Электрофизические свойства, мемристивное и резистивное переключение в заряженных доменных стенках в ниобате лития

Заряженные доменные стенки (ЗДС) в сегнетоэлектрических материалах интересны с фундаментальной и прикладной точек зрения, так как они обладают электрофизическими свойствами, отличными от объёмных. На уровне микроструктуры ЗДС в сегнетоэлектриках представляют собой двумерные дефекты, разделяющие области материала с различающимися направлениями векторов спонтанной поляризации. Компенсация электрического поля связанного ионного заряда ЗДС подвижными носителями приводит к формированию протяженных узких каналов с повышенной проводимостью в исходно диэлектрическом материале. Управляя положением и углом наклона ЗДС по отношению к направлению спонтанной поляризации, можно изменять её проводимость в широком диапазоне, что открывает широкие перспективы для создания устройств памяти, в том числе для нейроморфных систем. В обзоре представлено современное состояние исследований в области формирования и применения ЗДС, сформированных в монокристаллах одноосного сегнетоэлектрика ниобата лития (LiNbO₃, LN), в качестве устройств резистивного и мемристивного переключения. Рассмотрены основные методы формирования ЗДС в монокристаллах и тонких пленках LN, приведены современные данные по электрофизическим свойствам и способам управления электропроводностью ЗДС. Обсуждены перспективы применения ЗДС в устройствах памяти с резистивным и мемристивным переключением.

1. Vul B.M., Guro G.M., Ivanchik I.I. Encountering domains in ferroelectrics. Ferroelectrics. 1973; 6(1): 29—31. https://doi.org/10.1080/00150197308237691

2. Meier D., Selbach S.M. Ferroelectric domain walls for nanotechnology. Nature Reviews Materials. 2021; 7(3): 157—173. https://doi.org/10.1038/s41578-021-00375-z

3. Aristov V.V., Kokhanchik L.S., Voronovskii Y.I. Voltage contrast of ferroelectric domains of lithium niobate in SEM. Physica Status Solidi (a). 1984; 86(1): 133—141. https://doi.org/10.1002/pssa.2210860113

4. Werner C.S., Herr S.J., Buse K., Sturman B., Soergel E., Razzaghi C., Breunig I. Large and accessible conductivity of charged domain walls in lithium niobate. Scientific Reports. 2017; 7(1): 9862. https://doi.org/10.1038/s41598-017-09703-2

5. Vasudevan R.K., Wu W., Guest J.R., Baddorf A.P., Morozovska A.N., Eliseev E.A., Balke N., Nagarajan V., Maksymovych P., Kalinin S.V. Domain wall conduction and polarization-mediated transport in ferroelectrics. Advanced Functional Materials. 2013; 23(20): 2592—2616. https://doi.org/10.1002/adfm.201300085

6. Gureev M.Y., Tagantsev A.K., Setter N. Head-to-head and tail-to-tail 180° domain walls in an isolated ferroelectric. Physical Review B. Condensed matter. 2011; 83(18): 184104. https://doi.org/10.1103/PhysRevB.83.184104

7. Kubasov I.V., Kislyuk A.M., Ilina T.S., Shportenko A.S., Kiselev D.A., Turutin A.V., Temirov A.A., Malinkovich M.D., Parkhomenko Y.N. Conductivity and memristive behavior of completely charged domain walls in reduced bidomain lithium niobate. Journal of Materials Chemistry C. 2021; 9(43): 15591—15607. https://doi.org/10.1039/d1tc04170c

8. Sluka T., Tagantsev A.K., Bednyakov P., Setter N. Free-electron gas at charged domain walls in insulating BaTiO3. Nature Communications. 2013; 4(1): 1808. https://doi.org/10.1038/ncomms2839

9. Liu S., Cohen R.E. Stable charged antiparallel domain walls in hyperferroelectrics. Journal of Physics: Condensed Matter. 2017; 29(24): 244003. https://doi.org/10.1088/1361-648X/aa6f95

10. Seidel J., Martin L.W., He Q., Zhan Q., Chu Y.-H., Rother A., Hawkridge M.E., Maksymovych P., Yu P., Gajek M., Balke N., Kalinin S.V., Gemming S., Wang F., Catalan G., Scott J.F., Spaldin N.A., Orenstein J., Ramesh R. Conduction at domain walls in oxide multiferroics. Nature Materials. 2009; 8(30): 229—234. https://doi.org/10.1038/nmat2373

11. Evans D.M., Garcia V., Meier D., Bibes M. Domains and domain walls in multiferroics. Physical Sciences Reviews. 2020; 5(9). https://doi.org/10.1515/psr-2019-0067

12. Eliseev E.A., Morozovska A.N., Svechnikov G.S., Gopalan V., Shur V.Y. Static conductivity of charged domain walls in uniaxial ferroelectric semiconductors. Physical Review B. Condensed Matter and Materials Physics. 2011; 83(23): 235313. https://doi.org/10.1103/PhysRevB.83.235313

13. Kubasov I.V., Kislyuk A.M., Turutin A.V., Malinkovich M.D., Parkhomenko Y.N. Bidomain ferroelectric crystals: properties and prospects of application. Russian Microelectronics. 2021; 50(8): 571—616. https://doi.org/10.1134/S1063739721080035

14. Garrity K.F., Rabe K.M., Vanderbilt D. Hyperferroelectrics: Proper ferroelectrics with persistent polarization. Physical Review Letters. 2014; 112(12): 127601. https://doi.org/10.1103/PhysRevLett.112.127601

15. Cherifi-Hertel S., Voulot C., Acevedo-Salas U., Zhang Y., Crégut O., Dorkenoo K.D., Hertel R. Shedding light on non-Ising polar domain walls: Insight from second harmonic generation microscopy and polarimetry analysis. Journal of Applied Physics. 2021; 129(8): 81101. https://doi.org/10.1063/5.0037286

16. Lee D., Behera R.K., Wu P., Xu H., Li Y.L., Sinnott S.B., Phillpot S.R., Chen L.Q., Gopalan V. Mixed Bloch-Néel-Ising character of 180° ferroelectric domain walls. Physical Review B. 2009; 80(6): 060102. https://doi.org/10.1103/PhysRevB.80.060102

17. Gonnissen J., Batuk D., Nataf G.F., Jones L., Abakumov A.M., Van Aert S., Schryvers D., Salje E.K.H. Direct observation of ferroelectric domain walls in LiNbO3: wall-meanders, kinks, and local electric charges. Advanced Functional Materials. 2016; 26(42): 7599—7604. https://doi.org/10.1002/adfm.201603489

18. Zhang Y., Qian Y., Jiao Y., Wang X., Gao F., Bo F., Xu J., Zhang G. Conductive domain walls in x-cut lithium niobate crystals. Journal of Applied Physics. 2022; 132(4): 0144102. https://doi.org/10.1063/5.0101067

19. Poberaj G., Hu H., Sohler W., Günter P. Lithium niobate on insulator (LNOI) for micro-photonic devices. Laser & Photonics Reviews. 2012; 6(4): 488—503. https://doi.org/10.1002/lpor.201100035

20. Volk T.R., Gainutdinov R.V., Zhang H.H. Domain-wall conduction in AFM-written domain patterns in ion-sliced LiNbO3 films. Applied Physics Letters. 2017; 110(13): 132905. https://doi.org/10.1063/1.4978857

21. Lu H., Tan Y., McConville J.P.V., Ahmadi Z., Wang B., Conroy M., Moore K., Bangert U., Shield J.E., Chen L.-Q., Gregg J.M., Gruverman A. Electrical tunability of domain wall conductivity in LiNbO3 thin films. Advanced Materials. 2019; 31(48): e1902890. https://doi.org/10.1002/adma.201902890

22. Kämpfe T., Wang B., Haußmann A., Chen L.-Q., Eng L.M. Tunable non-volatile memory by conductive ferroelectric domain walls in lithium niobate thin films. Crystals. 2020; 10(9): 804. https://doi.org/10.3390/cryst10090804

23. Gainutdinov R., Volk T. Effects of the domain wall conductivity on the domain formation under AFM-tip voltages in ion-sliced LiNbO3 films. Crystals. 2020; 10(12): 1160. https://doi.org/110.3390/cryst10121160

24. Boes A., Corcoran B., Chang L., Bowers J., Mitchell A. Status and potential of lithium niobate on insulator (LNOI) for photonic integrated circuits. Laser and Photonics Reviews. 2018; 12(4): 1700256. https://doi.org/10.1002/lpor.201700256

25. Alikin D.O., Ievlev A.V., Turygin A.P., Lobov A.I., Kalinin S.V., Shur V.Y. Tip-induced domain growth on the non-polar cuts of lithium niobate single-crystals. Applied Physics Letters. 2015; 106(18): 182902. https://doi.org/10.1063/1.4919872

26. Shur V.Y., Rumyantsev E.L., Nikolaeva E.V., Shishkin E.I. Formation and evolution of charged domain walls in congruent lithium niobate. Applied Physics Letters. 2000; 77(22): 3636—3638. https://doi.org/10.1063/1.1329327

27. Gopalan V., Dierolf V., Scrymgeour D.A. Defect-domain wall interactions in trigonal ferroelectrics. Annual Review of Materials Research. 2007; 37(1): 449—489. https://doi.org/10.1146/annurev.matsci.37.052506.084247

28. Shao G., Bai Y., Cui G., Li C., Qiu X., Geng D., Wu D., Lu Y. Ferroelectric domain inversion and its stability in lithium niobate thin film on insulator with different thicknesses. AIP Advances. 2016; 6(7): 075011. https://doi.org/10.1063/1.4959197

29. Bednyakov P.S., Sturman B.I., Sluka T., Tagantsev A.K., Yudin P.V. Physics and applications of charged domain walls. npj Computational Materials. 2018; 4(1): 65. https://doi.org/10.1038/s41524-018-0121-8

30. Müller M., Soergel E., Buse K. Influence of ultraviolet illumination on the poling characteristics of lithium niobate crystals. Applied Physics Letters. 2003; 83(9): 1824—1826. https://doi.org/10.1063/1.1606504

31. Shur V.Y., Akhmatkhanov A.R., Baturin I.S. Fatigue effect in ferroelectric crystals: Growth of the frozen domains. Journal of Applied Physics. 2012; 111(12): 124111. https://doi.org/10.1063/1.4729834

32. Esin A.A., Akhmatkhanov A.R., Shur V.Y. Tilt control of the charged domain walls in lithium niobate. Applied Physics Letters. 2019; 114(9): 092901. https://doi.org/10.1063/1.5079478

33. Ievlev A.V., Alikin D.O., Morozovska A.N., Varenyk O.V., Eliseev E.A., Kholkin A.L., Shur V.Y., Kalinin S.V. Symmetry breaking and electrical frustration during tip-induced polarization switching in the nonpolar cut of lithium niobate single crystals. ACS Nano. 2015; 9(1): 769—777. https://doi.org/10.1021/nn506268g

34. Turygin A.P., Alikin D.O., Kosobokov M.S., Ievlev A.V., Shur V.Y. Self-organized formation of quasi-regular ferroelectric nanodomain structure on the nonpolar cuts by grounded SPM Tip. ACS Applied Materials & Interfaces. 2018; 10(42): 36211—36217. https://doi.org/10.1021/acsami.8b10220

35. Ievlev A.V., Morozovska A.N., Shur V.Y., Kalinin S.V. Ferroelectric switching by the grounded scanning probe microscopy Tip. Physical Review B. Condensed Matter and Materials Physics. 2015; 91(21): 214109. https://doi.org/10.1103/PhysRevB.91.214109

36. Reitzig S., Rüsing M., Zhao J., Kirbus B., Mookherjea S., Eng L.M. “Seeing Is Believing” – In-depth analysis by co-imaging of periodically-poled x-cut lithium niobate thin films. Crystals. 2021; 11(3): 288. https://doi.org/10.3390/cryst11030288

37. Kubasov I.V., Kislyuk A.M., Turutin A.V., Bykov A.S., Kiselev D.A., Temirov A.A., Zhukov R.N., Sobolev N.A., Malinkovich M.D., Parkhomenko Y.N. Low-frequency vibration sensor with a sub-nm sensitivity using a bidomain lithium niobate crystal. Sensors (Basel). 2019; 19(3): 614. https://doi.org/10.3390/s19030614

38. Alikin D.O., Shishkina E.I., Nikolaeva E.V., Shur V.Y., Sarmanova M.F., Ievlev A.V., Nebogatikov M.S., Gavrilov N.V. Formation of self-assembled domain structures in lithium niobate modified by ar ions implantation. Ferroelectrics. 2010; 399(1): 35—42. https://doi.org/10.1080/00150193.2010.489855

39. Ohnishi N. An etching study on a heat-induced layer at the positive-domain surface of LiNbO3. Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers. 1977; 16(6): 1069—1070. https://doi.org/10.1143/JJAP.16.1069

40. Евланова Н.Ф., Рашкович Л.Н. Влияние отжига на доменную структуру монокристаллов метаниобата лития. Физика твердого тела. 1974; 16(2): 555—557.

41. Nakamura K., Ando H., Shimizu H. Partial domain inversion in LiNbO3 plates and its applications to piezoelectric devices. IEEE 1986 Ultrasonics Symposium. Williamsburg, VA, USA. 17—19 November 1986. IEEE; 1986. P. 719—722. https://doi.org/10.1109/ULTSYM.1986.198828

42. Kubasov I.V., Timshina M.S., Kiselev D.A., Malinkovich M.D., Bykov A.S., Parkhomenko Y.N. Interdomain region in single-crystal lithium niobate bimorph actuators produced by light annealing. Crystallography Reports. 2015; 60(5): 700—705. https://doi.org/10.1134/S1063774515040136

43. Kubasov I.V., Kislyuk A.M., Bykov A.S., Malinkovich M.D., Zhukov R.N., Kiselev D.A., Ksenich S.V., Temirov A.A., Timushkin N.G., Parkhomenko Y.N. Bidomain structures formed in lithium niobate and lithium tantalate single crystals by light annealing. Crystallography Reports. 2016; 61(2): 258—262. https://doi.org/10.1134/S1063774516020115

44. Kugel V.D., Rosenman G. Domain inversion in heat-treated LiNbO3 crystals. Applied Physics Letters. 1993; 62(23): 2902—2904. https://doi.org/10.1063/1.109191

45. Rosenman G., Kugel V.D., Shur D. Diffusion-induced domain inversion in ferroelectrics. Ferroelectrics. 1995; 172(1): 7—18. https://doi.org/10.1080/00150199508018452

46. Nakamura K., Ando H., Shimizu H. Ferroelectric domain inversion caused in LiNbO3 plates by heat treatment. Applied Physics Letters. 1987; 50(20): 1413—1414. https://doi.org/10.1063/1.97838

47. Miyazawa S. Ferroelectric domain inversion in Ti-diffused LiNbO3 optical waveguide. Journal of Applied Physics. 1979; 50(7): 4599—4603. https://doi.org/10.1063/1.326568

48. Chen J., Zhou Q., Hong J.F., Wang W.S., Ming N.B., Feng D., Fang C.G. Influence of growth striations on para-ferroelectric phase transitions: Mechanism of the formation of periodic laminar domains in LiNbO3 and LiTaO3. Journal of Applied Physics. 1989; 66(1): 336—341. https://doi.org/10.1063/1.343879

49. Nakamura K., Shimizu H. Ferroelectric inversion layers formed by heat treatment of proton-exchanged LiTaO3. Applied Physics Letters. 1990; 56(16): 1535—1536. https://doi.org/10.1063/1.103213

50. Zhu Y.-Y., Zhu S.-N., Hong J.-F., Ming N. Ben domain inversion in LiNbO3 by proton exchange and quick heat treatment. Applied Physics Letters. 1994; 65(5): 558—560. https://doi.org/10.1063/1.112295

51. Zhang Z.-Y.Y., Zhu Y.-Y.Y., Zhu S.-N.N., Ming N.-B. Ben domain inversion by Li2O out-diffusion or proton exchange followed by heat treatment in LiTaO3 and LiNbO3. Physica Status Solidi (A). Applied Research. 1996; 153(1): 275—279. https://doi.org/10.1002/pssa.2211530128

52. Åhlfeldt H., Webjörn J., Arvidsson G. Periodic domain inversion and generation of blue light in lithium tantalate waveguides. IEEE Photonics Technology Letters. 1991; 3(7): 638—639. https://doi.org/10.1109/68.87938

53. Tasson M., Legal H., Peuzin J.C., Lissalde F.C. Mécanismes d′orientation de la polarisation spontanée dans le niobate de lithium au voisinage du point de Curie. Physica Status Solidi (a). 1975; 31(2): 729—737. https://doi.org/10.1002/pssa.2210310246

54. Tasson M., Legal H., Gay J.C., Peuzin J.C., Lissalde F.C. Piezoelectric study of poling mechanism in lithium niobate crystals at temperature close to the curie point. Ferroelectrics. 1976; 13(1): 479—481. https://doi.org/10.1080/00150197608236646

55. Luh Y.S., Feigelson R.S., Fejer M.M., Byer R.L. Ferroelectric domain structures in LiNbO3 single-crystal fibers. Journal of Crystal Growth. 1986; 78(1): 135—143. https://doi.org/10.1016/0022-0248(86)90510-5

56. Bykov A.S., Grigoryan S.G., Zhukov R.N., Kiselev D.A., Ksenich S.V., Kubasov I.V., Malinkovich M.D., Parkhomenko Y.N. Formation of bidomain structure in lithium niobate plates by the stationary external heating method. Russian Microelectronics. 2014; 43(8): 536—542. https://doi.org/10.1134/S1063739714080034

57. Blagov A.E., Bykov A.S., Kubasov I.V., Malinkovich M.D., Pisarevskii Y.V., Targonskii A.V., Eliovich I.A., Kovalchuk M.V. An electromechanical X-ray optical element based on a hysteresis-free monolithic bimorph crystal. Instruments and Experimental Techniques. 2016; 59(5): 728—732. https://doi.org/10.1134/S0020441216050043

58. Marchenkov N., Kulikov A., Targonsky A., Eliovich Y., Pisarevsky Y., Seregin A., Blagov A., Kovalchuk M. LiNbO3-based bimorph piezoactuator for fast X-ray experiments: Resonant mode. Sensors and Actuators A: Physical. 2019; 293: 48—55. https://doi.org/10.1016/j.sna.2019.04.028

59. Kulikov A., Blagov A., Marchenkov N., Targonsky A., Eliovich Y., Pisarevsky Y., Kovalchuk M. LiNbO3-based bimorph piezoactuator for fast x-ray experiments: Static and quasistatic modes. Sensors and Actuators A: Physical. 2019; 291: 68—74. https://doi.org/10.1016/j.sna.2019.03.041

60. Nakamura K., Shimizu H. Hysteresis-free piezoelectric actuators using LiNbO3 plates with a ferroelectric inversion layer. Ferroelectrics. 1989; 93(1): 211—216. https://doi.org/10.1080/00150198908017348

61. Nakamura K. Antipolarity domains formed by heat treatment of ferroelectric crystals and their applications. Japanese Journal of Applied Physics. 1992; 31(S1): 9—13. https://doi.org/10.7567/JJAPS.31S1.9

62. Nakamura K., Nakamura T., Yamada K. Torsional actuators using LiNbO3 plates with an inversion layer. Japanese Journal of Applied Physics. 1993; 32(5S): 2415—2417. https://doi.org/10.1143/JJAP.32.2415

63. Nakamura K., Ando H., Shimizu H. Bending vibrator consisting of a LiNbO3 plate with a ferroelectric inversion layer. Japanese Journal of Applied Physics. 1987; 26(S2): 198—200. https://doi.org/10.7567/JJAPS.26S2.198

64. Turutin A.V., Vidal J.V., Kubasov I.V., Kislyuk A.M., Kiselev D.A., Malinkovich M.D., Parkhomenko Y.N., Kobeleva S.P., Kholkin A.L., Sobolev N.A. Highly sensitive magnetic field sensor based on a metglas/bidomain lithium niobate composite shaped in form of a tuning fork. Journal of Magnetism and Magnetic Materials. 2019; 486: 165209. https://doi.org/10.1016/j.jmmm.2019.04.061

65. Kubasov I.V., Kislyuk A.M., Malinkovich M.D., Temirov A.A., Ksenich S.V., Kiselev D.A., Bykov A.S., Parkhomenko Y.N. Vibrational power harvester based on lithium niobate bidomain plate. Acta Physica Polonica A. 2018; 134(1): 90—92. https://doi.org/10.12693/APhysPolA.134.90

66. Vidal J.V., Turutin A.V., Kubasov I.V., Kislyuk A.M., Malinkovich M.D., Parkhomenko Y.N., Kobeleva S.P., Pakhomov O.V., Sobolev N.A., Kholkin A.L. Low-frequency vibration energy harvesting with bidomain LiNbO3 single crystals. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 2019; 66(9): 1480—1487. https://doi.org/10.1109/TUFFC.2019.2908396

67. Vidal J.V., Turutin A.V., Kubasov I.V., Kislyuk A.M., Kiselev D.A., Malinkovich M.D., Parkhomenko Y.N., Kobeleva S.P., Sobolev N.A., Kholkin A.L. Dual vibration and magnetic energy harvesting with bidomain LiNbO3-based composite. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 2020; 67(6): 1219—1229. https://doi.org/10.1109/TUFFC.2020.2967842

68. Webjorn J., Laurell F., Arvidsson G., Webjörn J., Laurell F., Arvidsson G., Webjorn J., Laurell F., Arvidsson G. Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second harmonic generation. Journal of Lightwave Technology. 1989; 7(10): 1597—1600. https://doi.org/10.1109/50.39103

69. Kugel V.D., Rosenman G. Ferroelectric domain switching in heat-treated LiNbO3 crystals. Ferroelectrics Letters Section. 1993; 15(3-4): 55—60. https://doi.org/10.1080/07315179308204239

70. Soergel E. Piezoresponse force microscopy (PFM). Journal of Physics D: Applied Physics. 2011; 44(46): 464003. https://doi.org/10.1088/0022-3727/44/46/464003

71. Kalinin S.V., Bonnell D.A. Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces. Physical Review B. Condensed Matter and Materials Physics. 2002; 65(12): 1—11. https://doi.org/10.1103/PhysRevB.65.125408

72. Yin Q.R., Zeng H.R., Yu H.F., Li G.R., Xu Z.K. Near-field acoustic microscopy of ferroelectrics and related materials. Materials Science and Engineering B: Solid-State Materials for Advanced Technology. 2003; 99(1–3): 2—5. https://doi.org/10.1016/S0921-5107(02)00438-5

73. Yin Q.R., Zeng H.R., Yu H.F., Li G.R., Lang S., Chan H.L.W. Near-field acoustic and piezoresponse microscopy of domain structures in ferroelectric material. Journal of Materials Science. 2006; 41(1): 259—270. https://doi.org/10.1007/s10853-005-7244-2

74. Berth G., Hahn W., Wiedemeier V., Zrenner A., Sanna S., Schmidt W.G. Imaging of the ferroelectric domain structures by confocal raman spectroscopy. Ferroelectrics. 2011; 420(1): 44—48. https://doi.org/10.1080/00150193.2011.594774

75. Rüsing M., Neufeld S., Brockmeier J., Eigner C., Mackwitz P., Spychala K., Silberhorn C., Schmidt W.G., Berth G., Zrenner A., Sanna S. Imaging of 180 ferroelectric domain walls in uniaxial ferroelectrics by confocal Raman spectroscopy: Unraveling the contrast mechanism. Physical Review Materials. 2018; 2(10): 103801. https://doi.org/110.1103/PhysRevMaterials.2.103801

76. Dierolf V., Sandmann C., Kim S., Gopalan V., Polgar K. Ferroelectric domain imaging by defect-luminescence microscopy. Journal of Applied Physics. 2003; 93(4): 2295—2297. https://doi.org/10.1063/1.1538333

77. Otto T., Grafström S., Chaib H., Eng L.M. Probing the nanoscale electro-optical properties in ferroelectrics. Applied Physics Letters. 2004; 84(7): 1168—1170. https://doi.org/10.1063/1.1647705

78. Pei S.-C., Ho T.-S., Tsai C.-C., Chen T.-H., Ho Y., Huang P.-L., Kung A. H., Huang S.-L. Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics. Optics Express. 2011; 19(8): 7153. https://doi.org/10.1364/oe.19.007153

79. Bozhevolnyi S.I., Pedersen K., Skettrup T., Zhang X., Belmonte M. Far- and near-field second-harmonic imaging of ferroelectric domain walls. Optics Communications. 1998; 152(4-6): 221—224. https://doi.org/10.1016/S0030-4018(98)00176-X

80. Neacsu C.C., Van Aken B.B., Fiebig M., Raschke M.B. Second-harmonic near-field imaging of ferroelectric domain structure of YMnO3. Physical Review B. Condensed Matter and Materials Physics. 2009; 79(10): 100107. https://doi.org/10.1103/PhysRevB.79.100107

81. Sheng Y., Best A., Butt H.-J., Krolikowski W., Arie A., Koynov K. Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation. Optics Express. 2010; 18(16): 16539. https://doi.org/10.1364/oe.18.016539

82. Kämpfe T., Reichenbach P., Schröder M., Haußmann A., Eng L. M., Woike T., Soergel E. Optical three-dimensional profiling of charged domain walls in ferroelectrics by Cherenkov second-harmonic generation. Physical Review B. Condensed Matter and Materials Physics. 2014; 89(3): 035314. https://doi.org/10.1103/PhysRevB.89.035314

83. Cherifi-Hertel S., Bulou H., Hertel R., Taupier G., Dorkenoo K.D.H., Andreas C., Guyonnet J., Gaponenko I., Gallo K., Paruch P. Non-ising and chiral ferroelectric domain walls revealed by nonlinear optical microscopy. Nature Communications. 2017; 8(1): 15768. https://doi.org/10.1038/ncomms15768

84. Irzhak D.V., Kokhanchik L.S., Punegov D.V., Roshchupkin D.V. Study of the specific features of lithium niobate crystals near the domain walls. Physics of the Solid State. 2009; 51(7): 1500—1502. https://doi.org/10.1134/s1063783409070452

85. Tikhonov Y., Maguire J.R., McCluskey C.J., McConville J.P.V., Kumar A., Lu H., Meier D., Razumnaya A., Gregg J.M., Gruverman A., Vinokur V.M., Luk’yanchuk I. Polarization topology at the nominally charged domain walls in uniaxial ferroelectrics. Advanced Materials. 2022; 34(45): 2203028. https://doi.org/10.1002/adma.202203028

86. Steffes J.J., Ristau R.A., Ramesh R., Huey B.D. Thickness scaling of ferroelectricity in BiFeO3 by tomographic atomic force microscopy. Proceedings of the National Academy of Sciences. 2019; 116(7): 2413—2418. https://doi.org/10.1073/pnas.1806074116

87. Alikin Y.M., Turygin A.P., Alikin D.O., Shur V.Y. Tilt control of the charged domain walls created by local switching on the non-polar cut of MgO doped lithium niobate single crystals. Ferroelectrics. 2021; 574(1): 16—22. https://doi.org/10.1080/00150193.2021.1888044

88. Eyben P., Bisiaux P., Schulze A., Nazir A., Vandervorst W. Fast fourier transform scanning spreading resistance microscopy: a novel technique to overcome the limitations of classical conductive AFM techniques. Nanotechnology. 2015; 26(35): 355702. https://doi.org/10.1088/0957-4484/26/35/355702

89. Shportenko A.S., Kislyuk A.M., Turutin A.V., Kubasov I.V., Malinkovich M.D., Parkhomenko Y.N. Effect of contact phenomena on the electrical conductivity of reduced lithium niobate. Modern Electronic Materials. 2021; 7(4): 167—175. https://doi.org/10.3897/j.moem.7.4.78569

90. Zhang W.J., Shen B.W., Fan H.C., Hu D., Jiang A.Q., Jiang J. Nonvolatile ferroelectric LiNbO3 domain wall crossbar memory. IEEE Electron Device Letters. 2023; 44(3): 420—423. https://doi.org/10.1109/LED.2023.3240762

91. McConville J.P.V., Lu H., Wang B., Tan Y., Cochard C., Conroy M., Moore K., Harvey A., Bangert U., Chen L., Gruverman A., Gregg J.M. Ferroelectric domain wall memristor. Advanced Functional Materials. 2020; 30(28): 2000109. https://doi.org/10.1002/adfm.202000109

92. Zahn M., Beyreuther E., Kiseleva I., Lotfy A.S., McCluskey C.J., Maguire J.R., Suna A., Rüsing M., Gregg J.M., Eng L.M. R2D2 – An equivalent-circuit model that quantitatively describes domain wall conductivity in ferroelectric LiNbO3. Condensed Matter. 2023. https://doi.org/10.48550/arXiv.2307.10322

93. Schröder M., Haußmann A., Thiessen A., Soergel E., Woike T., Eng L.M. Conducting domain walls in lithium niobate single crystals. Advanced Functional Materials. 2012; 22(18): 3936—3944. https://doi.org/110.1002/adfm.201201174

94. Godau C., Kämpfe T., Thiessen A., Eng L.M., Haußmann A. Enhancing the domain wall conductivity in lithium niobate single crystals. ACS Nano. 2017; 11(5): 4816—4824. https://doi.org/10.1021/acsnano.7b01199

95. Chai X., Lian J., Wang C., Hu X., Sun J., Jiang J., Jiang A. Conductions through head-to-head and tail-to-tail domain walls in LiNbO3 nanodevices. Journal of Alloys and Compounds. 2021; 873: 159837. https://doi.org/10.1016/j.jallcom.2021.159837

96. Wang C., Wang T., Zhang W., Jiang J., Chen L., Jiang A. Analog ferroelectric domain-wall memories and synaptic devices integrated with Si substrates. Nano Research. 2022; 15(4): 3606—3613. https://doi.org/10.1007/s12274-021-3899-5

97. Chaudhary P., Lu H., Lipatov A., Ahmadi Z., McConville J.P.V., Sokolov A., Shield J.E., Sinitskii A., Gregg J.M., Gruverman A. Low-voltage domain-wall LiNbO3 memristors. Nano Letters. 2020; 20(8): 5873—5878. https://doi.org/10.1021/acs.nanolett.0c01836

98. Kislyuk A.M., Ilina T.S., Kubasov I.V., Kiselev D.A., Temirov A.A., Turutin A.V., Shportenko A.S., Malinkovich M.D., Parkhomenko Y.N. Degradation of the electrical conductivity of charged domain walls in reduced lithium niobate crystals. Modern Electronic Materials. 2022; 8(1): 15—22. https://doi.org/10.3897/j.moem.8.1.85251

99. Shur V.Ya., Baturin I.S., Akhmatkhanov A.R., Chezganov D.S., Esin A.A. Time-dependent conduction current in lithium niobate crystals with charged domain walls. Applied Physics Letters. 2013; 103(10): 102905. https://doi.org/10.1063/1.4820351

100. Schröder M., Chen X., Haußmann A., Thiessen A., Poppe J., Bonnell D.A., Eng L.M. Nanoscale and macroscopic electrical ac transport along conductive domain walls in lithium niobate single crystals. Materials Research Express. 2014; 1(3): 035012. https://doi.org/10.1088/2053-1591/1/3/035012

101. Gerson R., Kirchhoff J.F., Halliburton L.E., Bryan D.A. Photoconductivity parameters in lithium niobate. Journal of Applied Physics. 1986; 60(10): 3553—3557. https://doi.org/10.1063/1.337611

102. Singh E., Beccard H., Amber Z.H., Ratzenberger J., Hicks C.W., Rüsing M., Eng L.M. Tuning domain wall conductivity in bulk lithium niobate by uniaxial stress. Physical Review B. 2022; 106(14): 144103. https://doi.org/10.1103/PhysRevB.106.144103

103. Qian Y., Zhang Y., Xu J., Zhang G. Domain-wall p-n junction in lithium niobate thin film on an insulator. Physical Review Applied. 2022; 17(4): 044011. https://doi.org/10.1103/PhysRevApplied.17.044011

104. McCluskey C.J., Colbear M.G., McConville J.P.V., McCartan S.J., Maguire J.R., Conroy M., Moore K., Harvey A., Trier F., Bangert U., Gruverman A., Bibes M., Kumar A., McQuaid R.G.P., Gregg J.M. Ultrahigh carrier mobilities in ferroelectric domain wall corbino cones at room temperature. Advanced Materials. 2022; 34(32): e2204298. https://doi.org/10.1002/adma.202204298

105. Beccard H., Beyreuther E., Kirbus B., Seddon S.D., Rüsing M., Eng L.M. Hall mobilities and sheet carrier densities in a single LiNbO3 onductive ferroelectric domain wall. https://doi.org/10.48550/arXiv.2308.00061

106. Pawlik A.-S., Kämpfe T., Haußmann A., Woike T., Treske U., Knupfer M., Büchner B., Soergel E., Streubel R., Koitzsch A., Eng L.M. Polarization driven conductance variations at charged ferroelectric domain walls. Nanoscale. 2017; 9(30): 10933—10939. https://doi.org/10.1039/c7nr00217c

107. Ohmori Y., Yamaguchi M., Yoshino K., Inuishi Y. Electron hall mobility in reduced LiNbO3. Japanese Journal of Applied Physics. 1976; 15(11): 2263—2264. https://doi.org/10.1143/JJAP.15.2263

108. Palatnikov M., Makarova O., Kadetova A., Sidorov N., Teplyakova N., Biryukova I., Tokko O. Structure, optical properties and physicochemical features of LiNbO3:Mg,B crystals grown in a single technological cycle: an optical material for converting laser radiation. Materials. 2023; 16(13): 4541. https://doi.org/10.3390/ma16134541

109. Volk T., Wöhlecke M., Reichert A., Jermann F., Rubinina N. The peculiar impurity concentration ranges in damage-resistant LiNbO3 crystals doped with Mg, Zn, In and Sn. Ferroelectrics Letters Section. 1995; 20(3-4): 97—103. https://doi.org/10.1080/07315179508204289

110. Hu M.-L., Hu L.-J., Chang J.-Y. Polarization switching of pure and MgO-doped lithium niobate crystals. Japanese Journal of Applied Physics. 2003; 42(12, Pt 1): 7414—7417. https://doi.org/10.1143/JJAP.42.7414

111. Yatsenko A.V., Evdokimov S.V., Palatnikov M.N., Sidorov N.V. Analysis of the conductivity and current-voltage characteristics nonlinearity in LiNbO3 crystals of various compositions at temperatures 300—450 K. Solid State Ionics. 2021; 365(2): 115651. https://doi.org/10.1016/j.ssi.2021.115651

112. Yatsenko A.V., Evdokimov S.V., Shul’gin V.F., Palatnikov M.N., Sidorov N.V., Makarova O.V. Effect of magnesium impurity concentration on electrical properties of LiNbO3 crystals. Physics of the Solid State. 2021; 63(12): 1851—1856. https://doi.org/10.1134/S1063783421100401

113. Li Y., Zheng Y., Tu X., Xiong K., Lin Q., Shi E. The high temperature resistivityof lithium niobate and related crystals. In: Proceed. of the 2014 Symposium on piezoelectricity, acoustic waves, and device applications (SPAWDA). Beijing, China. 30 October 2014 — 02 November 2014. IEEE; 2014. P. 283—286. https://doi.org/10.1109/SPAWDA.2014.6998581

114. Polgár K., Kovács L., Földvári I., Cravero I. Spectroscopic and electrical conductivity investigation of Mg doped LiNbO3 single crystals. Solid State Communications. 1986; 59(6): 375—379. https://doi.org/10.1016/0038-1098(86)90566-1

115. Schirmer O.F., Imlau M., Merschjann C., Schoke B. Electron small polarons and bipolarons in LiNbO3. Journal of Physics: Condensed Matter. 2009; 21(12): 123201. https://doi.org/10.1088/0953-8984/21/12/123201

116. Guilbert L., Vittadello L., Bazzan M., Mhaouech I., Messerschmidt S., Imlau M. The elusive role of Nb Li bound polaron energy in hopping charge transport in Fe: LiNbO3. Journal of Physics: Condensed Matter. 2018; 30(12): 125701. https://doi.org/10.1088/1361-648X/aaad34

117. Faust B., Muller H., Schirmer O.F. Free small polarons in LiNbO3. Ferroelectrics. 1994; 153(1): 297—302. https://doi.org/10.1080/00150199408016583

118. García-Cabaes A., Sanz-García J.A., Cabrera J.M., Agulló-López F., Zaldo C., Pareja R., Polgár K., Raksányi K., Fölvàri I. Influence of stoichiometry on defect-related phenomena in LiNbO3. Physical Review B. 1988; 37(11): 6085—6091. https://doi.org/10.1103/PhysRevB.37.6085

119. Kislyuk A.M., Ilina T.S., Kubasov I.V., Kiselev D.A., Temirov A.A., Turutin A.V., Malinkovich M.D., Polisan A.A., Parkhomenko Y.N. Tailoring of stable induced domains near a charged domain wall in lithium niobate by probe microscopy. Modern Electronic Materials. 2019; 5(2): 51—60. https://doi.org/10.3897/j.moem.5.2.51314

120. Jiang J., Chai X., Wang C., Jiang A. High temperature ferroelectric domain wall memory. Journal of Alloys and Compounds. 2021; 856: 158155. https://doi.org/10.1016/j.jallcom.2020.158155

121. Niu L., Qiao X., Lu H., Fu W., Liu Y., Bi K., Mei L., You Y., Chou X., Geng W. Diode-like behavior based on conductive domain wall in LiNbO ferroelectric single-crystal thin film. IEEE Electron Device Letters. 2023; 44(1): 52—55. https://doi.org/10.1109/LED.2022.3224915

122. Suna A., McCluskey C.J., Maguire J. R., Kumar A., McQuaid R.G.P., Gregg J.M. Ferroelectric domain wall logic gates. https://doi.org/10.48550/arXiv.2209.08133

123. Wang J., Ma J., Huang H., Ma J., Jafri H.M., Fan Y., Yang H., Wang Y., Chen M., Liu D., Zhang J., Lin Y.-H., Chen L.-Q., Yi D., Nan C.-W. Ferroelectric domain-wall logic units. Nature Communications. 2022; 13(1): 3255. https://doi.org/10.1038/s41467-022-30983-4

124. Park B.-E., Ishiwara H., Okuyama M., Sakai S., Yoon S.-M. (eds.). Ferroelectric-gate field effect transistor memories : Device physics and applications (Topics in applied physics book 131). Dordrecht: Springer Netherlands; 2016. 350 p. https://doi.org/10.1007/978-94-024-0841-6

125. Lupascu D.C. Fatigue in ferroelectric ceramics and related issues. Berlin, Heidelberg: Springer Berlin Heidelberg; 2004. Vol. 61. 228 p. https://doi.org/10.1007/978-3-662-07189-2

126. Baeumer C., Saldana-Greco D., Martirez J.M.P., Rappe A.M., Shim M., Martin L.W. Ferroelectrically driven spatial carrier density modulation in graphene. Nature Communications. 2015; 6(1): 6136. https://doi.org/10.1038/ncomms7136

127. Chai X., Jiang J., Zhang Q., Hou X., Meng F., Wang J., Gu L., Zhang D. W., Jiang A. Q. Nonvolatile ferroelectric field-effect transistors. Nature Communications. 2020; 11(1): 2811. https://doi.org/10.1038/s41467-020-16623-9

128. Sun J., Li Y., Zhang B., Jiang A. High-power LiNbO3 domain-wall nanodevices. ACS Applied Materials & Interfaces. 2023; 15(6): 8691—8698. https://doi.org/110.1021/acsami.2c20579