Direct observation of delithiation as the origin of analog memristance in Li_xNbO₂

Functional oxide memristors have the potential to revolutionize neuromorphic computing, which aims to mimic the operation of biological brains using artificial circuits.^1,2 While neuromorphic systems can be implemented with traditional CMOS circuitry, this requires a large number of conventional transistors, resulting in significant power consumption and scalability issues.^3–5 By contrast, truly biomimetic circuits would lead to scalable, low-power processors capable of hardware-level autonomous learning, power-efficient image recognition, and other exciting possibilities.^6,7 Neuristor circuits based on functional oxide memristors have the potential to enable these truly biomimetic circuits. However, the resistive switching of these memristors is typically attributed to a complex combination of processes (e.g., redox reactions, ionic transport, and phase changes.),⁸ which are highly dependent on device architecture and are not yet fully understood.^9,10

Lithium niobite (Li_xNbO₂), which has been previously studied due to properties such as superconductivity,¹¹ has recently shown great potential for memristive applications.^12,13 Whereas traditional filamentary devices typically require the migration of O²⁻ ions to form narrow conductive channels and access discrete resistive states, the resistive states of Li_xNbO₂ are analog in nature and are thought to be modulated by a more uniform diffusion of Li⁺ ions throughout the active layer.¹⁴ This more uniform ion diffusion mechanism may help to overcome some of the major disadvantages of traditional memristors, such as the need for an initial preforming/electroforming process to breakdown or otherwise alter the as-deposited material before the device can function.¹⁵ In addition, many sources of device failure, such as thermal stress from conduction through nanoscale pathways, nonuniform O²⁻ ion clustering, or other failure modes,¹⁶ may be completely absent in these LiNbO₂-based devices. Further investigation of these LiNbO₂ memristors is therefore needed to fully characterize this promising memristive mechanism.

It has been proposed that the electronic properties of Li_xNbO₂ are highly dependent on the Li⁺ content and that a bias-induced Li-gradient could enable precise control of the resistive state.¹⁷ This bias-induced Li gradient was previously investigated across an annular LiNbO₂ device using spatially resolved in situ oxygen K-edge x-ray absorption spectroscopy (XAS),¹⁴ revealing gradual changes in the spectral lineshape across the active layer interpreted as lithium concentration variations. Recent advances in x-ray absorption simulations of the O K-edge¹⁸ have now presented an opportunity to confirm the predicted evolution of Li_xNbO₂ within these devices and accurately describe their operational mechanism.

In this paper, we benchmark the intrinsic material properties responsible for the analog memristive behavior of Li_xNbO₂. High-quality single crystals were grown using liquid phase electro-epitaxy (LPEE) and then chemically delithiated for direct comparison to atomistic modeling. Li_xNbO₂ single crystals with well-defined lithium concentrations were preferred over active layer thin films in order to disentangle the effects of Li content variation from other phenomenon. Soft and hard x-ray spectroscopy techniques, as well as first-principles x-ray spectroscopic simulations, were used to monitor the niobium coordination and electronic structure evolution of Li_xNbO₂. Using x-ray absorption spectroscopy, we were then able to confirm the depopulation of the Nb 4d$z2$ orbital upon Li⁺ ion extraction, considered responsible for the memristive behavior. The excellent agreement between the theory and experiment allows us to explain the electronic structure evolution of Li_xNbO₂ up to x = 0.5, i.e., degenerate p-type semiconductor regime (above which the Li_xNbO₂ is metallic). After reexamining previous in situ oxygen K-edge x-ray absorption measurements of Li_xNbO₂,¹⁴ we conclude that the analog memristive switching in the devices occurs within the degenerate p-doping regime rather than being associated with a full insulator-to-metal transition.

LiNbO₂ single crystals were grown using a liquid phase electro-epitaxy (LPEE) method. The LPEE growth method makes use of Nb₂O₅ (99.9%) and LiBO₂ (99.9%). The LiNbO₂ crystals were grown over a 24 h period and nucleated on a niobium rod at 1.1 V with a 10:1 LiBO₂ to Nb₂O₅ ratio. Some LiNbO₂ crystals were delithiated in a 37% HCl aqueous bath at room temperature for 24 h followed by a rinse with DI water and then dried with nitrogen. Other crystals were set aside to act as pristine references, while some large crystals were reserved for device fabrication. To create the memristor devices, 100 nm of Ti and 500 nm of Au were deposited on the large crystals using evaporation and then patterned into device contacts using a lift-off process. These volatile ring dot devices were then tested with IV sweeps. Initial scans were performed to find minimum programming voltage starting at 0.1 V and increasing in steps of 0.1 V, followed by a collection of data at minimum programming voltage.¹⁹ 

Some crystals were ball milled or ground manually using a mortar and pestle for powder measurements. X-ray diffraction (XRD) was performed on powderized LiNbO₂ using a Bruker D8 Advance diffractometer with Bragg-Brentano geometry and a Cu K_α source at Georgia Institute of Technology. Phase identification was performed using Bruker DIFFRAC.EVA software coupled with the PDF-2016 database. X-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) measurements were also performed on powderized LiNbO₂ to determine the effective Nb oxidation state in the bulk, as well as local electronic/atomic structure. The XANES and EXAFS were performed at beamline 20-BM of the Advanced Photon Source at Argonne National Laboratory in Lemont, IL (see Sec. I A of the supplementary material).

Soft and hard x-ray photoelectron spectroscopy (XPS and HAXPES), which have an effective probing depth of ∼4 nm (surface) and ∼15 nm (sub-surface), respectively, were performed on LiNbO₂ crystals to determine the Li content, Nb oxidation state, and the valence band electronic structure. In addition, x-ray absorption spectroscopy (XAS) measurements of the oxygen K-edge were performed in total electron yield (TEY) mode, which can probe up to 5 nm deep.²⁰ The HAXPES was performed at beamline I09 of the Diamond Light Source at the Harwell Science and Innovation Campus in Oxfordshire, UK, while variable photon energy XPS and XAS were performed at beamline 29-ID of the Advanced Photon Source at the Argonne National Laboratory in Lemont, IL. Some additional XPS was performed at the Analytical and Diagnostics Laboratory at Binghamton University, while additional XAS was performed at beamline 8 of the Advanced Light Source at the Lawrence Berkeley National Laboratory in Berkeley, CA (see Secs. I A and I B of the supplementary material).

Density functional theory (DFT) electronic ground state calculations at various Li concentrations were performed within the Vienna Ab Initio Simulation (VASP) package,²¹ (see Sec. I C of the supplementary material).The x-ray formalism of the core-hole approach for simulating the O K-edge in pristine and delithiated cases was performed within the ShirleyXAS + MBXASPY environment.^18,22–24 The DFT information of the x-ray final state was obtained using full core-hole (FCH) approach in which an electron is removed from the inner shell of a designated excited atom within a supercell. Therefore, the interaction between the core hole and the electron was not explicitly included via many-body approaches, such as the Feynman diagram technique, but was instead accounted for using a modified oxygen pseudopotential with one electron removed from the 1s orbital for the O K-edge. The excited electron was then added to the occupied electronic structure. Next, the modified electronic system was relaxed to its ground state using DFT. Finally, the initial-state and final-state DFT orbitals and energies were provided as input for the MBXASPY software codes to produce the determinant spectra. We utilized a 1 × 1 × 1 supercell structure for the rutile and BCT NbO₂ calculations, as well as the Li_0.5NbO₂. The fully lithiated LiNbO₂ was calculated using a 3 × 3 × 1 supercell. All supercells were chosen such that their dimensions were large enough to avoid effects due to neighboring periodic images.

A representative pinched hysteresis IV curve taken on a high-quality, single crystal LiNbO₂ ring dot memristor is shown in Fig. 1(a), consistent with previous reports of analog memristive behavior for LiNbO₂.^19,25 Since the crystals show similar IV curve responses to LiNbO₂ devices grown via both molecular beam epitaxy^12,14 and sputter deposition,²⁶ we consider the underlying mechanism to be inherent to the material rather than the device processing. As such, chemically delithiated LiNbO₂ single crystals should display the same electronic structure modifications as those electrochemically induced in the thin film devices.

As shown in Fig. 1(b), the chemical potential (μ) is expected to lower into the Nb 4d$z2$-derived valence band as lithium is extracted, thereby favoring hole formation (p-type). Although the Nb–O bond length and O K-edge XAS lineshape are reportedly sensitive to d$z2$ occupancy,^14,17,27 direct measurement of Li concentration combined with accurate simulations of the O K-edge XAS are required to fully verify the electronic structure evolution of Li_xNbO₂ and understand the memristive mechanism.

To evaluate the quality of our pristine LiNbO₂ crystals, powder x-ray diffraction (XRD) was performed. Figure 2(a) shows the hexagonal P6₃/mmc crystal structure (inset) and XRD pattern of our LiNbO₂ powder with the reflections indexed with PDF 029-0815. The XRD pattern predominantly shows the expected structure with some negligible contribution from LiNbO₃ impurities, which were likely introduced during the powder preparation process. XPS studies confirmed that these impurities were mainly limited to the crystal surface and could be reduced by exposing fresh crystal surfaces using a razor blade (see Sec. II A of the supplementary material). Henceforth, all results shown were taken on carefully cleaved samples and/or measured using bulk-sensitive techniques to avoid spectral contamination from over-oxidized surface species.

Bulk-sensitive extended x-ray absorption fine structure (EXAFS) of lithium niobite ground pellets was performed to confirm the local atomic structure, as shown in Fig. 2(b). The data were fit using the LiNbO₂ crystal structure from the materials project database (ICSD-451)²⁸ (see Sec. II B of the supplementary material). The first peak around 1.654 Å corresponds to the Nb–O interaction in the first coordination shell, while the second peak around 2.596 Å is due to the Nb–Nb interaction in the second coordination shell. Excellent agreement between the experimental data and theory is achieved up to ∼5 Å.

HAXPES was then employed to confirm the bulk Nb oxidation states of our lithium niobite crystals, as shown in Fig. 2(c). NbO₂ and Nb₂O₅ thin films are used as Nb⁴⁺ and Nb⁵⁺ oxidation state references. The Nb 3d spectra consists of two distinct spin-split peaks (3d_5/2 and 3d_3/2), with the energetic positions of the primary 3d_5/2 peak at 204.1 eV, 206.7, and 207.3 for Nb³⁺, Nb⁴⁺, and Nb⁵⁺, respectively.^15,29–34 Our pristine LiNbO₂ displays no evidence of Nb⁴⁺; however, it does display a weak Nb⁵⁺-like component consistent with there being an over-oxidized LiNbO₃ surface. Taken together, the XRD, EXAFS, and HAXPES results confirm the overall phase purity of our LiNbO₂ crystals.

The effect of chemical delithiation on the electronic structure of LiNbO₂ was studied via more surface sensitive XPS and XAS, as shown in Fig. 3. The lower photon energy (hν = 700 eV) used for the XPS results in a higher Li 1s photo-ionization cross section than is possible with a traditional laboratory-based XPS system, thus improving our sensitivity to variations in Li content associated with delithiation (see Sec. II C of the supplementary material). After the crystal was soaked for 24 h in an HCl bath, a drop in the Li 1s peak intensity is observed in Fig. 3(a), associated with a reduction in bulk Li content. This delithiation is accompanied by a compensating change to a higher Nb oxidation state observed in both the Nb 4s and 3d core regions, as well as a reduced Nb–O bond length in EXAFS fitting and a shifted Nb K-edge XANES spectra (see Sec. II B of the supplementary material). This delithiation also results in the depopulation of Nb states near the Fermi level, as shown in Fig. 3(b). Importantly, the lack of a clear Fermi edge upon delithiation indicates that the material stays within p-type semiconductor regime, i.e., not fully metallic.

Figure 3(c) shows experimental O K-edge spectra taken using TEY mode XAS and simulations of the O K-edge calculated using the x-ray formalism of the core-hole approach.²² One feature that clearly changes with lithium content is a pre-edge feature located around 1–2 eV, which is found to increase in intensity with delithiation. While simulations show a complete lack of this pre-edge feature at 100% lithiation, our pristine experimental spectra still displays some weight at this energy, indicating that the pristine single crystals may not possess a 100% lithium concentration. This is somewhat expected, considering our LPEE growth requires dissolution and cleaning in a DI water bath, and DI water has been previously reported to remove 10%–11% of the lithium from LiNbO₂.³⁵ It is also important to note that our O K-edge lineshapes are in agreement with those previously reported by Greenlee et al. from spatially resolved in situ O K-edge XAS of LiNbO₂ devices. This indicates that perfectly stoichiometric LiNbO₂ is not necessary to achieve a memristive response.¹⁴ Additionally, the trends Greenlee et al. observed across their device from the positive to negative electrode match our observed changes with delithiation, confirming that changing Li content produces the observed analog memristive response.

Additional computational methods were used to qualitatively estimate the regime of p-type doping observed in our samples. Figure 4 shows the projected density of states of Li_xNbO₂ as a function of Li content. Starting with the stoichiometric x = 100% case, the calculations predict a ∼1.5 eV semiconducting gap generated by the Nb d manifold splitting. Although the experimentally observed gap is closer to 2 eV,¹⁷ these results are consistent with other theoretical predictions^27,36 and the general tendency of LDA methods to underestimate gap strengths.

Looking at the first principles simulations for delithiated cases (x < 100%), we can now clarify the electronic response without assuming a rigid band model. As Li is driven out of the system, there is a clear autodoping effect where the top of the valence band is heavily p-doped as previously reported;¹⁷ however, the band curvature is still high at marginal delithiation and only flattens out upon deeper delithiation. The onset of a divergent dielectric function, meaning the onset of metallicity, is not predicted to occur until nearly 50% delithiation (see Sec. II D of the supplementary material). This indicates that the formation of light hole states, namely, the depopulation of d$z2$ observed in operando O K-edge XAS,¹⁴ can give rise to the low field analog memristive response before truly metallic behavior sets in.

By comparing the measured valence band spectra [Fig. 3(b)] to simulations and operando XAS studies of active layers, we conclude that the memristive response is due to lithium variation within the p-type semiconductor (marginal delithiation) regime. We also conclude that the memristive response does not require the metallic phase (Fig. 4), suggesting the dominant turn-on effect is instead the formation of light p-carriers. In that regard, although the migration of lithium ions within LiNbO₂ is not confined within preformed filaments, the memristive mechanism is similar to that of some filamentary memristors investigated using XAS wherein the migration of oxygen ions modulates the conductivity of the semiconducting active layer.^16,37 However, in the case of LiNbO₂, the more uniform Li diffusion throughout the active layer results in a much more gradual (analog) conductivity response than is observed in traditional filamentary memristors.

In conclusion, the analog memristive behavior observed in Li_xNbO₂ single crystals has been investigated using a variety of experimental and theoretical techniques. We show intrinsic memristive behavior in lithium niobite phase-pure single crystals and use chemical delithiation of these crystals to benchmark the observed bias-induced electronic structure changes. We show that removal of Li⁺ oxidizes the Nb and thus depopulates the top Nb d-states within the valence band, facilitating the onset of p-type conduction prior to metallicity. This work clarifies that the field driven Li-ion motion inherent to Li_xNbO₂ is a viable analog switching mechanism that does not require any complex interfacial effects or preforming/electroforming to function.

See supplementary material for further details on the experimental and theoretical methodologies, as well as additional supporting data including EXAFS fitting results, XPS taken at multiple photon energies, and calculations of the dielectric tensor as a function of Li content.

This material is based on the work supported by the Air Force Office of Scientific Research under Award No. FA9550–18–1–0024. Galo J. Paez acknowledges doctoral degree grant support from the Fulbright Foreign Student Program (Grant No. E0565514), and Keith Tirpak was supported by a NSF-REU (Grant No. NSF DMR-1658990). We acknowledge Diamond Light Source for time on Beamline I09 under Proposals SI20647. This research used resources of the Center for Functional Nanomaterials and the National Synchrotron Light Source II, which are U.S. Department of Energy (DOE) Office of Science facilities at Brookhaven National Laboratory, under Contract No. DE-SC0012704. This research used resources of the Advanced Light Source and the Molecular Foundry, which are U.S. DOE Office of Science facilities at Lawrence Berkeley National Laboratory under Contract No. DE-AC02-05CH11231. This research used resources of the Advanced Photon Source, a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by the Argonne National Laboratory under Contract No. DE-AC02-06CH11357; additional support by the National Science Foundation under Grant No. DMR-0703406 is also acknowledged.