July 09, 2013
C 2013 American Chemical Society
Space- and Time-Resolved Mapping
of Ionic Dynamic and Electroresistive
Phenomena in Lateral Devices
Evgheni Strelcov,†,* Stephen Jesse,†Yen-Lin Huang,‡Yung-Chun Teng,‡Ivan I. Kravchenko,†Ying-Hao Chu,‡ and Sergei V. Kalinin†,*
†Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States and‡Department of Materials Science and
Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan
E
lectronic and ionic transport enables operation of numerous electrochemi-cal devices including fuel cells, batteries, separators, and gas sensors.16Similarly, ionic phenomena undergird the functionality of emergent memristive and electroresistive memory and logic devices.711Much efforthas been invested into the development of macroscopic strategies for separating the electronic and ionic responses, including electrochemical impedance spectroscopy and related methods.12,13However, in most, if not all, of these cases the transport is controlled by the nanoscale elements of a material's microstructure, including internal interfaces and grain boundaries in polycrys-talline ceramics, interfaces in thinfilms, or conductivefilaments in memristors. Typically, these elements possess a broad variability of properties, while only macroscopically aver-aged characterization is available experimen-tally. Therefore, probing local electronic and ionic transport phenomena is essential to understanding the fundamental mecha-nisms underpinning these devices. Beyond these applications, such information can facilitate understanding and mitigation of
detrimental effects such as surface ionic leakage that plagues microelectronic and MEMS applications and can contribute to corrosion and degradation of metal elec-trodes under electrochemical conditions.
Understanding the electronic transport in lateral devices has necessitated the de-velopment of several current- (AFM- and STM-based potentiometry and nanoimped-ance microscopies1418) and force-sensitive scanning probe microscopy (SPM) tech-niques. These techniques can be considered nanoscale analogs of the classical methods of determining potential distribution, such as moving vibrating reed electrometry19 and lateral electrode conductometry.2023 In particular, Kelvin probe force microscopy (KPFM)2429and electrostatic force micro-scopy (EFM)30,31have emerged as powerful characterization methods and have been used in recent decades for studies of charge transport and accumulation in transistors,32,33
solar and electrochemical cells,30,34
micro-electromechanical systems (MEMS),35,36
gas sensors,3739 ferroelectric devices, and electroceramics.4042 This approach was further extended to map out linear and
* Address correspondence to [email protected], [email protected].
Received for review April 11, 2013 and accepted July 9, 2013. Published online 10.1021/nn4017873 ABSTRACT A scanning probe microscopy-based technique for probing local ionic and electronic transport and
their dynamic behavior on the 10 ms to 10 s scale is presented. The time-resolved Kelvin probe force microscopy (tr-KPFM) allows mapping of surface potential in both space and time domains, visualizing electronic and ionic charge dynamics and separating underlying processes based on their time responses. Here, tr-KPFM is employed to explore the interplay of the adsorbed surface ions and bulk oxygen vacancies and their role in the resistive switching in a Ca-substituted bismuth ferrite thinfilm.
KEYWORDS: KPFM . ionic dynamics . Ca-BFO . surface potential distribution . oxygen vacancy
nonlinear frequency-dependent transport, as imple-mented in the scanning impedance microscopy (SIM) and its nonlinear analogs.29,4346
However, the fundamental limitation of these ap-proaches is that only the total potential distribution induced by changes of the electronic and ionic dis-tributions is probed. Moreover, these techniques usual-ly do not distinguish between different mechanisms governing charge rearrangement, such as surface ions versus bulk ion diffusion, electronic versus ionic dyma-nics, potential distribution due to different types of electronic conductivity, etc. Notably, in most interpre-tations of the KPFM data on lateral devices, observed phenomena are attributed solely to electronic trans-port. At the same time, formation of charge haloes during KPFM experiments on lateral devices as ob-served by multiple authors45,47,48is clear evidence of surface ionic effects and suggests that the ionic and electronic subsystems have vastly different response times (Figure 1a). In fact, the significantly higher reso-lution observed in SIM as compared to KPFM of lateral devices, such as nanotubes,49is primarily related to the mitigation of the ionic contribution to the signal.50 Recent work by Laboriante et al.35 explored these effects using an electrode system with predefined symmetry, transforming the slow scan direction into the time dimension47by changing the electrode bias several times, while one image was captured.
These observations suggest that different transport phenomena (electronic vs ionic, surface vs bulk ionic, etc.) can be separated based on responses in the time domain. Here, we report a novel SPM technique ;time-resolved Kelvin probe force microscopy (tr-KPFM); that probes the time dynamics of the surface potential in both bias-on and bias-off states at each spatial location with a temporal resolution as low as 10 ms and achievable spatial resolution equal to that of KPFM.
RESULTS AND DISCUSSION
The system we have chosen to demonstrate the feasibility and advantages of the tr-KPFM technique is a Ca-substituted BiFeO3(CaBFO) thinfilm. A fascinating
interplay between the ferroelectricity and ionic effects in this material has recently attracted much atten-tion.51,52Pure bismuth ferrite epitaxialfilms exhibit a structural monoclinicpseudotetragonal transition around 830°C. Substitution of Bi3þions for the
alkaline-earth ones (Ca2þ, Ba2þ) in this perovskite leads to a lowering of the transition temperature and, due to the highly stable oxidation state of Fe3þ, generation of oxygen vacancies as a means of charge compensation. At the Ca2þcontent of about 10%, a local minimum of the transition temperature associated with a ferroelectric instability is reached.51The instability region is known for a prominent resistive switching behavior with a con-ductivity change of up to 3 orders of magnitude. The associated insulatorconductor transition is thought
to be due to the redistribution of oxygen vacancies in CaBFO under the influence of an applied electric field.51Oxygen vacancies exist in a dynamic
equilibri-um with the electronic holes, and their motion should be linked to changes in the conductivity.
During switching, most of the 10% CaBFO film between a pair of lateral electrodes becomes highly p-conductive and depleted of oxygen vacancies, whereas a thin layer around the anode gains less in conductivity and turns into an n-type semiconductor.53 However, this bulk picture can be expected to be altered by surface ionic and electronic dynamics (Figure 1b). Namely, in ambient, the oxide surfaces are universally covered by water layers and can contain physisorbed ionic species (compensating polar termi-nations, as is explored in ferroelectric materials5457). These ions must create a space charge region near the film's surface, which depletes it of the main carriers and thus influences its conductivity. The thickness of the depletion region is on the order of the Debye length in CaBFO;quite comparable to the thin film's thickness. Formation of space charge region and modulation of the conduction channel through it constitutes the transduction function of the conductometric gas sensors58and can be expeted to affect electrochemical phenomena in thinfilms, as well. Under the applied electric field, the pre-existing charged species can redistribute, creating surface space charge layers (Figure 1b). Furthermore, the neutral molecules can split in the lateral electric fields, creating additional ionic carriers of both polarities. The question, then, arises whether the surface ions have any influence on the measured tr-KPFM data and on the insulator conductor transition in this material. Here, we endeav-or to investigate these behaviendeav-ors in real space.
Schematics of the tr-KPFM, which is an extension of the scanning surface potential microscopy,28 are shown in Figure 2a. Measurements are taken with a conventional AFM in dual pass mode a certain distance
Figure 1. (a) Example of distinguishing between various response mechanisms: schematic depiction of the di ffer-ence between the electronic and ionic response times trig-gered by an external step-like voltage excitation. (b) The initially linear surface potential profile between a biased and a grounded electrode curves down over time due to redis-tribution of the suface ions during the polarization process.
(z0) above the surface on a predefined spatial grid.
At each point of the grid, a four-step low-frequency probing voltage waveform is applied to the lateral electrodes, whereas the tip bias is modulated by a high-frequency AC signal. At step I, the device is polarized by a DC voltage Vl applied between the
electrodes, whereas Vtip= V0þ Vac cos(ωt) waveform
is applied to the tip. In order to avoid cross-talk, an AC frequency ω is chosen to be far away from the free resonance frequency of the cantileverω0, at which the
tapping piezo mechanically excites the cantilever. During step II, the bias between the electrodes is brought to zero, allowing the material to relax, while the tip bias waveform is kept unchanged. As the surface potential at each grid point between the electrodes changes over time, so does the tipsurface force, which is reflected in the deflection signal and is detected by the lock-in. Steps II and III are used to restore the system to its initial state (i.e., minimize charge accumulation and unwanted electrochemical processes) before moving to the next point of the grid, so that each measurement does not influence others. First, opposite biasVlis applied between the electrodes
(step II) and then the system is allowed to relax with both electrodes grounded (step III). As measurements are only taken during the first two steps, later the tip is kept grounded. Here, the duration of each step is chosen to be equal, albeit different pulse sequences and durations can be chosen depending on the nature of the physical phenomena under investigation.
The measured mechanical response of the cantilever can be quantified based on a simple electrostatic model. The periodic interaction force due to a capaci-tive coupling between the surface (at potential Vs) and
tip (z meters away) is given by26,28,59 Fc(z, t) ¼ 1 2(Vtip(t) Vs) 2DC(z) Dz Itsfirst harmonic is Fc1ω(z) ¼ DC(z) Dz (V0 Vs)Vac
When the cantilever is held a fixed distance (z0)
above the surface, the deflection signal changes as a
result of this periodic force, which is detected by the lock-in amplifier as the amplitude and phase of the signal: A(ω) ¼ Fc1ω m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (ω2 ω2 0)2þ ω2γ2 q tan(θ) ¼ ωγ ω2 ω2 0
Here, m is the effective mass of the cantilever, ω0
is its free mechanical oscillation frequency, andγ is the damping coefficient. Having recorded amplitude and phase of the signal, one can calculate the surface potential at each point of the grid as
Vs ¼ V0 1 f1ωDC(z) Dz z0 Vac A ¼ V0 K 3 Asin(θ)
where K is the calibration coefficient and f1ω is the
transference function of the cantilever for the first harmonic.
Since the tipsurface capacitance and its depen-dence on z are generally unknown, K can be found by including part of the grounded lateral electrode in the scan. Then, the K calculated for the over-the-electrode grid points can be used for potential calibration for the rest of the grid. Potential calibration relies on the independence of the capacitance gradient on the tip position in the xy plane (see Supporting Information). Note that, due to a stepwise height jump at thefilm electrode interface, the VsA linear dependence
as-sumption may fail and the potential may seem to jump, too. Recording several grid lines over theflat grounded electrode instead of just one line along the interface helps to eliminate thisflaw and calibrate the surface potential correctly. Application of bias to the lateral electrodes may change the transference function of the cantilever due to itsflexibility in the electrostatic field, in which case potential calibration should be done independently for bias-on and bias-off states (see Supporting Information).
We further note that determination of the local potential by KPFM is subject to several systematic corrections. First and foremost, the surface potential measured by KPFM differs from the absolute surface by a factor of the work function difference (Δχ) of the surface and tip materials: Vs= Vabs Δχ/e (e is the
elementary charge).60Albeit, this difference generally does not exceed a fraction of the volt (for the ground state) and, hence, can be ignored here. For small bias measurements, the ground-state KPFM image can provide the required correction. Second, geometrical aspects of the tipsurface and cantileversurface interactions may also influence the measured potential distribution.6163 However, these factors contribute to the spatial resolution. Finally, the feedback errors,
Figure 2. (a) Schematic of the tr-KPFM technique (descrip-tion in the text); (b) time-averaged surface potential during polarization by a polarization pulse of 10 V applied between the lateral electrodes; scale bar is 10μm; red arrow indicates position of the grounded electrode.
significant in KPFM,56,64 do not affect the present implementation of tr-KPFM due to the open-loop detection scheme.
As an example of the surface mapping ability of the technique, Figure 2b shows a time-averaged surface potential of a 20 105 μm2area of CaBFOfilm during a polarization pulse of 10 V lasting 10 s. Lines below the red arrow (Figure 2b) of the 20 30 grid were recorded over the grounded electrode, whereas the topmost line was adjacent to the biased electrode. In this example, extension of the collected data deep into the time domain decreased the spatial resolution of tr-KPFM as compared to standard EFM or SKPM techniques but simultaneously provided much more information on the surface potential dynamics. However, spatial resolu-tion of the tr-KPFM technique is not in principle inferior to that of EFM and SKPM, but rather is linked to the temporal resolution and the total time an experimentor would like to spend acquiring one image.
Behavior of the CaBFO film in response to the applied bias is summarized in Figure 3. When 5 V is
applied between the electrodes at room temperature, the detected potential (averaged over the pixels equi-distant from one of the electrodes) decays during 10 s from a maximal to a lower value, more so for the regions closer to the biased electrode (Figure 3a). Switching bias off leads to an instant drop of potential to values close to zero and a subsequent relaxation of the remaining component.
The spacetime distribution of potential is shown in Figure 3b, where both electrodes are represented with a gray shading. Initially (top dark-blue curve), the potential distribution between the electrodes is almost linear (except for the Schottky barrier at the biased electrode), but by the end of the 10 s polariza-tion period (top green curve), it becomes somewhat reduced close to the biased electrode and, thus, de-viates from linearity. As soon as both electrodes are grounded, potential drops and remains unevenly dis-tributed, being less than zero close to the formerly biased electrode (lower green curve). The next 10 s of relaxation linearizes the potential profile and brings it
Figure 3. (ac) Line-averaged surface potential vs time and position, and interelectrode current vs time as measured at room temperature with 5 V applied between the electrodes. (df) Same with90 Vapplied toelectrodes;grayrectanglesshowpositionofthe lateral electrodes. Arrows and color bars in (b,e) indicate time sequence of the curves. Averaging was performed over spatial locations equidistant from the grounded electrode, which created a set of“lines”, whose positions are indicated with the color bars in (a,d).
almost to zero all over the sample. The peach arrows in Figure 3 indicate the time progression of the curves (in addition to the color-coding of the curves themselves). Note that Figure 3a,b shows two ways of presenting the same data. The nonlinear distribution of potential at the end of the polarization period indicated possible accumulation of negative charges in the vicinity of the positively biased electrode, which is also seen in the same region as a negative potential dip in the beginning of relaxation. These charges may be the oxygen vacancies of the bulk or the surface ions (hydroxyl groups, oxygen ions, or impurity ions left after photolithography). Since the motion of oxygen vacancies must bring about changes in the conductiv-ity in CaBFO, whereas redistribution of the surface charges may not necessarily do so, and the current between the electrodes does not change (Figure 3c), we are likely dealing with surface ion motion in this case of low temperature and low bias. Notably, forma-tion of the remanent potential feature only at one of the electrodes suggests the polarization of the existing
ionic subsystem (e.g., mobile part of the surface double layers).
Increasing interelectrode bias to 90 V at room tem-perature leads to increased accumulation of the oppo-site ions, while not changing the overall behavior much. The linearity of the potential distribution is succeeded by its bending during the polarization, and later, the negative potential“pits” relax to flat zero (Figure 3df). However, in this case, ions presumably accumulate at both electrodes, and the polariza-tion current is higher. The current remains transient (Figure 3f) and does not increase over time, as it would in the case of oxygen vacancy motion. Hence, we still attribute the observed phenomena to the surface ion dynamics; however, in this case, the electrochemical split-ting of water molecules can be an integral part of the process, resulting in additional generation of mobile ions. Increasing temperature (e.g., to 100°C, Figure 4ac) but keeping the bias low significantly enhances kinetics of the polarization and relaxation processes. Faster polarization means a larger amount of accumulated
Figure 4. (ac) Line-averaged surface potential vs time and position and interelectrode current vs time as measured at 100 °C with 5 V applied between the electrodes. (df) Same with 90 V applied to electrodes; gray rectangles show position of the lateral electrodes. Arrows and color bars in (b,e) indicate time sequence of the curves. Averaging was performed over spatial locations equidistant from the grounded electrode, which created a set of“lines”, whose positions are indicated with the colorbars in (a) and (d).
ions and higher polarization current (Figure 4c) in the same 10 s polarization period. Thus, again, the poten-tial distribution in these conditions is presumably governed by the surface ions rather than oxygen vacancies. Note that at low biases surface charges again pile up only by the biased electrode. We spec-ulate that this behavior might be due to the splitting of the adsorbed water molecules in the high electricfield. Thus, at high biases, in addition to the accumulation of negative surface ions at the positive electrode, some negative ions are generated at the grounded elec-trode, which serves as a source of electrons:
H2O(s)þ ef H2v þO(s)
Finally, high temperature and high bias conditions trigger the oxygen vacancy dynamics in addition to the surface charges motion, and a complicated potential distribution ensues (Figure 4df). Within the first tenth of a second from the application of bias, the initially linear distribution acquires an S-shape, indicating a very fast separation of opposite charges that build up by the electrodes and give rise to a fast-decaying current. However, during the next 9.9 s, the potential distance curves slowly linearize again, and this process is accompanied by a gradual increase in current, as clearly visible in the black curve of Figure 4f.
This behavior must be explained by taking into account all three kinds of the charged particles existing in the system: the surface ions, bulk oxygen vacancies, and electrons/electronic holes of thefilm. We propose the following qualitative model for explaining the ob-served phenomena. Under a high driving force and while being thermally activated, surface ions redistrib-ute themselvesfirst (due to higher mobility), followed by the oxygen vacancies. Water splitting may also play a role here by generating more negative surface ions. The pile-up of the negative ions is then compensated by the electronic holes that are not only more mobile at high temperature but also more abundant, as they are generated alongside the oxygen vacancies' shift. This leads to a straightening of the potential distribution.
Relaxation only equilibrates the surface ions, as evi-denced by the small, quickly fading current, whereas the oxygen vacancies do not relax much, shifting further and further after each measurement and increasing thefilm's conductivity. This is seen in the progressive rise of the background current in Figure 4f, as indicated with the arrow.
The relaxation data can further be quantified using a simple phenomenological model similarly to earlier studies of relaxation in piezoresponse force micros-copy.6567The potential decay over time can befitted with the exponential law:Φ = A þ B 3 et/τ, whereΦ is the surface potential, A is the offset, B is the pre-exponential factor, andτ is the mean lifetime, which is inversely proportional to the diffusion coefficient of the surface ions.
Figure 5a displays temperature dependence of the mean lifetime averaged over half of the grid points (where thefitting was most successful) for data taken at 5 V bias. As seen,τ values for the polarization and relaxation processes are slightly different (due to the lower signal-to-noise ratio of the relaxation curve) and steadily decrease with increasing temperature. The Arrhenius plot gives the value of the activation energy as approximately 0.14 eV (Figure 5b), which is very close to the 0.12 eV of the proton diffusivity in water.68,69
The diffusivity of the surface ions can be estimated as D = d2/τ, where d is the distance ions have diffused in τ seconds. Obviously, it should be on the order of the interelectrode distance. The calculated value of di ffu-sivity (∼2 109m2/s) is close to the room
tempera-ture diffusivity of protons in water (∼108m2/s). This
serves as an additional indication of the surface, rather than bulk ionic dynamics at low biases.
These observations suggest that the tr-KPFM dy-namics readily observed on CaBFO surface is predomi-nantly controlled by the surface ionic dynamics and electrochemistry of water layers that can couple to the bulk conductance through electrochemical gating ef-fects. While providing only negligible current, these effects dominate the potential dynamics. In order to ex-tend these studies to probe the bulk insulatorconductor
Figure 5. (a) Averaged mean lifetime of the surface potential decay at 5 V bias as a function of temperature. (b) Arrhenius plot of the averaged mean lifetime. Inset in (a) defines the polarization (P) and relaxation (R) periods.
transition in CaBFO, one needs to either preactivate the sample or use longer polarization pulses. Both of these approaches were employed here, as discussed below. Preactivation was done by biasing the electrodes with 90 V at 100°C for ca. 40 min until current in-creased from 0.9 to 70 nA. The tr-KPFM imaging was started immediately after preactivation and showed that initially most of the film acquired the same potential as the biased electrode, and most of the potential drop took place close to the grounded electrode, where the p-n junction must have formed by the shifted oxygen vacancy density (Figure 6b). When the bias is switched off, this region remains more negatively charged than the rest of the film, indicating accumulation of negative ions in it, which dissipate during the relaxation period. The potential distribution linearization during polarization is accom-panied by a decrease in current (Figure 6c). Taking these facts together, the following explanation can be given. The application of bias redistributes negative surface ions, accumulating them not at the biased electrode but in the region of the highest potential, at the shortest distance from the grounded electrode, since all regions of thefilm farther away are equipoten-tial with the biased electrode. As negative ions pile up in the p-n junction region, they attract and trap electronic holes that partly compensate their charge. As a result, potential in the p-n junction region decreases and overall potential distribution straightens up by the end of the polarization period. Hole trapping also leads to a decrease in current. Thus, the surface ionic dynamics may play a role here in the resistive switching, acting as an impeding thermodynamic factor.
Prolonged application of high bias at elevated tem-peratures does eventually lead to the resistive switch-ing in CaBFOfilm. Figure 6df demonstrates potential and current evolution in the sample at 125°C under 100 s 90 V polarization pulses. In this case, all surface ion dynamics is condensed into thefirst several sec-onds and is almost invisible in the 100 s time scale, whereas the much slower motion of oxygen vacancies gradually increases the potential and current. The potential distribution remains nearly linear and would presumably curve upward at later stages (in ca. 40 min) to finally reach the shape of the dark-blue line in Figure 6b. Interestingly, next to no relaxation is ob-served in this case since the conductive CaBFOfilm is electroneutral and any excess charge relaxes very fast. We further extend these studies to explore local ionic dynamics as visualized in spatially resolved maps of thefitting coefficients. Figure 7b presents such maps for the polarization/relaxation process that occurred in pristine sample under 30 V during 10 s and at room temperature, and Figure 7a shows the same for 5 V polarization pulse at 100°C. The offset simply shows spatial distribution of potential: it is linear during polarization for room temperature and curved for 100°C (compare to Figure 4b, green line) but is close to zero during relaxation in both cases. The pre-exponential factor maps describe how much potential drop occurred locally over the given period of time. For room temperature data, they clearly show two extrema close to the electrodes, where most polarization and relaxation took place due to accumulation of negative surface ions. This is similar to what is shown in Figure 3e. The high-temperature pre-exponential
Figure 6. (ac) Line-averaged surface potential vs time and position and interelectrode current vs time as measured at 100 °C with 5 V applied between the electrodes. (df) Same at 125 °C and 90 V bias. Arrows and colorbars in (b,e) indicate time sequence; gray rectangles represent electrodes. Averaging was performed over spatial locations equidistant from the grounded electrode, which created a set of“lines”, whose positions are indicated with the colorbars in (a) and (d).
factor maps show maximal potential drop near the biased electrode. The mean lifetime maps also show some spatial variation but are only reliable in the regions of high potential drops, where the signal-to-noise ratio is highest andfitting is best. All in all, fitting coefficient maps condense the tr-KPFM data, reflecting both time and spatial information in one image and helping to extract useful information about the ma-terial behavior.
CONCLUSIONS AND OUTLOOK
In summary, we have presented a novel SPM-based technique for surface potential mapping in both space and time domains. The tr-KPFM allows one to probe ionic charge dynamcis even when corresponding cur-rents are extremely small: on insulating and nearly insulating surfaces. Using it to investigate the ionic dynamics in CaBFO thinfilm, we have found that, at low biases and temperatures, all polarization/relaxation of the potential is due to surface charge motion, and only at higher temperatures, stronger electric fields, and longer time scales do oxygen vacancy dynamics begins to play the dominant role in conductivity. It is shown
that in certain conditions surface ions may control the conductivity of the CaBFO thinfilm to a greater extent than the oxygen vacancies do.
Notably, this approach (a spatially resolved analog of the potentiostatic and galvanostatic intermittent titration techniques7072) can differentiate the ionic from
elec-tronic dynamics in time domain and can be combined with the classical electrochemical impedance spectro-scopy.12,13 We further note that the use of the band excitation technique73,74 will enhance resolution and sensitivity,75 half-harmonic band excitation76 detection can decouple potential and capacitive effects, and fast detection will allow measurements below the microse-cond level, where the electronic response happens.77The tr-KPFM method can be used for probing the potential distribution in nano- and microelectronic devices, includ-ing adsorbed surface charge dynamics in conventional microelectronics (parasitic currents on SiO2 and Si3N4
surfaces), surface versus bulk ionic dynamics in materials with the ion-controlled metalinsulator transition and resistive switching (Ca-BFO, as shown, NiOx, etc.), and
studies of gas interaction with solids, including spillover effects in catalysts and gas sensing in semiconductors.
METHODS
The studied sample was a 100 nm epitaxialfilm of 10% Ca-substituted BiFeO3grown on an insulating SrTiO3substrate. Lateral Au/Cr electrodes 100μm wide, 3 mm long, and 200 nm thick were deposited 100μm apart using a photolithographic mask and physical vapor deposition. Devices were fabricated by gluing thefilm to a chip carrier and performing wire bonding. Multimode AFM (Bruker) with a Nanonis (Specs) controller was used as a measuring platform. The bias application and signal recording was done by a computer via a National Instruments card controlled through Matlab and LabVIEW software. Two types of cantilevers with conductive coating tips were used for measurements: Budget Sensors (Cr/Pt coating, k = 3 N/m) and boron-doped diamond-coated (NT-MDT, k = 2891 N/m). The former, being moreflexible and sensitive, was used for mea-surements with biases lower than 10 V. When employing higher biases, the tr-KPFM grid was chosen outside the biased elec-trode, as accidental touching of the cantilever tip to it caused discharge and destruction of the tip. Current was measured with a Femto amplifier (DLPCA-200) connected in series with a 200 MΩ protective resistor. An external lock-in amplifier (SR844, Stanford Research) was used for signal processing, and a
function generator (DS345, Stanford Research) applied AC waveform to the tip. Data processing was done using custom-written Matlab codes. Some of the outlier points in the maps and averaged data that corresponded to abrupt changes in topography (SPM tip encountering surface particle or electrode edge) were removed manually.
Conflict of Interest: The authors declare no competing financial interest.
Acknowledgment. This research was conducted at the Cen-ter for Nanophase MaCen-terials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Divi-sion, Office of Basic Energy Sciences, U.S. Department of Energy. The work in National Chiao Tung University was supported by the National Science Council of Republic of China (under Contract No. NSC-101-2119-M-009-003-MY2), Ministry of Edu-cation (Grant No. MOE-ATU 101W961), and Center for Inter-disciplinary Science at National Chiao Tung University.
Supporting Information Available: Data on the variation of the calibration coefficient over distance and in time as mea-sured by tr-KPFM and band excitation open-loop KPFM are presented. This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 7. Fitting coefficients maps (spatial distribution of coefficients): A is the offset (in V), B is the pre-exponential factor (in V), and τ is the mean lifetime (in s) (a) for 5 V polarizing pulse at 100 °C, (b) for 30 V polarizing pulse at 23°C. Several leftmost and rightmost lines of each map were recorded over the electrodes and stand out from the rest of the maps. Scale bar is 10μm.
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