We study the local ionic conductivity of ferroelectric domain walls and domains in KTiOPO4 single-crystals. We show a fourfold increase in conductivity at the domain walls, compared to that of the domains, attributed to an increased concentration of defects. Our current-voltage measurements reveal memristive-like behavior associated with topographic changes and permanent charge displacement. This behavior is observed for all the voltage sweep-rates at the domain walls, while it only occurs for low frequencies at the domains. We attribute these findings to the redistribution of ions due to the applied bias and their effect on the tip-sample barrier.
KTiOPO4 (KTP) is one of the most attractive nonlinear optical materials for engineering of periodically poled domain structures, commonly used as frequency-conversion devices for laser radiation. Because of its large domain-velocity anisotropy, high aspect-ratio domain structures can be fabricated in this material. Moreover, domain gratings with sub-μm periodicity have been achieved over 1 mm-thick crystals, leading to very appealing novel optical components.1 The domain wall (DW) plays a profound role not only for the smallest domain size obtainable in ferroelectrics but also for its effect on other material properties such as defect concentration and local symmetry. The DWs in KTP have already demonstrated different properties than those in the bulk. For instance, the neighborhood of DWs in KTP presents a second-order nonlinear coefficient d11 that is absent in the single-domain regions.2 When the domain-size in nanostructured devices decreases, the impact of the DWs on the device performance will increase, meaning that their properties cannot be ignored. Indeed, the DWs themselves could become the central and active elements: It has been proposed that DWs may be used for applications such as high-density memory storage and reconfigurable electronic circuits,3,4 a prospect that has drawn a lot of attention to the electric properties of domain walls in ferroics. Since the pioneering work of Salje,5,6 a large number of experimental and theoretical studies have been performed,7–9 reporting DW conductivity in a wide range of materials such as BiFeO3,10,11 Pb(ZrxTi1−x)O3,12 ErMnO3,13 HoMnO3,14 and LiNbO3.15 Although the fundamental mechanisms governing DW charge transport are still not fully understood, DW conductivity is associated with an increase of charge-carrier density near the wall and the interplay between the type of charge carriers, the DW geometry, and spontaneous polarization. In contrast to the materials mentioned above, KTP cannot be classified as a semiconductor ferroelectric material. Instead KTP is considered as a quasi-one dimensional super-ionic conductor at room-temperature due to the high mobility of the K ions along the polar axis.16,17 Although its macroscopic ionic conductivity has been thoroughly investigated,18 the charge transport properties at the domain walls remain unexplored.
Here we study the local ionic conductivity at domains and domain walls in 100 μm thick KTP single-crystals, demonstrating a fourfold increase of conductivity at the domain walls as compared to the domains. The conductivity at the DW increases with the number of voltage-sweep cycles, for the whole frequency-range used; while at the domains, this memristive-like behavior is only seen for low sweeping rates. Our results are discussed in terms of ionic motion and the effect of charge-accumulation in the sub-surface layers.
KTP has an orthorhombic crystal structure and belongs to the acentric point group mm2 (space group Pna21).17 The crystal network consists of TiO6 chains corner-linked by PO4 tetrahedra bridges, resulting in quasi-one-dimensional channels along the [001] direction. The K ions are weakly bound to the TiO6–PO4 network and can move through the channels via a vacancy-hopping mechanism. The activation energy of such motion along the polar [001] axis is 0.3 eV, whereas the activation energies along the [100] and [010] axes are substantially higher, resulting in orders of magnitude lower conductivity along these directions than along the polar axis.16 Flux-grown KTP usually presents deviation from stoichiometry in the form of potassium and oxygen vacancies, as well as impurities, including OH− groups. The concentration of VK′ and V••O can vary between 500 ppm and 800 ppm depending on the growth conditions,19 giving rise to a large variation in conductivity.20
For our experiments, we fabricated domain gratings with a periodicity of 6.33 μm in several commercial, 1 mm-thick, c-cut, flux-grown KTP crystals, using standard periodic-poling techniques.21 The samples studied here had a bulk ionic conductivity of 7 × 10−7 S/cm and a coercive field of 2.4 kV/mm. The crystals were selectively etched and regions with homogeneous domain grating throughout the crystal thickness were selected. Afterwards, the polar faces were mechano-chemically polished, thinning the crystals down to a thickness of 100 μm. Finally, the samples were affixed to metal substrates using conductive Ag-paste. The domain and DW conductivities were studied using a Bruker Icon atomic force microscope system, equipped with a PF-TUNATM module. The platinum-coated tip (Mikromasch HQ:CSC17/Pt, 30 nm radius, and 0.18 N/m force constant) was grounded and a bias voltage, which could be varied from −10 V to +10 V, was applied to the metal holder. The sensitivity of the current amplification was 20 pA/V, and the scan-rate was typically 40 μm/s. The domain structure was imaged by piezo-force microscopy (PFM); a sample bias of 10 V at 150 kHz frequency (above first resonance) was used for these measurements. All measurements were performed under ambient conditions at room temperature (21 °C, relative humidity 19% – 31%).
Figure 1(a) shows the topography of a representative region of one of our samples. The 2-3 nm height difference between opposite domains results from shallow selective etching during chemo-mechanical surface polishing. The corresponding PFM image is shown in Fig. 1(b). The dark and bright contrasts correspond to Ps pointing out () and Ps pointing in (), respectively. Figure 1(c) displays the conductivity map of the same area, obtained with a sample bias of 10 V. A current profile, extracted along the dashed line of Fig. 1(c), is shown in Fig. 1(d). As it can be seen, the current increases significantly at the DWs, reaching four times the maximum value measured at the domains. This could be attributed to a larger concentration of vacancies around the DW, increasing the ionic mobility, together with the strain fields at the DW surroundings.9,22 Note that there is also conductivity contrast between domains of opposite Ps-orientation; the average current at the and domains being 0.6 pA and 0.9 pA, respectively. This contrast is ascribed to a corresponding work function difference between opposite domains.23 Shvebelman et al.24 attributed this band-gap difference to the selective accumulation of K ions and VK′ in the sub-surface layers near the and faces, respectively. It is worth noting that scanning at varying bias reveals a Schottky-like barrier between the AFM-tip and the sample, showing low current values for negative bias [see the supplementary material of (Fig. S1)].
In order to further investigate the local conductance of our crystals, current-voltage (IV) curves at different sweep-rates were acquired at the DWs and domains of opposite polarization.
Figure 2 shows five consecutive IV-curves for (a) DW, and (b) and (c) domains. The curves were obtained by ramping the bias from −10 V to +10 V (“forward sweep”) and then back from +10 V to −10 V (“backward sweep”) at a rate of 1 V/s, while the tip was kept at a fixed position in the sample. The graphs have been compensated for the tip-sample capacitance and the offset-current using the methods suggested by Rommel et al.:25 the offset between the forward- and backward-sweeps was measured at low voltage over the full range of ramp-rates used at DWs and domains. These measurements were used to calculate the capacitance contribution to the current that was found to be approximately 1 pA V−1 s, at both domains and at the walls. As previously seen, the conductivity is substantially higher at the DW than that at the domains. Both at the DW and the domains, the IV-curves show rectifying behavior for the forward sweeps: the current is very low while the bias is negative and increases exponentially when the bias becomes positive. In the positive branch of the backward sweep, the current is higher at any given voltage than that at the corresponding voltage during the forward sweep, giving rise to loop-opening. Moreover, the conductivity shows activation/memristive-like behavior, increasing with the number of IV-curves. Note that at negative bias, the current for the backward sweep is higher than for the forward one and also increases with the number of cycles. For and DW, the negative current reaches its peak before the bias reaches −10 V, whereas for , the peak occurs at −10 V. For all three cases, the current in the negative direction is mostly present in the backward sweep and after a certain number of cycles. This indicates that it is due to the partial relaxation of charges displaced during the positive bias. In these experiments, shows slightly higher conductivity at +10 V for the first cycle than does , contrary to what was observed in the biased scan of Fig. 1(c). At the 5th cycle, the current is again higher at . This discrepancy could be explained by taking into account that while scanning, the surface-response, related to the energy-gap difference, is the dominating effect. On the other hand, during the IV-curves, the bulk displacement of ions is expected to play a greater role. The selective accumulation of ions and defects at the surfaces has an impact on the work-function at the surface and thus on the local conductivity.23 As these species move in the applied field, their redistribution may modify the barrier-height, causing the memristive-like behavior and loop-opening. Macroscopic studies in LiNbO326 have previously revealed a similar behavior. Still, effects coming from surface contaminants or related to the quality of the tip-sample contact cannot be entirely ruled out.
Figure 3 shows the evolution of the current level at +10 V for several series of five consecutive IV-curves, each series acquired at a different sweep-rate and in a different position, for (a) DW, (b) , and (c) . The fact that the current depends on the sweep-rate clearly indicates that the conductivity is due to ionic movement, as expected for KTP. At the DWs, there is conductivity-activation at all sweep-rates; the final current increases substantially over the series of five cycles. For the domains, the activation-behavior is different: for the fastest ramps (5.0 V/s and 2.0 V/s), there is practically no current increase. For the slower ramps however, there is clear activation: the current increases by 4.5 times at 1.0 V/s and up to 20 times at 0.2 V/s. Note that the current tends to be higher at for higher sweep-rates, while is more conductive for the lower rates. Interestingly, the effects of the activation are visible both in topography and in current maps acquired after a series of IV-curves. For the domains, no changes are visible after the cycles at high sweep-rates, whereas for lower sweep-rates, there are changes to the topography as well as charge accumulation. At the DWs, the changes in topography and charge accumulation are observed for all sweep-rates, although the effects are more pronounced for the slower ramps. It is worth noting that both the charge accumulation and topographic changes prevail for at least 30 min after the cycles are acquired, pointing to irreversible surface modifications and charge displacement.
Figure 4 shows topographic images as well as current-maps at 0 V bias taken after five cycles at 0.5 V/s sweep-rate for [(a) and (b)] , [(c) and (d)] , and [(e) and (f)] DW. Here the conductivity images show the charge trapped at the surface that is picked up by the grounded tip. Although the tip was at a fixed point during the IV cycles, the affected area is orders of magnitude larger than the tip radius, extending by a few micrometers in each direction. Remarkably, the topographic changes (and the charge accumulation distribution) are different for the opposite domains, being elongated along the [010]-axis for and circular for , both with a roughness of 1-2 nm and current levels of 1-1.5 pA. For the DW, the changes extend both onto the and regions over a larger area, with detected currents of 2-2.5 pA. The wall and modified region consistently show higher conductivity than the surroundings, as can be clearly seen in the current map of the same region as in [(e) and (f)] at 10 V taken afterwards [Fig. 4(g)] and the corresponding current profile extracted from the center of the scan [Fig. 4(h)]. It should be pointed out that no wall movement could be detected by PFM.
These observations can be understood in the following way: at high sweep-rates, the displacement of ions in the domains is reversible, and consequently no displaced charge or topographic changes can be detected afterwards. This translates into similar IV-curves for each cycle (see Fig. S2 in the supplementary material). For 1 V/s and lower sweep-rates at the domains and for all sweep-rates at the DWs, there is conductivity activation and memristive-like behavior which indicates permanent displacement of ions and vacancies, most probably in combination with electrochemical reactions at the tip-sample interface.27 The greater topography modification and charge-accumulation at the DW, for all the ramp-rates employed, can be understood as a consequence of the local increase in carrier mobility. This increase, together with the high strain and associated electric fields,7 present at the DW can be expected to alter the local electrochemistry at the walls, causing the differences observed. Although further investigation is required to fully understand the difference in morphology between the changes in and domains, it can be ascribed to the interplay between the different sub-surface layers (i.e., K+ enrichment at and vacancy accumulation at ), the preferential movement of K+ in the direction,28 and the different reactivity with the water meniscus at the tip-sample interface.27
In conclusion, we have investigated the local conductivity of domains and DWs in 100 m thick single-crystal KTP, demonstrating a fourfold increase at the walls as compared to the domains. Our current-voltage measurements showed memristive-like behavior and surface modification at the DWs for all the sweep-rates used while, at the domains, it only occurs for low frequencies. These effects and their rate-dependence can be attributed to ionic migration and charge accumulation in sub-surface layers.
See supplementary material for a biased scan at varying voltage; and IV-curves acquired at a DW and a domain over an extended set of ramp-rates.
This work was supported by the Swedish Foundation for Strategic Research and the Swedish Research Council (VR).