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From Processing to Functionality: Engineering Accessible Material States in Cu-Embedded SiO$_x$ Memristive Devices

Tobias Gergs, Rouven Lamprecht, Sahitya Yarragolla, Ole Gronenberg, Luca Vialetto, Hermann Kohlstedt, Thomas Mussenbrock, Jan Trieschmann

arXiv:2609.30047v1cond-mat.mtrl-scics.LGphysics.plasm-ph

TL;DR

Predictively linking deposition conditions to device functionality remains an open challenge, including the relationship among deposition, atomistic defects, Cu redistribution, and macroscopic response. This paper combines complementary reverse- and forward-engineering approaches to connect those scales, and frames functionality as emerging through a probabilistic cross-scale cascade rather than a deterministic process-to-performance mapping.

Abstract

from arXiv · show

Resistive switching in oxide-based devices is widely governed by stochastic defect processes, yet a predictive link between fabrication conditions and functional behavior remains elusive. Here, we establish a multiscale framework connecting plasma-defined deposition conditions to macroscopic device functionality in sputtered SiO$_x$/Cu/SiO$_x$-based systems. By combining large-scale statistical analysis of more than 50,000 experimentally characterized devices with physics-based plasma and atomistic simulations, we show that device behavior does not emerge from deterministic process-to-performance mappings, but from a probabilistic cascade spanning defect formation, defect-state evolution, and functional-regime emergence. Data-driven clustering reveals a continuous functional state space composed of operational switching types, while inverse modeling identifies the reconstructed oxygen-vacancy density as an effective latent descriptor capturing the combined influence of structural disorder and defect topology. This latent descriptor is strongly coupled to both Cu redistribution and electrical response, linking otherwise hidden material properties to observable device characteristics. Furthermore, macroscopic switching behavior is argued to arise from ensemble integration across spatially heterogeneous subdomains, providing a physical explanation for the pronounced variability of large-area devices. These findings shift the perspective from deterministic defect engineering toward probabilistic defect-state design and establish a physically grounded framework for understanding and controlling functional variability in such oxide-based systems, such as memristive or resistive-switching devices.

I. INTRODUCTION

The introduction frames a multiscale challenge: linking deposition conditions and atomistic defect formation to macroscopic device functionality in systems whose behavior is stochastic and spatially heterogeneous. It presents complementary reverse- and forward-engineering paths as a way to connect process conditions, material formation, and device response.

Resistive switching in oxide-based memristive devices has attracted extensive interest

  • Stochastic defect processes and small local variations can produce large changes in device behavior, leaving deposition-to-functionality relationships difficult to predict.The unresolved challenge spans deposition conditions, internal defect states, and macroscopic functionality.Source: Resistive switching in oxide-based… · p. 3
  • The multiscale gap includes connecting reactor-scale plasma descriptions to intermediate device scales while retaining atomistic material variation.The intermediate device scale is described as µm–mm, and extending existing descriptions across it remains an open challenge.Source: Resistive switching in oxide-based… · p. 3

influence the emergence of distinct electrical response characteristics across these systems

  • The paper addresses the unclear relationship among deposition conditions, atomistic defects, post-deposition Cu redistribution, and macroscopic functionality with complementary engineering pathways.Reverse engineering reconstructs internal states from device behavior, while forward engineering models how growth conditions produce material structure and defect states.Source: influence the emergence of distinct… · p. 5
  • Together, the two pathways connect processing conditions to atomistic material formation and macroscopic device functionality.The framework combines device characterization and device-level simulations with plasma and atomistic simulations.Source: influence the emergence of distinct… · p. 5

II. RESULTS

Statistical analysis organizes device responses into emergent switching regimes and relates their populations to process conditions and reconstructed defect states. The results describe a continuous functional landscape, with process parameters modulating regime populations rather than specifying individual switching states.

A. Emergent switching regimes and functional state space

  • The reconstructed switching landscape contains 1,156 SOM variability clusters, organized into seven emergent switching regimes with distinct electrical-response classes.The U-matrix shows related responses in contiguous low-distance regions and functionally distinct domains across high-distance boundaries.Source: A. Emergent switching regimes and… · pp. 6–7

porting both the statistical robustness and physical interpretability of the derived regime

  • The regimes form a continuous stochastic landscape rather than strictly discrete categories, with mixed-characteristic transition zones between neighboring domains.Capacitive-like switching is strongly segregated by pronounced topological boundaries, marking it as a distinct operational regime.Source: porting both the statistical… · p. 8

B. Physics-informed inference of latent defect state landscapes

  • Device variability reflects a low-dimensional latent defect-state structure reconstructed through physics-informed inverse modeling of experimental I–V data and device simulations.The analysis identifies wafer radius, sputtering power, and deposition time as the three most influential process variables; substantial variability persists within and across wafers at identical nominal settings.Source: B. Physics-informed inference of… · p. 8
  • Regime populations depend on wafer position and deposition conditions, while substantial within-wafer variability indicates a stochastic contribution to switching behavior.Resistive-device fractions decrease with deposition time across conditions, while memristive and capacitive fractions show different trends.Source: B. Physics-informed inference of… · p. 8

regimes exhibit complementary, power dependent behavior: increasing deposition time shifts

Together, these observations indicate that process conditions do not deterministically

  • Across the seven regimes, Cu density and oxygen-vacancy density are correlated, indicating that they follow a shared defect-state trajectory rather than independent variation.The reconstructed regime representations are obtained from device-level simulations that reproduce corresponding I–V characteristics.Source: Together, these observations indicate… · p. 9

exponential dependence (cf. line plot in Figure 6),

Reconstructed oxygen-vacancy landscapes identify wafer position as the dominant axis of defect-state variability, with deposition power shaping radial defect accumulation. Plasma simulations also reveal radial changes in composition and ion conditions that provide physical context for the reconstructed landscapes.

exponential dependence (cf. line plot in Figure 6),

principal defect state coordinate in the following analysis. By weighting the regime-specific

  • Wafer position is the dominant determinant of defect-state variability: vacancy densities remain low and similar near the center, then rise nonlinearly toward the edge.The central region extends approximately to 20–25 mm radius.Source: principal defect state coordinate in… · pp. 10–11

This radial defect-density trend is consistent with the observed distribution of switching

125 W is associated with more resistive behavior. The predominance of memristive-family

  • Power regulates where edge-directed defect amplification begins and how severe it becomes: at 125 W, the radial defect increase emerges near 20 mm and reaches substantially higher edge densities than at 200 W.At 200 W, comparable amplification shifts to approximately 35 mm and remains significantly attenuated; deposition time acts as a secondary modulation of edge defect accumulation, particularly under low-power conditions.Source: 125 W is associated with more… · p. 11

To identify the physical mechanisms underlying the reconstructed defect state landscapes,

O atoms (due to O2 electron impact dissociation) and O+

  • Ar+ flux stays approximately constant to 20 mm radius before falling linearly toward zero at the edge, while ion energy falls from 25–27 eV centrally to up to 17 eV at the edge.Electron-induced heating is considered unlikely to be the primary origin of the structural modifications, though electron processes may contribute to short-lived local relaxation.Source: O atoms (due to O2 electron impact… · pp. 12–13

Together, these spatially varying compositional and energetic growth conditions define

Plasma-defined growth conditions produce composition-dependent atomistic responses, while device functionality emerges through a probabilistic cascade rather than a deterministic process-to-performance mapping. The simulations connect these responses to defect populations and structural changes across SiOx compositions.

Together, these spatially varying compositional and energetic growth conditions define

  • Substrate-specific plasma conditions define ion bombardment, but simulations underestimate absolute SiOx deposition by about one order of magnitude; ion flux and stoichiometry are expected to be more reliable relative quantities.The reported discrepancy is attributed primarily to underestimated sputtering yield and may also reflect uncertainties along the target-to-substrate pathway.Source: Together, these spatially varying… · p. 13

To identify the atomistic origin of ion bombardment induced defect formation, molecular

  • Across stoichiometries, incorporated Ar remains 1.23 ± 0.37 nm−3, indicating that structural transitions reflect network response to bombardment rather than differences in Ar uptake.The molecular-dynamics simulations capture ion energy deposition, local stoichiometry, and defect evolution in the amorphous network.Source: To identify the atomistic origin of… · p. 13

Figure 8 a) reveals that silicon dangling bonds (DBs), non-bridging oxygen defects

  • DB, NBO, and VO densities occupy distinct scales, while oxygen-vacancy densities agree qualitatively between atomistic and device-simulation ensembles and remain relevant to memristive functionality.NBOs and Si-Si bond formation primarily govern structural densification and mechanical response, whereas VO are critical for memristive defect functionality.Source: Figure 8 a) reveals that silicon… · p. 14

For O-rich compositions (1.7 ≤x ≤2.0), the amorphous SiO2-like network remains

  • For O-rich compositions (1.7 ≤x ≤2.0), the SiO2-like network remains structurally intact, and decreasing oxygen content introduces vacancies that partly relax into dangling bonds while preserving its topology.These changes occur in a largely Si-Si-bond-free regime.Source: For O-rich compositions (1.7 ≤x ≤2.0),… · pp. 14–15

Ion bombardment therefore acts predominantly through Si-O bond disruption, driving

  • Ion bombardment disrupts Si-O bonds, driving network densification, compressive stress, and NBO formation; intrinsic defects also emerge at minimal ion doses.The network is already compositionally modified and defect-enriched, so bombardment produces more immediate, compositionally offset defect accumulation.Source: Ion bombardment therefore acts… · p. 15

This stoichiometry driven transition distinguishes a densification dominated silica-like

III. DISCUSSION

  • Device functionality does not follow a direct deterministic process-to-performance mapping: plasma-defined conditions shape atomistic and latent defect states, then bias the likelihood of stochastic functional-regime occupation.Process parameters reshape the statistical accessibility of material response pathways rather than prescribing singular electrical states.Source: §III · p. 16

network-topology modifications while largely preserving local tetrahedral building blocks

The discussion links growth-dependent defect states to copper redistribution and electrical response, then explains device-level variability through spatially heterogeneous local states and probabilistic regime occupation.

network-topology modifications while largely preserving local tetrahedral building blocks

These growth-induced atomistic regimes subsequently define the effective defect-state

  • The reconstructed oxygen-vacancy coordinate is an effective latent descriptor of defects, structural disorder, and network compliance, not an isolated vacancy density.Source: These growth-induced atomistic regimes… · p. 17
  • The saturated exponential coupling between effective defect state and copper density suggests defect-enabled copper incorporation and restructuring that eventually saturate.Finite uptake, transport, or structural accommodation may impose the saturation.Source: These growth-induced atomistic regimes… · p. 17

but probabilistic functional device classes. The continuous transitions observed throughout

From an engineering perspective, these findings imply that functional control in sputtered

  • Wafer position selects local growth regimes, power shifts defect-state transitions, and deposition time changes statistical occupation; smaller active volumes are expected to reduce ensemble averaging.Device area had weak influence across the investigated 100–2500 µm2 range.Source: From an engineering perspective, these… · p. 18

IV. CONCLUSION

The conclusion presents a multiscale account in which process conditions shape material and defect states, which probabilistically yield device functionality. It connects latent defect-state descriptions and heterogeneous local responses to copper redistribution and electrical behavior.

To investigate the multiscale relationship between plasma-defined growth conditions,

This work establishes a multiscale framework linking plasma-defined growth conditions,

state landscape. At the device scale, spatial integration across heterogeneous local states

More broadly, these findings shift the perspective from deterministic control of individual

A statistically heterogeneous experimental device space comprising more than 50,000

50 wafers were statistically evaluated to establish a reduced functional-state representation

This section develops a reduced representation of device functionality, using SOM clustering to group devices into seven functional regimes and KDE-based analysis to estimate regime yield across the process space. It also describes a device-level model that couples oxygen-vacancy dynamics and electronic transport with Cu-dependent Schottky barriers and local electric-field redistribution, representing internal material state with effective defect-state coordinates.

50 wafers were statistically evaluated to establish a reduced functional-state representation

  • Device-to-device variability across the dataset required reducing individual I–V curves to a lower-dimensional functional representation.Measurements contained up to 203 points, and shorter curves were aligned by subsampling before analysis.Source: §50 · p. 21
  • K-means, spectral clustering, and HDBSCAN failed to yield physically interpretable, functionally coherent clusters, so the study adopted a self-organizing map (SOM).The curves were normalized to emphasize shape rather than absolute current magnitude.Source: §50 · p. 21

Clustering was performed using the MiniSom implementation of SOMs [53]. Each SOM

  • The SOM mapped 203-dimensional processed current data onto a two-dimensional neuron map while preserving local topological relationships.Rectangular and hexagonal topologies and Euclidean and cosine distances were evaluated.Source: Clustering was performed using the… · p. 22

Hyperparameters (HPs) were optimized using five consecutive 5-fold cross-validated grid

  • Lower training iterations (e.g., 5 × 104) produced equivalent clustering results, indicating convergence of the trained representation; the resulting 1,156 SOM clusters (neurons) were aggregated into seven higher-level functional regime classes.The aggregation exploited topology-preserving ordering.Source: Hyperparameters (HPs) were optimized… · p. 22

Cluster yield estimation

  • Because the process space was sampled non-uniformly during empirical optimization, KDE-based homogenization was used to estimate statistically comparable cluster occupancies.Source: Cluster yield estimation · p. 23

For this purpose, the multidimensional process parameter space x ∈R8 was represented

  • KDE yield estimates indicated weak sensitivity to Ar/O2 ratio within the explored 5–25% O2 poisoned-mode window, while radial wafer position showed rapidly varying functionality.The study cautions that this weak oxygen-fraction sensitivity is limited to the investigated window; the optimized bandwidth for gas ratio indicated relative invariance within that process window.Source: For this purpose, the multidimensional… · pp. 24–25

Device-level simulations

  • A reduced one-dimensional cloud-in-a-cell device simulation framework was used to derive physically plausible parameter sets reproducing experimentally observed switching responses.The simulations aimed to reconstruct internal defect-state characteristics underlying the observed behavior.Source: Device-level simulations · p. 25
  • The model captures field-driven oxygen-vacancy drift, Schottky and Poole–Frenkel transport, and Cu-mediated modulation of TiN/SiOx Schottky barriers.These mechanisms couple the electrical response to vacancy distributions and dynamics, the Cu-related defect landscape, and local electric-field redistribution.Source: Device-level simulations · p. 25
  • The model represents the internal material state only through effective defect-state coordinates, without explicitly incorporating its internal structure.Source: Device-level simulations · p. 25

ing detailed chemical composition, atomistic network topology, or mechanical and structural

This section treats reconstructed defect variables as effective descriptions and outlines forward plasma and atomistic modeling of process-induced defect formation. The forward simulations omit underlying TiN and Cu layers, whose influence is implicitly represented in reverse engineering.

ing detailed chemical composition, atomistic network topology, or mechanical and structural

The forward engineering workflow aims to identify the primary physical mechanisms

Regarding a theoretical forward prediction of the device processing steps, we initially

Plasma-surface simulations

  • Forward simulations omit TiN during first-layer deposition and Cu islands during second-layer deposition, while reverse engineering implicitly includes their influence in the reconstructed device state.Source: Plasma-surface simulations · p. 28
  • Reactive molecular-dynamics models span SiOx stoichiometries x=1.0–2.0, generating sub-stoichiometric networks through sequential oxygen removal and structural relaxation.Source: Plasma-surface simulations · p. 28

Ion bombardment under sputter deposition conditions was simulated using a hybrid

The simulations model Ar-ion bombardment of amorphous SiOx using a hybrid bulk/surface setup, followed by impact and relaxation stages. Structural and defect-density descriptors are extracted across stoichiometries and ion-to-Si flux ratios.

Ion bombardment under sputter deposition conditions was simulated using a hybrid

  • The bulk/surface setup treats amorphous SiOx as a periodic bulk system with incoming Ar ions interacting with a localized surface-like region.The authors note that this representation is supported primarily by the comparatively low ion energies considered.Source: Ion bombardment under sputter… · p. 28
  • Ar ions were simulated at approximately 35 eV across SiOx stoichiometries and ion-to-Si flux ratios from 0 to 1 using a hybrid ReaxFF/ZBL potential.Short-range ZBL interactions capture collision dynamics, while reactive interactions govern defect formation and structural relaxation.Source: Ion bombardment under sputter… · pp. 28–29
  • Each impact was propagated for 1 ps, with the local impact region undamped and outer regions thermostatted, before a further 1 ps of thermal and mechanical relaxation.The thermostat and barostat are intended for efficient relaxation, not rigorous isothermal–isobaric sampling of the nonequilibrium impact dynamics.Source: Ion bombardment under sputter… · p. 29
  • The analysis tracks oxygen-vacancy, dangling-Si, non-bridging-oxygen, mass, stress, Si–O-bond, and Si–Si-bond densities, with bond identification based on distance cutoffs.Si–O and Si–Si bond cutoffs are 1.8 Å and 2.7 Å, respectively.Source: Ion bombardment under sputter… · p. 29

neighbors within these cutoffs. Dangling Si defects were identified as under-coordinated

The supplementary material specifies how atomistic defects and structural descriptors are identified, then checks their robustness and shows cluster and wafer-level visualizations. These additions clarify the spatial context of functional regimes and the limits of the structural estimates.

neighbors within these cutoffs. Dangling Si defects were identified as under-coordinated

  • Dangling-Si defects are under-coordinated Si atoms, while non-bridging oxygen atoms have one or fewer Si neighbors; oxygen vacancies use a more restrictive geometric criterion.Candidate Si pairs must have compatible missing-oxygen bonding directions and no steric blocking in the relevant region.Source: neighbors within these cutoffs.… · pp. 29–30

The robustness of the structural descriptors with respect to the short impact-relaxation

  • The resulting structural properties remained largely unaffected, whereas stress-related quantities showed larger deviations; therefore, higher-resolution impact-series configurations were used to construct the structural maps in Section II.Source: The robustness of the structural… · p. 30

S1.1. Emergent switching regimes and functional state space

S1.2. Physics-informed inference of latent defect state landscapes

  • Off-center wafer distributions were re-centered by estimating the chamber symmetry center from azimuthal variance and shifting device coordinates into a common spatial frame.The resulting wafer-position parameter was used to evaluate process-dependent cluster yields.Source: S1.2. Physics-informed inference of… · pp. 39–40
  • The supplementary material presents reconstructed effective Cu density as a function of oxygen-vacancy density, describing the Cu-density view as technically redundant.Representative wafer maps provide the spatial distributions underlying the functional-cluster comparisons.Source: S1.2. Physics-informed inference of… · p. 40

The electron density and the corresponding electric potential obtained from the plasma

The supplementary simulations connect plasma conditions to ion and electron effects at the substrate, and visualize how bombardment changes amorphous SiOx structure and stress. They also estimate transient heating under a conservative electron-energy assumption.

The electron density and the corresponding electric potential obtained from the plasma

  • The plasma simulation places electrons in the magnetically confined ionization region, where their density falls with distance from the cathode and a dc self-bias of approximately −110 V is established.The electron density and electric potential are averaged over 500 rf-cycles.Source: The electron density and the… · p. 41, Figure S4 · p. 42

30 V. Ions created in the ionization region are predominantly subject to acceleration toward

  • These results therefore suggest electron-induced heating is unlikely to constitute the dominant origin of experimentally observed structural modifications, although it may contribute to short-lived local relaxation processes.Source: §30 · p. 42

To visualize the investigated material systems and their structural evolution under ion

Complementing the structural descriptors presented in the main paper, Figure S7 shows

  • Compressive stress rises continuously with bombardment in a-SiO2, but buildup weakens at lower stoichiometries and saturates in the structurally softened regime below x ≈ 1.7.The stress maps use additionally equilibrated configurations sampled equidistantly in ion-to-Si flux ratio.Source: Complementing the structural… · pp. 43–44, Figure S7 · p. 45

Plasma-surface simulations

  • A two-dimensional finite-difference heat-transport model uses composition-dependent thermal properties, an implicit Crank–Nicolson scheme, and a fixed-temperature boundary at the TiN electrode.Other boundaries are thermally insulating.Source: Plasma-surface simulations · p. 45

the transient heat equation

The transient heat equation models temperature evolution from deposited electron energy, while the atomistic methods use a hybrid bulk/surface representation. The supplementary checks find modest deviations for most structural descriptors but substantially larger ones for stress.

the transient heat equation

  • The transient heat equation evolves temperature using thermal conductivity, mass density, and specific heat capacity, with deposited electron energy set as the initial condition.The calculation assumes instantaneous conversion of a single 25 eV electron's full kinetic energy into heat within one surface cell, giving an upper-bound estimate.Source: the transient heat equation · pp. 45–46
  • The hybrid bulk/surface molecular-dynamics approach is justified for the approximately 35 eV ion regime, where energy dissipation is localized and produces point defects and local network rearrangements.The authors note that explicit growth simulations can introduce artificially high particle flux and methodological biases, so model choice depends on the physical regime of interest.Source: the transient heat equation · p. 46

10 ps of time averaging. Comparison between directly extracted impact-series configurations

  • Additional equilibration produced mean deviations of 3.22% for Si dangling-bond density, 1.80% for non-bridging-oxygen density, and 19.18% for oxygen-vacancy density.Si–O-bond density deviated by 0.01%, Si–Si-bond density by 1.92%, and mass density by 0.09%.Source: §10 · p. 47
  • Stress-related quantities deviated by up to 166.56%, so higher-resolution impact-series configurations were used to construct the structural maps.Stress is treated as a secondary descriptor in this work.Source: §10 · p. 47
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