**2. Anodic oxidation**

Generally speaking, Ti, Hf, Ta, Zr and, valve metals are potential candidates to be anodized. Anodic oxidation is an electrochemical technique that allows to grow nanometric oxide films at a metal surface, with controlled chemical composition, structure and thickness that are defined by properly choosing the relevant electrochemical parameters—cell voltage, electrolytic solution, process time [13–15].

The technique consists of polarizing the metal by imposing a current flow between the specimen and a counterelectrode immersed in a suitable electrolyte. Metal atoms are oxidized to cations, which progressively combine with oxygen (or oxygen-containing) anions from the electrolyte to form an oxide layer that deposits on the metal surface. It is both an inward and outward growth mechanism, with a slight predominance of O2− charge carriers transport across the oxide to reach the metal surface where metal cations are produced, owing to the higher mobility of oxygen anions with respect to metal cations [14]. Given a determined metal or metal alloy, oxide characteristics are then determined by the set of anodizing parameters: electrolytic solution composition, concentration and temperature; feeding voltage; method of voltage application (galvanostatic, potentiostatic, potential ramp). Two main classes of anodic oxides are of interest to obtain memristive behavior and will be described in the following, namely, compact thin films and nanotubular films; the switching behavior of anodic oxides will be addressed in Section 3.3.

#### **2.1. Thin compact films**

materials, as the two terms identify the same switching behavior [2, 3]—were identified as valuable candidates for alternative nanoelectronic devices [4–7], with particular reference to

Indeed, several oxides are capable of resistive switching, that is, their resistance can be switched through a suitable voltage pulse between at least two different values—a high resistance state, HRS, also addressed as OFF state, and a low one, LRS, identified as ON state, by

Oxide properties—thickness, composition, stoichiometry and defectiveness—are crucial to determine whether it shows memristive properties, and the values of main switching parameters. Hence, the production technique plays a major role, as in turn it determines oxide characteristics; yet, the most commonly employed oxide synthesis/deposition techniques imply

We here present and summarize current knowledge on the growth of oxides with resistive switching capability by anodic oxidation, a low-cost electrochemical technique that may find a new niche of application in the production of memristive metal oxides. In Paragraph 2, the principles of anodic oxidation are described to highlight the typical oxide characteristics that can be achieved. The discussion will be limited to thin oxide layers, and no reference will be made to thicker ceramic oxides produced in sparking regime, as they are not pertinent to the present application [12]. Paragraph 3 provides a comparison of the characteristics of different metal oxides that show memristive properties, focusing on those that can be obtained by anodic oxidation, and then specifically focuses on anodic oxides. Finally, in Paragraph 4, the

Generally speaking, Ti, Hf, Ta, Zr and, valve metals are potential candidates to be anodized. Anodic oxidation is an electrochemical technique that allows to grow nanometric oxide films at a metal surface, with controlled chemical composition, structure and thickness that are defined by properly choosing the relevant electrochemical parameters—cell voltage, electro-

The technique consists of polarizing the metal by imposing a current flow between the specimen and a counterelectrode immersed in a suitable electrolyte. Metal atoms are oxidized to cations, which progressively combine with oxygen (or oxygen-containing) anions from the electrolyte to form an oxide layer that deposits on the metal surface. It is both an inward and outward growth mechanism, with a slight predominance of O2− charge carriers transport across the oxide to reach the metal surface where metal cations are produced, owing to the higher mobility of oxygen anions with respect to metal cations [14]. Given a determined metal or metal alloy, oxide characteristics are then determined by the set of anodizing parameters: electrolytic solution composition, concentration and temperature; feeding voltage; method of voltage application (galvanostatic, potentiostatic, potential ramp). Two main classes of anodic oxides are of interest to obtain memristive behavior and will be described in the following,

high investment costs and rather long deposition times to achieve satisfactory results.

potential application of these materials in neuromorphic computing is discussed.

[8, 9], TiO<sup>2</sup>

[3], HfO<sup>2</sup>

nonvolatile memories and neuromorphic applications.

46 Advances in Memristor Neural Networks – Modeling and Applications

[11] are the most studied.

[10] and Ta2

O5

**2. Anodic oxidation**

lytic solution, process time [13–15].

operations of "set" (OFF-ON) and "reset" (ON-OFF). Among them, SiO<sup>2</sup>

Ion migration that allows oxide growth during anodizing takes place in a solid film tens, or hundreds, of nanometers thick; therefore, it is associated with very high electric fields, in the order of 107 V/cm. To achieve such conditions, current densities of some tens or hundreds of A/m<sup>2</sup> are used, and cell voltages to produce thin compact films are between 10 and 100 V [12, 16]. A very large number of electrolytes can be employed, from diluted acids to neutral salts, to alkaline solutions [17–19]. Such oxides generally show an amorphous, or predominantly amorphous, structure, especially at low voltages, where only some nonstoichiometric crystal phases like Magnéli phases may appear.

Oxide thickness increases linearly with applied cell voltage: anodizing ratios are in the range of 2 ± 0.5 nm/V depending on metal composition, electrolyte and growth mode—either galvanostatic or with potential ramp [12, 17–19]. The thicker the oxide already formed, the more onerous its further thickening: indeed, at growing voltages—and hence oxide thicknesses other parasitic processes may kick in, consuming part of the current supplied to the electrode. As a consequence, if the amount of charge employed in the process is used to estimate oxide thickness by coulometry [20, 21], the so-calculated thickness is affected by parasitic reactions, since a portion of current is dissipated, mostly in oxygen evolution, to an increasing extent with increasing cell voltage (**Figure 1**) [19, 20]. Most of research studies on the growth of thin films by anodic oxidation refer to titanium and its alloys and to aluminum [12–14, 22–25], given their relevance in already mature industrial applications. Some works are also proposed on other metals, such as zirconium, niobium, hafnium; yet, they generally focus on the obtaining of high specific surface area morphologies, such as nanotubes [26], which are described in next paragraph.

**Figure 1.** Thickness versus voltage curve of a typical galvanostatic anodic oxidation process performed in acid electrolyte: Measured oxide thickness grows linearly with voltage, while coulometry exponentially overestimates thickness due to parasitic reactions.

### **2.2. Nanotubular films**

In the presence of aggressive species that are capable of localized dissolution of the growing oxide, nanotubular films can be grown, as shown in **Figure 2**. The peculiar morphology is associated with the simultaneous electrochemical growth of the oxide and its chemical dissolution operated by fluoride ions or, less frequently, other halogen ions. To achieve the formation of a nanotubular layer, a potentiostatic process is applied, where the chosen cell voltage—in the range 20–120 V—is maintained constant for various times, from few minutes to few hours [27, 28].

• a change in stoichiometry induced by heating (thermochemical mechanism, TCM);

ECM, also called conductive bridge, CB) under the applied electrical field [4].

mechanisms in memristive oxides [4, 32–34].

• the formation of conductive filaments by migration of ions from an active electrode metal and their deposition at the counterelectrode (electrochemical metallization mechanism,

Memristive Anodic Oxides: Production, Properties and Applications in Neuromorphic Computing

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The most easily occurring switching mechanisms common to all metal oxides are VCM and ECM. Yet, mixed filamentary switching mechanisms, both by electrode ions migration and metal oxide reduction due to vacancies migrations, have been observed in the literature, as shown in **Figure 4**, where the two filament formation mechanisms are described [31]. Given the wide variety and complexity of switching mechanisms observed, we suggest to refer to specific reviews for a detailed explanation of the physics behind specific resistive switching

As already mentioned in the Introduction section, resistive switching implies the modification of the metal oxide of interest from a high resistance state (HRS) to a low resistance one (LRS), and vice versa (**Figure 4**). Conventionally, a set event is described as the switch from HRS to LRS, while reset, that is, restoring the initial high resistance of the oxide, causes the passage from LRS to HRS. Both events are driven by an electrical input, and more specifically by the application of a voltage. If set and reset require the application of reverse polarity, then the switching is defined bipolar, while in unipolar switching, the direction of change in resistance state depends on voltage amplitude, not on its polarity. Yet, materials usually do not show immediately a switching behavior: a first stage called electroforming is required, operated at higher voltages, which triggers the material switching ability, making subsequent cycles easier and occurring at lower voltages [35, 36]. Indeed, reset operations only allow to recover and redistribute defects (vacancies, electrode metal ions) at the oxide-electrode inter-

face, while a conductive path remains pre-set in the inner part of the oxide [5, 37].

**Figure 3.** Schematic diagram for the mechanism of resistive switching in Pt/ZnO/Pt devices. (a) the migration of oxygen vacancies toward the cathode (oxygen ions (O2−) toward the anode) and rearrangement of Zn-dominated ZnO1−*<sup>x</sup>*

to the formation of a conductive filament (b). (c) the rupture of the filament by joule heating. Owing to the migration of

oxygen ions, the ReRAM resets back to the off state. Reprinted with permission from Ref. [30].

leads

These nanostructures are usually developed on valve metals for applications in fields where an enhanced specific surface area is required, that is, in photocatalysis, photovoltaics, hydrogen production and sensing, where having the largest possible number of active sites of the oxide able to interact with the surrounding environment increases the material functional efficiency [27, 28]. Nevertheless, resistive switching capabilities were identified also in these nanostructures, as will be discussed in detail in Section 3.3.

**Figure 2.** Top and cross-section view of TiO<sup>2</sup> nanotubes grown by anodic oxidation of the titanium substrate in organic electrolytes. Adapted with permission from Ref. [29].
