Electrochemical anodic oxidation assisted fabrication of memristors

Owing to the advantages of simple structure, low power consumption and high-density integration, memristors or memristive devices are attracting increasing attention in the fields such as next generation non-volatile memories, neuromorphic computation and data encryption. However, the deposition of memristive films often requires expensive equipment, strict vacuum conditions, high energy consumption, and extended processing times. In contrast, electrochemical anodizing can produce metal oxide films quickly (e.g. 10 s) under ambient conditions. By means of the anodizing technique, oxide films, oxide nanotubes, nanowires and nanodots can be fabricated to prepare memristors. Oxide film thickness, nanostructures, defect concentrations, etc, can be varied to regulate device performances by adjusting oxidation parameters such as voltage, current and time. Thus memristors fabricated by the anodic oxidation technique can achieve high device consistency, low variation, and ultrahigh yield rate. This article provides a comprehensive review of the research progress in the field of anodic oxidation assisted fabrication of memristors. Firstly, the principle of anodic oxidation is introduced; then, different types of memristors produced by anodic oxidation and their applications are presented; finally, features and challenges of anodic oxidation for memristor production are elaborated.


Introduction
The exponential growth of data is putting increasing demands on the performance of digital computers.Although the shrinking size of complementary metal-oxide-semiconductor Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
(CMOS) devices has improved the energy efficiency and processing speed of computers, the continuation of Moore's law faces many challenges as the device size approaches physical limits [1,2].In addition, the von Neumann computer architecture [3,4], in which computing and memory units are physically separated, limits the performances of current computers.The frequent data transfer causes additional energy consumption, and the speed of the data processing is much faster than the speed of the data reading.These issues lead to performance constraints on central processing units, and significant waste of computing power [5].Mermristors or memristive devices are promising for computers beyond the von Neumann architecture.As a new electronic device, memristors are attracting more and more attention due to their ability for in-memory computing [5,6] and very small size (2 nm) [7].
Memristors, whose conductance varies with applied voltage, are the fourth type of basic circuit element proposed by Chua in 1971 [8].A memristor often has a metal-insulatormetal (MIM) sandwich structure consisting of a top electrode, a resistive layer and a bottom electrode [9,10].The distinct switching mechanisms of memristors can be classified into electronic effect, conductive filament, and phase change effect [11].As a common switching mechanism, conductive filaments in memristors include metallic or non-metallic ones.Generally, when a voltage is applied to a memristor, redox reactions occur within the functional layer, producing anions (such as O 2− ) or metal cations (such as Ag + ) that move and form filaments connecting the two electrodes.This process will make the memristor in a low-resistance state (LRS).When an opposing voltage is applied, the filaments will be broken due to the electric field and Joule heat effect.The memristor will switch to a high-resistance state (HRS).Materials used to fabricate memristors include binary metal oxides [12,13], multiple metal oxides [14][15][16], 2D materials [17][18][19][20], polymers [21,22], and so on.Due to their good endurance and non-volatility, memristors made of binary metal oxides such as titanium oxide [23], hafnium oxide [24,25], and tantalum oxide [26,27], are commonly referred to as resistive random access memories (ReRAMs).With the advantages of simple architecture, high-density scalability, low power consumption, good compatibility with the CMOS technique, and multi-level storage [28][29][30][31][32], ReRAMs are key candidates for the next generation non-volatile memories (NVMs) [33,34].For NVM applications, memristors require excellent endurance and retention, good yield, on/off ratio and linearity [35,36].Apart from NVMs, memristors are also applied to logic operations [37], bio-inspired neuromorphic computations [38][39][40][41][42], and data encryption [43,44].Common techniques used for the memristor film deposition include chemical vapour deposition, atomic layer deposition, electron beam evaporation (EBE), and pulsed laser deposition.They require high vacuum or heating conditions, and are often very expensive, power and time consuming.
As one of the electrochemical fabrication techniques [45], anodization is a room temperature, non-vacuum technique with the advantages of low cost, convenience and largearea coating with uniform thickness [46][47][48][49][50].The anodization requires only one voltage source, one electrolytic cell and two electrodes.It can fabricate a variety of memristors.Firstly, high-quality oxide films or nanotubes as the intermediate layer for memristors can be produced by anodization [51][52][53][54].By controlling voltage, current density, time, electrolyte composition, the thickness and morphology of oxides could be adjusted to regulate the performance of memristors.Besides this, it is also applied to produce anodized aluminium oxides (AAOs) with highly ordered nanopores.AAOs have the features of good thermal stability, mechanical stability, and easy control of pore size, spacing and depth [55][56][57].By combining with other techniques, AAOs can support the fabrication of largearea, low-cost, high-density arrays of nanowires (NWs) for the study of nanoscale resistive switching mechanisms [58,59].AAOs can also be applied to the preparation of nanodots to regulate and simplify the placement of conductive filaments, thereby improving the device stability [60,61].
Despite the unique advantages of the anodic oxidation for the preparation of memristors, a comprehensive review is currently absent.In this article, we firstly introduce the principle of the anodic oxidation technique, then the processes of preparing memristors by means of the anodic oxidation and applications of memristors are elaborated and discussed.Finally, we summarise the features and challenges of the anodic oxidation technique for preparing memristors.

Anodic oxidation
Anodizing is a surface modification technique with a long history.It is used as a mature process for the surface protection of metals in industry.When currents are applied in a specific electrolyte, the metal/alloy used as the anode is oxidized to form an oxide on the anode surface; this is the working principle of the anodic oxidation.The cathode materials are usually inert materials such as stainless steel, graphite and Pt.Under different oxidation conditions, anodic oxidation can be used to produce oxide thin films, nanotubes and AAOs.Furthermore, the anodic oxidation technique can be applied to fabricate memristors, as illustrated in figure 1.For example, memristors based on oxide thin films and nanotubes can be prepared directly, while those based on nanowires and nanodots are prepared indirectly.In this section, we will firstly give a general overview about the process of anodizing Ti metal to produce oxide thin films and nanotubes, as well as anodizing Al to produce AAOs.The specific process of the anodic oxidation for the preparation of memristors is presented in sections 3-5.And the applications of memristors are discussed in section 6.

Thin films of oxides
During the anodic oxidation of Ti metal, When Ti metal is placed at the anode, it loses electrons and combines with OH − and O 2− provided by the electrolyte to form TiO 2 (TiO x ), as shown in figure 2(a).Corresponding reactions are given in equations ( 1)- (3).At the same time, a small amount of oxygen is also produced at the anode, which dissipates the current [11,65].The cathode reaction, as given in equation ( 4), is the formation of H 2 from H + by getting electrons.During the oxidation of metals, two interfaces are created, one is the metal/oxide (M/O) interface and the other is the oxide/electrolyte (O/E) interface.Under the electric field, Ti 4+ moves to the O/E interface to cause the oxide film to grow outwards, while O 2− moves to the O/M interface to cause the oxide film to grow into the metal.As the thickness of the oxide film increases, the increase in resistance leads to a decrease in current, which in turn results in a slower growth rate of the oxide film.When the rate of oxide formation and dissolution reaches an equilibrium, the thickness of the oxide film will eventually be limited to a few hundred nanometres [66].Generally, dense films  [61].CC BY 4.0.Reprinted with permission from [53].Copyright (2022) American Chemical Society.Reproduced from [52].CC BY 4.0.Reproduced from [49].CC BY 4.0.Reprinted from [64], © 2021 Elsevier Ltd.All rights reserved.are formed after oxidation in acidic electrolytes such as phosphoric acid (H 3 PO 4 ), sulphuric acid (H 2 SO 4 ), and boric acid (H 3 BO 3 ) [66,67]. Figure 2(b) shows a TiO x thin film prepared by the anodic oxidation in H 3 PO 4 electrolyte; a dense oxide film can be observed on the Ti substrate.However, if the current density or the acid concentration is too high, a porous oxide film will be formed [49,54].When manufacturing thin film memristors by means of anodic oxidation, the base metal is usually used as the bottom electrode.Then, a top electrode is added directly to the oxide layer to prepare a memristor with a sandwich structure, Ti 4+ + 4OH − → Ti(OH) 4 (1)

Nanotubes of oxides
As shown in figure 2(c), when the electrolyte contains F − , a thin barrier layer (⩽50 nm) is firstly formed on the Ti surface, and then nanotubes are formed under the action of F − .Current models for the anodization of TiO 2 nanotubes are mainly based on the field-assisted dissolution theory.As given in equation ( 5), if the electrolyte contains F − , F − will react with TiO 2 in the barrier layer to form stable [TiF 6 ] 2− .This will dissolve TiO 2 to form pores, Irregular pores are formed at the initial stage of the dissolution reaction.Since the oxidation rate at the pore bottom is close to 0, the dissolution rate is much higher than the oxidation rate, resulting in the continuous dissolution of the oxide layer at the bottom of the pores and pore deepening.One model suggests that under the action of the volume expansion and compressive stress, TiO 2 changes from pores to holes [66].As the holes multiply and grow, the originally separate holes begin to interfere with each other, gradually forming regular, self-organising nanotubes [69].As shown in figure 2(d) and table 1, the diameters of nanotubes are usually 10-100 nm, and nanotubes have good homogeneity.
As shown in figure 2(d), individual TiO 2 nanotubes produced by the anodic oxidation are generally separated by gaps among them.The length of TiO 2 nanotubes produced by the anodic oxidation has increased from submicron to about 1000 µm, and the self-assembly has also been continuously improved [66].In addition to forming nanotubes in a one-step oxidation process, two-step anodization process is also widely used to prepare highly ordered hexagonal TiO 2 nanotubes [78][79][80].The first step is to remove the nanotubes left behind by the first oxidation and create pits.And the pits are used to carry out a second oxidation to distribute the electric field more evenly.

Anodic aluminium oxides (AAOs)
An anodized aluminium template is a membrane with a honeycomb pore structure produced by oxidizing high-purity Al (>99.99%) in a specific acidic electrolyte.Its hole size can be controlled in the range of 50-400 nm, with a hole density of 10 10 -10 14 holes•cm −2 .The diameter, density and depth of the holes can be adjusted by the electrolyte composition, anodizing parameters and the hole expansion process.AAOs are widely used to prepare nanodots and nanowires due to the advantages of controllable morphology, highly ordered holes, mature process and good chemical stability.
In 1995, Masuda and Fukuda [81] prepared AAO templates with highly ordered nanoholes by a two-step anodic oxidation method, which has become one of the most widely used methods for preparing AAO templates.As shown in figure 3(a), an Al sheet is firstly degreased and polished, followed by primary oxidation in diluted H 2 C 2 O 4 to form an oxide film.The template is then immersed in a solution containing a specific ratio of H 3 PO 4 and H 2 CrO 4 to remove the disorganized oxide film.Secondary oxidation is continued on the remaining hollows to obtain ordered pores, then the aluminium substrate and the barrier layer are removed, usually in NaOH solution, to obtain a double-pass AAO template.Some researchers proposed that repulsive forces induced by the volume expansion and compressive stresses generated by the differential properties at the metal/metal oxide interface during oxidation cause the selforganization of the pores [82,83].From figure 3(b) and table 1, it can be seen that the holes of AAO are well-distributed with diameters of tens of nanometres.Apart from the two-step

Thin film memristors
Oxide thin films can be prepared by the anodic oxidation as switching layers of memristors.This method has the advantage of room-temperature formation, fast preparation, simple operation and good film uniformity.The thickness of memristive switching layers is typically tens of nanometres or a few nanometres.By means of the anodic oxidation, one can quickly prepare oxide films of tens to hundreds of nanometres.One can also prepare various metal oxide films, such as titanium oxide, tantalum oxide, niobium oxide, hafnium oxide, and copper oxide.Table 2 lists the specific parameters of oxide film memristors fabricated by the anodization technique.From table 2, it can be seen that the anodic oxidation technique allows for rapid preparation of oxide thin films, and the oxidation process can be completed within 10 s.The memristors produced by this process have excellent properties, including high yield, good endurance and low variation.In this chapter, we will introduce various metal-oxide-thin-film memristors prepared by anodic oxidation.

Memristors based on titanium oxide films
Hewlett-Packard Labs fabricated titanium oxide-based memristors with a structure of Pt/TiO 2 /Pt in 2008 [96].By applying a voltage to the device, oxygen vacancies in the TiO x film moved, changing the distribution of the oxygen vacancies, thus achieving the reversible resistive switching between the HRS and the LRS.
In the beginning, most researchers fabricated memristors by anodizing millimetre-scale Ti foil.Diamanti et al [97] oxidized a 0.5 mm Ti foil in 0.5 M H 3 PO 4 or H 2 SO 4 at a constant current density of 10 mA•cm −2 , and stopped oxidation when the voltage reached the set value.The authors concluded that the oxide thickness and voltage were linearly correlated at about 1.8 nm•V −1 .This was based on a rough measurement of the film thickness.If the oxidation voltage was too high or too low, the electrical properties were poor; when the voltage was low, it was conductive.After optimization, the memristor exhibited a good loop opening when the voltage was between 25 V and 30 V. Liang et al [98] placed Ti coated Si wafers in 1-M H 2 SO 4 solution and the oxidation process lasted for 1 min at 20 V.In the end, Ti/amorphous-TiO 2 /Pt memristive devices were fabricated, which exhibited bipolar switching and excellent endurance (5 × 10 6 cycles).Gokcen et al [99,100] prepared TiO 2 memristors by oxidizing 0.125 mm Ti, and investigated the effect of the addition of metal cations Pb 2+ and Mn 2+ in the methanesulfonic acid electrolyte on the performance of the memristors.The oxidizing voltage was increased from −0.5 V at a rate of 10 mV•s −1 to 10 V.It was found that the addition of the two ions increased both the current density and the oxidation rate of Ti, resulting in a thicker oxide film.Pb 2+ formed Pb(OH) 2 2+ during the oxidation process and promoted the formation of TiO x , whereas Mn 2+ took part in the oxidation process and formed MnO x .Adding these two metal ions led to a wide hysteresis of I-V sweeping; Pt/TiO x /Ti/Pt memristors prepared by adding Pb 2+ showed good memristive behaviour after 10 4 I-V cycles.This study demonstrated the influence of the electrolyte composition on the film growth during the anodic oxidation.This study demonstrated the influence of electrolyte composition on film growth during anodic oxidation.The above work demonstrated the feasibility of producing titanium oxide memristors by anodic oxidation.
By optimizing the anodic oxidation process, some researchers have prepared titanium oxide memristors with excellent performance.In 2019, Chen et al [68]   voltage increased from 2.5 V to 30 V. The non-volatile memristor fabricated under the voltage of 2.5 V and in the NaOH electrolyte achieved low cycle-to-cycle variability for more than 4500 I-V cycles.The device also exhibited good cyclic stability at 120 • C, and the on-off ratio was greater than 100.Rather than conductive filaments, its resistive switching mechanism is the reversible redox of the interfacial oxide layer.This work shows that anodic oxidation can be used to produce oxide films in a very short time, greatly improving the fabrication efficiency of memristors.
The anodizing technique can also be used to prepare flexible titanium oxide memristors on flexible substrates as shown in figure 4(c).Siket et al [86] deposited 100 nm Ti on a flexible polyethylene naphthalate (PEN) substrate by electron beam deposition, and the Ti layer was oxidized under voltages up to 20 V increasing at a rate of 300 mV•s −1 in a pH 6 citric acid for 10 min.After depositing the Au top electrode, the nonvolatile Ti/TiO 2 /Au memristor showed good cyclic stability for more than 1000 I-V cycles at an on-off ratio of over 10 4 .
The most recent advancement in preparing TiO x thin film memristors through the anodic oxidation is the fabrication of a TiO x memristor array by Park et al in 2022 [52].A 100 nm Ti bottom electrode was firstly deposited by EBE, and then a 12 nm Ti interlayer was deposited.It was oxidized at 10 V in 0.05 M NaOH and 0.05 M NH 4 F electrolyte for 1 min to form 30 nm TiO x .As shown in figure 5, the prepared Ti/gradual TiO x /Pt device was a volatile memristor.The device was electroforming-free, with an on-off ratio of up to 10 3 .It also had self-rectifying characteristics and a rectification ratio was as high as 10 4 .The self-rectifying characteristics could effectively suppress sneak-path currents in an array.This is a very important issue in memristors.As shown in figures 5(d) and (e), among 30 randomly selected devices, the TiO x memristors exhibited high consistency, exceptionally uniform resistive switching with only 3.87% spatial variation (σ/µ).And the device exhibited current variability of 1.67% (σ/µ) over 50 pulse cycles.Because the activation energy for the migration of oxygen vacancies is 0.21 eV, oxygen vacancies can spontaneously diffuse under the concentration gradient, leading to volatility.The authors also prepared a 20 × 20 memristor array via combining the lift-off process and the reactive ion etching method.The memristor array was used to process time-sequential data and construct a memristive computing system.

Memristors based on tantalum oxide films
Tantalum oxide is a common resistive layer material.Memristors made from this material usually have the advantages of good data retention and endurance.Unlike titanium oxide, preparing tantalum oxide memristors by the anodic oxidation started relatively late; the earliest work was done by Wang et al [46] in 2015.
There are two types of tantalum oxide thin film memristors produced by anodic oxidation, i.e. porous and dense films.Porous tantalum oxide films have generally been prepared in highly concentrated acidic electrolytes and under high voltages, and the performance of the memristor can be adjusted by changing the voltage and time.Wang et al [46] applied a high voltage of 50 V for 20 s in high-concentration H 2 SO 4 (95%-98%) and 0.2 vol% HF to prepare a nanoporous (NP) Ta 2 O 5−x layer.Ten layers of graphene were then deposited on top of the NP Ta 2 O 5−x to prevent shortcircuiting between the porous structure and the top electrode Pt.The devices had good stability, showing good endurance over 2000 cycles, and 55 devices had similar on-off ratios (≈10), showing good uniformity.As shown in figure 6, Kwon et al [54] investigated Ta 2 O 5 film microstructure and performance of memristors prepared under different voltages and time in H 2 SO 4 (95%-98%) and 0.2 vol.%HF.It was found that porosity and homogeneity were primarily dependent upon the applied voltage, whereas porosity was jointly dependent upon applied voltage and time.As shown in figure 6(a), both the pore size and porosity increased as the voltage increased from 40 V to 50 V, and increasing oxidation time led to increasing porosity.The pores in the device with a lower oxidation voltage were smaller and more uniform, which improved the uniformity of the memristor as shown in figure 6(c).
As shown in figure 7(a), in 2018, Choi et al [49] oxidized 200 nm Ta in H 2 SO 4 (95%-98%) and 0.2 vol.%HF at 50 V for 10 s to prepare a porous Ta 2 O 5 film with a pore size of 20-50 nm.A 10 nm layer of TaO y (y ≈ 2.4) was then sputtered onto the oxide film, and the self-rectification effect was created by the Schottky barrier between the TaO y layer and the Pt electrodes.The device exhibited excellent operational retention (≈1.2 × 10 4 s) and endurance (5 × 10 3 cycles at 85 • C).The conductance of this memristor device was partially volatile, which might be related to the spontaneous movement of oxygen vacancies.In addition, a 16 × 16 memristor array was made with a low synapse-coupling value (I sneak /I on ) to suppress the sneak current.It is worth noting that the oxygen vacancies had a gradient concentration due to different degrees of oxidation of the film in the thickness direction, as shown in figure 7(b).The degree of oxidation at the top was high, and there were fewer oxygen vacancies.This phenomenon has also been found in other related research works [46,52].Though some researchers [101] have fabricated oxide films with oxygen vacancy concentration gradients by changing the ratio of oxygen content during the sputtering process, the vacancy concentration was discontinuous.Anodizing easily provides a continuous oxygen vacancy gradient, which promotes the release of conductive filaments at the oxide-electrode interface and improves the cycling stability of the device.
As shown in figure 8   that obtained by radio-frequency sputtering or electron beam deposition.The authors believed that the dense film improved the ion diffusion ability and was less affected by moisture, making performance more stable.
In 2021, Zrinski et al [88] placed 280 nm Ta in three electrolytes and gradually increased the voltage from 0 V to 8 V and then back to 0 V to prepare memristors with oxide films of about 15 nm.If the sweeping rate was too fast, the memory effect became unstable; when it was too slow, the chemical stability of the oxide was increased, preventing the effective formation of oxygen vacancies.The studies also demonstrated that electrolyte composition has a significant effect on cycle stability and retention performance.The devices prepared in phosphate had the longest endurance of 10 6 cycles, but the retention time was short.When prepared in citrate buffer, the devices had good retention properties.As shown in figure 8(b), Ta oxyphosphate was formed in the phosphate electrolyte to fix the spatial position of the conductive filament and improve the cyclic stability.Thus, for porous or dense tantalum oxide films, memristors with excellent properties can be fabricated under the appropriate oxidation process.

Memristors based on films of other metal oxides
In addition to titanium oxide and tantalum oxide, memristors of other metal oxides can also be fabricated by the anodic oxidation, such as NbO x [ Although anodized NbO x memristors could achieve a high on-off ratio of 1000 [92], the devices fabricated by the anodizing method often had large variability in set/reset voltages [89,92].Zrinski et al [91] studied the effect of the electrolyte composition on niobium oxide memristors, and concluded that the choice of electrolytes strongly affected the electrical characteristics of the devices.Due to the gradient distribution of oxygen vacancies in niobium oxide films, there was a synergistic effect between the insulator-to-metal (IMT) transition and oxygen vacancy filaments during the voltage sweep process [103], which would affect the device stability.
Kundale et al [94] prepared Cu/CuO x /Pt devices by oxidizing at constant current density (10 mA•cm −2 ) or constant voltage (6 V) for 150 s in three alkaline electrolytes.It was found that in the alkaline electrolytes, short nanowires/nanorods were obtained due to the attraction of high concentration of OH − ions to the anode, while the co-existence of other ions, such as Cl − , produced granular morphology.Devices with different morphologies exhibited different switching characteristics, such as digital and analogue switching.In addition to single metals, Zrinski et al also used the anodic oxidation to oxidize composite metals, such as Nb-Ta [104], Hf-Ta [105,106], and Nb-Hf [107], and some satisfactory results were obtained.

Performance comparison of memristors
In table 3, the performances of oxide memristors fabricated by anodization are compared with those of memristors prepared by other methods.The oxide memristors fabricated by anodization demonstrate good endurance, some even reaching 5 × 10 6 cycles, better than memristors fabricated by other methods.The oxide memristors fabricated by anodization also have low set/reset voltages, enabling the preparation of lowpower systems.
When preparing thin film memristors by the anodic oxidation, some issues should be paid special attention to.First, anodizing cannot prepare uniform VO 2 or NbO 2 due to the oxygen vacancy gradient distribution.Therefore, the simultaneous existence of oxygen vacancy filaments and IMT transition will affect the cycling stability.In addition, the oxidation behaviour of vanadium is quite unusual and anodized films dissolve rapidly in aqueous solutions; acetone or acetic acid based electrolytes are required to complete the oxidation process [115].With adequate initial metal source, the thickness of an oxide film shows a positive correlation with the applied voltage, but if it is too high, a voltage will result in surface porosity.At the same voltage, metals with different initial thicknesses will have different film thicknesses after oxidation.When the metal thickness is thin, the oxide film will not increase after the voltage reaches its saturation value.Furthermore, by increasing the oxidation time, the degree of oxidation of the film increases and the composition can be close to the stoichiometric ratio.
Acidic electrolytes, such as phosphoric acid, sulphuric acid, and citric acid, are common choices of electrolytes.Some ions in electrolytes can participate in various reactions and enter oxide films [90,99].For example, in the phosphoric acid electrolyte, phosphoric acid reacts with Ta to form Ta oxyphosphate, which enhances the stability.In general, if the electrolyte concentration is low, it takes a long time for an oxide film to form.If it is too high, the film will be dissolved to form a porous structure.By reasonably adjusting anodic oxidation parameters, memristors with high yield, good device consistency and cyclic stability can be reliably fabricated.

Fabrication of memristors using AAOs as templates
An AAO is a self-organized porous template for forming various nanostructures, with hole sizes ranging from tens to hundreds of nanometres.It has many favourable features, such as low manufacturing cost, good thermal/mechanical stability, high hole density, and controllable hole size, depth and shape.It can be used to deposit nanodots and prepare nanowires.It is important to note that ultra-thin AAOs need to be transferred with polystyrene film to prevent breakage during the process [76].

Nanowire memristors
Nanoscale fabrication of device arrays is an effective solution for achieving high-density storage and scaling down device size.Meanwhile, the unique properties of nanostructures are helpful in exploring complex nanoscale resistive switching mechanisms and understanding the scalability of ReRAMs.However, when the device size is reduced to the nanoscale, the top-down approach such as photolithography normally involves high production costs and long processing times.Therefore, a bottom-up approach using templates is more favourable for the fabrication of nanostructures.The preparation of nanowires (NWs) using AAOs often requires a combination of other processes.These include electrochemical deposition (ECD), thermal oxidation and sputtering.
Huang et al [116] prepared Pt/Ni multilayered nanowire arrays in an AAO template using the ECD technology, and then prepared Al/multilayer Pt-NiO/Pt memristors after annealing at 800 • C for 6 h.The nanowires were 70 nm in diameter and each multilayer nanowire consisted of approximately 100 NiO/Pt cells.The devices exhibited repeatable multilevel effects, up to 10 5 on-off ratios and at least 10 4 s retention time.Both the multilayer nanowire and the single-layer NiO nanowire had no multi-level states under different amplitudes or durations of voltage pulses.As shown in figure 9(a), Kim et al prepared Au/NiO/W nanowire memristors using AAOs in 2008 [117].They firstly prepared AAO with a hole size of 70 nm in a 0.3 M oxalic acid solution using a two-step anodic oxidation method at a voltage of 40 V. Then Au was plated on the bottom, Ni metal was deposited in the holes of the AAOs by the ECD technology.After that, Ni was oxidized at 450 • C for 7 h to obtain NiO, and W was deposited as the top electrodes.The memristor was composed of many individual nanowires (25 µm in length) between the two electrodes, and the forming voltage was much lower than that of corresponding thin film devices.
Liang et al [59] used a two-step anodic oxidation method to prepare AAO with a hole size of 50 nm, as shown in figure 9(b).Cu nanowires were prepared by ECD, which were then thermally oxidized at 400 • C for 10 h and 20 h to obtain CuO x nanowires.Finally, Ni/CuO x /Ni memristors without electroforming were prepared by adding Ni electrodes on both sides of the nanowires.The memristor had a large onoff ratio of more than 10 3 .When the oxidation time was 20 h, the complete oxidation of the oxides resulted in fewer oxygen vacancies and therefore, no switching characteristics were observed.
Berivio et al [118] used AAO with a hole size of 50 nm to prepare Au/NiO/Au nanowire memristors with a nanowire length of about 33 nm.The memristor had three stable resistance states, but during testing with the conductive atomic force microscope (AFM), it was found that the nanowires were shortened due to oxygen loss from NiO and stress on the AFM tip.Han and Lee [75] used a two-step anodic oxidation method to prepare an AAO template with an average hole size of 85 nm in a 0.3 M H 2 C 2 O 4 under a voltage of 40 V.Both Cu and CuO x were deposited by ECD.The total thickness of the memristor was about 180 nm.The nanowire memristor had a low set voltage (1.3 V)/reset voltage (−0.75 V) and an on-off ratio of 1000.Some researchers have used plasma process to oxidize metals.For example, Song and Lee [62] used a two-step method to prepare an AAO template with a hole size of 75 nm.Ni was deposited and then oxidized by plasma at 180 • C for 1 h.The device structure was Ni/NiO x /Ni, and total height was <100 nm.The device showed unipolar switching behaviour with a set voltage of 9 V and a reset voltage of 6 V.
In addition to the ECD method, the sputtering method can also be used to prepare nanowires.In 2012, Lyu and Lee [76] prepared Pt/HfO 2 /Au memristors by using AAO templates in combination with magnetron sputtering.The average value of the set voltage was 3.14 V and the reset voltage was 2.35 V. Liu et al [119] sputtered a 15 nm thick amorphous La 1−x Sr x MnO 3 interlayer and Ag top electrode in holes of AAO with an average hole size of 80 nm and a thickness of 200 nm.The set voltage of the prepared Pt/La 1−x Sr x MnO 3 /Ag nanowire memristors was about 6 V and the reset voltage changed significantly in 15 I-V cycles.The on-off ratio of device was more than 100.The AAO template can also be applied to prevent external oxygen and H 2 O from affecting the nanowire memristor, thereby improving the stability and lifetime of nanowire devices [58].

Nanodot memristors
One switching mechanism of memristors is the formation and breakage of conductive filaments; the set and reset voltages show large variations in switching operations due to the uncertainty of the filament formation and breakage positions.This remains one of the key challenges hindering the application of memristors.AAOs with highly ordered nanopores can form a uniform nanostructure to control the directional release of conductive filaments, thereby improving the device's reliability and reducing the set/reset voltage.
As shown in figure 10(a), Hua et al [61] introduced silver nanodots as a diffusion source in a bidirectional threshold switching memristor, using the EBE combined with an ultrathin AAO template.Such a memristor could suppress the sneak current and was used to prepare a one-selector-oneresistor (1S1R) element.Experiments demonstrated that rapidly thermally processed Ag nanodots could help to form multiple weak Ag filaments that broke spontaneously as the voltage decreased.Moreover, compared with Ag thin films, Ag nanodots as active electrodes could avoid excessive movement of Ag atoms into HfO 2 during operation, resulting in stable conductive filament growth.The device showed electroforming-free property and the on-off ratio was >10 9 .
Additionally, V th of the devices presented narrow distribution and good switching uniformity.
As shown in figure 10(b), Qu et al [64] deposited about 5 nm thick Ti nanodots on Pt through an AAO template to prepare Pt/Ti nano-island (NI)/WO x memristors.Ti nanodots could strengthen the electric field along the voltage direction and promote the formation of conductive filaments of oxygen vacancies.Compared with WO x /Ti/Pt devices, the variation coefficients of V set and V reset of WO x /Ti NI/Pt devices were reduced by about 84.9% and 83.7%, respectively.
Nanodots can also be embedded into the interlayer to improve the performance of the memristor.As shown in figure 11, Wang et al [120] used two kinds of AAO templates with different hole sizes (30/90 nm) to deposit Ti/Pt/Ag three metal nanodots in the middle of HfO 2 .Compared to the device without nanodots, the nanodots made the electric field more concentrated, which favoured the generation and accumulation of oxygen vacancies.For memristors deposited with Pd nanoparticles (diameter = 30 nm), the variation coefficients of LRS and HRS were reduced by 95% and 89%, respectively, as compared to devices without nanoparticles.Memristors prepared via AAOs with large hole sizes have lower set and reset voltages and wider distribution ranges than those with small hole sizes.Ag and Pt nanodots were more effective in enhancing uniformity than Ti nanodots.Figure 11(c) shows that as the position of the nanodots moved from middle down to bottom, the set voltage decreased; in such a way, the distance between the nanodots and the bottom electrodes decreased, which increased the Joule heating and the charge injection.Finally, Nb layers with a diameter of 100 µm were sputtered as the top electrode.As shown in figures 12(b) and (c), the nano-needles in this device had a higher surface area/volume.This enhanced the field strength and stabilized the forming position of conductive filaments, thereby reducing the set/reset voltage and minimizing set/reset voltages variations.As the NiO thickness increased to 100 nm, the field enhancement effect of the nano-needles became weakened.When the thickness increased to 150 nm, the enhancement effect basically disappeared.

Nano-tubular memristors
Some researchers also prepared oxide nanotubes as interlayers in memristors.TiO x and ZrO x nanotubes prepared by the anodic oxidation were often used to fabricate nano-tubular memristors.When preparing TiO x nanotubes by the anodic oxidation, a mixed solution of C 2 H 6 O 2 and NH 4 F was widely used as the electrolyte.Dorosheva et al [72] oxidized Ti at 10 V for 5-20 min in C 2 H 6 O 2 and C 3 H 8 O 3 containing 1 wt.%NH 4 F, and obtained nanotubes (NTs) with an outer diameter of approximately 45 nm and varying lengths.Ti/TiO x nanotube/Au memristors were fabricated after sputtering Au as the top electrodes.When the oxidation time was 15 min, the length of the nanotube was 160 nm; such a memristor had the best performance.It had an on-off ratio of about 134, but the on-off ratio was variable.Nirmal et al [53] used an electrolyte containing C 2 H 6 O 2 , H 2 O and 3 wt.%ammonium fluoride as the electrolyte to explore the impact of different water contents (1 vol.%-10 vol.%) on nanotube morphology and memristor performance as shown in figure 13(a).They found that the diameter of the nanotubes increased initially and then decreased as the water content increased, reaching a maximum of approximately 87 nm at 5 vol.%.A smooth structure was observed at a water content of 5 vol%, but at lower or higher water contents, the nanotubes showed defects such as disordered growth.Meanwhile, the memristors exhibited an on-off ratio of nearly 120 at a water content of 5 vol.%, and the I-V curve remained stable for up to 10 4 cycles.
As shown in figure 14(a), Choi et al [71] sputtered a 40 nm Ti film on the substrate, followed by oxidation at voltages of 5/10/15 V for approximately 6 min using a mixed electrolyte of C 2 H 6 O 2 and NH 4 F. Afterwards, Ag top electrodes were then sputtered onto TiO x .As the oxidation time increased, the defective titanium oxide was formed firstly, then the nanopore structure with a diameter of 10 nm grew on the defective layers, the total thickness of the oxidized layer was about 65 nm.This nanoporous structure is similar to the nanotube structure.As the oxidation time increased, the defective TiO x at the bottom became thinner and the composition closed to the stoichiometric ratio of TiO 2 .The defective titanium oxide layer at the bottom had an oxygen vacancy concentration gradient, which could effectively control the excessive growth of silver filaments and solve the trapping effect.By adjusting the stoichiometric ratio of the defective titanium oxide layer, the on-off ratio and endurance of the memristor could be tuned.The top nanotubes provided channels and confinement for silver wires, which effectively solved the Rayleigh instability and improved the stability and retention properties of the device.Compared to nanotubes with large hole diameters, nanotubes with small hole sizes could not easily provide additional space for Ag atoms to diffuse away; the retention time of the device was increased.The device had a lower forming voltage, a more stable resistance state and a higher on-off ratio than the TiO 2 memristor obtained by high-frequency sputtering.As shown in figure 14(b), the set voltage of the device changed by only 2.7% over 90 I-V cycles, whereas the set voltage of the sputtered device changed by 18.2%.Exploiting the ordered pit morphology at the initial stage of the nanotube formation could also regulate the growth path of conductive filaments, thereby increasing the device stability and yield.Some researchers also fabricated memristors using titanium oxide nanotubes, although the memristors did not perform well [73,74].

Neuromorphic computations
The high efficiency and low power consumption of the brain come from its internal structure.There are about 10 11 neurons and about 10 15 synapses connected to each other to form a complex neural network to process external information [122].Biological neurons receive a variety of excitatory or inhibitory signals from pre-neurons and integrate them into the membrane potential.Due to the leaky integration characteristics of neurons, if the applied signal strength is insufficient, the membrane potential fails to reach the threshold, and the membrane potential drops rapidly.When the membrane potential exceeds the threshold potential, a neuron generates an action potential and transmits it to the next neuron through synapses [52].A synapse is a node connecting neurons before and after a synapse, and its synaptic weight represents the connection strength between two neurons.Synaptic weights can be adjusted by the activity of pre-and post-synaptic neurons, thereby regulating the efficiency of signal transmission.This is called synaptic plasticity and is also the basis of the brain learning [98,101].Studies have found that the conductance of a memristor can act as the synaptic weight, and the memristor can change the conductance and emulate the plasticity of the synapse well under the modulation of external pulses; the synaptic plasticity obeys some learning rules, such as paired pulse facilitation, spike timing-dependent plasticity (STDP) and spike rate-dependent plasticity [123,124].
Non-volatile memristors are commonly used to emulate synaptic properties.As shown in figure 15(a), Chen et al [68] changed the memristor conductance by applying pulses to the Ti/TiO x /Pt memristor, emulating the change in synaptic weight.It can be seen that applying forward pulses increases the conductance, and applying backward pulses with different pulse amplitudes can change the conductance decrease rate.Different research groups have prepared Ti/TiO x NT/Al [44] and Cu/CuO x /Pt [94] memristors by the anodic oxidation, and used the same method to emulate the characteristics of biological synapses with two devices, as shown in figure 15(b).Different weight modification values ∆G⁄G 0 can be obtained by changing the positive and negative values of the peak time interval ∆t, which can be used to emulate the anti-symmetric Hebbian (ASH) and anti-symmetric anti-Hebbian (ASAH) learning of the STDP rules.In addition, a convolutional neural network (CNN) was simulated based on the synaptic weight of the devices, and the CNN structure similarity index measure could reach up to 80%, and the image edge detection was realized.
Most of the oxides fabricated by the anodic oxidation contain oxygen vacancies, which are easy to form oxygen vacancy conductive filaments, and then form non-volatile memristor devices.Therefore, some people have used the anodic oxidation to prepare volatile memristors.At present, only the Ti/gradient TiO x /Pt memristor array prepared by Park showed a fully volatile conductivity [52].The memristor exhibited conductivity volatility due to the low oxygen vacancy activation energy and oxygen vacancy gradient concentration.As shown in figure 16(a), the authors connected a conductancevolatile memristor and a capacitor in parallel to emulate the cell body of a neuron, and connected a fixed-value resistor in series to realize the function of a leaky-integrate and fire (LIF) neuron.They declared that if the soma received enough charge from the presynaptic spike within a given time interval, the capacitor voltage would increase.This would strengthen the memristor and cause it to discharge.It was possible to adjust neural firing thresholds by changing values of parallel capacitance and series resistance, as well as neural firing rates, and to determine if the neural firing occurred by adjusting the presynaptic peak frequency.The memristor was also used to process time-sequential data and to construct a neural memristive computing system.As shown in figure 16(c), the decay rate of the memristor was controlled by changing the duty cycle of the pulse to simulate different memory times, different recognition results were achieved for the same time series of inputs.

Non-volatile memories (NVMs)
Memristors have a simple MIM structure and can be integrated into densely interleaved arrays.Memories composed of memristors are called ReRAMs, which are very likely to become the mainstream for the next generation of information storage.As NVMs, memristors also have to overcome the problems of poor stability, consistency, data retention and leakage current of the array [35].Non-volatile memristors prepared by the anodic oxidation technique can achieve excellent stability and data retention.However, the realization of large-scale arrays still needs to optimize the consistency among devices, and to solve the problem of sneak current when reading and writing information in an array.The selfrectifying memristor array prepared by the anodic oxidation technique can reduce the sneak current problem to a certain extent.
As shown in figure 17(a), Wang et al [46] prepared porous tantalum oxide-based memristors using the anodic oxidation technique and obtained good self-rectifying behaviour under the 1/3 voltage reading (V r/3 ) scheme. Figure 17(b) shows the calculated readout margin of the nanopore (NP) Ta 2 O 5−x memristor under different voltage schemes using the cross-array equivalent circuit.Choosing the experimental I-V data with the highest nonlinearity close to ∼10 5 , the memristor can be further scaled up to ∼162 Gbit interleaved array.This performance was better than the maximum number of bits calculated by various integrated architectures such as one-diode-one-resistor (1D1R), one-selectorone-resistor (1S1R), and complementary resistive switch.Since such a technique does not require additional devices in series, it shows application in high-density information storage.

Conclusion
Compared with the magnetron sputtering, the atomic deposition and other techniques, the anodizing technique is a lowcost, convenient and controllable room temperature fabricating process.Firstly, the anodizing technique has found a wide range of applications in the preparation of memristors.Thin film memristors and nanotube memristors can be directly prepared, while nanowire memristors and nanodot memristors can be prepared via AAO templates.Secondly, the anodizing equipment is cost-effective, and experiments can be carried out at room temperature, and no vacuum is required.Meanwhile, it is also easy to regulate the performance of memristors.Via varying the applied voltage, time, electrolyte composition, concentration and other parameters during the anodic oxidation process, the oxide film thickness or nanotube length, and oxygen vacancy concentration can be adjusted.More importantly, memristors fabricated by means of anodizing have good consistency.Some researchers have fabricated memristors with good consistency, and even devices with 100% yield and low variability [52].
Compared to thin film memristors, nanotube memristors require a longer oxidation and post-processing time.The limited mechanical stability and long length of nanotubes make them less attractive for real-world applications.
AAOs can be used to fabricate large-area nanowire arrays.The size of such memristors is in the nanometre scale, and the conduction mechanism can be studied at the nanometre level.The purpose of using AAOs for nanodot electrode deposition or interlayer modification is to increase field strength through ordered nanostructures, fix filament position, and then stabilize device cycling stability and reduce set/reset voltages.

Perspective
Though the anodic oxidation technique has multiple advantages in fabricating memristors, it still faces some challenges: (1) The microstructure and morphology of oxide films or nanotubes fabricated by the anodic oxidation can be qualitatively controlled, but it is difficult to be predicted preciselysince it is controlled by a variety of factors such as electrolyte, oxidation process and substrate materials.Strict control of the anodic oxidation parameters is required to better regulate the performance of the memristors.
(2) Memristors with multi-layer oxides typically exhibit excellent conductivity retention and regulation properties.
Research on the anodic oxidation of multilayered memristors is promising but still deficient.(3) During the practical fabrication of a memristor array, in order to mitigate the sneak-path current, an access element is introduced to the memristor cell to form a composite cell, such as one diode-one memristor, one-transistorone-memristor (1T1R), and one-selector-one-memristor (1S1R).In the case of 1T1R, a memristor is deposited on the drain of a transistor fabricated by the CMOS technique.When combined with the anodizing technique, it is possible to mask the whole surface but the drain with photoresist firstly, then deposit a metal layer on the whole surface and oxidize it; afterwards, remove the photoresist to leave only the oxide on the drain.However, bubble formation during the oxidation process and photoresist detachment remain a problem of concern.(4) Some oxide materials, such as titanium oxide and zinc oxide, are sensitive to certain gases or light.The conductance of these oxide-based memristors responds to changes in the external environment, and thus the preparation of memristors with sensing effect using anodizing is a viable attempt.

Figure 4 .
Figure 4. Nonvolatile memristors based on titanium oxide prepared by anodic oxidation: (a) schematic of the electrochemical growth of TiO 2−x films on Ti substrate, I−V curves collected at room temperature, 75 • C and 120 • C. Reprinted with permission from [68].Copyright (2019) American Chemical Society.(b) I−V curves using different electrolytes.(c) A schematic diagram of TiO 2 memristor fabricated on polyethylene naphthalate (PEN) flexible substrate, I-V curves, high and low resistive states for about 1000 cycles.Reproduced from [86].CC BY 4.0.
performed oxidation separately in 0.5 M H 3 PO 4 , NaOH and NH 4 H 2 PO 4 for 15 s using a 2 mm Ti foil, as shown in figures 4(a) and (b).The oxide thickness increased from 10 nm to 65 nm as the applied

Figure 6 .
Figure 6.Pt/NP Ta 2 O 5−x /MLG/Pt memristors prepared by anodic oxidation.Reprinted with permission from [54].Copyright (2017) American Chemical Society.(a) Schematic diagram of the device structure and microstructure, the effect of oxidation process on the porosity of the oxide film.(b) Switching I-V curves of memristors prepared at 50 V using different anodizing time (5 s and 30 s).(c) Comparison of logarithmic Rmax values at different anodization voltages for 20 s.
(a), Zaffora et al[51] fabricated Ta/Ta 2 O 5 /Pt memristors by oxidizing 280 nm Ta in 0.42 M H 3 PO 3 and 0.08 M Na 3 BO 3 electrolyte at 10 V voltage; dense Ta 2 O 5 films of approximately 20 nm were obtained.The devices exhibited stable endurance for over 10 6 cycles and good retention at different conductance states for 10 4 s.The oxide film had a density of 8.5 g•cm −2 , higher than

Figure 9 .
Figure 9. Nanowire memristors fabricated by AAOs: (a) schematics of the process for the fabrication and electrical tests of NiO nanowire memristors.Reprinted from [117], with the permission of AIP Publishing.(b) Schematics of the fabrication processes of CuOx NW array.Reprinted with permission from [59].Copyright (2014) American Chemical Society.

Figure 10 .
Figure 10.Volatile and nonvolatile nanodot memristors fabricated using AAOs: (a) schematic illustration of fabrication process of Pt/HfO 2 /Ag nanodot memristors, bidirectional threshold switching behaviour and cumulative probability of turn-on voltage (V th ) of the device.Reproduced from [61].CC BY 4.0.(b) Schematic structure of WOx/Ti NI/Pt memristor and microstructure of Ti nanodots, cumulative probabilities for R HRS and R LRS , I-V curves of the WOx/Ti NI/Pt memristor.Reprinted from [64], © 2021 Elsevier Ltd.All rights reserved.

Figure 11 .
Figure 11.Template-directed nanoisland embedded hafnium oxide memristor using AAOs.[120] John Wiley & Sons.© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.(a) A cross-sectional view of the embedded structure and an SEM image of the AAO from a top-down view.(b) Resistance cumulative probability of embedded memristors with 30 nm and 90 nm diameter nanoislands.(c) Comparison of the resistive switching characteristics of memristors embedded by Pt nanodots in bottom and middle regions.

Figure 12 .
Figure 12.NiO memristors with Nb nanopin-shaped electrodes prepared by combining AAO and wet etching.Reproduced from [121] with permission from the Royal Society of Chemistry.(a) Schematic drawings of the process of forming Nb nanopin-shaped electrodes and NiO thin film.(b) Comparative illustrations of the conducting filaments in the NiO1 (Nb nanopin electrode) and NiO2 (Nb thin-film electrode) memristors.(c) Set and reset voltages as a function of switching cycle numbers for the NiO1 and NiO2 memristors.

Figure 15 .
Figure 15.Synaptic behaviours and neural network applications of nonvolatile memristors.(a) I-V characteristics and conductance change of Pt/10 nm TiO 2−x /Ti memristor under different pulses.Reprinted with permission from [68].Copyright (2019) American Chemical Society.(b) Conductance under different pulses and STDP-based synaptic learning rules such as antisymmetric Hebbian and antisymmetric anti-Hebbian based on Ti/TiO 2 nanotube/Al memristor.Reprinted with permission from [53].Copyright (2022) American Chemical Society.(c) Pt/CuxO/Cu memristor applied to CNN to process image edge detection.Reprinted from [94], © 2022 Elsevier Ltd.All rights reserved.

Figure 16 .
Figure 16.LIF neuron and neuromorphic computing systems.Reproduced from [52].CC BY 4.0.(a) Depiction of a biological neuron and an artificial LIF neuron based on memristors.(b) Artificial neuron's LIF operation.(c) for the gradual TiOx memristor-based artificial neuron.(d) Memristors' output through the entire input sequence in short-term, middle-term, and long-term memristors.

Figure 17 .
Figure 17.Self-rectifying NP Ta 2 O 5−x memristors for non-volatile storage.Reprinted with permission from [46].Copyright (2015) American Chemical Society.(a) Representative I-V characteristics of device with electric circuit array of V r/3 scheme.(b) Calculated readout margin ∆Vout/Vpu as a function of the number of word/bit lines under Vr scheme and V r/3 scheme.(c) The maximum size of bits and other integrated architectures under Vr, V r/2 , or V r/3 scheme.

Table 1 .
Anodized nanotubes and AAO templates for preparing the memristors.Oxidation process, structure characteristics and applications are listed.

Table 2 .
Anodized thin film memristors of different metal oxides.Device structure, oxidation conditions and resistive switching (RS) mechanism are listed.

Table 3 .
Performance comparison of memristors under different oxide thin film preparation processes.