Tunability of voltage pulse mediated memristive functionality by varying doping concentration in SrTiO₃

Neuromorphic hardware is actively being researched for energy efficient computing applications with a large focus on emerging devices, such as memristors.^1,2 Memristive materials and devices^3,4 possess physical attributes that can be sculpted to yield analog resistance states, distinguishing them from the binary response exhibited by conventional electronic devices. Their ability to exhibit different resistance states may stem from a wide variety of origins, including changes in the orientation or magnitude of electric or magnetic polarization, phase transitions, and ionic motion. This wealth in mechanisms found in material classes that have been studied is manifested as different responses in, for example, switching times, endurance, and retention characteristics.¹ Implementation of memristive devices, which typically have a metal–insulator–metal structure, as memory elements in complementary metal–oxide–semiconductor (CMOS) devices or in-memory computing for non-von-Neumann applications are envisioned. The potential applications of memristive devices extend far beyond what can be realized using digital computing and they are also being investigated for data encryption^5,6 and in mobile communication,^7,8 where ultra-high density is not a requirement. However, this necessitates the scope of memristive attributes to widen, such as using the intrinsic variability of the resistance ratio over time or between cycles for security applications and true random number generators.⁹ 

Resistive switching in such devices can be studied using gradual voltage sweeps, which provides the most transparent insight at every point of a switching cycle. For practical applications, however, resistance changes brought about by applying voltage pulses are of significant importance for emulating low-power synaptic behavior. Spiking neural networks (SNNs) are thought to more closely resemble biological neural networks.¹⁰ Neurons do not constantly transmit information, but rather transmit information in the form of spikes. This sparse activity greatly contributes to the high energy efficiency of the brain.^11,12 This further amplifies the need for harnessing new attributes in memristive devices, for example, in the resistance change brought about by voltage pulses that can be used to emulate synaptic weight changes induced by the spiking behavior of neurons.

Memristors are typically devised of electrodes and a dielectric layer which may be insulating or semiconducting; depending on the exact nature of both materials, a vast variety of switching mechanisms and memristive functionalities have been identified.¹³ In oxide materials, filamentary switching is the most frequently observed. This often requires an initial forming step to create filaments in an insulating matrix,¹⁴ such as SrTiO_3.¹⁵ These materials often exhibit an abrupt switch from low to high resistance and a more gradual switch in the opposite direction. This is in contrast with the switching found in Nb-doped SrTiO₃ (Nb:STO) Schottky junctions, where the interfacial mechanism is dominant. The resistive switching is generally found without a required forming step and both switching directions are gradual and fully analog.^16,17 This mechanism has been detailed in, for example, Refs. 16 and 18. Intermediate cases are also possible in which the resistive switching is a combination of filamentary and interfacial effects, such as in oxygen-deficient SrTiO₃ films.¹⁹ 

In this work, we investigate memristive devices consisting of Co electrodes on semiconducting Nb-doped SrTiO₃ (Nb:STO) substrates, where the interfacial mechanism is dominant, with different dopant concentrations. We study resistive switching in dopant concentrations varying from 0.01 to 0.5 wt. % by either a continuous voltage sweep or by a train of voltage pulses. Varying the dopant concentration gives us the extra handle to design the potential profile across the interface, modifying the electric field across the Schottky interface and giving rise to differences in their transport as manifested in distinct changes to the high and low resistance states of the devices. We also model the interface to study the correlation between the electric field and the doping concentration.

Furthermore, we extend the characteristic determinant of memristive properties by studying the effects of resistive switching by applying single or multiple pulses. By changing the pulse times, we find that the reset switch, from low to high resistance, occurs faster than the reverse switch. We also find that the switching speed, in particular, the switch from high to low resistance, increases as the doping concentration increases. For higher doping concentrations, we observe that we can reliably and repeatedly switch between clearly distinguishable resistance states with minimal cycle-to-cycle variation. Applying a positive pulse gives rise to a low resistance state (LRS) while a negative pulse gives rise to a high resistance state (HRS), which can subsequently be read with a low amplitude voltage pulse of either positive or negative polarity. When a sequence of two pulses is applied, and the small voltage signal current is read after, we see that while the last pulse has the most significant influence on the current, both pulses influence the resistance state. This allows information to be encoded in a train of pulses in a meaningful way, which is required for SNNs. It also establishes the potential of such memristive devices beyond those used in storage and computing to new possibilities, such as in data encryption.

To fabricate the studied memristive devices, we used a two-step electron beam lithography protocol, described in Ref. 20, to create Co contacts on Nb:STO substrates of different doping concentrations in which the devices are electrically isolated from each other using Al₂O₃ (Fig. 1). The measurements shown in this Letter were measured on circular devices with radii of 1 µm and doping concentrations of 0.01, 0.1, and 0.5 wt. %, corresponding to carrier concentrations of 10^–19, 10^–20, and 5 × 10^–20cm³.²¹ Measurements were conducted using either a source measurement unit (SMU) or Waveform Generator/Fast Measurement Unit (WGFMU) of a Keysight B1500A Semiconductor Device Analyzer.

Figures 2(a) and 3(a) show the device response upon sweeping the voltage repeatedly between a set voltage of +2 V and a reset voltage of −3 V for doping concentrations of 0.5 and 0.01 wt. %, respectively. Similar measurements for 0.1 wt. % can be found in Ref. 20.

For the higher doping concentration (0.5 wt. %), stable switching between two clearly distinguishable states is observed with minimal cycle-to-cycle variation over the 1000 cycles shown. This is also represented by the blue and black symbols in Figs. 2(b) and 2(c), showing the current extracted at reading voltages of −0.5 and +0.3 V, respectively. The realized ratios are ∼10⁶ at −0.5 V and ∼2 × 10⁴ at 0.3 V. These ratios decrease to ∼7 × 10⁴ at −0.5 V and ∼4 × 10³ at 0.3 V when the doping concentration is lowered to 0.1 wt. %, as shown in Fig. S2 of the supplementary material.

From Fig. 3, it is apparent that for 0.01 wt. % doped Nb:STO, the switching is significantly different with the same (re)set voltages. The cycle-to-cycle variation is much more pronounced in the first few cycles and then levels off. There is almost no difference in resistance between the high and low resistance in the forward bias direction making it unfeasible to read in this regime. However, in the reverse bias, we can observe an opening in the current–voltage loop, but due to the low current in the reverse bias, there is a large region in which the current is below the measurement limit of the apparatus. These factors limit the reading voltages to higher reverse bias voltages in the current experiment. Figure 3(b) shows that even at −1 V the HRS is still not clearly readable. It is, however, observed from the first few cycles that the resistance ratio between the two states is ∼10. The spread in data for both the LRS and HRS is significantly larger than that observed in Figs. 2(b) and 2(c). While for the HRS this can partially be explained by considering the measurement resolution of the experimental apparatus, this is not the case for the LRS and indicates that this is an attribute of the device itself. This inherent stochasticity is a key requirement for memristive data encryption, where random current fluctuations within a small range are needed.⁹ 

Next, we study the resistive switching behavior brought about by voltage pulses of ∼100 ms. Each cycle consists of administering a +2 V set pulse followed by a reading pulse and a −3 V reset pulse followed by another reading pulse. The results of the 0.5 wt. % doping concentration are shown in Fig. 2(b) (green) for reading pulses of −0.5 V and (c) (red) read at +0.3 V. Again the cycle-to-cycle variation is minimal, albeit small decreases in the resistance ratios are observed, but the states remain clearly distinguishable. The results for 0.1 wt. %, shown in Fig. S1 of the supplementary material, reveal a similar scenario where the cycle-to-cycle variation is small and the resistance ratio is diminished compared to the voltage sweeps. The resistance ratios achieved upon the different measurement schemes as a function of doping concentration are shown in Fig. S2 of the supplementary material. Similar measurements, with a reading voltage of −1 V, were conducted for the 0.01 wt. % Nb:STO sample as shown in Fig. 3(c) and in this case, no stable switching is observed, which may be related to the use of a relatively high reading voltage. It is, however, clear that the spread in data points is significantly larger than for the higher doping concentration, highlighting again a greater degree of random fluctuations.

The waveforms used to establish the reset and set times are shown in Table I [(a) and (b)], respectively. To determine the set (reset) speed, a voltage of −3 V (+2 V) was applied to realize a high (low) resistance state. The small signal current was then measured using a low voltage pulse (read 1). This was followed by applying a +2 V (−3 V) pulse of varying time (1 μs–1 s). Finally, a second low voltage reading pulse (read 2) was used and the current during reads 1 and 2 were compared. More details are presented in Fig. S5 of the supplementary material. The measurement results are shown in Figs. S3 and S4 of the supplementary material and the results for doping concentrations of 0.1 and 0.5 wt. % are summarized in Table I; due to the small ratios and unreliable switching behavior, we could not accurately determine switching times for the lowest doping concentration.

For both doping concentrations, we observe asymmetric switching times, with the reset switching being faster than the set operation. The minimal reset switching time in both cases was longer than the minimum pulse times we could apply and hence we cannot comment on whether the reset time depends on the doping concentration. For the set time, on the other hand, we found that the more highly doped sample showed faster switching. Figures S3 and S4 of the supplementary material show that the change in resistance depends on the pulse width, with longer pulses giving rise to a greater change. This also explains why the resistance ratio is lower when using shorter voltage pulses rather than voltage sweeps, as seen in Fig. 2.

As a proof of principle of the possibility of encoding information in a train of pulses that can be interpreted by the memristive devices in a meaningful way, we applied two-pulse sequences and observed the output response at a low reading voltage after. The results for 0.5 wt. % are shown in Fig. 4 for four different combinations of pulses followed by reading voltages of (a) 0.3 V and (b) −0.5 V. The pulse durations are ∼100 ms with amplitudes of +2 V and −3 V and combinations thereof, as shown in Figs. 4(c)–4(e). The starting current magnitude is lowest when two negative pulses were applied. This is followed by the case where a positive pulse precedes a negative pulse, the starting current magnitude further increases when a negative pulse is followed by a positive pulse. Finally, the highest current value is observed when two positive pulses were applied. Noteworthy is that the appearance of four distinct states clearly shows that each pulse in the sequence contributes to the reading current. Another observation is that there are two distinct trends: one showing a small increase in current, seen for the two cases where the last pulse was negative and one that shows a small decrease in current, seen when the last pulse was positive. Hence, we can conclude that the rate of change is determined by the last pulse in the sequence while the resistance state is influenced by both the first and last pulse. The rate of change of the current is greatest when the reading pulse has the opposite polarity to the subsequent writing pulse; this likely arises due to a small writing effect induced by the continuous application of the reading voltage. Given that the resistance level is influenced by the pulse time, as can be seen in Figs. S3 and S4 of the supplementary material, these differences can be controlled by tuning the pulse timing. By increasing the pulse times, the influence of the last pulse on the resistance will be amplified; this can be used in potential applications where earlier parts of a sequence are not important, such as last digit recollection. Alternatively, more weight can be attached to earlier terms in the sequence by decreasing the pulse times; this will be useful for encoding information in a spike train.

The above-mentioned findings demonstrate the expansion of memristive functionalities beyond those applied, thus far, and obtained by tailoring the potential landscape at the interface. To understand the differences observed for the different doping concentrations, we have to consider how the electric field is influenced by doping. The dependence of the electric field on temperature, T, and distance from the interface, x can be described by²² 

where a and b are temperature dependent parameters with values of 2.47 × 10¹⁵ V²/m² and 1.40 × 10¹⁰ V/m at room temperature, respectively. The carrier concentration, N_D (estimated from Ref. 21) and the depletion width, W, depend on the doping concentration and are summarized in Table S1 of the supplementary material. The field dependence of the dielectric permittivity of SrTiO₃ is given by^22,23

Figure 5(a) shows how the electric field varies as a function of distance from the interface. The field is strongest at the interface and becomes zero at the edge of the depletion region. With increasing doping densities, the interfacial field strength increases and the depletion region decreases.

Due to the field dependence of the dielectric constant, the different electric field profiles will result in decreases in ε_r in the depletion regions depending on the doping concentration as shown in Fig. 5(b). The strongest reductions of the ε_r are present at the interface where the value is reduced by 22% (0.01 wt. %), 75% (0.1 wt. %), and 94% (0.5 wt. %). Finally, this influences the Schottky barrier profile, causing an increasingly steep profile with higher doping as shown in Fig. 5(c). With increasing doping concentration we observe (i) a significant increase in the current flow in reverse bias, (ii) a large increase in the hysteresis in reverse bias, (iii) the appearance of an observable hysteresis in forward bias, and (iv) a more symmetric current-voltage curve. By fitting the thermionic emission equation for the virgin device state, as shown in Fig. S6 of the supplementary material, we can determine the ideality factor, describing how well the electron flow can be described by thermionic emission. We opted to compare the virgin device states, before any switching events have taken place, to ensure any conclusions drawn are not influenced by previously conducted measurements. It is determined that the ideality factor increases with increasing doping concentration from 1.36 ± 0.06 (0.01 wt. %) to 2.59 ± 0.17 (0.5 wt. %) (Fig. S6 of the supplementary material). This indicates that at higher carrier concentrations there is an increasing contribution from other transport mechanisms. This is enabled by the decreasing Schottky barrier width, facilitating electronic tunneling through the barrier. This suggests that in the low resistance state, an increased contribution of tunneling gives rise to a change in the current in both forward and reverse bias. In lower doped devices, the Schottky barrier is wider and tunneling is less pronounced giving rise to almost no hysteresis in forward bias and a less pronounced reverse bias hysteresis. It is well accepted that there exist defect states at the interface;^16–18 when tunneling is an important transport mechanism, electrons will interact more strongly with these trap states. In reverse bias, electrons may become trapped in these states giving rise to an HRS; this is amplified when the doping concentration is higher. In addition, it has been shown that mobile defect migration can play an important role in mediating the switching. The increased electric field can facilitate the movement of defects, such as oxygen vacancies when the doping is increased. The increasing electric field with doping concentration is also responsible for the faster switching reported in Table I as the resistive switching process is field-driven.

Hence, by tuning the doping concentration, we can change the Schottky barrier profile and consequently influence the transport mechanisms. With a low doping concentration, the Schottky barrier is wider and thermionic emission is the dominant mechanism which gives rise to a relatively low current and a significant rectification of forward compared to reverse bias. Increasing the doping concentration leads to an increasingly narrowing barrier which is accompanied by an increase in tunneling and gives rise to an overall higher current flow, less rectification, and an increase in the resistance window in both bias directions. The increasing field with doping concentration, furthermore, gives rise to faster switching.

Memristors have already been used in integrated circuits for memory applications and have the potential for a wide range of other applications in many technologies. The specific requirements that a device should fulfill strongly depends on the application.^9,24 In some architectures, it may be beneficial to have a relatively high resistance in both states to limit the impact of a voltage drop in other parts of the circuit.⁹ This can easily be achieved using a substrate with a lower doping concentration. If, on the other hand, a particular application calls for a large memory window in which a multitude of states can be defined, a higher doping concentration is more suitable.

An important issue in memristive networks, such as crossbar arrays, is sneak path currents flowing through non-selected devices during reading and writing. To avoid this, selector devices may be required to isolate a specific memristive element. Such devices, which typically may be transistors or diodes, limit the scalability and significant efforts are made to avoid having such elements.^25,26 Different schemes have been implemented aiming to either increase the nonlinearity or asymmetry of the current voltage characteristics of memristive devices.²⁷ This presents a significant challenge in many types of memristors, especially in the low resistance state which often has a strong metallic character. Due to the strong diodic nature of the devices investigated here, they possess both a high degree of nonlinearity as well as asymmetry between forward and reverse bias. This characteristic is most pronounced in the lower doping concentration, making these devices highly suitable for acting as self-selectors.

In this work, we have demonstrated the ability to controllably influence resistive switching in Nb-doped SrTiO₃-based interface memristors using voltage pulses. The resistance can either be reliably switched between different and clearly distinguishable states by applying single pulses or a train of pulses can be used to encode information that can be interpreted by the memristive device by analyzing the small signal current after the pulses. We find that the switch from LRS to HRS, which occurs in the reverse bias, is faster than the switch from HRS to LRS. The switching speed is also found to increase with doping concentration, most clearly evident from the HRS to LRS transition under forward bias. We attribute these findings to the increased interfacial electric field found for higher doping concentrations. Our results highlight the suitability of Nb:STO memristors for a wide variety of applications, whereby the doping concentration can be used to optimize specific task-dependent device parameters.

See the supplementary material for additional experimental results and further details on the modeling.

A.G. was supported by the CogniGron Center, University of Groningen. Device fabrication was realized using NanoLab NL facilities. The authors acknowledge the technical support from J. G. Holstein, H. H. de Vries, A. Joshua, and H. Adema. They thank the members of the Spintronics of Functional Materials group for beneficial discussions.