The Effect of Multi-Layer Stacking Sequence of TiOx Active Layers on the Resistive-Switching Characteristics of Memristor Devices

The oxygen vacancies in the TiOx active layer play the key role in determining the electrical characteristics of TiOx–based memristors such as resistive-switching behaviour. In this paper, we investigated the effect of a multi-layer stacking sequence of TiOx active layers on the resistive-switching characteristics of memristor devices. In particular, the stacking sequence of the multi-layer TiOx sub-layers, which have different oxygen contents, was varied. The optimal stacking sequence condition was confirmed by measuring the current–voltage characteristics, and also the retention test confirmed that the characteristics were maintained for more than 10,000 s. Finally, the simulation using the Modified National Institute of Standards and Technology handwriting recognition data set revealed that the multi-layer TiOx memristors showed a learning accuracy of 89.18%, demonstrating the practical utilization of the multi-layer TiOx memristors in artificial intelligence systems.


Introduction
Oxide-based memristive devices have attracted considerable interest due to their advantages such as non-volatile memory function, fast switching speed, low power consumption, good durability, process compatibility with complementary metal-oxide semiconductor technology, as well as the possibility of being implemented in real hardware and board-integrated systems [1][2][3][4][5][6]. In particular, the simple two-terminal crosspoint structure of memristors is expected to enable the high-density integration of computing devices by adopting three-dimensional stacking architectures [1,7]. Due to these advantages, various emerging electronics such as neuromorphic circuits and systems have been demonstrated by utilizing the memristors as one of their key elements [8,9]. From a conceptual point of view, the memristors are considered as the fourth fundamental circuit element in addition to resistors, capacitors, and inductors, which relate the charge q and the magnetic flux ϕ [10]. As an electronic device, on the other hand, the memristor behaves more like a memory device unit which stores the information in the form of resistance and changes according to the direction of the applied bias. Typically, the memristor devices are constructed with a metal−insulator−metal (MIM) structure with an active layer sandwiched between the two counter electrodes (bottom and top electrodes). Based on the history of the applied bias, the memristors are switched between high-resistive state (HRS) and low-resistive state (LRS) by the modulation of the resistance of the active layer. For the active layers, many different material candidates have been investigated such as TiO 2 , HfO 2 , NbO 2 , TaO x , ZnO and Al 2 O 3 [11][12][13][14][15]. Also, for the formation of oxide active layers, deposition methods such as sputtering and anodizing have been utilized [16][17][18][19]. Among the candidate materials, TiO 2 -or TiO 2 /TiO 2-x -based memristors have been intensively studied since the physical realization and understanding of the memristors in 2008 [20]. In TiO 2 -or TiO 2 /TiO 2−x memristors, the conducting state change is considered to originate in the formation and rupture of conducting channels [1,21]. As described by Carta et al., localized reduced TiO x phases with lower O:Ti ratio are formed underneath the top electrode (TE) under an applied electric field [22]. Since the reduced TiO x phases have a more metallic character than the stoichiometric TiO 2 phase, the electrical conductivity is increased and LRS is obtained. Carta et al. also suggested that the reduction of the O:Ti ratio is involved with the migration of both O and Ti atoms that move toward the opposite directions under an applied bias [22]. In addition, atomic level simulations on the formation of conducting channels using kinetic Monte Carlo simulation have been reported [21,23,24]. In particular, according to the report from Li et al., it is claimed that filament formation is involved with the vacancy hopping induced localized electric field [21]. Based on these previous studies on the TiO 2 -and TiO 2 /TiO 2−x -based memristors, it is likely that the oxygen vacancies play the key role in the operation of TiO x -based memristors.
Previously, various multilayer structure oxide memristors were investigated including TiO 2−x /TiO 2 , TiON/HfO y /HfO x , TiO 2 /ZrO 2 , and TaO x /HfAl y O x [25][26][27][28]. In this study, we constructed the active layer with a four-layer stacked structure of TiO x films having different oxygen vacancy concentrations. Specifically, by varying the O 2 partial pressure during the sputtering process of TiO x films, TiO x films with different oxygen-binding states could be obtained. Using these pre-defined deposition conditions, memristors with different stacking sequences are fabricated. To identify the role of the stacking sequence, we investigated the effect of stacking sequence on the memristive behaviours such as bistable switching characteristics, current on/off ratio, as well as their retention stability. Finally, for the practical demonstration of the fabricated device, we predicted the accuracy of Modified National Institute of Standards and Technology (MNIST) handwritten recognition by applying our device weight update characteristics.

Experimental Procedure
For the fabrication of TiO x -based memristor devices, a glass substrate was sonicated in acetone and isopropyl alcohol (IPA) for 10 min each. Then, the substrate was rinsed with IPA and dried with N 2 gas. On the cleaned glass substrate, a 50 nm-thick Al electrode was deposited by thermal evaporation with a deposition rate of~2 Å/s as a bottom electrode (BE). The patterning of the Al electrode was carried out by using a metal shadow mask and the width of the electrode was 50 µm. Next, for the deposition of multi-layer TiO x active layers, a radio-frequency magnetron sputtering system was used with sputtering power and deposition pressure of 100 W and 5 × 10 −3 Torr, respectively. To control the oxygen content in the TiO x film, the argon (Ar) and oxygen (O 2 ) gas flow rates were varied. Figure 1 shows the stacking sequence of the active layer. The patterning of TiO x active layers was carried out by using a metal shadow mask which had a dimension of 1500 × 1500 µm. Finally, a 50 nm-thick Al top electrode was deposited by thermal evaporation and patterned by using a metal shadow mask. The width of the top electrode was 100 µm.
The atomic binding states of TiO x films were analyzed by using X-ray photoelectron spectroscopy (XPS; Thermo Fisher Scientific, Waltham, MA, USA, ESCALAB 250). For the XPS analysis, each TiO x sample was prepared separately. The current-voltage characteristic and the retention characteristics of the memristors were analyzed by using a semiconductor parameter analyzer (Agilent Technologies, Santa Clara, CA, USA, 4155C) which is attached to a probe station in dark ambient condition. deconvoluted to two main peaks centred at around ~530 eV and 531.0~531.5 eV. The peaks at ~530 eV and 531.0-531.5 eV represent the oxygen species in metal-oxygen-metal (M-O-M) and near the oxygen vacancy (O-M-Ovac) [29], respectively. By increasing the PO2, the portion of oxygen vacancy was gradually decreased. For instance, in the case of A-TiOx film, the portion of O-M-Ovac was 35.9%, while it decreased to 33.5%, 30.1%, and 26.7% for the B-TiOx, C-TiOx, and D-TiOx film, respectively. Since the oxygen vacancy concentration in an oxide film is strongly related to the electrical conductivity of the film [30] and the oxygen vacancies play the key role in the operation of TiOx-based memristors, it is likely that the stacking sequence of oxygen-rich and oxygen-deficient TiOx films would influence the operation of the device. To investigate the effect of multi-layer stacking sequence on the resistive switching characteristics of the memristors, devices having four different stacking sequences were fabricated as schematically shown in Figure 1a. respectively. In all cases, the most oxygen-deficient layer, A-TiOx film was placed in the bottom-most part, while the other layers were positioned with different combinations. Here, the TE electrode was set as ground and the bias applied to the BE was swept in the range of −3 V to +3 V to induce the SET and RESET processes. As indicated, the devices with types I, II, and IV stacking sequences showed memristive characteristics, clearly indicating the SET and RESET processes. In the meanwhile, the type III device showed only insulating behaviour without the bistable behaviour. In the case of the type II device (Figure 2b), the device first showed HRS (OFF state) upon sweeping the bias from 0 V to +3 V. Then, at around +2.3 V, transition to the LRS (ON state)  Figure 1a shows the schematic device structures of the memristors having four TiO x sub-layers with different oxygen vacancy (O vac ) contents. Here, the stacking sequence of the four TiO x sub-layers was varied to find the structure to enhance the resistive switching characteristics of the device (types I, II, III, and IV). The four TiO x sub-layers with different oxygen vacancy contents were fabricated by using different sputtering conditions by varying the gas flow rates of Ar and O 2 gases (Ar:O 2 = 50:5 sccm, 50:7 sccm, 50:10 sccm and 50:13 sccm). The corresponding TiO x films are designated as A-TiO x , B-TiO x , C-TiO x , and D-TiO x , in the order of decreasing oxygen vacancy content ( Figure 1a). Consequently, the A-TiO x film is relatively oxygen-deficient, while the D-TiO x film is relatively oxygen-rich. Also, the thicknesses of A-TiO x , B-TiO x , C-TiO x , and D-TiO x films were approximately 14.0 nm, 11.5 nm, 11.5 nm, and 9.0 nm, respectively. To determine the variation of oxygen vacancy content, an XPS analysis was carried out.  [29], respectively. By increasing the P O2 , the portion of oxygen vacancy was gradually decreased. For instance, in the case of A-TiO x film, the portion of O-M-O vac was 35.9%, while it decreased to 33.5%, 30.1%, and 26.7% for the B-TiO x , C-TiO x , and D-TiO x film, respectively.

Results and Discussion
Since the oxygen vacancy concentration in an oxide film is strongly related to the electrical conductivity of the film [30] and the oxygen vacancies play the key role in the operation of TiO x -based memristors, it is likely that the stacking sequence of oxygen-rich and oxygen-deficient TiO x films would influence the operation of the device. To investigate the effect of multi-layer stacking sequence on the resistive switching characteristics of the memristors, devices having four different stacking sequences were fabricated as schematically shown in Figure 1a. , respectively. In all cases, the most oxygen-deficient layer, A-TiO x film was placed in the bottom-most part, while the other layers were positioned with different combinations. Here, the TE electrode was set as ground and the bias applied to the BE was swept in the range of −3 V to +3 V to induce the SET and RESET processes. As indicated, the devices with types I, II, and IV stacking sequences showed memristive characteristics, clearly indicating the SET and RESET processes. In the meanwhile, the type III device showed only insulating behaviour without the bistable behaviour. In the case of the type II device (Figure 2b), the device first showed HRS (OFF state) upon sweeping the bias from 0 V to +3 V. Then, at around +2.3 V, transition to the LRS (ON state) starts to occur, which is regarded as the SET process. After reaching +3 V, the LRS maintains, exhibiting the memorizing behaviour. Then, by sweeping the bias to the negative direction, a transition from LRS to HRS occurs at around −2.7 V, which indicates the RESET process. Similar memristive characteristics and switching behaviours were also observed in devices with other stacking sequences such as types I and IV, with slightly different SET and RESET voltages. However, the I ON /I OFF ratio was different depending on the device structure. In the tested device structures, the type II device (BE/A-C-B-D/TE) showed the highest I ON /I OFF ratio value of~45 (in average), while, the type I and type IV devices showed I ON /I OFF ratio values of~16 and~17, respectively. The type III device (BE/A-D-C-B/TE), however, showed no switching behaviour and only insulating I-V characteristics were observed. Figure 2 also shows the I-V data which are repeated for five consecutive cycles. All the devices showed relatively stable I-V behaviour, while the type IV device showed a slight change in the current levels. As shown in Figure 2, during the SET and RESET processes, the current changes gradually, indicating the interface-type mechanism is dominant rather than the filament-type [31]. Concerning the variation of memristive behavior by the stacking sequence, we expect that the supply and migration of oxygen vacancies from the underneath TiO x sub-layers to the TE/top-TiO x interface are important [31]. In our results, the type I, II, and IV devices showed the memristive behaviour while the type III device showed insulating characteristics. In particular, in the cases of types I and II, the most oxygen-rich TiO x layer (D-TiO x ) with the lowest concentration of oxygen vacancies is placed on the top-most layer, contacting the TE, while the relatively oxygen-deficient TiO x layers with larger concentrations of oxygen vacancies are placed underneath. Therefore, during the SET process, these relatively oxygen-deficient TiO x layers can efficiently supply the oxygen vacancies and can contribute to the interface-type resistive switching behaviour. Comparing the type I and II devices, the positions of B-and C-TiO x layers are different, where in type II, the second-most oxygen-deficient TiO x layer (B-TiO x ) is placed beneath the top D-TiO x layer. Therefore, compared to type I device, more oxygen vacancies can be supplied to the top D-TiO x layer, allowing larger resistive variation during switching. In the cases of types III and IV, the most oxygen-rich D-TiO x layer is placed in the middle parts of the stacking. Therefore, the supply of oxygen vacancies towards the TE/top-TiO x interface can be relatively smaller compared to type I and II devices. Also, considering that the oxygen vacancies migrate toward the TE/top-TiO x interface during the SET process, the decrease of resistance in the D-TiO x layer can be higher in type IV device compared to type III.
Micromachines 2020, 11, x 4 of 9 starts to occur, which is regarded as the SET process. After reaching +3 V, the LRS maintains, exhibiting the memorizing behaviour. Then, by sweeping the bias to the negative direction, a transition from LRS to HRS occurs at around −2.7 V, which indicates the RESET process. Similar memristive characteristics and switching behaviours were also observed in devices with other stacking sequences such as types I and IV, with slightly different SET and RESET voltages. However, the ION/IOFF ratio was different depending on the device structure. In the tested device structures, the type II device (BE/A-C-B-D/TE) showed the highest ION/IOFF ratio value of ~45 (in average), while, the type I and type IV devices showed ION/IOFF ratio values of ~16 and ~17, respectively. The type III device (BE/A-D-C-B/TE), however, showed no switching behaviour and only insulating I-V characteristics were observed. Figure 2 also shows the I-V data which are repeated for five consecutive cycles. All the devices showed relatively stable I-V behaviour, while the type IV device showed a slight change in the current levels. As shown in Figure 2, during the SET and RESET processes, the current changes gradually, indicating the interface-type mechanism is dominant rather than the filament-type [31]. Concerning the variation of memristive behavior by the stacking sequence, we expect that the supply and migration of oxygen vacancies from the underneath TiOx sub-layers to the TE/top-TiOx interface are important [31]. In our results, the type I, II, and IV devices showed the memristive behaviour while the type III device showed insulating characteristics. In particular, in the cases of types I and II, the most oxygen-rich TiOx layer (D-TiOx) with the lowest concentration of oxygen vacancies is placed on the top-most layer, contacting the TE, while the relatively oxygen-deficient TiOx layers with larger concentrations of oxygen vacancies are placed underneath. Therefore, during the SET process, these relatively oxygen-deficient TiOx layers can efficiently supply the oxygen vacancies and can contribute to the interface-type resistive switching behaviour. Comparing the type I and II devices, the positions of B-and C-TiOx layers are different, where in type II, the second-most oxygen-deficient TiOx layer (B-TiOx) is placed beneath the top D-TiOx layer. Therefore, compared to type I device, more oxygen vacancies can be supplied to the top D-TiOx layer, allowing larger resistive variation during switching. In the cases of types III and IV, the most oxygen-rich D-TiOx layer is placed in the middle parts of the stacking. Therefore, the supply of oxygen vacancies towards the TE/top-TiOx interface can be relatively smaller compared to type I and II devices. Also, considering that the oxygen vacancies migrate toward the TE/top-TiOx interface during the SET process, the decrease of resistance in the D-TiOx layer can be higher in type IV device compared to type III.  The data retention characteristics of memristors are important for realizing highly stable memory devices as well as neuromorphic or synaptic devices. Figure 3a shows the data retention characteristics of type I, II, and IV devices. Here, the LRS and HRS states were programmed with pulsed biases of +3 V and −3 V, respectively (pulse widths of 100 ms). Also, the programmed states were read for an interval of 200 s up to 10,000 s, with a read voltage of +1 V. As displayed, devices with types I, II, and IV showed stable operation up to 10,000 s without a considerable change in the current levels of ON (I ON ) and OFF (I OFF ) states. Therefore, the I ON /I OFF ratios are maintained correspondingly as shown in Figure 3b. Among the tested devices, the type II memristors exhibited the highest I ON /I OFF ratio, while the type I memristor showed the lowest I ON /I OFF ratio. Nonetheless, the results indicate that regardless of the stacking sequence, the TiO x -based memristors showed relatively stable operations.
Micromachines 2020, 11, x 5 of 9 The data retention characteristics of memristors are important for realizing highly stable memory devices as well as neuromorphic or synaptic devices. Figure 3a shows the data retention characteristics of type I, II, and IV devices. Here, the LRS and HRS states were programmed with pulsed biases of +3 V and −3 V, respectively (pulse widths of 100 ms). Also, the programmed states were read for an interval of 200 s up to 10,000 s, with a read voltage of +1 V. As displayed, devices with types I, II, and IV showed stable operation up to 10,000 s without a considerable change in the current levels of ON (ION) and OFF (IOFF) states. Therefore, the ION/IOFF ratios are maintained correspondingly as shown in Figure 3b. Among the tested devices, the type II memristors exhibited the highest ION/IOFF ratio, while the type I memristor showed the lowest ION/IOFF ratio. Nonetheless, the results indicate that regardless of the stacking sequence, the TiOx-based memristors showed relatively stable operations. Symmetric synaptic weight update characteristics between long-term potentiation (LTP) and long-term depression (LTD) is a crucial factor in designing synaptic devices that directly affects learning accuracy of neuromorphic computing [32,33]. As shown in Figure 4, we measured the long-term plasticity of the type II device by applying a pulse train consisting of potentiation (VPOT), depression (VDEP) and read pulses. The VPOT was fixed at +2 V during the potentiation process while the VDEP was varied as −1 V and −2 V as shown in Figure 4a ("A" pulse train) and b ("B" pulse train), respectively. Each potentiation and depression was performed for 300 cycles each. The duration time of each pulse was 50 ms and the pulse interval was ~1.45 s (see the inset of Figure 4 showing the pulse train of the three cycles). As shown in Figure 4, bidirectional switching behaviour was obtained in which the channel conductance was set to various conducting states between 0.136 μS and 2.02 μS for both conductance rise and fall processes. The acquired channel conductance represents a non-volatile behaviour. Thus, increasing and decreasing the channel conductance can be regarded as synaptic LTP and LTD, respectively. In addition to the symmetry, the change in linear conductance between LTP and LTD processes is also an important factor [32,33]. So, we calculated the nonlinearity values between LTP and LTD processes through the potentiation and depression data. The nonlinearity factors (α) were extracted from the characteristic curves shown in Figure 4. We use the device behavioural model [34], where the conductance change is represented with the following equations [34]: Symmetric synaptic weight update characteristics between long-term potentiation (LTP) and long-term depression (LTD) is a crucial factor in designing synaptic devices that directly affects learning accuracy of neuromorphic computing [32,33]. As shown in Figure 4, we measured the long-term plasticity of the type II device by applying a pulse train consisting of potentiation (V POT ), depression (V DEP ) and read pulses. The V POT was fixed at +2 V during the potentiation process while the V DEP was varied as −1 V and −2 V as shown in Figure 4a ("A" pulse train) and b ("B" pulse train), respectively. Each potentiation and depression was performed for 300 cycles each. The duration time of each pulse was 50 ms and the pulse interval was~1.45 s (see the inset of Figure 4 showing the pulse train of the three cycles). As shown in Figure 4, bidirectional switching behaviour was obtained in which the channel conductance was set to various conducting states between 0.136 µS and 2.02 µS for both conductance rise and fall processes. The acquired channel conductance represents a non-volatile behaviour. Thus, increasing and decreasing the channel conductance can be regarded as synaptic LTP and LTD, respectively. In addition to the symmetry, the change in linear conductance between LTP and LTD processes is also an important factor [32,33]. So, we calculated the nonlinearity values between LTP and LTD processes through the potentiation and depression data. The nonlinearity factors (α) were extracted from the characteristic curves shown in Figure 4. We use the device behavioural model [34], where the conductance change is represented with the following equations [34]: Micromachines 2020, 11, 154 where, P is number of pulses, B is a fitting parameter, A is the nonlinearity of potentiation (α pot ) and depression (α dep ), G LTP and G LTD are the conductance for LTP and LTD, and G max , G min and P max are the experimental data which represent the maximum conductance, minimum conductance and the maximum number of pulses required to change the device states between minimum and maximum conductance. The non-linearity values for "A" pulse train were α pot = 2.4 and α dep = −4.6 for the potentiation and depression, respectively (Figure 4a). The non-linearity values for "B" pulse train were α pot = 2.2 and α dep = −8.74 (Figure 4b).
Micromachines 2020, 11, x 6 of 9 where, P is number of pulses, B is a fitting parameter, A is the nonlinearity of potentiation ( ) and depression ( ), GLTP and GLTD are the conductance for LTP and LTD, and Gmax, Gmin and Pmax are the experimental data which represent the maximum conductance, minimum conductance and the maximum number of pulses required to change the device states between minimum and maximum conductance. The non-linearity values for "A" pulse train were = 2.4 and = −4.6 for the potentiation and depression, respectively (Figure 4a). The non-linearity values for "B" pulse train were = 2.2 and = −8.74 (Figure 4b). Using the "NeuroSim+" platform, a supervised artificial neural network learning simulation of the MNIST handwritten recognition data set was performed by applying the non-linearity, conductance level, and the cycle-to-cycle variation of our device [34,35]. In the simulation, we used a three-layer neural network with 400 pre-neurons, 100 hidden neurons and 10 output neurons which correspond to 10 classes of digits (0-9). The detail of the three-layer multilayer perceptron network is shown in Figure 5a [36]. The TiOx multi-layer memristor acts as a memory element in a crossbar array and their memristor conductivity change was used as the weight update to run the back-propagation algorithm. Here, the crossbar is considered as part of a "neuron core" that executes vector-matrix multiplication (inference) and outer-product updates (learning) operations [37]. The sum of the input neuron signal vector and the first layer of the synaptic weight is transferred to the input vector of the hidden layer after activation and binarization [9]. For each epoch, 60,000 training data set were used for training, and accuracy was obtained using a 10,000 test data set.
By using algorithmic methods which was stochastic gradient descent (SGD) and adaptive moment estimation (ADAM) weight update, the accuracy of MNIST handwritten recognition was obtained. As shown in Figure 5b, in the case of the "A" pulse train condition (VPOT = +2 V, VDEP = −1 V), the accuracy was 82.99% when using the SGD, and 89.18% when using the ADAM. On the other hand, in the case of 'B' pulse train condition (VPOT = +2 V, VDEP = −2 V), the accuracy was 20.80% when using the SGD, and 59.52% when using the ADAM. Because the LTD non-linearity value of the "A" pulse train condition is smaller compared to that of the "B" pulse train condition, it is advantageous for learning process which resulted in a higher accuracy. The learning algorithm also plays an important role in accuracy. The SGD method calculates an error from the current weight, predicting a direction in which the weight should change, and learns at a predetermined Using the "NeuroSim+" platform, a supervised artificial neural network learning simulation of the MNIST handwritten recognition data set was performed by applying the non-linearity, conductance level, and the cycle-to-cycle variation of our device [34,35]. In the simulation, we used a three-layer neural network with 400 pre-neurons, 100 hidden neurons and 10 output neurons which correspond to 10 classes of digits (0-9). The detail of the three-layer multilayer perceptron network is shown in Figure 5a [36]. The TiO x multi-layer memristor acts as a memory element in a crossbar array and their memristor conductivity change was used as the weight update to run the back-propagation algorithm. Here, the crossbar is considered as part of a "neuron core" that executes vector-matrix multiplication (inference) and outer-product updates (learning) operations [37]. The sum of the input neuron signal vector and the first layer of the synaptic weight is transferred to the input vector of the hidden layer after activation and binarization [9]. For each epoch, 60,000 training data set were used for training, and accuracy was obtained using a 10,000 test data set.
By using algorithmic methods which was stochastic gradient descent (SGD) and adaptive moment estimation (ADAM) weight update, the accuracy of MNIST handwritten recognition was obtained. As shown in Figure 5b, in the case of the "A" pulse train condition (V POT = +2 V, V DEP = −1 V), the accuracy was 82.99% when using the SGD, and 89.18% when using the ADAM. On the other hand, in the case of 'B' pulse train condition (V POT = +2 V, V DEP = −2 V), the accuracy was 20.80% when using the SGD, and 59.52% when using the ADAM. Because the LTD non-linearity value of the "A" pulse train condition is smaller compared to that of the "B" pulse train condition, it is advantageous for learning process which resulted in a higher accuracy. The learning algorithm also plays an important role in accuracy. The SGD method calculates an error from the current weight, predicting a direction in which the weight should change, and learns at a predetermined step size. However, the ADAM method stored the exponential average of the slopes calculated so far to modulate the weight direction, and also stored the exponent average of the squared slopes to set the step size [38,39]. Thus, when using the ADAM method, there were more data to store, but accurate learning could be achieved using our device.
Micromachines 2020, 11, x 7 of 9 step size. However, the ADAM method stored the exponential average of the slopes calculated so far to modulate the weight direction, and also stored the exponent average of the squared slopes to set the step size [38,39]. Thus, when using the ADAM method, there were more data to store, but accurate learning could be achieved using our device.

Conclusions
In this paper, we demonstrated the multi-layer TiOx memristors for potential memory and neuromorphic applications. The four TiOx sub-layers with different oxygen vacancy content were fabricated by using different sputtering conditions by varying the gas flow rates of Ar and O2. Also, through the XPS analysis, the ratio of M-O-M and M-Ovac of oxygen peaks at different gas flow conditions was determined. By comparing the memristor characteristics according to the stacking sequence of the memristor device with a multi-layer structure, it was confirmed that the ION/IOFF ratio value is the highest as 45 in the type II stacking sequence structure. Also, by measuring the retention time in the on state and off state, it was confirmed that the current is maintained without degradation over 10,000 s. In addition, the long-term plasticity (LTP/LTD) was measured for the type II stacking sequence structure to obtain LTP and LTD non-linearity according to different depression voltage pulses. Two depression pulse voltage conditions and algorithm methods (SGD and ADAM) were used, and the highest accuracy of 89.18% was obtained when VDEP = −1 V and with the ADAM algorithm.

Conclusions
In this paper, we demonstrated the multi-layer TiO x memristors for potential memory and neuromorphic applications. The four TiO x sub-layers with different oxygen vacancy content were fabricated by using different sputtering conditions by varying the gas flow rates of Ar and O 2 . Also, through the XPS analysis, the ratio of M-O-M and M-O vac of oxygen peaks at different gas flow conditions was determined. By comparing the memristor characteristics according to the stacking sequence of the memristor device with a multi-layer structure, it was confirmed that the I ON /I OFF ratio value is the highest as 45 in the type II stacking sequence structure. Also, by measuring the retention time in the on state and off state, it was confirmed that the current is maintained without degradation over 10,000 s. In addition, the long-term plasticity (LTP/LTD) was measured for the type II stacking sequence structure to obtain LTP and LTD non-linearity according to different depression voltage pulses. Two depression pulse voltage conditions and algorithm methods (SGD and ADAM) were used, and the highest accuracy of 89.18% was obtained when V DEP = −1 V and with the ADAM algorithm.