May 28, 2014
C 2014 American Chemical Society
Deep Data Analysis of Conductive
Phenomena on Complex Oxide
Interfaces: Physics from Data Mining
Evgheni Strelcov,†,^Alexei Belianinov,†,^Ying-Hui Hsieh,‡Stephen Jesse,†Arthur P. Baddorf,† Ying-Hao Chu,‡,§and Sergei V. Kalinin†,*
†Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States,‡Department of Materials Science and
Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, and§Institute of Physics, Academia Sinica, Taipei 105, Taiwan.^E. Strelcov and A. Belianinov contributed equally to this work.
T
he complexity of the world around us stems primarily from the fact that materials, particles, and phenomena in it exist in a mixed, entwined form. Much of the technological progress from the Bronze Age metal smelting to modern crude oil refinement was focused on extrac-tion of pure components from mixtures. Similarly, the power of science relies on the principle of explaining complex phenomena as originating from several simpler acts. One of the topical scientific challenges;data mining;is of the same nature. Whereas in the process of system characterization we can record voluminous multidimensional data sets, big data analysis becomes a serious problem. In this work we invoke the centuries-old paradigm of separation and address this issue by applying statisti-cal methods to the task of demixing com-plex charge transport behavior in a two-component oxide nanocomposite.Electronic transport in strongly correlated oxides has long been one of the key areas of condensed matter physics and is of interest
to multiple technological applications.15It was long recognized that properties of these systems can be strongly position de-pendent and controlled by defects, inter-faces, grain boundaries, and dislocations. The emergence of local scanning probe microscopy techniques610capable of ad-dressing transport locally, on the level of individual interfaces, defects, or grain bound-aries, has given a new impetus to thefield and blossomed into a number of remarkable studies including 2D electron gas on oxide interfaces,11,12 polarization-controlled tun-neling in ferroelectricfilms,1316conduction at grain boundaries, ferroelectric domain walls,1723and 1D topological defects.24In all of these works, mechanisms associated with origins of disorder, local electronic transport, and bias-activated switching of different regimes were obtained from pecu-liarities in currentvoltage (IV) curves.
Recently, it has been recognized that the electronic transport can be strongly af-fected by concurrent bias-induced electro-chemical processes,2529 thermal or field
* Address correspondence to sergei2@ornl.gov, strelcove@ornl.gov.
Received for review April 11, 2014 and accepted May 28, 2014. Published online 10.1021/nn502029b
ABSTRACT Spatial variability of electronic transport in BiFeO3CoFe2O4
(BFOCFO) self-assembled heterostructures is explored using spatially re-solvedfirst-order reversal curve (FORC) current voltage (IV) mapping. Multi-variate statistical analysis of FORC-IV data classifies statistically significant behaviors and maps characteristic responses spatially. In particular, regions of grain, matrix, and grain boundary responses are clearly identified. k-Means and Bayesian demixing analysis suggest the characteristic response be
separated into four components, with hysteretic-type behavior localized at the BFOCFO tubular interfaces. The conditions under which Bayesian components allow direct physical interpretation are explored, and transport mechanisms at the grain boundaries and individual phases are analyzed. This approach conjoins multivariate statistical analysis with physics-based interpretation, actualizing a robust, universal, data-driven approach to problem solving, which can be applied to exploration of local transport and other functional phenomena in other spatially inhomogeneous systems. KEYWORDS: conduction hysteresis . oxide heterostructures . multivariate analysis . big data . scanning probe microscopy . FORC-IV
metalinsulator transitions,3032or ferrolectric polari-zation dynamics,13,33,34evoking complex time-dependent phenomena. A paradigmatic example is the interfacial orfilament-controlled resistive switching in transition metal oxides, which is being actively explored in the context of neuromorphic and memristive elec-tronics.3538One characteristic facet of these systems is a complexfield history dependence of conductance, controlled by bias-induced changes in chemical com-position or polarization distribution. These convoluted processes, in turn, are controlled by surface structure with defects acting as nucleation and pinning cen-ters.39 Recently, we have introduced the first-order
reversal curve currentvoltage (FORC-IV) scanning probe microscopy (SPM) technique and demonstrated imaging on spatially uniform Ca-substituted BiFeO3
and NiO systems40,41as well as interfacial electroresis-tance in the BiFeO3CoFe2O4 (BFOCFO)
nano-composite.42Those studies show that the locally mea-sured hysteresis in the FORC-IV curves corresponds to changes of electronic conduction sensed by the SPM in response to a bias-induced electrochemical process, with the area of the IV loop, or loop opening, acting as a measure of the local ionic activity.
One of the obstacles facing IV and FORC-IV spectro-scopic imaging modes is data analysis and interpreta-tion. Namely, only an insignificant fraction of the collected data is traditionally explored in the form of
single local responses, or 2D cross sections, obviating the interpretation of physical behavior and extraction of information on local materials functionalities. For example, previously a spatially-resolved 4D FORC-IV data set, which consists of a measured current re-sponse for a bias waveform at a spatial pixel location, was analyzed to yield loop opening, threshold voltage, and minimal resistance at each peak bias,4042leaving the bulk of the spatially and bias-dependent transport data unassessed. Similar hindrances plague other spec-troscopic imaging modes, including 3D IV mapping in conductive atomic force microscopy (AFM) and con-tinuous imaging tunneling spectroscopy in scanning tunneling microscopy. In this work, we combine FORC-IV measurements with multivariate statistical methods, to discriminate between different behaviors based on the shapes of the local IV curves in the full spectro-scopic data set and use our data-driven interpretations to explore suitable physical models.
The essence of our approach is presented in Figure 1. FORC-IV data are acquired by recording current as a function of a positive bias voltage waveform (Figure 1b) applied to each pixel on a grid on the BFOCFO sample surface (Figure 1a). The spectro-scopic current data are then explored using multi-variate statistics and clustering methods to deter-mine the number of statistically significant dissimilar behaviors, yielding (a) the number of components
Figure 1. Experimental setup and data analysisflowchart. (a) Schematics of the CFOBFO nanocomposite sample and FORC-IV experimental setup; FORC-IV curves measured over BFO and CFO regions can be modeled as different (non)linear resistors, whereas resistance on the CFOBFO boundaries will be determined by both resistors connected in parallel. (b) A voltage waveform with several triangular pulses is applied at each spatial point of the sample, yielding a four-dimensional data set. (c) Information on the local behavior of IV curves becomes available via the statistical analysis of the FORC-IV data set. (d) The found components that represent typical material behavior can befitted with specific physical models to yield quantitative information on its behavior.
(behaviors), (b) components shapes (e.g., representa-tive IV curves in the case of FORC-IV data), and (c) intensity score maps of spatial distribution for each component. Figure 1c illustrates this for a simple case of a two-component system, with linear and nonlinear resistors. Here, local behavior can be modeled by sets of linear or nonlinear resistors connected in parallel; for example, interfacial resistance can be a combination of individual BFO and CFO resistors or conductivity channels corresponding to dissimilar carriers. In these cases, the component shape contains information on the physical mechanisms of local conduction and can befitted to the appropriate physical model (Figure 1d). Overall, the multidimensional data set efficiently un-dergoes a lossless compression to several spatial maps of distinct statistically significant conductivity channels at a specific pixel location, thus visualizing local nano-scale properties of the sample. We will now proceed with the description of the CFO-BFO sample, FORC-IV measurements, statistical analysis, and physical param-eters extraction in accordance with the scheme pre-sented in Figure 1.
RESULTS AND DISCUSSION
Qualitative Analysis of Conductance in the BFOCFO System. The CFOBFO system is a self-assembled tubular het-erostructure that forms spontaneously during pulsed laser deposition growth due to segregation of the perovskite BFO matrix and the CFO spinel inclusions.43
The CFO nanopillars are approximately 100 nm across and show high interfacial conductivity at low tip biases (100 mV); however their cores, as well as the surround-ing BFO matrix, are almost insulatsurround-ing (Figure 2a,b). Higher biases (7 to 8 V) lead to resistive switching in the interfaces; remarkably, the interfaces of a CFO
island can be switched independently.42This behavior can be explained with a dynamic dopant model,42,44,45 i.e., coupling oxygen vacancies, concentrated at inter-faces, and their motion in the external electric field with a related change of the doping level at a semi-conducting interface and a subsequent formation of a pn junction. The presence of interfacial ionic activity was also confirmed by FORC-IV.42 However, due to very high variability in the type of transport between dissimilar locations, the mechanism of the electronic transport in this system remains ambiguous. In other words, spatial averages mix responses from different regions, whereas single pixel responses have low signal-to-noise ratios and their veracity is unclear. Here, we combine multivariate statistical analysis with physics-based fitting to analyze these behaviors sys-tematically and reconstruct a comprehensive transport picture in these heterostructures.
FORC-IV data were collected on a 500 500 nm2 region shown in Figure 2. A 50 50 grid was overlaid onto the area with each point probed by a bias wave-form containing six triangular pulses going from 0 V to a peak bias value and back to 0 V. Peak bias (Vp)
increased from 0.5 to 3 V in 0.5 V steps, forming six distinct triangular pulses (corresponding to six IV loops, Figure 2c). The spatially averaged IV curves show non-linear behavior with diminutive hysteresis in the last two loops (Figure 2d). However, behavior at individual grid locations is drastically different: there are linear and nonlinear IV curves with different degrees of hyster-esis starting at different threshold biases. Naturally questions arise, with regard to spatial variability and uniformity of these behaviors across material interfaces, whether these behaviors can be identified and if in-dividual physical mechanisms can be determined.
The intrinsic four-dimensional nature of the FORC-IV data (current as a function of x, y position, voltage, and loop number) prevents the observer from immediately “seeing” spatial variation in behavior that is distributed over a 2D parameter space. One solution is to reduce the dimensionality to 3D, e.g., extract area vs loop number, or average IV curve in the forward and reverse directions. These data sets can then be plotted as (x, y) cross sections (such as loop area maps) or spectra at individual points (see Figure S1 in the Supporting Information). We found that this simplification leads to partial losses of highly relevant information origin-ally contained in the data. Indeed, the shapes of the local FORC-IV loops originate from the interplay of multiple physical mechanisms, such as local conduc-tion and resistive switching. Addiconduc-tionally, besides the pn junction mechanism mentioned above, these can include electrochemical processes of oxygen evolution and influence of surface states' population dynamics on the composite's conductivity (gas sensing effect46). Furthermore, local behavior can be strongly influenced by the degree of reversibility of the process responsible
Figure 2. BFOCFO nanocomposite. (a) Topographic im-age (scale bar is 100 nm). (b) CAFM imim-age recorded at a tip bias of 0.1 V showing high interfacial conductance (in yellow). (c) FORC-IV voltage waveform and a typical current response. (d) Averaged set of FORC-IV curves recorded on region shown in (a) for a 50 50 spatial grid (2500 sets of IV curves in total); arrows show six peak bias values, the turning points of each of the six IV curves.
for conduction and by stability of the tipsurface contact and instrument noise. Finally, whether these processes are controlled thermodynamically or kineti-cally is also irreducibly hidden in the full spectral data. Therefore, the need for a robust statistical approach capable of drawing conclusions from a complete data set free from compression loss becomes readily apparent.
Data Mining in FORC-IV. In order to decorrelate a high-dimensional FORC-IV data set in a way that allows physical interpretation, we need to know what is the smallest reasonable number of behaviors present in the system. The initial naïve hypothesis presented in Figure 1 was that the number of behaviors is equal to the number of materials in the nanocomposite. How-ever, both the current map (Figure 2b) and FORC-IV loop area maps (Figure S1, Supporting Information) suggest a more complex scenario, with the interface manifesting a different kind of conductive behavior than the BFO and CFO regions. To help establish the relevant number of behaviors, we have employed a k-means clustering scheme on the full spectrographic data set.47The k-means algorithm separates M points
that exist in N dimensions into a specified k number of clusters of curves that have similar behavior so that the sum of squares within a cluster is minimized.48,49
arg min
∑
k i¼ 1x∑
j∈Si jj xj μijj 2 (2)Here μiis the mean of points in Si. We have used a
Matlab2012b version of the algorithm to minimize the sum over all clusters of the within-cluster sums of point-to-cluster-centroid distances. As a minimization parameter, we have used a square Euclidian distance with each centroid being the component-wise median of the points in a given cluster.
The k-means algorithm divides the data set in a specified number of optimally selected clusters. How-ever, the number of clusters is a priori unknown. To get a measure of the quality of the separation as a function of the number of clusters, the data can be presented in the form of a dendrogram. The dendrogram plot in Figure 3a illustrates cluster arrangement in a top-down approach, where all observations are grouped into a single cluster initially and are recursively separated down the hierarchy. This is achieved by establishing
a distance metric between observations and linkage criteria used tofind the dissimilarity of clusters as a function of pairwise distances. As previously men-tioned, we have used square Euclidian distance as our distance metric and centroid linkage, ||Ca Cb||,
where Caand Cbare the centroids of clusters a and b.
That is to say, we look at how tight the information clusters in our data are as additional degrees of free-dom are introduced. Therefore, a larger vertical drop in each of the binary branches, in Figure 3a, indicates a better cluster classification scheme in the data, where small changes offer only a marginally better reduction in the within-cluster sum. It then follows that minor vertical differences in the dendrogram plot can be dis-missed, and the largest drops indicate major changes in data organization. Judging by the result shown in Figure 3a, we have concluded that separation of our data into four distinct types of behavior produces the most physically meaningful results. Therefore, we used four clusters as the inputs to our k-means clustering method. k-Means clustering results are shown in Figure 3b, where each individual color represents a cluster. Figure 3c shows the mean IV for the entire data spec-trogram, color coded with respect to the cluster it represents. The results show a trend in conduction behavior; the areas of highest conductivity with the least IV hysteresis are located within certain islands (red), with close second highest conductance being in other islands, shown in yellow. Closely following is the interface region shown in cyan. In this area we see some hysteresis and loop opening at higher peak biases. This trend continues with loops becoming con-tinuously more hysteretic as we move to the BFO matrix (navy in Figure 3b).
As we augment our understanding of the internal structure in the data using k-means, the next natural step is to try to extract statistical behavior in a way that can be understood physically. That is to say, we want to separate our data into well-defined clusters with a clear spectroscopic behavior that has an intensity weight component providing insight into the spatial dis-tribution of the behavior. Ideally, these components will also be physically viable, i.e., well-behaved, posi-tive, have additive weights, etc. This analysis can be achieved by Bayesian linear unmixing.50The Bayesian
Figure 3. k-Means analysis of the FORC-IV data. (a) Dendrogram plot of hierarchial binary cluster tree showing that four is the optimal number of clusters (red circles). (b)k-Means cluster algorithm resultant map with four clusters specified (scale bar is 100 nm). (c) Mean FORC-IV curves for each of the four cluster types shown in map b.
approach assumes data in a Y = MAþ N form, where the complete observations Y are a linear combination of position-independent endmembers, M, with respec-tive relarespec-tive abundances, A, corrupted by addirespec-tive Gaussian noise N. Additional features and applicability of this method to extracting meaningful physical be-havior out of end-members rely on non-negativity, full additivity, and sum-to-one constraints for both the end-members51,52and the abundance53,54coefficients.
The algorithm estimates the initial projection of end-members in a dimensionality-reduced subspace (PCA) via N-FINDR,55 whichfinds a simplex of max-imum volume that can be inscribed within the hyper-spectral data set using a simple nonlinear inversion. The end-member abundance priors as well as noise variance priors are chosen by a multivariate Gaussian distribution, where the posterior distribution is calcu-lated based on end-member independence using Markov chain Monte Carlo, which generates asympto-tically distributed samples probed by Gibbs sampling strategy. The resulting end-members M are non-nega-tive, and respective abundances add up to 1. Hence, the spectrum at each location is decomposed into a linear combination of spectra of individual com-ponents in corresponding proportions. Note that these particular constraints make transition from sta-tistical analysis to physical behavior significantly more straightforward, as geometry of our sample implies a parallel combination of conduction channels (Figure 1), where currents are additive (more details in section III in the Supporting Information). By making the abun-dances additive and the end-members positive we can start assigning physical behavior to the shape and nature of the end-member curves. By extension, anal-ysis of these curve's loading map adds the spatial component to the behavior that nonstatistical meth-ods of analysis generally do not allow. An additional unique aspect of Bayesian analysis is that the end-member spectra and abundances are estimated jointly
in a single step, unlike multiple least-squares regres-sion methods, where initial spectra should be known.50
Bayesian deconvolution results are shown in Figure 4. They corroborate behavior shown by k-means, but also display a more detailed separation. Unlike the k-means map (Figure 3b), the image of the CFO island in the upper left corner of the Bayesian loading map strongly resembles the corresponding region in the CAFM map (Figure 2b), with the central part of the island and its interface having different conductivity. However, it is now evident that separation is not based purely on overall conductivity in the central and inter-facial parts of this island, but rather on the shapes of the IV curves. Thefirst Bayesian end-member, stron-gest on the island's interface (as well as two other islands), shows ohmic behavior, whereas the second Bayesian end-member is nonlinear and manifests mostly in the inner part of this island. The third end-member highlights the BFO matrix and has a very low current response, a current offset, and some loop opening. Finally, the last end-member is present only in a few of the interfacial points and can be described by a high conductivity and strongly hysteretic be-havior. Thus, instead of separating conductivities of the BFO matrix and CFO islands (i.e., trivial case, which even classical CAFM can resolve), Bayesian unmixing extracted four different types of behavior, ranging from ohmic to nonlinear to memristive. Simultaneously, by definition (positively defined and sum-to-one) Bayesian end-member spectra, on one hand, allow direct physical interpretation (i.e., end-members are positive and scaled in nA) and, on the other hand, are different from the mean data found by k-means. Specifically, in cases when local transport can be represented as a super-position of parallel or series conductive channels, Bayesian components have direct meaning of indivi-dual components (see Supporting Information section III). The difference between the data averaged over some region and the strongest Bayesian end-member
Figure 4. Bayesian analysis of the FORC-IV data. Top row: four Bayesian end-members; bottom row: corresponding Bayesian loading maps. Notice the rich internal structure of conductance within the grains as revealed in the Bayesian maps.
spectrum in this region can be understood intuitively as the difference between a mixture and one of its constituent components, as explained in Supporting Information (Figure S6). Here, we just point out that the Bayesian end-members highlight the most representa-tive component behavior, rather than a simple average over the mix.
Physics behind Statistics. Having extracted the quin-tessential behaviors from the multidimensional data set, we now turn our attention to ascribing physical mean-ing to these behaviors. As suggested earlier (Figure 1), total local current through the BFOCFO interface can be represented as a sum of currents through the con-stituent materials, which can be, therefore, associated with the Bayesian end-members that are also additive (see Supporting Information section III). Furthermore, the local electronic transport through the nanocom-posite can be limited by either the electrode's surface junction, the conductance of the bulk, or a combina-tion of the two. Table 1 summarizes the possible tran-sport mechanisms, which we will compare to the Bayesian end-member spectra. The listed equa-tions16,56were derived for a semiconductor in a uni-form electric field, and therefore, in order to apply them to our tipnanocompositebottom electrode system, we will employ the following assumptions: (1) for the cases of FowlerNordheim and Schottky emis-sion mechanisms, we assume abrupt junction approxi-mation,56with the maximal electric field in the tip surface junction given by Emax= ((2q/εs)(Vþ Vbi))
1/2
, where V is the applied bias and Vbi is the built-in
potential due to the difference between the metal and semiconductor work functions; (2) for the cases
of PooleFrenkel and space-charge-limited bulk con-ductance, we note that the local conductivity will strongly depend on the strength of the electric field, and therefore, current will be limited by the resistivity of the deep layers of the film, lying close to the bottom electrode, where electric field is the weakest and is proportional to the tip bias: Ebulk=R(V/d). COMSOL
modeling shows that the field enhancement factorR is on the order of 10. It follows that none of the Bayesian end-members can be fitted well to the reverse-biased Schottky barrier emission equation (which could be the case for the positive tip bias; see bipolar IV curves in ref 42).
The second end-member can be equally wellfitted to the space-charge-limited conductance and Fowler Nordheim (FN) tunneling equations. Moreover, there is a transition in the voltage exponent from 1.6 to 2 as the peak bias increases (i.e., from loop 1 to loop 6). How-ever, the effective mass of the electron calculated from the Child's lawfitting is too high to be physically mean-ingful. The electron mobility extracted from the Mott Gurney lawfit is ca. 6 104cm2
/V 3 s, which is 9 orders of magnitude higher than the literature data for sintered powders57,58(3 1013cm2
/V 3 s at room temperature). The FNfit of the second end-member is shown in Figure 5a. Data (except for the few low-bias points) are well linearized in the normalized logarithmic coordi-nates and yield a potential barrier of 0.3 meV. This value is reasonable, considering that the second end-member behavior is concentrated in the same CFO island as that of thefirst one, which is ohmic and lacks
TABLE 1.Possible Transport Mechanisms in BFOCFO
Nanocompositea FowlerNordheim tunneling I¼ Seff3 q3m Pt 8πhmjBEmax 2e ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 128π2ms 9h2 q2 jB3 q Emax Schottky emission I¼ SeffAT e qjB0=kTe q=kT( ffiffiffiffiffiffiffi qEmax 4πεs p ) PooleFrenkel
conduction I ¼ SeffqμNDEbulke
q kT(jB ffiffiffiffiffiffiffiffi qEbulk πεs p ) h i
MottGurney law
I¼ Seff 9εμ 8d Ebulk Child's law I¼ Seff 4ε 9 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2q mdEbulk 3 r a
Seffis the effective tipsurface area; q is the elementary charge; mPtand m* are effective electron masses in Pt and the semiconductor; h is the Planck's constant, φB is the barrier height; Emaxis the maximal electricfield in the metalsemiconductor interface; A** is the effective Richardson constant; T is temperature; k is the Boltzmann constant;εsis the effective semiconductor permittivity; μ is the electron mobility in the semiconductor; NDis the dopant concentration; Ebulkis the electric field in the semiconductor bulk; d is the sample thickness.
Figure 5. Fitting Bayesian end-members to different trans-port mechanisms. (ac) Second, third, and fourth end-membersfitted to the FowlerNordheim tunneling equa-tion, correspondingly. d) Fourth end-memberfitted to the PooleFrenkel conduction model; blue and green crosses represent data for lower (forward) and upper (reverse) IV curves, correspondingly; bestfits are shown in red lines. The insets show linearization of the curves in the corresponding normalized coordinates. Only the last loop at a peak bias of 3 V is shown for the sake of simplicity.
any potential barrier at all. The third end-member can be satisfactorilyfitted with the FN tunneling equation (Figure 5b), which, likewise, gives a low potential barrier of 0.5 meV.
The fourth end-member is set apart from the rest by the virtue of its hysteresis, with the forward and reverse IV curves having distinctively different shapes above a peak bias of ca. 2 V (i.e., last two loops). It is noteworthy that the upper IV branch of the fifth loop almost coincides with the lower branch of the next, sixth, loop, which is indicative of retention of higher conductivity after gradual switching. The natural question to ask is whether the conduction mechanism changes during this switching process. As Figure 5d and c show (see insets), the lower (forward) IV branch is bestfitted by the PooleFrenkel (PF) conductance, whereas the upper one (reverse) is consistent with the FN tunneling. We can speculate that the switching between the two mechanisms may be due to the oxygen vacancy redis-tribution activated at the interfacial regions and high-lighted by this end-member. Initially, conductance is governed by the bulk PF transport, due to low bulk concentration of oxygen vacancies. Application of pos-itive bias polarizes the BFO matrix and drives vacancies away from it, concentrating them on the outer part of the interface and decreasing local conductivity. Mem-ristive switching occurs, and current henceforth is limited by the FN tunneling of the charge carriers from the metal-coated tip into the conduction band of the nanocomposite. Note, however, that the equations of Table 1 are derived under the immobile dopants assumption (bias-independent local dopant concen-tration), which is exactly the opposite of the mecha-nism underlying memristive behavior. The complexity of the nanoscale electrochemical processes makes it difficult to model it, and further studies are required to determine the exact mechanism behind the process manifested in the fourth Bayesian end-member. Finally, thefirst, ohmic, end-member can be used to estimate the conductivity of CFO, ca. 0.13 S/m, which is several orders of magnitude higher than reported before for pure CFO.57This is consistent with the hypothesis of
oxygen vacancies being accumulated at the tubular BFOCFO interface.42 The interface becomes highly
doped, almost metallic, which is detected experimen-tally and is reflected in the first Bayesian end-member (see Figure 4 left map).
Note that both thefirst and the fourth Bayesian end-members highlight the BFOCFO interface, the inner and outer part thereof, respectively. In both instances oxygen vacancies presumably play the key
role in the electronic transport behavior. However, the behaviors of the first and fourth end-members are strikingly different. An explanation for this can be found by recalling the dependence of semiconductor conductivity on dopant concentration. At low doping level, the semiconductor's electronic conductivity is low and very sensitive to small variations in doping level. A highly doped classical semiconductor, though, has a very high electronic conductivity, which does not change much in response to small variations in dopant concentration. Keeping in mind that oxygen vacancies act as a mobile dopant, whose concentration changes in response to the applied electricfield, they will have a significant effect on the local electronic conductivity of CFO if their local concentration is medium-low. This is presumably the case of the outer CFO interface seen in the Bayesian loading map 4 (Figure 4). The inner part of the CFO islands, on the other hand, is highly doped, and its nearly metallic conductivity is insensitive to small changes in local oxygen dopant concentration. Therefore, thefirst end-member is nonhysteretic.
CONCLUSIONS AND OUTLOOK
In summary, we have studied a BFOCFO nanocom-posite by a combination of the FORC-IV technique and data mining analysis. It was established that in the explored experimental parameter space the conduc-tive behavior of the composite is best described by four independent components: linear IV curves at the CFOBFO interface, parabolic-exponential at the CFO island cores, exponential with low conductivity at the BFO matrix, and memristive at a few interfacial locations. These behaviors were explained in the framework of the model, where conductivity was controlled by the oxy-gen vacancies accumulated at the BFOCFO interface, and the corresponding IV curves werefitted to different transport equations. It followed that the Fowler Nordheim tunneling mechanism best describes conduc-tivity of the BFO matrix, the core CFO island, and the upper part of the interfacial memristive curve, whereas PooleFrenkel transport can explain the lower branch.
More generally, these studies establish the pathway for exploring complex position-dependent phenomena in inhomogeneous systems. While spectroscopic imag-ing techniques often allow spatially resolved responses to be measured, analysis and interpretation consistently remain a challenge. The combination of the statistical data mining approaches for identification of statistically significant behaviors and the physics-based fitting yields a powerful methodology for extracting physical mean-ing from a complex multidimensional data set.
METHODS
A BFOCFO nanocomposite film of 100 nm was grown on 30 nm SrRuO3(SRO)-buffered SrTiO3(001) substrates by the
pulsed lased deposition technique. Growth was monitored in situ using high-pressure reflective high-energy electron diffraction. Electrical measurements (CAFM and FORC-IV) were
performed on a Cypher AFM (Asylum Research) equipped with a National Instruments data acquisition card controlled by a computer through custom-written Matlab/LabView soft-ware. Bias was applied to a conductive Cr/Pt-coated (Budget Sensors) AFM tip, and current was detected off the bottom electrode (SRO) with a Femto amplifier (DLPCA-200). Matlab codes were used for data processing, statistical analysis, and fitting.
Conflict of Interest: The authors declare no competing financial interest.
Acknowledgment. This research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. The work at National Chiao Tung University is supported by the National Science Council, R.O.C. (NSC-101-2119-M-009-003-MY2), Ministry of Education (MOE-ATU 101W961), and Center for Interdisciplinary Science of National Chiao Tung University.
Supporting Information Available: Figures S18 and descrip-tions thereof discuss loop area maps, principal component analysis of the FORC-IV data, applicability and limitations of Bayesian analysis, behavior of BFOCFO interfaces, and contact area influence on the FORC-IV measurements. This material is available free of charge via the Internet at http://pubs.acs.org.
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