Self-organized formation of domain arrays in TGS crystal by moving SPM tip

1. Introduction

Ferroelectric materials are commonly used in wide range of applications from nonlinear optics¹ and pyroelectric detection^2,3 to nonvolatile data storage^4,5 and nano-electronics^6,7 due to their high functional properties.

The uniaxial ferroelectric crystals possess the simple domain structure with $180^{\circ }$ domain walls only.⁸ This is the reason to use them as the main materials for the domain engineering,^{9,10,11,12,13} which represents the creation of the stable tailored domain patterns in commercially available ferroelectrics for improvement of the characteristics important for applications. The improvement of the piezoelectric properties can be achieved by creating domain patterns with high concentration of the domain walls (domain wall engineering).¹⁴ The tailored periodical domain structures allow to realize the light frequency transformation with record efficiency due to the realization of quasi-phase matching conditions.¹ The periodical poling can be created by external field application through the periodical stripe electrodes⁹ or by local switching using biased tip of scanning probe microscope (SPM).¹⁵ Further improvement of the domain engineering and domain wall engineering requires deep study of the domain structure evolution in uniaxial ferroelectrics.

Domain structure evolution during polarization reversal can be used for studying the kinetics of the solid–solid first-order phase transitions. The creation of self-organized structures during phase transformation presents is an important fundamental problem.¹⁶

The formation of the variety of domain shapes has been considered in terms of the universal kinetic approach to the domain growth based on analogy of domain and crystal growth.¹⁷ It is necessary to point out that almost all experimental study of the domain structure evolution is based on domain imaging on the sample surface. Whereas the micron-scale domains in bulk plates of ferroelectric crystals are always nonthrough with very complicated 3D domain shape.¹⁸

The local switching on polar^19,20,21 and nonpolar^22,23 cuts of uniaxial single crystals under the action of inhomogeneous electric field created by a biased SPM tip and domain imaging by piezoelectric force microscopy (PFM)^24,25 allows to study with high-spatial resolution the forward domain growth, leading to the formation in the crystal bulk of the wedge-like domains with charge domain walls (CDW).

It was demonstrated recently that the narrow stripe domains appeared at the polar surface in LN crystals possess the comb-like shape.²⁶ The shape transformation from comb-like to array of circular domains (1D–2D transition) was obtained under the action of pyroelectric field appeared in LN crystal as a result of irradiation by IR laser pulses.²⁶ The mechanism of the formation of the comb-like domain by tooth generation, when the charged domain wall tilt overcome the threshold value has been proposed.²⁷

Triglycine sulphate ((NH₂CH₂COOH)${}_3\cdot$H₂SO₄, TGS) is a uniaxial ferroelectric. Pure TGS undergoes a second-order phase transition at $49^{\circ }$C, with spontaneous polarization oriented along the $b$ axis. During this phase, transition space group changes from nonpolar $P{2}_1/m$ in paraelectric phase to polar $P{2}_1$ in ferroelectric phase.

The different axial systems have been used for the indication of TGS crystal.²⁸ In this work, we use axial system presented in Ref. 29 with angle between $a$ and $c$ axes equal to $105^{\circ }40^{\prime }$.

Excellent pyroelectric properties allow to use this material for high sensitive infrared receivers and detectors.^30,31 The TGS doping or deuteration is commonly used for tuning its $T_C$ and enhancement of pyroelectric properties.^32,33 During the phase transition from the paraelectric state, an initial domain structure arises, consisting of antiparallel lamellar domains. This structure is nonequilibrium and slowly relaxes with time.^34,35 Equilibrium domain shape in TGS is lenticular.³⁶ Both lenticular and lamellar domains are elongated roughly perpendicular to the $c$ axis.³⁷

It looks like the crystals of TGS family are convenient for investigation of the domain growth during local switching due to their low threshold fields and easy creation of atomically flat polar surfaces by sample cleavage.³⁷

Various SPM techniques can be used for domain structure imaging in TGS.^{35,38,39,40,41} The domain formation in TGS during local switching was studied by PFM.^{42,43,44,45,46,47,48} Recently, formation of 10$\mu$m-scale lenticular domains after local switching by SPM tip and self-organized “granular” nanodomain arrays oriented along $c$ axis into created domain after backswitching pulse were obtained.⁴⁶ Observed effect has been attributed to the interplay among bound charges, mobile H${}^{+}$ ions at the surface and the strong crystal anisotropy. Anisotropic growth of isolated domain in TGS during local switching was attributed to the stochastic nucleation for wall motion along $c$ direction and deterministic nucleation for wall motion along $a$ direction.⁴⁷ Also, the current limited wall motion regime driven by anisotropic bulk screening processes during local switching in polydomain TGS single crystals has been studied.⁴⁸ The dependence of the shape of the switched area on humidity was attributed to the change in the dominating screening mechanism from anisotropic bulk conductivity to isotropic surface conductivity through an adsorbed water layer.

In this paper, we present the investigation of self-organized formation of domain arrays in TGS crystal as a result of scanning by biased SPM tip. It was shown that the type of domain arrays depends on the scanning direction. The change of the domain shape at the polar surface from arrays of isolated domains to stripe domains has been revealed. The obtained results have been attributed to the formation of comb-like domain during scanning and its separation under the action of depolarization field. The obtained effect is important for further development of the domain engineering.

2. Materials and Methods

A deuterated TGS single crystals with degree of deuteration about 80% grown from an aqueous solution have been chosen for investigation due to their more stable domain structure. The measured phase transition temperature was $59.7^{\circ }$C. The studied samples represented the 1.5mm-thick plates with atomically flat surface over the tens-microns-width terraces made by crystal splitting perpendicular to the polar axis along the cleavage plane (010). The height of the steps (1.26nm) was equal to $b$ size of the TGS unit cell. The bottom surfaces of the studied samples were glued to the metal disk by the conductive silver paste. Temperature dependences of dielectric properties and hysteresis loops of the studied samples have been published in Ref. 48.

Local switching was realized using the Probe Nano Laboratory NTEGRA Aura (NT-MDT Spectrum Instruments, Russia) by a conductive biased SPM tip moved along crystallographic axis c and in perpendicular direction. The domain imaging at the surface was performed using PFM mode with amplitude of modulating voltage 3V and frequency 20kHz far from contact resonance. We used NSC18 probe sensors with a titanium–platinum conductive coating (Mikro Masch, Sofia, Bulgaria) with a tip curvature radius of 35nm, a resonance frequency of 70kHz, and a stiffness of 3.5N/m. Before switching, the samples were thermally depolarized by heating to $85^{\circ }$C, annealing at constant temperature for 60min and cooling to $30^{\circ }$C with heating/cooling rates of $5^{\circ }$C/min.

During local polarization, reversal SPM tip was moved with velocity 1$\mu$m/s and applied bias voltage ranged from 40 to 150V. All experiments were carried out in the atmosphere of dry nitrogen at constant temperature $30^{\circ }$C.

3. Results

The initial domain structure imaged just after thermal depolarization consisted of curved stripe domains with width about 5$\mu$m and short-dashed domains of submicron width (Fig. 1(a)).

For investigation of the domain growth during local switching the single-domain area of $100\times 100\mu$m² was created using scanning by biased SPM tip with a constant voltage of −100V (Fig. 1(b)). It was shown that the created single-domain state is stable enough for our investigation and did not change during several hours.

3.1. Scanning along c axis

It was demonstrated that the shape of the domains created in single domain area by moving of the biased SPM tip depends on applied voltage (Fig. 2). For scanning along $c$ axis the arrays of isolated domains with rounded shape appeared for voltage below 100V (Fig. 2(a)). The domain aspect ratio (ratio of a size along $c$ axis to a size in perpendicular direction) is close to unit. The average domain period (Fig. 2(b)) and domain width (Fig. 2(c)) increased linearly with voltage.

The change of the domain shape due to increasing of the domain length obtained for the voltage above 125V leads to increase of the average value of the aspect ratio to 2. The domain shape drastically changed from arrays to stripe domains at 150V (Fig. 2(a)).

3.2. Scanning perpendicular c axis

The shape of the created domain structure depends significantly on the scanning direction. It was shown that the scanning by the biased SPM tip perpendicular to $c$ axis led to formation of the quasi-regular array of the isolated dashed domains (Fig. 3(a)).

The threshold voltage for creation of the domain structure is about 40V. The averaged width of the dashed domains linearly increased with voltage (Fig. 3(b)) similar to the average period of the structure (Fig. 3(c)).

It is necessary to point out that increasing of the dashed domains length leads to the qualitative change of domain shape at 75V from arrays of dashed domains to solid stripe domain (Fig. 3(a)). The voltage dependence of the domain width also significantly changes at this voltage (Fig. 3(b)).

4. Discussion

The obtained formation of the discrete domain structures during scanning will be considered in terms of the kinetic approach to growth of ferroelectric domains.^9,17,49 The domain growth is considered in analogy with the crystal growth as a result of the step generation and kink motion.^17,23 The local values of the field excess $\mathrm{\Delta }E$ over the threshold values for step generation and kink motion are the driving forces of the domain growth.⁹

The change of the domain shape at the polar surface from the arrays of isolated domains to stripe domains has been revealed experimentally as a result of pulse laser irradiation of CLN crystals.²⁶ This fact has been attributed to the formation of comb-like nonthrough domains with charged domain walls in the crystal bulk.

The formation of the quasiregular comb-like domain is due to repetitive appearance of the domain spikes in the bulk during elongation of the stripe domain at the polar surface. The motion of the stripe domain end leads to increase in the tilt of the charged domain wall and, consequently, to increase in the bound charge density and depolarization field in the bulk (Fig. 5). The step generation at the wall starting in the area with the local value of the depolarization field above the threshold results in generation of a new spike at the wall in the bulk (Fig. 5). Similar effect has been observed also for formation of the jugged charged domain walls during slow wall motion in CLN crystals.^50,51

The appeared charged domain wall became unstable after biased SPM tip shift from the switched domain due to diminishing of the external field (Figs. 4(a) and 4(b)). As a result, the spontaneous backswitching under the action of the residual depolarization field starts (Fig. 4(c)). It was shown that the jugged shape of the charged domain wall leads to nonuniform distribution of the local field at the wall with maxima at the tooth and minima at the valleys.²⁶ The fast growth of the tooth to the polar surface results in the change of the comb-like domain shape (Fig. 4(d)). Finally, it results in splitting of the comb-like domain and transformation of the domain shape at the surface from stripe domain to array of circular or dashed domains (Fig. 4(e)).

The domain growth perpendicular to the scanning direction is determined by applied voltage and spatial distribution of the external field created by biased SPM tip. Decreasing of the domain width for dashed domains during backswitching is induced by sum of residual depolarization field and depolarization field appeared during the backward domain wall motion. Interaction of approaching domain walls hinders decreasing of the walls distance reduction thus stimulates formation of narrow residual stripe domains. The pronounced difference of the domain shape for different scanning directions can be attributed to significant dielectric anisotropy.⁵²

The domain wall motion is a result of step generation determined by an excess of the polar component of the local electric field $E_{\mathrm{\text{loc}}.z}$ over the threshold value $E_{\mathrm{\text{th}}.\mathrm{\text{st}}}$. It was considered that $E_{\mathrm{\text{loc}}}$ represents the superposition of the external field produced by biased SPM tip ($E_{\mathrm{\text{tip}}}$), depolarization field produced by bound charges ($E_{\mathrm{\text{dep}}}$) and external ($E_{\mathrm{\text{ex}}.\mathrm{\text{scr}}}$), and bulk ($E_{b.\mathrm{\text{scr}}}$) screening fields :

The increase of the domain width ($w_d$) is caused by the step generation under the dominant role of $E_{\mathrm{\text{tip}}.z}$. The field dependence of the velocity of domain width growth (domain wall motion) is as follows :

For used low-scanning velocity, the produced depolarization field is almost completely screened, and the obtained voltage dependence of the domain width can be fitted by the following equation :

It was revealed that the voltage dependence of the domain width is essentially different for growth of dashed domains for $U<70$V and solid stripe for $U>70$V (Fig. 3(b)).

The obtained difference of the voltage dependence of the domain width for dashed and solid stripe domain can be attributed to more pronounced backswitching effect for dashed domains. Thus, the dashed domain structure is less stable as compared with the stripe one.

The computer simulation of the spatially nonuniform CDW motion under the action of depolarization field has been done for explanation of the 1D–2D transformation of the domain shape by finite element method (FEM) using the commercial software COMSOL Multiphysics.

The simulation of CDW motion in the bulk at ZX cross- section for different distances from the biased SPM tip was performed by moving mesh and electrostatics modules in the COMSOL. The spatial distribution of the polar component of the electric field produced by biased SPM tip was simulated using stationary solver and second-order finite elements. A conical SPM tip with $40^{\circ }$ cone angle, 24$\mu$m cone length and 50nm contact radius has been considered in the simulations according to experimental conditions. The used dielectric constants of [001] TGS ${\epsilon }_{11}=8.7$, ${\epsilon }_{22}=25$, ${\epsilon }_{33}=4.7$⁵² were rotated into [010] by the Euler angles ($0^{\circ }$, $90^{\circ }$, $0^{\circ }$).

2D approach in simulation has been used with respect to middle narrow part cut along the comb-like domain. The initial sinusoidal shape of CDW in the vicinity of the SPM tip has been expected. The dependence of the local bound charge density on the domain wall on its tilt from the polar axis :

The local velocity of the CDW motion in polar direction depends on the local field access over the threshold value :

It was demonstrated that the field distribution leads to pronounce stretching of CDW far from the SPM tip whereas the ends of domain teeth remain fixed (Fig. 5). The transformation of the comb-like wall shape and appearance of the array of isolated domains took place when the domain ends grow to the polar surface.

5. Conclusion

We studied the formation of self-organized domain arrays created by moving biased tip of SPM in deuterated TGS crystals. The shape of created domains depends significantly on scanning direction and applied voltage. For scanning along c axis, the arrays of rounded isolated domains appeared for voltage ranged from 20 to 100V. The domain shape drastically changed from arrays to stripe domains at 150V. Scanning perpendicular to $c$ axis led to the formation of the quasi-regular array of the isolated dashed domains. The averaged width of the dashed domains linearly increased with voltage similar to the average period of the structure, whereas, the number of dashed domains per unit length essentially decreases. Increasing of the dashed domains length leads to the qualitative change of domain shape from the arrays of dashed domains to solid stripe domain.

The obtained formation of the discrete structures during scanning has been considered in terms of the kinetic approach to growth of ferroelectric domains. The appearance of domain arrays and stripe domains at the polar surface has been considered in terms of formation of comb-like nonthrough domain with charged domain walls in the crystal bulk. It was proposed that the formation of the comb-like domain is due to repetitive appearance of the domain spikes in the bulk during elongation of the stripe domain at the polar surface. The appeared charged domain wall became unstable after SPM tip shift due to diminishing of the external field and the spontaneous backswitching starting under the action of the residual depolarization field. The jugged shape of the charged domain wall leads to nonuniform local field at the wall with maxima at the tooth and minima at the valleys. The fast growth of the tooth to the polar surface results in transformation of the domain shape at the surface from stripe domain to array of circular or dashed domains. The difference of the domain shape for different scanning directions has been attributed to significant dielectric anisotropy. The computer simulation of the nonuniform motion of charged domain wall under the action of depolarization field allows to explain the domain shape transformation. The obtained effects emphasize the critical importance of spontaneous backswitching on the domain shape and contribute to further improvement of domain wall engineering methods.

Acknowledgments

This research was made possible by the Russian Science Foundation (Project No. 19-12-00210). The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University (Reg. No. 2968) was used with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2021-677).

ORCID

Anton P. Turygin  https://orcid.org/0000-0002-4843-0662

Vera A. Shikhova  https://orcid.org/0000-0002-5612-6222

Mikhail S. Kosobokov  https://orcid.org/0000-0002-0909-2613

Andrey R. Akhmatkhanov  https://orcid.org/0000-0002-2802-9134

Olga N. Sergeeva  https://orcid.org/0000-0001-9469-4063

Vladimir Ya. Shur  https://orcid.org/0000-0002-6970-7798