Self-organized formation of quasi-regular ferroelectric nanodomain

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Functional Nanostructured Materials (including low-D carbon)

Self-organized formation of quasi-regular ferroelectric nanodomain structure on the non-polar cuts by grounded SPM tip Anton Pavlovich Turygin, Denis Olegovich Alikin, Mikhail S. Kosobokov, Anton V. Ievlev, and Vladimir Ya. Shur ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 25 Sep 2018 Downloaded from http://pubs.acs.org on September 25, 2018

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ACS Applied Materials & Interfaces

Self-organized formation of quasi-regular ferroelectric nanodomain structure on the non-polar cuts by grounded SPM tip

Anton P. Turygin1, Denis O. Alikin1, Mikhail S. Kosobokov1, Anton V. Ievlev2, Vladimir Ya. Shur1* 1 2

School of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia

The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA *Corresponding author: [email protected]

ABSTRACT: The understanding of self-organization processes at the micro- and nanoscale is of fundamental interest and is important to meet the great challenges in further miniaturization of electronic devices to the nanoscale. Here we report, self-organized quasi-regular nanodomain structure formation on the non-polar cut of ferroelectric lithium niobate single-crystal. These structures were formed along the trajectory of grounded scanning probe microscope tip approaching or moving away from the freshly switched region. Detailed analysis of the formed structures revealed internal organization by the length of the needle-like domains, which ranged from uniform to quasi-periodic and even chaotic modes as a function of distance from the switched region. Comprehensive investigations and numerical simulations allowed to attribute explored phenomena to charge injection during the field application and further switching under the action of electric field induced by injected charges near the tip. Self-organization and quasiperiodicity were explained by the effective screening and long-range electrostatic interaction between the individual needle-like domains. Keywords: domain structure; self-organization; piezoelectric force microscopy; non-polar cut; lithium niobate; charge injection; local switching INTRODUCTION Miniaturization of portable electronic and mechanical devices requires new nanoscale elements, which can be realized using ferroelectric materials with functionality defined on the nanometer level.1–4 These developments are supported by a rich set of the properties demonstrated by any ferroelectric, including piezoelectricity, high non-linear optical activity, pyroelectricity and many others. The active study of the domain structure evolution in ferroelectric single crystals is stimulated by the needs of domain and domain wall engineering.5,6 It is mostly focused on the fabrication of electro-optical and non-linear optical devices, such as laser frequency converters based on periodically poled lithium niobate (LiNbO3, LN).6–9 The main target of the domain engineering is to improve the important for application characteristics of commercially available ACS Paragon Plus Environment

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ferroelectrics by manufacturing of stable tailored domain patterns, which allows improving of the device performance by introducing of the spatial modulation of the piezoelectric, electrooptic, photorefractive, and nonlinear optical properties.10 The manufacturing of tailored domain patterns with desired geometrical parameters is based on deep understanding of the physical fundamentals of domain structure evolution and polarization reversal process.11 However, such investigations are impossible without using the nanoscale characterization tools, as ferroelectric properties are defined and controlled at the length-scale of the single domain wall or as low as a few nanometers. Scanning probe microscopy (SPM) is a perfect candidate for ferroelectric studies, as it allows both nanometer scale imaging of the ferroelectric domain structures and nanoscale manipulating of them via local polarization reversal (switching) under the action of electric field produced by the biased tip. In particular, this method can be used as a basis for ultrahigh density data storage and processing devices.12,13 It also enables the fundamental investigations of the domain structure evolution and polarization behavior in the nanometer regions underneath the tip.14–20 In particular, it was recently demonstrated that interaction of ferroelectric domains during local switching by the SPM tip can lead to formation of the rich spectrum of domain patterns, including intermittent, quasiperiodic and chaotic.14 It has been claimed that the domain interaction effect is very promising in connection to the emergent computing paradigm known as a memcomputing and resulting in future brain-like computing architectures.21,22 Recently local polarization reversal on non-polar cuts of LN single crystals allowed studying one of the main stages of the domain structure evolution, so-called forward growth or (domain wall propagation in along the polar direction).23–26 The details of the forward growth are still unknown as the process is hidden in the crystal bulk. Despite the first direct optical observation of the forward growth in barium titanate single crystals published in the classical paper of W. Merz,27 this process is insufficiently studied due to spatial resolution limitations in the optical microscopy. Furthermore, the local polarization reversal on the non-polar cuts were studied in LN by local application of electric field using metallic needle,28 electron beam,29,30 and conductive SPM tip.23–25 In particular, it is shown that on the non-polar cuts the backswitching after termination of the external field leads to either change of the switched domain shape or even formation of the domain in the opposite direction.23 A key role of local charge injection31–35 and screening of the applied electric field

36–38

was also demonstrated. The effects of domain interaction and self-

organization during local switching by biased SPM tip on nonpolar cut of MgO:LN were studied by us earlier and attributed to electric field localized at the charged domain walls of the needlelike domains.25 ACS Paragon Plus Environment

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In this manuscript, we report formation of the quasi-regular self-organized structures of needle-like domains along the trajectory of grounded SPM tip moving in contact with the nonpolar cut of LN single-crystal. These measurements were performed in the vicinity of the freshly switched region and showed formation of the arrays of needle-like domains with regularly mediated length. The geometrical parameters of these structures and corresponded distribution of the surface potential were evaluated by different SPM modes. The effects of the period multiplication inside the structure, including doubling, quadrupling and chaotic modes were revealed. Systematic experimental studies and finite element theoretical simulations allowed us to explain the observed phenomena. In particular, self-organized domain structure formation has been attributed to charge injection, polarization screening, and electrostatic interaction of the individual domains in the array. Obtained results are important for fundamental understanding of the ferroelectric phenomena and practical applications of ferroelectrics in electro-optical and non-linear optical devices.

RESULTS AND DISCUSSION In the experiments we used single domain plates of X- and Y- non-polar cuts of congruent LN. The LN crystal is an important material for application in nonlinear optical devices due to its large electro-optical and nonlinear optical coefficients that can be used as a model uniaxial ferroelectric with high uniformity and simple domain structure (180° walls only).39 The samples have been characterized using SPM in piezoresponse force microscopy (PFM) mode for domain visualization and Kelvin probe force microscopy (KPFM) for surface potential measurements. All measurements were done in dry air atmosphere with relative humidity below 5%. We performed local switching by applying of voltage pulses through the conductive SPM tip. First, we applied rectangular voltage pulse in the point of bias application, which led to the formation of the initial isolated wedge-like domain typical for the switching in non-polar LN cuts (Fig. 1a).23,24 After termination of the voltage pulse the grounded tip was staying in contact with the surface for approximately 0.1 s. Two experimental procedures were performed afterwards. First, the tip was moved away from the point of bias application, but still in contact with the surface in the direction normal to polar axis with velocity about 1 µm/s (Fig. 1b). Second, the tip was withdrawn ~5 µm from the sample surface and moved about 30 µm away from the point of bias application, then it was brought back in contact with the surface, and moved back towards the point of the bias application (Fig. 2b,c).

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Self-organized domain structure formation The first experiment represented the application of a single negative or positive electric field pulse (±200 V, 10 s) to the point of bias application (Fig. 1a) and subsequent motion of the grounded tip up to 30 µm in the direction normal to polar axis (Fig. 1b).

Figure 1. The first experiment: (a) Initial switching by single bias pulse, (b) motion of the grounded tip from the point of bias application. PFM amplitude images of the resulted domain structures formed at: (c), (e) X-cut, (d), (f) Y-cut of LN. Initial switching with (c), (d) positive, (e), (f) negative single rectangular bias pulse with duration of 10 s and amplitude ±200 V. The scale bars are 10 µm.

Application of the positive pulse resulted in formation of the partially backswitched single wedge-like domain elongated in polar direction in the point of bias application (Fig. 1c,d). The motion of the grounded tip hasn’t reveal any secondary domain structures along the tip trajectory. The wedge-like domain appeared after application of the negative pulse was oriented towards the same direction (Fig. 1e,f). This fact has been reported earlier and attributed to backswitching after negative pulse termination, which leads to disappearance of the initially formed domain and formation of the new one oriented towards opposite direction.23 At the same time we surprisingly found formation of self-organized quasi-periodic array of needle-like domains along the tip trajectory within ten microns from the point of bias application (Fig. 1e,f). Similar behavior was observed for both X- (Fig. 1e) and Y-cuts (Fig. 1f). The effect was absent for increased values of relative humidity, including measurements performed at the ambient conditions.


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Figure 2. The second experiment: (a) Initial switching by single bias pulse, (b) motion of the withdrawn tip from the point of bias application, (c) motion of the grounded tip in the contact with the surface towards the point of bias application. (d, e) PFM images of the resulted domain structures on the surface of X and Y non-polar cuts. Voltage pulse duration 10 s, amplitude -200 V. The scale bars are 10 µm.

To further understand explored phenomenon, we modified experimental procedure. After the negative bias application (Fig. 2a), the tip was withdrawn and moved more than 30 µm away from the point of bias application (Fig. 2b). Then, the grounded tip was brought back in contact with the surface and moved back towards the point of the bias application (Fig. 2c). These experiments also demonstrated formation of the self-organized structure along the tip trajectory, which started approximately 10 µm from the point of the bias application (Fig. 2d,e). The average domain period in the array was found to be around 100 nm (Fig. 2d,e). Relaxation of the switched area To get further insight into explored phenomena we performed experiments varying time between initial switching and motion of the grounded tip. It was found that switched area (the area of all domains in the self-organized array) decreases exponentially (Fig. 3) with relaxation time about 25 minutes.

Figure 3. (a) PFM images of the domain structures obtained in the second experiment for the different time intervals after initial switching, (b) relaxation of the normalized switched area. Single rectangular switching pulse 10 s,200 V.

Quasi-regularity of the needle-like structures Careful analysis of the self-organized domain arrays revealed existence of the regular pattern in the length of individual needles. Various types of the ordering (“array types”) were observed: (I) uniform, (II) doubling, (III) quadrupling, and (IV) chaotic (Fig. 4). The consistent ACS Paragon Plus Environment


change of array type from uniform to chaotic was observed, while approaching to the point of the bias application. The most exotic pattern was period “quadrupling”. The needle-like domains were classified by their length in three groups: (1) long (L) with length 1.6-1.9 µm, (2) medium (M) – 1.0-1.4 µm, and (3) small (S) – 0.5-0.8 µm (Fig. 4). In this classification we observed domain pattern L-S-M-S. We also found chaotic behavior with irregular changing of the domain length.

Figure 4. Various types of the domain arrays: I - uniform switching, II - doubling, III - quadrupling, IV - chaotic behavior revealed by PFM

At the first glance these results are consistent with observation of quasi-periodic and chaotic patterns explored on the polar cut of LN.14 However, needle-like domain structures revealed in this research are self-organized, while structures studied on polar LN cut were manufactured by application of the electric field in each point. This self-organized domain structure formation can be attributed to the action of the various electric fields: (1) residual (partially screened) depolarization field of the initial domain;37,40 (2) electric field produced by injected charges localized on deep traps;28,32,34 and (3) electric field caused by flexoelectric effect.41 The significant distance (above 10 µm) from the point of bias application allows to exclude the influence of residual depolarization field. In turn, flexoelectric effect is not spatially correlated with previously switched region. Thereby it is also unlikely to cause observed phenomena.

Figure 5. (a) Spatial distribution of the surface potential measured by KPFM after the application of the negative pulse. (b) The surface potential relaxation. (c) Schematic image of the “switched area” (red shading) with the experimental points (white), where the domain arrays started to appear during scanning towards the point of bias application. The point of bias application of the electric field application is marked by blue.


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In order to clarify role of the charge injection we have performed KPFM measurements to study spatial distribution of the surface potential in the vicinity of freshly switched regions (Fig. 5a). In the case of switching by negative bias the surface potential maximum was found to be localized near the point of bias application, but shifted 5 µm along the polar axis (Fig. 5a). This fact can be attributed to charge transport along the conductive walls of the fresh wedge-like domain.42–44 The injected charge was found to spread tens of microns from the point of bias application and the relaxation time measured in the point of surface potential maximum was around 170 min (Fig. 5b). The KPFM results confirmed that injected charges play a crucial role in the process of formation of self-assembled quasi-periodic structure. The series of additional experiments has been done to reveal an area of self-organized structure formation. In this experiments tip approached to the point of bias application from different directions. All experiments were started at distance exceeding 100 µm from each other to avoid results interference. The position of the point, where the domain arrays started to appear, were measured for all experiments (Fig. 5c). The obtained experimental points were fitted by the elliptic shape corresponding to spatial distribution of the surface potential:

+

= 1,

(1)

where a = 9.3 µm and b = 9.6 µm are the ellipse semi-axes. The experimentally measured value of surface potential at the edge this ellipse Uth = -30.1±6.7 V was identified as a threshold voltage required to induce polarization reversal by the grounded tip. Model of the polarization reversal To further understand process of switching under the action electric field induced by the grounded SPM tip in the vicinity injected charges, we simulated numerically non-uniform electric field of the tip. The used model assumed that the application of the pulse leads to charge injection localized on the deep traps over the large area (Fig. 6a). The injected charges induced the electric field on the apex of the grounded conductive tip (Fig. 6b,c). It should be noted that the polarity of the electric field induced in the tip is opposite to polarity of the initial switching pulse. Furthermore, it is known that the external screening of the depolarization field by the current in the external circuit decreases significantly the threshold field value.39 Finite-element modeling (FEM) in COMSOL environment (Fig. 6) was used to calculate local distribution of the electric field induced by the grounded SPM tip near the region with injected charges. Assuming 2D Gaussian distribution of surface charge density, the



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experimentally measured surface potential (Fig. 6a) has been fitted using COMSOL Optimization module. Nevertheless, self-organization kinetics is not fully controlled by the field of the grounded tip, but also mediated by depolarization field induced by previously formed needle-like domains. During formation of the self-assembled domain structure new domain nucleates and grows in the resulted electric field of the conductive tip as well as electric field produced by the whole trace of previously formed needle-like domains. As a result of the interaction between charged apexes, quasi-regular modes can show up.

Figure 6. Results of the COMSOL simulation of (a) spatial distribution of the injected charge, (b) spatial distribution of the polar component of the electric field produced by the injected charge in the vicinity of grounded SPM tip, (c) averaged electric field induced by grounded tip vs distance from the center of the injected charge. (d) field dependence of domain length with simulated points (black) fitted by Eq. 3 (red line). Inset in (c) is zoomed spatial distribution of electric field in the vicinity of the SPM tip. The scale bars are 20 µm,

In the considered case, the local switching electric field Esw inducing domain growth can be represented by the sum of several components: , = , + , + , ,

(2)

where Einj(r,t) is the field produced by injected charges (almost uniform in an area of switching due to wide spread of the charge), Etip(r,t) is the field induced in the grounded tip by injected charges, Edep(r,t) is the depolarization field created by array of conical domains with charged walls. The detailed expressions for each of the components can be found in Supplementary. In order to simulate formation of the self-organized quasi-periodic domain structures a series of calculations of Etip(r,t) were performed as a function of tip position (Fig. 6c). Polar components of the depolarization field produced by needle-like domains with lengths 1, 0.66, and 0.33 µm, and aspect ratio 1:20 were calculated. These lengths correspond to large (L), medium (M), and small (S) domains in the array, respectively. Calculation has been done using ACS Paragon Plus Environment

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domain shapes measured with high spatial resolution by SEM after shallow chemical etching (Fig. S5 in Supplementary). Depolarization field produced by the individual domain was assumed to be generated by conical part only, while domain base was considered to be completely screened (Fig. 6b). The resulted distributions of local depolarization field for all experimentally observed combinations of three neighboring domains (L-S-M, S-M-S, M-S-L, and S-L-S) were simulated. The interpolation allowed to estimate depolarization field of domain of arbitrary length l: Edep(l,x), where x is the distance from its center. Using this data, we were , able to calculate resulted field of sequence of three neighboring domains =

∑ , , which was used to calculate length of the freshly formed domain l(E) (Fig. 6d): = !,

(3)

where a is the parameter, is the depolarization field created by domain array, Eth is

threshold field for the local switching.

Figure 7. (a) Simulated domain patterns. (b) The phase diagram of the domain pattern as a function of electric field and spacing: I - uniform switching, II - doubling, III - quadrupling, IV - chaotic behavior. (c) Bifurcation map obtained by simulation of domain array with spacing of 100 nm.

To analyze simulated results we plotted diagrams of the length of n+1 domain xn+1 on the length of previous one xn: xn+1 = q(xn), where q is empirical function, defined by domain interaction in array (see details in Supplementary). The calculation allowed identification of all experimentally observed domain patterns: I - uniform switching, II - doubling, III - quadrupling, IV - chaotic behavior (Fig. 7a). Corresponded phase diagram as a function of the electric field and domain period was also simulated (Fig. 7b). The analysis of the simulated data also allowed building of bifurcation diagram (Fig. 7c), demonstrating dependence of all observed domain lengths in array on Etip value. This diagram clearly demonstrates uniform, quasi-regular (doubling and quadrupling) as well as chaotic modes. The complexity of the pattern increases with increase of Etip or approaching of the point of bias application (Fig. 7c). The complex spectrum of dynamic behaviors corresponding to chaotic mode was revealed at higher Etip values.



SUMMARY. Here, we explored formation of the self-assembled quasi-regular and chaotic domain structures on non-polar cuts of lithium niobate. These structures were found to form along the trajectory of the grounded SPM tip near the freshly switched region. Formation of these self-organized structures started at the distance above ten micrometers from the point of bias application. The KPFM measurements allowed to attribute explored phenomenon to the surface charge injection during the electric field application. Different quasi-periodic and chaotic patterns inside the self-organized needle-like domain structures were found and explained by the electrostatic interaction between individual needle-like domains in the array. Using the finiteelement modeling the phase diagram of the domain pattern as a function of electric field and domain spacing were calculated. All types of the numerically predicted domain arrays were proved by the experiment. The discovered phenomena shed light on the domain interaction in ferroelectrics and paves the way to development of the ferroelectric electronic, electro-optical and non-linear optical devices. METHODS Samples Samples of Y and X cuts of LN were cut off from 1-mm-thick Z oriented LN wafer (Yamaju Ceramics, Japan) and mechanically polished. The surface roughness of all samples was about 1 nm. Domain structure imaging The domain structures were created and visualized using Probe NanoLaboratory NTEGRA Aura (NT-MDT, Spectrum Instruments, Russia) in PFM mode. Commercial probes NSC21 with titanium-platinum conductive coating (MikroMash, Estonia) with a radius of curvature R = 35 nm, resonance frequency f = 230 kHz, and spring constant k = 20 N/m were used. PFM measurements were carried out using 3-5 V AC voltage with frequency far from the contact resonance of the tip. Local polarization reversal was done using NI-6251 multifunction Data Acquisition board (National Instruments, USA) and high-voltage amplifier Trek-677B (TREK, Inc., USA) by 200 V, 10 s DC pulse application and following motion of the grounded tip in vicinity of point of bias application. The spatial distribution of the surface potential was measured by closed loop two-pass KPFM with 0.1 V AC voltage applied to the tip and 50 nm tip-surface distance at the second pass. The dry atmosphere with relative humidity less than 5% was provided by the constant flow of the dry air through the SPM chamber. Selective chemical etching in HF:HNO3 1:1 during 2 min was used to reveal nanodomain structure and shape of individual domain. Domain imaging with high spatial resolution after


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shallow selective chemical etching was done using the scanning electron microscope Merlin (Carl Zeiss, Germany). Imaging was done using Carl Zeiss in-lens detector (10 kV accelerating voltage, 4.2 mm working distance). Numerical simulations For numerical simulations COMSOL Multiphysics finite element modeling software was used. The electric potential distribution at the surface of lithium niobate was simulated using tetrahedral elements with approximation by the third order polynomials. 35 nm curvature and 10 µm length grounded tip touching the surface was considered in the simulations to mimic experimental conditions. εa= 85 and εc= 29 dielectric constants were used.45 All calculations have been done in static approximation. 200×200×200 µm3 in the x, y, z directions physical sample dimensions were chosen for the simulation. Approximately 450,000-element and 550,000-node mesh was used in the solution with about 1 nm minimum element size. ACKNOWLEDGMENT The equipment of the Ural Center for Shared Use “Modern nanotechnology” UrFU was used. The research was made possible by Russian Science Foundation (Project №14-12-00826). AVI was supported by Center for Nanophase Materials Sciences at Oak Ridge National Laboratory, which is a DOE Office of Science User Facility. Supporting Information Dependence of domain structure on tip motion velocity; change of array type during tip approaching towards point of bias application; SEM image of domain structure after shallow etching; calculation of electric field spatial distribution.

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Self-organized formation of quasi-regular ferroelectric nanodomain

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