Nanosized Conducting Filaments Formed by Atomic-Scale Defects in

Article pubs.acs.org/cm

Nanosized Conducting Filaments Formed by Atomic-Scale Defects in Redox-Based Resistive Switching Memories Hongchu Du,*,†,‡ Chun-Lin Jia,†,¶,§ Annemarie Koehl,¶ Juri Barthel,†,‡ Regina Dittmann,¶ Rainer Waser,¶,∥,⊥ and Joachim Mayer†,‡,⊥ †

Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich GmbH, Jülich 52425, Germany Central Facility for Electron Microscopy (GFE), RWTH Aachen University, Aachen 52074, Germany ¶ Peter Grünberg Institute, Forschungszentrum Jülich GmbH, Jülich 52425, Germany § School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China ∥ Institut für Werkstoffe der Elektrotechnik II (IWE II), RWTH Aachen University, Aachen 52074, Germany ⊥ Section Fundamentals of Future Information Technology (JARA-FIT), Jülich-Aachen Research Alliance, Germany ‡

ABSTRACT: Redox-based resistive switching phenomena are found in many metal oxides and hold great promise for applications in next-generation memories and neuromorphic computing systems. Resistive switching involves the formation and disruption of electrically conducting filaments through ion migration accompanied by local electrochemical redox reactions. These structural changes are often explained by point defects, but so far clear experimental evidence of such defects is missing. Here, nanosized conducting filaments in Fedoped SrTiO3 thin-film memories are visualized, for the first time, by scanning transmission electron microscopy and core-loss spectroscopy. Conducting filaments are identified by a high local concentration of trivalent titanium ions correlating to oxygen vacancies. Strontium vacancies and lattice distortions also exist in the filaments. Despite a high concentration of defects in the filaments, their general SrTiO3 perovskite structure is essentially preserved. First insights into the switching mechanism are deduced from a snapshot simultaneously showing multiple nanosized filaments in different evolutionary stages. The coexistence of a high Ti3+ concentration along with Sr- and O-vacancies in the conducting filaments provides atomic scale explanations for the resistive switching mechanisms. The results shed unique light on the complexity of the conducting filament formation that cation and anion defects need to be considered jointly.

R

such as TiO2 and SrTiO3. In these oxides the formation and disruption of electrically conducting filaments is widely explained by a redox process based on the migration of oxygen ions along with the formation of oxygen vacancies (Ovacancies) and reduced metal oxide phases.5,6 For both ECM and VC switching mechanisms, the conducting filaments are therefore the key elements. In previous studies, different microscopy techniques, including scanning tunneling microscopy,6,7 local conduction atomic force microscopy,8 X-ray absorption spectroscopy (XAS), 9 − 1 3 and transmission electron microscopy (TEM),14−21 have been applied to study the conducting filaments and to obtain a better understanding of their structural nature. In particular for ECM materials (i.e., SiO2), TEM has shown the capability to reveal the structural details of the ECM mechanism.14,15 For the best-known prototype VC material SrTiO3, XAS has been demonstrated to be a successful technique to explore the Ti valence change and O-

edox-based resistive random access memories (ReRAM) have attracted great attention in the recent years because of their superior properties compared to Si-based Flash memory and their additional potential for applications in neuromorphic computing systems.1−3 ReRAM relies on the switchable change in resistance of a metal−insulator−metal structure under externally applied electrical stimuli. An initial electroforming process or the first current voltage cycle presets the pristine device, which can subsequently be switched hysteretically between its conductive ON and less conductive OFF states.4 The resistive switching process involves the formation and disruption of electrically conducting filaments through the migration of ions along with local electrochemical redox reactions. Depending on the nature of the mobile ions, two distinct fundamental switching mechanisms, electrochemical metallization (ECM) and valence change (VC), have been proposed.2 The ECM mechanism is related to the generation and migration of metal cations originating from one of the metal electrodes.2,5 The VC mechanism, on the other hand, is related to oxygen anion mobility in the insulator. The thin insulator film in a VC cell is typically a transition metal oxide © 2017 American Chemical Society

Received: January 17, 2017 Revised: March 8, 2017 Published: March 8, 2017 3164

DOI: 10.1021/acs.chemmater.7b00220 Chem. Mater. 2017, 29, 3164−3173

Article

Chemistry of Materials vacancies.9−12 Nevertheless, by means of XAS it is hardly possible to visualize the local structural details of individual filaments on the atomic scale due to the limit of the lateral resolution of the technique (≥25 nm). SrTiO3 model systems, i.e., epitaxial structures,22,23 bicrystals,24−26 and engineered dislocations,8 are currently under intense investigation in order to understand the fundamental mechanism of resistive switching. Extended defects, such as one-dimensional dislocations8,20,27 and two-dimensional stacking faults,11,28 as well as secondary oxygen deficient phases, e.g., Sr2Ti6O13/SrTi11O20 in polycrystalline films,16 have been associated with the conducting filaments. The defects essential to the conducting filament formation and disruption are still under debate. On the basis of an ion migration mechanism, resistive switching is necessarily caused by point defects; however, quantification of point defects on the atomic scale in a realistic device remains a challenge. So far clear experimental evidence of conducting filaments formed exclusively by point defects is missing. The question still remains as to whether point defects alone are sufficient for the formation of conducting filaments. Scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS) nowadays allows us to routinely resolve structural details and to map both compositional and bonding information on the atomic scale.29−32 EELS core-loss edges inherently result from the electron transition from a core orbital to unoccupied states in the conduction band.32,33 For SrTiO3, EELS fingerprints of the O-K and Ti-L2,3 core-loss edges provide a wealth of information on the local composition and chemical bonding of O and Ti atoms.24,34 STEM and EELS imaging techniques are therefore particularly suitable for mapping the distribution of the titanium valence change in conducting filaments of SrTiO3 based ReRAMs. In this work we apply these techniques to quantitatively characterize nanosized conducting filaments in electroformed Au/Fe:SrTiO3/Nb:SrTiO3 thin-film ReRAMs, providing direct experimental evidence of the point defect nature of the conducting filaments.

Figure 1. (a) Schematic of an electroformed ON-state Au/Fe:SrTiO3/ Nb:SrTiO3 memory device. (b) I−V curve of the electroforming process by the first current voltage sweep from the studied device. The “cc” denotes the current compliance. In overview (c) HAADF and (d) ABF STEM images of the device cross-section, darker image contrast areas indicate conducting filaments. Arrows in (c) and (d) indicate the film/substrate interface. Please note that the Au anode of the device was delaminated and replaced by a Pt layer.

the film/cathode interface. The V-shaped areas exhibit different levels of development. The one on the right side extends across the film penetrating into the cathode, while another on the left side of the image stops in the film before reaching the cathode. In both ABF and HAADF images, the darker contrast in the Vshaped areas compared with their surroundings implies that these areas contain lattice defects, providing a first indication that these areas are conducting filaments viewed in crosssection. We therefore analyzed these areas in detail by EELS in order to determine whether they contain a high concentration of Ti3+ and O-vacancies as would be expected for conducting filaments in SrTiO3.4,5 Quantification of Ti3+ Distribution. Monochromated EELS spectrum imaging, with the spectrum energy range simultaneously covering both the O-K and Ti-L2,3 edges, was performed from the region shown in Figure 1c,d including the filaments, the film matrix, and the substrate. Two constituent spectra showing distinctly different features of the O-K and TiL2,3 edges (Figure 2a,b) were identified from the experimental spectrum data cube by multivariate data analysis using a joint Bayesian algorithm.35 The algorithm relies on the assumption that each acquired spectrum is a linear combination of constituent spectra plus additive noise. On the basis of the fraction maps, one constituent spectrum is attributed to the normal film matrix and substrate, while the other is ascribed to the defect V-shaped areas. The changes in the fine structures of the O-K (O 1s → 2p) and Ti-L2,3 (Ti 2p → 3d) edges present evidence for a high concentration of O-vacancies and Ti3+ in the V-shaped areas. Figure 2a shows the O-K edge representing unoccupied O pstates, including hybrid states,37,38 in the presence of a core hole. The detailed features of the O-K edge for the normal film matrix and substrate are very similar to those reported for pure SrTiO3 using monochromated EELS.39 The fine structures of the O-K edge are evidently diminished for the spectrum of the V-shaped areas. This change is consistent with the results

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RESULTS Forming Filaments. Conducting filaments were created by electrical forming on individual devices by a sweep to +5 V with a current compliance of 10 mA, through which the devices (Figure 1a) were set into the ON-state. The current voltage curve of the electrical forming process is shown in Figure 1b. The top Au electrode of the devices was delaminated and replaced by a Pt layer to protect the film from ion beam damage during the TEM sample preparation. The cross-sectional TEM specimens were cut by focused ion beam (FIB) milling across the regions where Ti3+ has been detected by XAS combined with X-ray photoemission electron microscopy (X-PEEM) within the 10 μm × 10 μm area of the respective top electrodes to include the filaments in the TEM samples. The as-cut samples with initial thickness of about 100 nm were stepwise thinned by Ar-ion beam milling at 500−900 V acceleration voltages and inspected by TEM alternatingly until the thickness decreased to about 25 nm. Figure 1c,d shows, respectively, a high angle annular dark field (HAADF) STEM image and the simultaneously recorded annular bright field (ABF) STEM image of the cross-section of an electroformed device. V-shaped areas with darker contrast than the film matrix and cathode (substrate) can be recognized in the film from both images. An individual V-shaped area has lateral dimensions of 10−30 nm, starting from the top surface of the film and extending toward 3165


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Figure 2. Electron energy-loss spectra and Ti3+ distribution map for the area shown in Figure 1c,d. (a and b) The fine structures for O-K and Ti-L2,3 edges, respectively. Blue line: EELS spectrum of normal SrTiO3 for the stoichiometric film matrix and substrate dominated by Ti4+. Red line: EELS spectrum of defect SrTiO3 with the upper limit amount of Ti3+ for the conducting filaments. Raw spectra for the O-K edge (scattered symbol) are noisy and therefore were smoothed (solid line) by a nonlinear filter,36 whereas the presented spectra for Ti-L edge are the raw data. (c) Ti3+ distribution map obtained from the EELS analysis. The amount of O-vacancies contributing to the respective of Ti3+ is one-sixth of the Ti3+ concentration. All concentrations are relative to the respective atom sites in the regular SrTiO3 structure.

observed for SrTiO3 with a high amount of O-vacancies,24,34 indicating a higher degree of oxygen deficiency in the V-shaped areas compared with the film matrix and substrate. As indicated in Figure 2b, the Ti-L2,3 edges show the crystal field splitting of the 2t2g and 3eg levels originating from the local Ti−O atomic coordination.39,40 The crystal field splitting has been found to be very sensitive to the Ti3+/Ti4+ valence change.10,41 For the Ti-L2,3 spectrum obtained from the normal film matrix and substrate, the average splitting energy Ecf between 2t2g and 3eg is 2.43 eV, which agrees well with the reported value of 2.41 eV for regular SrTiO3.39 The value of Ecf decreases to 2.15 eV for the constituent spectrum corresponding to the V-shaped areas. The trend of this change is consistent with the results reported on reduced SrTiO3 with a large amount of Ti3+ and oxygen vacancies.10,34 By a linear interpolation from a decrease in Ecf of about 20% for ∼50% Ti3+ concentration reported in literature,10 the maximum Ti3+ concentration in the defect areas observed here is estimated to be 30%. This value was used to calibrate the fraction map of the corresponding constituent spectrum thereby transforming it into a Ti3+ distribution map (Figure 2c). All concentrations and deficiencies are given relative to the number of respective atom sites in regular SrTiO3 unless otherwise stated. The valence change of Ti4+ is considered as a result of each O-vacancy (V•• O in Kröger-Vink notation) donating two electrons to the Ti 3d states, thereby reducing two Ti4+ ions to Ti3+ according to the reactions OO →

1 O2 (g) + V •• O + 2e′ 2

Ti Ti + e′ → Ti′Ti

developed to different stages of completion from the top anode toward the cathode, i.e., the conducting substrate. The areas of high Ti3+ concentration are identical with the darker areas in the STEM images shown in Figure 1c,d. Because no such V-shaped defect areas with enrichment of Ti3+ were present in the as grown samples, it can be concluded that the Vshaped areas have been created by the electroforming process. These areas therefore can be identified as the conducting filaments responsible for the resistive switching, since Ti3+ and O-vacancies enable n-type conductivity. The conducting filaments exhibit abrupt boundaries against the surrounding film matrix in the Ti3+ concentration map (Figure 2c). The Ti3+ concentrations measured in the filament areas range between 9% and 30% with an average value of 15% for the two complete filaments on the right side of the map. In each filament, the maximum Ti3+ concentration occurs at the center near the anode and decays symmetrically perpendicular to the filament axis. Considering that the symmetric concentration decay is as a result of a two-dimensional projection of the real three-dimensional object, we are aware of that in three dimensions several different filament shapes may be compatible with our observations. However, on the one hand, we have never observed any laterally elongated filaments from cross-sectional TEM samples cut along arbitrarily selected low-index directions. On the other hand, complementary XPEEM analysis also indicates that the filaments are dot-shaped from the top-view of the devices.22,23 These facts provide supportive evidence for the filaments being radially symmetric in three dimensions. The formation of axially symmetric filaments can be explained by the cubic structure of the SrTiO3 affording isotropic mobilities for the constitute ions and by the ion drift/diffusion dominating the lateral growth of the filaments driven by the electric potential and chemical gradients around them. The largest filament on the right side of the map exhibits also a second maximum at the film/cathode interface, which is very

(1) (2)

Further, considering the Ti to O ratio of 1:3 in a unit cell of SrTiO3, the concentration of O-vacancies contributing to the Ti4+/Ti3+ valence change is one-sixth of the Ti3+ concentration. The Ti3+ distribution map in Figure 2c clearly reveals four different V-shaped defect areas in the film, which have 3166


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EDX spectra for the filament areas, the film matrix, and the substrate (Figure 3). The deficiency of Sr relative to Ti is clearly manifested by the reduction of the Sr-L line intensities measured from the filament areas. Spectra from the marked regions (Figure 3) were summed for quantification of the atomic ratios of Sr/Ti and O/Ti by using the substrate as an internal standard for calibration by k factors:

similar to the O-vacancy distribution of the conducting path observed in a Cr-doped SrTiO3 single crystal memory.42 This second maximum of the Ti3+ concentration can be explained by the attraction of additional O-vacancies drifting toward the cathode as the filament connects the two electrodes, thereby reducing additional Ti4+ ions to Ti3+. Despite all the three studied filaments having been found in a 25 nm thin section (as will be discussed later) of the device, we would be cautious in drawing a conclusion about the density of filaments from local TEM analysis. Indeed, the X-PEEM analysis of the devices reveals that filaments are distributed in a very irregular way.22,23 The density of nucleation sites and the preferential locations of the filaments could be key parameters for a nucleation site engineering and optimization in the future. However, in view of the current diversity of findings more research is required to draw definitive conclusions in this regard. Quantification of Cation Defects. In order to clarify the role of cation defects in the VC processes, the chemical composition of the filaments was investigated by quantitative energy dispersive X-ray (EDX) spectroscopy. EDX spectrum imaging was performed over the whole image area shown Figure 3. The specimen was tilted away from the [100] zone

k Sr =

kO =

Tiatom%,sub Sratom%,sub

(3)

Tiatom%,sub Oatom%,sub

(4)

The calibrated atomic ratios were then calculated as Sr/Ti = k Sr

Sratom% Tiatom%

(5)

O/Ti = k O

Oatom% Tiatom%

(6)

The error of A/B was estimated according to σA/B =

2 A ⎛⎜ σA ⎞⎟2 ⎜⎛ σB ⎟⎞ + ⎝B⎠ B ⎝A⎠

(7)

The quantified compositions and their error estimates are listed in Table 1. Compared with the matrix and substrate, Srdeficiencies in the filaments are evident and consistent. The well developed filaments (f2 and f3) exhibit 17% and 19% Srdeficiency as well as 6% and 7% O-deficiency relative to the film matrix and substrate. These values are significantly larger than the uncertainty of 3% estimated for the EDX analysis. It is particularly interesting that a Sr-deficiency of 7% is already found for the incomplete filament in its growth stage. Since the measured concentrations discussed above represent effective values averaged over the transmitted sample thickness of 25 nm, the actual Sr- and O-deficiencies as well as the Ti3+ concentration in the filaments are significantly larger as will be discussed next. Projection Effects and Consistency of Quantifications. The sample thickness was estimated with 25 nm independently by means of image simulations (as will be discussed later in Figure 6) and t/λ EELS analysis. Assuming rotational symmetry of the filaments, their average diameter can be roughly estimated from the STEM images in Figure 1c,d and from

Figure 3. Composition quantification by EDX spectrum imaging. The upper HAADF image was simultaneously acquired with EDX spectrum imaging. EDX spectra from 0 to 20 keV were summed from the regions of interest located at the filaments, film matrix, and substrate marked in the upper HAADF image to enhance the signal-tonoise ratio. The lower plots show the deconvoluted spectra of Sr-L and Ti-K lines normalized to the Ti Kα.

axis by α = 7.28° and β = 4.07° in order to minimize channeling effects. Atomic Sr/Ti and O/Ti ratios were determined from

Table 1. Quantified Composition of the Filaments, Matrix, and Substrate Labeled in the HAADF Image Shown in Figure 3 Calibrated by the Substrate for Sr and Oa EDX Sr/Ti s m f1 f2 f3

1.00 1.05 0.93 0.83 0.81

O/Ti ± ± ± ± ±

0.03 0.05 0.04 0.03 0.03

3.0 3.0 2.9 2.8 2.8

± ± ± ± ±

0.1 0.5 0.1 0.1 0.1

EELS

[VSr] (%) 0 −5 7 17 19

± ± ± ± ±

b

[VO,Sr] (%)

3 5 4 3 3

0 −2 2 6 6

± ± ± ± ±

1 2 1 1 1

[VO] (%)

[Ti ] (%)

[VO,Ti]b (%)

± ± ± ± ±

  11 14 16

  1.8 2.3 2.7

0 0 3 7 7

3 4 4 3 3

3+ c

a

The uncertainty of the quantified deficiencies is estimated with 3% (1σ root mean square). Results from EELS quantification are also listed for comparison. All concentrations are relative to the number of atom sites in the regular SrTiO3 perovskite structure. b[VO,Sr] denotes O-vacancies formed accompanied by the Sr-vacancies, and [VO,Ti] denotes O-vacancies that contributed to the formation of Ti3+ in the filaments. cAveraged values of Ti3+ for the respective filaments from EELS measurement. 3167


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Chemistry of Materials the Ti3+ distribution map in Figure 2c with 8 to 15 nm depending on their evolutionary state. Consequently, the signal from defect-rich filament material and defect-free film material overlap in projection by an approximate 3:5 ratio for the two complete filaments, and the true average Sr- and O-deficiencies and Ti3+ concentrations are by about a factor of 1.7 larger than the values listed for f2 and f3 in Table 1. The diameter of the incomplete filament (f1) is about 3 times smaller than the sample thickness. Correcting for the projection effect on the measured concentrations for this small filament yields a similar corrected Ti3+ concentration of around 30 ± 6% but much less Sr-deficiency (20 ± 10%) compared to that of the two large filaments (30 ± 5%). This finding indicates a reduced progression of ion migration in the small filament. Specifically, the lower Sr-deficiency implies a reduced Joule heating effect, which can be explained by this smaller filament being still in its growing state. In contrast to Ti3+ and O-vacancies, Sr-vacancies in SrTiO3 have been rarely considered in the resistive switching processes because of their very low mobility at temperatures below ∼1400 K.43,44 Just recently, cation defects have been recognized to occur in the resistive switching processes mostly because Joule heating effects may significantly raise the local temperature up to 1000 K in the filaments.22,45 Such high local temperatures may eventually promote the motion of Sr2+ and thereby cause the formation of SrO on the top surface of the film according to the reaction5,22,45 SrSr + OO → SrO(s) + V •• O + V″ Sr

Figure 4. Atomic details of an area across the boundary between the film matrix and the filament. (a) High-resolution ABF image of the region marked in Figure 1d. The lines denote the interface between the film and the substrate. (b) Magnified part of the ABF image marked in (a). (c) The simultaneously acquired HAADF image corresponding to (b). Atomic columns are indicated by the projected unit cell of SrTiO3 (Sr: green, Ti: red, O: blue).

HAADF STEM images, the measured Sr- and O-deficiency alone or preferential thinning in the filament area cannot be the reasons for the reduced mean intensity. Owing to its Rutherford scattering nature, the intensity of the HAADF images depends on the composition projected along the beam direction through Zζ of the scattering cross-section, where Z is the atomic number and ζ is about 2 depending on the actual value of the collection angle of the HAADF detector. A thinner sample would have a lower intensity in the HAADF image and the opposite for the ABF image, as shown in Figure 5a,b. Because the mean intensities for both ABF and HAADF images observed from the filament are lower compared to the defectfree SrTiO3, these values indicate inconsistent sample thicknesses (40 and 18 nm, respectively, Figure 5a). Similarly, the same trends, a lower mean HAADF intensity and a higher ABF intensity, are expected for samples with a higher Srdeficiency (Figure 5c). Besides sample thickness and atom occupancy, another structural feature which may lead to reduced image intensities is static atomic displacements such as lattice strain or distortions often occurring in defect structures.46 Since serious Sr- and O-deficiencies have been measured by EDX in the filament areas, strong lattice distortions are expected in the respective volumes. STEM Image Simulation. The overall reduction of the intensity in the filament areas for both ABF and HAADF images can be reproduced by image simulations using structure models with Sr- and O-vacancies together with random static atomic displacements accounting for the lattice distortions. The microscope parameters applied in the simulation resemble those of the aberration-corrected FEI Titan G2 80-200 ChemiSTEM instrument applied during the experimental image acquisition and are listed in Table 2. The sample thickness was determined by pattern correlation between experimental ABF and HAADF images of the film matrix and image simulations of SrTiO3 in [100] orientation. Indeed the pattern correlation between the experimental ABF images of the film matrix and simulations of SrTiO3 in [100] orientation shows a strong variation over the sample thickness that ranges

(8)

We should note here that the SrO on the top surface of the film of the presented device was smeared away by the deposition of a Pt layer in order to protect the film from ion beam damage during the TEM sample preparation. The ratio of the O-deficiency to Sr-deficiency measured from the filaments by EDX is close to 1/3 and consistent with the stoichiometry of the reaction in eq 8. A slight excess of Ovacancies is expected to account for the valence change of titanium ions from Ti4+ to Ti3+. However, the amount of Ovacancies contributing to the corresponding quantity of Ti3+ measured by EELS is just as large as the error of the EDX analysis and, hence, difficult to be unequivocally detected in the present case. Our EDX and EELS results can therefore be considered as being basically consistent within the confidence levels given by the error estimates. STEM Imaging of Atomic Structural Details. STEM imaging and image simulations were performed in detail in order to reveal the essential lattice defects in the filaments. Figure 4a shows a magnified image of the filament marked on the right side of the ABF image in Figure 1d, displaying atomic details of the filament as well as of the surrounding film matrix and substrate. ABF and HAADF images of the selected region across a boundary between the filament and the film matrix are further enlarged in Figure 4b,c, respectively. All images reveal that the typical features of the perovskite structure are essentially preserved in the filament. Since no indication of secondary phases is found in the filament areas, the high amounts of Sr- and O-vacancies are expected to be distributed randomly in the perovskite lattice. A prominent feature of the ABF and HAADF STEM images in Figure 4 is a significant reduction of the mean intensity in the filament areas. The mean intensity of the ABF images was reduced to 94% and the HAADF to 79%, with respect to the film matrix. Since this feature is observed in both ABF and 3168


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Figure 6. Sample thickness determination based on maximum pattern correlation between experiments and simulations. The correlation coefficients of experimental and simulated (a) ABF and (b) HAADF images of SrTiO3 are both maximum for a sample thickness of 25 nm. The image patches on the right show the experimental ABF (c) and HAADF (d) images and the corresponding best matched images (e and f) from image simulations. The gray scale of the ABF images ranges from 0.375 (black) up to 0.415 (white) with respect to the incident beam intensity and from 0.03 up to 0.13 for the HAADF images, respectively.

sandwiched by two 5 nm thick defect-free SrTiO3 as illustrated in Figure 7a, thereby realizing a total sample thickness of 25 nm as has been determined by pattern correlations (Figure 6). The size of 15 nm is a rough estimate for the average diameter of the complete filaments observed on the right side of Figure 1d,

Figure 5. Correlation between mean intensity of ABF and HAADF STEM images and sample thickness. (a) Mean intensity of simulated ABF and HAADF STEM images with sample thickness for defect-free SrTiO3 projected along [100] axis, relative to the values from the sample with thickness of 25 nm. Dashed lines indicate the corresponding relative mean intensity values for the images of the defective SrTiO3 from the filaments. Simulated ABF and HAADF images of 2 × 2 unit cells of [100] oriented samples are shown in (b) defect-free SrTiO3 with sample thickness of 20−30 nm and (c) 25 nm thick Sr1−xTiO2.8 with random vacancy distributions, including distortions by a random static atomic displacement of 20 pm rms amplitude. Images in each column are displayed in the same intensity scale with respect to the incident beam intensity. The number labeled in each image indicates its mean intensity.

Table 2. STEM Image Simulation Parameters parameter

value

electron energy probe semiconvergence angle detector angles (ABF) detector angles (HAADF) geometric source size

200 keV 18.4 mrad 6−14 mrad 67−250 mrad 1.4 Å (fwhm)

from 5 nm up to 50 nm as displayed in Figure 6a because the ABF STEM image simulations show a strong change of the image pattern depending on the sample thickness. Maximum correlation of 0.96 for the ABF pattern is obtained at a sample thickness of 25 nm. A second but slightly lower local correlation maximum is found at 42 nm sample thickness. Considering also the correlation of experimental and simulated HAADF images displayed in Figure 6b, a sample thickness of 25 nm consistently produces best matching for both ABF and HAADF images. The best matching experimental and simulated ABF and HAADF image pairs are presented in Figure 6c,e and in Figure 6d,f, respectively. Image simulations clarify that lattice distortions, i.e., atomic displacements, indeed lead to reduced intensities in ABF and HAADF images. The model structures for these simulations contain Sr- and O-deficient material of 15 nm thickness,

Figure 7. Simulated ABF and HAADF STEM images for a 25 nm thick sample including Sr- and O-deficient material with different amounts of random static atomic displacements. (a) Schematic of the model applied to simulate the sample structure in the filament areas with a 15 nm thick block of Sr0.7TiO2.6 containing different amounts of random lattice distortions, sandwiched by two 5 nm thick blocks of defect-free SrTiO3. (b) Mean intensities of ABF (circles) and HAADF (diamonds) from image simulations for the structure model compared to those for the defective SrTiO3 with 25 nm thickness (dashed and dotted lines). The lower image patches show the simulated ABF (top row) and HAADF (bottom row) STEM images: (c) defect-free SrTiO3 and (d) the illustrated structure model. Images are displayed using a common grayscale relative to the incident beam intensity ranging from 0.35 (black) to 0.43 (white) for the ABF and from 0.02 to 0.13 for the HAADF images, respectively. 3169


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Chemistry of Materials assuming that the filament diameters are isotropic. On the basis of the ratio between this average diameter and the total sample thickness, the effective average Sr- and O-deficiencies measured by EDX need to be multiplied by a factor of 1.7, yielding an estimate of 30 ± 5% for the Sr-deficiency and of 12 ± 5% for the O-deficiency in the defective volume. Accordingly, a stoichiometry of Sr0.7TiO2.6 was applied in the center part of the structure model by introducing respective amounts of randomly distributed vacancies. Since full relaxations of such big structures are rather complicated and time-consuming, instead we simulated the atomic displacements resulting from the vacancies by introducing random static displacements to all atoms in the center part of the structure model. The amount of displacement was varied realizing different root-mean-square (rms) displacement amplitudes in steps of 10 pm from 0 pm up to 40 pm. The images simulated with the structure models described above yield quite strong variations of the mean ABF and HAADF intensity. The mean intensities are plotted in Figure 7b relative to the mean intensity of calculations for a 25 nm thick, defect-free SrTiO3 sample, and the simulated images are displayed in Figure 7c,d. As expected, the consideration of Srand O-deficiencies alone leads to an increase of the ABF and a decrease of the HAADF intensities. The effect of random static atomic displacements is qualitatively different for the two imaging modes. While the ABF intensity decreases monotonously with increasing displacement amplitude, the HAADF intensity first increases, reaching a maximum at around 20 pm, and decreases then with further increasing displacement amplitude. A consistent match of the mean image intensity reductions in simulations and experiment is found for a displacement amplitude of 30 pm (rms) for both imaging modes, thereby providing qualitatively convincing evidence for an inhomogeneous strain field in the sample. Here, we should note that applying random static atomic displacements to all the atoms instead of real physical lattice distortions of atoms around the vacancies is a crude simplification that allows running the simulations in a realistic time. The 30 pm rms displacement dose not mean the realistic lattice distortions in the sample we studied. Furthermore, the general features of the projected perovskite structure are preserved despite of the strong static atomic displacements. In contrast to these general agreements, especially the ABF image patterns obtained with the models containing random static atomic displacements show no convincing resemblances to the experimental image pattern. Most probably this qualitative disagreement is caused by the crude simplification applied with random displacements, instead of using realistic lattice distortions. We consider it as an intriguing result of our study that the perovskite lattice is maintained intact at such high defect concentrations and considerable lattice distortions. This indicates further opportunities to optimize the functional properties of such devices by defect engineering on the atomic level. Moreover, this result also manifests that point defects alone are sufficient and neither secondary phases nor extended defects appear to be a prerequisite for the formation of conducting filaments in the studied ReRAMs.

different times, potentially implicating multistep nucleation. Alternately, the filaments could grow at a different rate, possibly due to variations in local electric field strength due to variations in the top electrode or the electrode/film interface. In both cases, we could consider that these filaments represent different evolutionary states concerning the positions of their frontiers between the two electrodes. Moreover, the V-shape and the position of these filaments indicate they were growing down from the top contact. On the basis of these interpretations, it would be appropriate to describe the electroforming process as involving three stages of filament formation: nucleation, growth, and completion (Figure 8a).

Figure 8. Schematic of the proposed stages in an electrically forming process resulting in the resistive switching ON-state. (a) Schematic illustration of the nucleation (i), growth (ii), and completion (iii) of the filament formation. The red spheres represent O-vacancies and green spheres Sr-vacancies. (b and c) Electric potential distributions around a nucleus of the filament and a growing V-shaped filament based on point and line charge models, respectively. The white arrows indicate the preferred direction for oxygen anion drift due to the stronger local electric field strength.

In the nucleation stage, oxygen release by anode oxidation (eq 1) creates O-vacancies in the surface region of the film. It is very likely that the contact between the anode and the film as well as point defects in the film are inhomogeneously distributed on the nanometer scale. In some locations, where the electrode film contact is better and initial defects exist, the oxygen release is favored, which in turn may result in the nucleation of filaments by forming O-vacancy clusters in the surface region of the film. In the next stage, oxygen anions are driven by the applied field to migrate from deep inside the film toward the surface regions where the O-vacancies are created. Thereby Ovacancies migrate into the inside of the film, manifesting a growth of the O-vacant regions toward the bottom electrode. This growth direction of the filament is consistent with the results found by X-ray fluorescence in Cr-doped SrTiO3 single crystals42 but is opposite to the observations made by electrocoloration in Fe-doped SrTiO3 single crystals.47 The growth direction of filaments might depend on the oxygen release rate (eq 1) and the oxygen drift/diffusion rate,2 which in turn may depend on the specific device configuration and dimensions.48 For the thin-film devices studied here, a fast oxygen anode release and a slow oxygen ion migration would explain the direction of growth from the anode toward the cathode. During the growth stage of the filament, O-vacancies will induce a valence change of titanium ions from Ti4+ to Ti3+ according to eqs 1 and 2, which enables n-type conductivity in the growing filament. From this stage on, continuous Joule heating increases the local temperature thereby promoting the migration of Sr2+ and O2− from the cores of the still growing

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DISCUSSION The observation of several filaments of different sizes (Figures 1 and 2) and with different levels of Sr-deficiency (Figure 3 and Table 1) could imply that the filaments started growing at 3170


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filaments provides an atomic scale explanation for the mechanisms involved in the resistive switching process. In this complex scenario, cation and anion defects need to be considered jointly. Our findings may provide a good starting point for theoretical explorations of the dynamics of the conducting filament evolution and the interplay between point defects of the same type as well as between different types. Such work may hopefully lead to a better understanding of the structure property relationships, not only for resistive switching phenomena but also for a wide variety of other functional properties found in relevant perovskite oxides.

filaments to the film surface, where segregation of SrO occurs according to reaction eq 8. The last stage of the filament formation describes the moment when the growth toward the cathode is completed. Completion refers to the fact that the filament reaches the film/ substrate interface forming an electron conducting path between the two electrodes. Completed filaments may grow further along the lateral directions driven by the chemical gradients as will be discussed in the following. The V-shaped form of the filaments can be explained by taking the effects of the local electric potential and chemical gradients into account. A point charge model approximation for the filament nucleus under electrical bias exhibits the strongest electric field in the direction from the nucleus straight toward the cathode compared to all other directions (Figure 8b). The growth of the filament toward the cathode by O2− drift is thus preferred, favoring an anisotropic filament shape. Hence, it is reasonable to assume a line charge model to approximate a growing filament within the film, from which the anisotropic growth is further enhanced as implied by the electrical potential distribution in Figure 8c. The electrical potential distribution of the line charge model manifests also strong lateral components, which consequently cause also a lateral extension of the filament. Indeed, the shape of the electrical potential distribution in Figure 8c resembles the V-shape of the observed filaments. In addition to the electric field, also chemical gradients between the filament and the film matrix act as a driving forces for the ion diffusion, promoting further growth of the filament into the film matrix perpendicular to all filament boundaries. The combination of a fast filament growth from the anode/film interface straight toward the cathode and a slower growth along the lateral directions naturally results in V-shaped filaments.

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MATERIALS AND METHODS

Electroforming of the Devices. SrTi0.98Fe0.02O3 thin films with a thickness of about 17 nm were expitaxially grown on a conducting 0.5 wt % Nb doped SrTiO3 substrate (commercial product from Crystec, Germany) by pulsed laser deposition. For the deposition of the films the laser fluence was set to 0.7−0.8 J/cm2 along with a substrate temperature of 800 °C, an oxygen partial pressure of 0.1 mbar, and a repetition rate of 5 Hz. Top Au electrode arrays with thickness of 25 nm, on 10 μm × 10 μm areas and with a separation of 1−2 μm, were prepared by optical lithography. The edges of the electrodes were parallel to the [100] and [010] directions of the film. Electric forming was performed on individual devices by a sweep to +5 V with a current compliance of 10 mA through which the resistance was switched from an initial value of above 1 GΩ to a few kΩ, consequently setting the devices into the ON-state. TEM Sample Preparation. Cross-sectional TEM specimens from the delaminated, electronically formed, and as-grown devices were prepared by focused ion beam (FIB) milling using an FEI Helios NanoLab 400S system with a Ga ion beam,49 across the regions where Ti3+ has been detected by XAS combined with X-PEEM within the 10 μm × 10 μm area of the respective top electrodes to include the filaments in the specimens. TEM specimens were further thinned and cleaned with an Ar ion beam in a Fischione Nanomill 1040 at 900 and 500 eV beam energies, respectively. STEM and EDX. STEM and EDX spectrum imaging was conducted with an FEI Titan G2 80-200 ChemiSTEM microscope50 operated at 200 kV accelerating voltage. Quantification of EDX spectra was carried out by Cliff-Lorimer method with series fitting for deconvolution of the overlapping peaks. EDX spectrum imaging was performed under conditions where the specimen was tilted away from the [100] zone axis by α = 7.28° and β = 4.07° in order to minimize channeling effects. Spectra from the substrate were also acquired and used as an internal standard for calibration of the composition analysis. Noise reduction for the atomic resolution STEM images was performed by frame averaging and smoothing.36 Monochromated EELS. Monochromated EELS spectrum imaging was performed with the FEI Titan G3 50-300 PICO microscope51 operated at 200 kV accelerating voltage. An energy dispersion of 0.05 eV was used to simultaneously record the Ti-L2,3 and O-K edges in each spectrum. The energy resolution in the spectra is 0.2−0.3 eV as estimated from the fwhm of the zero-loss peak. The raw EELS spectra over the complete recorded energy range and without background subtraction were used for multivariate data analysis by a joint Bayesian algorithm.35 The algorithm relies on the assumption that each recorded spectrum is a linear combination of constituent spectra plus additive noise. Non-negativity constraints for constituent spectra as well as additivity and non-negativity for their fractions are jointly considered. The constituent spectra were first geometrically determined by the N-FINDR method52 and subsequently optimized by a linear Bayesian model through a Markov chain Monte Carlo method.35 On the basis of the fraction maps and the fine structures of the respective constituent spectra, one constituent spectrum corresponds to the defect structure with the upper limit amount of Ti3+ from the conducting filaments, while another constituent spectrum matches with the normal structure from the normal

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CONCLUSION The present work, for the first time, provides clear experimental evidence for the existence of multiple nanosized conducting filaments formed solely by atomic-scale point defects in a SrTiO3 based thin-film ReRAM device. As visualized by means of STEM and EELS, V-shaped conducting filaments are formed with high concentrations of Ti3+ and O-vacancies. These two fundamental point defects enable n-type conductivity and are found to be accompanied by significant amounts of Srdeficiency and lattice distortions. Despite the high defect concentrations, the general perovskite lattice is structurally preserved, indicating that neither secondary phases nor extended defects are essential for the formation of conducting filaments. The observation of multiple nanosized conducting filaments in different growth states provides first insights into the mechanisms involved in the formation process of conducting filaments in thin-film VC resistive switching devices. The filament formation process can be separated into nucleation, growth, and completion stages, primarily based on the fielddriven release of oxygen and migration of oxygen ions, resulting in oxygen vacancies in the film. As a direct consequence of these oxygen vacancies, the Ti valence change leads to n-type conductivity allowing higher electrical currents in the biased thin-film device. The resulting Joule heating increases the mobility of Sr- and O-ions in the lattice promoting their migration toward the film surface causing Sr- and additional Ovacancies in the material. The coexistence of a high Ti3+ concentration along with Sr- and O-vacancies in the conducting 3171



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stoichiometric film matrix and substrate dominated by Ti4+. The distribution of Ti3+ was transformed from the fraction map for the spectrum of the filaments. A nonlinear filter was used for smoothing the O-K edge spectra.36 Image Simulation. STEM HAADF and ABF image simulations were performed with the Dr. Probe software package.53 Models of the atomic structure were built based on a cubic perovskite unit cell with a lattice constant of a = 3.905 Å, with Sr at the origin, Ti in the center, and oxygen atoms at the face center positions. The small Fe content of 2% in the actual film material is neglected in the simulations, since the electron scattering factors of Fe (Z = 26) and Ti (Z = 22) differ only by about 10%. Thermal atomic vibrations are described by isotropic parameters for Debye−Waller factors with BSr = 0.66 Å2, BTi = 0.51 Å2, and BO = 1.08 Å2. The supercells used in the calculations extend over 4 × 4 unit cells in the projected (001) plane. The electron diffraction calculations were performed with a multislice algorithm.54 For this purpose, the supercells were partitioned into thin slices along the projection direction (c-axis), such that each slice contains one atomic layer. Atomic form factors for the elastic high-energy electron scattering were taken from the tables of Weickenmeier and Kohl.55 Thermal diffuse scattering was simulated by following the frozen phonon approach,56 where small random atomic displacements according to the isotropic B-parameters listed above are introduced resembling frozen states of the thermal motion. The STEM images are generated by scanning the focused electron probe in a grid of 78 × 78 positions over a sample area of 0.78 nm × 0.78 nm, which corresponds to 2 × 2 projected perovskite units. The STEM image intensity for these raw scan image pixels is obtained each by an individual multislice calculation with a unique frozen state of the object and by integrating the resulting electron probe intensity below the sample in the back-focal plane over the ABF and HAADF angular detection ranges listed in Table 2. With this approach, each pixel of the resulting STEM image represents the intensity for a different frozen state of thermal motion. Finally, the finite geometrical source size was considered by a convolution of the obtained scan image intensity distribution with a normalized Gaussian of 1.4 Å fwhm, which effectively also achieves an averaging over approximately 100 frozen states of thermal motion.

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AUTHOR INFORMATION

Corresponding Author

*(H.D.) E-mail: [email protected]. Phone: +49 (0)2461 619337. Fax: +49 (0)2461 616444. ORCID

Hongchu Du: 0000-0002-4661-4644 Author Contributions

A.K. prepared the memristive devices and performed the electronic experimental investigation. H.D performed STEM and EELS spectrum imaging experiments and analyzed the data. C.-L.J. and H.D. interpreted the experimental results. J.B. performed the multislice STEM simulations. H.D., J.B., and C.L.J. drafted the manuscript. All authors have discussed the results, commented on the manuscript, and given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Doris Meertens for preparation of the TEM lammelae by FIB. We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) under Grant SFB 917 Nanoswitches and under the core facilities Grant MA 1280/40-1. 3172


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Nanosized Conducting Filaments Formed by Atomic-Scale Defects in

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