**2. Fabrication Process and Conduction Mechanism**

To implement the synapse devices in bio-inspired neuromorphic computing systems (Figure 1a), we fabricated the two-terminal Au/Ti/IGZO/SiO2/p <sup>+</sup>-Si memristors as shown Figure 1b. The p+-Si conductive substrate acts as a global bottom electrode (BE), and the 4-nm-thick SiO<sup>2</sup> was formed on the BE as the tunnel barrier in the interface between p+-Si and IGZO. Then, the 80-nm-thick a-IGZO film was deposited on SiO2/p <sup>+</sup>-Si using radio frequency sputtering with a power of 150 W at room temperature. We controlled the concentration of oxygen vacancies (VOs) during the IGZO sputtering by modulating the oxygen flow rates (OFR) to 1.0, 1.15, and 1.3 sccm at a fixed Ar flow rate of 3 sccm and at a constant gas pressure in the sputter chamber of 0.880 Pa. Subsequently, 10-nm-thick Ti was deposited using e-beam evaporation to form an oxygen reservoir layer and act as the top electrode (TE) of the memristor. Finally, the 40-nm-thick Au was deposited using e-beam evaporation to prevent the oxidation of the Ti layer in air.

To analyze the electrical characteristics, the DC current–voltage (*I*−*V*) characteristics were measured at room temperature and dark conditions using a Keithley-4200 semiconductor characterization system (Tektronix, Seoul, South Korea). In all the measurements, a voltage was applied to the TE, and the BE was always connected to the ground. The TE voltage was symbolized as *V*TE, and the current flowing through the IGZO memristor was called *I*mem, as shown in Figure 1b.

Figure 1c–f shows the energy band diagrams under various conditions: before forming the junction (Figure 1c), at the thermal equilibrium (Figure 1d), at a low *V*TE (Figure 1e), and at a high *V*TE (Figure 1f). Here, we considered the lowering of the height of the effective SB and denoted it as *q*Φ<sup>B</sup> (eV). While SB lowering was insignificant at a thermal equilibrium, *q*Φ<sup>B</sup> became low as the *V*TE increased. At a low *V*TE, most of the *V*TE was applied across the thin SiO<sup>2</sup> layer (Figure 1e), whereas the increased *V*TE was used mainly to deplete the IGZO film (Figure 1f). Energy band diagrams suggested the fabricated IGZO memristors operated as non-filamentary RS devices based on the SB modulation. The two main concerns were whether the modulated *q*Φ<sup>B</sup> was nonvolatile and whether its decrease was inversely linear with the increase of *V*TE. These two concerns will be discussed later.

fixed *V*TE increased as the OFR decreased. This was attributed to the increase of the VO concentration with the decrease in the OFR because the VO is a well-known electron donor in the IGZO film [21,22]. Along with the SB-modulated non-filamentary RS devices in Figure 1e,f, a gradual resistance

**Figure 1.** Schematic illustration of (**a**) the implementation of the synapse devices in bio-inspired neuromorphic computing systems and (**b**) the two-terminal Au/Ti/(amorphous indium-gallium-zincoxide) a-IGZO/SiO2/p+-Si memristors. Energy band diagram (**c**) before forming the junction, and under three conditions: (**d**) in a thermal equilibrium, (**e**) at a low (top electrode voltage) *V*TE, and (**f**) at **Figure 1.** Schematic illustration of (**a**) the implementation of the synapse devices in bio-inspired neuromorphic computing systems and (**b**) the two-terminal Au/Ti/(amorphous indium-gallium-zinc-oxide) a-IGZO/SiO<sup>2</sup> /p <sup>+</sup>-Si memristors. Energy band diagram (**c**) before forming the junction, and under three conditions: (**d**) in a thermal equilibrium, (**e**) at a low (top electrode voltage) *V*TE, and (**f**) at a high *V*TE.

a high *V*TE. Figure 2b also shows the *I*mem−*V*TE characteristic of the IGZO memristor with OFR = 1 sccm. In Figure 2b, the positive *V*TE voltage sweep was repeated four consecutive times by changing the stop voltage of the *V*TE sweep (*V*SS) from 2 to 6 V. When the *V*TE sweep was performed four times, the readout current *I*mem at *V*TE = 1 V increased very slightly for *V*SS < 6 V, as seen in Figure 2c. The continuous and hysteretic increase of current, which is a typical behavior of a memristor, is clearly observed in Figure 2a and b. There was a significant increase in *I*mem only when *V*SS ≥ 6 V, which means We measured the OFR-dependent *I*mem while using a positive *V*TE sweep (SET process), that is, 0 V → 6 V → 0 V was repeated four times. Then, a negative *V*TE sweep (RESET process), that is, 0 V → −2 V → 0 V was repeated four times, as shown in Figure 2a. We observed that the current at a fixed *V*TE increased as the OFR decreased. This was attributed to the increase of the V<sup>O</sup> concentration with the decrease in the OFR because the V<sup>O</sup> is a well-known electron donor in the IGZO film [21,22]. Along with the SB-modulated non-filamentary RS devices in Figure 1e,f, a gradual resistance modulation rather than an abrupt RS was clearly observed during repeated *I*−*V* sweeps (Figure 2a).

that the *potentiation threshold* voltage between the gradual/abrupt RS (*V*PT) was 6 V. Similarly, the *depression threshold* voltage was found to be −2 V. To determine the conduction mechanism, we investigated the relationship between *I*mem and *V*TE. Figure 3a shows the OFR-dependent ln(*I*mem) versus (*V*TE)1/2 relationships, which were taken from the *I*−*V* characteristics of the first sweep in Figure 2a. In Figure 3a, we observed that the ln(*I*mem) was piecewise linear with (*V*TE)1/2, which was strongly reminiscent of the thermionic emission. Noticeably, these linear relationships were clearly classified into two distinguishable values of the slopes A (at a low *V*TE) and B (at a high *V*TE). Figure 2b also shows the *I*mem−*V*TE characteristic of the IGZO memristor with OFR = 1 sccm. In Figure 2b, the positive *V*TE voltage sweep was repeated four consecutive times by changing the stop voltage of the *V*TE sweep (*V*SS) from 2 to 6 V. When the *V*TE sweep was performed four times, the readout current *I*mem at *V*TE = 1 V increased very slightly for *V*SS < 6 V, as seen in Figure 2c. The continuous and hysteretic increase of current, which is a typical behavior of a memristor, is clearly observed in Figure 2a,b. There was a significant increase in *I*mem only when *V*SS ≥ 6 V, which means that the *potentiation threshold* voltage between the gradual/abrupt RS (*V*PT) was 6 V. Similarly, the *depression threshold* voltage was found to be −2 V.

To determine the conduction mechanism, we investigated the relationship between *I*mem and *V*TE. Figure 3a shows the OFR-dependent ln(*I*mem) versus (*V*TE) 1/2 relationships, which were taken from the *I*−*V* characteristics of the first sweep in Figure 2a. In Figure 3a, we observed that the ln(*I*mem) was piecewise linear with (*V*TE) 1/2 , which was strongly reminiscent of the thermionic emission. Noticeably, these linear relationships were clearly classified into two distinguishable values of the slopes A (at a low *V*TE) and B (at a high *V*TE).

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**Figure 2.** (**a**) The (oxygen flow rate) OFR-dependent *I*−*V* characteristics repeated four times. (**b**) The *I*−*V* characteristics with OFR = 1 sccm repeated four consecutive times with changes made to the (stop voltage of the *V*TE sweep) *V*SS. (**c**) The *V*SS-dependent readout current *I*mem at *V*TE = 1 V. **Figure 2.** (**a**) The (oxygen flow rate) OFR-dependent *I*−*V* characteristics repeated four times. (**b**) The *I*−*V* characteristics with OFR = 1 sccm repeated four consecutive times with changes made to the (stop voltage of the *V*TE sweep) *V*SS. (**c**) The *V*SS-dependent readout current *I*mem at *V*TE = 1 V. *I*−*V* characteristics with OFR = 1 sccm repeated four consecutive times with changes made to the (stop voltage of the *V*TE sweep) *V*SS. (**c**) The *V*SS-dependent readout current *I*mem at *V*TE = 1 V.

**Figure 3.** (**a**) The OFR-dependent ln(*I*mem)−(*V*TE)1/2 relationships. (**b**) The OFR-dependent ΦB extracted **The number of VTE sweeps The number of VTE sweeps Figure 3.** (**a**) The OFR-dependent ln(*I*mem)−(*V*TE)1/2 relationships. (**b**) The OFR-dependent ΦB extracted at low and high *V*TE. The ΦB modulation depending on the number of *V*SS from the slopes (**c**) A at high **Figure 3.** (**a**) The OFR-dependent ln(*I*mem)−(*V*TE) 1/2 relationships. (**b**) The OFR-dependent Φ<sup>B</sup> extracted at low and high *V*TE. The Φ<sup>B</sup> modulation depending on the number of *V*SS from the slopes (**c**) A at high *V*TE and (**d**) B at low *V*TE.

at low and high *V*TE. The ΦB modulation depending on the number of *V*SS from the slopes (**c**) A at high

*V*TE and (**d**) B at low *V*TE.

*V*TE and (**d**) B at low *V*TE.

The current due to the thermionic emission through SB is given as:

$$I\_{\rm mem} = AA^\* T^2 \exp\left(\frac{q\left(\sqrt{q\mathbb{E}/4\pi\varepsilon} - \Phi\_\mathbb{B}\right)}{kT}\right) = AA^\* T^2 \exp\left(\frac{q\left(\sqrt{qV\_{\rm TE}/4\pi\varepsilon X\_\rm T} - \Phi\_\mathbb{B}\right)}{kT}\right) \tag{1}$$

where *A* is the area of device, *A*\* is the Richardson constant, *T* is the absolute temperature, *k* is Boltzmann's constant, *E* is the electric field; *q* is the electric charge, ε is the dielectric constant, *X*<sup>T</sup> is the effective thickness of thermionic emission, and Φ<sup>B</sup> is the effective SB height. Then, Equation (1) is used for extracting ΦB. By reformulating from Equation (1) to (2), Φ<sup>B</sup> can be extracted by using the y-intercept of the linear relationship between *kT q* · ln *I*mem *AA*∗*T*<sup>2</sup> and <sup>√</sup> *VTE*:

$$\frac{kT}{q} \cdot \ln\left(\frac{I\_{\text{mem}}}{AA^\*T^2}\right) = \sqrt{\frac{q/X\_T}{4\pi\varepsilon}} \times \sqrt{V\_{TE}} - \Phi\_\text{B} \tag{2}$$

Figure 3a,b suggests that at a specific OFR, there existed two Φ<sup>B</sup> values taken from the slopes A and B, that is, a large value for a low *V*TE (<1 V) and a small value for a high *V*TE (1–5 V). Interestingly, we observed this bimodal distribution of Φ<sup>B</sup> regardless of the OFR condition and suggest that the SB lowering is nonvolatile and significantly nonlinear with the increase in *V*TE. In addition, Φ<sup>B</sup> at a specific *V*TE was lower because the V<sup>O</sup> concentration increases (with decreasing OFR).

However, from Figure 2a, we can see that the Φ<sup>B</sup> modulation depended on the number of positive *V*TE sweeps (see Figure 3c,d). At a specific *V*TE and OFR, Φ<sup>B</sup> gradually decreased when the number of *V*SS sweeps increased.
