Neuromorphic auditory classification based on a single dynamical electrochemical memristor

Designing compact computing hardware and systems is highly desired for resource-restricted edge computing applications. Utilizing the rich dynamics in a physical device for computing is a unique approach in creating complex functionalities with miniaturized footprint. In this work, we developed a dynamical electrochemical memristor from a static memristor by replacing the gate material. The dynamical device possessed short-term fading dynamics and exhibited distinct frequency-dependent responses to varying input signals, enabling its use as a single device-based frequency classifier. Simulation showed that the device responses to different frequency components in a mixed-frequency signal were additive with nonlinear attenuation at higher frequency, providing a guideline in designing the system to process complex signals. We used a rate-coding scheme to convert real world auditory recordings into fixed amplitude spike trains to decouple amplitude-based information and frequency-based information and was able to demonstrate auditory classification of different animals. The work provides a new building block for temporal information processing.


Introduction
The initial step of our brain to understand the external world begins with sensory information processing.The underlying processing mechanisms of different organs have been used to create a variety of neural networks [1][2][3][4][5] that has led to great advancement of artificial intelligence (AI) in the last fifteen years.Despite huge success of deep learning and other artificial neural networks (ANNs), information processing efficiency of these computational-heavy models are still quite different from the brain.One unique property of the brain is the high degree of spatial and temporal network dynamics inside a biological neural network so that even a small neural circuit could provide complex network functionalities [6,7].Therefore, it is a highly rewarding research thrust to build compact neural networks that embrace intrinsic network dynamics rather than monotonically upscaling network sizes (figure 1).Following this inspiration, spiking neural networks (SNNs) have been developed by encoding and processing information in both spatial and temporal domains [7][8][9][10].Information processing inside SNNs changes from static, synchronized numerical computations into dynamical and event-driven process [11,12].In a more extreme case, in materia computing has been proposed and demonstrated which used intrinsic physical properties inside a bulk of material or an electronic device as a dynamic physical network [13].It presents a miniaturized and low power hardware design for efficient information processing.
Even though there are many material systems that worth exploring, developing a dynamical device from a well-established computing device could be more practical.In recent years, analog and neuromorphic computing based on memristors have been widely adopted as a key solution to next generation AI hardware [14][15][16][17][18].The memristors are a group of devices that use controlled ion migration to modulate device conductance.Static memristors based on two-terminal HfO 2 , Ta 2 O 5 devices have been used extensively in designing compute-in-memory hardware for acceleration of ANNs [19][20][21][22][23].By changing switching material to phase change NbO 2 or VO 2 , volatile dynamic switching of these devices was observed and led to the development of memristor-based artificial neurons [6,8,[24][25][26][27].Meanwhile, by inserting Ag clusters into the static memristors, dynamical switching was also achieved [28].Two-terminal or three-terminal devices displaying short-term dynamics have found application in constructing dynamic neural networks, such as reservoir computing systems, facilitating efficient processing of temporal signals with a power consumption ranging from micro to milliwatts [29][30][31][32][33][34][35][36].Nonetheless, without a quantitative characterization of the temporal dynamics in these devices, a readout layer is usually required [34], adding noticeable processing overheads in these applications.
In this work, we developed a three-terminal dynamical memristor from a static electrochemical memristor by replacing the gate material.The device demonstrated controllable frequency-dependent responses from its dynamical switching process and allowed us to develop a highly efficient frequency classifier based on only a single dynamic memristor, without the need of training or adding a readout layer.This design is more efficient than other frequency classification methods, such as filtering [37], supporting vector machine [38], and perceptron [39].The device showed distinct and repeatable responses to different spike-encoded pulse signals ranges from 1 Hz to 1 MHz with more prominent responses at lower frequency including audible frequency ranges.We created a behavior model to help us understand the working principle of the classification process which unveiled the additive relationship of the conductance change in responses to signals with multiple frequency components.The device was further used as a single device based auditory classifier and was able to faithfully identify recordings of different animals with high reproducibility.

Methods
The dynamical electrochemical memristor is developed from a static device that we previously reported [40].We used WO x as the channel material, yttria-stabilized-zirconia (YSZ) as the ion-conducting dielectric layer (figure 2(a)).The device fabrication process was largely adopted from the fabrication process of the static device [40] except a highly conducting TiO x (c-TiO x ) reservoir layer was added between the gate and electrolyte in the static memristor.The devices were fabricated atop a p-type silicon substrate with a 100 nm SiO 2 layer.Photolithography and liftoff processes were employed to define the patterns of all device layers.First, bottom source/drain electrodes (Ti (5 nm)/Pt (40 nm)/W (5 nm)) were deposited via DC sputtering.Subsequently, a 100 nm WO x channel was deposited using reactive sputtering under an Ar/O 2 ratio of 1:1.The channel oxides underwent thermal annealing through a rapid thermal processing at 400 • C to modulate crystallinity and initial conductivity.Following this, a 50 nm 8 wt.% YSZ layer was added as ion-conducting layer using RF sputtering under Argon ambient.Before depositing the gate electrode (Pt, 50 nm), 50 nm TiO x was deposited by reactively sputtered from a Ti target under an Ar/O 2 ratio of 10:1.
Electrical measurements of the three-terminal dynamical memristor were primarily carried out at ambient temperature using a semiconductor parameter analyzer (B1500A, Keysight) for DC measurement and current monitoring, while the pulse stimulations to the gate terminal were provided by a functional generator (33600A, Keysight).DC transfer characteristic curves were recorded by scanning the gate voltage while monitoring the source and drain current with a readout voltage of 0.1 V.For pulse stimulation experiments, the channel current was monitored under a constant voltage of 0.1 V while input signals with different frequencies were sent out by pulse generator.The short-term device responses were recorded for further analysis and classification.
To induce substantial device responses to auditory and other temporal signals, the signal strength should match the programming voltage of the dynamical memristor, which could be done at the analog front-end of the recording devices.The amplified auditory signal may be passed directly to the single device classifier (with peak amplitude 4 V).However, for real world signals such as auditory signal, different envelopes of the signal could also affect the device responses, additional encoding were used to decouple the frequency information from the amplitude information.We used a spike-encoding method based on rate coding scheme.Specifically, the input signal was sampled at 10 Hz and the number of zero crossings within each sampling window were counted and used to produce a spike train with spike rate proportional to the number of zero crossings.The rate-based spike encoding process was done in software but could also be achieved by using an artificial neuron device [8].The conductance change induced by the input signals was then directly used as tokens for different frequency-related classification tasks.

Frequency-dependent responses from the dynamical memristor
Figure 2(b) shows the typical transfer curve (Id-Vg, left panel) and the gate current (Ig-Vg, right panel) of the dynamic electrochemical memristor.The device demonstrated a substantial dynamic range coupled with a low gating current (less than 0.2 nA), enabling efficient low-power operations at the nanowatt scale.The channel conductance (G) modulation is attributed to the reversible drift/diffusion of oxygen ions between the reservoir and channel layers mediated by the electrolyte, manifesting in three stages (i, ii, iii in the left panel of figure 2(b)).Stages i and iii are dominated by the ion drift process driven by positive and negative gate voltage, respectively.In contrast, stage ii is characterized by ions' backward diffusion, contributing to the short-term or fading memory property of this device.
The accumulated conductance change over a fixed period of time is a combinational effect of conductance potentiation by the external stimulations and the intrinsic conductance relaxation due to short-term dynamics.The amount of potentiation can be roughly estimated by the total duration of the stimulations, which is an integration over time and insensitive to the frequency of the signal, while the amount of depression is dominated by the number of relaxation events (i.e.number of pulses) since the nonlinear relaxation occurs on every falling edge of the stimulation pulses, and thus is frequency dependent.Therefore, it is expected that higher frequency signals would show smaller accumulated responses due to more counts of relaxation events.To experimentally demonstrate the frequency-dependent conductance change, we applied consecutive squared pulses of varying frequency from 1 Hz to 1 MHz (3 V, 50% duty cycle and 10 s stimulation duration) at the gate terminal of the memristor (figure 2(c)), and the conductance changes of the channel were depicted in figure 2(d).A clear frequency-dependent responses were observed in the drain current of the dynamical memristor.We further extracted the values of relative conductance changes and shown in figure 2(e), which indicate a nonlinear relationship between the conductance change and signal frequencies, with prominent responses at lower frequencies between 1 Hz and 1 KHz.
To better understand the frequency-dependent behavior of the device, we performed spectral analysis and modeling based on experimental results, as shown in figure 3. Four testing pulse signals of 1 Hz, 10 Hz, 100 Hz and 1 KHz over 3 s period was displayed in figure 3(a), while their corresponding frequency spectra were shown in figure 3  component is thought to be additive but should be ratioed nonlinearly over frequency since high frequency signals would experience more relaxations.A frequency fading weight function of A (f ) = A 0 (f) × f −0.5 was applied to each frequency components in frequency domain, where A, A 0 and f represent weighted amplitude, FFT-derived amplitude, and the frequency, respectively.Figure 3(c) illustrates the weighted amplitude of frequency spectra, showcasing a diminishing contribution of various frequency components to the ultimate device response as the frequency increases.The summation of all weighted frequency components was calculated as the overall device response to different frequency signals (figure 3(d)), which shows the expected frequency-dependent responses to the input signals (figure 3(e)).The single parameter of weight function was fitted by experimental data and was sufficiently to accurately characterize the frequency-dependent responses of our experimental data (figure 3(f)).

Encoding schemes for temporal signals
The additive responses of multiple frequency components make it possible to handle real world signals with broadband frequency components.However, for most temporal signals such as auditory sound, the envelope of the signal also changes dynamically.Directly applying the signal as input stimulation to devices (figure 4(a)) will lead to unexpected output since the response may be dominated by the amplitude information.To decouple the frequency information from amplitude information, a spike-coding method was proposed to produce spike trains with fixed amplitudes (figure 4(b)).The frequency encoding process is further illustrated in figure 4(c).The sampling and conversion process, as described in method section, produces spike trains with dynamically changing spike rates.We investigated the device responses to varying animal voices in simulation.Recordings of Cicada, Sea Lion, Ape and Lion were chosen for the test with noticeable differences in their voice spectra (figure 4(d)).The device responses to direct signal input and spike-encoded input are shown in figures 4(e) and (f), respectively.Due to the interference of amplitude information, stimulation under direct input was not clear enough to distinguish between different animals, especially for sea lion, ape and lion samples.However, by employing our spike-encoding scheme, good classification was observed, offering a reliable encoding process for temporal signal processing using our dynamical memristors.

Auditory classification with dynamical memristors
To validate the proposed encoding and classification methods, we experimentally performed the animal sound classification task using our dynamical electrochemical memristors, as shown in figure 5. Input signals were spike-encoded to input pulse train with a fixed amplitude of 4 V, and applied to the gate terminal of the dynamical memristor, while the channel conductance after the completion of the pulse stimulation was recorded using a read voltage of 0.1 V (figure 5(a)).Four animal recordings were cascaded, encoded and applied to the device in series and the conductance change of the channel current was read out for classification, as shown in figure 5

Conclusion
In this work, we explored intrinsic switching dynamics in a three-terminal electrochemical memristors for computing.By re-designing the device's material system, we were able to convert a static memristor into a dynamic one with short-term memory and frequency-dependent characteristics.A highly compact frequency-dependent classifier based on a single device was built for identify auditory recordings of different animal species with high reproducibility.A rate-based spiking encoding scheme was developed which improved classification capability by isolating frequency information in the signal.The single device-based design provides a new approach for energy-efficient computing using intrinsic device physics.These findings open the door to the prospect of efficiently implementing spiking intelligent systems for resource-restricted applications.

Figure 1 .
Figure 1.Schematic illustration of efficient signal processing using dynamical systems.

Figure 2 .
Figure 2. Frequency-dependent fading memory with dynamical electrochemical memristors.(a) Schematic illustration of device structure, (b) device characteristics of transfer Id-Vg curves and gate current during gate voltage sweep, the sweep rate of gate voltage is 2 V s −1 , (c) schematic representation of voltage pulse applied to the gate for frequency-dependent response exploration, (d) and (e) frequency response of the device, illustrating reduced overall response as pulsing frequency increases.

Figure 3 .
Figure 3. Spectral analysis and proposed frequency classifying models.(a) Time-domain waveforms of input pulses at frequency of 1, 10, 100, and 1000 Hz, respectively, (b) corresponding frequency spectra of input signals by FFT, only positive components were shown, (c) the device response after applying an empirical nonlinear weight function, (d) summation of all weighted frequency components of each input signal.(e) Side-by-side comparison of device responses induced by input signals of different frequencies, showing frequency-dependent responses of the device, (f) the simulation results are in good agreement with the experimental data.
(b), obtained by fast Fourier transform (FFT).Only positive components were shown for better clarity.The spectrum of each signal composed of a base frequency and a series of low amplitude harmonic frequency components, due to the use of squared pulse shape.The contribution of each frequency

Figure 4 .
Figure 4. Rate coding-based encoding scheme of input signals.(a) Input signals are directly applied at the device, (b) input signals are encoded by rate-dependent spikes, (c) illustration of the spike-encoding process.The original waveform signals were sampled and converted to spike trains with varying frequency.(d) Typical frequency spectra of input signals by FFT for lion, ape, cicada and sea lion.(e) Device responses to auditory recordings of animals based on direct input scheme, (f) device responses to spike-encoded recordings, showing good classification capability.

Figure 5 .
Figure 5. Neuromorphic auditory classification with dynamical electrochemical memristors.(a) Schematic illustration of the animal classification using a single dynamical memristor, (b) device responses to various animal voices, showcasing its capability to distinguish between different species with distinct spectral features, (c) evolution of the dynamical memristor under stimulations from different spike-encoded animal recordings, (d) statistical data of the classification results, showing highly reproducible classification capability.
(b).The zoomed-in view of device responses for each animal was shown in figure5(c) and depicts short-term evolution of conductance in response to different input signals.Devices responses from different animals were clearly separated, showing faithful frequency-dependent classification capability.The reproducibility of the classification process was also studied with statistical results shown in figure5(d).We prepared around 20 recordings of each animal and clear boundaries were shown for devices responses to different animal recordings.