Domain Patterning in Ion-Sliced LiNbO 3 Films by Atomic Force Microscopy

Photonic structures denoted as LNOI (LiNbO3-on-insulator) are of considerable interest for integrated optics due to a high refractive-index contrast provided by the interface LiNbO3/insulator. A topical problem for LNOI-based optical waveguides is optical-frequency conversion, in particular realized on ferroelectric domains on the basis of quasi phase-matching principle. This paper presents extended studies on the fabrication of domain patterns by atomic force microscopy (AFM) methods (raster lithography, piezo-force microscopy, conductive AFM) in single-crystal ion-sliced LiNbO3 films forming LNOI sandwiches. A body of data obtained on writing characteristics of domains and specified 1D and 2D domain patterns permitted us to manipulate the domain sizes and shapes. Of special importance is the stability of created patterns, which persist with no degradation during observation times of months. The domain coalescence leading to the transformation of a discrete domain pattern to a continuous one was investigated. This specific effect—found in thin LiNbO3 layers for the first time—was attributed to the grounding of space-charges accumulated on domain walls. Observations of an enhanced static conduction at domain walls exceeding that in surrounding areas by not less than by five orders of magnitude supports this assumption. AFM domain writing in ion-sliced films serves as a basis for studies in nonlinear photonic crystals in integrated optical schemes.


Introduction
Lithium niobate is the key material for integrated photonics/optics due to a unique combination of excellent optical, acousto-, and nonlinear-optical properties demanded by integrated devices.Over the past decade, the manufacture of thin (hundreds of nanometers thick) single-crystal LiNbO3 films was elaborated with the use of ion-slicing technology [1].Sandwich structures fabricated by bonding ion-sliced single-crystal LiNbO 3 films to insulator substrates-denoted as LNOI ("lithium niobate-on-insulator")-have attracted considerable interest.Physical phenomena and fundamental technologies underlying the fabrication of ion-sliced LiNbO 3 films, methods of bonding them to various insulating substrates, and relevant bibliography can be found, for example, in reviews [2,3].An interest in LNOI structures is primarily because embedding a LiNbO 3 film in a low refractive-index insulator substrate provides a high-index-contrast optical waveguide.Some encouraging results were obtained in studies of LNOI-based optical elements, such as photonic crystals [4,5], high-Q microresonators [6][7][8], ridge-waveguides [9,10], proton-exchanged waveguides [11][12][13] and modulators [14], hybrid lightwave circuits LNOI-SOI [15], etc.These results indicate that LNOI is an appropriate platform for integrated optics.
A typical problem for LNOI-based waveguides is the nonlinear-optical frequency conversion, which can be realized on the basis of either phase-matching (PM) or quasi-phase-matching (QPM) principles.In the latter case, an artificially created ferroelectric domain pattern serves as a frequency convertor.Traditionally, periodically-poled LiNbO 3 (PPLN) elements are produced by the application of external fields to an electrode pattern deposited onto the crystal surfaces.Alternative methods such as domain writing by atomic force microscope (AFM)-tip voltages or electron-beam of SEM permit the creation of domain patterns up to the nanoscale (e.g., [16]).To fabricate ion-sliced PPLN films, the authors of [17,18] applied the technique of ion-slicing to a bulk PPLN plate.At the same time, the abovementioned non-contact microscopic methods of domain fabrication are especially appropriate for use in thin layers, since in this case an undesirable decrease of the field across the layer thickness and resulting domain-wall inclination observed in crystal plates (e.g., [16]) are negligible.
In [19] we reported on domain writing by dc AFM-tip voltages in ion-sliced LiNbO 3 films forming LNOI.2D domain patterns were written-both discrete (consisting of isolated domains up to the nanoscale) and arbitrary-shaped continuous ones.All patterns were completely stable and revealed no degradation in real-time.These results promise LNOI structures to be a platform for studies in nonlinear photonic crystals [20].The authors of [21] reported the fabrication of stable domain patterns in LNOI sandwiches by applying external fields.A specific feature of the domain evolution found by us [19] was the coalescence of adjacent domains as the distance between them was decreased (this coalescence occurring in an array of isolated domains has no relation to the domain coalescence terminating the polarization reversal under uniform external fields).
In this connection, the writing of nanodomain arrays in ion-sliced LiNbO 3 films is of interest in the context of high-density data storage in ferroelectrics [22,23].The authors of [24,25] reported on the writing of nanodomain patterns in ultrathin single-crystal LiTaO 3 plates.The minimum domain-dot diameter of 6 nm together with the inter-domain distance of about tens of nm provided a memory density as high as 1-10 Tbits in 2 .In these works, contrary to our results [19], no domain coalescence was mentioned.So, the question arises as to which factors promote or suppress domain coalescence and how it can influence the tolerable interdomain spacing (i.e., the storage density).
The ion-sliced films under study seem to be an appropriate medium for investigations of ferroelectric phenomena-specifically of domain formation-in LiNbO 3 films and thin layers as a whole.This paper presents extended studies of these subjects started in [19].
Our experiments were performed in LNOI samples provided by Nanoln Electronics (Jinan, China).

Results and Discussion
The schematic diagram of our experiments is shown in Figure 1. Figure 1a,b display two types of samples (S1 and S2) under study and the scheme of AFM domain writing.Methods of domain fabrication and investigation with the use of scanning probe microscopy are described, for example, in [26].Figure 1c illustrates the domain state of samples after applying AFM dc-voltages; the spontaneous polarization directions P up and P down correspond to the initial and reversed states, respectively; the reversal from P up to P down occurs under positive +U tip .
Samples of S1 type are composed of a +Z-cut ion-sliced single-domain LiNbO 3 film bonded to a SiO 2 -coated LiNbO 3 wafer.An Au/Cr layer is incorporated between the bottom film surface and SiO 2 layer.Sample 2 is composed of a +Z cut ion-sliced single-domain LiNbO 3 film bonded directly to a SiO 2 -coated LiNbO 3 wafer without a metal interlayer.

Writing of Isolated Domains
In this section, we briefly characterize the dependences of domain formation on the exposure conditions.Figure 1d exemplifies piezoelectric force microscopy (PFM) images of written isolated domains.The minimum achieved domain diameter D, determined by the tip radius R, is 50 nm.D linearly grows with Utip at a given tp (Figure 2a).Domains appear after the application of certain threshold tip-voltage Uthr, which decreases with growing pulse duration (Figure 2b).So, for a given Utip, a certain pulse duration is required to retain formed domains, whereas they decay at shorter tp.This is a manifestation of a backswitching effect which is characteristic of LiNbO3 [16].The linear dependences D(Utip) qualitatively resemble those reported, for example, for AFM-domain writing in thin stoichiometric LiNbO3 crystals [27][28][29].On the contrary, the exposure dependences of the domain diameter at Utip = const differ markedly from D(tp) reported earlier [27][28][29], and are worthy of a more detailed discussion.
Figure 3a shows D(tp) in the logarithmic scale for different tip voltages.The domain diameter grows up to a salient point, whereupon it comes to a plateau.These curves are fundamentally different from linear D(tp) in ultrathin LiNbO3 crystals [28].Following the method proposed in [30], we calculated the average velocity of the domain widening (i.e., the sideways domain-wall (DW)

Writing of Isolated Domains
In this section, we briefly characterize the dependences of domain formation on the exposure conditions.Figure 1d exemplifies piezoelectric force microscopy (PFM) images of written isolated domains.The minimum achieved domain diameter D, determined by the tip radius R, is 50 nm.D linearly grows with U tip at a given t p (Figure 2a).Domains appear after the application of certain threshold tip-voltage U thr , which decreases with growing pulse duration (Figure 2b).So, for a given U tip , a certain pulse duration is required to retain formed domains, whereas they decay at shorter t p .This is a manifestation of a backswitching effect which is characteristic of LiNbO 3 [16].

Writing of Isolated Domains
In this section, we briefly characterize the dependences of domain formation on the exposure conditions.Figure 1d exemplifies piezoelectric force microscopy (PFM) images of written isolated domains.The minimum achieved domain diameter D, determined by the tip radius R, is 50 nm.D linearly grows with Utip at a given tp (Figure 2a).Domains appear after the application of certain threshold tip-voltage Uthr, which decreases with growing pulse duration (Figure 2b).So, for a given Utip, a certain pulse duration is required to retain formed domains, whereas they decay at shorter tp.This is a manifestation of a backswitching effect which is characteristic of LiNbO3 [16].The linear dependences D(Utip) qualitatively resemble those reported, for example, for AFM-domain writing in thin stoichiometric LiNbO3 crystals [27][28][29].On the contrary, the exposure dependences of the domain diameter at Utip = const differ markedly from D(tp) reported earlier [27][28][29], and are worthy of a more detailed discussion.
Figure 3a shows D(tp) in the logarithmic scale for different tip voltages.The domain diameter grows up to a salient point, whereupon it comes to a plateau.These curves are fundamentally different from linear D(tp) in ultrathin LiNbO3 crystals [28].Following the method proposed in [30], we calculated the average velocity of the domain widening (i.e., the sideways domain-wall (DW) The linear dependences D(U tip ) qualitatively resemble those reported, for example, for AFM-domain writing in thin stoichiometric LiNbO 3 crystals [27][28][29].On the contrary, the exposure dependences of the domain diameter at U tip = const differ markedly from D(t p ) reported earlier [27][28][29], and are worthy of a more detailed discussion.
Figure 3a shows D(t p ) in the logarithmic scale for different tip voltages.The domain diameter grows up to a salient point, whereupon it comes to a plateau.These curves are fundamentally different from linear D(t p ) in ultrathin LiNbO 3 crystals [28].Following the method proposed in [30], we calculated the average velocity of the domain widening (i.e., the sideways domain-wall (DW) velocity V DW ) against the domain diameter D. The velocity was taken from D(tp) as V DW = ∆D i /∆t i , where ∆D i is the increment of D in a time ∆t.The obtained nonmonotonic curves V DW (D) are displayed in Figure 3b.Comparison of Figure 3a,b shows that a "saddle" in curves D(t p ) corresponds to a sharp slowing-down (practically, to stopping) of DW motion.Based on the approach of [30], which models the AFM tip as a sphere, we evaluated the axial fields E at the domain boundaries.For salient points in Figure 3a these estimates give E of 0.26 10 8 V/m and 0.29 10 8 V/m, respectively, for U tip = 35 V and 50 V.These values are rather close to the coercive field Ec = 0.22 10 8 V/m in LiNbO 3 bulk crystals.Despite the approximate nature of these estimates, this result seems to be not occasional and permits us to interpret the saddles in D(t p ) curves (Figure 3a) as a threshold-like slowing down of the sideways DW motion just at that distance D from the tip contact-point, at which the field drops below E c .Based on the approach of [30], which models the AFM tip as a sphere, we evaluated the axial fields E at the domain boundaries.For salient points in Figure 3a these estimates give E of 0.26 10 8 V/m and 0.29 10 8 V/m, respectively, for Utip = 35 V and 50 V.These values are rather close to the coercive field Ec = 0.22 10 8 V/m in LiNbO3 bulk crystals.Despite the approximate nature of these estimates, this result seems to be not occasional and permits us to interpret the saddles in D(tp) curves (Figure 3a) as a threshold-like slowing down of the sideways DW motion just at that distance D from the tip contact-point, at which the field drops below Ec.

Coalescence of Domains
As mentioned above, the closely spaced domains tend to coalesce [19].Here we present the extended investigations of this effect (Figure 4).In samples S1 (Figure 1a), domain chains (Figure 4a,b) and domain squares (Figure 4c-f) were written by means of step-by-step in-plane displacements of the tip by a specified distance Λ.For a given pattern, Λ is constant; in the written squares, Λ along the both sides are equal.
Figure 4a,d demonstrate the evolution (bottom-up) of a domain chain as Λ decreases from 1000 to 100 nm (for all chains Utip = 50 V, tp = 1 ms).Figures 4b,e and 4c,f display images of the discrete and continuous domain squares written with Λ = 500 and 200 nm, respectively (Utip = 50 V, tp = 10 ms).Both the discrete domain chain and square transform to unbroken ones.PFM amplitude images of terminating continuous patterns (the upper rows of Figure 4d and the square in Figure 4f) reveal inboard no traces of domain boundaries, appearing as dark contours.In other words, the domain coalescence leads to the formation of a large completely uniform 2D domain.All written patterns-both discrete and continuous-are completely stable for up to several months.
The coalescence is determined by only the distance between DWs, and does not depend on the domain sizes.Rough estimates based on the examination of chains with varied domain diameter permit us to conclude that the coalescence occurs if the inter-domain distance becomes lesser than 20-30 nm.Interestingly, this "critical" value is on the same order of magnitude as the inter-domain distances in nanodomain patterns, providing an ultrahigh storage density in LiTaO3 films [24,25].
The domain sizes are unaffected by the inter-domain spacing; e.g., in the discrete domain chains displayed in three lower rows of Figure 4a,b, the domain diameters are the same to within 1%, as is the width of the continuous domain line (the upper rows in Figure 4a,b).

Coalescence of Domains
As mentioned above, the closely spaced domains tend to coalesce [19].Here we present the extended investigations of this effect (Figure 4).In samples S1 (Figure 1a), domain chains (Figure 4a,b) and domain squares (Figure 4c-f) were written by means of step-by-step in-plane displacements of the tip by a specified distance Λ.For a given pattern, Λ is constant; in the written squares, Λ along the both sides are equal.
Figure 4a,d demonstrate the evolution (bottom-up) of a domain chain as Λ decreases from 1000 to 100 nm (for all chains U tip = 50 V, t p = 1 ms).Figure 4b,e and Figure 4c,f display images of the discrete and continuous domain squares written with Λ = 500 and 200 nm, respectively (U tip = 50 V, t p = 10 ms).Both the discrete domain chain and square transform to unbroken ones.PFM amplitude images of terminating continuous patterns (the upper rows of Figure 4d and the square in Figure 4f) reveal inboard no traces of domain boundaries, appearing as dark contours.In other words, the domain coalescence leads to the formation of a large completely uniform 2D domain.All written patterns-both discrete and continuous-are completely stable for up to several months.
The coalescence is determined by only the distance between DWs, and does not depend on the domain sizes.Rough estimates based on the examination of chains with varied domain diameter permit us to conclude that the coalescence occurs if the inter-domain distance becomes lesser than  The patterns are rather regular with the off-duty ratios of 0.5 and 0.6, respectively.Figure 5c shows a PFM image of an arbitrary-shaped domain pattern written in S1; the reversed domain areas are dark.A compliance of samples S1 to shaping of domain patterns of any specified design seems to be akin to the effect of domain coalescence described above.The coalescence of closely-spaced domains in sample S1 has not been reported before and disagrees with the data reported on AFM domain writing in LiNbO3.In thin LiNbO3 crystals [31], a domain instability was observed as the inter-domain spacing was decreased.In thin He-implanted The domain sizes are unaffected by the inter-domain spacing; e.g., in the discrete domain chains displayed in three lower rows of Figure 4a,b, the domain diameters are the same to within 1%, as is the width of the continuous domain line (the upper rows in Figure 4a,b).
Figure 5a,b present PFM images of domain gratings written in a sample S1 by raster lithography.The grating periods are Λ = 300 and 2000 nm, the grating sizes are of 4 × 4 µm 2 and 20 × 20 µm 2 , the total times of writing of the smaller and larger patterns were 30 and 300 s, respectively.The patterns are rather regular with the off-duty ratios of 0.5 and 0.6, respectively.Figure 5c shows a PFM image of an arbitrary-shaped domain pattern written in S1; the reversed domain areas are dark.A compliance of samples S1 to shaping of domain patterns of any specified design seems to be akin to the effect of domain coalescence described above.
The coalescence of closely-spaced domains in sample S1 has not been reported before and disagrees with the data reported on AFM domain writing in LiNbO 3 .In thin LiNbO 3 crystals [31], a domain instability was observed as the inter-domain spacing was decreased.In thin He-implanted LiNbO 3 layers, a reduction of the inter-domain spacing was accompanied by a decrease of the domain diameter [32].These effects were interpreted as a consequence of the inter-domain electrostatic repulsion.While writing domain chains in thin LiNbO 3 crystals [33], no domain coalescence was observed.By contrast, chaotic discrete patterns appeared as the chain links were reduced.
lithography.The grating periods are Λ = 300 and 2000 nm, the grating sizes are of 4 × 4 µm 2 and 20 × 20 µm 2 , the total times of writing of the smaller and larger patterns were 30 and 300 s, respectively.The patterns are rather regular with the off-duty ratios of 0.5 and 0.6, respectively.Figure 5c shows a PFM image of an arbitrary-shaped domain pattern written in S1; the reversed domain areas are dark.A compliance of samples S1 to shaping of domain patterns of any specified design seems to be akin to the effect of domain coalescence described above.The coalescence of closely-spaced domains in sample S1 has not been reported before and disagrees with the data reported on AFM domain writing in LiNbO3.In thin LiNbO3 crystals [31], a domain instability was observed as the inter-domain spacing was decreased.In thin He-implanted

Relation of Domain Coalescence to the Domain-Wall Conduction
The domain coalescence evidences the freedom from electrostatic repulsion between the adjacent domains.According to the approach developed recently [34][35][36][37], DWs represent the areas of an enhanced conduction owing particularly to a charge accumulation/depletion, which is caused by a variety of reasons.Intuitively, we related the domain coalescence to effects of an enhanced conduction at DWs.To support this assumption, research into the conduction at DWs was performed.
Domain-wall conduction (DWC) in LiNbO 3 was recently investigated in (15-500)-µm-thick plates [38][39][40].The first studies of DWC in thin LiNbO3 films were performed recently by us [41].The conduction was measured in domain gratings with the period Λ= 3.6 µm.For clarity, the results of these measurements discussed in detail in [41] are shown schematically in Figure 6.LiNbO3 layers, a reduction of the inter-domain spacing was accompanied by a decrease of the domain diameter [32].These effects were interpreted as a consequence of the inter-domain electrostatic repulsion.While writing domain chains in thin LiNbO3 crystals [33], no domain coalescence was observed.By contrast, chaotic discrete patterns appeared as the chain links were reduced.

Relation of Domain Coalescence to the Domain-Wall Conduction
The domain coalescence evidences the freedom from electrostatic repulsion between the adjacent domains.According to the approach developed recently [34][35][36][37], DWs represent the areas of an enhanced conduction owing particularly to a charge accumulation/depletion, which is caused by a variety of reasons.Intuitively, we related the domain coalescence to effects of an enhanced conduction at DWs.To support this assumption, research into the conduction at DWs was performed.
Domain-wall conduction (DWC) in LiNbO3 was recently investigated in (15-500)-µm-thick plates [38][39][40].The first studies of DWC in thin LiNbO3 films were performed recently by us [41].The conduction was measured in domain gratings with the period Λ= 3.6 µm.For clarity, the results of these measurements discussed in detail in [41] are shown schematically in Figure 6.The current peaks at DWs persist during observation times of up to several months; i.e., their steadiness is determined by the stability of the written patterns.Studies in piezoelectric hysteresis loops presented in [41] permitted us to unambiguously relate these currents to a static DWC.Preliminary estimates have shown [41] that the conduction at DWs is at least five orders of magnitude higher than in surrounding areas.
The existence of an enhanced static conduction at DWs permits one to regard them as stable conducting wires embedded into an insulating matrix.As mentioned above, there is evidence of an electrostatic repulsion between closely-spaced domains in LiNbO3 [31,32], which is evidently related to charge accumulation at DWs.We assume that domain coalescence in sample S1 is due to the grounding of space charges accumulated at DWs through the bottom metal interlayer.Figure 6a,b display, respectively, a PFM phase image of a written grating and a line profile of currents measured by conductive atomic force microscopy (C-AFM) method; current peaks I max are observed at DWs. Figure 6c illustrates an increase of I max with increasing measuring voltage U tip (the measuring voltage is positive, thus directed along P up ).The current peaks at DWs persist during observation times of up to several months; i.e., their steadiness is determined by the stability of the written patterns.Studies in piezoelectric hysteresis loops presented in [41] permitted us to unambiguously relate these currents to a static DWC.Preliminary estimates have shown [41] that the conduction at DWs is at least five orders of magnitude higher than in surrounding areas.The existence of an enhanced static conduction at DWs permits one to regard them as stable conducting wires embedded into an insulating matrix.As mentioned above, there is evidence of an electrostatic repulsion between closely-spaced domains in LiNbO 3 [31,32], which is evidently related to charge accumulation at DWs.We assume that domain coalescence in sample S1 is due to the grounding of space charges accumulated at DWs through the bottom metal interlayer.
To support this assumption, we performed writing of domain chains in sample S2.The fundamental distinction of sample S2 (Figure 1b) from sample S1 (Figure 1a) is the absence of a metal interlayer between LiNbO 3 film and the insulating SiO 2 substrate.
Figure 7 presents the formation of domain chains written in sample S2 by the same procedure as in S1.The observed domain evolution is dramatically different from that in S1 (Figure 4).In Figure 7a-c, PFM phase images present the chains written with decreasing distances Λ between the writing points (bottom-up); Λ was reduced from 1000 to 100 nm.The images shown in Figure 7a-c   As can be seen, the fundamental distinctions of the domain formation in S2 from that in S1 are first an irregularity and discreteness of all written patterns, and second, their instability.The domain diameter decreases from the chain "heads" (the starting writing points) to "tails" (from right to left in Figure 7a,b).At minimum specified distances between the writing points, a chain remains discrete.On turning-off Utip, the chains rearrange over the course of tens of minutes, coming to a stable shape which then persists in real-time.The observed irregular patterns qualitatively resemble chaotic patterns appearing at short inter-domain distances when writing domain chains in thin LiNbO3 crystals [33].These effects were interpreted as a manifestation of screening with emphasis on the humidity influence [33].A fundamental difference in domain formation in samples S1 and S2 cannot be interpreted in this framework, since all results described above were obtained at an identical humidity of 40%.
The attempts made to write domain gratings by raster lithography in sample S2 failed, since the arising patterns were irregular and quite unstable.This ruled out the possibility of measurements of DWC in S2.
The difference in domain formation in samples S1 and S2 supports our assumption that in S1 the charges accumulated at DWs are grounded through the metal inter-layer.This grounding eliminates the inter-domain electrostatic repulsion, which impedes the domain coalescence.Additionally, it assists in the establishment of charge equilibrium.Stable domain patterns in sample S1 are observed immediately on writing (i.e., the charge equilibrium is achieved instantaneously).In S2, a slow rearrangement of written patterns to stable shapes occurs over the course of tens of minutes (Figure 7), which evidently means a slow approach to equilibrium.
Our conclusion concerning the grounding through DWs is still qualitative and requires deeper investigations.At the same time, it is consistent with the observations mentioned in [38,39], according to which DWs serve as "nanoscale vias" assisting in controlled domain fabrication.
We comment qualitatively on the observed static DWC.Until recently, it was attributed to the accumulation of a screening charge on inclined domain walls (e.g., [42]).In particular, a static conductivity observed in domain patterns of various orientation fabricated in (15-500)-μm-thick LiNbO3 plates [38,39] was unambiguously accounted for by this model.However, the results presented in [41] and cited here differ fundamentally from [38,39] because the currents observed in As can be seen, the fundamental distinctions of the domain formation in S2 from that in S1 are first an irregularity and discreteness of all written patterns, and second, their instability.The domain diameter decreases from the chain "heads" (the starting writing points) to "tails" (from right to left in Figure 7a,b).At minimum specified distances between the writing points, a chain remains discrete.On turning-off U tip , the chains rearrange over the course of tens of minutes, coming to a stable shape which then persists in real-time.The observed irregular patterns qualitatively resemble chaotic patterns appearing at short inter-domain distances when writing domain chains in thin LiNbO 3 crystals [33].These effects were interpreted as a manifestation of screening with emphasis on the humidity influence [33].A fundamental difference in domain formation in samples S1 and S2 cannot be interpreted in this framework, since all results described above were obtained at an identical humidity of 40%.
The attempts made to write domain gratings by raster lithography in sample S2 failed, since the arising patterns were irregular and quite unstable.This ruled out the possibility of measurements of DWC in S2.
The difference in domain formation in samples S1 and S2 supports our assumption that in S1 the charges accumulated at DWs are grounded through the metal inter-layer.This grounding eliminates the inter-domain electrostatic repulsion, which impedes the domain coalescence.Additionally, it assists in the establishment of charge equilibrium.Stable domain patterns in sample S1 are observed immediately on writing (i.e., the charge equilibrium is achieved instantaneously).In S2, a slow rearrangement of written patterns to stable shapes occurs over the course of tens of minutes (Figure 7), which evidently means a slow approach to equilibrium.Our conclusion concerning the grounding through DWs is still qualitative and requires deeper investigations.At the same time, it is consistent with the observations mentioned in [38,39], according to which DWs serve as "nanoscale vias" assisting in controlled domain fabrication.
We comment qualitatively on the observed static DWC.Until recently, it was attributed to the accumulation of a screening charge on inclined domain walls (e.g., [42]).In particular, a static conductivity observed in domain patterns of various orientation fabricated in (15-500)-µm-thick LiNbO 3 plates [38,39] was unambiguously accounted for by this model.However, the results presented in [41] and cited here differ fundamentally from [38,39] because the currents observed in [38,39] only appeared under a photoactive illumination.This means that an ultra-low dark conductivity of LiNbO 3 could not provide a sufficient charge density at DWs in darkness.A drastic jump of the conduction at DWs observed in our case is obviously related to reasons other than the screening of macroscopically inclined domain walls.The number of approaches to the DWC grows permanently, but no general model has been proposed so far.For example, recent experiments in periodically-poled LiNbO 3 [43] have shown that 180 • DWs in these artificially created domain patterns are essentially meandered, and contain local inclinations and even head-to-head or tail-to-tail local configurations.A local charging of DWs occurring at these nonunformities might be responsible for DWC.
Interestingly, the charge accumulation/depletion at DWs in oxide ferroelectrics are usually discussed in the framework of the dominant role of oxygen vacancies (e.g., [34,37]).According to the current concept of the LiNbO 3 intrinsic defect structure [16], congruently melting LiNbO 3 (CLN) crystals are free of O-vacancies, so the microscopic mechanism of DWC in this material can be related to quite different charge-transport schemes.

Materials and Methods
The samples under study were produced of congruently melting LiNbO 3 (CLN).Ion-sliced z-cut CLN films forming S1 and S2 samples were either 0.5 or 0.3 µm thick.In sample S1 (Figure 1a), the Au/Cr layer incorporated between the bottom film surfaces and the SiO 2 layer was 100 nm thick.In all samples, the SiO 2 layer was 1.4 µm thick.All samples were of the total size X × Y × Z = 11 × 9 × 0.5 mm 3 .
The local polarization reversal was induced by applying dc-voltages to a conductive AFM tip contacting the sample surface.To create isolated domains, dc-voltage with a given magnitude U tip and rising pulse duration t p (or, vice versa, with a fixed t p and rising U tip ) was applied step-by-step to the tip, U tip and t p ranging from 0 to 50 V and from 0.1 to 1000 ms, respectively.At each step, this surface region was scanned by piezoelectric force microscopy (PFM).Based on these data, the dependences D(U tip ) for t p = const and D(t p ) for U tip = const were constructed.2D domain patterns were written by raster lithography method with graphic templates, whereupon they were examined by PFM scanning.PFM amplitude and phase images of written patterns were obtained by measuring the electromechanical response signal H f .
where d 33 is the piezoelectric coefficient; k is the force constant of the tip, C is the tip-sample capacity, is the average contact potential difference between the tip and the crystal surface, and U ac is the ac voltage between the tip and the electroded counter surface.PFM images consist of x-y maps of the amplitude and phase PFM signal.The conduction in the domain gratings written by raster lithography method was measured by the conductive atomic force microscopy (C-AFM).C-AFM maps were obtained by applying positive bias voltages U tip in the range from 2 to 5 V between the grounded conductive tip and the Cr/Au interlayer.
All AFM experiments were carried out with an NTEGRA PRIMA AFM (NT-MDT, Moscow, Russia).Si probes with Pt conducting coating (SPM-PIT, Bruker, Billerica, USA) were utilized; the tip radius R = 20 nm and 50 nm, the cantilever stiffness k ~2.8 N/m, and resonance frequency f ~75 kHz.

Conclusions
In summary, we have shown that domain writing by AFM-tip voltages in ion-sliced LiNbO3 films permits the manipulation of the sizes and shapes of written stable patterns in wide limits from nanosized domain dots to large (of tens of microns) arbitrarily-shaped patterns by means of varying the exposure conditions and interdomain spacing.The compliance of these films to domain patterning make them an appropriate laboratory medium for studies on the fabrication of nonlinear photonic crystals [20] and optical-frequency conversion on them.Additionally, studies in AFM-domain writing in these films can be helpful for analyzing the factors determining storage density in memory systems based on domain writing in thin layers.

Figure 1 .
Figure 1.Schematic presentation of an atomic force microscope (AFM)-tip domain writing in samples (a) S1 and (b) S2 and (c) the written domains (Pup and Pdown show the initial and reversed polarization, respectively, DW denotes domain walls); (d) exemplifies isolated domains written by Utip = 50 V, tp = 0.1 ms.

Figure 1 .
Figure 1.Schematic presentation of an atomic force microscope (AFM)-tip domain writing in samples (a) S1 and (b) S2 and (c) the written domains (P up and P down show the initial and reversed polarization, respectively, DW denotes domain walls); (d) exemplifies isolated domains written by Utip = 50 V, tp = 0.1 ms.

Figure 2 .
Figure 2. (a) Domain diameter vs. voltage for t p = 1, 10 and 1000 ms (squares, circles, and triangles, respectively); (b) the threshold voltages of domain appearance at different exposure times.

Crystals 2017, 7 ,
x FOR PEER REVIEW 4 of 11 velocity VDW) against the domain diameter D. The velocity was taken from D(tp) as VDW = ΔDi/Δti, where ΔDi is the increment of D in a time Δt.The obtained nonmonotonic curves VDW(D) are displayed in Figure 3b.Comparison of Figure 3a,b shows that a "saddle" in curves D(tp) corresponds to a sharp slowing-down (practically, to stopping) of DW motion.

Figure 3 .
Figure 3. (a) Domain diameter versus exposure time for Utip = 35, 45, and 50 V (denoted by triangles, circles, and squares, respectively); (b) Velocity of domain widening against the domain diameter for 35 and 50 V (the left and right curves, respectively).

Figure 3 .
Figure 3. (a) Domain diameter versus exposure time for U tip = 35, 45, and 50 V (denoted by triangles, circles, and squares, respectively); (b) Velocity of domain widening against the domain diameter for 35 and 50 V (the left and right curves, respectively).

Figure
Figure 5a,b present PFM images of domain gratings written in a sample S1 by raster lithography.The grating periods are Λ = 300 and 2000 nm, the grating sizes are of 4 × 4 µm 2 and 20 × 20 µm 2 , the total times of writing of the smaller and larger patterns were 30 and 300 s, respectively.The patterns are rather regular with the off-duty ratios of 0.5 and 0.6, respectively.Figure5cshows a PFM image of an arbitrary-shaped domain pattern written in S1; the reversed domain areas are dark.A compliance of samples S1 to shaping of domain patterns of any specified design seems to be akin to the effect of domain coalescence described above.

Figure 5 .
Figure 5. (a), (b) and (c): phase PFM images of domain gratings and of an arbitrary-shaped pattern written in samples S1 by raster lithography.Periods of the left and right gratings are Λ = 300 and 2000 nm, respectively, the bright contrast corresponds to the switched stripes.In (c) the dark contrast corresponds to the switched areas.

Figure 5 .
Figure 5. (a), (b) and (c): phase PFM images of domain gratings and of an arbitrary-shaped pattern written in samples S1 by raster lithography.Periods of the left and right gratings are Λ = 300 and 2000 nm, respectively, the bright contrast corresponds to the switched stripes.In (c) the dark contrast corresponds to the switched areas.

Figure 5 .
Figure 5. (a-c): phase PFM images of domain gratings and of an arbitrary-shaped pattern written in samples S1 by raster lithography.Periods of the left and right gratings are Λ = 300 and 2000 nm, respectively, the bright contrast corresponds to the switched stripes.In (c) the dark contrast corresponds to the switched areas.

Figure 6 .
Figure 6.Schematic presentation of the domain-wall conduction in a written domain grating.(a) PFM phase image of a domain grating with Λ = 3.6 µm; (b) a line profile of conductive atomic force microscopy (C-AFM) map exemplifies current anomalies observed at DWs; the current peaks Imax under Utip ≤ 5 V are in the range of 20-100 pA, whereas away from DWs Imax < 0.03 pA (the sensitivity of our equipment); (c) Imax in a fixed DW point vs. Utip.

Figure
Figure6a,b display, respectively, a PFM phase image of a written grating and a line profile of currents measured by conductive atomic force microscopy (C-AFM) method; current peaks Imax are observed at DWs. Figure6cillustrates an increase of Imax with increasing measuring voltage Utip (the measuring voltage is positive, thus directed along Pup).The current peaks at DWs persist during observation times of up to several months; i.e., their steadiness is determined by the stability of the written patterns.Studies in piezoelectric hysteresis loops presented in[41] permitted us to unambiguously relate these currents to a static DWC.Preliminary estimates have shown[41] that the conduction at DWs is at least five orders of magnitude higher than in surrounding areas.The existence of an enhanced static conduction at DWs permits one to regard them as stable conducting wires embedded into an insulating matrix.As mentioned above, there is evidence of an electrostatic repulsion between closely-spaced domains in LiNbO3[31,32], which is evidently related to charge accumulation at DWs.We assume that domain coalescence in sample S1 is due to the grounding of space charges accumulated at DWs through the bottom metal interlayer.

Figure 6 .
Figure 6.Schematic presentation of the domain-wall conduction in a written domain grating.(a) PFM phase image of a domain grating with Λ = 3.6 µm; (b) a line profile of conductive atomic force microscopy (C-AFM) map exemplifies current anomalies observed at DWs; the current peaks I max under Utip ≤ 5 V are in the range of 20-100 pA, whereas away from DWs I max < 0.03 pA (the sensitivity of our equipment); (c) I max in a fixed DW point vs. U tip .
were obtained at 6, 12, and 24 min subsequent to writing.Crystals 2017, 7, x FOR PEER REVIEW 7 of 11writing points (bottom-up); Λ was reduced from 1000 to 100 nm.The images shown in Figure7a-cwere obtained at 6, 12, and 24 min subsequent to writing.

Figure 7 .
Figure 7. Evolution of domain chains written in sample S2, subsequent to writing.PFM phase images (a-c) were obtained in 6, 12, and 24 min, respectively, subsequent to writing.The chains were written with the distances between writing points Λ = 1000, 500, 200, 100 nm (bottom-up).