Microscopy Microanalysis

Microsc. Microanal. 20, 72–77, 2014 doi:10.1017/S1431927613013895



Dynamic Nanoimpedance Characterization of the Atomic Force Microscope Tip-Surface Contact Mateusz Tomasz Tobiszewski,* Artur Zielin´ski, and Kazimierz Darowicki Department of Electrochemistry, Corrosion and Materials Engineering, Gdan´sk University of Technology, Narutowicza 11/12, 80-233 Gdan´sk, Poland

Abstract: Nanoimpedance measurements, using the dynamic impedance spectroscopy technique, were carried out during loading and unloading force of a probe on three kinds of materials of different resistivity. These materials were: gold, boron-doped diamond, and AISI 304 stainless steel. Changes of impedance spectra versus applied force were registered and differences in the tip-to-sample contact character on each material were revealed. To enable comparison between materials and phases, a new standardization method is proposed, which simulates conditions of initial contact. Key words: AFM, SPM, DEIS, nanoimpedance, impedance, nanocontact

I NTR ODUCTION Progressing miniaturization of electronic devices and rapid development in scientific areas that are concerned with nanomaterials require new techniques for characterization of materials on the nanoscale ~Binnig et al., 1982, 1986!. An essential property of electronic nanosystems is their resistance to DC current and impedance to AC current ~Tschöpe et al., 2001; Burke, 2004!. AC measurements allow collection of information about inductance, resistance, and capacitance present in examined system. DC measurements give information only about resistance. Therefore, AC measurements provide more complete information. Two methods of measuring impedance on the nanoscale are feasible. In scanning impedance microscopy, a probe is used as a mobile electrode that detects surface potential changes ~Kalinin & Bonnell, 2001, 2002!. The probe does not touch the surface and influence of the tip-surface impedance is eliminated. In the second method, nanoimpedance microscopy, the probe is in contact with the surface and the current flow between them is measured ~Shao et al., 2003; O’Hayre et al., 2004a!. An inherent part of the results is the tip-surface impedance, which can distort nanoimpedance results. This is the reason why electrical and mechanical characterization of the tip-to-surface contact is a subject of this study. A commonly used circuit model for tip-surface impedance analysis, proposed by O’Hayre et al. ~2004b!, is presented in Figure 1. The Rtip is the resistance of the tip, which depends on the material and geometry of the tip. RSR is the spreading resistance, which is associated with a small volume of material near the tip-to-sample contact. RSR is expressed by equation R SR ⫽ ~r/4r!, where r is resistivity of the sample and r is the contact radius. Rcont and Ccont are resistance and capacitance of the tip-to-surface contact, respectively. Due to Ohm’s law linking electrical resistance with resistivity and geometry of a material, resistance is Received April 29, 2013; accepted November 4, 2013 *Corresponding author. E-mail: [email protected]

inversely proportional to a surface area. On the other hand, capacitance is directly proportional to a surface area, which is assumed in the equation for capacity of a plate capacitor. Nanoimpedance is therefore dependent on the tip-tosurface contact area and this in turn depends on the force applied by a tip to a surface. The higher the force, the deeper the penetration of a probe into a sample, and the contact area increases. Thus, impedance decreases with increasing force. Similar considerations can also be applied to the type of measurements called “conductive indentation” ~Stauffer et al., 2012!. A limitation of electrical impedance spectroscopy ~EIS! measurements is the relatively long time required to obtain a single result, which is a full impedance spectrum. Depending on the lowest frequency limit, it can take from a few to a few hundred seconds. Owing to changes in the measuring system, mainly scanner drift, spectra are made pointwise ~Layson et al., 2003; Layson & Teeters, 2004; Birbilis et al., 2009; Arutunow et al., 2011, 2013a, 2013b!. An alternative is to measure impedance at one characteristic frequency. Full EIS spectra are made at each phase/element of a sample and frequency differences between them is chosen. Usually this frequency ranges from hundreds to thousands of hertz ~Eckhard et al., 2007; Szocin´ski et al., 2013!. Therefore, the time required at each point is shortened to a fraction of a second and impedance maps for this selected frequency can be registered ~Pingree & Hersam, 2005!. Unfortunately, a single frequency measurement gives less information than the EIS measurement and usually is unable to show specificity of the system ~O’Hayre et al., 2004a!. EIS requires the examined system to be invariable during measurement, and the single frequency technique gives only limited information about the system ~only one point out of the full spectrum is measured!. Therefore, Darowicki et al. ~2008! proposed dynamic impedance spectroscopy ~DIS! for imaging of surface electrical properties. DIS, the same as EIS, is based on two fundamental elements: generation of the voltage perturbation signal and an analysis of a response signal. However, in DIS all frequencies are gener-

Dynamic Nanoimpedance Characterization


Figure 1. Equivalent circuit of the tip-to-sample contact proposed by O’Hayre et al. ~2004b!.

ated simultaneously and this implies more complicated analysis of the response signal. Generation and analysis will be described in the following paragraphs. To best describe a system under investigation, the range of frequencies used should be as wide as possible. On the other hand, if the system varies with time, the signal should be compact, to make a frequency decomposition within short intervals of time. Simultaneous generation of all frequencies leads to overlapping of individual components. Therefore, proper adjustment of the perturbation signal is required in order to reduce the resultant amplitude. In most systems, impedance decreases with increasing frequency. Thus, reduction of amplitudes of high frequency components does not impair the response signal, but allows reduction of the resultant amplitude. The second issue with the perturbation signal is proper selection of initial phase shifts so the maximums do not superimpose. To obtain DIS spectra, the knowledge about amplitudes and phase shifts of all components in the potential perturbation signal as well as in the current response signal is required. In the EIS technique transformation from time to frequency domain is performed using the Fourier transformation. As a result, averaged signal is registered and information about changes in the examined system in time is lost. Contrary to this, in DIS short time Fourier transformation ~STFT! is applied, which analyzes signal within the specified interval of time. By implementing STFT transformation for consecutive periods of time, the time-frequency characteristic of the signal is obtained. When selecting the length of time interval in which STFT is performed, it is important to make sure that it contains only complete periods of generated sinusoids. The more periods of a particular sinusoid that are analyzed, the more precise is the result. In EIS, where frequencies are generated one after another, n periods of each sinusoid is generated. In DIS all frequencies are generated at a time, and during STFT analysis high frequencies fit into an analyzed interval of time more times than low frequencies. Consequently, the higher the frequency used, the better the quality of the result. Moreover, averaging inside each interval of time allows avoidance of situations when variation of the examined system causes mismatch between the initial part and terminal parts of the spectrum. The most important advantage of the DIS technique is that it reduces the time required to register a single spectrum. Therefore, changes of impedance in time can be recorded even for fast processes. Calculation of the time

Figure 2. Scheme of the contact mode atomic force microscope nanoimpedance system used in the experiment.

required to register a single spectrum of 15 frequencies used in this project and ranging from 70 Hz to 4.01 kHz, gives 0.1 s for the multisinusoidal activation signal with a 0.1 s analysis time interval. Among others, seven periods of the lowest and 401 periods of the highest frequency are analyzed for each interval of time. If frequencies are generated one by one, and sinusoids of each frequency last for seven periods, the total time required to register the spectrum is ;0.32 s. The detailed theoretic description of DIS was described by Darowicki ~2000! and the first application to electrochemical systems was presented by Darowicki and S´lepski ~2003!. The aim of this work is to present the tip-surface impedance characteristics versus force applied by the tip to the surface during atomic force microscope ~AFM!-nanoindentation measurements. The tip-sample geometry changed over time, so DIS was selected as the measuring method.




The measuring system used in this investigation is presented in Figure 2. It consists of the NTEGRA Aura ~NTMDT, Moscow, Russia!, AFM coupled with a data acquisition PXI 6120 card ~National Instruments, Austin, TX, USA!, and low-noise current preamplifier SR570 ~Stanford Research Systems, Sunnyvale, CA, USA!. Before impedance measurements, samples were scanned in the contact mode in order to register surface topography. Scan rate was 0.7 Hz over an area of 5 ⫻ 5 mm. The probe used was the CDTP-NCHR ~Nanosensors, Neuchatel, Switzerland! with 70 nm thick boron-doped diamond layer, which assured good conductivity. As stated by the manufacturer spring constant of the cantilever was 110 N/m and tip radius between 200 and 300 nm. The nominal, total resistance of the tip, measured in contact with a platinum surface was ,3 kV. Impedance was measured in ambient conditions in a two electrode configuration ~tip-sample!. The voltage perturbation signal was generated by a PXI 6120 card and applied to electrodes. Current reply signal was amplified with a low-noise current preamplifier and registered by PXI 6120 card. The whole process was controlled by software developed in LabView. The generated signal was composed


Mateusz Tomasz Tobiszewski et al.

of 15 frequencies ranging from 70 Hz to 4.01 kHz. The amplitude of each component gradually decreased from 100 mV for low frequencies to 50 mV for high frequencies. Initial phase shifts were randomly distributed in order to reduce resultant amplitude, which did not exceed 0.6 V. No DC bias was applied. Four signals were registered during measurements: AC potential and current, DFL signal from photodiode ~proportional to a cantilever deflection!, and scanner position along the Z-axis. Potential and current signals were analyzed with STFT inside a moving time interval of 0.1 s. DFL and scanner signals were averaged inside each interval to receive values corresponding to each impedance spectrum. The low frequency limit was set to 70 Hz in order to register relatively fast impedance changes. In this case 10 spectra/s were measured. The high frequency limit was 4 kHz, which enabled precise measurement in the wide range of impedances. The same set of frequencies was used to examine several materials with different resistivity. The first material used in this investigation was a commercially available microbalance quartz crystal with 100 nm thick gold layer on a silicon wafer with a 10 nm thick chromium interlayer. No special preparation was carried out, except cleaning in acetone in an ultrasonic bath. The second sample was a probe identical to the one used in this investigation and was a 70 nm thick boron-doped diamond coating on silicon. Resistivity of the diamond coating given by the manufacturer was 0.003–0.005 V{cm. As for the gold sample, no special preparation was carried out, except for cleaning in acetone in an ultrasonic bath. The third material was AISI 304 SS ~stainless steel!. It was ground on fine grade abrasive paper up to 4,000 grade. Then, it was polished with a commercially available ~Akasel ApS, Roskilde, Denmark! polycrystalline diamond suspension of 3 mm particle size and subsequently with a silica suspension of 0.05 mm particle size. The polished sample was cleaned in acetone in an ultrasonic bath and left in ambient air for 24 h to create a native passive layer. The thickness of the passive layer was 1–3 nm ~Olsson & Landolt, 2003!. Therefore, three tipsample systems of different nature were examined: semiconductor-metal, semiconductor-semiconductor, and semiconductor-insulator-metal. Figure 3 presents exemplary Nyquist spectra obtained during loading and unloading of the probe on the surface of AISI 304 SS. As the force applied increased with time, the contact area also increased and impedance decreased. Starting from the 60th second, the force was slowly removed hence the impedance increased to the initial level. Impedance spectra were analyzed with ZSimpWin software, using Randles circuit, to show changes of resistance and capacitance in the examined systems. After measurement on electronic resistors it was concluded that the capacitive part of the results comes from stray capacitance and should be rejected. The real part of impedance Z ' was in agreement with nominal values of resistors. A simple estimation of tip-tosample contact capacitance gives a result of about attoFarads ~Shao et al., 2003!, which is far less than the measured

Figure 3. Exemplary changes of impedance spectra during a single measurement on AISI 304 stainless steel.

Figure 4. DFL signal and logarithm of the total tip-gold resistance Rtotal versus time. Black squares indicate deflection of the cantilever and red circles indicate logarithm of the total tip-surface resistance Rtotal .

stray capacitance. Calculation of spectra in ZSimpWin software allows for decomposition of results to R and C parameters and extraction of Rtotal ⫽ Rtip ⫹ Rcont ⫹ RSR as the most important value, which is unaffected by stray capacitance.

R ESULTS The tip-gold system was examined first to assess impedance on the highly conducting substrate, and to check if a phase shift was present in the applied frequency range. Within this range, measured impedance had a resistive character and the phase angle was zero ~f ⫽ 0!. When the probe was pressed against the surface, the resistance was between 2 and 3 kV. The resistive character of the gold tip-gold sample contact in the wide range of frequencies ~40 Hz– 30 MHz! was reported by Shao et al. ~2003!. Figure 4 presents the total resistance Rtotal and DFL signal versus time. It is possible to correlate resistance with cantilever deflection ~force applied by the probe to the sample!. Resistance rapidly decreased when the probe touched the surface and a further increase in force did not cause significant resistance reduction. The middle area from the 15th to 20th second, is the period when the piezoelectric scanner was stopped. The force was still applied and the cantilever

Dynamic Nanoimpedance Characterization

Figure 5. DFL signal and logarithm of the total tip-boron-doped diamond resistance Rtotal versus time. Black squares indicate deflection of the cantilever and red circles indicate logarithm of the total tip-surface resistance Rtotal .

deflection decreased because of surface plastic deformation under the tip. After the hold period, the load was taken off and resistance remained very low even with negative force measurements. This indicates that adhesion force kept the tip in contact with the surface. Resistance suddenly increased when the adhesion force was overcome. Very low resistance within all ranges of applied force means that gold is a very good conductor. In the tip-boron-doped diamond a capacitive component was present. It was extracted during calculation of individual electrical parameters in ZSimpWin and eliminated. Therefore, only Rtotal was later analyzed. DFL signal and Rtotal versus time are presented in Figure 5. Distinct changes in the tip-to-sample contact resistance were noticeable. It started decreasing when the probe touched the sample, but not as rapidly as with gold. Continuous reduction of resistance was noticeable up to a maximum force. During hold periods no changes were observed. The diamond sample did not deform under the tip and force stayed at a constant level. Resistance also did not change during this period. After the hold period, the load was taken off and resistance increased up to the initial level. Adhesive force was not noticed this time. Owing to high impedance values, some dispersion of data points is present, but the character of changes was clearly stated. The tip-AISI 304 SS covered with a passive layer had the highest impedance. The capacitive part of the impedance was eliminated as in the diamond sample. Figure 6 presents Rtotal of the examined system and DFL signal versus time. In this case, the moment of resistance drop was later than the moment of tip-to-surface contact establishment. This could be caused by the presence of the passive layer. The minimum resistance plot occurred when the probe was maximally loaded and contact area was the greatest. The short hold period did not contribute to the shape of the resistance plot. When the force was taken away, the resistance increased to the initial level. The moment of resistance growth did not overlap with the moment when the tip-sample contact was lost.


Figure 6. DFL signal and logarithm of the total tip-AISI 304 stainless steel resistance Rtotal versus time. Black squares indicate deflection of the cantilever and red circles indicate logarithm of the total tip-surface resistance Rtotal .

Figure 7. Typical behavior of the total tip-gold resistance Rtotal ⫽ Rtip ⫹ Rcont ⫹ RSR versus force. Blue circles indicate loading ~approach! curve and black squares indicate unloading ~retract! curve. The black line is a linear equation fit to data for loading curve, log R ⫽ 3.53–0.18 F. The red line is linear equation fit to data for the unloading curve, log R ⫽ 3.43–0.15 F.

D ISCUSSION To enable comparison of nanoimpedance results, some specific value from each measurement was necessary. It was impossible to assess penetration depth and actual tip-tosample contact area continuously during loading and unloading. Therefore, the authors propose correlation of impedance with the force applied to the probe. Figure 7 presents the typical resistance Rtotal versus force during loading and unloading of the probe on the gold sample. A similar behavior was observed for other measurements on gold. It was noticed that plots differ one from another because of deformation of a material under the tip. While unloading, the tip had a relatively large contact area with the sample, so the resistance was low until the force was nearly zero and in some cases even negative. The intention was to eliminate the influence of the material deformation and consequently only loading curves


Mateusz Tomasz Tobiszewski et al.

Figure 8. The contact resistance Rtotal on the diamond, the AISI 304 stainless steel ~SS!, and the gold, versus force during loading. Blue circles indicate AISI 304 SS, red triangles indicate diamond, and black squares indicate gold sample. The red line is a linear equation fit to data for AISI 304 SS, log R ⫽ 8.90–1.46 F. The black line is a linear equation fit to data for diamond, log R ⫽ 5.89–0.87 F. The blue line is a linear equation fit to data for gold, log R ⫽ 3.53–0.18 F.

for the three examined materials were analyzed. Their upper parts ~;50–60% of data points below maximal forces on Figs. 4–6! were fitted to line function y ⫽ ax ⫹ b, where y was the logarithm of total resistance Rtotal and x was force F in mN applied by the probe to the surface. Rejection of initial parts of the curves was made to reduce the influence of surface roughness and to analyze only the part of each curve where tip-surface contact was firm. The aim of this procedure was to determine the value of impedance, independent of the contact area, when the contact between the tip and nondeformed material was initiated. It allowed comparison of electrical parameters of samples examined with the same probe. Figure 8 presents typical changes of the resistance Rtotal versus force applied by the tip to the sample. Results indicated that resistance of the tip-gold contact was low within the measured range and weakly dependent on the applied force. Gold, as a very good conductor, assured a current path even in the range of low forces and increasing force did not induce significant changes in the resistance. It was confirmed by the minimal slope of the fitted line ~⫺0.18! and low value of the logarithm of resistance at F ⫽ 0, which is 3.53. The resistance of the tip-diamond contact was higher when compared to the tip-gold contact resistance and had higher dependency on force. Boron-doped diamond is a worse conductor than gold, so the resistance was higher and the logarithm of resistance at F ⫽ 0 is 5.89. Diamonds do not undergo a deformation, so the resistance did not depend much on force. The slope of the fitted line is ⫺0.87. Among examined systems, the tip-AISI 304 SS contact had the highest resistance and was the most dependent on applied force. Extrapolation to F ⫽ 0 gave a logarithm of resistance equal to 8.9, and a high slope of the fitted curve ~⫺1.46! indicates

that resistance significantly decreased with increasing force. Clearly, stated differences in results for three different tipsample systems, registered with the same probe, indicated that results depend on the examined material, not the probe. Results presented here are exemplary results. Statistics calculated from the rest of the results indicate that logarithm of resistance can be determined with an uncertainty of 10% and the slope with 30% uncertainty. It is possible to make some qualitative indentation measurements. However, it is worthwhile to keep in mind that AFMs were not designed to make indentation measurements on hard substrates. Thus, the nanoindenter may be a better tool for this kind of measurement. Another important issue is the quality of impedance results. In the case where resistance/impedance is low, results are precise and can be considered as quantitative. When impedance is very high, results are less precise and influenced by stray capacitance. However, they inform about the character of changes. Some work has been done to improve the quality of impedance results, mainly by reducing the capacitance between a cantilever and a sample ~Layson et al., 2003; Kopanski et al., 2004; Yang et al., 2012! or by increasing resolution of the measuring system ~Pingree & Hersam, 2005!. Extrapolation of the tip-sample resistance leads to the estimation of initial contact resistance. The initial contact is when the tip touches the surface, but the force is zero. Therefore, results correspond to the surface that was not deformed by the tip.

C ONCLUSIONS DIS, as one possible method to measure impedance on the nanoscale, is useful for characterization of systems that vary with time. Results presented here show changes of resistance Rtotal during a single loading and unloading of the probe. The proposed method allows analysis of results comparing electro-mechanical properties of materials and phases. The slope of the data plot informs about dependency of contact resistance on applied force. Comparison of slopes ⫺1.46 for AISI 304 SS, ⫺0.87 for diamond, and ⫺0.18 for gold indicates that the AISI 304 SS resistance depends most strongly on applied force. Extrapolation of resistance to force F ⫽ 0 gives values for nondeformed surfaces ~initial contact!, which are 10 8.90 V ~794 MV! for AISI 304 SS, 10 5.89 V ~776 kV! for diamond, and 10 3.53 V ~3.39 kV! for gold. These values can be subsequently compared to assess which surface has the lowest resistance.

A CKNOWLEDGMENTS This work was supported by the Polish National Science Center under grant 2011/01/N/ST5/05594.

R EFER ENCES 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.

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Dynamic nanoimpedance characterization of the atomic force microscope tip-surface contact.

Nanoimpedance measurements, using the dynamic impedance spectroscopy technique, were carried out during loading and unloading force of a probe on thre...
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