Review Article |
Corresponding author: Aleksandr M. Kislyuk ( akislyuk94@gmail.com ) © 2023 Aleksandr M. Kislyuk, Ilya V. Kubasov, Alexander A. Temirov, Andrei V. Turutin, Andrey S. Shportenko, Viktor V. Kuts, Mikhail D. Malinkovich.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Kislyuk AM, Kubasov IV, Temirov AA, Turutin AV, Shportenko AS, Kuts VV, Malinkovich MD (2023) Electrophysical properties, memristive and resistive switching of charged domain walls in lithium niobate. Modern Electronic Materials 9(4): 145-161. https://doi.org/10.3897/j.moem.9.4.116646
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Charged domain walls (CDWs) in ferroelectric materials raise both fundamental and practical interest due to their electrophysical properties differing from bulk ones. On a microstructure level, CDWs in ferroelectrics are 2D defects separating regions with different spontaneous polarization vector directions. Screening of electric field of the CDW's bound ionic charges by mobile carriers leads to the formation of elongated narrow channels with an elevated conductivity in initially dielectric materials. Controlling the position and inclination angle of CDW relative to the spontaneous polarization direction, one can change its conductivity over a wide range thus providing good opportunities for developing memory devices, including neuromorphic systems. This review describes the state of art in the formation and application of CDWs in single crystal uniaxial ferroelectric lithium niobate (LiNbO3, LN), as resistive and memristive switching devices. The main CDWs formation methods in single crystal and thin-film LN have been described, and modern data have been presented on the electrophysical properties and electrical conductivity control methods of CDWs. Prospects of CDWs application in resistive and memristive switching memory devices have been discussed.
lithium niobate, charged domain wall, memristive effect, resistive switching, ferroelectric domains
Theoretical insight in the possibility of forming charged domain walls (CDWs) started in 1973 from a classic work of Soviet physicists [
The first direct evidence of the existence of conductive domain walls was obtained in the pioneering experiments with BiFeO3 [
The electrical conductivity σ of CDW largely depends on the angle a between the spontaneous polarization vector and the tangent to the CDW surface (the so-called tilt or inclination angle) since there is the proportional relation σ ∝ 2Pssin α, where 2Ps is the spontaneous polarization of adjacent domains. At α < 90 deg the domain wall is partially charged and its conductivity is below the maximum possible one. The Landau–Ginzburg–Devonshire theory predicts an increase in the conductivity by one order of magnitude in comparison with that of the monodomain material at small CDW inclination angles (α ~ π/40) and by three orders of magnitude at a right inclination angle [
One of the most interesting classical intrinsic ferroelectrics from the CDWs formation viewpoint is lithium niobate. Lithium niobate (LN) has a uniaxial domain structure in which the spontaneous polarization vectors of adjacent domains are always antiparallel to each other, enabling the existence of only three domain wall configuration types: “head-to-tail” ones which are neutral, and “head-to-head” and “tail-to-tail” ones which have bound ionic charge (Fig.
Schematics of different domain wall types existing in uniaxial ferroelectric crystals: (a) neutral “head-to-tail”; (b) partially charged with the inclination angle α; (c) charged “head-to-head”; (d) ”tail-to-tail”. Image adapted from [
The temperature and chemical stability, the high Curie point (about 1140 °C for congruent composition crystals) and the absence of lead in the composition make LN the perfect model object for studying CDWs properties. There is a wide range of technologies allowing one to produce, in single-crystal LN wafers, metastable CDWs having almost any morphology and capable of existing for unlimited time over a wide range of temperatures [
At an early stage of LN domain structure studies, great attention was paid to crystals having regular (periodic) domain structures (RDS) which can efficiently generate second harmonics of laser radiation. These crystals are distinguished by the presence of head-to-tail neutral domain walls (Fig.
Study of RDS formation in LN crystals upon electric field application showed that at room temperature, domain structure switching in the polar axis direction includes an intermediate stage at which needle-like domains form with small (few degrees) inclination angles (Fig.
There are methods allowing one to obtain domain walls in LN that are orthogonal to the spontaneous polarization vector on large areas and have a bound charge close to the maximum possible one, i.e., the so-called bidomain structures (Fig.
Below is a brief review of main achievements in CDWs studies for LN crystals and description of promising CDWs application areas in electronic devices.
One should distinguish two types of single crystal LN specimens used in CDWs studies: those cut from bulk single crystals and those obtained from thin films (ranging from hundreds of nanometers to several microns in thickness) by chipping off onto the substrate after ion implantation (most commonly using helium), i.e., the so-called Lithium Niobate on Insulator (LNOI) [
CDWs formation methods in bulk single crystal and thin LNOI films are generally similar except that LNOI films are not suitable for high-temperature treatment (near the Curie point). Therefore the CDWs formation methods are arbitrarily divided hereinbelow in low-temperature ones that are conducted at room temperature and high-temperature ones.
Most low-temperature methods are based on the application of an external electric field that locally switches the domain structure. Thus, partially charged domain walls, with inclination angles within the range of 0 < α < 90 deg, typically around 10 deg, are produced. Unfortunately, application of an external electric field from conducting electrodes does not allow forming CDW with a high inclination angle α on large area due to the growth of needle-like domains with a tooth-shaped domain boundary [
Switching of a domain structure in LN at room temperature requires applying strong electric fields: a coercive field of at least 2 kV/mm for stoichiometric composition crystals and at least 20 kV/mm for congruent composition crystals [
CDWs formation in macroscopic single crystal LN specimens is commonly achieved by switching domain structures with coercive electric fields applied between flat conducting electrodes in a capacitor structure (Fig.
Appearance of CDWs formed using different methods: (a) flat electrodes in a capacitor structure; (b) voltage application to AFM probe; (c) flat electrodes in lateral direction of non-polar x-cut; (d) diffusion annealing with Li2O deficiency. Image (b) copied from [
Another widely used method of CDWs formation in LN under laboratory conditions is local domain structure switching in a surface layer by applying voltage to the cantilever probe of an atomic force microscope (AFM). The advantage of this method is the possibility of studying the conductive state of CDWs immediately after switching by c-AFM on the same instrument without removing the specimen. This approach is similarly effective for polar and non-polar crystal cuts. The main distinctive feature of the method is the presence of a heavily inhomogeneous super-coercive electric field in the material bulk which is quite slowly screened by free charges. Slow external field screening can trigger unexpected phenomena upon domain structure switching. For example, if the cantilever moves between two unpolarized points in contact with the specimen surface when a negative voltage is applied to the specimen, domains can form with spontaneous polarization vectors directed against the cantilever electric field. If the cantilever is withdrawn from the crystal surface before movement to the next point, the spontaneous polarization directions of the forming domains are the same as that of the cantilever electric field (Fig.
Despite the relative availability of the AFM cantilever probe field application method, only CDWs with low inclination angles relative to spontaneous polarization direction can be formed. Domain walls with a bound charge close to the maximum one can be formed in surface areas of unpolar x-cuts using periodical thin-film electrodes [
High coercive fields in LN crystals entail the stability of almost any domain strcture configurations at room temperature and a strong dependence of switching processes on external and internal electric screening of charges. Where technolgy requires, CDWs formation at room temperature can be simplified by reducing switching fields with a surface buffer layer for internal and external screening fields reduction that can be synthesized, e.g. by ion implantation [
The high-temperature approach to CDWs formation in LN single crystals implies the use of gradients of several scalar bulk parameters, e.g. point defect concentration, impurity atoms or bulk temperature distribution, upon crossing the Curie point during cooling [
From the technological viewpoint, the methods of controlling the domain structure of LN crystals without external electric field application can be categorized into two groups: aimed at forming an inhomogeneous distribution of composition or temperature in LN crystals. The former group methods include diffusion and out-diffusion anneals of lithium oxide [
The latter group includes various methods of forming inhomogeneous thermal fields in the crystal bulk, e.g. by placing crystals in containers with macroinhomogeneous steady-state temperature distribution subjected to slow cooling [
Using the above methods one can produce domain structures in crystals with elongated head-to-head or tail-to-tail CDW. Depending on the pattern of internal fields, polydomain, bidomain-polydomain or bidomain structures with sharp interdomain boundaries can form [
CDWs formed in LN crystals can be visualized using various methods, either by contrast with adjacent domains having different spontaneous polarization directions or by contrast of the boundaries themselves. Among the wide variety of methods for visualizing domain walls in LN crystals, the most important are selective etching and piezoresponse force microscopy (PFM). Due to its simple implementation, selective etching is very often used for rapid control of domain structures although the method is destructive. Typical etchants are fluoric acid based ones. Boiling etchants are often used for rapid optical microscopy specimen preparation. If more gentle treatment is required, e.g. for studying small domains or thin surface layers with spontaneous polarization vector inversion, long-term room temperature etching can be used [
Along with the two abovementioned methods, domain structures in LN crystals can be studied with less widely used nondestructive methods such as acoustic microscopy [
The primary methods to study the local electrical conductivity of CDWs in LN crystals include recording and analyzing I-V curves, conducting impedance spectroscopy, and monitoring the temporal changes in current through CDWs at a constant voltage.
The following two approaches are mainly used in practice. First, the tip of AFM cantilever is used as a conducting electrode and second, the crystal is coated with continuous electrodes to contact with the CDW. The main advantage of AFM for CDW studies is the high localization: this method allows studying nanosized features of structure and current through boundaries. However, the high electric fields induced by the probe can affect the measured parameters or even cause CDW movement and local electric breakdown. Furthermore, the use of AFM allows controlling CDW morphology only at distances of about 10 mm from the probe tip [
Wall conductivity mechanism identification is important for practical CDW application in electronic devices. Separation of bulk effects and contact phenomena is a primary task in these experiments. Ohmic conductivity in contact/CDW/contact systems can only occur in weak electric fields (when recording I–V curve with flat metallic electrodes) [
In strong electric fields, I–V curve obtained for head-to-head CDW in LONI films exhibit space-charge-limited current conductivity (SCLC) [
Despite far weaker suitable electric fields compared with those for AFM cantilevers, flat Ohmic contacts often allow detecting greater amplitude currents at the same voltages. This can be easily accounted for by the greater contact area with the material. The use of probes with micron contact areas also allows one to tangibly (by 6 orders of magnitude) increase the current detectable on CDW as compared with monodomain regions [
Although CDWs in LN crystals accumulate additional charges in their vicinity, the current amplitude is typically small and its measurement can cause many difficulties. First, to exhibit conductivity distinct from that of the single domain bulk, the wall should contain a sufficient number of sections with microscopic head-to-head structure. Secondly, even if the conductivity of the CDW is several orders of magnitude higher than that of the monodomain neighborhood, the current is nevertheless quite low since the conductive channel is narrow. Indeed, from the crystallographic viewpoint the width of the region in which the spontaneous polarization vector direction changes does not exceed several lattice parameters [
For this reason the first electrical conductivity measurements in CDW in LN crystals were conducted with super-band UV irradiation of the specimens [
Typical I–V curve pattern of LN : Mg crystals measured with flat electrodes from CDW with low inclination angles before and after condutivity “tuning” according to method [
It seems that the conductive state of CDW largely depends on domain structure switching method or electric field amplitude near domain wall at the time of its initial formation: in earlier work [
Interestingly, uniaxial mechanical stresses can also affect the CDW conductivity [
Due to the far smaller thickness of the specimens, measurement of current through CDW formed in thin LNOI films initially faced less difficulties than measurements for bulk single crystals [
The majority carriers in head-to-head CDWs are electron polarons. This is confirmed by Hall measurement data [
In most cases, electrophysical properties of CDWs in magnesium-doped LN specimens are studied. It is well known that Mg ions in bulk LN single crystals occupy niobium positions, thereby reducing the concentration of NbLi antisite defects. This effectively suppresses the photorefractive effect, increases the photoconductivity, reduces the external switching electric fields and increases induced domain structure stability [
Studies of the properties of CDWs with inclination angles close to 90 deg (maximum possible for the LN structure) are most often conducted for chemically reduced LN crystals. Although this material has been well studied in the monodomain state, literary data on CDWs conductivity in reduced LN are quite scarce. Chemical reduction which is technologically achieved by annealing in an oxygen free atmosphere leads to crystal “self-doping” with electrons upon removal of molecular oxygen. The loss of one Li2O and one O2 molecules by the crystal during this heat treatment releases four electrons from covalent bonds in NbO6 octahedra [
For example, while head-to-head CDWs in chemically reduced LN crystals exhibit higher conductivity than that of neighboring single-domain regions, their conductivity proves to be unstable over time. The current passing through CDWs in crystals tempered for three months after reduction annealing is an order of magnitude lower than immediately after heat treatment. This effect has been demonstrated to be a bulk phenomenon, unrelated to atmospheric impact on the surface [
Literary data on the temperature dependence of CDWs conductivity in LN crystals are contradictory, primarily due to the absence of a universally accepted method for studying carrier transport in 2D defects. In the temperature range of 110–170 °C, a conductivity activation energy of 0.79 eV was determined for head-to-head CDWs in chemically reduced LN crystals, as reported in reference [
Dependences from which polaron conductivity activation energies were determined for (a) reduced LN crystal with CDW and (b) LNOI crystal. Image (a is copied from [
From an electronics viewpoint, the electrode/CDW/electrode system can be represented by an equivalent circuit simulating the electrical properties for the passage of DC and AC current. The search for the simplest equivalent circuits of CDWs is an important task for future CDWs modeling in devices. Based on nanoimpedance microscopy data, an equivalent circuit was suggested [
Equivalent circuits of electrode/CDW/electrode system (a) suggested for AC [
This equivalent circuit was called the R2D2 model. A description of the electric circuit of a specimen with CDW as a set of elementary electronic components allows predicting diode behavior of CDWs conductivity and significantly simplifying the development of those electronic devices, e.g. diodes [
As mentioned earlier, the local conductivity of CDWs can be continuously varied over a range of values, and the established state persists over time. Therefore, an obvious practical application field of ferroelectric CDWs is the design of logic elements [
A straightforward design for a ferroelectric CDW-based RAM includes a crossbar structure with individual domains at electrode crossings (Fig.
It was reported [
Along with sub-coercive electric field magnitude pulses that locally change the inclination angle and hence the conductivity of CDWs, memristive switching can also be achieved with pulses that are stronger than the domain structure switching field [
Another possible configuration of CDWs device structures is a planar structure in which the conducting wall is at some depth and the electrodes are connected through cavities etched in necessary points (Fig.
Another type of device structure for CDWs memory cells are three-electrode cells with a control electrode [
Such three-electrode CDW memory cells in LN : Mg crystals [
Head-to-head CDW memristor array configuration in LN crystal surface area. Image adapted from supplementary information for [
(a) CDW conductive state switching sequence in three-electrode cell and (b) scanning electron microscopy structure image. (a) G gate, D drain, S source, controlling voltages Vd = 8.5 V, Vt1 = –4.70 V, Vt2 = –4,72 V and Vg = –8 V, 0 V and –5 V at each stage, respectively. Images copied from [
The low switching voltages and the potential for implementing nonvolatile memory make three-electrode CDW structures viable candidates as synapses for artificial neural networks [
Quite promising option is to combine the properties of head-to-head and tail-to-tail CDWs in a single device. Two opposite CDWs formed in LNOI : Mg located at a small distance from each other form a rectifying p–i–n diode having a forward voltage drop of 10–15 V. To increase the current density through this diode one can connect several conducting CDWs in parallel [
An important task in developing binary and memristive memories is cell miniaturization. In ferroelectrics, reduction of the dimensions of single domains formed by local switching increases the specific contribution of the domain wall energy to the free energy of the crystal in a local volume. Therefore, walls with the highest surface charge densities formed at room temperature by external fields exhibit only moderate stability. They can be “deleted” by their macroscopic single-domain neighborhood or transform into neutral ones due to weak screening of bound ionic charges, inducing high depolarization fields. By polarizing CDWs at elevated temperatures one can produce memory cell regions with a concentration gradient of point defects redistributed within the device due to electrodiffusion [
The commitment to utilizing structural defects as active device elements is a logical consequence of the development of research and engineering ideas in microelectronics materials science. CDWs in ferroelectric materials are the perfect group of defects for being formed in their most natural manner, i.e., by applying external electric fields. Lithium niobate, which is well-studied, chemically and thermally stable and produced in commercial quantities, is a perfect platform for devices making use of the unique CDWs properties. The most actively studied CDWs application field is the production of CDWs memristors, i.e., electronic components capable of varying their electrical resistivity upon external current or voltage application and retain the preset state for a long time. CDWs memristors formed in LN are primarily interesting for the possibility of producing arrays of neuromorphic devices with reproducible and time-stable parameters using conventional microelectronics methods. Although the main achievements in the studies and applications of CDWs in LN were obtained for magnesium doped crystals, the high conductivity and memristive properties are also found in CDWs formed in chemically reduced crystals. Chemically reduced LN crystals are the ones that allow the formation of CDW with inclination angles close to 90 deg, making them of great fundamental interest.
Despite the significant progress in LN CDWs research there are many directions for further research and engineering effort. Of great interest are CDWs properties in crystals and films doped with electrically active impurities allowing to reduce the coercive fields of domain structure switching or increase the wall conductivity. Furthermore, CDWs application in prospective electronics devices requires further analysis of factors potentially affecting CDWs performance for each specific device type, search for methods to increase parameter stability of these devices and identification of miniaturization and substrate device density limits.
The study was carried out with financial support from the Russian Science Foundation (grant No. https://rscf.ru/project/21-19-00872/).