Degradation of the electrical conductivity of charged domain walls in reduced lithium niobate crystals

of the electrical conductivity of charged domain walls in reduced Abstract In this work, the effect of long-term room temperature exposure on the electrical conductivity of the charged domain wall (CDWs) in nonpolar x -cut congruent lithium niobate (LiNbO 3 , LN) crystals has been studied. Bidomain ferroelectric structures containing head-to-head charged domain boundaries have been produced by diffusion annealing in air near the Curie temperature and by infrared annealing. The crystals have been reduction annealed in a nitrogen atmosphere for the formation of color centers and growth of the electrical conductivity. The current measured during the recording of the I-V curves of the specimens using scanning probe microscope after room temperature exposure for 91 days has been found to decrease. The effect of storage conditions on the electrical conductivity of the CDWs has been studied. Degradation of the electrical conductivity does not originate from the effect of environment on the crystal surface. It has been hypothesized that the degradation is caused by distribution of charge carriers shielding the bound charge of the CDWs.


Introduction
Domain walls are topographic defects in ferroics which separate domains having different random polarization directions. Lithium niobate (LiNbO 3 , LN) show good promise for the fabrication of devices in which the unique properties of domain walls are implemented, because lithium niobate is a single-axis ferroelectric with 180-deg domain walls, high Curie temperature, refractory properties and chemical stability. The absence of lead in its composition and the availability of various diameter wafers and crystal cuts with reproducible properties in markets make this material one of the most industrially important ferroelectrics. Depending on the mutual orientation of random polarization vectors P s adjacent domains may have three types of domain walls in LN: "head-to-tail", "head-to-head" (H-H) and "tailto-tail". The charge of the domain wall is characterized by the angle θ between the direction of the vector P s and the wall line, 0 < θ < 90°. The charge density at the domain boundary is proportional to sin(θ) and hence charged domain walls (CDWs) with |θ| ≈ 90° are the most charged ones [1][2][3]. The electrophysical properties of ferroelectric materials in the vicinity of CDW differ from those in the bulk thus raising both fundamental and applied interest to these objects. Although ferroelectric materials are wide-gap dielectrics, CDWs in these materials may have elevated electrical conductivity. The CDW are characterized by the presence of strong local electric fields induced by bound ion charge. Free carriers trapped by this electric field concentrate in the vicinity of the CDW hence potentially forming a conductive channel inside the dielectric material [4-6] or locally change the contact properties of the material [7]. The behavior of free carriers in the vicinity of CDW in some materials can be described by the model of quasi-2D electron gas, with the electrical conductivity being metallic [8,9]. Atomic force microscopy methods allow local study of the electrophysical properties of the CDWs and the morphology of domains induced by applied bias to atomic force microscope (AFM) probe [10-12]. The possibility of forming high-density CDWs in ferroelectrics allows designing various electronic devices including new types of computer memory [13-15] and memristors which are promising for neuromorphic calculations [16][17][18][19][20]. For the fabrication of commercial devices on the basis of CDWs one should ensure reproducible and non-degradable electrophysical properties of domain boundaries in commercial products.
Multiple techniques of producing CDWs in LN single crystals have been reported. Most of them are based on the application of an external electric field which provides for local switching of the domain structure. Thus tilted partially charged domain walls form at an angle of 0 < θ < 90° with the polar axis. Unfortunately the application of an external electric field from electrodes does not allow producing large-area CDWs with tilt angles of θ>30° due to the growth of needle-shaped domains with jagged domain walls [1,11,21,22]. Furthermore the dimensions and morphology of the domains forming in LN crystals under external electric field depend on polarization conditions and vary between different crystallographic cuts [23][24][25].
Another approach to the formation of CDWs in LN single crystals is to use force field gradients in the bulk. Examples of these fields are point defect or impurity atom concentrations as well as spatial temperature distribution upon cooling through the Curie point [26]. In this case the crystal wafer is split in two macrodomains separated by one CDW with θ ≈ 90° (the so-called bidomain crystal). The domain inversion phenomenon in LN upon heat treatment in the vicinity of the Curie temperature accompanied by Li 2 O out-diffusion was discovered [27,28] and studied [29][30][31][32][33][34]. Along with diffusion annealing of LN crystals near the Curie point, bidomain ferroelectric structures can be alternatively produced by annealing of crystals subjected to proton exchange [35][36][37][38] and heat treatment of crystals in an inhomogeneous thermal field [39][40][41][42]. Bidomain crystals are also promising as materials for the fabrication of precision actuators [39,[43][44][45][46][47][48][49], low-frequency vibration gages [50] and magnetic field sensors (as a constituent of composite magnetoelectric materials) [51] as well as for waste heat power systems [52,53].
LN is a good insulator and therefore most studies of CDWs use Mg doped crystals since Mg increases the electrical conductivity [3,21,[54][55][56]. Currents in CDWs formed in Mg : LN can be further increased by super-bandgap photoexcitation [3,56] and domain engineering [54]. Along with doping, an alternative approach to increasing the electrical conductivity of the crystals is annealing in a reducing environment (vacuum, hydrogen, nitrogen or inert atmosphere) [57][58][59][60][61][62]. Chemically reduced crystals become almost transparent, with a wide optical absorption band having a maximum at 2.5 eV which is attributed in literature to bound bipolarons [58,63]. It has been found recently [7] that local switching of "head-to-head" CDW domain structures in LN crystals after reduction annealing provides for efficient control of AFM probe / CDW point contact conductivity. However the stability of the electrophysical properties of these domains has not been studied in detail yet. The aim of this work is to study the stability of the electrophysical properties of CDWs in reduced LN crystals.

Experimental
The test specimens were commercial congruent z-cut LN crystals (The Roditi International Corporation Ltd). The wafers were cut into rectangular 10 × 10 × 1 mm 3 pieces that were further diffusion annealed in air [28,33,47] for the formation of a H-H bidomain ferroelectric structure. As a result a long CDW was formed in the middle of the bulk of the whole wafer. For AFM studies following the method described earlier [10, 29,39], thin transverse cuts of the crystals were made so the polar axis is in the specimen plane and the nonpolar axis is perpendicular to the specimen surface. Thereafter one of the planes so obtained was sequentially polished with ASM3/2 diamond powder and cerium oxide powder with the main fraction size of 0.8 mm. For increasing the electrical conductivity and surface recrystallization after mechanical treatment the specimens were reduction annealed at 1030 °C for 60 min in a ULVAC VHC-P610 infrared furnace in 6.0 Grade dried nitrogen atmosphere (purity grade 99.9999%). After reduction annealing a chromium electrode was magnetron-sputtered onto the surface opposite to the polished side. Chromium forms an Ohmic contact to lithium niobate [64,65]. The crystals were attached by the chromium electrode side to a metallic substrate using Leitsilber 200 conducting silver paste. The schematic of specimen preparation is shown in Fig. 1.
Study of the CDWs by piezoresponse force microscopy, conductive atomic force microscopy (c-AFM) and I-V curve recording methods was carried out under an Asylum Research MFP-3D Stand Аlone probe microscope. High-resolution silicon cantilevers with NSG30/ Pt platinum coating were used. The cantilever bias for c-AFM imaging of CDW areas was +7 V. For studying the time stability of the electrophysical properties of the CDWs in the LN bidomain crystals the I-V curves were recorded at several CDW points and c-AFM images were taken for the CDW crystal region immediately after reduction annealing and after long-term exposure for 91 days.
At the first phase of the study the threshold switching voltages of the domain structure were measured using the AFM probe. To this end, square pulses 20 sec ranging from 0 to ±200 V at a 10 V step were applied to different points of the monodomain region of the specimen. The domain structure was visualized using piezoresponse force microscopy. The results showed that the switching of the domain structure is caused by biasing of the cantilever with ≥+30 V and ≤-50 V. For avoiding repolarization during I-V curve measurement all the subsequent measurements were carried out in the -20 to +20 V range. The positive and negative I-V curve branches were taken separately at several CDW points. The I-V curves were taken from CDW regions with tilt angles close to 90 deg with a 10 sec sawtooth signal for 20 cycles, the data being averaged over the measurement cycles. Then the specimen was divided in two halves. For studying the effect of environment on the stability of the electrophysical properties of the CDWs one half of the specimen was placed into n-hexane and the other left in air. Hexane is a nonpolar aprotonic solvent that prevents the CDWs of the reduced crystal from oxidation in ambient oxygen and is supposed not to shield the CDWs field. The specimens were held in dark air-proof containers at room temperature. The temperature and humidity in the room were not stabilized. After exposure the I-V curves and c-AFM images were taken again.

Results and discussion
AFM topographic study of the bidomain LN crystal x-cut surface containing the H-H CDW showed that reduction annealing of the crystal smoothens the sur-  face and reduces the quantity of scratches (Fig. 2). The RMS surface roughness decreased from 5,59±1,56 nm to 2,91±1,06 nm. This change seemingly originates from specimen surface recrystallization.
The smoothening of the specimen surface roughness is accompanied by the formation of an elongated trench coincident with the CDW line in the c-AFM scan (Fig. 3 a and b). This phenomenon was described in literature earlier [66]. The depth of the trench was approximately 0.3 nm, its width being 70 nm. The formation of the elongated trench on the crystal surface can be caused by the more intense O 2 and Li 2 O evaporation during annealing [67].
The c-AFM images taken with a +7 V probe bias before exposure allow visualizing the CDW (Fig. 3 b). However after exposure the current measured at the CDW at a +7 V bias was below the scanning probe microscope sensitivity. CDW visualization in the specimens after exposure in air and in n-hexane was achieved at a higher bias, i.e., +10 V (Fig. 3 c). The I-V curves taken after long exposure suggest degradation of the CDW electrical conductivity (Fig. 4). The current measured for the I-V curves of the CDW biased to +20 V decreased by almost one order of magnitude as a result of exposure. Noticeably there was no tangible difference in the I-V curves and the c-AFM images between the specimens exposed to air and to n-hexane.
After air and n-hexane exposure the surface of the specimens still had the trench and hence the degradation of the electrical conductivity was not caused by adhesion of contaminants. There were attempts to recover the electrical conductivity, but crystal surface cleaning with various solvents, fast etching in a mixture of hydrochloric and nitric acids and etching in ionized argon did not give any results. It should be noted that repeated surface polishing during reduction annealing restored the electrical conductivity to its initial high level.
In order to understand whether the degradation of the electrical conductivity has a surface or bulk origin the crystals were cleaved after exposure. Although the crystal's cleavage surface pattern differs considerably from  the as-annealed surface pattern, the c-AFM scans for +10 V bias showed currents close to those for surface before cleaving (Fig. 5 a). However the crystals cleaved immediately after reduction annealing had a high CDW electrical conductivity (Fig. 5 b), i.e., electrical conductivity degradation occurs in the entire crystal bulk.
An experiment was set up in which electrical conductivity degradation was stimulated by radiation absorption near the crystal's self-absorption edge. The bidomain LN crystal after reduction annealing was irradiated with a solid-state 320 nm UV laser at a radiation power of 5 mW. UV radiation absorption by the crystal surface layers led to local heating and generation of hole polarons [68]. c-AFM study of the unirradiated and as-irradiated CDWs showed a dramatic degradation of the electrical conductivity down to the scanning probe microscope sensitivity threshold after 1 min irradiation. The c-AFM images of the as-irradiated LN crystal did not visualize the CDW for scans taken at a bias of below +20 V.
Chemical reduction of the lithium niobate crystals can be described with the following reaction formula [69]: Free conductivity band electrons are trapped by Nb Li and Nb Nb defects each of which forms a small-radius polaron. Eventually, Nb Li 4+ and Nb Nb 4+ polarons localized at adjacent lattice sites (along the polar axis) form a stable bound pair, i.e., a small-radius bipolaron [59,60,[69][70][71]. Presumably the conditions of bound bipolaron formation differ between the CDW and the single domain region.

Conclusion
The phenomenon of I-V curve current reduction was studied using AFM. The electrophysical properties of the bidomain LN crystals after reduction annealing proved to be unstable in time, the electrical conductivity decreasing by one order of magnitude after long-term exposure. This phenomenon was found to be not associated with the effect of environment on the surface; rather it is caused by redistribution of carriers shielding the bound charge of the CDW.

Acknowledgments
The reported study was funded by RFBR, project num-