Coexistence of short- and long-term memory in NbO_x-based memristor for a nonlinear reservoir computing system

Abstract

In this study, TiN/NbO_x/Pt memristor devices with short-term memory (STM) and self-rectifying characteristics are used for reservoir computing. The STM characteristics of the device are detected using direct current sweep and pulse transients. The self-rectifying characteristics of the device can be explained by the work function differences between the TiN and Pt electrodes. Furthermore, neural network simulations were conducted for pattern recognition accuracy when the conductance was used as the synaptic weight. The emulation of synaptic memory and forgetfulness by short-term memory effects are demonstrated using paired-pulse facilitation and excitatory postsynaptic potential. The efficient training reservoir computing consisted of all 16 states (4-bit) in the memristor device as a physical reservoir and the artificial neural network simulation as a read-out layer and yielded a pattern recognition accuracy of 92.34% for the modified National Institute of Standards and Technology dataset. Finally, it is found that STM and long-term memory in the device coexist by adjusting the intensity of pulse stimulation.

Graphical abstract

Keywords

memristor / resistive switching / neural network / reservoir computing

1 Introduction

In a traditional von Neumann system, a central processing unit (CPU) exchanges data from memory and performs calculations, which is unsuitable for processing large amounts of data. Following the development of artificial intelligence (AI) and the Internet of Things, the amount of information that needs to be processed is exponentially increasing. However, the von Neumann architecture is responsible for efficiency degradation owing to the serial processing structure and bottlenecks between the CPU and memory when processing large data, such as in generative AI applications [1, 2]. In addition, the existing complementary metal-oxide semiconductor technology has reached its limits [3, 4]. The hardware-based neuromorphic systems using memristor arrays can offer improved data processing by using the matrix multiplication method at low-power settings [5−7]. Furthermore, brain-inspired artificial neural network-based computing systems with parallel networks composed of artificial synapses and neurons, are becoming increasingly popular as alternatives [8, 9]. Neuromorphic devices have the advantages of low power consumption and fast data processing speed for complex tasks such as pattern recognition [10−12]. Memristors available as neuromorphic devices include phase-change random access memory [13], ferroelectric random access memory [14], magnetic random access memory [15], and resistive random access memory (RRAM) [16−18]. Among them, the RRAM has a simpler metal–insulator–metal structure with 4F² [19]. When a voltage bias is applied to the electrode of the RRAM cell, the state of the device can be repeatedly written and erased during high- and low-resistance transitions [20]. There are two typical types of RRAM device switching mechanisms, namely interfacial and filamentous [21, 22]. In the filament-switching type, conducting filaments (CFs) are formed in the insulator by the oxygen vacancies (V_o). Because oxygen vacancies diffuse owing to the voltage applied to the electrode, the device achieves a low-resistance state (LRS) when CFs are formed (through which the current can flow well). Conversely, when the CFs are ruptured with a bias voltage, the device becomes a high-resistance state (HRS). Conversely, for the interfacial type, the number of oxygen vacancies at the interface between the electrode and oxide determines the resistance state. Both resistance switching types are observed in various oxide-based switching layers, such as TaO_x, TiO_x, HfO_x, AlO_x, and NbO_x [23−27]. Among them, NbO_x has recently attracted attention as a switching material used to implement memristor devices [28, 29]. Kumar et al. [30] reported a micrometer-scale memristor with low-read-power (~nW) and high-endurance (>10⁶) responses. Furthermore, Kozen et al. [31] reported memristor-based neuromorphic circuits that can implement various memristor functions using NbO_x thin films. However, short-term memory (STM) attributes were rarely reported in NbO_x-based memristors [32]. Synaptic plasticity refers to biological synaptic properties that mimic the human brain to control the intensity of stimuli [32, 33]. Depending on the intensity of the stimulus and the magnitude of the frequency, short-term plasticity (STP) and long-term plasticity (LTP) can be achieved [34]. The STM of synaptic devices is in the spotlight owing to its efficient use of energy based on a mechanism that is similar to that used in biological synapses [35, 36].

In this study, we characterize the resistive switching of interface-type NbO_x-based memristors with self-rectifying and STM behaviors. The TiN/NbO_x/Pt device yields uniform resistive switching responses in repetitive switching cycles. Subsequently, multiple conductance values are obtained by pulse responses, and an analysis of the modified National Institute of Standards and Technology (MNIST) dataset is used for neuromorphic device tests. We used this device to adjust the synaptic weights that change in response to pulse strings expressing external stimuli. To demonstrate this, we used synaptic paradigms, including potentiation, depression, paired-pulse facilitation (PPF), and reservoir computing (RC) [37, 38]. This demonstrates the transition from STM to long-term memory (LTM) by controlling pulse numbers, pulse width, pulse amplitude, and spike rate [40].

2 Experiments

The TiN/NbO_x/Pt memristor device was fabricated as follows. First, a Pt electrode (thickness = 100 nm) was deposited on a SiO₂/Si substrate using direct current (DC) sputtering with Ar (20 sccm) at a pressure of 5 mTorr and a sputtering power of 120 W. Many previous studies have been conducted that the decay can be controlled when the thickness of the metal-oxide is above 200 nm [39]. Therefore, in order to process an RRAM in which STM and LTM coexist, a thickness of about 200 nm was necessary for metal-oxide [40, 41]. NbO_x (thickness = 200 nm) was then deposited using an Nb target. It was sputtered with Ar (20 sccm) and O₂ (3 sccm) at a sputtering pressure of 5 mTorr, and a radio frequency (RF) power of 250 W. Subsequently, a TiN top electrode layer (thickness = 100 nm) was deposited using reactive sputtering at room temperature. Finally, a lift-off process was performed to define an RRAM cell with the size of 100 μm × 100 μm. For the electrical measurements, DC I–V curves were obtained by using a Keithley 4200-SCS parameter analyzer, and the pulse transient was measured with a 4225-PMU. The voltage bias on the top electrode (TiN) was controlled while the bottom electrode (Pt) was grounded.

3 Results and discussion

Fig.1(a) shows a schematic of the TiN/NbO_x/Pt memristor cells. Fig.1(b) shows the cross-section transmission electron microscopy (TEM) image of the TiN/NbO_x/Pt cell. The thicknesses of TiN, NbO_x, and Pt were observed to be approximately 100 nm, 200 nm, and 100 nm, respectively. Fig.1(c) shows the energy dispersive spectroscopy (EDS) outcomes (generated by line scanning) which are used to analyze the atomic composition of each layer. Fig.1(d) and (e) show the X-ray photoelectron spectroscopy (XPS) spectra for Nb 3d and O 1s of NbO_x deposited with RF sputtering. According to previous research, the Nb 3d core-level spectrum depicted in Fig.1(d) features three distinct double lines [42]. The best fitting results were achieved by deconvoluting the spectra into three different oxidation states of Nb(Nb⁵⁺, Nb⁴⁺, and Nb³⁺). In addition, as illustrated in Fig.1(e), the O 1s doublet spectrum appears at binding energies of roughly 529.9 eV and 530.9 eV, corresponding to Nb−O bonds and oxygen vacancies (V_o¹⁺), which confirms the presence of an NbO_x switching layer. The TEM and EDS data support the presence of a stacked structure and elemental components of the TiN/NbO_x/Pt memristor device.

Fig.2(a) shows the I–V curves of a TiN/NbO_x/Pt device based on which a total of 100 cycles were swept without any compliance current. It was observed that sweeping up to −5 V gradually decreased the resistance; re-sweeping up to 4 V gradually increased the resistance. As there is no sudden change in current during this switching scheme, it can be classified as a typical interface switching scheme. In Fig.2(a), the half-log hysteresis loop is observed. The maximum current during the negative voltage sweep phase is approximately 10 mA, while the maximum current during the positive voltage sweep phase is 0.1 mA, which is approximately 100 times smaller. The memristor device has a progressive current change with self-rectifying behaviors. Fig.2(b) shows the STM effects visualized by examining repeated DC sweeps. It can be observed that the current is reduced by the read sweep after the set process. This indicates that the device has volatile properties over time. Fig.2(c) summarizes the endurance test outcomes of a TiN/NbO_x/Pt device (the test was performed by measuring 100 cycles at a read voltage of −1 V). The device shows stable switching characteristics without significant changes in the LRS and HRS for 100 cycles. Fig.2(d) presents the retention measurement results that represent the time-dependent conductance changes in the LRS and HRS of the device over 110 s. While the HRS of the device is constant, the LRS decreases gradually; thus, it can be observed that it converges to the conductance value of the HRS at 100 s. In general, when the retention time in the memory decreases within seconds, it can be defined as STM, thus proving that this device has the characteristic of STM with retention loss [43].

The model of the interface resistive switching in RRAM has been reported in several publications [44, 45]. Fig.3(a) shows a schematic summarizing the switching mechanism in the pristine state of the TiN/NbO_x/Pt memristor device. The switching layer NbO_x includes both oxygen ions (O²⁻) and oxygen vacancies (V_o) to maintain the neutrality of the device. Fig.3(b) shows a set process for resistive switching. When a negative voltage is applied to the top electrode, oxygen ions move away from the TiN interface, increasing the oxygen vacancies region. As a result, the conductivity of the device increases. Conversely, Fig.3(c) shows a reset process for resistive switching. When a positive voltage is applied to the top electrode, the oxygen ions move away from the Pt interface and move to the top of the NbO_x layer. As a result, the oxygen vacancy region is reduced, and the conductivity of the device is decreased for the transition to the HRS. This is also manifested by the fact that the positive current value was 100 times smaller than that induced when the negative voltage was applied. The asymmetric I–V curve with this rectifying effect can be explained with an energy band diagram in Fig.3(d) and (e). The work function of TiN is ~4.7 eV and the work function of Pt is ~5.65 eV; thus, the electron affinity (4.2 eV) of the NbO_x memristor is closer to that of TiN [46−48]. Therefore, electron injection into the interface is more advantageous at the TiN interface than that at Pt.

To apply a memristor device to a neuromorphic system, the conductance value of the device is required to have multiple state values. The multilevel conductance in the TiN/NbO_x/Pt device is obtained by applying identical pulse responses. It is found that the TiN/NbO_x/Pt device has volatile properties in retention measurements, but long-term plasticity can be achieved through pulse mode without long delays between successive pulses [49]. Therefore, we continuously applied large pulse amplitudes to the device for a short period, dividing the possible conductance range into several levels. Fig.4(a) presents a graph obtained by applying 50 potentiation and depression pulses. To obtain potentiation and depression, voltages equal to ‒5.5 V and 4 V were respectively applied to the device, and a read voltage of 1 V was used between each set and each reset pulse. For potentiation, the conductivity increased gradually as a function of the pulse number. In potentiation, the average conductance increased by 0.7 μS at a pulse interval of 10 μs. For depression, the conductance decreased significantly by the first pulse and then gradually decreased, thus resulting in an average conductance decrease of 0.58 μS. Figure S2 shows variable states by varying the voltage width interval and number of Potentiation. Fig.4(b) shows the reproducibility of the potentiation/depression obtained by applying the same pulse sequence 10 consecutive times. Moreover, a neural network system was developed to assess the potentiation and depression properties, aiming to determine its suitability for pattern recognition tasks [50, 51]. Fig.4(c) shows a deep-neural network framework used in conjunction with the MNIST database. The neural network consisted of 784 input neurons and 10 output neurons. In addition, the accuracy was increased by adding hidden neurons. In the input neurons, the sample image consisted of 784 pixels with a size of 28 × 28 pixels per sheet and provided 10 nodes corresponding to output values in the range of 0–9. By utilizing 50000 training images and 10 000 test images, the recognition accuracy was 94.25% as shown in Fig.4(d).

PPF is a phenomenon observed in biological synapses. It occurs when the response to a second pulse is greater than that of the first pulse, with both pulses being transmitted through synaptic membranes at intervals over a certain period [52, 53]. The properties of PPF are determined based on the STM effects. Fig.5(a) shows the voltage of the two pulses applied to obtain the PPF of the TiN/NbO_x/Pt memristor device. Figures S3(a)‒(f) illustrate the STM effects through the pairing of two identical pulses with varying intervals between the pre- and post pulses. The time intervals between the pulses applied to the device were set to 10 μs, 50 μs, 200 μs, 500 μs, 1 ms, 5 ms, 10 ms, 20 ms, 50 ms, and 100 ms. Figures S3(a)‒(f) show that as the interval between the two successive pulses increases, the increase in the current of the second pulse decreases. This indicates that the device loses memory during the interpulse time interval. The PPF index can be expressed using Eq. (1):

(1)\mathrm{P}\mathrm{P}\mathrm{F}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}={\displaystyle \frac{I_2-I_1}{I_1}}\times 100\left(\mathrm{\%}\right),

where I₁ represents the average current of the first pulse, and I₂ represents the average current of the second pulse. Fig.5(b) shows that an augmentation in the interval between voltage pulses correlates with a reduction in the PPF index. The red line in Fig.5(b) is fitted with a double-phase exponential function. This fitting curve is defined by the following equation:

(2)y=y_1+A_1\times {\mathrm{e}}^{-\left(\frac{x-x_0}{t_1}\right)}+A_2\times {\mathrm{e}}^{-\left(\frac{x-x_0}{t_2}\right)},

where x₀ and y₀ are 18.8 × 10⁻⁵ and 1.16, A₁ and A₂ are 9.8 and 5.05 (initial facilitation amplifiers), and t₁ and t₂ are 7.52 μs and 2.3 ms (characteristic relaxation timings), respectively.

Fig.5(c) shows the change in the current when intrinsic pulses with an amplitude of −4.5 V and a width of 10 ms at different pulse intervals (2 Hz, 5 Hz, 10 Hz, 20 Hz, 50 Hz, and 100 Hz) are used. When the pulse is repeated 10 times, the current increases regardless of the STM properties. Fig.5(c) shows the current difference between the first and 10th pulses by applying 10 pulses at each frequency. Fig.5(d) shows the values obtained by subtracting the first pulse current from the 10th pulse current (denoted as ∆I). From Fig.5(d), it can be inferred that the increase in the current as a function of the number of pulses significantly increases at pulse intervals shorter than <10 Hz compared with longer pulse interval frequencies. However, at frequencies >10 Hz, an observed saturation in the current increase indicates that beyond this frequency, the pulse interval does not significantly affect the element. The increase in pulse number and frequency resembles the process of transformation from STM to LTM through repeated learning in human synapses. Based on this, we demonstrate that this device achieved LTM through larger voltages and pulse numbers.

The RC system was then implemented using the TiN/NbO_x/Pt device, which effectively processes sequential data using a fixed, randomly connected network, as shown in Fig.6. Compared with the recurrent neural network approach, RC systems can reduce training costs because they only train the connection weights of the reading function between the repository and the output. As RC systems do not have memory, the readout function is simply based on a linear weight combination of reservoir neural node values. As the reservoir state can be determined by the current input within a certain period in the past, RC has STM. Therefore, the TiN/NbO_x/Pt memristor is suitable for demonstrating RC systems [54]. Fig.6(a) illustrates the concept of an RC system consisting of an input layer, a reservoir, and an output layer. The input layer u(t) accepts time-dependent inputs, and the output layer y(t) is mapped to a nonlinear, high-dimensional space through the reservoir. The reservoir plays a role in mapping the temporal input layer u(t) to the high-dimensional output by providing the dynamic data as much as possible. The advantage of a reservoir is that it has nonlinear characteristics and can map u(t) to a high dimension. The reservoir state is expressed as x(t) and uses a readout function for pattern analysis. Subsequently, the readout is learned, and the output layer y(t) is provided. Fig.6(b) shows a system configured to represent data by inputting 16 different states into five devices using 4 bits. Inputting a pulse corresponding to 4 bits into each system changes the state of the device and induces STM effects. This yields the desired character; additionally, during in period when no stimulation is applied, the memory of the previous pulse disappears, and the memory state returns to its initial value. Fig.6(c) shows a total of 16 states from 0000 to 1111 using 4 bits. If the reading current is less than 2.2 μA, the “0” state is expressed, and if it is greater than 4.7 μA, the state “1” can be implemented. However, the current difference between the two states (0 and 1) is large, thus indicating that it is an easy device to distinguish all 16 states. In addition, as the first pulse converges to almost 2 μA, the current state does not affect the previous state and returns directly to the initial state to enable accurate character or number implementation. Fig.6(d) shows the example of the number “2” represented using 5 × 4 pixels. Additionally, “1111”, “0001”, and “1000” are used to express the state “1” in black, and the state “0” in white. This was just one example, and the versatility of reservoir computing makes it applicable to a broad range of tasks where sequential data analysis and pattern recognition are essential. Fig.6(e) shows a plot of pattern accuracy as a function of the epoch number (maximum accuracy of 92.34% after 20 training processes). For this analysis, the MNIST dataset was used; during the process, the current value was scaled from 0 to 1 using the min–max normalization. The scaled current value enters the input layer, and is learned on a hidden layer consisting of 100 hidden neurons. The results are derived as output layers. Finally, the accuracy for each epoch can be obtained based on simulations. Fig.6(f) shows a plot of the confusion matrix derived from the pattern test inference results. The averages of 10 000 test images were used 10 times, and the confusion matrix was obtained after the classification of the MNIST test set by the large weights of the diagonal values [Fig.6(f)]. Additionally, the energy consumption statistics of the applied pulses were obtained and proved to be superior to other previously studied devices in terms of energy consumption. The energy consumption of the TiN/NbO_x/Pt memristor is shown in Fig. S5. Finally, we emulated the synaptic behaviors for the bio-inspired computing system. Fig.7 shows several methods used to quantify changes in the TiN/NbO_x/Pt memristor devices that manifest the synaptic behavior of long-term plasticity in STM synapses. As a fundamental component of synaptic plasticity, spike-rate-dependent plasticity (SRDP), is an attribute associated with the performances of learning and memory functions in neuromorphic systems by varying synaptic widths [55]. Fig.7(a) shows the transient current obtained by fixing the pulse interval at 100 μs and varying the pulse numbers (1, 2, 5, 10, 25, and 50). When observing the read current for 10 ms after the application of the pulse number, the read current is proportional to the pulse number. The large change in the read current according to the pulse number becomes clearer, as shown in Fig.7(b). The figure shows the change value of the read current as a function of the pulse number when the pulse width is 100 μs, 500 μs, 1 ms, and 5 ms. The difference in current after the application of the pulse number and the waiting period of 10 ms is referred to as the change value of the read current. When the interpulse spacing decreases, the change in the read current increases as the pulse number increases. Accordingly, the relationship between the pulse interval of the memristor and the stimulation speed with the change of current becomes clear. As the interpulse spacing decreases rapidly, the conductance according to the pulse number increases significantly. This shows a strong dependence of conductance on the spiking speed, as defined by SRDP, proving that it is an element suitable for synaptic properties. Changes in synaptic weights were observed according to the pulse number in the pulse amplitude under the same conditions. Fig.7(c) shows the read current value that appears after the reduction of the number of pulses by 10, 15, 20, 50, and 100 times at the pulse amplitude of ‒4.8 V. When stimuli are applied (up to 20), the change in the current due to pulse amplitude increases followed by rapid decreases of the read current, thus indicating the characteristics of STP. When 50 stimuli are applied, EPSC is increased to 120 μA, and a transition state that maintains a relatively higher level of current than that elicited by the previous 20 stimuli is observed. For excitations using 100 pulse numbers, the weight of the synapse is converted into the state of permanent LTP, as shown in Fig.7(d). In the model of Fig.7(d), the conversion from STM to LTM occurs through the rehearsal process, and the conversion probability increases as the rehearsal is repeated. The pulse amplitude changes to LTP when 100 pulses with an amplitude of ‒4.8 V are applied. An experiment was performed with the use of 100 pulses to apply voltages up to the highest voltage that the TiN/NbO_x/Pt device can withstand. As shown in Fig.7(e), the pulse amplitudes of ‒2 V, ‒5 V, ‒8 V, and ‒11 V were applied. Although a large pulse number was applied at ‒2 V, it still had the STP characteristics; however, when the pulse amplitudes were ≥‒5 V, the synaptic weight was transformed into LTP. It can be observed that as the pulse amplitude increased, stronger oxygen vacancies were formed at ‒8 V and ‒11 V. In the neural network simulation, we assessed the MNIST classification accuracy by distinguishing between the mixed STM + LTM properties and the weight range that represents pure LTM properties. As depicted in Fig.4(c), we configured a neural network with three hidden layers to analyze the MNIST classification performance in relation to retention loss. Weight changes due to retention loss were integrated into the simulation for each fully connected layer. To represent the retention loss features of the neural network, it is essential to use the learned weights to analyze the changes in accuracy with retention. Therefore, we implemented a neural network that relies on offline learning to verify accuracy in inference conditions. In order to include the retention loss in the simulation, we adjusted the retention applied for 20 s in Fig.7(e) to align with the scale of the simulation weight and applied the corresponding retention loss based on the nearest normalized programmed current for each weight. For example, with STM + LTM, the highest weight utilized in the simulation experienced a weight loss of 89.86% under the 20 s condition, whereas smaller weights resulted in a weight loss closer to 0%. Fig.7(f) illustrates the classification accuracy achieved with the MNIST dataset according to the programmed current range. An accuracy loss of 7.84% was obtained based on 97.7% under the 20 s holding condition under the STM + LTM condition. Constraining the weight to the LTM range leads to a significant reduction in accuracy loss, bringing it down to 2.1%. Therefore, when the stimulation was stronger, similar to biological memory, a relatively stronger set process was established, and the relaxation time was lengthened, which improved memory function. In addition, we proved that a device based on NbO_x achieved permanent memory (by using 100 pulses), or LTM (by using 200 pulses) [56]. Finally, we compare Pt/NiO/TaN with other reported Nb-based resistive memory in Tab.1.

4 Conclusions

We demonstrated that NbO_x-based memristor devices can exert biological synaptic functions using both STM and LTM. STM characteristics in TiN/NbO_x/Pt device were confirmed by the interval between successive pulses, pulse width, and pulse amplitude. Potentiation and depression characteristics were realized following the application of continuous pulses. Based on the results, it was shown that the device can be applied to neuromorphic systems. Moreover, we implemented an RC system capable of temporal learning using the STM characteristics of the device. We also demonstrated that it converted STM to LTM by increasing pulse stimulation or reducing the pulse repetition interval. The coexistence of volatile and nonvolatile memory characteristics of the device can achieve the conversion of synapses into LTM.

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