Impact of titanium doping and pulsing conditions on the analog temporal response of hafnium oxide based memristor synapses

As traditional computing has been facing limits associated with the end of conventional device scaling,^1,2 a new computing paradigm is desired. Neuromorphic computing^3–13 has gained widespread attention to circumvent the challenges of traditional computing by mimicking information processing associated with the brain enabling computational tasks such as vector-matrix multiplication, pattern recognition, and adaptation in the real-world environment.^14–17 Memristors^7,18–22 are considered a leading candidate for artificial synapses in neuromorphic computing. Memristors based on transition metal oxides (e.g., HfO₂,^23–26 TaO_x,^27,28 TiO₂,^29,30 WO₃,^31–33 SrTiO₃,^33–35 ZnO,^36,37 and SiO₂^38,39) have gained widespread attention because of their multiple attractive features such as high scalability, multi-level capability, low energy consumption, and compatibility with large-scale integration. Among these, HfO_x exhibits additional advantages such as CMOS compatibility, scalability, lower power consumption, large memory window (>100), high density, fast-switching speed (∼ns), and good endurance (≥10¹⁰ cycles).^3,40–42 Beyond these features of digital Resistive Random Access Memory (RRAM), promising analog synaptic characteristics have also been reported for HfO_x memristors. The change of the weight of biological synapses when pulsed with an action potential is associated with the motion of neurotransmitters.^43–46 Similarly, the resistance change in filamentary oxide memristors is caused by the motion of oxygen vacancies (V_o) or ions across the conducting filament. A variety of biological synaptic responses such as short-term depression/potentiation (STD/STP),⁴⁷ long-term depression/potentiation (LTD/LTP),^48,49 and spike-time-dependent plasticity (STDP)^48,50 have also been demonstrated for HfO_x artificial synapses for analog applications.

Pattern recognition accuracy of analog neuromorphic architectures has been shown to be dependent on the control and linearity of the resistance change of the artificial memristor synapse as a function of applied voltage pulses.⁵¹ However, a linear change in resistance as a function of identical voltage pulses is not easily achieved for HfO_x memristor synapses.⁵² Non-identical voltage pulses and transistors can be used for HfO_x memristor synapses to improve the linearity. However, this requires complex peripheral circuits for pulse generation and increases the burden of latency, energy, and chip area.^51,53–55

It is known that the motion of a small number of ions is involved in the analog resistive switching of HfO_x memristors.⁵⁶ Therefore, the incorporation of layers of other oxides with HfO_x^23,57 as well as the addition of dopants to HfO_x^58,59 have been considered to alter ion motion and improve resistive switching properties. For example, a previous study reported that adding TiO_x layers to sputtered HfO_x improves the uniformity in digital switching and provides multi-level capability.^23,60 Another study showed that sputtered HfO_x/TiO_x multilayered devices consume less energy compared to HfO_x devices and can be integrated in the large-scale neuromorphic visual system.⁴⁰ Nickel doping in sputtered HfO_x has been shown to decrease power consumption and improve multi-level resistance behavior with identical pulses.⁶¹ Synaptic behavior such as long-term potentiation and depression has been reported for a memristor with sputtered HfO_x doped with manganese⁶² yet the switching window was small and an abrupt increase of the conductance with applied pulse voltage was observed. While sputtering can be useful for demonstration purposes, atomic layer deposition (ALD) is more compatible with large-scale integrated circuit fabrication.⁶³ A previous study has reported using ALD deposited electro thermal modulation layer to improve the linearity of analog HfO_x RRAM.⁶⁴ However, a compliance transistor is used during measurement, and the impact of measurement conditions on the observed behavior was not studied. Aluminum doping of HfO_x devices has been reported to improve analog switching; however, a complex pulsing scheme was used.^58,65 Chakrabarti et al.^66,67 and a recent study⁶⁸ have explored the use of titanium doped HfO_x deposited using ALD for multi-level memory; however, the impact of these dopants on the analog switching behavior was not evaluated.

This study investigates the analog switching properties of ALD HfO_x and titanium doped HfO_x memristors using identical voltage pulses. In addition, the impact of titanium doping on the analog resistance change is analyzed for different measurement conditions such as pulse amplitude and width. The impact of these measurement conditions on analog features such as off state resistance and linearity is assessed. While the measurement characteristics are observed to strongly impact the analog characteristics, the results are largely independent of titanium doping. Density functional theory (DFT) calculation of oxygen ion motion in these materials suggests that this is due to the resistance change being primarily controlled by the HfTi metallic conducting filament and not the oxide itself.

Metal-insulator-metal memristors with HfO_x and Hf_xTi_yO_z amorphous oxides were fabricated as shown in Fig. 1(a). Silicon wafers with 310 nm of SiO₂ were cleaned with acetone, methanol, and isopropanol. Bottom electrodes (BE) with size 10 × 10 μm² were formed using mask-less ultraviolet photolithography followed by lift off. The BEs consisted of a ∼5 nm titanium adhesive layer and ∼70 nm of gold deposited using electron beam evaporation at a rate of 0.1 nm/s at a pressure 2.5 × 10⁻⁶ Torr. For the standard device, the ∼5 nm HfO_x active layer was synthesized using thermal ALD at 250 °C with de-ionized water and tetrakis(dimethylamido) hafnium (TDMAHF) as precursors. For the titanium doped devices, Hf_xTi_yO_z was synthesized using thermal ALD by sequential deposition of three cycles of tetrakis(dimethylamido)hafnium (TDMAHF) and de-ionized water followed by one cycle of tetrakis(dimethylamido)titanium (TDMAT) and de-ionized water. This was repeated 12 times for 48 total cycles to achieve a thickness ∼5 nm Hf_xTi_yO_z oxide. X-ray photoelectron spectroscopy analysis indicates a Hf:Ti ratio of 3.14:1 (Fig. S2 in the supplementary material) which is close to the estimated 3:1 ratio from the synthesis conditions. Spectroscopic ellipsometry was utilized to verify the thicknesses of the oxides. The ∼5 nm titanium capping layer and ∼150 nm gold top electrode were deposited using electron beam evaporation and patterned using lift off. Before the deposition of the TE, BE, and oxide, an oxygen plasma descum process for 30 s (at a flow-rate of 50 SCCM, plasma power of 150 W RF, and pressure of 60 mT) was performed to remove the residual photoresist and surface hydrocarbons.

A Keithley 4200 SCS semiconductor parameter analyzer was used to conduct the electrical testing. Identical square pulses of a given pulse width and amplitude were applied. The resistance of the device was measured between each pulse by performing a current–voltage sweep from 0 to 0.1 V. These measurements were repeated using different pulse amplitudes (−0.1 to −0.8 V) and pulse widths (160 ns to 1 ms), on both HfO_x and Hf_xTi_yO_z devices. Each measurement condition was repeated on multiple devices. Figure S1 in the supplementary material illustrates the conditions used for the measurements.

We employed the density functional theory (DFT) provided by VASP to calculate the diffusion barrier of neutral oxygen vacancy. For each case, we obtained the optimized structure of a supercell cell with one oxygen vacancy (Hf_xTi_yO_z) or one interstitial oxygen (HfTi metal) first. Then, the nudged elastic band method combined with the climbing image method⁶⁹ was used to calculate the neutral oxygen vacancy diffusion barrier. For HfO₂, the structure optimization was performed on a supercell of 2 × 2 × 2 with one oxygen vacancy. For the titanium doped case, the effect is studied by replacing Hf with Ti performing the DFT with neutral oxygen vacancies in both oxides and metals. For Hf_1.5Ti_0.5O₂, we first performed the structure optimization in the unit cell with the ratio of Hf:Ti being 3:1, and then, we constructed the supercell of 2 × 2 × 2 using the unit cell obtained above. A similar method was used to obtain the structure of HfTi metal with a supercell of 4 × 4 × 3.

The memristor devices were formed and stabilized prior to performing pulse measurements. The conductive filament was formed by applying a positive voltage sweep at the top electrode from 0 to 3.5 V with a current compliance ∼0.1 mA (Fig. S3 in the supplementary material). The forming voltage is observed to be lower for the Hf_xTi_yO_z devices (∼2.5 V) compared to the HfO_x devices (∼3.1 V). The forming step was followed by a gradual reset from 0 to a maximum negative reset voltage with an increment of ∼−0.1 V and several set–reset stabilization loops (Figs. S4 and S5 in the supplementary material). This stabilization is performed to ensure the devices are toggling between the HRS and the LRS and that the conducting filaments are stable. After forming and stabilization, the resistances of the devices were measured as shown in Fig. S6 in the supplementary material. It is observed that after stabilization the resistance states were nearly identical for both HfO_x and Hf_xTi_yO_z devices, confirming that any difference in the analog temporal response is independent of the initial device state.

Figures 2(a) and 2(b) show the change in resistance under identical negative pulses for the HfO_x and Hf_xTi_yO_z devices, respectively. As mentioned previously, the application of identical pulses is advantageous because it dramatically simplifies the pulse generation module design.^40,41 In general, the resistance is observed to increase dramatically upon the first pulse and then eventually saturates. This highly nonlinear “first pulse effect” is typically observed in HfO_x based devices,⁶² and it degrades the performance of analog neuromorphic architectures.⁷⁰ The large resistance change with the first pulse is less dramatic with decreasing pulse amplitude and pulse width. The maximum temperature of the filament is known to be strongly dependent on the current and, hence, voltage. For the first negative voltage pulse, the temperature initially increases causing oxygen ions to move from the titanium capping layer into the filament. The oxidation of the filament increases the resistance, thus quickly reducing the current and the temperature. Subsequent pulses at the same negative voltage, therefore, result in a lower temperature and a slower change in resistance as compared to the first pulse. A smaller pulse width generally results in a smaller initial change in resistance and temperature (Fig. S7 in the supplementary material) because the time for oxygen ion diffusion at peak temperature is reduced.

As shown previously, the resistance of the devices saturate after multiple pulses (∼200) to a value that we term as off-resistance (R_off), which depends on the pulsing conditions. Figures 3(a) and 3(b) show R_off as a function of pulse amplitude, in the range from −0.5 to −0.8 V with two different pulse widths (160 ns and 1 ms). It is observed that R_off is strongly dependent on the pulse voltage while being almost independent of the pulse width. This trend is observed in both standard HfO_x and Hf_xTi_yO_z devices. The strong effect of negative pulse voltage on R_off can be attributed to the fact that voltage primarily controls the reset behavior of the bipolar memristors.^71,72 The impact of pulse width on R_off is not significant compared to the pulse amplitude because total energy input has a second-order relationship with the voltage and a linear relationship with time.⁷³ Moreover, there is a voltage below which no significant change in R_off is observed because the energy input to move oxygen ions is too low to cause any change in resistance. This voltage at which a resistance change is measured is similar (∼ − 0.6 V) for both the HfO_x and Hf_xTi_yO_z devices. The observed results indicate that by adjusting the pulse amplitude, the saturated resistance of the device can be increased, which can be applied to neuromorphic applications.

Figures 4(a) and 4(b) illustrate the analog resistance change of HfO_x and Hf_xTi_yO_z devices under pulse amplitudes of −0.7 and −0.8 V and pulse widths of 1 ms and 160 ns. It can be observed that for the −0.8 V and 160 ns pulsing condition, the titanium doped device (dark red curve-closed symbol) has a lower first pulse effect and improved linearity compared to the HfO_x device (light red curve-closed symbol). A parameter $α$ can be introduced here to quantify linearity, which is defined as the smaller the value of $α$ higher the linearity is.^74,75 Details of the model describing the $α$ parameter can be found in Eq. (S1) in the supplementary material. While for the HfO_x device, the $α$ parameter value is ∼15, for titanium doped device, the value is ∼2, for the −0.8 V and 160 ns pulsing condition, shown in Figs. 4(c) and 4(d). Although a previous study has reported an alpha value of −0.63, the applied voltage (−1.5 V) was higher than in our case (−0.8 V). Therefore, the titanium doped HfO_x device has a comparable alpha value and is a low-power device with a comparable alpha value.

Therefore, although the saturated resistance (R_off) is larger for the HfO_x device than the titanium doped device, due to the “first pulse effect,” it has a higher value of $α$ and suffers from poor linearity. The addition of titanium dopant appears to lower the “first pulse effect,” improving the linearity. Moreover, the alpha fittings at different pulsing conditions for HfO_x and Hf_xTi_yO_z devices are shown in Fig. S8 in the supplementary material. It is also that for a given device, the alpha value decreases for the lower pulse amplitude condition. This provides further evidence for the conclusion made earlier, which is lower pulse amplitude improves the linearity. The linearity improvement is a core requirement for the synaptic devices to achieve a high pattern recognition accuracy.⁴¹ 

While there are subtle differences in the linearity of the HfO_x and Hf_xTi_yO_z devices, the analog behavior is quite comparable. It has been reported that for the switching of oxide-based devices, oxygen ion inducing redox reactions and mixed electronic–ionic transport in the oxide region play a critical role. As the oxygen ions will diffuse through the pathways of the lowest barrier, the activation energy of oxygen ion migration has a direct impact on the analog switching. Theoretically, the migration barrier in bulk oxide is expected to be impacted significantly by adding titanium as the Gibbs free energy of formation HfO_x is −1088.2 eV and TiO_x is −888.8 eV. Therefore, a quantitative analysis of the oxygen vacancy migration barrier is needed once the conductive filament is formed for both HfO_x and Hf_xTi_yO_z devices.

To analyze the effect of titanium doping on the oxygen ion migration, we have employed the density functional theory (DFT) with the nudged elastic band (NEB) method to theoretically calculate the neutral oxygen ion diffusion barrier in both HfO_x and Hf_xTi_yO_z systems. A point should be noted that once the CF forms, most oxygen vacancies have aggregated in the CF, and the bulk region has a low concentration of oxygen vacancies. In the system of low concentration of oxygen vacancies, the hopping of oxygen ions is equivalent to oxygen vacancies moving forward. Therefore, the diffusion barrier of neutral oxygen ion (vacancy) is relevant in this case. Moreover, an interstitial oxygen ion has very high formation energy (1.69–2.76 eV) and charged oxygen vacancies are likely to be present near the interfaces. As a result, these are not likely true in this case. A detailed description of our calculations for the neutral oxygen ions can be found in Sec. II.

The DFT calculation results of the neutral oxygen ion diffusion barrier for HfO_x and Hf_xTi_yO_z are illustrated in Fig. 5. It can be observed that the diffusion barrier is ∼four times lower for Hf_xTi_yO_z (∼0.6 eV) compared to HfO_x (∼2.49 eV) oxide. The calculated barrier energy in HfO_x oxide is consistent with the previously published results.^76,77 The lower diffusion barrier for titanium doped HfO_x oxide is expected since the neutral oxygen ion diffusion barrier in pure TiO₂ is much lower than in pure HfO₂. A ∼fourfold decrease in the energy barrier of titanium doped HfO_x oxide compared to pure HfO_x oxide is expected to cause a pronounced change in the analog responses in Hf_xTi_yO_z devices.

However, the observed differences in the experimental results of analog responses for both HfO_x and Hf_xTi_yO_z devices are not large, suggesting that the bulk oxide does not play the dominant role in the analog response suggesting that the diffusion of oxygen ions within the conducting filament should be explored.

Since there are much fewer oxygen ions inside the CF, the CF primarily consists of either a Hf or HfTi alloys system for HfO_x and Hf_xTi_yO_z devices, respectively.^69,70 As a result, we employ the DFT with NEB to calculate the diffusion barrier of the oxygen ion at interstitial sites in Hf and HfTi alloy metals, and our results are summarized in Figs. 6 and 7. Previous DFT study on the oxygen diffusion in HCP Hf metal has shown that stable oxygen interstitial sites are either octahedral O $2a(0,0,0)$⁠) or tetrahedral T $4f(23,13,18)$ with a site energy difference of $ET−EO=0.91eV$⁠. The diffusion barriers were found to be 1.97 eV in the path from O to T and 1.06 eV in the reverse direction.⁷⁸ Same definition was followed to perform the NEB for HfTi alloy with Hf:Ti being 3:1 in this study. Four stable oxygen interstitial sites in HfTi alloy metal were found, and diffusion barriers in paths between them were calculated. In each path, three images were calculated using the NEB method to obtain the diffusion barrier height, the difference between the peak in energy and the endpoints (stable interstitial sites). Since the diffusion barrier is defined as the energy difference between peak and the endpoints along the path, site C, the site with lowest site energy from our calculations was chosen as the reference point. Tables I and II summarize the simulation results. It is observed that the minimal diffusion barrier occurs in the path from A to D with a value of 2.02 and 0.84 eV in the reverse direction, which is close to the values found in the pure Hf HCP metal. Our results suggest that Hf and HfTi metallic filaments have similar oxygen ion diffusion barriers.

Similar diffusion barriers of oxygen ion in both Hf metal and HfTi alloy metal systems indicate that the oxygen ion diffusion dynamics are same in both metallic systems as shown in Fig 7. Moreover, it has been reported that in HfO_x memristors, digital switching involves movement of a few atoms within a fast-switching time scale. During analog switching, pulses are applied in even shorter timescales such as pulse widths of milliseconds or nanoseconds range. Therefore, very few numbers of oxygen ions are involved during the analog temporal response. If the oxygen ions primarily move through the Hf or HfTi metal-rich CFs having similar diffusion barriers, only then the analog responses will be comparable.

In summary, HfO_x based memristors having a ∼5 nm HfO_x and Hf_xTi_yO_z amorphous oxide were fabricated. The analog switching of the fabricated devices were analyzed under identical pulsing conditions. The impact of measurement conditions on the key analog features such as linearity and off-resistance were assessed. The results suggest that although a small pulse width helps decrease the abrupt resistance increase at the first pulse, pulse amplitude has a pronounced impact on the resistance change. A smaller pulse amplitude decreases the first pulse effect and improves the linearity. This is likely because a small pulse amplitude causes a smaller change in the initial filament temperature. However, a larger pulse amplitude is also necessary to achieve a higher saturated resistance (R_off) and a larger memory window. Therefore, there is a trade-off between the saturated resistance and linearity. Moreover, although an improvement in the linearity is observed for the titanium doped HfO_x device, analog responses are comparable to the HfO_x device_. The DFT calculation verifies that the titanium addition in HfO_x decreases the oxygen ion migration barrier in the bulk oxide by almost ∼four times; however, the migration barriers are similar in the HfTi and Hf metallic systems. Therefore, the Hf and HfTi conducting filaments, not the bulk oxide, play the dominating role during the analog temporal response of HfO_x and Hf_xTi_yO_z devices.

See the supplementary material for the detailed fabrication method, characterization of the HfO_x and Hf_xTi_yO_z films, and specifics of the alpha parameter used to measure the linearity of the devices. Digital measurement results (forming, gradual reset, and stabilization), simulated temperature distribution during the analog temporal response, and standard distribution of the measured data can also be found in the supplementary material.

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 (NSF) (No. ECCS-2025462). This material is based upon the work supported by the Georgia Tech ECE Fellowship and National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650044.

The authors have no conflicts to disclose.

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