Quantum Conductors Formation and Resistive Switching Memory Effects in Zirconia Nanotubes
A.S. Vokhmintsev, I.A. Petrenyov, R.V. Kamalov, I.A. Weinstein
QQuantum Conductors Formation and
Resistive Switching Memory Effects in Zirconia Nanotubes
A.S. Vokhmintsev , I.A. Petrenyov , R.V. Kamalov , I.A. Weinstein * NANOTECH Center, Ural Federal University, Ekaterinburg, 620002, Russia Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg 620016, Russia *e-mail: [email protected]
Abstract
The development prospects of memristive elements for non-volatile memory with use of the metal-dielectric-metal sandwich structures with a thin oxide layer are due to the possibility of reliable forming the sustained functional states with quantized resistance. In the paper we study the properties of fabricated memristors based on the non-stoichiometric ZrO nanotubes in different resistive switching modes. Anodic oxidation of the Zr foil has been used to synthesize a ZrO layer of 1.7 μm thickness, consisting of an ordered array of vertically oriented nanotubes with outer diameter of 75 nm. Zr/ZrO /Au sandwich structures have been fabricated by mask magnetron deposition. The effects of resistive switching in the Zr/ZrO /Au memristors in unipolar and bipolar modes have been investigated. The resistance ratios between high-resistance ( HRS ) and low-resistance (
LRS ) states have been evaluated. It has been founded the conductivity of
LRS is quantized in a wide range with minimum value of 0.5 G S due to the formation of quantum conductors based on oxygen vacancies ( V O ). Resistive switching mechanisms of Zr/ZrO /Au memristors with allowing for migration of V O in an applied electric field have been proposed. It has been shown that the ohmic type and space charge limited conductivities are realized in the LRS and
HRS , correspondingly. We present the results which can be used for development of effective memristors based on functional Zr/ZrO /Au nanolayered structure with multiple resistive states and high resistance ratio. Keywords
ZrO , memristor, quantum conductive filaments, resistance state, oxygen vacancies Introduction
Today zirconium dioxide is being actively used in various high-tech fields such as the generation and storage of electrical energy [1, 2, 3], optical and laser technology [4], catalysis [5, 6, 7], photonics [8], solid-state dosimetry of ionizing radiation [9,10], nanoelectronics [11,12,13], biomedicine [3, 14, 15,], etc. The prospect of creating memristor elements of non-volatile memory based on metal-dielectric-metal (MDM) sandwich structures with a ZrO layer is due to their outstanding properties. Among the latter are low energy consumption [16, 17, 18, 19, 20], high on/off current ratio [19, 20, 21, 22, 23, 24], high-speed performance [16, 18, 19, 20, 24, 25, 26, 27, 28] and meantime-to-failure (endurance), a variety of morphology and methods of manufacturing the active layer, the possibility of scaling [17, 18, 24, 28] and creating three-dimensional integrated circuits [21, 29], applications in flexible electronics [21], as well as compatibility with the existing CMOS technology [16, 30]. It is known that the resistive switching in the oxide layer of MDM structures underlying the memory device operation is usually provided by the mobility of anionic (V O ) vacancies [20, 25, 27, 28,29, 31, 32, 33], ions of impurity metals [18, 19, 20, 24, 26, 33, 34, 35] or Zr + [16, 28, 36] in the active layer under an external electric field. The electrical resistance of the memristor in low-resistance ( LRS ), high-resistance (
HRS ) and intermediate states are governed by the thickness and imperfection of the dioxide layer [23, 24, 28, 31, 32, 37]. In this case, one of the most probable echanisms of resistive switching in as-grown ZrO -based structures is the chain-ordering of V O vacancies followed by the formation of conductive channels or filaments between metal contacts. Subsequently, in applying a control voltage U , the conductive filaments (CF) are partially destroyed and/or restored. Thus, a reversible switching of the memristor between the corresponding resistive states ( LRS ↔ HRS ) in both unipolar [22] and bipolar [36] modes is realized. There are various methods for improving the characteristics of memristors based on functionalized ZrO layers. To improve the stability and operational lifetime of memristor structures, in this context, the selection of materials for electrodes [21, 17, 25], the creation of nanocomposites with organic compounds [34], and combinations of several oxide layers [23] should be worth mentioning. Conductive metal filaments made of materials embedded in the active layer at the stage of electroforming the memristors can be provided by ion implantation [36, 26] and incorporation of metal nanocrystals into the oxide [24]. A rise in the degree of dioxide non-stoichiometry in oxygen makes it easier for further electroformation of Zr [16] or V O [22] filaments in the active layer. An oxygen deficiency increase in various oxide structures during their synthesis can be achieved by the method of electrochemical oxidation through fitting conditions and anodizing parameters [21, 38, 39, 40, 41, 42]. In particular, it was shown in [38, 43, 44, 45, 46, 47, 48] that MDM structures based on nanotubular layers of non-stoichiometric TiO obtained by the anodization technique, are breakthrough materials as memristor memory cells. To date, only one scientific group has examined the effects of resistive switching in 40 nm thick ZrO layers produced by the method of anodic oxidation at room temperature in the galvanostatic mode in an aqueous solution of phosphoric acid [21, 49]. Earlier, we have reported the results of studies of the current-voltage characteristics of nanotubular ZrO layer-based as-grown MDM structures with unidirectional conductivity, obtained by the anodic oxidation method [37, 32] in the potentiostatic mode. The present paper is aimed at measuring and analyzing the static current-voltage ( I-V ) characteristics of fabricated nanoelectronic devices based on a ZrO nanotubular layer in unipolar and bipolar resistive switching modes, and also at describing the peculiarities of electroformation of memristors and the latter’s switching mechanisms. Experimental
Synthesis of a Nanotubular ZrO Layer
A layer of nanotubular zirconium dioxide (ZrO -nt) was fabricated by two-stage anodic oxidation of a Zr substrate containing Hf < 4% in a two-electrode cell at a constant voltage of 20 V. A 100 μm-thick Zr foil was preliminarily degreased with acetone, treated with an acid solution in the ratio HF:HNO :H O = 1:6:20, washed with distilled water and dried in air. The electrolyte was a solution of ethylene glycol containing 5 wt.% H O and 1 wt.% NH F [42]. During anodization, the anode and electrolyte were maintained at constant temperatures of 10 and 20 °C, respectively. The duration of the primary and secondary anodizing amounted to 5 min. After primary anodization, the obtained oxide layer was etched with the above acid solution.
Creating Zr/ZrO -nt/Au Sandwich Structures
50 nm-thick Au contacts were deposited onto the as-grown ZrO -nt layer by magnetron sputtering of gold through a mask mounted on a combined system Q150T ES, Quorum Technologies. Within the sequence-linked operations of the technological cycle specified, more than 100 independent Zr/ZrO -nt/Au sandwich structures were produced in such a way. Characterization of Zr/ZrO -nt /Au Sandwich Structures The morphology of the as-grown oxide layer was analyzed using a SIGMA VP scanning electron microscope (SEM), Carl Zeiss. The obtained SEM images were processed by a SIAMS 800 automatic system. Imaging the fabricated sandwich structures was carried out using an Axio CSM 00 confocal optical microscope, Carl Zeiss. Built-in standard tools of the Axio CSM 700 Software program provided analyzing the pictures. Figure 1 a shows an optical microscope image for a series of memristor structures under study. It can be inferred that all the fabricated memristors have a diameter of 140 ± 5 m and surface roughness parameters such as arithmetical mean deviation of the assessed profile R a = 250 nm and root mean squared R q = 350 nm. Structural characterization of as-grown oxide layer was performed by Rigaku Min-iFlex 600 diffractometer with a copper anode using the Rietveld method. The scanning speed was 0.3 °/min with step of 0.02 . The diffraction data analysis was carried out in the SmartLab Studio II software. Recording Current-Voltage Characteristics
The measurements of
I-V characteristics of the fabricated Zr/ZrO -nt/Au memristors were taken using a PXIe-4143 NI modular controlled power supply unit and a Cascade Microtech MPS 150 microprobe station [50]. The Zr substrate was grounded, and the harmonic voltage U(t) with a frequency of 0.01 Hz and amplitude U max = 4 V was applied to the Au contact (see Figure 1 b ). Before measuring the I-V curves, each as-grown memristor was subjected to electroformation (EF). This procedure was implemented by applying a positive or negative polarity voltage
U(t) that harmonically varied from 0 to U max . The current flowing through the structure was limited to ± 0.1 mA (see Figure 1 c,d , EF line). Once the EF procedure finished, the memristors saved LRS . The subsequently resistive switching was carried out both in bipolar and unipolar modes. In bipolar mode, a positive polarity signal of U ( t ) first switched the memristors from LRS to HRS ( LRS → HRS ), which corresponded to the “Reset” operation. Then, a negative polarity signal of
U(t) returned them in the initial state (
HRS → LRS ). Such an operation was identified as the “Set” one (see Figure 1 c ). In unipolar mode, only a positive polarity voltage U(t) brought about switching the memristors. First, the “Reset” operation and then the “Set” operation were implemented (see Figure 1 d ). The “Reset” and “Set” operations successively performed comprise one complete cycle of the resistive switching of the memristor. Figure 1 e sketches a flowchart of the I-V recording process. Thus, the
I-V curves of the fabricated memristors were recorded over 20 full cycles of both resistive switching modes. The electrical resistance of the memristors in
LRS ( R LRS ) and
HRS ( R HRS ) was determined from the experimental dependencies of the current passing through the memristor on the applied voltage of U = ± 0.5 V, I ( U ). So, a schematic representation of the Zr/ZrO -nt/Au memristor with connected electrical contacts and the order of the I-V curve measurements are shown in Figure1 b – e . Electric Capacity Measurement
The electric capacity of the memristors at hand was measured after switching
LRS → HRS . For this, a NI PXI-4072 modular digital multimeter and a Cascade Microtech MPS 150 microprobe station were used.
Results
Structural Characterization
Figure 2 a contains SEM images of a synthesized nanotubular ZrO -nt layer. In the presented image, the oxide layer has a thickness of b ), and closed on the side of the Zr-substrate (Figure 2 c ). Figure 2 d displays a histogram and a curve of the normal internal-diameter-distribution (solid black line in the Figure) for a series of 10 nanotubes. Analyzing the obtained images showed that the synthesized oxide layer consists of an ordered array of nanotubes whose average values of inner and external diameters are (55 ± 7) and (75 ± 10) nm, respectively. The average wall thickness of nanotubes amounts to (10 ± 5) nm. Figure 1.
Images of fabricated Zr/ZrO -nt/Au memristors and the I-V measurement sequence. ( a ) Optical image of Au contacts on the surface of the oxide layer. ( b ) Schematic representation of the structure of a single memristor with connected electrical contacts. ( c, d ) Schematic I-V curves of memristors operating in bipolar and unipolar switching modes, respectively. ( e ) The sequence of changes in the resistive states of memristors. Figure 3 shows the XRD pattern of ZrO -nt layer. When the background signal (see Fig. 3, dash line) is taken into account, it can be seen that there are a halo (Fig. 3, gray filling) and two broad peaks with maxima near 2θ = 30 and 50 (Fig. 3 , violet filling) on the experimental curve. The halo is due to the amorphous phase, the peaks are related to the crystal structure of the ZrO -nt sample. The observed peaks can be presented by reflexes superposition from tetragonal (t) (scattering angles 2 θ = 30.86, 34.32, 36.49, 43.29, 50.96, 52.57, 59.32, 62.21, 64.30, 72.33, 77.54, 78.14, 83.22 , see Fig. 3, green pattern) and monoclinic (m) (at 2 θ = 18.41, 25.47, 27.54, 35.25, 35.32б 37.32, 39.81, 49.94, 50.94, 52.32, 53.80, 55.55, 57.35, 57.67, 61.67, 65.97, 70.29 , see Fig. UI “ Set” “Reset”“EF” 0 LRSHRS c UI “Set”“Reset” “EF”0 LRS HRS d a b LRS “Reset”“EF” HRS“Set”As-grown e , red pattern) phases. Using standard analysis, it was evaluated that the nanotubes composition is characterized by mixture of t- (43%), m- (32%) and a-ZrO2 (25%) phases. It is well known that for bulk zirconia the phase transition of the monoclinic structure to the tetragonal one takes place at 1170 °С [51]. However, the data obtained are in satisfactory agreement with studies of phase transformations in the low-temperature sintering process (200 – 350 °C) during the crystallization of an amorphous ZrO nanopowder performed by decomposition of zirconium carbonate [52]. The crystallization [52] proceeds with the formation of predominantly t-phase with 36 ± 6 nm grain size and the appearing of m-ZrO (15 – 20 %). In our case, the dominance of the tetragonal symmetry may exhibit the presence of structural features < 30 nm – for example, the wall thickness of the synthesized zirconia nanotubes is near 10 nm, see Structural Characterization section . Figure 2.
SEM characterization of an anodized ZrO -nt layer. ( a – c ) Cross-section, top view (from the side of Au contacts deposited) and bottom view (from the side of the Zr substrate) of the synthesized oxide layer, respectively. ( d ) A histogram of the internal-diameter distribution of nanotubes. The black solid line is a normal distribution.
30 40 50 60 70 800102030 P e r ce n t a g e o f n a no t ub e s , % Inner diameter D in , nm a b c d X R D i n t e n s it y , ґ c oun t s Experimental Background Amorphous Crystalline Calculation m-ZrO t-ZrO
10 20 30 40 50 60 70 80 90 100
Tetragonal43 %Monoclinic32 % Amorphous25 %
Figure 3.
XRD patterns and phase composition analysis for synthesized ZrO -nt layer. Current-Voltage Characteristics
Figures 4 a , b presents the experimental I-V curves of the memristors investigated for 20 cycles of bipolar and unipolar switching, respectively. Vertical arrows indicate the instants of a sharp change in current through memristors due to the transition of the structure between resistive states ("Reset" and "Set" operations). Some
I-V characteristics contain short-term surges and jumps. This can be explained by a change in the electrical resistance of the structure when U slightly increases. It is clear from the EF curves that the as-grown Zr/ZrO -nt/Au structure exhibits characteristics close to those being in HRS . A further increase in applied voltage leads to the primary formation of CFs at U EF ≈ -2.4 and 4V for bipolar and unipolar switching modes, respectively. Subsequently, the “Reset” operation is realized at voltages of U RES = 0.6 ± 0.1 and 1 ± 0.1 V, and the “Set” operation takes place at voltages of U SET = -2 ± 0.3 and 3.5 ± 0.5 V for bipolar and unipolar modes, respectively. Thus, the formation of CFs in the oxide layer shunts the Schottky barrier at the Au/ZrO interface [25, 35] and eliminates the unidirectional conductivity effect in the as-grown Zr/ZrO -nt/Au structure [42]. -2 -1 0 110 -11 -8 -5 -2 LRSHRS"Set" "Reset" C u rr e n t ( I ) , A Applied voltage ( U ), V Cycle number: EF 1 10 20 b -14 -11 -8 -5 -2 "Reset" "Set"Cycle number: EF 1 10 20 C u rr e n t ( I ) , А Applied voltage ( U ), V HRSLRS
Figure 4.
Current-voltage characteristics of Zr/ZrO -nt/Au memristors in ( a ) bipolar and ( b ) unipolar resistive switching modes, respectively. Vertical arrows indicate a change in the resistive state of the memristors. Dotted lines denote the limitation level of current passing through the memristors during their HRS → LRS switching. EF is electroforming curves. Digits are numbers of complete measurement cycles.
Discussion
For discussing the findings secured, all the experimental
I-V characteristics (see Figure 4) were plotted in the following coordinates: surface current density J depending on an electric field E, with the oxide layer thickness d = 1.7 m and memristor’s Au contact area S = 1.5 ґ m taking into account. An analysis of the J(E ) curves accounts for the geometric dimensions of the memristor structures and compares their resistive switching characteristics with those in other papers. Table 1 summarizes the switching mode parameters and morphological features of the Zr/ZrO -nt/Au structure in comparison with independent data for memristors based on amorphous [22, 23, 24, 26, 36], polycrystalline [16, 17, 20, 29, 31, 33, 53] and nanocomposite [34] ZrO layers. Analysis of C-V Curves
Figures 5 a , b illustrates changes in the values of the electric field strength ( E SET and E RES ) and resistance ( R LRS and R HRS ) for 20 complete cycles of resistive switching of the memristors in bipolar nd unipolar modes, respectively. The experimental values of E for the switching memristors are in the ranges E SET = -10 – -14 and 17 – 23 kV/cm and E RES = 2.9 – 4.1 and 5.4 – 6.4 kV/cm for bipolar and unipolar modes, respectively. It should be emphasized that E SET ≈ (3 – 4) E RES for both switching modes of the memristors tested. At the same time, the scatter of the E SET and E RES values for the memristors may take place because of the variation of the ZrO -nt layer thickness within 1.7 ± 0.1 μm and the uncontrolled creation of a multitude of conductive filaments during electroforming. From Table 1, it is seen that the primary formation of filaments and further resistive switching in the synthesized Zr/ZrO -nt/Au is realized at lower E values despite a thicker oxide layer compared to the memristor structures presented. This appears to be caused by several factors, for example, firstly, due to a high concentration of oxygen vacancies in the anodized ZrO . So in [54], the X-ray photoelectron spectroscopy method demonstrates a high photocatalytic activity of oxygen vacancies in nanotubular ZrO obtained by the anodization method. Secondly, the oxide layer of the memristors has the nanotubular morphology. Simulating the distribution of the electric field strength throughout the nanotubular structure confirms the emergence of increased strength regions in the base of the nanotubes, which determines their growth during anodization (see the example of TiO in [55]). Besides, the influence of surface roughness of the Au/TiO interface for memristor structures based on a 20 nm thick TiO film synthesized by magnetron sputtering was explored in [56]. The authors showed that the values of memristor resistive switching voltages diminish with increasing the roughness in the range of Rq = 4.2 – 13.1 nm. This is due to the fact that the sharp roughness peaks heighten the electric field strength. In this case, the formation of CFs occurs in the active layer at lower voltages [56]. Note that in our case, the value of the Rq roughness parameter is noticeably larger (see Section Results. Structural characterization). Thus, the electric and physical characteristics of memristor structures can be improved by the synthesis of thinner nanotubular oxide layers. Thirdly, the content of Hf impurities in the active layer also can be among the aforementioned factors. This is confirmed by the results of the performed quantitative chemical analysis. Independent data calculated by the density-functional method testifies that the incorporation of isovalent Hf into ZrO contributes to a slight decrease in the V O -formation energy in the oxide and the improvement of memristor characteristics [27]. It is evident from Figure 5 and Table 1 that the structure resistance in LRS is hundreds of , and tens and hundreds of M in HRS . It is worth noting that the values of R HRS and R LRS coincide with similar parameters for ZrO -based memristor structures despite the significantly larger thickness of the ZrO -nt layer. There are a lot of papers that contain the fact that the R HRS / R LRS resistance ratios in different states lie in the range of 10 – 10 (see Table 1). In our case, r = R HRS /R LRS > and 8 for unipolar and bipolar switching modes, respectively. The experimental values are comparable with those of the best memristor structures based on thin amorphous ZrO films obtained by electron beam evaporation [22] and subsequent implantation of Zr [36] or Cu [24] ions, see Table 1. Having compared the obtained parameters of the resistive switching of thin ZrO -layer-based Zr/ZrO -nt/Au structure memristors, the following can be stated: in bipolar mode, lower values of the electric field strength contribute to switching between HRS and
LRS . In the process, lower values of r are recorded. The values of the experimentally measured switching parameters of the structures studied allow one to claim that anodized ZrO based nanotubular layers are promising to use as memristor memory cells. Figure 5.
Change in electric field strength ( E ) and resistance ( R ) for 20 complete cycles of resistive switching of Zr/ZrO -nt/Au memristors for ( a ) bipolar and ( b ) unipolar modes. Rectangles indicate the regions of variation of the evaluated characteristics. -20-1001010 S w it c h i ng e l ec t r i c f i e l d ( E ) , k V / c m Resistance ( R ), R LRS = 60±30 R HRS = 11±3 M E RES = 3.5±0.6 kV/cm E SET = -12±2 kV/cm RR LRSHRS R LRS = 350±100 R HRS = 280±110 M E RES = 3.9±0.5 kV/cm E SET = 20±3 kV/cm RR LRSHRS ab able 1. Switching electric field ( E ) and electrical resistance ( R ) values for memristors structures based on the ZrO layers with different morphologies and thickness ( d ) № Mode Operation, state E , kV/cm R , r = R HRS / R LRS
Conduction mechanism and/or behavior Memristor: structure, size, CFs type Active layer: thickness, morphology, synthesis technique Reference
1 – EF, as-grown 23.5 10 – Ohm I Zr/ZrO -nt/Au, Ø 140 m (1.4 ґ m ), V O m, nanotubular PC VIII layer, anodization This work -14 1.7∙10 Unipolar Set,
HRS > 37 SCLC II Reset,
LRS
HRS -12±2 (11±3) > 8 SCLC Reset,
LRS /Au, Ø 500 m or 25 ґ m
40 nm, no data, anodization [21, 49] Unipolar Set,
HRS > 10 Reset,
LRS + -Si, 9 ґ -6 cm , Zr +
120 nm, PC ( t IX and m X ) film, magnetron sputtering [16] Unipolar Set, HRS
135 1…10 > 3 SE III , Ohm Reset,
LRS
90 Ohm 4 Bipolar Set,
HRS ±430 10 > 3 SCLC Au/Cr/ZrO :Zr + / n + -Si, from 50 ґ m to 800 ґ m
70 nm, Zr-implanted amorphous film, EBE IV [36] Reset, LRS
5 – EF, as-grown 1400 10 No data No data Au/Cr/ZrO :Au/ n + -Si, from 100 ґ m to 1000 ґ m
70 nm, Au-implanted amorphous film, EBE [26] Unipolar Set,
HRS > 66 SCLC Reset, LRS
290 (1–300)∙10 VRH V Bipolar Set,
HRS ±570 (2–500)∙10 SCLC Reset,
LRS (1–300)∙10 VRH 6 – EF No data > 10 – No data Ag/ZrO :Cu/ Pt, 0.5 ґ m
40 nm, amorphous layer with Cu nanocrystal, EBE [24] Bipolar Set,
HRS
125 (1–300)∙10 > 3 Reset,
LRS -50 200…320 Bipolar Set,
HRS
420 9∙10 > 2 SE, Ohm Al/ZrO /Al, Ø 80 m 60 nm, amorphous stoichiometric film, magnetron sputtering [22] Reset, LRS -80 40 Ohm 8 Bipolar Set,
HRS > 600 10 –10 > 10 …10 P-F VI ITO/ZrO /Ag, 60 ґ m , Ag 20…50 nm, solid PC (c XI ) film, sol-gel process [17] Reset, LRS < -1400 10 Ohm 9 – EF 850 No data – No data Cu/ZrO /TiO /Ti, no data 50 nm, solid amorphous film, EBE [23] Bipolar Set, HRS > 10 Reset,
LRS < -1000 10
10 – EF 1375 No data No data No data Pt/Ti/ZrO /Pt/Ti 100 ґ m
20 nm, solid film, no data [25] Bipolar Set,
HRS
LRS -250±25 130 Ohm 11 Unipolar Set,
HRS
50 No data No data No data Ag/ZrO /Pt, Ø 200 m, Ag 50 nm, no data, EBE [18] Reset, LRS
10 12 – EF, as-grown – No data Cu/ZrO /Pt, Ø 200 m, Cu 50 nm, PC film, EBE [31] Unipolar Set, HRS > 100 Reset, LRS ~140 Bipolar Set,
HRS -(120±20) Reset,
LRS
13 – EF 6000 No data – No data Ni/ZrO /TaN, Ø 150 m 10 nm, PC film, magnetron sputtering [53] Unipolar Set, HRS (1.6–2.6)·10 > 10 Reset, LRS (6–13)·10
14 Unipolar Set,
HRS > 10 No data Cu/ZrO :Cu/Pt, from 3 ґ m to 20 ґ m , Cu 20 nm, Cu-doped layer, EBE [19] Reset, LRS Bipolar Set,
HRS Reset,
LRS
15 Bipolar Set,
HRS > 10 Complex Cu/ZrO :Ti/Pt, Ti/ZrO :Ti/Pt, from 50 ґ m to 800 ґ m , Ti 70 nm, Ti-implanted PC film, EBE [20] Reset, LRS Ohm 6 – EF /Pt, TaN/ZrO :Gd/Pt, TaN/ZrO :Dy/Pt, TaN/ZrO :Ce/Pt, Ø 100 m (13…25) nm, pure, Gd-, Dy- or Ce-doped PC (t and c) film, sol-gel process [29, 33] Bipolar Set, HRS
No data > 10 Reset,
LRS
17 Bipolar Set,
HRS ±75 11.5·10 > 44 SCLC ITO/ZrO :PVP VII /Ag 100 ґ m
200 nm, nanocomposite layer, spin coating [34] Reset,
LRS
263 Ohm 18 Bipolar Set,
HRS (1.5…1.8) ·10 > 130 > 32 for Ag/ZrO /ITO, > 1.7 for Ag/ZrO /Ag SCLC Ag/ZrO /Ag, Ag/ZrO /ITO, no data, Ag +
100 nm, PC (m) film, magnetron sputtering [57] Reset,
LRS (0.7…1.5) ·10 < 115 Ohm I Ohm is Ohmic conduction II SCLC is space-charge-limited conduction II SE is Schottky emission IV EBE is electron beam evaporation V VRH is Mott variable range hopping VI P-F is Poole-Frenkel emission
VII
PVP is Poly (4-vinylphenol)
VIII
PC is polycrystalline IX t is the tetragonal phase X m is the monoclinic phase XI c is the cubic phase onduction Mechanisms HRS
Figure 6 shows the
J(E) data in double logarithmic coordinates for both resistive switching modes. It is seen that the measured dependencies for
HRS contain three linear segments with different tangents of inclination angles. In browsing the literature [58, 59, 60], it can be concluded that the above behavior corresponds to the
I-V characteristics of a dielectric with monoenergetic traps capable of filling with injected electrons. The theory of injection currents reads that such systems can implement the space-charge-limited conduction (SCLC) mechanism [58]. The SCLC model succeeds at describing carrier transport through a dielectric layer by the following equations [58, 59, 60]:
OhmOhm
I UJ e n e n ES d = = = , (1)
TFLTFL eff eff
I U EJ S d d = = = , (2) eff = , (3) c eff tr eff tr d dU E = = , (4) d eff en = , (5) tTFLTFL eN dUE d = = , (6) where J Ohm is Ohm’s law current density, A/cm ; I Ohm is Ohm’s law current, A/cm ; S is the memristor area, cm ; e is the electron charge, C; μ is the electronic drift mobility, cm /(V∙s); n is carrier concentration in thermal equilibrium, cm -3 ; U is applied voltage, V; d is the thickness of oxide layer, cm; E is applied electric field, V/cm; J TFL is trap-filled limit current density, A/cm ; I TFL is trap-filled limit current, A; μ eff is effective electron mobility, cm /(V∙s); ε is the static dielectric constant; ε is the permittivity in vacuum, F/cm; θ is the ratio of the free carrier density to total carrier density; c is carrier transit time, s; U tr is transition voltage, V; E tr is transition electric field, V/cm; d is dielectric relaxation time, s; n is the concentration of the free carriers in the oxide, cm -3 ; E TFL is the trap-filled limit electric field, V/cm; U TFL is the trap-filled limit voltage, V; N t is the trap density, cm -3 . In our case, electrons are the charge carriers in the ZrO -nt layer, and oxygen vacancies V O s are traps. From now on, when discussing experimental data within the SCLC model [58, 59, 60], we will adhere to this statement. For E < E tr , the J ( E ) dependence is linear ( J Ohm E ) and obeys Ohm's law in Eq. (1). Such a regime for ZrO is typical of an electrically quasi-neutral state that corresponds to the early stage of filling the V O s at weak injection N t0 →
0. In the case of E = E tr , the number of injected and free electrons in the active memristor layer coincides ( n = n ), and the transit times (see Eq. (4)) and electron relaxation (see Eq. (5)) are equal, i.e. с = d . Moreover, → N t,0 →
0. For E tr < E < E TFL , the condition of strong injection holds. In the concerned range of E , the traps continue filling up, and the dependence becomes quadratic ( J TFL E ). As E grows, the concentration of free injected electrons increases, which in turn leads to a shift in the position of the Fermi quasi-level to the position of the level of traps in the bandgap. For E E TFL , the current flowing through the structure abruptly goes up, and the double logarithmic dependence J ( E ) has a slope k J E k ). This fact evidences the complete filling of raps and the possibility of freely moving the injected electrons in the ZrO layer. Thus, the E TFL strength matches the V O levels completely filled (see Eq. (6)) and (or) the coincidence of the positions of the Fermi quasi-levels and monoenergetic V O levels in the bandgap [58, 59]. Then, a very strong injection is the reason for CFs to form in the electric field range in question. a -7 -4 -1 E TFL E ў J ~ E J ~ E J ~ E J ~ E
LRS HRS C u rr e n t d e n s it y J , A / c m Electric field E , V/cm b -6 -4 -2 E TFL E ў J ~ E J ~ E J ~ E J ~ E LRS HRS C u rr e n t d e n s it y J , A / c m Electric field E , V/cm Figure 6.
Dependencies of current density ( J ) on strength ( E ) in double logarithmic coordinates for bipolar ( a ) and unipolar ( b ) switching modes. Symbols are the experimental data. Solid lines represent a linear approximation. To evaluate the parameters of the ZrO -nt layer using Eq. (1) – (6), we measured the electric capacitance of memristors in HRS , which amounted to C = 1 pF. In the case of the geometry of a flat capacitor, we obtain the relative permittivity of ε = 20
2. This value is quite consistent with ε = 14 – 40 for continuous thin zirconium films [28, 61, 62] and coincides with the estimate of ε = 21 for an anodized ZrO layer synthesized in a galvanostatic mode at room temperature in an electrolyte of ammonium tetraborate [63]. Here, the morphology of the oxide layer is not covered. The electric and physical characteristics of the ZrO -nt layer in HRS : μ eff μ = ( -3 cm ( V s) -1 N t = (1 – 3) cm -3 , c = 0.3 – 1.3 ms and n = (1 – 3) cm -3 were calculated according to Eq. (1) – (6). It is seen that the mobility values obtained at room temperature are omparable with independent estimates of μ = 23 -3 [64] and 5.8 -3 cm ∙(V∙s) -1 [65] at 900 С for single-crystal ZrO stabilized Y O . It is important to note that, in a number of independent works, both theory and experiment confirm a high concentration of V O in various anodized oxides [38,63,66,67,68,69]. For example, when treated at a temperature of 500 °C for 4 h in a reducing atmosphere of 5% H /N , TiO nanotubular array increases the concentration of active surface defects, with the charge carrier density becoming equal to 9.86·10 cm –3 [68]. Large values of 2.5∙10 cm –3 for the V O concentration in ZrO single crystals stabilized by Y O were previously determined by the electron paramagnetic resonance (EPR) method [65]. The significantly lower value of N t = (1 – 3)∙10 cm -3 , obtained in the present work can be explained by the presence of F – ions. It is known that fluorine substitutes for oxygen vacancies in ionic crystals, which leads to a decrease in the concentration of V and eliminates allowed capture levels in the bandgap of oxides [70]. X-ray fluorescence and photoelectron spectroscopy methods confirm the presence of fluorine in the samples under study. The fluorine and hafnium contents are found to amount to 2.5 and 1 at. %, respectively. LRS
It is clear from Figure 6 that, for a low resistive state, all the J ( E ) dependencies in double logarithmic coordinates are linear with the slope tangent
1 ( J Ohm E ), which corresponds to Ohm's law. Such a behavior is also typical of memristor structures based on continuous ZrO layers in LRS (see Table 1) [16, 17, 20, 22, 25, 34]. In addition, the
I-V curves have a region of switching at U = 0.4 – 1 V during the LRS → HRS transition. In this case, the G conductance of the memristor structure stepwise decreases. For example, with increasing U , the magnitude of G diminishes by a factor to one-half and half-integer values of the quantum of electrical conductance G = 2 e / h G → G → G → G → G → G → G → G → G → G → G → G → G → G HRS . The resistive switching of various memristor structures as a result of the formation of quantum conductive filaments (QCFs) at room temperature is an experimentally and theoretically confirmed fact [71 and ref. in it]. For example, it is established in [31] that quantum conductive filaments (QCFs) in Cu/ ZrO /Pt memristors are formed in a controlled manner. Based on the experimental R LRS values (see Table 1), it can be argued that when performing the “EF” and “Set” operations, tens and hundreds of QCFs are formed and restored between the electrodes in memristors. This corresponds to the formation of one QCF per 10 -10 ZrO nanotubes, whereas their number in the memristor is pieces. It is safe to say that QCFs fully determine electron transport through the memristor in the LRS , and the discreteness of the change in the conductance values leads to the quantization of the mobility values.
Let one QCF have a volume V QCF , in which two electrons reside. Then, according to Eq. (1), the mobility of elementary charges in
LRS is discrete: QCFLRS xVSd = , (7) Where µ = ed / h ·(V·s) -1 . The data of speculations are consistent with theoretical calculations of electron mobility in multi-walled carbon nanotubes within an ideal multi-box model, for which μ is quantized and proportional to the square of the nanotube length [72]. Eq.(7) implies that μ LRS depends on the ratio of the geometric dimensions of the memristor and QCF, as well as the number of filaments formed. So, comparing the volumes of memristor and QCFs ( Sd → x V QCF ), we get that µ LRS → µ . Thus, a possible increase in electron mobility in ZrO -nt during the transition of the memristor from HRS to LRS is a result of the quantization of energy states in one-dimensional channels arising from the motion of charge carriers over QCFs in a dielectric layer. It was previously reported that μ = 12-13 cm ∙(V∙s) -1 at temperatures of 425-475K or thin amorphous oxide films in the Al/ZrO /p-Si structure using the modified Schottky emission model [73]. C u rr e n t , m A Voltage, V 53 G G G G G G G X G G G G G G G Figure 7.
Experimental
I-V characteristics of memristors in
LRS (solid red lines) and a series of theoretical
I-V characteristics for CFs with quantum conductance xG (thin black lines), where x is the number of QCFs and G = 2 e / h -nt layer are stable even at room temperature and retain their conducting state when E is turned off. Subsequently, during the “Reset” operation, QCFs are destroyed. Next, we explain the mechanisms of electroforming and resistive switching of memristors with the participation of V O2+ oxygen vacancies, O oxygen and F – fluorine ions in these processes. Resistive Switching Mechanisms
Figure 8 schematically sketches the processes that occur in nanotubes in the bipolar memristive switching mode. The as-grown nanotube whose fragment is outlined by a dark frame has increased non-stoichiometry in oxygen at the ZrO -nt/Zr interface [38, 66, 74]. Independent data on the ZrO -nt layer, obtained by transmission electron microscopy and energy dispersive X-ray analysis, show that the content of F – ions is also high in this region [74]. When electroforming (see Figure 8, operations EF), several complementary processes can proceed in the Zr/ZrO -nt/Au structure at hand. Firstly, positively charged oxygen vacancies + V migrate outwards and towards the Au-contact in an applied electric field at E > 0 and E < 0, respectively. The aforementioned vacancy centers have a positive charge relative to the crystal lattice, and their motion appears to obey the exchange mechanism in the anion sublattice due to the diffusion of O [75] and F – ions along the grain boundaries of the nanotubes in an external electric field. econdly, the motion of negatively charged F – and/or O ions outwards and towards the Au contact is initiated at E > 0 and E < 0, respectively. In this case, extra oxygen vacancies emerge in the ZrO nanotubes. It is known that the mobility of fluorine in anodized oxides is almost twice that of oxygen [76, 77]. Consequently, the transition of F from the O position to the -i F -interstice in an external electric field results in V O -forming as a most probable process. The latter proceeds according to the -i2OO FVF +→ ++ mechanism [70]. It should be underscored that the diffusion of O and the formation of voids at the “active layer/electrode” interface during the EF process were experimentally confirmed by studying the distribution of chemical elements in a Pt/TiO /Pt memristor using two-dimensional energy-dispersive X-ray spectroscopy [78]. Thus, the QCFs are formed upon locally reaching a certain threshold concentration of V O in the ZrO -nt layer, and the memristor passes into the LRS state (see Figure 8, a red frame). It is worth emphasizing that the EF process for memristors at E < 0 is less energy-consuming as compared to that at E > 0 since it proceeds at lower E EF values (see Table 1). Further, resistive switching is possible to implement after the mandatory EF procedure. So when placing the memristor being in the LRS into an electric field E , current flows through the QCFs formed. Once heated up due to the Joule heat, they are locally destroyed as a result of diffusion of V O , F and/or O (see Figure 8, Reset operation). Chances are, the QCFs collapse, first of all, inside the nanotube walls far from the metal contacts, and the memristor passes into the HRS state (see Fig. 8, a blue frame). Subsequently, the applied field E initiates the diffusion process of V O , F, and/or O in locally destroyed areas of the QCFs (see Figure 8, operation Set). When restored, the V O chains make the memristor go into the LRS state. As it becomes clear from Table 1, E SET > E
RES for both switching modes of the memristors tested. Thus, partial destruction of the QCFs in the active layer requires less energy than their restoration. The similar behavior of the Zr/ZrO -nt/Au structure is consistent with a number of independent works [16, 21, 22, 24, 26, 49] for continuous-ZrO layer-based memristors. Figure 8.
Schematic representation of the processes of formation (EF), destruction (Reset), and restoration (Set) of a quantum conductive filament in a ZrO nanotube for a bipolar switching mode. Detailed explanations for the figure are given in the text. EF LRS
ZrO -ntAu Zr HRS
ZrO -ntAu Zr As-grown
ZrO -ntAu Zr EF oxygenvacancies, V O F - or O ionselectrons Reset Set E > 0 ZrO -nt E > 0 E < 0 E < 0 Au ZrZrO -nt Au ZrZrO -ntAu ZrZrO -nt Au ZrZrO -nt onclusion Memristor structures based on a 1.7 μm thick ZrO nanotubular layer synthesized by anodic oxidation were fabricated. An analysis of SEM images showed that the oxide layer consists of an ordered array of vertically oriented nanotubes with average internal and external diameters of 55 and 75 nm, respectively. The I-V curves of the Zr/ZrO -nt/Au memristors investigated exhibit a unipolar and bipolar mechanisms of the LRS ↔ HRS resistive switching over several tens of complete switching cycles. The ranges of changes in the resistances of the synthesized structures, R HRS R LRS ≤ 450 Ω, as well as the ratio R HRS / R LRS , were determined. Based on the analysis of the I-V curves, it can be inferred that the conductivity either of the ohmic type or limited by space charge (SCLC) is realized in the
LRS and
HRS states, respectively. The effective carrier mobility μ eff = (0.1-12)∙10 -3 cm /(V∙s) in the studied structure was calculated. The concentration of charge carrier traps based on oxygen vacancies, N t = (1-3) cm -3 , in the non-stoichiometric nanotubular ZrO layer was estimated. The prospects of using the Zr/ZrO -nt/Au layered structure as a functional medium for memristor memory elements, as well as possible trends for improving their functional characteristics, are shown. Acknowledgements
The work was supported by Minobrnauki research project FEUZ-2020-0059. Authors thank I.N. Bainov for help in XRD measurements.
References [1] Minh N.Q. Ceramic Fuel Cells // Journal of the American Ceramic Society, Volume 76, Issue 3, March 1993, Pages 563-588. https://doi.org/10.1111/j.1151-2916.1993.tb03645.x [2] Ishihara T., Sato K., Takita Y. Electrophoretic deposition of Y O -stabilized ZrO -, Tb - and Eu -doped ZrO nanocrystal // Journal of Physics D: Applied Physics, Volume 43, Issue 46, 24 November 2010, Article number 465105 https://doi.org/10.1088/0022-3727/43/46/465105 [9] P. Salas, E. De la Rosa-Cruz, L.A. Diaz-Torres, V.M. Castaño, R. Meléndrez, M. Barboza-Flores “Monoclinic ZrO as a broad spectral response thermoluminescence UV dosemeter”, Radiation Measurements, Volume 37, Issue 2, April 2003, Pages 187-190 https://doi.org/10.1016/S1350-4487(02)00174-9 [10] Nikiforov S.V., Kortov V.S., Savushkin D.L., Vokhmintsev A.S., Weinstein I.A. Thermal quenching of luminescence in nanostructured monoclinic zirconium dioxide // Radiation Measurements, Volume 106, November 2017, Pages 155-160. https://doi.org/10.1016/j.radmeas.2017.03.020 [11] Shin H., Jeong D.-K., Lee J., Sung M.M., Kim J. Formation of TiO and ZrO nanotubes using atomic layer deposition with ultraprecise control of the wall thickness // Advanced Materials, Volume 16, Issue 14, 19 July 2004, Pages 1197-1200. https://doi.org/10.1002/adma.200306296 [12] H. Yan, H.S. Choe, S. Nam, Y. Hu, S. Das, J.F. Klemic, J.C. Ellenbogen, C.M. Lieber Programmable nanowire circuits for nanoprocessors, Nature, Volume 470, Issue 7333, 10 February 2011, Pages 240-244 https://doi.org/10.1038/nature09749 [13] Ha Y.-G., Everaerts K., Hersam M.C., Marks T.J. Hybrid gate dielectric materials for unconventional electronic circuitry // Accounts of Chemical Research, Volume 47, Issue 4, 15 April 2014, Pages 1019-1028. https://doi.org/10.1021/ar4002262 [14] Manicone P.F., Rossi Iommetti P., Raffaelli L. An overview of zirconia ceramics: Basic properties and clinical applications // Journal of Dentistry, Volume 35, Issue 11, November 2007, Pages 819-826. https://doi.org/10.1016/j.jdent.2007.07.008 [15] Hisbergues M., Vendeville S., Vendeville P. Review zirconia: Established facts and perspectives for a biomaterial in dental implantology // Journal of Biomedical Materials Research - Part B Applied Biomaterials, Volume 88, Issue 2, February 2009, Pages 519-529. https://doi.org/10.1002/jbm.b.31147 [16] Lee D., Choi H., Sim H., Choi D., Hwang H., Lee M.-J., Seo S.-A., Yoo, I.K. Resistance switching of the nonstoichiometric zirconium oxide for nonvolatile memory applications // IEEE Electron Device Letters, Volume 26, Issue 10, October 2005, Pages 719-721. https://doi.org/10.1109/LED.2005.854397 [17] S. Lee, T. Kim, B. Jang, W.-Y. Lee, K.C. Song, H.S. Kim, G.Y. Do, S.B. Hwang, S. Chung and J. Jang “Impact of Device Area and Film Thickness on Performance of Sol-Gel Processed ZrO RRAM” 2018
IEEE Electron Device Lett.
668 https://doi.org/10.1109/LED.2018.2820141 [18] Du G., Wang C., Li H., Mao Q., Ji Z. Bidirectional threshold switching characteristics in Ag/ZrO /Pt electrochemical metallization cells // AIP Advances 6, 085316 (2016). https://doi.org/10.1063/1.4961709 [19] Guan W., Long S., Liu Q., Liu M., Wang W. Nonpolar Nonvolatile Resistive Switching in Cu Doped ZrO // IEEE Electron Device Letters, Volume 29, Issue 5, May 2008, Pages 434-437. DOI: 10.1109/LED.2008.919602. https://ieeexplore.ieee.org/document/4494620 [20] Liu Q., Long S., Wang W., Zuo Q., Zhang S., Chen J., Liu M. Improvement of resistive switching properties in ZrO -Based ReRAM with implanted Ti ions // IEEE Electron Device Letters, Volume 30, Issue 12, December 2009, Pages 1335-1337. DOI: 10.1109/LED.2009.2032566. https://ieeexplore.ieee.org/document/5332367 [21] Kundozerova T.V., Stefanovich G.B., Grishin A.M. Binary anodic oxides for memristor-type nonvolatile memory // Physica Status Solidi (C) Current Topics in Solid State Physics, Volume 9, Issue 7, July 2012, Pages 1699-1701. https://doi.org/10.1002/pssc.201100625 [22] Wu X., Zhou P., Li J., Chen L.Y., Lv H.B., Lin Y.Y., Tang T.A. Reproducible unipolar resistance switching in stoichiometric ZrO films // Appl. Phys. Lett. /TiO stack structure, 2015 Nanotechnol. ACS Nano
10. https://doi.org/10.1021/nn1017582 [25] Lei X.-Y., Liu H.-X., Gao H.-X., Yang H.-N., Wang G.-M., Long S.-B., Ma X.-H. and Liu M. “Resistive switching characteristics of Ti/ZrO /Pt RRAM device” 2014 Chinese Physics B Volume 23, Issue 11, 1 November 2014, Article number 117305. http://dx.doi.org/10.1088/1674-1056/23/11/117305 [26]Liu Q., Guan W., Long S., Liu M., Zhang S., Wang Q. and Chen J. Resistance switching of Au-implanted-ZrO film for nonvolatile memory application, 2008 J. Appl. Phys. with Implication for Memristive Device Performance // ACS Appl. Electron. Mater. 2019, 1, 467−477. https://doi.org/10.1021/acsaelm.8b00090 [28] Panda D., Tseng T.Y. Growth, dielectric properties, and memory device applications of ZrO thin films // Thin Solid Films, Volume 531, 15 March 2013, Pages 1-20. https://doi.org/10.1016/j.tsf.2013.01.004 [29] Lee M.S., Choi S., An C.-H., Kim H. Resistive switching characteristics of solution-deposited Gd, Dy, and Ce-doped ZrO films // Applied Physics Letters, Volume 100, Issue 14, 2 April 2012, Article number 143504. https://doi.org/10.1063/1.3700728 [30] Yang J.J., Strukov D.B., Stewart D.R. Memristive devices for computing // Nature Nanotechnology, Volume 8, 2013, Pages 13–24. https://doi.org/10.1038/NNANO.2012.240 [31] Du G., Li H., Mao Q., Ji Z. Controllable volatile to nonvolatile resistive switching conversion and conductive filaments engineering in Cu/ZrO /Pt devices // Journal of Physics D: Applied Physics, Volume 49, Issue 44, 13 October 2016, Article number 445105. https://doi.org/10.1088/0022-3727/49/44/445105 [32] Petrenyov I.A., Vokhmintsev A.S., Kamalov R.V., Weinstein I.A. Conduction mechanisms in memristors based on nanotubular arrays of zirconium oxide // AIP Conference Proceedings, Volume 2174, 6 December 2019, Article number 020242. https://doi.org/10.1063/1.5134393 [33] Lee M.S., An C.-H., Park K., Choi J.-Y., Kim H. Effect of Y, Gd, Dy, and Ce Doping on the Microstructural and Electrical Properties of Sol-Gel-Deposited ZrO Film // Journal of the Electrochemical Society, 158(6), Pages G133-G136. https://doi.org/10.1149/1.3562971 [34]Khan M.U., Hassan G.and Bae J. Non-volatile resistive switching based on zirconium dioxide: poly (4-vinylphenol) nano-composite, 2019
Appl. Phys. A Mater. Sci. Process.
378 https://doi.org/10.1007/s00339-019-2659-9 [35] Awais M.N., Choi K.H. Resistive switching mechanism in printed non-volatile Ag/ZrO /ITO sandwiched structure // Electronics Letters Volume 51, Issue 25, 10 December 2015, Pages 2147-2149 http://dx.doi.org/10.1049/el.2014.2517 [36] Liu Q., Guan W., Long S., Jia R., Liu M., Chen J. Resistive switching memory effect of ZrO films with Zr + implanted // Appl. Phys. Lett. -NT/Au layered structure // Proceedings - 2018 Ural Symposium on Biomedical Engineering, Radioelectronics and Information Technology, USBEREIT 2018, Pages 348-351. https://doi.org/10.1109/USBEREIT.2018.8384620 [38] Trivinho-Strixino F., Guimarães F.E.G., Pereira E.C. Zirconium oxide anodic films: Optical and structural properties // Chemical Physics Letters, Volume 461, Issue 1-3, 8 August 2008, Pages 82-86.https://doi.org/10.1016/j.cplett.2008.06.072 [39] Yoo J.E., Lee K., Tighineanu A., Schmuki P. Highly ordered TiO nanotube-stumps with memristive response // Electrochemistry Communications, Volume 34, 2013, Pages 177-180. https://doi.org/10.1016/j.elecom.2013.05.038 [40] Valeeva A.A., Kozlova E.A., Vokhmintsev A.S., Kamalov R.V., Dorosheva I.B., Saraev A.A., Weinstein I.A., Rempel, A.A. Nonstoichiometric titanium dioxide nanotubes with enhanced catalytical activity under visible light // Scientific Reports, Volume 8, Issue 1, 1 December 2018, Article number 9607. https://doi.org/10.1038/s41598-018-28045-1 [41] Valeeva A.A., Dorosheva I.B., Kozlova E.A., Kamalov R.V., Vokhmintsev A.S., Selishchev D.S., Saraev A.A., Gerasimov E.Y., Weinstein I.A., Rempel A.A. Influence of calcination on photocatalytic properties of nonstoichiometric titanium dioxide nanotubes // Journal of Alloys and Compounds, Volume 796, 5 August 2019, Pages 293-299. https://doi.org/10.1016/j.jallcom.2019.04.342 [42] Petrenyov I.A., Kamalov R.V., Vokhmintsev A.S., Martemyanov N.A., Weinstein I.A. Nanostructural features of anodic zirconia synthesized using different temperature modes // Journal of Physics: Conference Series, Volume 1124, 2018, Article number 022004. https://doi.org/10.1088/1742-6596/1124/2/022004 [43] Miller K., Nalwa K.S., Bergerud A., Neihart N.M., Chaudhary S. Memristive behavior in thin anodic titania // IEEE Electron Device Letters, Volume 31, Issue 7, July 2010, Article number 5473038, Pages 737-739. https://doi.org/10.1109/LED.2010.2049092 [44] Vokhmintsev A.S., Weinstein I.A., Kamalov R.V., Dorosheva I.B. Memristive effect in a nanotubular layer of anodized titanium dioxide // Bulletin of the Russian Academy of Sciences: Physics, Volume 78, Issue 9, 2014, Pages 932-935. https://doi.org/10.3103/S1062873814090317 [45] Conti D., Lamberti A., Porro S., Rivolo P., Chiolerio A., Pirri C.F., Ricciardi C. Memristive behaviour in poly-acrylic acid coated TiO nanotube arrays // Nanotechnology, Volume 27, Issue 48, 7 November 2016, Article number 485208. https://doi.org/10.1088/0957-4484/27/48/485208 [46] Dorosheva I.B., Vokhmintsev A.S., Kamalov R.V., Gryaznov A.O., Weinstein I.A. Oxide layer thickness effects on the resistance switching characteristics of Ti/TiO -NT/Au structure // Proceedings - 2018 Ural Symposium on Biomedical Engineering, Radioelectronics and Information Technology, USBEREIT 2018, 13 June 2018, Pages 279-282. https://doi.org/10.1109/USBEREIT.2018.8384604 [47] Chen J., Wu Y., Zhu K., Sun F., Guo C., Wu X., Cheng G., Zheng R. Core-shell copper nanowire-TiO nanotube arrays with excellent bipolar resistive switching properties // Electrochimica Acta, Volume 316, 1 September 2019, Pages 133-142. https://doi.org/10.1016/j.electacta.2019.05.110 [48] Hazra A., Jan A., Tripathi A., Kundu S., Boppidi P.K.R., Gangopadhyay S. Optimized resistive switching in TiO SIBCON 2016 Proc. /TaN memory device, Journal of Physics D: Applied Physics, Volume 48, Issue 3, 28 January 2015, Article number 035108. https://doi.org/10.1088/0022-3727/48/3/035108 [54] Chen Q., Yang W., Zhu J., Fu L., Li D., Zhou L. In situ fluorine doped ZrO nanotubes for efficient visible light photocatalytic activity // Journal of Materials Science: Materials in Electronics, Volume 30, Issue 1, 15 January 2019, Pages 701-710. https://doi.org/10.1007/s10854-018-0339-8 [55] Yang D., Wang Y.-Q., Ren G.-B., Feng S., Chen Y.-Y., Wang W.-Z. Formation mechanistism study of TiO film comprising nanotubes and nanoparticles // Chinese Journal of Chemical Physics, Volume 25, Issue 1, February 2012, Article number 013, Pages 91-95. https://doi.org/10.1088/1674-0068/25/01/91-95 [56] Hamidreza Arab Bafrani, Mahdi Ebrahimi, Saeed Bagheri Shouraki, Alireza Z. Moshfegh A facile approach for reducing the working voltage of Au/TiO /Au nanostructured memristor by enhancing the local electric field // Nanotechnology 29 (2018) 015205 https://doi.org/10.1088/1361-6528/aa99b7 [57] Yuan Y., Cao X., Sun Y., Su J., Liu C., Cheng L., Li Y., Yuan L., Zhang H., Li J. Intrinsic mechanism in nonvolatile polycrystalline zirconium oxide sandwiched structure // Journal of Materials Science: Materials in Electronics, Volume 29, Issue 3, 1 February 2018, Pages 2301-2306. https://doi.org/10.1007/s10854-017-8146-1 [58] Lampert M.A., Mark P. Current Injection in Solids. Academic Press, New York, 1970, 354 pp. [59] Chiu F.-C. A Review on Conduction Mechanisms in Dielectric Films// Advances in Materials Science and Engineering, Volume 2014, Article ID 578168, 18 pages. http://dx.doi.org/10.1155/2014/578168 [60] Lim E.W., Ismail R. Conduction mechanism of valence change resistive switching memory: A survey // Electronics (Switzerland), Volume 4, Issue 3, 9 September 2015, Pages 586-613. https://doi.org/10.3390/electronics4030586 [61] Lin C.Y., Wang S.Y., Lee D.Y., Tseng T.Y. Electrical Properties and Fatigue Behaviors of ZrO2 Resistive Switching Thin Films // Journal of Electrochemical Society, Volume 155, Issue 8, 2008, Pages H615-H619. https://doi.org/10.1149/1.2946430 [62] Pimenov A., Ullrich J., Lunkenheimer P., Loidl A., Rüscher C.H. Ionic conductivity and relaxations in ZrO –Y O solid solutions // Solid State Ionics, Volume 109, Issues 1–2, 1 June 1998, Pages 111-118. https://doi.org/10.1016/S0167-2738(98)00082-4 [63] Llewelyn Leach J.S., Pearson B.R. The effect of foreign ions upon the electrical characteristics of anodic ZrO films // Electrochimica Acta, Volume 29, Issue 9, September 1984, Pages 1271-1282. https://doi.org/10.1016/0013-4686(84)87190-X [64] Weppner W. Electronic transport properties and electrically induced p-n junction in ZrO + 10 m/o Y O // Journal of Solid State Chemistry, Volume 20, Issue 3, March 1977, Pages 305-314. https://doi.org/10.1016/0022-4596(77)90167-0 [65] Sasaki K., Maier J. Re-analysis of defect equilibria and transport parameters in Y O -stabilized ZrO using EPR and optical relaxation // Solid State Ionics, Volume 134, Issue 3-4, 2 October 2000, Pages 303-321. https://doi.org/10.1016/S0167-2738(00)00766-9 [66] Chen C.-C., Say W.C., Hsieh S.-J., Diau E.W.-G. A mechanism for the formation of annealed compact oxide layers at the interface between anodic titania nanotube arrays and Ti foil // Applied Physics A: Materials Science and Processing, Volume 95, Issue 3, June 2009, Pages 889-898. https://doi.org/10.1007/s00339-009-5093-6 [67] Roh B., Macdonald D.D. Effect of oxygen vacancies in anodic titanium oxide films on the kinetics of the oxygen electrodereaction // Russian Journal of ElectrochemistryVolume 43, Issue 2, February 2007, Pages 125-135. https://doi.org/10.1134/S1023193507020012 [68] Sang L.X., Zhang Z.Y., Ma C.F. Photoelectrical and charge transfer properties of hydrogen-evolving TiO nanotube arrays electrodes annealed in different gases // International Journal of Hydrogen Energy, Volume 36, Issue 8, April 2011, Pages 4732-4738. https://doi.org/10.1016/j.ijhydene.2011.01.071 [69] Hanzu I., Djenizian T., Knauth P. Electrical and point defect properties of TiO nanotubes fabricated by electrochemical anodization // Journal of Physical Chemistry C, Volume 115, Issue 13, 7 April 2011, Pages 5989-5996. https://doi.org/10.1021/jp1111982 [70] Tse K., Robertson J. Defect passivation in HfO2 gate oxide by fluorine // Applied Physics Letters. Volume 89, Issue 14, 2006, Article number 142914. https://doi.org/10.1063/1.2360190 [71]. Xue W., Gao S., Shang J., Yi X., Liu G., Li R.-W. Recent Advances of Quantum Conductance in Memristors // Advanced Electronic Materials. Volume 5, Issue 9, 1 September 2019, Article number 1800854. https://doi.org/10.1002/aelm.201800854 [72] Grado-Caffaro M.A., Grado-Caffaro M. Theoretical evaluation of electron mobility in multi-walled carbon nanotubes // Optik, Volume 115, Issue 1, 2004, Pages 45-46. https://doi.org/10.1078/0030-4026-00326 [73] Fu-Chien Chiu, Zhi-Hong Lin, Che-Wei Chang, Chen-Chih Wang, Kun-Fu Chuang, Chih-Yao Huang, Joseph Ya-Min Lee, and Huey-Liang Hwang “Electron conduction mechanism and band diagram of sputter-deposited Al/ZrO /Si structure”, Journal of Applied Physics 97, 034506 (2005). https://doi.org/10.1063/1.1846131 [74] Muratore F., Baron-Wiechéc A., Hashimoto T., Gholinia A., Skeldon P., Thompson G.E. Growth of nanotubes on zirconium in glycerol/fluoride electrolytes // Electrochimica Acta, Volume 56, Issue 28, 1 December 2011, Pages 10500-10506. https://doi.org/10.1016/j.electacta.2010.12.089 [75] Wu Y., Chen J., Hu W., Zhao K., Qu P., Shen P., Zhao M., Zhong L., Chen Y. Phase transformation and oxygen vacancies in Pd/ZrO2 for complete methane oxidation under lean conditions // Journal of Catalysis, Volume 377, September 2019, Pages 565-576. https://doi.org/10.1016/j.jcat.2019.04.047 [76] Habazaki H., Fushimi K., Shimizu K., Skeldon P., Thompson G.E. Fast migration of fluoride ions in growing anodic titanium oxide // Electrochemistry Communications, Volume 9, Issue 5, May 2007, Pages 1222-1227. https://doi.org/10.1016/j.elecom.2006.12.023 [77] Shimizu K., Kobayashi K., Thompson G.E., Skeldon P., Wood G.C. The migration of fluoride ions in growing anodic oxide films on tantalum // Journal of the Electrochemical Society, Volume 144, Issue 2, February 1997, Pages 418-423. https://doi.org/10.1149/1.1837425 [78] Carta D., Salaoru I., Khiat A., Regoutz A., Mitterbauer C., Harrison N.M., Prodromakis T. Investigation of the Switching Mechanism in TiO2