The performance of neuromorphic computing (NC) in executing data-intensive artificial intelligence tasks relies on hardware network structure and information processing behavior mimicking neural networks in the human brain. The functionalities of synapses and neurons, the key components in neural networks, have been widely pursued in memristor systems. Nevertheless, the realization of neuronal functionalities in a single memristor remains challenging. By theoretical modeling, here we propose asymmetric ferroelectric tunneling junction (AFTJ) as a potential platform to realize neuronal functionalities. The volatility, a necessary property for a memristor to implement a neuron device, is enhanced by the co-effect of polarization asymmetry and Joule heating. The simulated polarization reversal dynamics of the AFTJ memristor under trains of electric pulses reproduces the leaky integrate-and-fire functionality of spiking neurons. Interestingly, multiple spiking behaviors are found by modulating the pulse width and interval of trains of electric pulses, which has not yet been reported in ferroelectric neuron. The influences of several key factors on the neuronal functionalities of AFTJ are further discussed. Our study provides a novel design scheme for ferroelectric neuron devices and inspires further explorations of ferroelectric devices in neuromorphic computing.

Topics
Ferroelectric devices, Tunnel junctions, Joule heating, Memristor, Information technology, Neuromorphic engineering, Artificial intelligence, Artificial neural networks, Ferroelectric materials, Thin films

Neuromorphic computing (NC) is more efficient than von Neumann computing architecture in performing data-intensive artificial intelligence tasks.1 It aims to construct the neural network mimicking the information processing behavior of the human brain on the hardware level, with a primary goal being to develop artificial neurons and synapses. Many synaptic functionalities have been realized via a single nonvolatile memristor.1–3 In contrast, the construction of single-component artificial neurons remains challenging. Early CMOS-based neuron requires dozens of transistors and capacitors, with poor scalability.4 A scalable artificial neuron prototype based on the capacitor and the memristor was proposed in 2012.5 Since then, the capacitor–memristor combination has attracted extensive interest in developing artificial neurons.6–8 Despite this strategy being simple, capacitor downscaling is a long-term technological difficulty for integrated circuits and a foreseeable problem for large-scale electronic neural networks.9 

Only a few single-component artificial neurons based on memristors such as redox memristor,10 Mott memristor,11 and phase change memristor12 have been reported. For their excellent nonvolatility and multistates, ferroelectric devices such as ferroelectric tunneling junction (FTJ), diode, and field effect transistor (FeFET) have been widely used in artificial synapses.13 Interestingly, very recent studies showed that FeFETs have potential in artificial neuron devices. In 2018, Mulaosmanovic et al. proposed that a FeFET can be used to realize artificial neuron.14 However, they pointed out that the disability of self-reset should be solved by enhancing the volatile feature of FeFET for further device optimization. To extend its applications in artificial neuron, a leaky-FeFET with self-reset, where polarization degradation is assisted by the depolarization field, was then proposed.15 A recent study reported an anti-FeFET neuron where polarization degradation is achieved by ferroelectric to anti-ferroelectric transition.16 In addition, the instability of the ferroelectric domain wall can also trigger polarization degradation in FeFET neurons.17 Despite the self-reset ability in the reported ferroelectric neurons, an additional waiting period (>μs) is necessary for self-reset operation. This feature is different from biological neurons and adverse to high-speed application. Mechanisms that provide fast polarization degradation are hence desired in ferroelectric memristor for artificial neuron application.

Here, we propose a novel neuron device prototype based on the asymmetric ferroelectric tunneling junction (AFTJ). To realize the neuron functions, the AFTJ device is designed to be a second-order memristor,18 which is described by two state variables, polarization and temperature. Moreover, the self-reset ability is realized by polarization degradation due to asymmetric polarization stability.19 The dynamics of temperature change depends on the thermal environments of the device and its Joule heating power upon application of electric pulses, like those high order memristors reported previously.18 Our simulations show that ferroelectric polarization reversal dynamics of the proposed AFTJ under trains of electric pulses can mimic the membrane potential of biological neurons. Interestingly, multiple neuron dynamic behaviors are found in AFTJ, which has not been reported in ferroelectric and anti-ferroelectric neurons. The effect of the polarization reversal mechanism on neuronal dynamics is also discussed.

Neurons are mainly responsible for signal transducing and computing operations in the brain. The key neuronal dynamics of biological neurons is the action potential. Neuron accumulates input stimuli, and its cell membrane potential increases gradually from the initial level (resting potential). The increased cell membrane potential tends to relax to the resting potential spontaneously during the intervals of input stimuli or if there are no more stimuli. Once the membrane potential exceeds a certain level (or threshold), neuron fires an output spike accompanied by instantaneous recovery of the membrane potential to the resting potential. Several models have been proposed for neuron simulation to emulate the membrane potential of biological neurons in electronic circuits.20,21 In hardware realization, the LIF model is preferable due to its simplicity and capability to describe the basic functionalities of neurons.22 The function of LIF neurons in a neural network is shown in Fig. S1 in the supplementary material. In the LIF model, a neuron can be equivalent to a compact circuit consisting of capacitor (C), parallel resistor (R), and threshold switch (TS, typically implemented by volatile memristor) as shown in Fig. 1(a). Under the application of electric pulses, the voltage dynamics of this compact circuit is similar to the membrane potential of biological neurons. When the voltage of the circuit is smaller than the threshold voltage (i.e., V < Vth), the threshold switch remains open, and the circuit voltage gradually increases by capacitor charging under electric pulse inputs. Also, the capacitor could discharge slowly during the interval of electric pulse inputs via the parallel resistor. The threshold switch is closed once V > Vth. Then, fast discharging of the capacitor occurs, and the circuit voltage is reset to the initial level, forming an electric spike. To utilize the conductance state of memristors to emulate the cell membrane potential of neurons, the gradual accumulation and spontaneous recovery features of neurons require the resistive switching of memristors to possess an electric-triggered transition from being slightly nonvolatile to volatile. Such a transition is not universal in memristors and hence the advancements of single-component artificial neurons are hindered.

FIG. 1.
(a) Membrane potential of neuron simulated by a compact circuit consisting of capacitor (C), resistor (R), and threshold switch (TS) based on the leaky integrate-and-fire model. (b) Operation principle of neuron device based on the asymmetric ferroelectric tunneling junction.
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(a) Membrane potential of neuron simulated by a compact circuit consisting of capacitor (C), resistor (R), and threshold switch (TS) based on the leaky integrate-and-fire model. (b) Operation principle of neuron device based on the asymmetric ferroelectric tunneling junction.

FIG. 1.
(a) Membrane potential of neuron simulated by a compact circuit consisting of capacitor (C), resistor (R), and threshold switch (TS) based on the leaky integrate-and-fire model. (b) Operation principle of neuron device based on the asymmetric ferroelectric tunneling junction.
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(a) Membrane potential of neuron simulated by a compact circuit consisting of capacitor (C), resistor (R), and threshold switch (TS) based on the leaky integrate-and-fire model. (b) Operation principle of neuron device based on the asymmetric ferroelectric tunneling junction.

Close modal

Based on the above physical picture, we propose an operation principle of AFTJ to implement an artificial neuron as schematically shown in Fig. 1(b). The membrane potential of biological neuron is simulated by ferroelectric polarization reversal dynamics of AFTJ. With a built-in electric field pointing to the bottom electrode of this asymmetric structure, the free energy landscape of ferroelectrics (the ferroelectric polarization is assumed in the out-of-plane direction) is intrinsically asymmetric and the ferroelectric polarization is preferably oriented parallel to the built-in electric field (i.e., downward).23 In addition, AFTJ is designed to have high (low) conductance with upward (downward) polarization. Electric pulses switch ferroelectric polarization upward, but the upward polarization could evolve into downward polarization spontaneously due to the built-in electric field during electric pulse intervals. At the same time, the high conductance state of AFTJ provides significant Joule heating for rising device temperature. Phenomenologically, the rate of ferroelectric polarization reversal is dominated by an energy barrier,24 which is vanished by rising temperature. Therefore, fast polarization reversal driven by the built-in electric field occurs once device temperature exceeds a threshold, i.e., T > Tth. In other words, the volatile feature of a ferroelectric device is electrically tunable. Under trains of electric pulse inputs, the ferroelectric polarization reversal dynamics of AFTJ is expected to reproduce similar LIF characteristics mimicking the membrane potential of biological neurons. Due to the fast polarization reversal, an additional waiting period is not necessary for self-reset in AFTJ. This is more consistent with biological neuronal dynamics compared to recent advanced (anti-)ferroelectric neuron prototypes.15–17 

Polarization reversal dynamics is described by the nucleation-limited-switching (NLS) model. Recent studies show that the NLS model can well capture the experimental results of polarization reversal dynamics in ferroelectric thin films.25 In the NLS model, the thin film system is considered an ensemble of elementary regions. Polarization reversal dynamics is independent for every elementary region. For individual elementary regions, the local polarization reversal dynamics follows a stretched exponential law,
(1)
where s is the cumulative fractional area of reversed polarization initiated by the external electric field. Index β is related to the dimensionality of ferroelectric domain growth and is equal to 2 for thin film.26  τ is the switching time of elementary region. Note that Eq. (1) is only suitable for one-shot polarization reversal dynamics, i.e., the applied electric field is constant and τ is time independent. For the case that τ is time-dependent or/and the applied electric field is alternative, we adopt the differential form of Eq. (1) to describe the polarization reversal dynamics of an elementary region in a tiny time increment Δt at arbitrary time t,27 
(2)
and
(3)
For the whole thin film system, the total fractional area of reversed polarization is the summation of the elementary regions,
(4)
where F(logτ) is the distribution function for logarithmic local switching time in thin films. We assume that the switching time of elementary regions follows the Lorentzian distribution,
(5)
where ω and logτmean are the halfwidth at half-maximum and the characteristic switching time of Lorentzian distribution. τmean follows Merz's law to an electric field as
(6)
where Ea, Ed, and τ0 are the activation electric field, the effective electric field driving polarization reversal, and the limit of switching time at an infinite electric field, respectively. Activation field Ea is proportional to U/kBT, where U is the energy barrier for polarization reversal.24,26
The ferroelectric polarization state of AFTJ is described by the phenomenological Landau-type theory. The total free energy of the ferroelectric thin film is given by
(7)
where fbulk, felas, and felec are the densities of bulk Landau free energy, elastic energy, and electrostatic energy, respectively. Mathematical formulas for these energy densities can be found in our previous work.28 Based on Eq. (7), the ferroelectric polarization P, the energy barrier U for polarization reversal, the free energy landscape F of AFTJ, and their temperature dependence can be calculated.
The current density of AFTJ under applied bias Va contains tunneling and thermionic injection mechanisms as J = JDT + JTI. Here, Va is assumed to be applied to the bottom electrode. For the tunneling mechanism,29 
(8)
where D(Ez) is the probability that an electron can tunnel through the potential barrier. Here, the potential barrier is along the z-direction, i.e., the out-of-plane direction of AFTJ. EF and Ez are Fermi level of top electrode and energy component of the incident electron in the z-direction, respectively. Using WKB approximation, D(Ez) is given by
(9)
where d is the thickness of the ferroelectric layer and φ(z) is the potential barrier profile. Considering a trapezoidal barrier profile across the ferroelectric layer and finite screening length in electrodes, φ(z) is given by30 
(10)
(11)
(12)
where Φ1(2) is the difference between the work function of the bottom (top) electrode and the electron affinity of ferroelectrics. VFM1(2) is the potential change at the interface between the ferroelectric thin film and the bottom (top) electrode.
To decide VFM1(2), we assume that potential profiles within the bottom and top electrodes follow Thomas–Fermi screening,
(13)
(14)
(15)
(16)
where V1(2) is the potential profile within bottom (top) electrodes. Here, zero potential is considered in the bottom electrode. l1(2) and ɛ1(2) are the finite screening length and dielectric constant of bottom and top electrodes, respectively. Vbi is the built-in potential across the AFTJ. ρs is the screening charge density, and it is positive when positive screening charge is accumulated in bottom electrode. ρs is given by
(17)
(18)
(19)
where ɛF and EFE are the dielectric constant and electric field of the ferroelectric layer. Finally, potential barriers at the film–electrode interfaces are given by
(20)
(21)
where l1(2) and ɛ1(2) are the finite screening length and dielectric constant of bottom and top electrodes, respectively. ɛF is the dielectric constant of ferroelectric layer.
For thermionic injection mechanism,31 
(22)
where φmax is the maximum barrier height of the ferroelectric layer, A** is effective Richardson's constant, and ɛifl is the permittivity of the ferroelectric responsible for image force lowering. Tdev is the device temperature.
For the sake of simplifying, the device temperature dynamics is modeled by uniform Joule heating and heat dissipation,32 
(23)
(24)
where C and ρ are the specific heat capacity and density of ferroelectrics. k is the heat dissipation coefficient of the device. Va,eff is the effective applied voltage in ferroelectric thin films. Tamb is the ambient temperature. Total current density Jtotal is calculated by the parallel conduction model,33 
(25)
where J↓ and J↑ are the current density of regions with downward and upward polarization, respectively. To calculate J↑ and J↓, barrier profiles across ferroelectric layer with +P and −P states are obtained first according to Eqs. (10), (20), and (21), respectively. Then, J↑ and J↓ are determined by Eqs. (8), (9), and (22).

Polarization reversal and device temperature evolution dynamics are simulated by mathematically solving Eqs. (2) and (23) based on the finite difference method. Parameters used in calculations are summarized in Tables S1 and S2 in the supplementary material.

We consider an AFTJ with a BTO thin film with asymmetric polarization bistability. Due to dissimilar electrodes and asymmetric polar interfaces in AFTJ,34,35 a built-in potential is induced across the ferroelectric layer, resulting in asymmetric polarization bistability. For simplicity, we assume a built-in potential of ∼0.45 eV pointing to the bottom electrode according to the work function difference between the top and bottom electrodes (a discussion on the effect of built-in potential will be shown later). The BTO thin film is subjected to a compressive misfit strain and develops a tetragonal phase with two out-of-plane polarization states (i.e., downward and upward polarization states). The schematic free energy landscape and thermodynamic stability of the two polarization states are shown by the misfit strain-temperature phase diagram in Fig. S2 in the supplementary material. In the blue region of the phase diagram, the free energy landscape of AFTJ is an asymmetric double-well and the upward polarization state is metastable due to the downward built-in electric field. The AFTJ can work as a memristor with a slightly nonvolatile feature in this regime due to the finite energy barrier separating the two polarization states. More importantly, rising temperature makes the upward polarization state thermodynamically unstable, which leads to the transition of AFTJ into volatile mode. This feature is key to the achievement of LIF functionality in AFTJ. From the phase diagram, we know that larger compressive strain increases the transition temperature. To ensure nonvolatile memory of AFTJ at room temperature, a compressive strain of −3.8% is set in the following calculations. Experimentally, it can be achieved by depositing BTO thin film epitaxially on substrates like NdGaO3.36,37

We first study the polarization reversal and device temperature evolution dynamics of AFTJ under 0.9 V single electric pulse stimulation with different widths (i.e., 56, 72, and 88 μs) as shown in Fig. 2(a). The electric pulse is applied to ATFJ at t = 0 s. We simulate two polarization reversal processes, i.e., forward switching (from downward to upward) and backward switching (from upward to downward) initiated by the applied electric field (during the pulse application) and the built-in electric field (after the pulse application), respectively. We calculate free energy landscapes with and without applied voltage as shown in Fig. S3(a) in the supplementary material. Energy barriers for forward and backward switching are the same. It means that forward and backward switching have the same characteristic switching time. The temperature-dependent normalized energy barrier (U/U300K) and the characteristic switching time (τmean) and distribution of switching time are shown in Figs. S3(b)–S3(d) in the supplementary material. One can see that the energy barrier for polarization switching decreases linearly with increased temperature. The characteristic switching time τmean decreases over several decades as device temperature increases, consistent with the theoretical study reported by Vopsaroiu et al.38 It is attributed to the lower thermodynamic barrier for reversed domain nucleation with increased temperature and, thus, the smaller activation field.26 Note that we have assumed a sharp Lorentzian distribution of switching time, which represents a high quality of the epitaxial BTO thin films. Under the applied electric pulse, the initial downward polarization is partially or completely switched to upward polarization. At the same time, the application of electric pulse can generate significant Joule heating to raise the device temperature due to the electroresistance (ER) effect associated with the polarization reversal. As shown in Fig. S4 in the supplementary material, the potential barrier of the ferroelectric layer is lower when downward polarization is switched to upward polarization, leading to an enhancement of current density. The ER effect, defined by (J↑ − J↓)/J↓,39–41 is in turn enhanced by the increased device temperature. It is found that the “memory” of ferroelectric polarization reversal is dependent on the electric pulse width. For short electric pulse (56 or 72 μs), backward switching is slow and the switched area Sup with upward polarization partially retains after the electric pulse is removed, showing a slightly nonvolatile feature. However, in the case of applying an electric pulse of 88 μs, backward switching becomes instantaneous after pulse application, and no remnant upward polarization is retained. Polarization reversal of AFTJ has a strong volatile feature in this case. The rising device temperature is the driving force for such a fast backward switching. It is found that the device temperature rises over 350 K within 88 μs and τmean reduces by two orders of magnitude [Fig. S3(c) in the supplementary material]. Detailed polarization reversal and device temperature dynamics as a function of applied pulse width are shown in Fig. S5 in the supplementary material. Note that the relationship between the remnant proportion of upward polarization and pulse width is not monotonous. For evaluating the “memory” feature of AFTJ, we define a factor r,
(26)
where Sup,max and ΔSup are the maximum fractional area of upward polarization produced by the electric pulse and the change of Sup at the time 50 μs after the electric pulse is removed, respectively. r = 0 represents no remnant upward polarization. In Figs. 2(b) and 2(c), we depict the calculated r and the maximum device temperature as a function of pulse width. It is obvious that rising device temperature weakens the “memory” of AFTJ. The volatile feature of AFTJ is characterized by a criterion of r < 2%, corresponding to the shadow region in Fig. 2(b). A threshold of Tth ≈ 340 K triggering the volatile feature of AFTJ can be determined. Such a Tth is higher than our expectation, since according to the results in Fig. S3(c) in the supplementary material, τmean is less than 10 μs at 330 K, which seems to be short enough for complete backward switching. To better understand this, we investigate the temperature-dependent backward switching and heat dissipation of AFTJ in Fig. S6 in the supplementary material. Here, the AFTJ is assumed to be in full upward polarization initially. Solid (dashed) lines represent backward switching with (without) heat dissipation in Fig. S6(a) in the supplementary material. Indeed, backward switching becomes faster when the device temperature increases. Without heat dissipation, it can finish within 50 μs when the device temperature is higher than 330 K [see the third dashed line counted from right in Fig. S6(a) in the supplementary material]. Taking account of heat dissipation, backward switching is slowed down significantly for temperatures below 340 K [as shown by the deviation of the solid lines from the dashed lines in Fig. S6(a) in the supplementary material]. In our simulations, heat dissipation mainly occurs in time between 5 × 10−6 and 10−4 s as shown in Fig. S6(b) in the supplementary material. A device temperature over 340 K ensures that backward switching finishes mostly before heat dissipation. Therefore, pulse width-modulated “memory” of polarization reversal is governed by the device temperature dynamics dependent on the Joule heating generated during the application of electric pulse and subsequent heat dissipation.
FIG. 2.
Volatile characteristic of asymmetric ferroelectric tunneling junction. (a) Simulated pulse width-dependent polarization reversal and device temperature dynamics. (b) Remnant fractional area of upward polarization at 50 μs after electric pulse is removed and (c) max device temperature as a function of pulse width.
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Volatile characteristic of asymmetric ferroelectric tunneling junction. (a) Simulated pulse width-dependent polarization reversal and device temperature dynamics. (b) Remnant fractional area of upward polarization at 50 μs after electric pulse is removed and (c) max device temperature as a function of pulse width.

FIG. 2.
Volatile characteristic of asymmetric ferroelectric tunneling junction. (a) Simulated pulse width-dependent polarization reversal and device temperature dynamics. (b) Remnant fractional area of upward polarization at 50 μs after electric pulse is removed and (c) max device temperature as a function of pulse width.
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Volatile characteristic of asymmetric ferroelectric tunneling junction. (a) Simulated pulse width-dependent polarization reversal and device temperature dynamics. (b) Remnant fractional area of upward polarization at 50 μs after electric pulse is removed and (c) max device temperature as a function of pulse width.

Close modal

The tunable volatile feature of polarization reversal in AFTJ makes it possible to achieve LIF functionality. Simulated polarization reversal dynamics under trains of short electric pulses in Fig. 3(a) verifies typical LIF functionality. The process is schematically illustrated in Fig. 3(b). The switched area Sup is gradually increased by applying electric pulses with a leaky feature during pulse intervals. Also, the average device temperature is gradually increased. It is due to the accumulated area of upward polarization and larger Joule heating produced by subsequent electric pulses. After integrating several electric pulses, a spike of polarization reversal is formed, and the new regular period of spike event starts. Obviously, the self-reset of AFTJ does not need an additional waiting period, owing to the capability of fast backward switching driven by the built-in electric field. Corresponding dynamics of current density shows the same spike feature due to its coupling with ferroelectric polarization (Fig. S7 in the supplementary material). Note also that the integrated number Nfire for subsequent regular spiking events is less than the first spiking event due to the residual heat of the device. Nfire of electric pulses for regular spiking behavior is equal to 3. It is reported that Nfire is related to pulse duration ton and interval toff.10,22 In AFTJ, the applied voltage can drive polarization reversal and produce Joule heating. With longer ton, both polarization reversal and Joule heating are enhanced. This effect can accelerate device spiking. In turn, longer toff can enhance backward switching of ferroelectric polarization and heat dissipation. Therefore, Nfire can be modulated by both ton and toff. We demonstrate the modulation of toff on Nfire by setting a constant ton as shown in Fig. S8 in the supplementary material. Nfire increases with increased toff because it leads to larger heat dissipation and more degradation of upward polarization. The device temperature averaged in a pulse period is lower for longer pulse interval, and thus the average polarization switching time is larger. It means that more electric pulses are needed to be integrated for spiking.

FIG. 3.
Leaky integrate-and-fire neuronal functionality of asymmetric ferroelectric tunnel junction. (a) Simulated polarization reversal and device temperature dynamics under trains of electric pulses, showing regular spiking. (b) Schematic evolution of polarization reversal under trains of electric pulses. (c) Additional spiking modes of neuronal functionality modulated by electric pulse width and interval: (i) fast mode, (ii) chattering mode, and (iii) irregular mode. (d) Diagram of spiking mode modulated by pulse width and interval.
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Leaky integrate-and-fire neuronal functionality of asymmetric ferroelectric tunnel junction. (a) Simulated polarization reversal and device temperature dynamics under trains of electric pulses, showing regular spiking. (b) Schematic evolution of polarization reversal under trains of electric pulses. (c) Additional spiking modes of neuronal functionality modulated by electric pulse width and interval: (i) fast mode, (ii) chattering mode, and (iii) irregular mode. (d) Diagram of spiking mode modulated by pulse width and interval.

FIG. 3.
Leaky integrate-and-fire neuronal functionality of asymmetric ferroelectric tunnel junction. (a) Simulated polarization reversal and device temperature dynamics under trains of electric pulses, showing regular spiking. (b) Schematic evolution of polarization reversal under trains of electric pulses. (c) Additional spiking modes of neuronal functionality modulated by electric pulse width and interval: (i) fast mode, (ii) chattering mode, and (iii) irregular mode. (d) Diagram of spiking mode modulated by pulse width and interval.
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Leaky integrate-and-fire neuronal functionality of asymmetric ferroelectric tunnel junction. (a) Simulated polarization reversal and device temperature dynamics under trains of electric pulses, showing regular spiking. (b) Schematic evolution of polarization reversal under trains of electric pulses. (c) Additional spiking modes of neuronal functionality modulated by electric pulse width and interval: (i) fast mode, (ii) chattering mode, and (iii) irregular mode. (d) Diagram of spiking mode modulated by pulse width and interval.

Close modal

In addition to regular spiking mode, a variety of spiking modes including fast mode, chattering mode, and irregular mode can be obtained by varying the ton and toff of electric pulse trains as shown in Fig. 3(c). In Fig. 3(d), spiking modes at different values of ton and toff are recorded. With small toff, the device works in fast mode with Nfire equal to one. In this case, polarization reversal and device temperature evolution dynamics reach dynamic equilibrium with an oscillation frequency equal to that of the applied electric pulse. As toff increases, the transition from fast mode to chattering mode occurs first. Heat dissipation is insufficient in fast and chattering mode, leading to high device temperature and small switching time of polarization reversal. Thus, spiking events are consecutive. With further increase of toff, spiking mode alternates between irregular and regular modes.

We have shown theoretically that the polarization reversal of AFTJ under trains of electric pulses can mimic the LIF functionality of neurons. In the following, we would like to discuss the effect of polarization reversal mechanism on the neuronal functionality of AFTJ. Figure 4(a) depicts the constant-field-induced polarization reversal dynamics, which obeys the NLS model with different halfwidth at half-maximum of Lorentzian distribution ω and Kolmogorov-Avrami-Ishibashi (KAI) model. When ω is 0.01, the NLS model is close to the KAI model, which represents an ideally homogeneous polarization reversal and is characterized by a constant switching time. Therefore, ω reflects the inhomogeneity of polarization reversal in ferroelectrics. For the NLS model with ω = 0.01 and 0.5, the polarization reversal dynamics of AFTJ under trains of electric pulses are shown in Figs. 4(b) and 4(c), respectively. For ω = 0.01, the LIF functionality can be reproduced perfectly. However, it deviates LIF functionality when ω = 0.5 regardless of various configurations of ton and toff. The upward polarization cannot be switched back completely by the built-in electric field after spiking although the device temperature rises over 360 K. This is due to the nature of gentle polarization reversal dynamics with a wide distribution of switching time. Unlike ferroelectric synapse devices whose polarization reversal dynamics follows the NLS model with a wide distribution of switching time,42,43 we suggest that a more centralized distribution of switching time (i.e., homogeneous polarization reversal) is beneficial to the ferroelectric neuron devices. Recent studies suggest that a wide distribution of switching time mainly results from dipole defects in ferroelectrics.26,44,45 Therefore, high-quality ferroelectric thin film is required for neuron devices. In addition, Mulaosmanovic et al. reported abrupt polarization reversal in a sub-microscale ferroelectric device and proposed its application in neuron devices.46 Less grains are contained in a single device with scaled device size, which possibly captures a more uniform distribution of switching time.

FIG. 4.
Effect of polarization reversal mechanism on neuronal functionality. (a) Fraction of upward polarization as a function of time predicted by the KAI model and the NLS model with different ω of switching time distributions. The inset shows the distribution functions. Simulated polarization reversal and device temperature dynamics under trains of electric pulses with (b) ω = 0.01 and (c) ω = 0.5, respectively.
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Effect of polarization reversal mechanism on neuronal functionality. (a) Fraction of upward polarization as a function of time predicted by the KAI model and the NLS model with different ω of switching time distributions. The inset shows the distribution functions. Simulated polarization reversal and device temperature dynamics under trains of electric pulses with (b) ω = 0.01 and (c) ω = 0.5, respectively.

FIG. 4.
Effect of polarization reversal mechanism on neuronal functionality. (a) Fraction of upward polarization as a function of time predicted by the KAI model and the NLS model with different ω of switching time distributions. The inset shows the distribution functions. Simulated polarization reversal and device temperature dynamics under trains of electric pulses with (b) ω = 0.01 and (c) ω = 0.5, respectively.
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Effect of polarization reversal mechanism on neuronal functionality. (a) Fraction of upward polarization as a function of time predicted by the KAI model and the NLS model with different ω of switching time distributions. The inset shows the distribution functions. Simulated polarization reversal and device temperature dynamics under trains of electric pulses with (b) ω = 0.01 and (c) ω = 0.5, respectively.

Close modal

Finally, we investigate the LIF functionality by weakening the built-in electric field as shown in Fig. S9 in the supplementary material. The LIF functionality can also be reproduced with a smaller built-in field. However, the reduction of built-in field lowers the operation speed of device due to slower backward switching. These results further emphasize the significance of built-in electric field on enhancing the volatile feature of AFTJ and the overall device performance.

In summary, by theoretical modeling, we show that a single AFTJ can realize neuronal functionalities. Built-in electric field is employed as an intrinsic factor for spontaneous polarization degradation to guarantee the volatility of ferroelectric neurons. Also, device temperature rising results from Joule heating is considered to enhance the polarization reversal, which provides a fast self-reset for the AFTJ neuron device after firing. Combining the NLS model and calculations of free energy and electric transport, polarization reversal and device temperature evolution dynamics of AFTJ are simulated. Polarization reversal dynamics under a single electric pulse shows that the volatile feature of AFTJ is enhanced by rising device temperature. Under trains of electric pulses, polarization reversal dynamics of AFTJ shows LIF neuronal functionality. The spiking mode can be modulated by pulse width and interval of electric pulse trains, which is demonstrated in ferroelectric neuron device prototype for the first time. Finally, the effects of polarization reversal mechanism and built-in field on neuronal functionality are discussed. We suggest that the ferroelectric device with the concentrated distribution of switching time of polarization reversal is beneficial to the neuronal functionality, in contrast with the ferroelectric synapse device. Our study provides a novel design scheme for ferroelectric neuron devices based on AFTJ and inspires further explorations of ferroelectric devices for neuromorphic computing.

Additional details and results are included in the supplementary material.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12132020, 12222214, 12002400, and 11972382), the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices (No. 2022B1212010008), and the Shenzhen Science and Technology Program (Grant Nos. 202206193000001 and 20220818181805001).

The authors have no conflicts to disclose.

Zhenxun Tang: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Linjie Liu: Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Validation (supporting); Visualization (supporting). Jianyuan Zhang: Formal analysis (supporting); Validation (supporting); Visualization (supporting). Weijin Chen: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Yue Zheng: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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