Bias history impacts the analog resistance change of HfO_x-based neuromorphic synapses

Analog resistive random-access memory (RRAM) devices have gained much attention for compute in-memory technologies due to their ability to perform matrix–vector multiplication in hardware.^1–4 This leads to lower latency, power, and on-chip area compared to traditional technologies.^5,6 Many different material systems have been considered for RRAM devices; however, one of the most studied systems is filamentary RRAM devices based on Ti/HfO_x due to their industry readiness and large retention times.^7–11 Applying an electric field across the device generates defects within the oxide, resulting in a conducting path known as the filament.^12,13 The dissociated oxygen ions in the HfO_x layer migrate into the titanium layer, often referred to as the capping layer or oxygen reservoir.¹¹ When the polarity of the bias is reversed, oxygen ions migrate back from the titanium capping layer into the filament, causing the resistance to increase.^14,15 Incremental, analog changes in the resistance are achieved by applying multiple, short voltage pulses to the device.^16–19 While these devices are being considered for neuromorphic and analog computing systems, they tend to suffer from high variability, non-linear resistance changes, and asymmetric resistance change with respect to opposite polarity pulses—all limiting the overall effectiveness of these devices in large arrays.^16,20 Of these non-idealities, cycle-to-cycle variation of the resistance change is the most detrimental to the circuit's accuracy; thus, single device variations occurring from bias history must be understood.¹⁶ Numerous studies have reported improvements in linearity by changing the device materials,^19,21 pulsing schemes,^18,22 or peripheral circuitry.²³ However, the impact of prior biasing conditions on the analog resistance change is not fully understood.

In this work, we investigate the effect of prior bias sweeps on the analog resistance change of identical devices with identical pulses applied. Differences in the linearity and symmetry of the analog resistance change are typically ascribed to differences in the associated materials or device structures. However, the bias conditions used prior to analog testing are many times not reported. It is well known that analog resistance changes in RRAM devices are extremely sensitive to the physics of the local electrical, chemical, and thermal environment.^{9,10,21,24,25} Prior biasing conditions may impact the distribution of oxygen ions in the filament or capping layer causing the devices to “remember” prior biasing conditions. Varied ion concentrations may cause significant resistance variation and cycle-to-cycle variation. Experimental results supported by simulation suggest that a device's previous biasing condition leads to a change in the observed resistance trend with pulse number. This underscores the importance of only comparing devices that have experienced exactly the same biasing history.

Maskless photolithography was used to fabricate 10 × 10 μm² crossbars with gold top and bottom electrodes (TE & BE), a titanium capping layer, and a HfO_x active layer on an oxidized 4-in. silicon wafer with approximately 300 nm of SiO₂. Standard liftoff procedures were used to pattern the BE, and wet etching was used to pattern the TE. Electron beam evaporation (<6.7 × 10⁻⁴Pa) was used to deposit the BE Ti adhesion layer (∼20 nm), gold BE (∼70 nm), Ti capping layer (∼5 nm), and gold TE (∼150 nm). The device structure is illustrated in the inset of Figs. 1 and S1. Thermal atomic layer deposition (ALD) at 250 °C was used to deposit ∼5 nm HfO_x by alternating pulses of Tetrakis(dimethylamido)hafnium (TDMA-Hf) (0.25 s) and water vapor (0.06 s). X-ray photoelectron spectroscopy was used to calculate the stoichiometry of the oxide layer, which was determined to be HfO_x (x ≈ 1.85), see Fig. S2.

After fabrication, the filament is formed by applying a positive voltage sweep from 0 to 3.5 V to the TE with the BE grounded. A current compliance (I_cc) of 0.1 mA was used to ensure that the oxide did not permanently breakdown. Devices were then gradually reset to a high resistive state (HRS) by applying negative voltages from −0.1 V to a final reset voltage (−1, −1.3, or −1.5 V) in increments of −0.1 V. Following the gradual reset process, the device was then set back to a low resistance state (LRS) with a voltage sweep from 0 to 1.2 V (I_cc = 0.5 mA). Devices were then cycled ten times between the LRS and HRS to stabilize the filament. Set sweeps were identical for all devices (0 to 1.2 V, I_cc = 0.5 mA). Reset sweeps were conducted with low (−1 V), medium (−1.3 V), or high (−1.5 V) voltage magnitudes. Each condition was tested on at least eight devices. Characteristic set/reset IV curves are plotted in Fig. 1. Since the same set procedure was used in all cases, and the resistance of the LRS is dominated by the current compliance,²⁶ the LRS resistance was very similar in all cases (median ∼900–1000 Ω). The resistance of the HRS is determined by the magnitude of the reset voltage with median values of ∼17, 38, and 61 kΩ for the −1, −1.3, and −1.5 V devices, respectively. The box plot in Fig. 2 shows a statistical distribution of the LRS and HRS of the devices used in this study.

Analog pulsing begins in the LRS for all three stabilization conditions (∼1000 Ω). To increase the resistance of the devices, −0.7 V pulses with a 1 μs pulse width were applied to the TE with the BE grounded. All devices start at nearly the same resistance and have the exact same voltage pulse applied. However, the trend in resistance change varies according to the reset stabilization voltage previously applied to the device. Higher magnitude stabilization voltages cause a greater rate of change in the resistance with respect to the pulse number. This translates to devices with higher reset stabilization voltages reaching a higher resistance value after 30 reset pulses. Additionally, devices previously biased with lower reset voltages show a more gradual resistance increase between 0 and 30 pulses, while the higher reset voltage leads to large initial resistance changes that start saturating around pulse 10. The average device resistance with respect to the number of applied pulses for each reset condition is plotted in Fig. 3. With identical pulses applied, the −1.5 V stabilized devices reach an ultimate resistance of 2500 Ω. This is compared to 1750 and 2000 Ω for the −1 and −1.3 V stabilized devices, respectively. For identical positive voltage pulses (0.6 V, 1 μs), the devices stabilized with the highest reset voltage have large initial decreases in the resistance that then saturate. It is difficult to directly compare these results since the devices start from different resistance values; however, devices stabilized with lower reset voltage have less abrupt reductions in the resistance leading to a more symmetric and linear resistance response.

The trend with reset voltage observed in Fig. 3 is particularly interesting because it is not caused by the devices saturating in their HRS. As shown in Fig. 2, the lowest HRS for these devices is 17 kΩ (−1 V reset), though the analog resistances are between 1 and 2.6 kΩ (Fig. 3). If operated for more pulses, the devices would likely saturate near their HRS; however, the slope to achieve that value would be altered depending on its prior reset voltage. Since these devices are fabricated identically on the same chip, this suggests that the stabilization reset voltage must be impacting either the filament or the distribution of oxygen ions in the titanium capping layer. Due to the similarity in LRS for the three stabilization voltages, it is not likely that the filament geometry is changed from the reset stabilization voltage. If the filament structure was different, it would be expected that the LRS for these three stabilization voltages would follow a trend, but they do not. The −1.5 V stabilization devices have the lowest LRS on average (∼900 Ω), followed by −1 V (∼958 Ω) and −1.3 V (∼1005 Ω). Instead, it is hypothesized that higher magnitude stabilization voltages increase the local concentration of oxygen ions stored in the titanium layer close to the filament.

The biasing history of the devices helps us to explain how the local ion concentration can be different for identically fabricated devices. Forming is the first electrical bias applied; thus, all the devices in this study had statistically identical forming voltages (∼2.65 ± 0.1 V). This relatively high voltage is needed to cause electrons to tunnel through the oxide and break the bonds between the Hf and O atoms. The high electric field facilitates the migration of oxygen ions from the filament into the titanium layer. Once a filament is fully formed, the large current increase causes extreme local heating,^9,10,25 which further facilitates the migration of ions out of the filament. A schematic representation of the ion distribution after forming is illustrated in Fig. 4(a). After forming, the reset process returns some of the oxygen ions back to the filament. High amplitude voltages result in a higher HRS, indicating more oxygen ions are returned to the filament compared to lower amplitude reset voltages [Figs. 4(b1) and 4(b2)]. This can be explained by the exponential relationship between the magnitude of ionic drift and voltage.²⁷ Exponential ionic drift comes from the high fields (>1 MV·cm⁻¹), reducing the activation barrier for ion migration.²⁷ The set voltage of 1.2 V is low compared to the forming voltage of ∼2.65 V. When the ions move back to the Ti capping layer, the lower electric field confines them closer to the filament tip [Figs. 4(c1) and 4(c2)]. This results in a slightly higher concentration of oxygen ions in the titanium capping layer after stabilization and prior to analog pulsing [i.e., Fig. 4(c1) has a lower concentration of oxygen ions above the filament compared to Fig. 4(c2)]. A previously validated electro-thermal model was used to support this hypothesis and is explained in detail by Pahinkar et al.²⁵ 

The electro-thermal model considers drift, diffusion, and thermophoresis as migration mechanisms for oxygen vacancies. Although the model is based on the migration of vacancies, the concentrations have been converted to oxygen ions to be consistent with the prior discussion. The model is unable to solve the forming process; thus, an initial filament with a 6 nm diameter is assumed for all cases. All parameters in the model are constant except for the initial concentration of oxygen ions in the titanium capping layer. To estimate the oxygen concentrations, the capping layer is assumed to be rutile TiO₂ with a unit cell volume of 64 Å.²⁸ This is considered a reasonable assumption because titanium is known to get oxygen from surfaces it is deposited on and because the removed oxygen from the filament during forming is stored in the titanium layer.⁸ Removal of 10%, 13%, and 15% oxygen from the stoichiometric ratio corresponds to oxygen concentrations of 9.33 × 10²⁷, 9.02 × 10²⁷, and 8.81 × 10²⁷ m⁻³, respectively. These oxygen concentrations showed excellent agreement with the experimentally obtained analog data (Fig. 5). The small variations in concentration translate to a difference of just tens of atoms near the filament. This underscores the difficulty of comparing the performance of RRAM devices to one another and suggests it is important to only compare devices that have undergone the same biasing history.

Identical devices fabricated on the same chip exhibit different analog resistance change trends with respect to pulse number depending on the prior reset stabilization voltage. This is due to different reset voltages changing the concentration of oxygen ions stored in the titanium capping layer. An electro-thermal finite elements model confirms that varied oxygen content in the titanium layer would result in the observed trend in the experiments. This finding highlights the importance of only comparing analog data to other filamentary RRAM devices that have been biased in the same way and demonstrates the complexity of stating incremental improvements on device linearity. Repeatable resistive switching is extremely sensitive to the local physics of both the filamentary layer and the capping layer. Lowering the magnitude of the initial reset voltage reduced the initial large resistance jumps from the first few pulses and led to a more symmetric resistance response during potentiation and depression.

See the supplementary material for the device architecture, a transmission electron micrograph of the active area, and the x-ray photoelectron spectroscopy data used to determine the stoichiometry.

This work was supported by the Air Force Office of Scientific Research MURI entitled, “Cross-disciplinary Electronic-ionic Research Enabling Biologically Realistic Autonomous Learning (CEREBRAL)” under Award No. FA9550-18-1-0024. This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (No. ECCS-2025462). This material is based upon the work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650044.