Microsc. Microanal. 20, 582–585, 2014 doi:10.1017/S1431927613013974
© MICROSCOPY SOCIETY OF AMERICA 2014
Application of Dynamic Impedance Spectroscopy to Scanning Probe Microscopy Mateusz Tomasz Tobiszewski,* Anna Arutunow, and Kazimierz Darowicki Department of Electrochemistry, Corrosion and Materials Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland
Abstract: Dynamic impedance spectroscopy, designed for measuring nonstationary systems, was used in combination with scanning probe microscopy. Using this approach, impedance mapping could be carried-out simultaneously with topography scanning. Therefore, correlation of electrical properties with particular phases of an examined sample was possible. The sample used in this study was spheroidal graphite cast iron with clearly defined phases having significantly different properties. Additionally, impedance-force curves were made at graphite precipitation and ferrite matrix to illustrate the relation between impedance and the force applied to a probe. Key words: AFM, SPM, DEIS, nanoimpedance, impedance, nanocontact
I NTRODUCTION AC impedance techniques are commonly used in many research areas. Usually they are employed to characterize macroscopic surfaces or bulk properties of materials. Thus, obtained results are averaged over the area or volume of an examined sample. In order to register local impedance spectra on different grains, phases, and inclusions on the surface, important developments have been made. Two main approaches are available: a micro-cell technique (Lohrengel et al., 2006; Galicia et al., 2009; Huang et al., 2011) and scanning probe microscopy (SPM) (Kalinin & Bonnell, 2001, 2002; Shao et al., 2003; O’Hayre et al., 2004b). The micro-cell technique is well established and used for in situ examination of metals in electrolytes while impedance measurements performed by means of SPM are mainly ex situ evaluations. Therefore, impedance measured with a micro-cell is electrochemical whereas SPM-based impedance is electrical. The time required to register the full impedance spectrum is relatively long since in both techniques impedance spectra are made point by point (Layson et al., 2003; Layson & Teeters, 2004; Birbilis et al., 2009; Arutunow et al., 2011, 2013a, 2013b). If impedance mapping is required, a single frequency is utilized in order to minimize the time of scanning (Kalinin & Bonnell, 2002; O’Hayre et al., 2004b; Pingree & Hersam, 2005). The probe moves across the surface while the time at each point needs to be relatively short. Unfortunately, the single frequency measurement is less informative than the one where a full impedance spectrum is obtained. To make a compromise between full spectra and single frequency measurements, the dynamic impedance spectroscopy (DIS) technique was proposed and applied to atomic force microscopy (AFM) (Darowicki et al., 2008). Received June 7, 2013; accepted November 26, 2013 *Corresponding author. [email protected]
In the DIS technique, the voltage perturbation signal consists of several frequencies, which are generated simultaneously. The response signal is registered and decomposed to individual components with short time Fourier transformation. Details of DIS, which was originally applied to electrochemical phenomena, are described in a series of publications (Darowicki, 2000; Darowicki et al., 2000; Darowicki & Ślepski, 2003, 2004). The aim of this project involves implementation of the DIS technique to AFM making it possible to continuously register relative impedance changes along with topography imaging and the changeable force applied to the probe.
MATERIALS
AND
METHODS
Spheroidal graphite cast iron, a classical diphase metal with phases of different mechanical and electrical properties, was investigated. The sample was ground on fine-grade silicon carbide abrasive paper up to 2,500 grade. Then, it was polished with commercially available polishing paste dedicated to steels, and finally cleaned and degreased with acetone in an ultrasonic bath. DIS was used in this investigation for impedance mapping and to conduct impedance-force curves of spheroidal graphite and the matrix. A description of the experimental system, equipment used, and principles of measurement can be found in Tobiszewski et al. (in press). The only modification introduced to the set-up regarded the lowest frequency, which in the case of impedance mapping had to be increased to 500 Hz. This enabled reduction of time the interval between each single spectrum to 0.01 s and made the scanning process faster. An advantage of DIS over conventional impedance measurement, where perturbation signals change frequency by frequency, is that more periods at each frequency are registered. The more full periods of each frequency registered, the more precisely the
Application of DIS to SPM
583
impedance can be measured. For example, the time required to obtain a spectrum at 15 frequencies ranging from 70 Hz to 4.01 kHz is only 0.1 s for DIS. Seven periods of the lowest frequency are registered at this time and the higher frequency, the more periods registered. A conventional way of generation and acquisition of seven periods at each of 15 frequencies would take ∼0.32 s. Registered impedance maps were 128 × 128 points and it was 60 × 60 µm in size. Impedance-force curves were registered at 27 points at graphite and 27 points at ferrite matrix.
RESULTS AND D ISCUSSION Topography and contact error images of spheroidal graphite cast iron are presented in Figures 1a and 1b. Parts of two graphite spheroids are visible at the top and the bottom of images. An impedance map was simultaneously obtained with topography and error images. Therefore, it is apparent that the same area is presented in Figures 1a–1c. Example spectra representing the white line drawn at the top of the impedance map are presented in Figure 2. It should be emphasized that recorded impedance changes are strictly of relative character. Initial spectra present high impedance response obtained at the ferrite matrix. The following sudden decrease of impedance is related to the probe movement from the matrix to the graphite inclusion. An electronic model proposed by O’Hayre et al. (2004a) was used in calculations of the impedance spectra in ZSimpWin software. Expected tip-sample contact capacitance was in the range of atto-Farads (Shao et al., 2003), which was far less than capacitances obtained in this project. Thus, capacitance was considered as stray capacitance and we present tip-to-surface R-value as the sum of resistances, where R = Rtip + Rcont + RSR, as the most meaningful and unaffected by stray capacitance value (Tobiszewski et al., in press). The spheroidal graphite cast iron surface was simultaneously scanned for topography and impedance. As a result, height and error images can be correlated with resistance distribution. All three images are presented in Figure 1, which clearly shows that graphite-tip contact has lower resistance than the ferrite-tip contact. Some distortions are naturally present, as the surface is not perfectly flat and geometry of the tip-sample contact changes during scanning. The surface was scanned in a constant force mode, therefore the tip penetrated into the soft phase (graphite) deeper than into the ferrite matrix. An enlarged contact area could be another reason for better graphite-tip conductivity. Impedance-force curves were performed 27 times at several graphite spherulites and 27 times at the ferrite matrix. Piezoelectric scanner movement in the Z direction was controlled and fixed in a constant range. Resulting DFL signal (proportional to the cantilever deflection and force applied to a probe) was registered. Therefore, measurement of the soft material caused smaller cantilever deflection
Figure 1. Topography (a), contact error (b), and tip-to-surface resistance R (c) images of 60 × 60 µm area for spheroidal graphite cast iron. The white line in (c) indicates the area for which examples of impedance spectra are presented in Figure 2.
and deeper tip indentation as compared to that of the hard material. The average cantilever deflection at the bottom scanner position on graphite was 1 and 1.35 nA on ferrite. In order to eliminate the influence of force and
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Mateusz Tomasz Tobiszewski et al.
Figure 2. Examples of impedance spectra corresponding to the white line at the top of image in Figure 1c.
The procedure for analysis of impedance–DFL curves was described previously (Tobiszewski et al., in press). Examples of curves for graphite and the ferrite matrix are presented in Figure 3. Each of the 27 curves recorded for graphite and for the matrix, correspondingly, was fitted to a linear equation and respective averages were made. Average curves for both phases and their equations are presented in Figure 4. The initial contact resistance was calculated to be 0.63 MΩ for graphite and 31.6 MΩ for ferrite matrix. Results indicate that the spheroidal graphite cast iron conducted current significantly better at graphite inclusions than at the matrix. This statement concerns only the surface properties, which may be far different from the bulk properties, for example, due to oxidation phenomena.
CONCLUSIONS
Figure 3. Examples of changes of the tip-to-surface resistance R on the ferrite and graphite inclusion versus DFL signal during loading.
DIS is useful in measurements of rapidly changing systems, which was in this case the tip-surface contact. The contact may change as the position of the tip changes during surface scanning or during pseudo-indentation measurements. Impedance mapping provides an overview of surface electrical properties, which is essential in many research areas. We strongly believe that impedance mapping or scanning spreading resistance microscopy techniques should always be supplemented by DFL–impedance/resistance curves. Extrapolation of curves to force F = 0 (DFL = 0) gives the results for undeformed surface, when the tip initially contacts the surface. The above allows for more precise and unique comparison of electrical properties for each phase. Moreover, the methodology presented here is a good starting point for in situ electrochemical impedance mapping.
ACKNOWLEDGMENT This work was supported by the Polish National Science Center under grant 2011/01/N/ST5/05594.
REFERENCES
Figure 4. Averaged results of the tip-to-surface resistance R, obtained from 27 points at the ferrite and the graphite inclusion respectively, versus DFL signal during loading.
contact area on the resistance parameter, a new value of “initial contact” was proposed. The resistance of initial contact is calculated from an impedance–DFL curve during loading for extrapolation of DFL (force) to DFL = 0.
ARUTUNOW, A., DAROWICKI, K. & TOBISZEWSKI, M.T. (2013a). Electrical mapping of AISI 304 stainless steel subjected to intergranular corrosion performed by means of AFM–LIS in the contact mode. Corrosion Sci 71, 37–42. ARUTUNOW, A., DAROWICKI, K. & ZIELIŃSKI, A. (2011). Atomic force microscopy based approach to local impedance measurements of grain interiors and grain boundaries of sensitized AISI 304 stainless steel. Electrochim Acta 56, 2372–2377. ARUTUNOW, A., ZIELIŃSKI, A. & TOBISZEWSKI, M.T. (2013b). Localized impedance measurements of AA2024 and AA2024-T3 performed by means of AFM in contact mode. Anti-Corros Methods Mater 60, 67–72. BIRBILIS, N., MEYER, K., MUDDLE, B.C. & LYNCH, S.P. (2009). In situ measurement of corrosion on the nanoscale. Corrosion Sci 51, 1569–1572. DAROWICKI, K. (2000). Theoretical description of the measuring method of instantaneous impedance spectra. J Electroanal Chem 486, 101–105.
Application of DIS to SPM DAROWICKI, K., ORLIKOWSKI, J. & LENTKA, G. (2000). Instantaneous impedance spectra of a non-stationary model electrical system. J Electroanal Chem 486, 106–110. DAROWICKI, K. & ŚLEPSKI, P. (2003). Dynamic electrochemical impedance spectroscopy of the first order electrode reaction. J Electroanal Chem 547, 1–8. DAROWICKI, K. & ŚLEPSKI, P. (2004). Instantaneous electrochemical impedance spectroscopy of electrode reactions. Electrochim Acta 49, 763–772. DAROWICKI, K., ZIELIŃSKI, A. & KURZYDŁOWSKI, K.J. (2008). Application of dynamic impedance spectroscopy to atomic force microscopy. Sci Technol Adv Mater 9, 045006. GALICIA, G., PÉBČRE, N., TRIBOLLET, B. & VIVIER, V. (2009). Local and global electrochemical impedances applied to the corrosion behaviour of an AZ91 magnesium alloy. Corrosion Sci 51, 1789–1794. HUANG, V.M., WU, S.L., ORAZEM, M.E., PÉBČRE, N., TRIBOLLET, B. & VIVIER, V. (2011). Local electrochemical impedance spectroscopy: A review and some recent developments. Electrochim Acta 56, 8048–8057. KALININ, S.V. & BONNELL, D.A. (2001). Scanning impedance microscopy of electroactive interfaces. Appl Phys Lett 78, 1306–1308. KALININ, S.V. & BONNELL, D.A. (2002). Scanning impedance microscopy of an active Schottky barrier diode. J Appl Phys 91, 832–839.
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LAYSON, A., GADAD, S. & TEETERS, D. (2003). Resistance measurements at the nanoscale: Scanning probe AC impedance spectroscopy. Electrochim Acta 48, 2207–2213. LAYSON, A.R. & TEETERS, D. (2004). Polymer electrolytes confined in nanopores: Using water as a means to explore the interfacial impedance at the nanoscale. Solid State Ion 175, 773–780. LOHRENGEL, M.M., HEIROTH, S., KLUGER, K., PILASKI, M. & WALTHER, B. (2006). Microimpedance—Localized material analysis. Electrochim Acta 51, 1431–1436. O’HAYRE, R., FENG, G., NIX, W.D. & PRINZ, F.B. (2004a). Quantitative impedance measurement using atomic force microscopy. J Appl Phys 95, 3540–3549. O’HAYRE, R., MINHWAN, L. & PRINZ, F.B. (2004b). Ionic and electronic impedance imaging using atomic force microscopy. J Appl Phys 95, 8382–8392. PINGREE, L.S.C. & HERSAM, M.C. (2005). Bridge-enhanced nanoscale impedance microscopy. Appl Phys Lett 87, 233117. SHAO, R., KALININ, S.V. & BONNELL, D.A. (2003). Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy. Appl Phys Lett 82, 1869–1871. TOBISZEWSKI, M.T., ZIELIŃSKI, A. & DAROWICKI, K. (2013). Dynamic nanoimpedance characterization of the AFM tip-surface contact. Microsc Microanal. Published online 13 December 2013. Available at http://dx.doi.org/10.1017/S1431927613013895.
© MICROSCOPY SOCIETY OF AMERICA 2014
Application of Dynamic Impedance Spectroscopy to Scanning Probe Microscopy Mateusz Tomasz Tobiszewski,* Anna Arutunow, and Kazimierz Darowicki Department of Electrochemistry, Corrosion and Materials Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland
Abstract: Dynamic impedance spectroscopy, designed for measuring nonstationary systems, was used in combination with scanning probe microscopy. Using this approach, impedance mapping could be carried-out simultaneously with topography scanning. Therefore, correlation of electrical properties with particular phases of an examined sample was possible. The sample used in this study was spheroidal graphite cast iron with clearly defined phases having significantly different properties. Additionally, impedance-force curves were made at graphite precipitation and ferrite matrix to illustrate the relation between impedance and the force applied to a probe. Key words: AFM, SPM, DEIS, nanoimpedance, impedance, nanocontact
I NTRODUCTION AC impedance techniques are commonly used in many research areas. Usually they are employed to characterize macroscopic surfaces or bulk properties of materials. Thus, obtained results are averaged over the area or volume of an examined sample. In order to register local impedance spectra on different grains, phases, and inclusions on the surface, important developments have been made. Two main approaches are available: a micro-cell technique (Lohrengel et al., 2006; Galicia et al., 2009; Huang et al., 2011) and scanning probe microscopy (SPM) (Kalinin & Bonnell, 2001, 2002; Shao et al., 2003; O’Hayre et al., 2004b). The micro-cell technique is well established and used for in situ examination of metals in electrolytes while impedance measurements performed by means of SPM are mainly ex situ evaluations. Therefore, impedance measured with a micro-cell is electrochemical whereas SPM-based impedance is electrical. The time required to register the full impedance spectrum is relatively long since in both techniques impedance spectra are made point by point (Layson et al., 2003; Layson & Teeters, 2004; Birbilis et al., 2009; Arutunow et al., 2011, 2013a, 2013b). If impedance mapping is required, a single frequency is utilized in order to minimize the time of scanning (Kalinin & Bonnell, 2002; O’Hayre et al., 2004b; Pingree & Hersam, 2005). The probe moves across the surface while the time at each point needs to be relatively short. Unfortunately, the single frequency measurement is less informative than the one where a full impedance spectrum is obtained. To make a compromise between full spectra and single frequency measurements, the dynamic impedance spectroscopy (DIS) technique was proposed and applied to atomic force microscopy (AFM) (Darowicki et al., 2008). Received June 7, 2013; accepted November 26, 2013 *Corresponding author. [email protected]
In the DIS technique, the voltage perturbation signal consists of several frequencies, which are generated simultaneously. The response signal is registered and decomposed to individual components with short time Fourier transformation. Details of DIS, which was originally applied to electrochemical phenomena, are described in a series of publications (Darowicki, 2000; Darowicki et al., 2000; Darowicki & Ślepski, 2003, 2004). The aim of this project involves implementation of the DIS technique to AFM making it possible to continuously register relative impedance changes along with topography imaging and the changeable force applied to the probe.
MATERIALS
AND
METHODS
Spheroidal graphite cast iron, a classical diphase metal with phases of different mechanical and electrical properties, was investigated. The sample was ground on fine-grade silicon carbide abrasive paper up to 2,500 grade. Then, it was polished with commercially available polishing paste dedicated to steels, and finally cleaned and degreased with acetone in an ultrasonic bath. DIS was used in this investigation for impedance mapping and to conduct impedance-force curves of spheroidal graphite and the matrix. A description of the experimental system, equipment used, and principles of measurement can be found in Tobiszewski et al. (in press). The only modification introduced to the set-up regarded the lowest frequency, which in the case of impedance mapping had to be increased to 500 Hz. This enabled reduction of time the interval between each single spectrum to 0.01 s and made the scanning process faster. An advantage of DIS over conventional impedance measurement, where perturbation signals change frequency by frequency, is that more periods at each frequency are registered. The more full periods of each frequency registered, the more precisely the
Application of DIS to SPM
583
impedance can be measured. For example, the time required to obtain a spectrum at 15 frequencies ranging from 70 Hz to 4.01 kHz is only 0.1 s for DIS. Seven periods of the lowest frequency are registered at this time and the higher frequency, the more periods registered. A conventional way of generation and acquisition of seven periods at each of 15 frequencies would take ∼0.32 s. Registered impedance maps were 128 × 128 points and it was 60 × 60 µm in size. Impedance-force curves were registered at 27 points at graphite and 27 points at ferrite matrix.
RESULTS AND D ISCUSSION Topography and contact error images of spheroidal graphite cast iron are presented in Figures 1a and 1b. Parts of two graphite spheroids are visible at the top and the bottom of images. An impedance map was simultaneously obtained with topography and error images. Therefore, it is apparent that the same area is presented in Figures 1a–1c. Example spectra representing the white line drawn at the top of the impedance map are presented in Figure 2. It should be emphasized that recorded impedance changes are strictly of relative character. Initial spectra present high impedance response obtained at the ferrite matrix. The following sudden decrease of impedance is related to the probe movement from the matrix to the graphite inclusion. An electronic model proposed by O’Hayre et al. (2004a) was used in calculations of the impedance spectra in ZSimpWin software. Expected tip-sample contact capacitance was in the range of atto-Farads (Shao et al., 2003), which was far less than capacitances obtained in this project. Thus, capacitance was considered as stray capacitance and we present tip-to-surface R-value as the sum of resistances, where R = Rtip + Rcont + RSR, as the most meaningful and unaffected by stray capacitance value (Tobiszewski et al., in press). The spheroidal graphite cast iron surface was simultaneously scanned for topography and impedance. As a result, height and error images can be correlated with resistance distribution. All three images are presented in Figure 1, which clearly shows that graphite-tip contact has lower resistance than the ferrite-tip contact. Some distortions are naturally present, as the surface is not perfectly flat and geometry of the tip-sample contact changes during scanning. The surface was scanned in a constant force mode, therefore the tip penetrated into the soft phase (graphite) deeper than into the ferrite matrix. An enlarged contact area could be another reason for better graphite-tip conductivity. Impedance-force curves were performed 27 times at several graphite spherulites and 27 times at the ferrite matrix. Piezoelectric scanner movement in the Z direction was controlled and fixed in a constant range. Resulting DFL signal (proportional to the cantilever deflection and force applied to a probe) was registered. Therefore, measurement of the soft material caused smaller cantilever deflection
Figure 1. Topography (a), contact error (b), and tip-to-surface resistance R (c) images of 60 × 60 µm area for spheroidal graphite cast iron. The white line in (c) indicates the area for which examples of impedance spectra are presented in Figure 2.
and deeper tip indentation as compared to that of the hard material. The average cantilever deflection at the bottom scanner position on graphite was 1 and 1.35 nA on ferrite. In order to eliminate the influence of force and
584
Mateusz Tomasz Tobiszewski et al.
Figure 2. Examples of impedance spectra corresponding to the white line at the top of image in Figure 1c.
The procedure for analysis of impedance–DFL curves was described previously (Tobiszewski et al., in press). Examples of curves for graphite and the ferrite matrix are presented in Figure 3. Each of the 27 curves recorded for graphite and for the matrix, correspondingly, was fitted to a linear equation and respective averages were made. Average curves for both phases and their equations are presented in Figure 4. The initial contact resistance was calculated to be 0.63 MΩ for graphite and 31.6 MΩ for ferrite matrix. Results indicate that the spheroidal graphite cast iron conducted current significantly better at graphite inclusions than at the matrix. This statement concerns only the surface properties, which may be far different from the bulk properties, for example, due to oxidation phenomena.
CONCLUSIONS
Figure 3. Examples of changes of the tip-to-surface resistance R on the ferrite and graphite inclusion versus DFL signal during loading.
DIS is useful in measurements of rapidly changing systems, which was in this case the tip-surface contact. The contact may change as the position of the tip changes during surface scanning or during pseudo-indentation measurements. Impedance mapping provides an overview of surface electrical properties, which is essential in many research areas. We strongly believe that impedance mapping or scanning spreading resistance microscopy techniques should always be supplemented by DFL–impedance/resistance curves. Extrapolation of curves to force F = 0 (DFL = 0) gives the results for undeformed surface, when the tip initially contacts the surface. The above allows for more precise and unique comparison of electrical properties for each phase. Moreover, the methodology presented here is a good starting point for in situ electrochemical impedance mapping.
ACKNOWLEDGMENT This work was supported by the Polish National Science Center under grant 2011/01/N/ST5/05594.
REFERENCES
Figure 4. Averaged results of the tip-to-surface resistance R, obtained from 27 points at the ferrite and the graphite inclusion respectively, versus DFL signal during loading.
contact area on the resistance parameter, a new value of “initial contact” was proposed. The resistance of initial contact is calculated from an impedance–DFL curve during loading for extrapolation of DFL (force) to DFL = 0.
ARUTUNOW, A., DAROWICKI, K. & TOBISZEWSKI, M.T. (2013a). Electrical mapping of AISI 304 stainless steel subjected to intergranular corrosion performed by means of AFM–LIS in the contact mode. Corrosion Sci 71, 37–42. ARUTUNOW, A., DAROWICKI, K. & ZIELIŃSKI, A. (2011). Atomic force microscopy based approach to local impedance measurements of grain interiors and grain boundaries of sensitized AISI 304 stainless steel. Electrochim Acta 56, 2372–2377. ARUTUNOW, A., ZIELIŃSKI, A. & TOBISZEWSKI, M.T. (2013b). Localized impedance measurements of AA2024 and AA2024-T3 performed by means of AFM in contact mode. Anti-Corros Methods Mater 60, 67–72. BIRBILIS, N., MEYER, K., MUDDLE, B.C. & LYNCH, S.P. (2009). In situ measurement of corrosion on the nanoscale. Corrosion Sci 51, 1569–1572. DAROWICKI, K. (2000). Theoretical description of the measuring method of instantaneous impedance spectra. J Electroanal Chem 486, 101–105.
Application of DIS to SPM DAROWICKI, K., ORLIKOWSKI, J. & LENTKA, G. (2000). Instantaneous impedance spectra of a non-stationary model electrical system. J Electroanal Chem 486, 106–110. DAROWICKI, K. & ŚLEPSKI, P. (2003). Dynamic electrochemical impedance spectroscopy of the first order electrode reaction. J Electroanal Chem 547, 1–8. DAROWICKI, K. & ŚLEPSKI, P. (2004). Instantaneous electrochemical impedance spectroscopy of electrode reactions. Electrochim Acta 49, 763–772. DAROWICKI, K., ZIELIŃSKI, A. & KURZYDŁOWSKI, K.J. (2008). Application of dynamic impedance spectroscopy to atomic force microscopy. Sci Technol Adv Mater 9, 045006. GALICIA, G., PÉBČRE, N., TRIBOLLET, B. & VIVIER, V. (2009). Local and global electrochemical impedances applied to the corrosion behaviour of an AZ91 magnesium alloy. Corrosion Sci 51, 1789–1794. HUANG, V.M., WU, S.L., ORAZEM, M.E., PÉBČRE, N., TRIBOLLET, B. & VIVIER, V. (2011). Local electrochemical impedance spectroscopy: A review and some recent developments. Electrochim Acta 56, 8048–8057. KALININ, S.V. & BONNELL, D.A. (2001). Scanning impedance microscopy of electroactive interfaces. Appl Phys Lett 78, 1306–1308. KALININ, S.V. & BONNELL, D.A. (2002). Scanning impedance microscopy of an active Schottky barrier diode. J Appl Phys 91, 832–839.
585
LAYSON, A., GADAD, S. & TEETERS, D. (2003). Resistance measurements at the nanoscale: Scanning probe AC impedance spectroscopy. Electrochim Acta 48, 2207–2213. LAYSON, A.R. & TEETERS, D. (2004). Polymer electrolytes confined in nanopores: Using water as a means to explore the interfacial impedance at the nanoscale. Solid State Ion 175, 773–780. LOHRENGEL, M.M., HEIROTH, S., KLUGER, K., PILASKI, M. & WALTHER, B. (2006). Microimpedance—Localized material analysis. Electrochim Acta 51, 1431–1436. O’HAYRE, R., FENG, G., NIX, W.D. & PRINZ, F.B. (2004a). Quantitative impedance measurement using atomic force microscopy. J Appl Phys 95, 3540–3549. O’HAYRE, R., MINHWAN, L. & PRINZ, F.B. (2004b). Ionic and electronic impedance imaging using atomic force microscopy. J Appl Phys 95, 8382–8392. PINGREE, L.S.C. & HERSAM, M.C. (2005). Bridge-enhanced nanoscale impedance microscopy. Appl Phys Lett 87, 233117. SHAO, R., KALININ, S.V. & BONNELL, D.A. (2003). Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy. Appl Phys Lett 82, 1869–1871. TOBISZEWSKI, M.T., ZIELIŃSKI, A. & DAROWICKI, K. (2013). Dynamic nanoimpedance characterization of the AFM tip-surface contact. Microsc Microanal. Published online 13 December 2013. Available at http://dx.doi.org/10.1017/S1431927613013895.
