Analog TaOx/HfOx ReRAM

• Analog TaOx/HfOx ReRAM is a bilayer resistive switching device that leverages oxygen vacancy redistribution and defect modulation for gradual, accumulative conductance updates.
• Combined ab initio, reactive molecular dynamics, and analytical models reveal that filament formation in HfOx and oxygen exchange with TaOx are key to device performance.
• System-level demonstrations show these devices enable multi-level states with low programming noise and high accuracy in matrix-vector operations for analog computing.

Analog TaOx/HfOx ReRAM denotes a class of bilayer valence-change resistive switching devices in which a tantalum oxide layer is coupled to HfOx so that conductance is modulated through oxygen-defect redistribution, electro-thermal confinement, and filament-interface coupling rather than by a strictly abrupt two-state transition. Across ab initio interface studies, reactive molecular dynamics, analytical transport models, and BEOL-integrated hardware, the recurring physical picture is a conductive path initiated in HfOx and shaped by a TaOx region that acts as an oxygen reservoir, an electric-field and temperature confinement layer, and a defect-density modulator supporting gradual, accumulative, bidirectional updates (Honet et al., 2024, Lahkar et al., 30 May 2025, Falcone et al., 17 Sep 2025).

1. Material realizations and device architectures

The TaOx/HfOx platform appears in several structurally distinct forms. At the most idealized level, interface-specific density-functional calculations model cubic TaO/HfO2 and TiO/HfO2 bilayers with CMO[110]/HfO2[110] interfaces, two-probe transport geometry, and a central region containing 68 atoms. In that study, TaO, TiO, and HfO2 were represented by cubic phases with relaxed lattice parameters of 4.508 Å, 4.294 Å, and 5.077 Å, respectively, and oxygen-rich CMO configurations were generated by adding four oxygen atoms in nine distinct geometries denoted FO1–FO9 (Honet et al., 2024).

More device-realistic studies use amorphous bilayers. Reactive molecular dynamics on TaOx/HfO2-based ReRAMs modeled an amorphous Ta2O5 layer representing TaOy on top of amorphous HfO2, with a 5 nm functional bilayer and two 1 nm amorphous Ta2O5 regions serving as frozen electrodes. The corresponding experimental architecture was described as a conductive TaOx layer on top of an oxygen-rich amorphous TaOy interlayer above amorphous HfO2 between inert TiN electrodes, with a total stack thickness of approximately 25 nm and each functional dielectric layer in the 2–4 nm range (Lahkar et al., 30 May 2025).

At array level, BEOL-integrated analog CMO/HfOx cells have been reported in 1T1R form on 130 nm and 350 nm CMOS nodes. One all-in-one analog AI platform used a 20 nm TiN bottom electrode, 4 nm HfOx deposited by PEALD at $300\,^\circ\mathrm{C}$, a 20 nm sputtered CMO layer, and a 20 nm TiN + 50 nm W top electrode on metal-8 of a 130 nm CMOS node; the device area was $12\times 12\ \mu\mathrm{m}^2$. That work did not disclose the exact CMO composition, but explicitly related its behavior to TaOx/HfOx bilayers through prior literature and transport modeling (Falcone et al., 6 Feb 2025). A separate ONN demonstration used BEOL-integrated CMO/HfOx 1T1R cells with TiN bottom electrodes, ALD-grown sub-stoichiometric HfOx, a conductive metal oxide layer, and TiN/W top metallization, fabricated from 200 nm to $2\ \mu\mathrm{m}$, with $2\ \mu\mathrm{m}$ cells used experimentally (Choi et al., 18 Mar 2025).

This architectural spread is significant because reported analogity depends strongly on phase choice, stoichiometry, and the role assigned to the Ta-containing oxide. In idealized cubic TaO/HfO2, the key variable is interface connectivity of an atomically thin vacancy filament. In amorphous TaOx/TaOy/HfO2, the key variable becomes defect confinement and electro-thermal shaping inside the upper oxide.

2. Atomistic mechanisms of switching and analog conductance

In the ab initio TaO/HfO2 study, filamentary conduction was introduced by removing one oxygen atom per HfO2 layer in the central region, producing an atomically thin diagonal vacancy chain across HfO2. That filament reduced the computed zero-bias resistance from approximately $1.55\times 10^{30}\ \Omega$ to $1.71\times 10^{4}\ \Omega$ in TaO/HfO2, with a connected electron-localization-function path of approximately $0.5$ across HfO2. Oxygen excess in the CMO then modulated resistance through two distinct mechanisms: degradation of the HfO2 filament path itself, and formation of an interface bottleneck when the HfO2 conductive path no longer connected to an intermediate-ELF region in the CMO. Within that model, TaO/HfO2 produced two regimes, approximately $10$–$20\ \mathrm{k}\Omega$ and $50$–$12\times 12\ \mu\mathrm{m}^2$0, with an HRS/LRS ratio of approximately $12\times 12\ \mu\mathrm{m}^2$1, whereas TiO/HfO2 showed a continuous spectrum of low, intermediate, and high resistances with HRS/LRS ratio approximately $12\times 12\ \mu\mathrm{m}^2$2 (Honet et al., 2024).

Reactive molecular dynamics on TaOx/HfO2 forming refined that picture by separating electric-field-driven nucleation from thermally activated growth. Under applied bias, tantalum ions exhibited the largest displacement, followed by hafnium ions, while oxygen ions responded only minimally. The result was a tantalum-depleted, oxygen-rich zone near the positive top electrode and oxygen-vacancy clustering near the negative HfO2-side cathode, where the conductive filament nucleated. A threshold between 0.6 V and 1.2 V was required to initiate vacancy clustering in a 5 nm bilayer over 500 ps; below that threshold, temperature increased ionic mobility but did not nucleate the filament. Once nucleated, growth proceeded locally at the filament edge through thermally activated generation and stabilization of oxygen vacancies, while the anode-side ionic segregation partially shielded the bulk dielectric from the applied field (Lahkar et al., 30 May 2025).

Taken together, these studies identify two coupled switching loci. One is the vacancy-rich conductive path in HfO2, especially near the cathode. The other is the TaOx-side interfacial or near-interfacial region, where oxygen redistribution can either preserve a low-resistance connection or introduce a bottleneck. This suggests that analogity in TaOx/HfOx is not a generic consequence of “having a filament,” but of how the filament terminates into, and exchanges oxygen with, the TaOx side of the stack.

3. Transport formalisms and compact physical descriptions

The first-principles transport calculations used zero-bias NEGF and the Landauer expression

$12\times 12\ \mu\mathrm{m}^2$3

with finite-bias current written for completeness as

$12\times 12\ \mu\mathrm{m}^2$4

Within that framework, resistance changes were read directly from transmission at the Fermi level and interpreted through ELF connectivity rather than from explicit band offsets or work functions, which were not reported (Honet et al., 2024).

The analytical model developed specifically for analog TaOx/HfOx ReRAM describes current transport in the TaOx region by trap-to-trap tunneling in a defect sub-band and describes switching as modulation of defect density inside a half-spherical TaOx “dome” above the HfOx filament. The electron current is written as

$12\times 12\ \mu\mathrm{m}^2$5

with extracted parameters $12\times 12\ \mu\mathrm{m}^2$6, $12\times 12\ \mu\mathrm{m}^2$7, $12\times 12\ \mu\mathrm{m}^2$8, and $12\times 12\ \mu\mathrm{m}^2$9, $2\ \mu\mathrm{m}$0, $2\ \mu\mathrm{m}$1. Ionic transport of oxygen vacancies is treated by an analogous hopping expression,

$2\ \mu\mathrm{m}$2

with $2\ \mu\mathrm{m}$3, $2\ \mu\mathrm{m}$4, $2\ \mu\mathrm{m}$5, and $2\ \mu\mathrm{m}$6. In this model, the low thermal conductivity and modest conductivity of TaOx confine both electric field and Joule heating to the TaOx dome, making conductance updates gradual and volumetric rather than gap-closure dominated (Falcone et al., 17 Sep 2025).

The broader CMO/HfOx array model used for BEOL hardware adopts the same electrothermal logic at a less material-specific level. Current is described by Mott–Gurney hopping, while local field and temperature are computed from

$2\ \mu\mathrm{m}$7

The CMO conductivity was modeled as $2\ \mu\mathrm{m}$8 in the post-forming low-field regime and $2\ \mu\mathrm{m}$9 after defect redistribution, consistent with the view that analog state evolution corresponds to radial modulation of defect density in the upper conductive oxide rather than simple binary rupture in HfOx (Falcone et al., 6 Feb 2025). The forming simulations based on CTIP + EChemDID add a complementary atomistic description of how local potentials propagate through evolving conductive clusters under bias (Lahkar et al., 30 May 2025).

4. Programming behavior and reported analog metrics

At array level, the most advanced CMO/HfOx BEOL platform reported reliable resistive switching with voltage amplitudes below 1.5 V, more than 32 nonvolatile stable states in a conductance window of approximately $2\ \mu\mathrm{m}$0–$2\ \mu\mathrm{m}$1, and 35 representative levels without overlap during programming in closed loop. With a 0.2% acceptance range around $2\ \mu\mathrm{m}$2, the programming noise was below $2\ \mu\mathrm{m}$3; with a 2% acceptance range it was below $2\ \mu\mathrm{m}$4; and the discussion reported record-low programming noise down to $2\ \mu\mathrm{m}$5. Forming was extracted at approximately $2\ \mu\mathrm{m}$6 with $2\ \mu\mathrm{m}$7, average convergence required approximately 11 pulses per state for 2% acceptance and approximately 89 pulses for 0.2% acceptance, and the average relaxation error after 1 hour was approximately $2\ \mu\mathrm{m}$8 (Falcone et al., 6 Feb 2025).

The ONN hardware demonstration used generic CMO/HfOx cells as resistive couplers and showed gradual analog programming through identical 60 ns pulses: partial SET with $2\ \mu\mathrm{m}$9, partial RESET with $1.55\times 10^{30}\ \Omega$0, and 300 pulses per programming cycle in each direction in the example shown. Across 25 devices, the mean forming voltage was $1.55\times 10^{30}\ \Omega$1 with standard deviation $1.55\times 10^{30}\ \Omega$2. Active couplers were pre-programmed to approximately $1.55\times 10^{30}\ \Omega$3, unused devices were kept unformed at approximately $1.55\times 10^{30}\ \Omega$4, and retention of programmed couplings was verified for more than two months (Choi et al., 18 Mar 2025).

A related Ta/HfO$1.55\times 10^{30}\ \Omega$5/Mo single-cell device, although not an explicit TaOx/HfOx bilayer, is relevant because the switching was attributed to oxygen-vacancy redistribution with Ta acting as a strong oxygen getter or reservoir and likely forming an interfacial TaOx layer. That device showed bipolar analog conductance modulation, long-term potentiation under $1.55\times 10^{30}\ \Omega$6 pulses, long-term depression under $1.55\times 10^{30}\ \Omega$7 pulses, stable HRS/LRS over 3000 reads at $1.55\times 10^{30}\ \Omega$8, $1.55\times 10^{30}\ \Omega$9, and paired-pulse facilitation fitted by $1.71\times 10^{4}\ \Omega$0 with $1.71\times 10^{4}\ \Omega$1 and $1.71\times 10^{4}\ \Omega$2. Direct spectroscopic confirmation of interfacial TaOx was not provided in that work (Karatas et al., 2024).

5. System-level roles in analog computing

The main system-level motivation for analog TaOx/HfOx-type ReRAM is in-memory matrix computation and online learning. In the BEOL CMO/HfOx accelerator, matrix-vector multiplication follows the crossbar relation

$1.71\times 10^{4}\ \Omega$3

with a linear conductance-to-weight mapping. Hardware-aware simulation of a $1.71\times 10^{4}\ \Omega$4 tile gave RMSE of approximately 0.06 at 1 s after programming and approximately 0.2 at 10 years, while on-chip training with AGAD reached 96.9% accuracy on MNIST versus 98.3% for the floating-point baseline. Open-loop training characterization yielded an average of 22 device states, symmetry-point skew of approximately 61%, and NSR of approximately 90%, identifying symmetry rather than state count as the dominant training bottleneck in that platform (Falcone et al., 6 Feb 2025).

The ONN demonstration mapped six programmed CMO/HfOx couplers into a $1.71\times 10^{4}\ \Omega$5 ring-oscillator network for associative memory. Positive coupling produced in-phase locking and negative coupling anti-phase locking, with synchronized operation at approximately 8.6 kHz in the shown example. Horizontal, vertical, and diagonal $1.71\times 10^{4}\ \Omega$6 patterns were retrieved correctly, and phase locking occurred within one oscillation period, approximately $1.71\times 10^{4}\ \Omega$7–$1.71\times 10^{4}\ \Omega$8 at 8.6 kHz (Choi et al., 18 Mar 2025).

Within the broader filamentary TaOx class, crossbar co-design studies have shown why such devices remain attractive for training accelerators. A multiscale analysis of a TiN/Ta/TaOx/TiN analog device reported approximately $1.71\times 10^{4}\ \Omega$9, a $0.5$0 energy and $0.5$1 latency advantage over a comparable digital-ReRAM block, and a $0.5$2 energy and $0.5$3 latency advantage over an SRAM-based accelerator, while also showing that accuracy loss is dominated by state-dependent update nonlinearity and asymmetry rather than by stochasticity alone (Marinella et al., 2017). For TaOx/HfOx bilayers, the implication is that device-level symmetry control and update linearity are as important as raw state count.

6. Variability, interpretation limits, and unresolved questions

Several limitations recur across the literature. The ab initio interface study used cubic HfO2 for interface tractability even though monoclinic HfO2 is the most stable polymorph, and its GGA-PBE treatment underestimates oxide band gaps; only zero-bias conductance was computed, and the use of Fermi–Dirac broadening at 1000 K can broaden features near $0.5$4. The reactive MD work operated on hundreds-of-picoseconds timescales, used frozen electrodes, did not solve Joule heating self-consistently with current flow, and inferred conduction from undercoordinated cation networks rather than from explicit electronic transport (Honet et al., 2024, Lahkar et al., 30 May 2025).

Experimental hardware brings additional interpretive constraints. In the all-in-one AI platform and ONN demonstration, the active layer was described generically as CMO/HfOx and the exact CMO composition was not disclosed; the relevance to TaOx/HfOx is therefore partly indirect, established through cited TaOx/HfOx physics and benchmarking rather than by direct compositional identification inside those arrays. In the all-in-one platform, relaxation dominates long-term inference error, while IR-drop becomes the dominant error source in larger arrays such as $0.5$5 (Falcone et al., 6 Feb 2025). In the ONN hardware, detailed endurance, RTN, and large-scale variability statistics were not reported (Choi et al., 18 Mar 2025).

Adjacent HfOx-array studies clarify which stability problems are likely to matter for TaOx/HfOx as well. A 1 kbit HfOx analog RRAM array showed that the coefficient of variation of the temperature coefficient $0.5$6 depended strongly on conductance range: 5.48% in the 12.5–25 $0.5$7 range, 16.30% in 25–50 $0.5$8, and 32.62% in 50–100 $0.5$9. Under a two-layer perceptron for MNIST, compensation improved recognition accuracy from 79.8% to 89.6% at 400 K (Xu et al., 2021). A separate 64-cell 1T1R HfOx array showed that a fully digital, relaxation-aware method based on erase-width modulation and a 5 s verify delay could realize four non-overlapping levels at 1000 s, and explicitly stated that the same principle should transfer to TaOx with process-specific retuning (Erfanijazi et al., 2023). A plausible implication is that high-quality analog TaOx/HfOx operation depends not only on achieving intermediate states, but on selecting conductance windows and pulse schemes that suppress fast relaxation and temperature-induced dispersion.

The central unresolved issue is therefore not whether TaOx/HfOx can switch analogically, but under what material and electro-thermal conditions it does so reproducibly. Idealized TaO/HfO2 calculations emphasize binary-like separation in stable Ta-containing interfaces, whereas amorphous bilayer simulations, analytical models, and BEOL hardware emphasize localized cathode nucleation, TaOx-side defect modulation, and multi-level conductance evolution. The literature collectively indicates that analog TaOx/HfOx ReRAM is best understood as a controlled interfacial-defect system in which HfOx filament formation, TaOx oxygen exchange, and electro-thermal confinement must be co-optimized rather than treated as separable phenomena.