In this study, an Ag/hafnium oxide (HfO_x)/Pt TS selector was fabricated and investigated. The schematic illustration of the Ag-based TS selector is shown in Figure 1A. The Pt bottom layer was first deposited on a Ti/Si substrate using electron beam evaporation, followed by the silicon dioxide (SiO₂) layer deposition using plasma-enhanced chemical vapor deposition. After the photolithography process, the reactive ion etching of SiO₂ was applied to form a via contact with a diameter of 1 μm, which defines the effective device area. Then, the 4.5-nm-insulating HfO_x layer was deposited using atomic layer deposition. After that, 2-nm-thick Ag was deposited on the HfO_x layer using electron beam evaporation followed by rapid thermal annealing (RTA) at 500°C for 5 min to form Ag nanoparticles (NPs) as the active electrode. Finally, a 60-nm-thick Ni capping layer was deposited using electron beam deposition to prevent the oxidation of Ag NPs. Electrical measurements were performed using an Agilent B1500A and B1530A waveform generation/fast measurement unit at room temperature. Figure 1B shows the scanning electron microscope (SEM) image of Ag NPs. The size distribution of NPs is shown in the inset. Figure 1C shows the DC current-voltage (I-V) characteristics of the Ag/HfO_x/Pt TS selector with 500 DC cycles of TS and a compliance current (I_cc) of 0.1 mA. The device provides an extremely high on/off ratio (∼10⁹) and small V_th and hold voltage (V_hold) for both positive and negative bias, showing typical behaviors of Ag-based TS selectors as reported in the literature (Yoo et al., 2017).

To emulate neuromorphic hardware in which synapses and neurons are connected in the neural network (Figure 2A), the measurement setup adopted in this study is illustrated in Figure 2B. The effective resistor connected in series (R_series) represents the total resistance of multiple synaptic devices in the synaptic array connecting in parallel to the same TS neuron. A parasitic capacitor (C_parasitic) of the TS selector is exploited; therefore, no extra capacitor is needed for signal integration. The evolution of the total current (I_total) flowing through R_series and the voltage across TS selector (V_selector) is described in Figure 2C: when a constant input voltage (V_input) is applied to the neuron circuit, most of the voltage initially drops across the TS selector in the off-state. Then, V_selector is gradually increased by charging C_parasitic. Once V_selector reaches V_th, the TS selector is switched to the on-state due to the formation of a volatile conducting filament, and an increase in I_total can be observed. However, V_selector drops right after the TS selector is switched to the on-state due to the discharge of C_parasitic, and I_total starts to decrease. The TS selector returns to the off-state when V_selector reduces to V_hold because of the rupture of the volatile conducting filament. t_on and t_off define the required period of time for the selector to be turned on (V_selector to increase from V_hold to V_th) and off (V_selector to decrease from V_th to V_hold) in the neuron circuit, respectively. When the circuit is biased, a series of continuous current and voltage spikes are generated, and the spike frequency can be calculated as the number of spikes per second (Hz) accordingly. To fulfill the requirement of neural network applications, artificial neurons should be capable of generating different spike frequencies according to the weights of connected synapses, i.e., R_series. In the RC Model (Chen et al., 2016; Wang et al., 2020), the t_on in the TS neuron circuit is obtained by

In this study, we assume that the IR voltage drop on R_series is negligible when the TS selector is at its off-state due to the low leakage current (below pA in our case). Figure 3A illustrates the statistically measured t_on of the TS neuron when connecting to different R_series, and the inset is an example of experimentally obtained current spikes (I_total) when R_series is 3,300 kΩ. Figure 3B presents the calculated spike frequency, as shown in Figure 3A. The results indicate that, with the decrease of R_series, t_on is decreased and the spike frequency is increased accordingly. However, the spike frequency cannot be further increased when R_series is < 100 kΩ. It is worth mentioning that R_series in the neuron circuit also acts as current compliance, where it controls the morphology and the size of conducting filaments in the TS selector (Chae et al., 2017). If R_series is too small, the filaments of extremely large size become non-volatile and cannot be ruptured even at V_hold = 0 V. Consequently, t_off increases and limits the spike frequency due to the difficult dissolution of large-size filaments in the TS selector. As a result, the resistance range of R_series requires careful adjustment (> 100 kΩ in our case) to prevent the dysfunction of neuron circuits. With a suitable range of R_series and with t_off being much smaller than t_on, the spike frequency is the inverse of t_on, thus proportional to the inverse of R_series, i.e., the effective total conductance of the synaptic array.

An important assumption of the RC Model in Equation 1 is that the V_th of the TS selector is constant. Figure 4A compares the measured V_th captured by an oscilloscope with R_series of 150 and 470 kΩ, and the statistical results are indicated in Figure 4B. Instead of remaining constant, the V_th of the TS selector varies with R_series. Different R_series modulate the charging rate of V_selector and give rise to the history-dependent V_th. The naïve RC model does not consider the history-dependent V_th of the TS selector, thus reducing the accuracy and prediction capability of the neuron model.

To include the characteristic of history-dependent V_th into the neuron model, the V–t Model is proposed. Starting from considering the switching dynamics of TS selectors when constant voltage stress (V_CVS) is applied directly on the device, i.e., V_selector equals to V_CVS. This is the case similar to Figure 2B but without the external R_series. The time delay before turning on the selector (t_{on_CVS}) is determined by the nucleation theory (Karpov et al., 2008; Lee et al., 2020):

where τ₀ is the intrinsic time constant of the device, W₀ is the nucleation barrier energy without electric field, α is a geometric factor of a nucleus, E₀ is the voltage acceleration factor, d is the effective thickness of the insulating layer, k is Boltmann’s constant, and T is the ambient temperature. We define 𝔸 as a material-related constant at a fixed T, and (2) can be rewritten as

where 𝔸 and τ₀ can be obtained from fitting the measured V_CVS and t_{on_CVS}. We assume 𝔸 remains constant when measuring the same device. Therefore, the V–t equation can be used to describe the transformation relation between any two arbitrary CVS voltages, V_CVS1 and V_CVS2, and their corresponding turn-on times, t_{on_CVS1} and t_{on_CVS2} as

When connecting the TS selector with R_series to form a complete TS neuron circuit, as shown in Figure 2B, V_selector becomes time-varying according to the RC equivalent circuit. The time-varying V_selector could be approximated using a finite number of CVS steps as depicted in Figure 5, which increase from (t₁, V₁) to (t₂, V₂) and eventually to (t_on, V_th) indicated by the blue line. ΔV and Δt are the voltage and time intervals, respectively. A similar conversion between CVS and ramp voltage stress has been reported and validated in resistive switching memory devices (Luo et al., 2013). As indicated in Figure 5, the stress effect of the (t₁, V₁) step indicated by the blue-filled rectangle on the device is transformed to that of an equivalent (t′₁, V₂) step indicated by the red dashed rectangle based on (4), t′₁ is therefore expressed as:

A new equivalent CVS step of (t2¯, V₂) with an equivalent stress time of t2¯ = t′₁ + Δt at V₂ includes the history effect of the previous (V₁, t₁) step. This equivalent stress time is accumulated until it reaches the t_{on_CVS} at the stop voltage, i.e., V_th, which could be calculated by Equation 2. Under these circumstances, V_th becomes history-dependent and is affected by the RC charging process and R_series. The larger R_series, the lower V_th, and longer t_on.

To confirm the feasibility of the V–t Model on the prediction of the TS neuron behavior, the simulation results obtained from the RC Model (Chen et al., 2016; Wang et al., 2020) and the proposed V–t Model are compared in Figures 6A,B with the measurement. The RC Model only describes the RC behavior of the neuron circuit with a constant V_th of the TS selector, therefore it not only underestimates t_on but also fails to depict the history-dependent V_th of the TS selector. In contrast, the proposed V–t Model predicted well t_on and V_th of the TS selector under different R_series.

In this section, we explored the impact of the TS selector on TS neurons, and the effect of t_on and 𝔸 on V_th can be predicted based on Equation 2. As shown in Figure 7, when t_on approaches τ₀, the voltage required for nucleation (V_th) approaches infinity. In addition, the TS selector with larger 𝔸 requires a higher V_th to be turned on. These results indicated that, under the same t_on, the TS selector with larger τ₀ and 𝔸 needs a higher applied voltage than the one with smaller τ₀ and 𝔸. However, the required high applied voltage is not favorable because it not only may result in an irreversible breakdown of the device but also may increase the difficulty of circuit integration. Therefore, the TS selector with larger τ₀ and 𝔸 may require an additional external integration capacitor to maintain a reasonable V_th, which on the other hand increases the circuit footprint and t_on and decreases the spike frequency. The energy consumption per spike of the neuron circuit could also increase due to slow spiking (Liang et al., 2021).

Table 1 lists the reported parameters of τ₀ and 𝔸 of different TS devices (Park et al., 2016; Yoo et al., 2017; Lee et al., 2019b,2020), and the simulated t_on and V_th of the neuron circuit based on the V–t Model are indicated in Figure 8. In this study, the R_series is given from 10 to 1,000 kΩ. The value of the integration capacitor in the neuron circuit is adjusted to keep the maximum V_th below 1.2 V at R_series = 10 kΩ, and the adopted capacitance corresponding to each TS device is also given. Among IMT, OTS, and Ag-based TS devices, the OTS neuron matched with the lowest capacitance is the most favorable for reducing the neuron circuit area. It is noted that the minimal integration capacitor is limited by the parasitic capacitor of the TS selector itself. As a result, the device area scaling would be necessary to achieve a low enough capacitance value. Moreover, the simulated t_on in Figure 8A shows that the OTS neuron is capable of achieving GHz-level spike frequency due to its extremely small τ₀ (10 ^{– 21}s), even though its 𝔸 is larger. Furthermore, in Figure 8B, the OTS selector with the smallest τ₀ results in a large t_on/τ₀; therefore, the V_th is less history dependent. The OTS selector shows promising potential not only in generating high spike frequency but also consuming less area and energy in the neuron circuit.