Evolution of Nanodomains and Formation of Self-Organized Structures during Local Switching in X-Cut LNOI

: The features of nanodomain growth during local switching in X-cut lithium niobate on insulator (LNOI) were comprehensively studied using the biased tip of a scanning probe microscope. The obtained results were discussed in terms of the kinetic approach. The revealed differences in domain growth in bulk LN and LNOI were attributed to the higher bulk conductivity of LNOI. The obtained inﬂuence of humidity on the shape and growth of isolated domains was attributed to the water meniscus. Analysis of the transition between the “forward growth” and “sideways growth” stages was performed by switching to the stripe electrode. A sand-glass-shaped domain was formed due to growth in the opposite direction after the domain touched the electrode. Stable periodical domain structures down to 300 nm were created and characterized in LNOI. Highly ordered comb-like domains of various alternating lengths, including four- and eight-fold increase periods, were produced by performing biased tip scanning along the Y axis. The obtained knowledge is important for the future development of nanodomain engineering methods in monocrystalline ferroelectric thin ﬁlms on insulators.

It is known that the creation of stable periodical domain structures with nanoscale period reproducibility (periodical poling) can improve the efficiency of light frequency conversion by producing a quasi-phase matching (QPM) effect [23][24][25]. Numerous prototypes of very efficient wavelength converters, including second harmonic generators (SHGs), sumfrequency generators (SFGs), and difference frequency generators (DFGs) [14,15,[26][27][28], have already been demonstrated. Particular attention has been paid to the production of periodically poled LNOI (PPLNOI) with submicron periods, to enable backward optical harmonic generation, which could be used to create a mirrorless optic parametric oscillator (MOPO) [29]. The production of PPLNOI with submicron periods remains a challenging task, due to domain-domain interactions and backswitching in LN crystals. The creation of periodical domain structures down to 200 nm in Z-cut LNOI using the biased tip of a scanning probe microscope (SPM) [30,31] has been reported recently.
Nowadays, SPM is successfully used in LNOI wafers to create domain structures and domain imaging using piezoelectric force microscopy (PFM) [32][33][34][35][36][37]. Investigations have primarily been performed on Z-cut LNOI. Periodical poling in X-cut LNOI has been realized using lithographically produced electrodes with a minimal period of 600 nm [15,26,38]. However, the creation of domain structures with lower periods in X-cut LNOI, which are attractive for applications, has still not been studied. This paper is devoted to an investigation of the formation of domain structures during local switching in X-cut LNOI. The study of the growth, interaction, and stability of isolated nanodomains and periodical domain structures facilitated the creation of X-cut PPLNOI with a submicron period. The formation of self-organized nanoscale domain structures was revealed and discussed.

Materials and Methods
The studied X-cut LNOI wafers (LN film/SiO 2 /LN substrate) were provided by Jinan Jingzheng Electronics (NanoLN, Jinan, China). The thicknesses of different layers of the wafer were as follows: LN film-300 nm; SiO 2 layer-1 µm; LN substrate-500 µm. Domain growth in LN thin film and bulk X-cut LN crystal with a thickness of 500 µm was compared. The surface roughness of both samples was below 1 nm.
The scanning probe microscope Ntegra Aura (NT-MDT, Zelenograd, Russia) was used for domain creation and imaging. The isolated domains were created using local switching by single DC pulses with an amplitude of 50 to 300 V and duration of 10 ms to 100 s (Figure 1a). Comb-like domains were formed by scanning using a biased tip along the Z axis ( Figure 1c). Moreover, we studied the domain growth towards the Pt 30 nm-thick and 200 µm-wide stripe electrode deposited by magnetron sputtering and oriented along the Y axis ( Figure 1b). The electrode pattern was produced using electron beam lithography by the "lift-off" process. All the measurements were carried out in a nitrogen atmosphere with relative humidity (RH), controlled by an internal sensor in SPM, with an accuracy of about 1%.
ing the biased tip of a scanning probe microscope (SPM) [30,31] has been rep cently.
Nowadays, SPM is successfully used in LNOI wafers to create domain struct domain imaging using piezoelectric force microscopy (PFM) [32][33][34][35][36][37]. Investigati primarily been performed on Z-cut LNOI. Periodical poling in X-cut LNOI has b ized using lithographically produced electrodes with a minimal period of [15,26,38]. However, the creation of domain structures with lower periods in X-cu which are attractive for applications, has still not been studied. This paper is devoted to an investigation of the formation of domain structu ing local switching in X-cut LNOI. The study of the growth, interaction, and sta isolated nanodomains and periodical domain structures facilitated the creation PPLNOI with a submicron period. The formation of self-organized nanoscale structures was revealed and discussed.

Materials and Methods
The studied X-cut LNOI wafers (LN film/SiO2/LN substrate) were provided Jingzheng Electronics (NanoLN, Jinan, China). The thicknesses of different laye wafer were as follows: LN film-300 nm; SiO2 layer-1 µm; LN substrate-500 main growth in LN thin film and bulk X-cut LN crystal with a thickness of 500 compared. The surface roughness of both samples was below 1 nm.
The scanning probe microscope Ntegra Aura (NT-MDT, Zelenograd, Rus used for domain creation and imaging. The isolated domains were created us switching by single DC pulses with an amplitude of 50 to 300 V and duration of 100 s (Figure 1a). Comb-like domains were formed by scanning using a biased t the Z axis ( Figure 1c). Moreover, we studied the domain growth towards the P thick and 200 µm-wide stripe electrode deposited by magnetron sputtering and along the Y axis ( Figure 1b). The electrode pattern was produced using electr lithography by the "lift-off" process. All the measurements were carried out in a atmosphere with relative humidity (RH), controlled by an internal sensor in SPM accuracy of about 1%. Domain imaging was carried out using PFM and an electron channeling (ECM). We used single-frequency PFM with a voltage amplitude of 3-6 V and a fr far from the resonance. PFM collects the piezoelectric signal from a depth of hun nanometers [39]. The ECM is based on the change in intensity of the back-scatte trons, depending on the crystallographic structure of the sample [40]. The high se of ECM to the surface crystallographic structure facilitates ferroelectric domain in the layer with a depth of tens of nanometers [41][42][43]. The ECM was performed EVO-LS10 scanning electron microscope (Carl Zeiss NTS, Jena, Germany) using a selected, four-quadrant, back-scattered electron detector. Domain imaging was carried out using PFM and an electron channeling method (ECM). We used single-frequency PFM with a voltage amplitude of 3-6 V and a frequency far from the resonance. PFM collects the piezoelectric signal from a depth of hundreds of nanometers [39]. The ECM is based on the change in intensity of the back-scattered electrons, depending on the crystallographic structure of the sample [40]. The high sensitivity of ECM to the surface crystallographic structure facilitates ferroelectric domain imaging in the layer with a depth of tens of nanometers [41][42][43]. The ECM was performed with an EVO-LS10 scanning electron microscope (Carl Zeiss NTS, Jena, Germany) using an angle-selected, four-quadrant, back-scattered electron detector.

Isolated Domains
The growth of the isolated domains in the polar direction, under local switching, was studied in an X-cut bulk crystal and a thin film. The domains were created by rectangular pulses with voltages ranging from 75 to 200 V and a 5 s duration at an RH of 30%. The dependence of the domain shape on the pulse polarity was analyzed.
In the LNOI film, the application of negative pulses led to the formation of wedge-like domains, whereas the application of positive pulses led to the appearance of domains with several "spikes" (Figure 2a). The number of "spikes" decreased with the pulse amplitude. In the bulk LN crystals, long narrow domains were formed after the application of negative pulses, whereas wedge-like domains appeared after the application of positive pulses

Isolated Domains
The growth of the isolated domains in the polar direction, under local switching, was studied in an X-cut bulk crystal and a thin film. The domains were created by rectangular pulses with voltages ranging from 75 to 200 V and a 5 s duration at an RH of 30%. The dependence of the domain shape on the pulse polarity was analyzed.
In the LNOI film, the application of negative pulses led to the formation of wedgelike domains, whereas the application of positive pulses led to the appearance of domains with several "spikes" (Figure 2a). The number of "spikes" decreased with the pulse amplitude. In the bulk LN crystals, long narrow domains were formed after the application of negative pulses, whereas wedge-like domains appeared after the application of positive pulses (Figure 2b    For an explanation of the obtained difference in the domain shape and voltage dependences of the domain sizes between the bulk crystal and LNOI, the domain growth was considered in terms of the kinetic approach [44]. According to the kinetic approach, domain growth occurs under the polar component of an electric field (E loc . z ) by generating the elementary steps with charged kinks and kink motion along the wall. E loc . z represents the sum of the external field applied by the tip (E ex·z ), the local depolarization field (E dep·z ), and the screening field (E scr·z ).
Step generation occurs at the domain base in the vicinity of the tip, under the action of E ex . z . It is close to zero at a distance of around one micron from the tip.
Domain elongation (forward growth) is caused by partially screened E dep . z produced far from the domain base by charged kinks, which stimulates kink motion. The screening field E scr . z slows down the kink motion and prevents spontaneous backswitching after pulse termination.
The screening effectiveness depends on the conductivity of the charged domain walls (CDWs) of the wedge-like domains and bulk conductivity. It is necessary to take into account that the "head-to-head" CDWs that appeared after the application of the positive pulse possess at least an order of magnitude higher conductivity than the "tail-to-tail" CDWs that appeared after the application of the negative pulse [45,46]. Moreover, the conductivity in LNOI (10 −13 Sm/mm) is about five orders of magnitude higher than that in bulk crystals [47,48], due to the point defects induced by ion irradiation and incompletely removed by annealing.
In bulk LN, formation of the stable wedge-like domain under the positive pulses can be attributed to the high conductivity of the "head-to-head" CDWs, which provide effective screening and, thus, prevent backswitching.
In LNOI, more effective screening, caused by high bulk conductivity, diminishes the field produced by kinks. This results in a decrease in the domain elongation by kink motion and an increase in the CDW tilt, which leads to the formation of additional narrow "spikes" [49].
Formation of the narrow wedge-like domains under negative pulses in bulk LN can be attributed to the pronounced backswitching effect, caused by the low conductivity of "tail-to-tail" CDWs. In this case, the domain width determined by the interaction of approaching walls is independent of the applied voltage.
Domains created in LNOI by negative pulses have low conductive "tail-to-tail" CDWs, which leads to the growth of long wedge-like domains. At the same time, the high bulk conductivity prevents backswitching and the width of the created wedge-like domain persists after pulse termination.
The influence of humidity on domain growth was studied at an RH ranging from 20% to 70%, with pulses of −125 V to −200 V and a duration of 1 s (Figure 3). Three RH regions, characterized by different domain shapes, were distinguished.
For low humidity (RH < 45%), the length of the wedge-like domains is almost independent of RH, whereas the significant increase in the domain width leads to a decrease in the aspect ratio (Figure 3b-d).
For moderate humidity (45% < RH < 60%), the formation of domains with a wide base and narrow tail was observed. The base width was almost independent of RH, whereas the base length slightly decreased (Figure 3c,d).
For high humidity (RH > 60%), the base width decreased significantly with RH and the domain length continued to decrease (Figure 3c,d); thus, the aspect ratio increased significantly (Figure 3b).  For low humidity (RH < 45%), the length of the wedge-like domains is almost ind pendent of RH, whereas the significant increase in the domain width leads to a decrea in the aspect ratio (Figure 3b-d).
For moderate humidity (45% < RH < 60%), the formation of domains with a wide ba and narrow tail was observed. The base width was almost independent of RH, where the base length slightly decreased (Figure 3c,d).
For high humidity (RH > 60%), the base width decreased significantly with RH an the domain length continued to decrease (Figure 3c,d); thus, the aspect ratio increas significantly (Figure 3b).
Domain shape transformation with RH can be attributed to the formation and grow of a water meniscus in the tip-surface contact [50]. The appearance of the small menisc at RH < 45% led to the delocalization of Eex.z and an increase in the domain width. T continuous growth of the meniscus at a moderated RH improved the screening of Edep which led to the formation of a domain with a wide base and narrow tail. The decrease domain width at a high RH was attributed to the significant diminishing of Eex.z, due strong delocalization.
The domain growth towards the stripe electrode was studied for switching usi pulses with various voltages and durations at an RH of 30% (Figure 4a-d). The biased t was placed 4 µm from the grounded stripe electrode. The nonuniform domain contrast the PFM (Figure 4a,b) and ECM (Figure 4c,d) images allowed the local domain depth be qualitatively characterized and the domain growth to be restructured. The darker r gions correspond to the deeper domain. Domain shape transformation with RH can be attributed to the formation and growth of a water meniscus in the tip-surface contact [50]. The appearance of the small meniscus at RH < 45% led to the delocalization of E ex . z and an increase in the domain width. The continuous growth of the meniscus at a moderated RH improved the screening of E dep . z , which led to the formation of a domain with a wide base and narrow tail. The decrease in domain width at a high RH was attributed to the significant diminishing of E ex . z , due to strong delocalization.
The domain growth towards the stripe electrode was studied for switching using pulses with various voltages and durations at an RH of 30% (Figure 4a-d). The biased tip was placed 4 µm from the grounded stripe electrode. The nonuniform domain contrast in the PFM (Figure 4a,b) and ECM (Figure 4c,d) images allowed the local domain depth to be qualitatively characterized and the domain growth to be restructured. The darker regions correspond to the deeper domain.  The wedge-like domains with CDWs started to grow towards the electrode. After the domain had touched the electrode, the domain growth from the electrode towards the tip led to the formation of "head-to-head" CDWs, thus creating a sand-glass-shaped domain. The subsequent growth promoted its rapid transformation to the stripe domain with a The wedge-like domains with CDWs started to grow towards the electrode. After the domain had touched the electrode, the domain growth from the electrode towards the tip led to the formation of "head-to-head" CDWs, thus creating a sand-glass-shaped domain. The subsequent growth promoted its rapid transformation to the stripe domain with a neutral domain wall. The obtained results allowed the transition between the main stages of the domain evolution-from "forward growth" to "sideways growth"-to be observed [51].

Periodical Domain Structures
Arrays of isolated domains with various periods were created to investigate domaindomain interactions. Domain length alternation in arrays with small periods had already been demonstrated on polar and nonpolar cuts of bulk LN [52,53]. A decrease in the period leads to intermittent quasiperiodic and chaotic behavior. This effect has never been observed in Z-cut LNOI [33].
We obtained a uniform domain length for the entire range of periods from 4 to 0.3 µm (Figure 5a-c). The width of the domain increased over the period, while the aspect ratio essentially decreased from 25 to 7 (Figure 5e,f). The domain length increased linearly with voltage ( Figure 5g). The variation in domain lengths was obtained for the 300 nm period, switched at voltages above −200 V (Figure 5d,g). It is necessary to point out that the achieved domain length above 3 µm is sufficient for LN waveguides with a width of around 1 µm.

Self-Organized Domain Structures
The self-organized domain structures were formed during scanning with a biased tip along the Y axis with a voltage of −175 V and scanning rate of 5 µm/s at various levels of RH ( Figure 6). The strongly pronounced dependence of the domain structure on RH was revealed. Only a few isolated narrow domains appeared in dry nitrogen and at an RH of 60% (Figure 6a,c). Self-organized "comb-like" structures, consisting of narrow domains, were formed at a humidity of around 25% (Figure 6b). A similar effect had been previously obtained on nonpolar cuts of bulk LN [54].

Self-Organized Domain Structures
The self-organized domain structures were formed during scanning with a biased tip along the Y axis with a voltage of −175 V and scanning rate of 5 µm/s at various levels of RH ( Figure 6). The strongly pronounced dependence of the domain structure on RH was revealed. Only a few isolated narrow domains appeared in dry nitrogen and at an RH of 60% (Figure 6a,c). Self-organized "comb-like" structures, consisting of narrow domains, were formed at a humidity of around 25% (Figure 6b). A similar effect had been previously obtained on nonpolar cuts of bulk LN [54]. The self-organized domain structures were formed during scanning with a biased tip along the Y axis with a voltage of −175 V and scanning rate of 5 µm/s at various levels of RH ( Figure 6). The strongly pronounced dependence of the domain structure on RH was revealed. Only a few isolated narrow domains appeared in dry nitrogen and at an RH of 60% (Figure 6a,c). Self-organized "comb-like" structures, consisting of narrow domains, were formed at a humidity of around 25% (Figure 6b). A similar effect had been previously obtained on nonpolar cuts of bulk LN [54].  The self-organization was attributed to the electrostatic interaction betwee boring domains in the array, where large (L) or medium (M) domains suppre growth of the neighboring domains and led to the formation of tiny (T) and sma mains. It should be noted that only quadruple-and double-length periods had b viously observed in the bulk LN [53]; the eight-fold increase in the periods was o for the first time in the current study.
The obtained knowledge is important for the future development of dom neering methods in monocrystalline ferroelectric thin films on insulators. It form sis for the implementation of periodical domain pattering in mass production switching on X-cut thin films using lithographically produced electrodes with su periods. The self-organization was attributed to the electrostatic interaction between neighboring domains in the array, where large (L) or medium (M) domains suppressed the growth of the neighboring domains and led to the formation of tiny (T) and small (S) domains. It should be noted that only quadruple-and double-length periods had been previously observed in the bulk LN [53]; the eight-fold increase in the periods was observed for the first time in the current study.
The obtained knowledge is important for the future development of domain engineering methods in monocrystalline ferroelectric thin films on insulators. It forms the basis for the implementation of periodical domain pattering in mass production by local switching on X-cut thin films using lithographically produced electrodes with submicron periods.

Conclusions
A comprehensive investigation of the features of domain growth during local switching in X-cut LNOI, using the biased tip of a scanning probe microscope, was performed. The obtained results have been discussed in terms of the kinetic approach. The revealed differences in domain growth in bulk LN and LNOI are attributed to the unusual screening of the depolarization field, caused by the high bulk conductivity of LNOI. The obtained significant influence of humidity on the shape and growth of isolated domains in LNOI is attributed to the formation of the water meniscus.
The transition between the main stages of the domain evolution-"forward growth" and "sideways growth"-was performed by local switching toward the stripe electrode in LNOI. It was shown that after the domain had touched the electrode, the growth in the opposite direction from the electrode toward the tip led to the formation of a sand-glassshaped domain. The subsequent domain growth promoted its rapid transformation to the stripe domain with neutral walls.
It was shown that weak domain-domain interactions enabled the creation of periodical domain structures with submicron periods in LNOI. Stable periodical domain structures with periods down to 300 nm were created and characterized, which are essentially lower than those achieved using lithographically produced electrodes [15,26,38].
Highly ordered comb-like domains of various alternating lengths, including four-and eight-fold increases in periods, were produced using biased tip scanning along the Y axis.
The obtained knowledge is important for the future development of domain engineering methods in monocrystalline ferroelectric thin films on insulators. It forms the basis for the implementation of periodical domain pattering by local switching on X-cut thin films using lithographically produced electrodes with submicron periods.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.