Enhancing the Domain Wall Conductivity in Lithium Niobate Single Crystals Christian Godau, Thomas Kam ̈ pfe, Andreas Thiessen, Lukas M. Eng,* and Alexander Haußmann Institut für Angewandte Physik, and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, 01062 Dresden, Germany S Supporting Information *
ABSTRACT: Domain walls (DWs) in ferroelectric/ferroic materials have been a central research focus for the last 50 years; DWs bear a multitude of extraordinary physical parameters within a unit-cell-sized lateral confinement. Especially, one outstanding feature has recently attracted a lot of attention for room-temperature applications, which is the potential to use DWs as two-dimensional (2D) conducting channels that completely penetrate bulk compounds. Domain wall currents in lithium niobate (LNO) so far lie in the lower pA regime. In this work, we report on an easy-to-use and reliable protocol that allows enhancing domain wall conductivity (DWC) in singlecrystalline LNO (sc-LNO) by 3 to 4 orders of magnitude. sc-LNO thus has become one of the most prospective candidates to engineer DWC applications, notably for domain wall transport both with and without photoexcitation. DWs were investigated here for several days to weeks, both before and after DWC enhancement. 2D local-scale inspections were carried out using adequate local-probe techniques, i.e., piezoresponse force microscopy and conductive atomic force microscopy, while Cerenkov second-harmonic generation was applied for mapping the DW constitution in threedimensional space across the full LNO single crystal. The comparison between these nano- and microscale inspections allows us to unambiguously correlate the DW inclination angle α close to the sample surface to the measured domain wall current distribution. Moreover, ohmic or diode-like electronic transport characteristics along such DWs can be readily interpreted when analyzing the DW inclination profile. KEYWORDS: ferroelectric domain walls, lithium niobate, domain wall conductivity, conductive atomic force microscopy, piezoresponse force microscopy, Cerenkov second-harmonic generation. the possibility for electronic circuiting on the 1 nm length scale9 using these DW topologies. First investigations of DWC were reported for so-called 109° and 180° DWs in bismuth ferrite (BiFeO3, BFO) thin films. Both types of DWs exhibited an ohmic current−voltage (I−U) behavior,10 which was attributed to either an increased charge carrier density or a lowered band gap at the ferroelectric/ ferroelastic DW.11 In contrast, 71° DWs in the same material displayed a diode-like I−U characteristic,12 with oxygen vacancies that reduce the Schottky barrier at the DW being responsible here. Recent BFO investigations showed remarkably high currents on switched domain areas, especially at crossovers of 71° and 180° DWs.13 Furthermore, DWC was reported to occur in lead-zirconate-titanate [Pb(Zr0.2,Ti0,8)O3, PZT] thin films as well,14 arguing that an enhanced trap density
F
erroelectric materials have been of central interest for many years by now, with ferroelectric random access memories certainly constituting one of the most popular applications of this.1 Nevertheless, the majority of such ferroelectric-based devices make use of the domain properties only, i.e., utilizing the change of (spontaneous) polarization between domains, notably through different means and methods. In addition, to the best of our knowledge, no devices have been established or realized so far that make use of the ferroelectric domain walls (DWs), the tiny intersections that separate two areas/domains with different order parameters, i.e., either the dielectric or the magnetic polarization. Most interestingly, the DW width in such materials has a size of a few unit cells only2−5 and thus constitutes a delta-function-like intersection across an otherwise perfect (ferroic) domain. Its dielectric,6 optical,7 magnetic,8 and conductive properties thus are very appealing in order to bottom-up assemble DW-based nanodevices. Especially the effect of domain wall conductivity (DWC) has witnessed a great boom recently, since providing © 2017 American Chemical Society
Received: February 20, 2017 Accepted: April 27, 2017 Published: April 27, 2017 4816
DOI: 10.1021/acsnano.7b01199 ACS Nano 2017, 11, 4816−4824
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Figure 1. Macroscopic measurements of domain wall conductivity. (a) Sketch of the measurement setup in the cryostat as used for sample tuning and DWC recording. (b) I−U characteristics as recorded during the enhancement process: note the quasi linear behavior (see also c). This is followed by a non-ohmic characteristic, which indicates domain wall movement and irreversible domain shape changes; the switchover between the two regimes is marked by arrows for both samples. (c) Linear plot of the I−U characteristics for low voltages (U < 200 V). (d) Typical low-voltage characteristics before and after DWC enhancement. (e) Temporal stability measurements at a 10 V bias directly (sample 2) and 48 h (sample 1) after DWC tuning.
manganite (HoMnO3),20 as well as in (Ca,Sr)3Ti2O721 and YbMnO3.22 Furthermore, experiments on proper ferroelectric single crystals such as barium titanate (BaTiO3, BTO) showed DWC to be of several orders of magnitude larger as compared to the bulk conductivity.23 Theoretical approaches18 predict an equally high DWC for sc-LNO, with the DWC proposed to strongly depend on the angle α, as enclosed between the (charged) DW and the polar c-axis. Recent high-angle annular dark-field (HAADF) experiments of ferroelectric DWs in periodically poled sc-LNO (PPLN) using a scanning transmission electron microscope (STEM)24 in fact revealed that α nanoscopically consists of a multitude of meanders and kinks and will never be perfectly straight. These findings are in full accordance with macroscopic investigations, performed by piezoelectric and dielectric resonance spectroscopy on the same PPLN structures,25 as well as with recent near-field scanning microwave impedance spectroscopy (SMIM) results on PZT and BFO thin films.17 α in fact is the lead control parameter to render DWs in sc-LNO highly conductive. We will apply Cerenkov second-harmonic generation (CSHG) to quantify their inclination, also providing
arising through the local DW inclination might be the driving force here. Note, at this stage, that the origins for DWC in thin-film ferroelectrics may be quite scattered: All thin-film DWC investigations so far were always carried out under extremely high local electric fields that typically were on the order of 2 V per 100 nm (which is the film thickness), independent of whether using scanning probe techniques [conductive atomic force microscopy (cAFM), piezoresponse force microscopy (PFM)] or using planar electrodes in a plate capacitor-like fashion. The local field strengths thus may easily reach values of 2 × 105 V cm−1, a field strength large enough to induce quite a multitude of different physical transport effects in these thin films, including the ones mentioned above. In particular, we want to emphasize the possibility of further domain nucleation, which may lead to transient switching currents and to changes in the DW roughness and/or inclination, which would directly influence the DW conductivity.15−18 DWC is not limited to ferroelectric thin films; recent results nicely reported DWC to occur in the improper ferroelectric single crystals of erbium manganite (ErMnO3)19 and holmium 4817
DOI: 10.1021/acsnano.7b01199 ACS Nano 2017, 11, 4816−4824
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Figure 2. Microscopic measurements: (a) PFM image before DWC tuning; note the hexagonal DW shape. (b) PFM data after enhancement. (c) Cerenkov SHG before enhancement displayed as the projection of the inclination angle α into the z plane, with data points at the outward rim and in the center facing the z− and the z+ surface, respectively. Red and blue colors denote h2h and t2t DW configurations, respectively. d) Cerenkov SHG after DWC enhancement. Note that the topmost layer (at the z− surface is purposely displayed separately from the rest of the data. (e) Correlation between inclination angle α at the z− surface (dots, red: α > 0, blue: α < 0) and measured cAFM currents (black line). (f) cAFM at a +10 V bias with currents reaching up to 60 pA (note that the scale of the current was purposely capped at 15 pA for improved display reasons; the uncapped picture can be found in the Supporting Information as Figure S1).
an elegant tool for visualizing the effective DW constitution across the full bulk crystal volume, in three-dimensional (3D) space26−28 noninvasively. In this contribution, we present an experimental procedure that allows enhancing DWC in sc-LNO by 3 to 4 orders of magnitude. This allows recording I−U characteristics from single LNO DWs in the dark, i.e., without photoexcitation.29,30 Our method is based on tuning the DWC in LNO under moderate electric fields up to 104 V cm−1 using planar chromium (Cr) electrodes. This electric field physically moves and bends the DWs (as directly visualized in this paper by CSHG) until conductive paths are formed up to the LNO/ electrode interface. Note that our procedure reproducibly allows DW bending to both positive or negative α values, resulting in either head-to-head (h2h) or tail-to-tail (t2t) DW topologies. As-tuned DWs remain stable for further investigations over weeks. While CSHG is used to map the DW inclination close to the sample surface, PFM and cAFM were successfully applied in order to allocate the domain/DW
polarization and transport currents across domains and DWs, respectively. As a result, we are able to directly correlate the DWC of a single DW to its inclination angle α.
RESULTS As-grown DWs in sc-LNO typically show a very low dark conductivity due to either (Schottky) barriers formed at the electrode−LNO interfaces or the small DW inclination angles α with respect to the polar c-axis. Macroscopic I−U measurements applying ±10 V hence result in typical DW currents of less than 0.5 pA, also showing a very limited signal-to-noise ratio (SNR). Nevertheless, increasing the drive voltage up to several hundreds of volts finally results in measuring an appreciable DWC. Figure 1b shows I−U curves of two such samples (sample 1 and sample 2) that went through the steps of DWC enhancement (see the Methods section). The z+ side was grounded while a potential was applied to the z− side. As seen, the DW current increases linearly for a drive voltage between 0 4818
DOI: 10.1021/acsnano.7b01199 ACS Nano 2017, 11, 4816−4824
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Figure S1 in the Supporting Information]. Comparing the PFM (Figure 2b) and the cAFM (Figure 2f) images proves that sample tuning indeed boosts the DW current, while no nonDW-related breakdown channels are created. Nevertheless, as seen from Figure 2f, not all DW sections conduct equally well; we measure local currents of up to 60 pA at corners labeled (V) and (VI), while area (I) shows hardly any DWC. Note that the z-scale display of the as-measured current was purposely truncated at 15 pA in Figure 2f for better visualization reasons (check also the Supporting Information, where Figure 2f is displayed over the full DWC range without truncation). The distortions in the DW rim obviously seem to influence the DWC very positively. In order to access the effective DW geometry and to connect the DW inclination to the measured DWC, we applied CSHG, which maps the whole domain wall shape across the LNO crystal in 3D space.26,27 Figure 2c and d display this behavior before and after DW tuning, respectively. In order to visualize and quantify the complex behavior of our 3D data (z, ϕ, α), we decided to display these data through a planar map, with data points closer to the center of the picture representing the z+ surface and data points at the periphery standing for the z− side (similar to a perspective view into a tube or tunnel; see also Supporting Information S6, revealing how to achieve this transformation). Different colors then directly represent different local inclination angles α with respect to the z-axis (positive (red) and negative (blue) values denote h2h and t2t DW configurations), while the radial position of every spot decodes its 3D spatial origin, respectively. The beauty of this rather unusual projection method is to provide an excellent view of the total DW behavior that otherwise would not be possible. From these pictures, we see immediately that sample tuning affects the DW inclination not only close to the sample surfaces but equally well in the bulk of the 3D LNO crystal. Furthermore, massive changes in DWC occur at DW asperities, i.e., the vertices along the crystallographic y directions. Also, the initial state characterized by the hexagonal domain shape mostly constitutes h2h configurations (Figure 2c), while only some minor areas exhibiting t2t or straight DWs are seen. Nevertheless, even the (initial) walls are never perfectly parallel to the z-axis, with α varying from −0.1° to 0.2°. This is in excellent accordance with the recent HAADF-STEM experiments on DWs in sc-LNO.24 After sample tuning, the highly conductive h2h configuration of DWs is mostly preserved (Figure 2d), however, with α becoming much larger as compared to Figure 2c. Again, for display reasons, α values were capped at 1°. Note that points lying between the middle of the crystal and the z+ surface (points in the center of the figure) feature especially high angles α of up to 6°. Again, distinct parts of the DW appear in the t2t state or having no inclination at all; nevertheless, their absolute number became much smaller than before DWC enhancement. The distribution of h2h, t2t, and noninclined wall segments after DWC treatment follows a systematic pattern and is less random after sample tuning than it was before. We mostly witness an h2h DW configuration at the z+ surface, except for the corners, where we have t2t or no inclination. Meanwhile at the z− surface, we find rather strong h2h configurations at corners surrounded by small t2t/noninclined parts. As clearly noticeable, this topmost inclination pattern at the z− surface has great similarities to the current distribution that we obtained from cAFM measurements.
V and approximately 160 V (see Figure 1c), with sample 1 behaving linearly even up to 350 V. At higher voltages, the majority of samples follow a nonlinear (mostly exponential) I− U characteristic, however, with sample 2 illustrating also a much more complex evolution. Note though that applying a drive voltage above the linear I−U regime always results in irreversible domain shape changes. Notably, too large currents may destroy the sample. As a rule of thumb, applying several 10 μA while keeping the applied voltage well below 60% of the coercive field has proven safe for DWC tuning, resulting in persistent and high DWCs in these LNO samples. As a result, DWC increases by 3−4 orders of magnitude (see Figure 1d), exhibiting DW currents at a 10 V bias of ∼90 and ∼70 nA for samples 1 and 2, respectively. Furthermore, the transport characteristics in the lower current regime are always observed to behave either ohmic/bidirectional-like, exhibiting a kink at 0 V (sample 2), or diode/unidirectional-like with an almost vanishing current for negative bias voltages (sample 1). Note that only these two possibilities were observed in all our measurements performed on a multitude of samples prepared in exactly the same way. We also investigated the temporal stability of DWC of astreated samples (see Figure 1e): In general, DWC relaxes subsequent to DW treatment and then saturates after a couple of hours, exhibiting a nearly constant current value for at least several days (note that the stability test for sample 1 was performed 2 days after DWC enhancement). Over a time of months the current along the domain walls decreases again. cAFM inspections of a sample kept at room temperature right after the enhancement (also shown in Figure 2b and f) and six months later can be found in the Supporting Information, S4. Now, we proceed to analyzing the changes in the DW configuration on the micrometer to nanometer length scale involving our dedicated analysis tools. Nucleation of additional domains within the previously inverted structure of 50 μm diameter is unlikely to happen when applying the sample tuning procedure, as the applied field reaches values of E = 2 kV mm−1 for a 400 V bias only. That field strength is well below the coercive field as would be needed for reverse poling of 5% Mg-doped congruent LNO (Ec = 5.5 kV mm−131). We doublechecked this assumption by applying a thorough analysis using PFM and optical polarization microscopy,32 finding no indications for any additional domains to be generated. Hence, the nucleation of additional domains (which consequently would increase the effective domain wall area) can be excluded as the origin for the observed enhanced DWC. Nevertheless, PFM measurements at the z− side before and after sample tuning show a severe change in domain shape at the LNO surface (see Figure 2a,b). While the initial single LNO domain always exhibits a clear hexagonal shape, a rather triangular morphology after treatment is observed. More clearly, the three nonadjacent domain vertices along the crystallographic y-axes33−35 show an increased mobility upon electric field tuning (see Figure 2b) with these vertices moving inside toward the center of the original hexagon, hence effectively shrinking the initial domain area. Overall the c+ domain area at the sample surface is reduced by ∼48.2% from 3649 μm2 to 1890 μm2. The changes in the geometrical DW periphery turn out to be very beneficial for cAFM measurements along such DWs; while hardly any DWC was detected before sample tuning, our cAFM inspection with a 10 V bias applied to the bottom contact (z+ side) reveals a dramatic DWC increase (see Figure 2f and 4819
DOI: 10.1021/acsnano.7b01199 ACS Nano 2017, 11, 4816−4824
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Figure 3. DW inclination angles α plotted in cylindrical coordinates z−ϕ. Red to blue colors represent h2h and t2t DW states, respectively. (a) α plot for the as-grown LNO DW state; (b) α values after DWC tuning. Note the much larger values here, which were truncated due to display reasons. (c and d) α(z) cross sections for selected ϕ, before (c) and after (d) enhancement. Note the much larger h2h fraction in (d).
In order to provide a clear comparison between as-poled and postenhanced DWC states in our LNO samples, we plotted the CSHG data from Figure 2c and d in a slightly different manner using cylindrical coordinates z and ϕ, resulting in a domain-wall world-map (additional explanations for this representation can be found in the Supporting Information, S6). The result is illustrated in Figure 3a and b before and after DWC tuning, respectively, again using the same color coding for α. Quoting Eliseev,18 we expect an increased DWC (stemming from higher inclination angles) in conjunction, as nicely proven by the macroscopic DWC measurements in Figure 1c. Although an appreciable t2t fraction is present in the initial stage of this LNO sample (see Figure 3a at ϕ = 220°), DWC tuning significantly increases the h2h fraction at the z+ surface, with h2h DWs and large α values now penetrating across half the LNO crystal thickness (as manifested in Figure 3b by the deep red colors between 0 and 100 μm in depth). To underline these increased inclination angles, we plot in Figure 3c and d z-sections for specific angles ϕ and compare their behavior. We contrast qualitatively completely different configurations of DWs: In Figure 3c at ϕ = 30°, we witness a pure h2h behavior before DWC tuning, while a majority of t2t or noninclined DWs is obvious at ϕ = 220° and ϕ = 255° in the same crystal. At ϕ = 120°, h2h gradually merges into the t2t configuration. The local inclinations are, on average, very low (
