image from a 1 ␮m area of the gold/nitride test pattern, scale adjusted to show the contrast details in the gold film impedance. 共b兲 The same impedance modulus image scale adjusted to bring out the contrast details in the nitride film impedance. The apparent nitride film details are likely associated with the noise structure of the instrument. Images acquired at 1 kHz with a 10 mV excitation signal and 0 V dc bias.

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FIG. 8. 共a兲 SEM image of a 50 ␮m region of a polished, cross-sectioned commercial ZnO varistor. 共b兲 AFM topography deflection image of the same 50 ␮m region, acquired at 2 Hz scan speed, 512⫻512 pixel resolution. 共c兲 Impedance modulus image of the same 50 ␮m region acquired according to the experimental configuration in Fig. 1共a兲. Impedance modulus image data were acquired at 1 kHz with a 100 mV excitation signal and 5 V dc bias. The bulk electrode for this measurement is located approximately 30 ␮m above and to the left of the image field of view.

end of the impedance range are visible, 关Fig. 7共a兲兴 further detail is resolved. Slight impedance variations, possibly due to changes in the thickness and topography of the gold film at the boundary with the nitride region, are apparent. Similar contrast adjustments at the high end of the impedance range allow variations in the nitride film to be seen 关Fig. 7共b兲兴. The true impedance of the nitride film exceeds the measurement capabilities of our instrument at 1 kHz. Therefore, it is believed that these apparent variations in the nitride film impedance are simply a visualization of the error and noise structure of the instrument. C. Impedance imaging application to ZnO varistors

A practical example of AFM impedance imaging in the electronic domain is provided by a study of grain/grain boundary transport in commercial polycrystalline ZnO varistors. Following Fig. 1共a兲, the impedance of a cross-sectioned commercial ZnO varistor was probed laterally between the AFM tip and a bulk top electrode. Thus, in addition to the local impedance response at the AFM tip, nonlocal impedance contributions from any intervening grain boundaries between the tip and the bulk electrode are also probed.

Coupled scanning electron microscopy 共SEM兲, AFM topography deflection, and AFM Z 0 images from a 50 ␮m region of the ZnO varistor are shown in Fig. 8. The Z 0 image was acquired with a 100 mV excitation signal under ⫹5 V dc bias at 1 kHz. Several distinct ZnO grains are visible in the images. The ZnO grains at the upper left of the image show purely ohmic behavior at a ⫹5 V dc bias. These grains are closest to the bulk top electrode, which was positioned approximately 30 ␮m above and to the left of the image field of view. The highly nonlinear IV properties of ZnO varistors arise from double-Schottky like barriers formed at the grain boundaries of the material. Below a critical grain-boundary breakdown voltage 共typically 3– 4 volts兲, transport across the boundary is almost purely capacitive and the boundary is highly insulating. Above the critical voltage, however, transport across the grain boundary becomes ohmic.29,30 Figure 9 shows a set of Z 0 and ␪ images for the same 50 ␮m area at five different bias voltages ranging from 0 V dc to ⫹8 V dc 共measurements acquired at 1 kHz with a 100 mV excitation兲. Note how individual grain boundary barriers are shorted one by one during the dc bias voltage ramp, starting from the upper left with the grains closest to the electrode.

FIG. 9. Impedance modulus 共top row兲 and impedance phase 共bottom row兲 images measured as a function of dc bias for the same 50 ␮m ZnO region documented in Fig. 8. From left to right, the images are acquired with increasing dc bias; 0 V, 3 V, 4 V, 5 V, 8 V. All images acquired at 1 kHz with a 100 mV excitation signal. Note the grain-by-grain ‘‘cascade’’ with increasing dc bias as the grains become conductive, starting with the grains on the upper left closest to the bulk electrode.

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FIG. 10. Impedance modulus 共top row兲 and impedance phase 共bottom row兲 images measured as a function of frequency for the same 50 ␮m ZnO region documented in Figs. 8 and 9. From left to right, the images are acquired with decreasing measurement frequency; 100 kHz, 10 kHz, 1 kHz, 100 Hz. All images were acquired with a 100 mV excitation signal and 4 V dc bias. Note the improved impedance contrast at lower frequency.

This grain-by-grain cascade visibly demonstrates the highly nonlinear IV characteristics of the polycrystalline varistor. The first grains to exhibit ohmic transport characteristics do so at 3– 4 V dc, indicating that they are removed by a single grain boundary from the top electrode. The other grains become ohmic between 5– 8 V dc, indicating that they are probably separated by two grain boundaries from the top electrode. This result is reasonable given the varistor’s 40 ␮m average grain size and the location of the top electrode 30 ␮m above and to the left of the images. Figure 10 presents Z 0 and ␪ images as a function of measurement frequency for the same 50 ␮m area explored in Figs. 8 and 9 共measurements acquired at ⫹4 V dc bias with a 100 mV excitation兲. Note the improved impedance contrast at lower frequency. This contrast improvement is expected based on an analysis of the RC-impedance behavior of the varistor grains. In single-frequency impedance imaging, careful choice of the imaging frequency based on the characteristic behavior of the analyzed system is necessary in order to achieve maximum impedance contrast. A theoretical treatment is intended for a later publication.

Figure 11 demonstrates the submicron resolution capabilities of the AFM impedance imaging technique with a series of ‘‘zoom-in’’ magnifications on a ZnO triple junction. The small triangular shaped region at the junction between the three ZnO grains 共clearly visible in the 6 ␮m image兲 is a Bi2 O3 second-phase inclusion confirmed by energy dispersive x-ray analysis 共EDAX兲. Bi2 O3 is added to ZnO varistors to control the grain-boundary properties of the material. Excess Bi2 O3 typically phase segregates to the ZnO triple junctions. It is nonconductive. In addition to single-frequency impedance images, full impedance spectra can be acquired at specified locations on a sample. Figure 12 compares impedance spectra acquired at several distinct locations on the varistor sample. Locations 共a兲 and 共b兲 are within ZnO grains, and show a transition from capacitive, blocked behavior at low dc bias to ohmic, conductive behavior at high dc bias. Location 共c兲 is inside a second phase Bi2 O3 inclusion, and shows insulating behavior over the entire dc bias range.

FIG. 11. AFM topography deflection 共top row兲 and impedance modulus 共bottom row兲 images, increasing in magnification from left to right. 共50 ␮m, 15 ␮m, and 6 ␮m scan regions, respectively.兲 Impedance-modulus images are acquired at 1 kHz with a 100 mV excitation signal and 5 V dc bias. The images ‘‘zoom’’ into a triplejunction region between 3 ZnO grains. The V-like intrusion between the three grains is a highly insulating Bi2 O3 second phase inclusion 共confirmed by EDX analysis.兲

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FIG. 12. Impedance spectra 共Nyquist format兲 from various locations on the ZnO-sample surface. 共a兲 Impedance spectra vs dc bias acquired at location a. Capacitive blocking behavior is seen for 0 V and 3 V applied dc bias. At 5 V applied dc bias, an impedance loop develops. 共b兲 Similar impedance behavior vs dc bias is observed at location b on the sample surface. 共c兲 At location c, capacitive behavior is observed at all levels of applied dc bias. Location c corresponds to a Bi2 O3 second phase inclusion.

D. Impedance imaging application to Nafion solid polymer electrolyte

The AFM impedance technique may also be applied to studies of ionic materials and/or electrochemical systems. In this section, we report localized impedance measurements on the protonated form of Nafion solid polymer electrolyte. Following the experimental setup in Fig. 1共c兲, a platinum coated AFM tip is used as a local probe of the proton (H3 O⫹ ) density in a Nafion 117 membrane 共30 nm Pt sputtered over the standard conductive diamond AFM tip兲. Hydrogen gas is provisioned to a sealed anode compartment underneath the electrolyte membrane sample, providing a continuous supply of protons into the membrane. 共The anode is a standard polymer-electrolyte fuel cell catalyst electrode, details given elsewhere.31,32兲 Applying a dc bias to the platinum-coated AFM tip 共the bias is applied relative to the anode electrode, which is pseudoreversible because of its much larger size兲 causes a Faradaic charge transfer reaction to occur, with protons from the membrane combining with oxygen from the air to produce water. Essentially, the Ptcoated AFM tip, in contact with the electrolyte membrane, becomes a tiny, moveable, fuel cell cathode. The kinetics of the cathode reaction will be proportional to the local concentration of protons in the membrane. Using the AFMimpedance technique to probe this Faradaic charge transfer reaction permits the local activity of the electrolyte membrane to be visualized. The impedance spectra in Fig. 13 confirm the ability of the Pt-coated AFM tip to act as a localized electrochemical probe. A Faradaic-like charge transfer loop is seen in the impedance response only if all of the following conditions are met. 1兲 A Pt-coated tip is used. 2兲 H2 gas is provisioned to the anode compartment. 3兲 A cathodic dc bias is applied.

4兲 The tip is in hard physical contact with the electrolyte membrane. Observation of this response only when all four conditions are met indicates that the loop most likely corresponds to a Faradaic reaction at the tip-electrolyte interface. This conclusion is supported by the behavior of the impedance loop with applied dc bias, as shown in Fig. 14. The loop shrinks with increasing dc bias, highly characteristic of a Faradaic charge-transfer reaction.

FIG. 13. Representative Nyquist impedance spectra for localized AFM impedance measurements on Nafion membrane. Impedance spectra are measured according to the experimental configuration in Fig. 1共c兲 over the frequency range 100 kHz–100 mHz with a 30 mV excitation signal. An impedance loop appears only when H2 gas is provisioned to the anode, the AFM tip is in hard contact with the membrane, the AFM is coated with platinum, and a cathodic dc bias is applied to the tip. If any combination of the above conditions in not met, purely capacitive blocking behavior is observed instead. These observations suggest that the impedance loop behavior arises from a Faradaic charge transfer reaction occurring at the tip/ electrolyte membrane interface.

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FIG. 14. Nyquist spectra of the Pt-tip/Nafion impedance response as a function of applied dc bias. Impedance spectra are measured according to the experimental configuration in Fig. 1共c兲 over the frequency range 100 kHz– 100 mHz with a 30 mV excitation signal. H2 gas is provisioned to the anode, the AFM tip is in hard contact with the membrane, and the AFM is coated with platinum. The impedance loop shrinks with increasing dc bias, characteristic of a Faradaic charge transfer process.

Translation of the AFM tip across the surface of the electrolyte permits spatially resolved ‘‘electrochemical’’ impedance images to be acquired, just as electrical impedance images were acquired for the gold patterns and the ZnO varistors. Figure 15 shows sets of fixed-frequency AFM impedance images of a Nafion electrolyte membrane. These images were acquired at 1 Hz with a 30 mV excitation signal, 0.4 V dc cathodic bias 共the bias favors the oxygen reduction reaction, thus decreasing the Faradaic chargetransfer resistance and improving the signal to noise兲. The images compare the impedance response from a dry Nafion membrane 共imaged under dry, 0% relative humidity, room temperature air兲 versus the same area of the same membrane when hydrated 共imaged under 30% relative humidity, room temperature air兲. The hydration level of the Nafion electrolyte significantly influences its solvated proton (H3 O⫹ •nH2 O) concentration and conductivity. This is

O’Hayre, Lee, and Prinz

readily apparent from the AFM impedance images, which show a dramatic change in the impedance response 共note change in the impedance scale兲. The corresponding topography images are not shown, but bear no relation to the impedance response. Membrane swelling and consequent dimensional expansion prohibited measurement of the membrane under still higher humidity levels. It is well known that Nafion is not a homogeneous material, but instead consists of hydrophilic and hydrophobic phase-segregated regions. The apparent features seen in the Nafion impedance images of Fig. 15 may correspond to hydrophilic domains in the membrane. The apparent sizes of these domains 共refer to the 1 ␮m image兲 are on the order of several hundred nanometers. This is larger than the 40–100 nm domains visualized by a SSPM study of dry Nafion recently published by Kiyoshi et al.33 Kiyoshi and co-workers’ study looked at the variation in surface potential across a Nafion membrane. Several tens of high-surface potential spots were seen in a 10 ␮m by 10 ␮m scan of a Nafion membrane, and were attributed to hydrophilic watercontaining regions in the Nafion electrolyte. The larger domain size in our results may be due to several factors, including drift, ‘‘smearing,’’ and the possible existence of a water meniscus at the tip/sample contact. The images in Fig. 15 were acquired in a vertical scan mode. A possible vertical distortion or smearing effect can be seen in the 1 ␮m images. We hypothesize that water from the hydrophilic domains on the Nafion surface might be captured on the tip as it steps from point to point, resulting in an extension, or smearing of the apparent hydrophilic domain sizes, especially in the scan direction. The formation of a water meniscus at the tip/ sample junction would also serve to increase the overall apparent size of the hydrophilic Nafion domains. Nevertheless, these qualitative results show an overall decrease in impedance and an expansion of the low-impedance domains with increasing hydration, which are consistent with current knowledge on the behavior of Nafion.

FIG. 15. Impedance modulus 共top row兲 and impedance phase 共bottom row兲 images of the Nafion electrolyte membrane as a function of humidity. The image sets on the left compare the impedance response under dry 共0% relative humidity兲 vs ambient 共30% relative humidity兲 conditions for a 40 ␮m area of the Nafion membrane. The image sets on the right compare the impedance response under dry vs ambient humidity conditions for a 1 ␮m area of the Nafion membrane. Images acquired at 1 Hz with a 30 mV excitation signal, 0.4 V dc cathodic bias. The hydration level of the Nafion electrolyte significantly influences its H3 O⫹ concentration and ionic conductivity, as is readily apparent from the impedance images 共note change in the impedance modulus scale for the left image set兲.

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IV. CONCLUSIONS

Measurement speed is one of the most significant limitations of the current AFM impedance imaging technique. Long measurement times introduce a host of associated problems including temperature stability, tip and sample drift issues, image distortion, and nonstationary impedance concerns 共especially when imaging electrochemical systems兲. As previously discussed, acquisition of a single AFM impedance map can take several hours, and information is only collected for a single frequency. In future implementations, Fourier impedance methods could provide a way to probe multiple frequencies simultaneously.34 –36 While such techniques would not significantly reduce measurement time, they would significantly increase measurement bandwidth. AFM impedance measurement is conducted by a combination potentiostat/impedance analyzer system, which can enforce controlled potentials 共i.e., fixed dc bias兲 during impedance measurements. This ability allowed us to establish highly repeatable, stationary, well-defined dc bias points for the ZnO and Nafion electrolyte studies. In the future, other capabilities of the potentiostat could also be harnessed to perform additional localized electrochemical techniques such as cyclic voltammetry, potential-sweep and stepmeasurements, galvanostatic methods, etc. The instrument can also be used to take simple DC measurements, 共similar to SSRM measurements兲, but with the high accuracy, precision and voltage control of potentiostatic regulation. Such dc measurements sacrifice information bandwidth 共loss of frequency, phase information兲 for significantly improved measurement speed. They also achieve higher resolution, and thus can provide a valuable supplement to ac impedance measurements. Figure 16 shows a dc measurement example from a gold test structure 关Fig. 16共a兲兴 and a ZnO varistor 关Fig. 16共b兲兴. These dc images were acquired at a rate approaching 2 min per image in a dynamic scanning mode 共rather than point by point兲. The resolution in these images is sub-100 nm, probably approaching 10 nm. Because the spreading resistance volume sampled by the tip is essentially the same in a dc versus ac measurement, these images imply that the ac impedance method could also achieve 10–50 nm resolution if stray capacitance, pixilation, sample drift, distortion, and other sources of ac error can be mitigated. Reduction of stray capacitance and other sources of spurious ac response can be achieved through careful tip design, thus allowing access to smaller RC time constants. The RC characteristics of the tip can be improved via selected area conductive patterning of the tip. Ideally, only the extreme end of the tip should be conductive, with only a small conductive pathway leading out to the measurement system. Further noise reduction and bandwidth improvement can be gained through tip shielding, for example, with the development of innovative coaxial-type tip geometries. Because the properties of an increasing number of materials depend strongly on nanoscale structure and processes, nanoscale characterization techniques such as AFMimpedance imaging are likely to be increasingly useful. Localized ac impedance and transient potential techniques may be especially critical in the domain of electrochemical sys-

FIG. 16. 共a兲 AFM topography and corresponding dc resistance image from a 100 nm region of the gold/nitride test structure 共at the boundary between the gold and the nitride兲, acquired using the experimental configuration in Fig. 1共b兲. dc resistance data acquired in scan mode with 64⫻64 pixel resolution at 0.2 Hz per line. 共b兲 AFM topography and corresponding dc resistance image from a 1.5 ␮m region of a ZnO varistor 共at the boundary between two grains兲 acquired using the experimental configuration in Fig. 1共a兲. dc resistance data acquired in scan mode with 64⫻64 resolution at 0.5 Hz per line with 5 V dc bias. dc measurements show improved resolution compared to their ac counterparts 共compare to Figs. 5 and 11兲 but sacrifice information bandwidth.

tems. Faradaic reactions, ionic transport, and diffusion are best studied with transient techniques, making AFM impedance measurement extremely attractive for these applications. ACKNOWLEDGMENTS

The authors would like to warmly thank the members of the Rapid Prototyping Laboratory and especially the fuel cell team for their support and lively discussions. The authors would like to acknowledge financial support by The Office of Naval Research Contract No. N000140210220 and the Stanford Global Climate Energy Project 共GCEP兲. J. Fleig and J. Maier, Solid State Ionics 85, 9 共1996兲. J. Fleig, S. Rodewald, and J. Maier, Solid State Ionics 136, 905 共2000兲. 3 R. S. Lillard, P. J. Moran, and H. S. Issacs, J. Electrochem. Soc. 139, 1007 共1992兲. 4 F. Zou, D. Thierry, and H. S. Issacs, J. Electrochem. Soc. 144, 1957 共1997兲. 5 E. Bayet, F. Huet, M. Keddam, K. Ogle, and H. Takenouti, J. Electrochem. Soc. 144, L87 共1997兲. 6 M. Pilaski, T. Hammelmann, A. Moehring, and M. M. Lohrengel, Electrochim. Acta 47, 2127 共2002兲. 7 P. De Wolf, J. Snauwaert, L. Hellemans, T. Clarysse, W. Vandervorst, M. D’Olieslaeger, and D. Quaeyhaegens, J. Vac. Sci. Technol. A 13, 1699 共1995兲. 8 A. C. Diebold, M. R. Kump, J. J. Kopanski, and D. G. Seiler, Proc.Electrochem. Soc. 94, 78 共1994兲. 9 P. De Wolf, M. Geva, T. Hantschel, W. Vandervorst, and R. B. Bylsma, Appl. Phys. Lett. 73, 2155 共1999兲. 1 2

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