Switching Characteristics and Mechanism Using Al 2 O 3 Interfacial Layer in Al / Cu / GdO x / Al 2 O 3 / TiN Memristor

: Resistive switching characteristics by using the Al 2 O 3 interfacial layer in an Al / Cu / GdO x / Al 2 O 3 / TiN memristor have been enhanced as compared to the Al / Cu / GdO x / TiN structure owing to the insertion of Al 2 O 3 layer for the ﬁrst time. Polycrystalline grain, chemical composition, and surface roughness of defective GdO x ﬁlm have been investigated by transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), X-ray di ﬀ raction (XRD), and atomic force microscopy (AFM). For bipolar resistive switching (BRS) characteristics, the conduction mechanism of high resistance state (HRS) is a space-charge limited current for the Al / Cu / GdO x / TiN device while the Al / Cu / GdO x / Al 2 O 3 / TiN device shows Schottky emission. However, both devices show Ohmic at a low resistance state (LRS). After the device has been SET, the Cu ﬁlament evidences by both TEM and elemental mapping. Oxygen-rich at the Cu / GdO x interface and Al 2 O 3 layer are conﬁrmed by energy dispersive X-ray spectroscopy (EDS) line proﬁle. The Al / Cu / GdO x / Al 2 O 3 / TiN memristor has lower RESET current, higher speed operation of 100 ns, long read pulse endurance of > 10 9 cycles, good data retention, and the memristor with a large resistance ratio of > 10 5 is operated at a low current of 1.5 µ A. The complementary resistive switching (CRS) characteristics of the Al / Cu / GdO x / Al 2 O 3 / TiN memristor show also a low current operation as compared to the Al / Cu / GdO x / TiN device (300 µ A vs. 3.1 mA). The transport mechanism is the Cu ion migration and it shows Ohmic at low ﬁeld and hopping at high ﬁeld regions. A larger hopping distance of 1.82 nm at the Cu / GdO x interface is obtained as compared to a hopping distance of 1.14 nm in the Al 2 O 3 layer owing to a larger Cu ﬁlament length at the Cu / GdO x interface than the Al 2 O 3 layer. Similarly, the CRS mechanism is explained by using the schematic model. The CRS characteristics show a stable state with long endurance of > 1000 cycles at a pulse width of 1 µ s owing to the insertion of Al 2 O 3 interfacial layer in the Al / Cu / GdO x / Al 2 O 3 / TiN structure.

In order to mitigate those difficulties, the bi-layer concept has been introduced which leads to filament stability by controlling the Cu ion migration and reducing the RESET current [7,8,21,22]. Although there are numerous advantages of RRAM, the sneak path current is affecting its use in practical applications. To resolve the sneak path leakage current, the CRS concept has been introduced in which two BRS devices are anti-serially connected to one another [25,26]. Soni et al. [27] have reported the CRS characteristics in two anti-serially connected Pt/SiO x /Ge 0.3 Se 0.7 /Cu structures as well as in serially connected Pt/SiO x /Ge 0.3 Se 0.7 /Cu and Pt/Ge 0.3 Se 0.7 /SiO x /Cu structures. In our previous study [28], we have reported CRS characteristics using the IrO x /GdO x /Al 2 O 3 /TiN RRAM structure. Although there are some reports on BRS and CRS characteristics by using different structures [28,29], however, the Al 2 O 3 interfacial layer in a Al/Cu/GdO x /Al 2 O 3 /TiN structure has been reported for the first time. A defective GdO x film [30] will be formed, which will easily help the migration of Cu ions under external bias and impact of inserting a thin Al 2 O 3 layer leads to control of Cu ions migration owing to its lower ionic mobility [31]. Hence, insertion of Al 2 O 3 interfacial layer in the Al/Cu/GdO x /Al 2 O 3 /TiN structure helps control the metallic filament formation/dissolution. This will also help reduce the operation current in BRS/CRS performance as compared to the single Al 2 O 3 switching layer [13]. In this new structure, the GdO x is used as a Cu buffer layer, which easily helps the Cu filament forming/dissolving in the Al 2 O 3 layer under low energy. As compared to other structures, this is very useful in the near future.
In this work, the BRS and CRS characteristics by using a new Al/Cu/GdO x /Al 2 O 3 /TiN device have improved performance as compared to the Al/Cu/GdO x /TiN devices. A small device size of 0.6 × 0.6 µm 2 with a polycrystalline grain and defective GdO x films are confirmed by TEM, XPS, and XRD. The surface roughness of GdO x film is also observed by AFM. The Cu filament is observed by using high-resolution TEM (HRTEM) and EDS mapping. The CRS characteristics are also observed. The current conduction mechanism is also explained. By inserting a thin Al 2 O 3 interfacial layer in the Al/Cu/GdO x /Al 2 O 3 /TiN memristor, this shows excellent BRS and CRS characteristics owing to control the Cu ion migration.

Memristor Fabrication Process
First, a 200 nm-thick SiO 2 layer was grown by thermal oxidation on an 8-inch Si wafer. For a bottom electrode (BE), a 50 nm-thick TiN layer followed by a 150 nm-thick Ti was deposited on the SiO 2 /Si substrate. Then, a 150 nm-thick SiO 2 as an insulating layer was deposited on the TiN/Ti/SiO 2 /Si stack. This SiO 2 layer was the patterned via-holes. Then, a thin Al 2 O 3 interfacial layer with a thickness of 2 nm was deposited on TiN BE by the rf sputtering process. The Al 2 O 3 target with a purity of 99.9% was used. Next, the Gd 2 O 3 layer with a thickness of approximately 17 nm was deposited. During deposition, some amount of oxygen was removed and the Gd 2 O 3 film became GdO x (x < 1.5). In order to deposit a top electrode (TE), a Cu layer with a thickness of 40 nm and a 160 nm-thick Al as a capping layer were deposited in situ by thermal evaporation. Finally, the lift-off process was performed to obtain Al/Cu/GdO x /Al 2 O 3 /TiN (S2) memristors. The memory structure is shown by the sketch (Supplementary Information). For comparison, the Al/Cu/GdO x /TiN (S1) structure was also prepared without an Al 2 O 3 interfacial layer. Microstructure, device size, and EDS mapping were observed by using the TEM-FEI Osiris system, which was operated at 200 kV. A crystalline Gd 2 O 3 film was found by using the standard BRUKER XRD system with a Cu-kα source and wavelength was 1.541 Å. Non-stoichiometric GdO x and stoichiometric Al 2 O 3 films were investigated by XPS with an Al (Kα) monochromatic X-ray and energy of 1486.6 eV was applied. The base vacuum pressure was 1 × 10 −9 Torr. The crystalline film was confirmed by grazing incidence XRD (GIXRD), and the film was deposited on the Si substrate. AFM images were taken in tapping mode by using the Innova scanning probe microscope (AFM-SPM) system. Resistive switching characteristics were obtained by applying sweep voltage on the Al/Cu TE whereas the TIN BE was grounded. The electrical characterizations were performed by using both Agilent 4156C and B1500A semiconductor parameter analyzers. Figure 1a shows a typical TEM image of a S2 memristor. The device size is approximately 0.6 × 0.6 µm 2 . Figure 1b,c represents a high-resolution TEM image of inside and outside of the via-hole device, respectively. Each layer is observed clearly and thicknesses of the GdO x and Al 2 O 3 layers are found to be 17 and 1.6 nm, respectively. The HRTEM image shows a polycrystalline GdO x film whereas an Al 2 O 3 film shows amorphous. A clear crystallinity of GdO x film shows in the middle as compared to the GdO x /Cu interface and this interface shows a white color than the middle. This indicates that oxygen content at the Cu/GdO x interface is higher than the middle of the GdO x layer, which has been explained later. The inset of Figure 1c shows the Fast Fourier Transform (FFT) image of the GdO x film. The ring pattern of FFT indicates polycrystalline of the GdO x film. The d-spacing of highly intensive dots is calculated to be 3.11 Å, which represents the d-spacing value (3.06 Å) of Gd 2 O 3 (100) plane [32]. observed by using the TEM-FEI Osiris system, which was operated at 200 kV. A crystalline Gd2O3 film was found by using the standard BRUKER XRD system with a Cu-kα source and wavelength was 1.541 Å. Non-stoichiometric GdOx and stoichiometric Al2O3 films were investigated by XPS with an Al (Kα) monochromatic X-ray and energy of 1486.6 eV was applied. The base vacuum pressure was 1 × 10 −9 Torr. The crystalline film was confirmed by grazing incidence XRD (GIXRD), and the film was deposited on the Si substrate. AFM images were taken in tapping mode by using the Innova scanning probe microscope (AFM-SPM) system. Resistive switching characteristics were obtained by applying sweep voltage on the Al/Cu TE whereas the TIN BE was grounded. The electrical characterizations were performed by using both Agilent 4156C and B1500A semiconductor parameter analyzers.

Material Characteristics
3.1.1. TEM Image of Pristine Memristor Figure 1a shows a typical TEM image of a S2 memristor. The device size is approximately 0.6 × 0.6 µm 2 . Figure 1b,c represents a high-resolution TEM image of inside and outside of the via-hole device, respectively. Each layer is observed clearly and thicknesses of the GdOx and Al2O3 layers are found to be 17 and 1.6 nm, respectively. The HRTEM image shows a polycrystalline GdOx film whereas an Al2O3 film shows amorphous. A clear crystallinity of GdOx film shows in the middle as compared to the GdOx/Cu interface and this interface shows a white color than the middle. This indicates that oxygen content at the Cu/GdOx interface is higher than the middle of the GdOx layer, which has been explained later. The inset of Figure 1c shows the Fast Fourier Transform (FFT) image of the GdOx film. The ring pattern of FFT indicates polycrystalline of the GdOx film. The d-spacing of highly intensive dots is calculated to be 3.11 Å, which represents the d-spacing value (3.06 Å) of Gd2O3 (100) plane [32].

XPS Analysis
The composition and chemical bonding of the GdOx/Al2O3 bilayers on the SiO2/Si substrate are analyzed by XPS spectra with their appropriate peak fitting ( Figure 2). An XPS spectrum of Gd shows

XPS Analysis
The composition and chemical bonding of the GdO x /Al 2 O 3 bilayers on the SiO 2 /Si substrate are analyzed by XPS spectra with their appropriate peak fitting ( Figure 2). An XPS spectrum of Gd shows 3d 3/2 and 3d 5/2 doublet with a binding energy of 1220.5 and 1188.3 eV, respectively (not shown here), which correspond to the binding energy of Gd3d 3/2 and 3d 5/2 spin-orbits at 1218 and 1186 eV for the Gd 2 O 3 film, respectively [33]. The XPS spectrum of Gd3d 5/2 is shown in Figure 2a 3d3/2 and 3d5/2 doublet with a binding energy of 1220.5 and 1188.3 eV, respectively (not shown here), which correspond to the binding energy of Gd3d3/2 and 3d5/2 spin-orbits at 1218 and 1186 eV for the Gd2O3 film, respectively [33]. The XPS spectrum of Gd3d5/2 is shown in Figure 2a. The peak positions at 1188.71 and 1185.82 eV are identified to be Gd2O3 3d5/2 and metallic Gd3d5/2 peaks, respectively. The area ratio of Gd/Gd2O3 is approximately 0.69:1, which shows a higher percentage of Gd in the Gd2O3 film.  Figure 2b shows the O1s core-level spectra for the Gd2O3 films. This spectrum shows three distinct peaks. The strong peak at 531.6 eV corresponds to the oxygen in the Gd2O3 film, whereas lower and higher binding energy peaks at 529.4 eV (O1s B) and 532.9 eV (O1s A) are attributed to the hydroxyl and carbonate groups raised from the atmospheric exposure because of reactivity of Gd2O3 material [34,35]. Moreover, the lower binding energy peak at 529.4 eV can also correspond to the Gd-O bonding which indicates Gd-rich Gd2O3 [36]. On the other hand, oxygen can bind loosely with Gd on a polycrystalline grain or defective Gd2O3 switching material (SM), i.e., GdOx film. The Al2p and O1s peaks in Al2O3 layer are shown in Figure 2c,d, respectively. The Al2p and O1s peaks are located at 75.8 and 532.5 eV, respectively. This indicates a strong Al-O bonding with a stoichiometric Al2O3 interfacial layer.

XRD Pattern and AFM Image
In addition, the crystalline Gd2O3 film is confirmed by XRD pattern (Figure 3a). The peak at 28.7° (2θ) corresponds to (100) plane of Gd2O3 [31] whereas the peak at 55.02° (2θ) corresponds to (311) plane of Si [37]. This low intensity (100) peak is owing to the thin and defective (or oxygen vacancy) polycrystalline GdOx film. Figure 3b,c represents the AFM images on SiO2/Si and GdOx/Si substrates, respectively. The root-mean-square (Rq) and average (Ra) values of the GdOx films are found to be 0.688 and 0.518 nm, and those values are higher than the values of 0.321 and 0.257 nm for the SiO2 layer, respectively. This higher roughness of the GdOx films comes from the polycrystalline grains.
An explanation of higher defective GdOx film is as follows. During deposition of Al2O3, the film will contain some defects because of plasma. After Gd2O3 deposition on AlOx layer, the underneath layer took oxygen (O 2− ) from the Gd2O3 layer resulting in higher defective GdOx and stoichiometric  Figure 2b shows the O1s core-level spectra for the Gd 2 O 3 films. This spectrum shows three distinct peaks. The strong peak at 531.6 eV corresponds to the oxygen in the Gd 2 O 3 film, whereas lower and higher binding energy peaks at 529.4 eV (O1s B) and 532.9 eV (O1s A) are attributed to the hydroxyl and carbonate groups raised from the atmospheric exposure because of reactivity of Gd 2 O 3 material [34,35]. Moreover, the lower binding energy peak at 529.4 eV can also correspond to the Gd-O bonding which indicates Gd-rich Gd 2 O 3 [36]. On the other hand, oxygen can bind loosely with Gd on a polycrystalline grain or defective Gd 2 O 3 switching material (SM), i.e., GdO x film. The Al2p and O1s peaks in Al 2 O 3 layer are shown in Figure 2c,d, respectively. The Al2p and O1s peaks are located at 75.8 and 532.5 eV, respectively. This indicates a strong Al-O bonding with a stoichiometric Al 2 O 3 interfacial layer.

XRD Pattern and AFM Image
In addition, the crystalline Gd 2 O 3 film is confirmed by XRD pattern (Figure 3a). The peak at 28.7 • (2θ) corresponds to (100) plane of Gd 2 O 3 [31] whereas the peak at 55.02 • (2θ) corresponds to (311) plane of Si [37]. This low intensity (100) peak is owing to the thin and defective (or oxygen vacancy) polycrystalline GdO x film. Figure 3b,c represents the AFM images on SiO 2 /Si and GdO x /Si substrates, respectively. The root-mean-square (R q ) and average (R a ) values of the GdO x films are found to be 0.688 and 0.518 nm, and those values are higher than the values of 0.321 and 0.257 nm for the SiO 2 layer, respectively. This higher roughness of the GdO x films comes from the polycrystalline grains.
An explanation of higher defective GdO x film is as follows. During deposition of Al 2 O 3 , the film will contain some defects because of plasma. After Gd 2 O 3 deposition on AlO x layer, the underneath layer took oxygen (O 2− ) from the Gd 2 O 3 layer resulting in higher defective GdO x and stoichiometric Al 2 O 3 layers that can be formed. In the case of the GdO x /Al 2 O 3 bilayers, the Gd 2 O 3 SM can be defective by two ways: (1) During deposition by electron beam evaporation and (2) oxygen consumption by the Al 2 O 3 layer. Therefore, this higher defective GdO x layer or oxygen vacancy will easily help the migration of Cu ions whereas the Al 2 O 3 layer will help in formation/dissolution of the filaments under an external electric field, which has a benefit for improvement of resistive switching memory characteristics as discussed later. Al2O3 layers that can be formed. In the case of the GdOx/Al2O3 bilayers, the Gd2O3 SM can be defective by two ways: (1) During deposition by electron beam evaporation and (2) oxygen consumption by the Al2O3 layer. Therefore, this higher defective GdOx layer or oxygen vacancy will easily help the migration of Cu ions whereas the Al2O3 layer will help in formation/dissolution of the filaments under an external electric field, which has a benefit for improvement of resistive switching memory characteristics as discussed later.

Current-Voltage Switching and Transport Mechanism
Bipolar current-voltage (I-V) characteristics and transport mechanism of the S1 and S2 memristors are shown in Figure 4. Typical forming voltages (Vform) are 2.4 and 2.1 V for the S1 and S2 devices, respectively ( Figure 4a). However, the S2 devices have shown a lower and uniform Vform value as compared to the S1 devices (2.44 vs. 2.62 V at 50% probability) because of GdOx/Al2O3 bilayers (not shown here). Hundred devices for each structure have been measured randomly.
Typical bipolar I-V characteristics of the S1 and S2 devices after forming are shown in Figure 4b. The sweeping voltage direction is shown in arrow marks 1 to 4 (0→+2→0→−1→0 V). The SET voltage (VSET) is approximately 0.7 V. The S2 device has a lower RESET current (IRESET) than the S1 devices (630 µA vs. 2.85 mA), which is due to the Al2O3 interfacial layer. Similarly, the average IRESET value of

Current-Voltage Switching and Transport Mechanism
Bipolar current-voltage (I-V) characteristics and transport mechanism of the S1 and S2 memristors are shown in Figure 4. Typical forming voltages (V form ) are 2.4 and 2.1 V for the S1 and S2 devices, respectively ( Figure 4a). However, the S2 devices have shown a lower and uniform V form value as compared to the S1 devices (2.44 vs. 2.62 V at 50% probability) because of GdO x /Al 2 O 3 bilayers (not shown here). Hundred devices for each structure have been measured randomly.
Typical bipolar I-V characteristics of the S1 and S2 devices after forming are shown in Figure 4b. The sweeping voltage direction is shown in arrow marks 1 to 4 (0→+2→0→−1→0 V). The SET voltage (V SET ) is approximately 0.7 V. The S2 device has a lower RESET current (I RESET ) than the S1 devices Electronics 2020, 9, 1466 6 of 17 (630 µA vs. 2.85 mA), which is due to the Al 2 O 3 interfacial layer. Similarly, the average I RESET value of S2 devices at 50% probability is approximately 540 µA from 100 devices (not shown here). Figure 4c depicts the cumulative probability of leakage current for both the S1 and S2 devices. It is known that the leakage current increases by decreasing the switching layer thickness or by increasing the number of defects [38]. Even though the GdO x /Al 2 O 3 bilayer has a larger thickness of 19 nm than a single GdO x layer (17 nm), however, the S2 devices show a higher leakage current than the S1 devices (8.09 × 10 −10 A vs. 3.05 × 10 −11 A at 50% probability). This is due to a higher defective GdO x as explained in XPS characteristics ( Figure 2).
Considering the device-to-device distribution, the HRS/LRS values at 50% probability are 8.2/0.64 and 9.7/1.4 kΩ for the S1 and S2 devices, respectively. The LRS value of the S2 devices is higher than the S1 devices because of the smaller CF diameter. During formation, Cu atoms can be stored into the GdO x layer (or buffer layer) and a small diameter of conducting filament (CF) could be formed/dissolved in the Al 2 O 3 layer under SET/RESET. However, transport mechanism is one of the key issues to understand the switching characteristics for both the devices as follows. For the S1 devices, the HRS currents for both positive and negative bias regions are plotted in a log-log scale (Figure 4d). The slope values are found to be 1.03-1.11 and 1.85-2.15, which have confirmed the space-charge-limited current (SCLC) conduction mechanism. Sun et al. [39] have also reported the SCLC conduction mechanism even if they have used the Au/CuO-DNA-Al/Au/Si structure. However, both S1 and S2 devices show Ohmic conduction at LRS currents. S2 devices at 50% probability is approximately 540 µA from 100 devices (not shown here). Figure 4c depicts the cumulative probability of leakage current for both the S1 and S2 devices. It is known that the leakage current increases by decreasing the switching layer thickness or by increasing the number of defects [38]. Even though the GdOx/Al2O3 bilayer has a larger thickness of 19 nm than a single GdOx layer (17 nm), however, the S2 devices show a higher leakage current than the S1 devices (8.09 × 10 −10 A vs. 3.05 × 10 −11 A at 50% probability). This is due to a higher defective GdOx as explained in XPS characteristics (Figure 2). Considering the device-to-device distribution, the HRS/LRS values at 50% probability are 8.2/0.64 and 9.7/1.4 kΩ for the S1 and S2 devices, respectively. The LRS value of the S2 devices is higher than the S1 devices because of the smaller CF diameter. During formation, Cu atoms can be stored into the GdOx layer (or buffer layer) and a small diameter of conducting filament (CF) could be formed/dissolved in the Al2O3 layer under SET/RESET. However, transport mechanism is one of the key issues to understand the switching characteristics for both the devices as follows. For the S1 devices, the HRS currents for both positive and negative bias regions are plotted in a log-log scale ( Figure 4d). The slope values are found to be 1.03-1.11 and 1.85-2.15, which have confirmed the space-charge-limited current (SCLC) conduction mechanism. Sun et al. [39] have also reported the SCLC conduction mechanism even if they have used the Au/CuO-DNA-Al/Au/Si structure. However, both S1 and S2 devices show Ohmic conduction at LRS currents. To find the HRS current conduction, the HRS currents of the S2 devices are plotted in ln(J/T 2 ) vs. √E (Figure 4e). The result is well fitted with Schottky emission (SE) at low field region [40]. By solving the equation of Schottky conduction, the dielectric constant (εSE) and barrier height (ΦB) are obtained as follows: To find the HRS current conduction, the HRS currents of the S2 devices are plotted in ln(J/T 2 ) vs. √ E (Figure 4e). The result is well fitted with Schottky emission (SE) at low field region [40]. By solving the equation of Schottky conduction, the dielectric constant (ε SE ) and barrier height (Φ B ) are obtained as follows: Electronics 2020, 9, 1466 7 of 17 where k B is the Boltzmann's constant, T is the absolute temperature, q is the electronic charge, and ε 0 is the permittivity of free space, S is the slope, and I is the intercept of linear plot in ln(J/T 2 ) vs.
√ E plot. However, an interesting point to be noted is that when we consider the pristine device thickness, i.e., approximately 19 nm the obtained ε SE value is quite low approximately 2. This does not follow the ε SE = n 2 (n = refractive index) relation because the reported n value of GdO x film is <2 within the visible wavelength [41]. If we consider the effective thickness 7.5 nm (dissolution gap after RESET) then the ε SE value becomes approximately 3.9, which is within the considerable range and follows the ε SE = n 2 . This conflict signifies that after the RESET process some of the Cu atoms accumulate inside the GdO x switching material and reduce the effective thickness of dissolution gap. From Equations (1) and (2), the corresponding Φ B value at HRS is approximately 0.48 eV.
By considering electron affinities of GdO x (2.05 eV [42]) and Al 2 O 3 (1 eV [43]), energy gaps of GdO x (5.4 eV [41]) and Al 2 O 3 (7.1 eV [44]), and work functions of Cu (4.46 eV [45] and TiN (4.6 eV [46]), the energy bands are shown in dotted lines under thermal equilibrium at 300 K (Figure 4f). To emit the electron, it is found that the barrier height at the Al 2 O 3 /TiN interface is higher than the GdO x /Cu interface (2.5 vs. 0.94 eV). Under a positive bias on the Cu TE, the energy gap of GdO x is reduced owing to the Cu migration. After RESET, a dissolution gap at the GdO x /Al 2 O 3 interface and the Al 2 O 3 layer is observed, which represents the HRS. Then, Schottky emission is obtained under a positive bias before SET because the electron conducts from the TiN BE and crosses the Al 2 O 3 conduction barrier. Furthermore, we can speculate that the filament formation-and dissolution is controlled by the Al 2 O 3 interfacial layer. However, the Cu ion migration under an external field is responsible to change HRS to LRS or vice versa, which has been evidenced below.

Evidence of Cu Migration
To find an evidence of Cu ion migration under SET, the S2 memristor with a typical size of 0.6 × 0.6 µm 2 switches with two consecutive cycles at a high CC of 10 mA. After that, this device was kept at LRS and the device was used for TEM observation, elemental depth profile, and EDS mapping ( Figure 5). All layers are observed (Figure 5a), which are seen in a fresh device (Figure 1), except a Cu filament in the GdO x /Al 2 O 3 bilayers. Figure 5b shows the HRTEM image, where a few nanometer size of the dark spots (or Cu filament) are clearly observed in the marked region. To know the elemental composition with and without Cu filament regions, the same device is characterized by the scanning transmission electron microscope (STEM) and corresponding images are shown in Figure 5c,d. The EDS depth profiles with and without Cu filament regions are shown in Figure 5e,f, respectively. The EDS line scans of Ti, N, Gd, O, Al, and Cu elements are taken from the Ti BE to Al capping layer, as shown with arrows in Figure 5c,d.
From the EDS depth profiles of nitrogen (Figure 5f), it is found that the TiN layer with a thickness of approximately 30 nm is shown on Ti. The thickness of GdO x layer is approximately 17 nm. A low atomic concentration (5.5%) of the Al peaks at the GdO x /TiN interface is observed because of a thin (2 nm) Al 2 O 3 interfacial layer. It is interesting to note that the atomic concentration of O at the TiN BE/GdO x interface is higher than the value at the GdO x /Cu TE interface (20.3 vs. 13.2%), which indicates the oxygen consumption at the Al 2 O 3 interfacial layer. Therefore, the Gd 2 O 3 layer becomes more defective, which is consistent with XPS results (Figure 2). The EDS line scan profile along the Cu filament is marked at four positions 1, 2, 3, and 4, as shown in Figure 5c Figure 5g-l. All elements in these layers are observed clearly. In Figure 5h, the Cu elemental mapping represents a beautiful Cu filament. Thanks to the Cu migration mechanism for real non-volatile memory applications. A hump-like shape of Cu at the Cu/GdOx interface is observed under the SET operation, which initiates the formation of CF. Figure 6a shows the HRTEM image of Cu/GdOx interface without the Cu filament region. The inset in Figure 6a shows the FFT image of marked region. The d-spacing values from the FFT image are found to be d1 = 1.99 Å, d2 = 3.08 Å, and d3 = 3.91 Å. The value of 1.99 Å is much closer to the reported value (2.088 Å) of Cu (111) plane [47]. However, values of 3.08 and 3.91 Å are higher due to overlapping of two Cu crystals, where the d-spacing of moire' fringes is increased [48]. As further investigation of Cu diffusion in TiN BE we have analyzed the HRTEM, as shown in Figure 6b. The Cu filament region is marked as a conical shape with a dotted line. We can clearly observe the diffused Cu in the TiN BE.
The mass percentage values from the EDS depth profile (Figure 5e) of Ti and N are approximately 50 and 20, respectively, which shows non-stoichiometric TiNx (x < 1). Under the high current, this TiNx BE can allow the Cu diffusion through grain boundaries or defects. Olowolafe et al. [49] have reported the diffusion of Cu through the TiNx layer at high temperatures in the Cu/TiNx/Si structure. Mühlbacher et al. [50] have reported Cu diffusion in a single crystalline TiN All elements in these layers are observed clearly. In Figure 5h, the Cu elemental mapping represents a beautiful Cu filament. Thanks to the Cu migration mechanism for real non-volatile memory applications. A hump-like shape of Cu at the Cu/GdO x interface is observed under the SET operation, which initiates the formation of CF. Figure 6a shows the HRTEM image of Cu/GdO x interface without the Cu filament region. The inset in Figure 6a shows the FFT image of marked region. The d-spacing values from the FFT image are found to be d 1 = 1.99 Å, d 2 = 3.08 Å, and d 3 = 3.91 Å. The value of 1.99 Å is much closer to the reported value (2.088 Å) of Cu (111) plane [47]. However, values of 3.08 and 3.91 Å are higher due to overlapping of two Cu crystals, where the d-spacing of moire' fringes is increased [48]. As further investigation of Cu diffusion in TiN BE we have analyzed the HRTEM, as shown in Figure 6b. The Cu filament region is marked as a conical shape with a dotted line. We can clearly observe the diffused Cu in the TiN BE.
The mass percentage values from the EDS depth profile (Figure 5e)   Other researchers have reported the Cu or Ag migration in different oxide or solid-electrolyte materials [54,55]. The CF with nanocrystals (NCs) are also reported in the Ag/a-Si/Pt structure by Yang et al. [54] and Cu protrusion in Cu/HfO2/Pt devices is observed by Lv et al. [19]. Vianello et al. [55] have shown the evidence of the Ag filament using the Ag/Sb-doped GeS2/W structure. Liu et al. have observed the localized and controllable Ag nano-filament growth in the Ag/ZrO2/Cu NC/Pt structure by using an in situ TEM technique [56]. The Cu NC was decorated on Pt BE. The superior uniformity of resistive switching properties is obtained, which is owing to enhance and concentrate the electric field on Cu NC sites. This will control the location and orientation of the Ag CFs. On the other hand, the Ag nano-filament is formed by a mass transfer from Ag nano clusters in the Au nanotip/SiO2/Ag NC/p-Si structure [16]. The discrete CF is observed by in situ TEM. However, proper decoration of nanocrystals/clusters on the nanoscale device is one of the critical tasks. Yuan et al. have reported the Cu tip size dependent CF nature in the Cu tip/SiO2/W structure by an in situ TEM [57]. For a smaller Cu tip size, the CF shows as thin and in the shape of discrete clusters owing to the limited ion supply. On the other hand, a wide CF in continuous is observed for the larger Cu tip owing to sufficient ion injection and lower surface energy. This suggests that the discrete CF under nano-ampere operation may be not sufficient for a reliable non-volatile memory application. Further investigation is still needed of nano-ionic memristive switching dynamics at higher resolution and dimensions for experimental study [58,59]. The switching mechanism evolution in greater resolution is a key part for the real non-volatile memory and memory in computing applications. In our study, it is possible to say that the Cu filament formation/dissolution in the Al2O3 interfacial layer, which is observed by ex situ HRTEM, will control the resistive switching performance. This has been discussed below.

Device Performance and Low Current Operation
Figure 7a represents program/erase (P/E) endurance of the S1 and S2 devices with a high-speed operation. The P/E voltage and pulse width are applied +1.5 V/−0.8V and 100 ns/1 µs, respectively. The S2 devices show longer P/E cycles as compared to the S1 devices. After a few P/E cycles (~30), the S1 devices show failure because of uncontrolled Cu migration whereas the Cu filament formation/dissolution is controlled by the Al2O3 interfacial layer. Figure 7b shows read pulse Other researchers have reported the Cu or Ag migration in different oxide or solid-electrolyte materials [54,55]. The CF with nanocrystals (NCs) are also reported in the Ag/a-Si/Pt structure by Yang et al. [54] and Cu protrusion in Cu/HfO 2 /Pt devices is observed by Lv et al. [19]. Vianello et al. [55] have shown the evidence of the Ag filament using the Ag/Sb-doped GeS 2 /W structure. Liu et al. have observed the localized and controllable Ag nano-filament growth in the Ag/ZrO 2 /Cu NC/Pt structure by using an in situ TEM technique [56]. The Cu NC was decorated on Pt BE. The superior uniformity of resistive switching properties is obtained, which is owing to enhance and concentrate the electric field on Cu NC sites. This will control the location and orientation of the Ag CFs. On the other hand, the Ag nano-filament is formed by a mass transfer from Ag nano clusters in the Au nano-tip/SiO 2 /Ag NC/p-Si structure [16]. The discrete CF is observed by in situ TEM. However, proper decoration of nanocrystals/clusters on the nanoscale device is one of the critical tasks. Yuan et al. have reported the Cu tip size dependent CF nature in the Cu tip/SiO 2 /W structure by an in situ TEM [57]. For a smaller Cu tip size, the CF shows as thin and in the shape of discrete clusters owing to the limited ion supply. On the other hand, a wide CF in continuous is observed for the larger Cu tip owing to sufficient ion injection and lower surface energy. This suggests that the discrete CF under nano-ampere operation may be not sufficient for a reliable non-volatile memory application. Further investigation is still needed of nano-ionic memristive switching dynamics at higher resolution and dimensions for experimental study [58,59]. The switching mechanism evolution in greater resolution is a key part for the real non-volatile memory and memory in computing applications. In our study, it is possible to say that the Cu filament formation/dissolution in the Al 2 O 3 interfacial layer, which is observed by ex situ HRTEM, will control the resistive switching performance. This has been discussed below. Figure 7a represents program/erase (P/E) endurance of the S1 and S2 devices with a high-speed operation. The P/E voltage and pulse width are applied +1.5 V/−0.8V and 100 ns/1 µs, respectively. The S2 devices show longer P/E cycles as compared to the S1 devices. After a few P/E cycles (~30), the S1 devices show failure because of uncontrolled Cu migration whereas the Cu filament formation/dissolution is controlled by the Al 2 O 3 interfacial layer. Figure 7b shows read pulse endurance of the S1 and S2 devices with a small pulse width of 1 µs. The S1 devices show failure after 5 × 10 8 cycles whereas the S2 devices show a long read endurance of >10 9 cycles even at low current operation of 100 µA. The values of HRS/LRS are approximately 27/260 Ω and 348/379 Ω for the S1 and S2 devices at CC of 500 µA, respectively. The S2 device shows higher resistance ratio of 900 than the value of 100 for the S1 devices owing to the narrower Cu filament formation/dissolution in the Al 2 O 3 layer. The HRS (~259 kΩ) and LRS (~1.57 kΩ) of the S2 devices at a CC of 100 µA also show good stability with a resistance ratio of >150. Figure 7c represents a stable data retention of about 20,000 s of our S2 memory device at CC of 100 µA. Figure 7d shows typical bipolar resistive switching (BRS) characteristics of the S2 devices under at a very low CC of 1.5 µA. A high resistance ratio of >10 5 at a V read of 0.5 V is achieved, even a low RESET current of <1 nA is observed. Therefore, the S2 device can have a high speed (100 ns) and low current operation of 1.5 µA. Further, the S2 devices has the possibility to exhibit a multi-level cell operation. However, proper controlling of the operation voltage of these devices will have complementary resistive switching (CRS) characteristics in a single cell, which have been reported for the first time in this study below.

Device Performance and Low Current Operation
Electronics 2020, 8, x FOR PEER REVIEW 10 of 16 endurance of the S1 and S2 devices with a small pulse width of 1 µs. The S1 devices show failure after 5 × 10 8 cycles whereas the S2 devices show a long read endurance of >10 9 cycles even at low current operation of 100 µA. The values of HRS/LRS are approximately 27/260 Ω and 348/379 Ω for the S1 and S2 devices at CC of 500 µA, respectively. The S2 device shows higher resistance ratio of 900 than the value of 100 for the S1 devices owing to the narrower Cu filament formation/dissolution in the Al2O3 layer. The HRS (~259 kΩ) and LRS (~1.57 kΩ) of the S2 devices at a CC of 100 µA also show good stability with a resistance ratio of >150. Figure 7c represents a stable data retention of about 20,000 s of our S2 memory device at CC of 100 µA. Figure 7d shows typical bipolar resistive switching (BRS) characteristics of the S2 devices under at a very low CC of 1.5 µA. A high resistance ratio of >10 5 at a Vread of 0.5 V is achieved, even a low RESET current of <1 nA is observed. Therefore, the S2 device can have a high speed (100 ns) and low current operation of 1.5 µA. Further, the S2 devices has the possibility to exhibit a multi-level cell operation. However, proper controlling of the operation voltage of these devices will have complementary resistive switching (CRS) characteristics in a single cell, which have been reported for the first time in this study below. Figure 7. Bipolar resistive switching performance of the S1 and S2 devices. (a) Comparison of P/E endurance for the S1 and S2 devices with a high speed of 100 ns. The S1 device has shown failure after a few cycles while the S2 device show longer endurance because of Al2O3 interfacial layer. (b) Read endurance of >10 9 cycles of the S2 devices at a low current of 100 µA. (c) The S2 device also shows longer retention time about 20,000 s with a good stability at low current compliance of 100 µA. (d) The S2 device shows a low current operation of 1.5 µA with a large HRS/LRS ratio of 10 5 at a read voltage of 0.5 V.

I-V and Transport Characteristics
Although there are numerous advantages of BRS memory, the sneak path current is affecting its use in practical three-dimensional (3D) cross-point applications. Recently, the CRS phenomena has been proposed to resolve the sneak path effect by using two anti-serially cells [25,26]. In our study, both S1 and S2 memristors show CRS characteristics after adjusting the sweeping voltage ( Figure 8). . Bipolar resistive switching performance of the S1 and S2 devices. (a) Comparison of P/E endurance for the S1 and S2 devices with a high speed of 100 ns. The S1 device has shown failure after a few cycles while the S2 device show longer endurance because of Al 2 O 3 interfacial layer. (b) Read endurance of >10 9 cycles of the S2 devices at a low current of 100 µA. (c) The S2 device also shows longer retention time about 20,000 s with a good stability at low current compliance of 100 µA. (d) The S2 device shows a low current operation of 1.5 µA with a large HRS/LRS ratio of 10 5 at a read voltage of 0.5 V.

I-V and Transport Characteristics
Although there are numerous advantages of BRS memory, the sneak path current is affecting its use in practical three-dimensional (3D) cross-point applications. Recently, the CRS phenomena has been proposed to resolve the sneak path effect by using two anti-serially cells [25,26]. In our study, both S1 and S2 memristors show CRS characteristics after adjusting the sweeping voltage ( Figure 8). The voltage sweeping direction is indicated by arrow 1-2. The resistance states are denoted as "0", "ON" and "1", respectively.
The electroforming process is applied under a negative bias for both pristine S1 and S2 memristors. The values of V SET1 , V SET2 , V RESET1 , and V RESET2 for the S1 devices (Figure 8a) are found to be 0.88, −0.88, −1.4, and 1.3 V, while those values are found to be 0.78, −0.76, −1.3, and 1.1 V for the S2 devices (Figure 8b), respectively. Both devices have been operated under a low voltage of ±1.5 V. However, the operation current (~300 µA) of the S2 devices is about 11 times lower than that of the S1 devices (3.1 mA), which is very useful for low power operation of the cross-point memory arrays. Therefore, the Al 2 O 3 layer has been beneficial. The voltage sweeping direction is indicated by arrow 1-2. The resistance states are denoted as "0", "ON" and "1", respectively. The electroforming process is applied under a negative bias for both pristine S1 and S2 memristors. The values of VSET1, VSET2, VRESET1, and VRESET2 for the S1 devices (Figure 8a) are found to be 0.88, −0.88, −1.4, and 1.3 V, while those values are found to be 0.78, −0.76, −1.3, and 1.1 V for the S2 devices (Figure 8b), respectively. Both devices have been operated under a low voltage of ±1.5 V. However, the operation current (~300 µA) of the S2 devices is about 11 times lower than that of the S1 devices (3.1 mA), which is very useful for low power operation of the cross-point memory arrays. Therefore, the Al2O3 layer has been beneficial. To understand the current transport characteristics, the I-V curves of the S2 devices are fitted, as shown in Figure 8c,d. Both "0" and "1" states at low field of negative and positive bias regions confirm the Ohmic conduction with slope values from 1.06 to 1.15. The high field region is plotted in ln(J) vs. E for the hopping conduction [28], which is expressed below: where Jhopping is the current density due to the hopping conduction, 'a' is the mean hopping distance, n is the electron concentration in the conduction band of dielectric, v is the frequency of thermal vibration of electrons at trap sites, and Ea is the activation energy. From Equation (4), we have obtained an equation for hopping distance (a) below: To understand the current transport characteristics, the I-V curves of the S2 devices are fitted, as shown in Figure 8c,d. Both "0" and "1" states at low field of negative and positive bias regions confirm the Ohmic conduction with slope values from 1.06 to 1.15. The high field region is plotted in ln(J) vs. E for the hopping conduction [28], which is expressed below: where J hopping is the current density due to the hopping conduction, 'a' is the mean hopping distance, n is the electron concentration in the conduction band of dielectric, v is the frequency of thermal vibration of electrons at trap sites, and E a is the activation energy. From Equation (4), we have obtained an equation for hopping distance (a) below: where S is the slope. By using Equation (4), the hopping distance values for both "0" state at a positive bias and "1" state at a negative bias are found to be 1.80 and 1.82 nm (Figure 8c), while those values for both "0" state at a negative bias and "1" state at a positive bias are found to be 1.14 and 1.41 nm (Figure 8d), respectively. Yan et al. [60] have also reported the hopping distance of approximately 2 nm by using the TiW/Cu 2 O/Cu structure. Figure 8e shows read stable endurance of 1000 cycles with a small pulse width of 1 µs. The "ON" state and "1" state are read at a V read of −1 V, whereas the "0" state is read at a 1/2V read of −0.5 V. The non-linearity factor is approximately 6, which is useful for 3D cross-point arrays in the near future.

Memristor Mechanism
The switching mechanism of the CRS characteristics is demonstrated schematically in Figure 9.
where S is the slope. By using Equation (4), the hopping distance values for both "0" state at a positive bias and "1" state at a negative bias are found to be 1.80 and 1.82 nm (Figure 8c), while those values for both "0" state at a negative bias and "1" state at a positive bias are found to be 1.14 and 1.41 nm (Figure 8d), respectively. Yan et al. [60] have also reported the hopping distance of approximately 2 nm by using the TiW/Cu2O/Cu structure. Figure 8e shows read stable endurance of 1000 cycles with a small pulse width of 1 µs. The "ON" state and "1" state are read at a Vread of −1 V, whereas the "0" state is read at a 1/2Vread of −0.5 V. The non-linearity factor is approximately 6, which is useful for 3D cross-point arrays in the near future.

Memristor Mechanism
The switching mechanism of the CRS characteristics is demonstrated schematically in Figure 9. From this model, the CRS depends on Cu ions' migration through the GdOx/Al2O3 bilayer. Initially, both the Al2O3 layer and GdOx/Cu TE interface are less defective than GdOx layer, as we can see from the oxygen-rich layer (Figure 5f). When a negative bias is applied on the Cu TE, Gd-O bonds at grain boundary break easily and O 2− ions are migrated towards the GdOx/TiN interface. On the other hand, O 2− ions are accumulated at the Cu/GdOx interface because of the inert Cu electrode or repel O 2− ions by Cu electrode, which results in oxygen vacancy filament formation at the Cu/GdOx interface ( Figure  9a).
When a positive voltage is applied on the Cu TE (>VSET1), the Cu ions are generated by oxidation method (Cu° → Cu z+ + ze − , z = 1, 2) [5] and these Cu ions migrate towards the Al2O3/TiN interface through oxygen vacancy under an electric field as well as a Cu filament can be formed in the Al2O3 layer and current increases (Figure 9b). Due to more oxygen vacancies in the GdOx grain boundaries, the Cu ions arrange accordingly and those neutralize by taking the electron from the BE through reduction process (Cu z+ + ze − → Cu°). At VSET1, the "0" state changes to "ON" state. Further increment of a positive voltage up to 1 V leads to a larger filament diameter in the Al2O3 layer. However, if the positive voltage is more than 1 V then the electric field is developed across the Cu/GdOx interface and the filament is dissolved (Figure 9c). Maximum dissolution of the filament is observed up to VRESET2 and the "ON" state changes to "1" state of "OFF" state.  When a positive voltage is applied on the Cu TE (>V SET1 ), the Cu ions are generated by oxidation method (Cu • → Cu z+ + ze − , z = 1, 2) [5] and these Cu ions migrate towards the Al 2 O 3 /TiN interface through oxygen vacancy under an electric field as well as a Cu filament can be formed in the Al 2 O 3 layer and current increases (Figure 9b). Due to more oxygen vacancies in the GdO x grain boundaries, the Cu ions arrange accordingly and those neutralize by taking the electron from the BE through reduction process (Cu z+ + ze − → Cu • ). At V SET1 , the "0" state changes to "ON" state. Further increment of a positive voltage up to 1 V leads to a larger filament diameter in the Al 2 O 3 layer. However, if the positive voltage is more than 1 V then the electric field is developed across the Cu/GdO x interface and the filament is dissolved (Figure 9c). Maximum dissolution of the filament is observed up to V RESET2 and the "ON" state changes to "1" state of "OFF" state.
Similarly, when a negative voltage (<V SET2 ) is applied on the TE, the Cu ions migrate towards the Cu/GdO x interface from GdO x grain boundaries and the Cu filament is formed at the Cu/GdO x interface as current increases (Figure 9d). The "1" state changes to "ON" state. By decreasing the negative voltage up to −1.06 V the filament diameter is becoming thicker at the Cu/GdO x interface. If the negative voltage is less than −1.06 V the dissolution of filament is started in the Al 2 O 3 layer and it has a maximum dissolution up to V RESET1 as well as "ON" state changes to "0" state or "OFF" state ( Figure 9e). In our study, we did not fabricate the back to back memristor structure. Two cells are the Cu/GdO x interface and Al 2 O 3 layer where the Cu incorporated GdO x layer is a virtual common electrode in a single Al/Cu/GdO x /Al 2 O 3 /TiN memristor, which is equivalent to the back to back memristor structure. The Cu filament formation/dissolution happens at the Cu/GdO x interface and Al 2 O 3 layer alternately by optimizing the RESET voltage and the CRS mechanism explained as well.
Similarly, the CRS mechanism of the Al/Cu/GdO x /TiN structure can be explained because of TiN x O y layer formation at the GdO x /TiN interface during a negative bias applied on the pristine device ( Figure 8a). From Figure 8, it is observed that the Cu ions are transported by hopping. The hopping distance at the Cu/GdO x interface is higher than the Al 2 O 3 layer (1.80 to 1.82 nm vs. 1.14 to 1.41 nm). Therefore, the filament length at the Cu/GdO x interface is longer than the Al 2 O 3 layer. These CRS characteristics show a stable and long endurance of >1000 cycles and are promising for next generation 3D cross-point memory applications.

Conclusions
Improved BRS and CRS characteristics of the Al/Cu/GdO x /Al 2 O 3 /TiN memristors have been reported as compared to the Al/Cu/GdO x /TiN devices, for the first time, owing to insertion of Al 2 O 3 interfacial layer. The defective polycrystalline grain and composition of the GdO x film are observed by TEM, XPS, and XRD. The Al/Cu/GdO x /Al 2 O 3 /TiN devices show stable BRS characteristics with lower RESET current, stable P/E endurance with a high speed of 100 ns, long read endurance of >10 9 cycles with a pulse width of 1 µs, good data retention, and good device-to-device uniformity. This is due to the Cu filament formation/dissolution in the Al 2 O 3 interfacial layer under external bias, which evidences by TEM, EDS elemental mapping, and line scan. The S1 device shows SCLC while the S2 device shows Schottky emission with a barrier height of 0.48 eV. However, both devices show Ohmic conduction at LRS. The S2 devices can be operated at low current of 1.5 µA with a large resistance ration of >10 5 , which is very useful for a multi-level operation with low power non-volatile memory applications.
It is found that the CRS characteristics of the S2 memristor are observed at low current operation as compared to the S1 (300 µA vs. 3.1 mA) because insertion of the Al 2 O 3 layer has been beneficial. Transport mechanism of the CRS characteristics is Ohmic at low field and hopping conduction at high field regions. The hopping distance of Cu ion migration is 1.82 nm at the Cu/GdO x interface while it is 1.14 nm in the Al 2 O 3 layer. The CRS characteristics have been explained by using the schematic model. Therefore, the Al/Cu/GdO x /Al 2 O 3 /TiN memristor is very useful in the future 3D cross-point memory architecture. This memristor can be extended to an artificial synapse, bio-sensing with a Cu reduction-oxidation mechanism, as well as artificial intelligence (AI) in the future.