Engineering Structural Discontinuity in Ordered Co3O4 Nanocube Arrays for Volatile Memristive Dynamics

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Here, we demonstrate a fundamental transition from stochastic bulk conduction to reliable interface-mediated volatile switching by deliberately introducing structural discontinuity in spinel-type Co 3 O 4 nanocube (NC) arrays. While continuous oxide thin films suffer from irreversible breakdown and featureless transport, our self-assembled NC architecture enables a stable and low-power functional response. Utilizing an automated metrology framework based on the Segment Anything Model (SAM), we confirm the formation of a highly ordered, non-percolated square lattice with sub-nanometer precision in interparticle spacing. This structural determinism confines the active conduction volume to nanoscale junctions, achieving an ultralow operating current of 10 nA and exceptional statistical uniformity (coefficient of variation < 9%). Quantitative analysis identifies Schottky emission and Fowler-Nordheim tunneling at NC-gap-NC interfaces as the dominant mechanisms. Furthermore, time-resolved measurements reveal dual-mode relaxation dynamics characterized by microsecond electronic detrapping and long-term ionic back-diffusion, which facilitate complex temporal dynamics for biomimetic signal processing. Our findings suggest that nanogap-driven tunneling, rather than bulk percolation, can serve as a useful design principle for energy-efficient electronic primitives beyond conventional continuous media. Nanocube array Interparticle gap Automated metrology Volatile memristive behavior Fowler-Nordheim tunneling Conduction mechanism Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The precise engineering of nanoscale gaps between discrete building blocks offers a powerful strategy for defining new charge transport regimes in functional materials. Unlike continuous media, where electronic properties are often limited by stochastic bulk processes, architectures with deliberate structural discontinuity allow for the confinement of active conduction volumes to localized interfaces. This level of structural determinism is particularly critical for modulating memristive behavior, the dynamic evolution of resistance in response to external electrical stimuli [ 1 – 6 ], which is often unstable or irreversible in conventional thin-film systems. While continuous oxide films are effective for non-volatile switching [ 7 , 8 ], the inherent structural continuity often stabilizes filamentary pathways even after the bias is removed [ 9 ], leading to a gradual drift toward non-volatility. This phenomenon is fundamentally linked to energetically demanding bulk transport through the lattice and redox-driven structural changes [ 10 , 11 ]. In contrast, the creation of a non-percolated network of nanoscale junctions prioritizes shallow energy pathways at localized interfaces, facilitating volatile memristive behavior where conductance spontaneously returns to its initial state [ 12 , 13 ]. Such behavior is generally governed by interfacial processes, including rapid detrapping from shallow states or ion migration along grain boundaries [ 13 , 14 ], providing a distinct pathway for emulating biological temporal dynamics in logic-in-memory circuits [ 15 , 16 ] and signal processing [ 17 , 18 ]. Spinel-type Co 3 O 4 provides a rich landscape for such investigations due to its mixed-valence states of Co 2+ and Co 3+ , which are conducive to intricate charge transport and trapping dynamics. However, the dominance of bulk-governed conduction in conventional Co 3 O 4 thin films often masks these subtle interface-mediated phenomena, necessitating device geometries that can suppress persistent filament formation [ 19 ]. In this study, we investigate the emergence of unique conduction physics enabled by structural discontinuity in a network of self-assembled Co 3 O 4 nanocubes (NCs). By engineering a non-percolated architecture in which NCs are separated by well-defined nanogaps, we induce a transition in the dominant transport behavior from bulk-dominated percolation to interface-mediated tunneling and localized trapping. Unlike continuous Co 3 O 4 thin films which exhibit negligible memory effects, our NC array reveals a stable and highly reliable volatile response. This structural determinism achieves an ultralow operating current of 10 nA with exceptional statistical uniformity, yielding a coefficient of variation below 9%. Our findings demonstrate that leveraging nanogap-driven transport physics in discontinuous nanoscale architectures provides a robust pathway for developing energy-efficient electronic functionalities unattainable in conventional continuous media [ 20 , 21 ]. 2. Experimental Section 2.1. Materials The following chemicals were used in this study: cobalt(II) perchlorate hexahydrate (Co(ClO 4 ) 2 ·6H 2 O, 99.5%), cobalt(II) chloride hexahydrate (CoCl 2 ·6H 2 O, 98%), 1-octanol (CH 3 (CH 2 ) 7 OH, 99%), oleylamine (CH 3 (CH 2 ) 7 CH = CH(CH 2 ) 7 CH 2 NH 2 , 70%), oleic acid (CH 3 (CH 2 ) 7 CH = CH(CH 2 ) 7 COOH, 90%), all purchased from Sigma-Aldrich. n -Hexane (CH 3 (CH 2 ) 4 CH 3 , 95%) and toluene (C 6 H 5 CH 3 , 99.8%) were obtained from Daejung Chemicals & Metals. All reagents were used as received without further purification. AZ GXR-601 positive photoresist (Merck Performance Materials), LOR lift-off resist (MicroChem/Kayaku Advanced Materials), and APOL-LO 3200 negative lift-off photoresist (KemLab Inc.) were employed for i-line (365 nm) photolithography. p-type Si (100) wafers with a 100 nm SiO 2 layer grown by dry oxidation were used as substrates. A 2-inch Co 3 O 4 sputtering target (TASCO, 99.9%) was used for Co 3 O 4 thin film deposition, and 1.5-inch Pt and Ti sputtering targets (TASCO, 99.99%) were used for the electrode deposition. 2.2. Device fabrication SiO 2 /Si substrates were sequentially cleaned with acetone, ethanol, and deionized water, followed by photolithographic patterning and lift-off to define the electrode geometry. A 5 nm Ti adhesion layer and a 20 nm Pt bottom electrode were deposited using an RF magnetron sputtering system equipped with multiple targets. Photolithography was then used to define 25 × 25 µm 2 square trenches in the photoresist, into which the Co 3 O 4 NC arrays were subsequently assembled. Monodisperse Co 3 O 4 NCs were synthesized via a colloidal method [ 22 ]. Cobalt(II) perchlorate hexahydrate (370 mg) was dissolved in 15 mL of 1-octanol containing 3.32 mL of oleylamine. The mixture was gradually heated to 120°C under magnetic stirring, and 0.7 mL of distilled water was added prior to reaching the target temperature. The reaction was maintained for 2 h to promote NC growth, then cooled to room temperature. The products were collected by adding acetone and ethanol followed by centrifugation and washing. To form Co 3 O 4 NC arrays inside the pre-defined trenches, the synthesized NCs were redispersed in a 1:1 (v/v) mixture of hexane and toluene containing oleic acid (18 µL·mL -1 ). The dispersion was ultrasonicated for 10 min to ensure homogeneity, and the patterned substrates were immersed in the dispersion. During natural solvent evaporation at 25°C, convective flow induced lateral assembly of NCs into ordered two-dimensional arrays within the trench regions. After drying, the assembled layers were annealed at 400°C in air for 30 min to remove residual organic ligands and achieve well-ordered Co 3 O 4 NC arrays. The photoresist surrounding the trenches was then removed by lift-off, leaving the NC arrays only inside the patterned regions. After this process, Pt top electrodes with 25 × 25 µm 2 square geometry were patterned by photolithography and defined by a lift-off process to complete the Pt/Co 3 O 4 /Pt device structure. Co 3 O 4 thin films were subsequently deposited under identical conditions using a 2-inch Co 3 O 4 ceramic target (99.9%, TASCO) at a substrate temperature of 400°C. During sputtering, Ar (40 sccm) and O 2 (10 sccm) were introduced to maintain a total pressure of 5 × 10 − 3 Torr, with an RF power of 70 W and a base pressure of 5.8 × 10 − 6 Torr. Top Pt electrodes for the Co 3 O 4 thin film devices were fabricated using the same photolithography and lift-off process as for the NC-array devices. 2.3. Material characterization The structural properties such as crystallinity and crystalline phase were analyzed by XRD (SmartLab diffractometer, Rigaku, λ = 1.5418 Å). The surface morphology of as-prepared samples was analyzed by scanning electron microscope (SEM, JSM-7500F, JEOL). The chemical properties were estimated using X-ray photoelectron spectroscopy (XPS, NEXAS, Thermo Fisher Scientific). To calculate the valence band maximum and work function of Co3O4 on Pt, UPS (KRATOS AXIS Supra model) was employed with a UV source He I (21.2 eV) under a sample bias − 9 eV. The TEM samples were prepared by focused ion beam (FIB) system (NX5000, Hitachi) using a Ga + ion beam source. A carbon protection layer was deposited to prevent specimen degradation and protect the surface of the TEM samples. The elemental mapping across the cross-section and structural information were obtained with a TEM apparatus (Tecnai G2 F30 S-Twin, FEI) operated at 300 kV and equipped with an energy-dispersive spectrometer (EDS). All characterizations were performed at the GIST Advanced Institute of Instrumental Analysis (GAIA). 2.4. Device test A probe station connected to a Keithley 4200A-SCS parameter analyzer (Tektronix Inc., USA) was used for all electrical measurements. To ensure high signal integrity at low current levels, Keithley 4200-PA remote preamplifiers were employed, effectively reducing the system noise floor from the nA range to below 1 pA. This enhancement provided a high signal-to-noise ratio (SNR > 10 5 ) for accurately capturing the volatile switching characteristics of the NC array, which operates at an ultralow current level of ~ 100 nA. Measurements were performed at room temperature under ambient conditions, with the bottom electrode used for voltage bias and the top electrode grounded. 3. Results and Discussion 3.1. Structural and Crystallographic Characterization of Co3O4 Thin Film and NC Array To systematically investigate the influence of structural configuration on memristive behavior, we established two distinct model systems: a continuous thin film and discontinuous NC arrays. As detailed in the Experimental Section, the continuous Co 3 O 4 thin films were deposited via radio frequency (RF) magnetron sputtering, whereas the discontinuous NC arrays were constructed through a Marangoni flow-driven self-assembly process (Fig. 1 a) [ 23 ]. The internal structural integrity of the NC active layer within the device environment was first verified. Cross-sectional analysis via focused ion beam (FIB) reveals that the NC layer is well-confined between the electrode interfaces ( Fig. S1 ), while energy dispersive X-ray spectroscopy (EDS) mapping confirms the precise spatial distribution of Co and O without interlayer diffusion ( Fig. S2 ). The crystalline integrity and orientation of the Co 3 O 4 layers were characterized using X-ray diffraction (XRD). As shown in Fig. 1 b, the Co 3 O 4 NC powder displays diffraction peaks consistent with the standard spinel cubic phase (JCPDS #42-1467) [ 22 ]. While the sputtered thin film exhibits multiple reflections such as (111), (222), and (511), indicating a polycrystalline nature, the NC array shows an exclusive and intense reflection at the (004) plane. The magnified XRD view in Fig. 1 c further confirms this strong out-of-plane orientation, suggesting that the NCs are precisely aligned with their {100} facets parallel to the substrate. The surface morphology, captured via top-view scanning electron microscopy (SEM) in Fig. 1 d, reveals that the self-assembled NCs form a long-range ordered, densely packed two-dimensional (2D) array over a large area. Such high structural uniformity and reproducibility of the NC arrays ensure a reliable platform for subsequent integration into memristive devices. The chemical state and purity of the self-assembled Co 3 O 4 NC array were further verified using X-ray photoelectron spectroscopy (XPS). As presented in Fig. 1 e and 1 f, the O 1s and Co 2p spectra exhibit the characteristic features of a conventional spinel Co 3 O 4 phase [ 24 ]. The Co 2p spectrum shows the typical 2p 3/2 and 2p 1/2 doublets along with their respective satellite peaks, confirming the expected mixed-valence states of Co 2+ and Co 3+ . Similarly, the O 1s spectrum reflects the presence of lattice oxygen and surface-adsorbed species consistent with standard oxide surfaces. These results confirm that the NCs maintain high chemical integrity throughout the self-assembly process without the formation of secondary phases or detectable impurities. Finally, the atomic-scale crystalline structure was further characterized via high-resolution transmission electron microscopy (HR-TEM). Figure 1 g shows a clear lattice fringe pattern of the assembled NCs. The corresponding Fast Fourier Transform (FFT) patterns from the grain interior (Area 1, Fig. 1 h) and the interfacial region (Area 2, Fig. 1 i) both exhibit well-defined diffraction spots along the [110] zone axis. These two well-defined systems, a continuous thin film and a discontinuous NC array, were therefore selected as representative structural models for subsequent electrical characterization. 3.2. Quantitative Structural Analysis of the Co 3 O 4 NC Array To establish a rigorous structural model, we optimized the assembly process to yield a discrete monolayer of Co 3 O 4 NCs for statistical characterization. This intentional single-layer configuration was essential to prevent overlapping particle images, thereby ensuring the pixel-resolved boundaries required for precise automated analysis. The quantitative evaluation was performed using an automated segmentation framework based on the Segment Anything Model (SAM), as detailed in Supplementary Note 1 [ 25 ]. As shown in Fig. 2 a, instance-level binary masks were generated for four representative regions (Regions 1–4), with original SEM images and exhaustive labeled masks provided in Fig. S3 and S4 , respectively. Using this framework, we extracted the critical parameters including physical dimensions, in-plane orientation ( θ i , Supplementary Note 2 and Fig. S5 ), and positional coordinates for every identified particle. To evaluate the structural uniformity across the large-area assembly, we analyzed the distribution of particle sizes (Fig. 2 b– 2 d) and interparticle gaps (Fig. 2 e– 2 g). The cumulative analysis revealed a highly monodisperse size distribution with a mean of 10.22 nm ( σ = 0.67 nm) and a precisely controlled interparticle gap of 2.84 nm ( σ = 0.64 nm). These gaps, which serve as fundamental tunneling junctions, were resolved at the pixel level using a robust contour-resolved method ( Supplementary Notes 3 , 4 and Fig. S6 , S7 ). The exceptionally low coefficient of variation for both parameters confirms that the array possesses high structural determinism. The long-range ordering was further quantified by computing the radial distribution function, g ( r ), as shown in Fig. 2 h. The prominent periodic peaks correspond precisely to the characteristic distance to a square lattice, including \(\varvec{d}\) , \(\sqrt{2}\varvec{d}\) , and \(2\varvec{d}\) ( Supplementary Notes 5 , 6 and Fig. S8 , S9 ). Notably, the first peak is observed at 13.04 nm, which shows an exceptional agreement with the theoretical center-to-center distance of 13.06 nm calculated from the sum of the mean particle size (10.22 nm) and the interparticle gap (2.84 nm). This numerical consistency confirms that the Co 3 O 4 NCs form a well-defined, non-percolated network with high geometric fidelity. This translational order is complemented by the bond-orientational correlation function, g orient ( r ) (Fig. 2 i), which exhibits a long-range plateau. This result confirms the preservation of global orientational alignment across the entire assembly ( Supplementary Note 7 and Fig. S10 ). 3.3. Fabrication and Electrical Characterization of Co 3 O 4 NC Array Devices To investigate the influence of nanoscale architecture on electrical switching performance, we fabricated Pt/Co 3 O 4 NC array/Pt and a Pt/Co 3 O 4 thin film/Pt device. The detailed fabrication sequence, involving the selective deposition of the Co 3 O 4 active layer within pre-defined trenches, is illustrated in Fig. 3 a. Optical and microscopic imaging in Fig. 3 b confirms the structural integrity and precise alignment of these NC-assembled active regions. Initial characterization revealed a striking disparity in the switching mechanisms between the two configurations. The architectural impact on switching behavior is clearly evidenced by the contrasting electrical responses of the two systems. While the NC array device achieves stable volatile memristive switching at a low operating current of ~ 10 nA (Fig. 3 c), its continuous thin film counterpart fails to exhibit any functional switching, presenting only a featureless and nearly linear I–V response without discernible hysteresis ( Fig. S11a ). This disparity indicates that the bulk-like environment of the continuous film facilitates non-selective charge transport [ 26 ], which prevents the formation of the localized, reversible switching paths uniquely enabled by the discontinuous, NC-assembled geometry. The structural robustness of the NC array was further validated during the initial activation process. As shown in Fig. 3 d, the NC array requires an initial forming step (indicated by the arrow), where the current significantly drops at high bias (> 10 V), signifying an irreversible transition to a high-resistance state (HRS) [ 27 ]. Notably, even after this breakdown-like event, the NC array immediately establishes a stable and repeatable volatile hysteresis loop within the nA range. When the same electrical sequence was applied to the thin film ( Fig. S11b ), a similar irreversible increase in resistance occurred; however, the thin film failed to exhibit any subsequent memory effect. Instead, the thin film exhibited unstable current fluctuations and a featureless I–V curve lacking any repeatable hysteresis, suggesting that the catastrophic bulk failure [ 28 ] completely suppressed the charge dynamics. These findings demonstrate that while high bias causes irreversible modifications in both systems, the discontinuous NC-gap-NC geometry maintains its interfacial integrity even after the initial HRS transition. This allows the NC array to preserve localized charge trapping or ionic displacement within the gaps, thereby maintaining electrically reversible switching that is unattainable in the homogenized, failed bulk material. The reliability and uniformity of the switching parameters were statistically validated through a rigorous analysis of 100 consecutive cycles. As shown in the cumulative probability plot (Fig. 3 e), the transition voltages for both V set and V reset exhibit a steep and linear slope, indicating a highly predictable switching behavior within a well-defined voltage window. This is further supported by the distribution histograms (Fig. 3 f), where the operating voltages exhibit exceptional uniformity, characterized by a mean set voltage ( µ set ) of 8.75 V (with a standard deviation, σ set = 0.54 V) and a mean reset voltage ( µ reset ) of 4.38 V ( σ reset = 0.39 V). To further evaluate the device's stability, we calculated the coefficient of variation ( σ / µ ), which yielded remarkably low values of 6.17% for V set and 8.90% for V reset . The narrow Gaussian distributions and consistent alignment in the cumulative plots reflect a high degree of reproducibility, which can be attributed to the localized switching occurring within the NC-assembled architecture. This statistical consistency suggests that the NC-based geometry helps to regulate the stochastic nature of charge dynamics and ionic motion. By providing a more controlled environment for these processes, the NC array achieves the level of uniformity necessary for reliable memristive applications [ 13 , 29 ]. 3.4. Conduction Mechanisms and Relaxation Dynamics of the Co 3 O 4 NC Array To understand the physical origin of the reliable volatile switching observed in our NC array, we examined the I–V characteristics using log–log plots under positive bias [ 30 , 31 ] (Fig. 4 a). The device shows distinct transport regimes, shifting from low-voltage Ohmic conduction to field-assisted emission as the bias increases [ 32 ]. In the intermediate (0.7~-5.8 V) and high-field (> 5.8 V) regions, the conduction is well-described by Schottky emission (Eq. 1 ) and Fowler–Nordheim (FN) tunneling (Eq. 2 ) models [ 33 ], respectively: $${\text{J}}_{\text{S}\text{E}}\propto{\text{T}}^{2}\text{e}\text{x}\text{p}(\text{A}\frac{\sqrt{\text{E}}}{\text{T}}-\text{B})$$ 1 $${\text{J}}_{\text{F}\text{N}}\propto{\text{E}}^{2}\text{e}\text{x}\text{p}\left(\frac{-\text{A}}{\text{E}}\right)$$ 2 where J represents the current density, E is the electric field, and T is the temperature. Constants A and B are material-specific parameters related to the interface barrier and dielectric properties. The excellent linear fits in Fig. 4 b (R 2 = 0.9964) and Fig. 4 c (R 2 = 0.9846) confirm that charge transport is primarily limited by the potential barriers at the NC interfaces rather than bulk conduction [ 34 ]. This conclusion is supported by the clear distinction from bulk-dominated transport; if the Co 3 O 4 bulk were the governing factor, the I–V characteristics would typically remain confined to ohmic ( J ∝ E ) or trap-limited space-charge-limited current (SCLC, J ∝ E 2 ) [ 35 ] regimes. Notably, the high-electric field data in Fig. 4 c exhibit a clear linear relationship with a characteristic negative slope in the ln(I/V 2 ) vs. 1/V plot, which is a definitive signature of FN tunneling. This confirms that under strong electric fields, the interface barrier narrows into a triangular shape, allowing carriers to tunnel through the junction [ 36 ]. Given the discontinuous nature of the NC array, where each NC is physically separated by nanoscale gaps, these results validate that the interfacial junctions act as the primary structural determinants of the electrical response of NC array device [ 37 ]. The volatile nature of this switching is further clarified by time-dependent measurements. Unlike the continuous thin film, which shows high mA-range currents and abrupt failure, the NC array operates at an ultralow nA level and exhibits a gradual, analog relaxation (Fig. 4 d). Such a contrast is consistent with the fact that resistive switching in continuous oxide stacks is often dominated by filamentary conduction, where localized conductive paths can concentrate Joule heating and accelerate irreversible degradation under large current stress [ 38 , 39 ]. In comparison, the discontinuous NC-gap-NC geometry effectively confines the active conduction volume to nanoscale junctions, which can mitigate uncontrolled filament overgrowth and help preserve interfacial integrity even after irreversible high-bias perturbations [ 40 ]. This relaxation follows an exponential decay [ 41 ]: $$\text{I}\left(\text{t}\right)\propto\text{A}\text{e}\text{x}\text{p}(-\text{t}/{\tau})$$ 4 where A is the initial current amplitude and τ represents the characteristic decay time constant. Following a short 1 ms pulse, we observe fast relaxation with τ fast values between 1.20 and 1.95 µs (Fig. 4 e). Given the short timescale, this transient relaxation is most plausibly dominated by electronic processes, such as rapid detrapping or interfacial charge redistribution, which are widely observed as the origin of short-term plasticity in volatile memristive systems [ 42 , 43 ]. To further investigate the long-term dynamics under maximum stimulus, a prolonged bias (10 V for 60 s) was applied. This intense stimulus can induce pronounced ionic redistribution within the NC network, driving the device into a distinct HRS [ 1 , 44 ]. While similar high-bias conditions in continuous thin films can lead to permanent failure modes accompanied by electrode/oxide damage and loss of switching functionality, the NC array uniquely maintains its dynamic recovery even in this regime [ 39 ]. Under subsequent read biases, the device exhibits a slow relaxation component with τ slow values ranging from 67.63 to 175.8 s (Fig. 4 f). The stark difference in these timescales suggests a dual-process model where short-term relaxation originates from electronic processes and long-term recovery is controlled by the stochastic back-diffusion of localized ionic species within the interfacial gaps [ 45 ]. Notably, as the read bias increases, τ slow also increases; this trend is consistent with an external electric field that can bias ionic drift and oppose spontaneous relaxation toward equilibrium [ 46 , 47 ]. Ultimately, these dual-mode dynamics underpin the exceptional functional uniformity observed in our device. It is particularly intriguing that the NC array exhibits intrinsic leaky integrate-and-fire (LIF)-like behavior within a single-device architecture, as evidenced by the biomimetic neuronal firing responses [ 48 , 49 ] in Fig. S12 . While the Co 3 O 4 NC array currently operates at relatively high voltages, this could be further optimized by engineering the interfacial gaps during the self-assembly process, for instance, by tailoring the length and chemical nature of the organic surfactants to reduce the effective tunneling barrier and strengthen inter-NC coupling [ 50 ]. Importantly, the ultralow operating current and reproducible relaxation observed here suggest that the NC-gap-NC junction can serve as a controllable physical motif to program volatile memristive dynamics. In this sense, nanoscale gaps provide a fundamental design handle to access and tune interface-mediated transport regimes that are often masked in continuous films, offering useful guidance for constructing energy-conscious neuromorphic primitives. 4. Conclusion In summary, we have established a deterministic design rule for modulating charge transport by engineering the structural dimensionality of Co 3 O 4 architectures. Our comparative study demonstrates that the transition from irreversible hard breakdown in continuous thin films to reliable, low-power switching in self-assembled NC arrays is fundamentally driven by the deliberate introduction of structural discontinuity. The rigorous statistical framework, integrating SAM-based segmentation and spatial correlation functions, proves that the high translational and orientational ordering of the NC lattice is the key determinant of reproducibility and functional uniformity. Specifically, the formation of an ordered array with an average particle size of 10.22 nm and a precisely controlled interparticle gap of 2.84 nm effectively localizes charge trapping and tunneling processes at the nanoscale junctions. This structural determinism enables stable volatile memristive switching at an ultralow operating current of 10 nA with exceptional statistical uniformity, yielding coefficient of variation values for switching voltages below 9%. Furthermore, the identification of dual-mode relaxation dynamics, which encompass rapid microsecond electronic and slow long-term ionic processes, enables the emulation of complex temporal dynamics essential for biomimetic signal processing. By bridging the gap between automated image-based metrology and macroscopic electronic functionality, this work provides a scalable and predictable platform for the development of robust, next-generation functional hardware. Ultimately, leveraging the unique transport physics of discontinuous nanoscale architectures offers a versatile pathway for engineering energy-conscious electronic systems with high structural and functional determinism. Declarations Acknowledgements Inhyeok Oh and Jun Beom Hwang contributed equally to this work. This research was supported by the program of Future Hydrogen Original Technology Development (RS-2021-NR057808), through the National Research Foundation of Korea (NRF), funded by the Korean government (Ministry of Science and ICT (MSIT)). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-00563779). Data Availability Statement The data that support the findings of this study are available from the corresponding author upon reasonable request. Author Contributions I. Oh: Writing – original draft, Formal analysis, Visualization, Conceptualization. J. B. Hwang: Writing – original draft, Formal analysis, Visualization, Conceptualization. M. Kang: Formal analysis, Writing–review & editing. D. Kim: Formal analysis. S. Kim: Investigation. J. Lee: Validation. H. Kim: Investigation. D. Lee: Validation. M. H. Oh: Writing – review & editing, Supervision, Project administration. S. 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Appl Surf Sci 257:2717–2730. https://doi.org/10.1016/j.apsusc.2010.10.051 Kirillov A, Mintun E, Ravi N, Mao H, Rolland C, Gustafson L et al (2026) Segment Anything. 2023 [cited 2026 Mar 7]. pp. 4015–26. https://openaccess.thecvf.com/content/ICCV2023/html/Kirillov_Segment_Anything_ICCV_2023_paper.html . Accessed 7 Mar Waser R, Aono M (2007) Nanoionics-based resistive switching memories. Nat Mater Nat Publishing Group 6:833–840. https://doi.org/10.1038/nmat2023 Jeong DS, Thomas R, Katiyar RS, Scott JF, Kohlstedt H, Petraru A et al (2012) Emerging memories: resistive switching mechanisms and current status. Rep Prog Phys IOP Publishing 75:076502. https://doi.org/10.1088/0034-4885/75/7/076502 Zhao M, Gao B, Tang J, Qian H, Wu H (2020) Reliability of analog resistive switching memory for neuromorphic computing. Appl Phys Rev 7:011301. https://doi.org/10.1063/1.5124915 Byun U, Na H, Kim S (2025) Universal Neuromorphic Element: NbOx Memristor with Co-Existing Volatile, Non‐Volatile, and Threshold Switching. Adv Funct Mater e19431. https://doi.org/10.1002/adfm.202519431 Lampert MA (1956) Simplified Theory of Space-Charge-Limited Currents in an Insulator with Traps. Phys Rev Am Phys Soc 103:1648–1656. https://doi.org/10.1103/PhysRev.103.1648 Crowell CR, Sze SM (1966) Current transport in metal-semiconductor barriers. Solid State Electron 9:1035–1048. https://doi.org/10.1016/0038-1101(66)90127-4 Chiu F-C (2014) A Review on Conduction Mechanisms in Dielectric Films. Adv Mater Sci Eng 2014:578168. https://doi.org/10.1155/2014/578168 Lim EW, Ismail R (2015) Conduction Mechanism of Valence Change Resistive Switching Memory: A Survey. Electron publisher 4:586–613. https://doi.org/10.3390/electronics4030586 Jeong DS, Thomas R, Katiyar RS, Scott JF, Kohlstedt H, Petraru A et al (2012) Emerging memories: resistive switching mechanisms and current status. Rep Prog Phys IOP Publishing 75:076502. https://doi.org/10.1088/0034-4885/75/7/076502 Grinberg AA, Luryi S, Pinto MR, Schryer NL (1989) Space-charge-limited current in a film. IEEE Trans Electron Devices 36:1162–1170. https://doi.org/10.1109/16.24363 Simmons JG (1963) Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film. J Appl Phys Am Inst Phys 34:1793–1803. https://doi.org/10.1063/1.1702682 Talapin DV, Lee J-S, Kovalenko MV, Shevchenko EV (2010) Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications. Chem Rev Am Chem Soc 110:389–458. https://doi.org/10.1021/cr900137k Kwon D-H, Kim KM, Jang JH, Jeon JM, Lee MH, Kim GH et al (2010) Atomic structure of conducting nanofilaments in TiO2 resistive switching memory. Nat Nanotech Nat Publishing Group 5:148–153. https://doi.org/10.1038/nnano.2009.456 Kumar S, Wang Z, Huang X, Kumari N, Davila N, Strachan JP et al (2017) Oxygen migration during resistance switching and failure of hafnium oxide memristors. Appl Phys Lett 110:103503. https://doi.org/10.1063/1.4974535 Niu G, Calka P, Auf der Maur M, Santoni F, Guha S, Fraschke M et al (2016) Geometric conductive filament confinement by nanotips for resistive switching of HfO2-RRAM devices with high performance. Sci Rep Nat Publishing Group 6:25757. https://doi.org/10.1038/srep25757 Ohno T, Hasegawa T, Tsuruoka T, Terabe K, Gimzewski JK, Aono M (2011) Short-term plasticity and long-term potentiation mimicked in single inorganic synapses. Nat Mater Nat Publishing Group 10:591–595. https://doi.org/10.1038/nmat3054 Dutta M, Brivio S, Spiga S (2024) Unraveling the Roles of Switching and Relaxation Times in Volatile Electrochemical Memristors to Mimic Neuromorphic Dynamical Features. Adv Electron Mater 10:2400221. https://doi.org/10.1002/aelm.202400221 Berdan R, Vasilaki E, Khiat A, Indiveri G, Serb A, Prodromakis T (2016) Emulating short-term synaptic dynamics with memristive devices. Sci Rep Nat Publishing Group 6:18639. https://doi.org/10.1038/srep18639 Kumar S, Wang Z, Huang X, Kumari N, Davila N, Strachan JP et al (2016) Conduction Channel Formation and Dissolution Due to Oxygen Thermophoresis/Diffusion in Hafnium Oxide Memristors. ACS Nano Am Chem Soc 10:11205–11210. https://doi.org/10.1021/acsnano.6b06275 Strukov DB, Williams RS (2009) Exponential ionic drift: fast switching and low volatility of thin-film memristors. Appl Phys A 94:515–519. https://doi.org/10.1007/s00339-008-4975-3 Aguilera-Pedregosa C, Maldonado D, González MB, Moreno E, Jiménez-Molinos F, Campabadal F et al (2023) Thermal Characterization of Conductive Filaments in Unipolar Resistive Memories. Micromachines. Multidisciplinary Digit Publishing Inst 14:630. https://doi.org/10.3390/mi14030630 Choi S, Lee J, Kim S, Lu WD (2014) Retention failure analysis of metal-oxide based resistive memory. Appl Phys Lett 105:113510. https://doi.org/10.1063/1.4896154 Park S-O, Jeong H, Park J, Bae J, Choi S (2022) Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing. Nat Commun Nat Publishing Group 13:2888. https://doi.org/10.1038/s41467-022-30539-6 Ye F, Kiani F, Huang Y, Xia Q (2023) Diffusive Memristors with Uniform and Tunable Relaxation Time for Spike Generation in Event-Based Pattern Recognition. Adv Mater 35:2204778. https://doi.org/10.1002/adma.202204778 Liu Y, Gibbs M, Puthussery J, Gaik S, Ihly R, Hillhouse HW et al (2010) Dependence of Carrier Mobility on Nanocrystal Size and Ligand Length in PbSe Nanocrystal Solids. Nano Lett Am Chem Soc 10:1960–1969. https://doi.org/10.1021/nl101284k Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9079219","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":617335929,"identity":"cd2e8066-d546-4b83-9fa0-fcbe17b5368e","order_by":0,"name":"Inhyeok Oh","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Inhyeok","middleName":"","lastName":"Oh","suffix":""},{"id":617335934,"identity":"76ea9877-88c8-4b00-912d-415349ab1dd8","order_by":1,"name":"Jun Beom Hwang","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"Beom","lastName":"Hwang","suffix":""},{"id":617335938,"identity":"65d21975-4f9c-4bee-9c49-4be8709dc8ac","order_by":2,"name":"Minwoo Kang","email":"","orcid":"","institution":"Korea Institute of Energy Technology","correspondingAuthor":false,"prefix":"","firstName":"Minwoo","middleName":"","lastName":"Kang","suffix":""},{"id":617335945,"identity":"4e66da43-1d22-48c2-9b29-715061f7a3ab","order_by":3,"name":"Daehyeok Kim","email":"","orcid":"","institution":"Korea Institute of Energy Technology","correspondingAuthor":false,"prefix":"","firstName":"Daehyeok","middleName":"","lastName":"Kim","suffix":""},{"id":617335946,"identity":"c9caa4c5-a07e-4ccc-a09e-56958cc44309","order_by":4,"name":"Seohyeon Kim","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Seohyeon","middleName":"","lastName":"Kim","suffix":""},{"id":617335949,"identity":"05a3db8c-7720-4d5b-a9b5-f814ccc2df8e","order_by":5,"name":"Jungdae Lee","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jungdae","middleName":"","lastName":"Lee","suffix":""},{"id":617335950,"identity":"217c9ea4-f131-4fdc-8e0b-ebbc40024991","order_by":6,"name":"Hyeon Kim","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hyeon","middleName":"","lastName":"Kim","suffix":""},{"id":617335951,"identity":"2bf9e029-eccb-429a-a9e4-92ebab25f3e6","order_by":7,"name":"Donghyeon Lee","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Donghyeon","middleName":"","lastName":"Lee","suffix":""},{"id":617335952,"identity":"99e628a1-6be1-4663-8506-976428d91e0c","order_by":8,"name":"Myoung Hwan Oh","email":"","orcid":"","institution":"Korea Institute of Energy Technology","correspondingAuthor":false,"prefix":"","firstName":"Myoung","middleName":"Hwan","lastName":"Oh","suffix":""},{"id":617335954,"identity":"39377dd2-64d0-44b1-9267-7644f2b8fcc6","order_by":9,"name":"Sanghan Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYJACZiCWA5MgIEGsFmMgydhAkpZEoHIitci3nz38uqDmTvp8d/bnDxhq7BgkZx/Ar8XgTF6a9Yxjz3I3HuYxbGA4lswgzZdAQAtDjpkxD9vh3I3NPECHsR1gkOMh5LD+N0At/w6nGzazP2xg+EeEFoYbOcaPedsOJ8gzMxg2MLYdYJAmpMXgxhszZt6+w4YbmHkMZyT2JfNI9hB0WI7xZ55vh+Xl+48/+PDhm52cxBlCDmNgYAPHhMEBIJHAwEDQJyDA/AFsXQMxakfBKBgFo2BEAgB2Uz3DGHIFSAAAAABJRU5ErkJggg==","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Sanghan","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2026-03-10 05:08:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9079219/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9079219/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106244838,"identity":"88de2851-599a-4470-906c-9f4d9aeaa63d","added_by":"auto","created_at":"2026-04-06 15:48:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":401319,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic illustration of the fabrication process for Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e-based memristive devices, comparing thin film (top) and NC array (bottom) structures. (b) Out-of-plane XRD patterns and (c) magnified XRD views in the 40–50° range for Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC arrays, thin films, and reference NC powder. XPS spectra of (e) O 1s and (f) Co 2p levels and (d) Top-view SEM for Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC arrays. (g) HR-TEM image of the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NCs, with red and blue boxes indicating the analyzed areas at the NC lattice and interface. (h, i) FFT patterns correspond to Area 1 and Area 2 in (g).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/57b14d98afcfda1a31958864.png"},{"id":106403595,"identity":"572ccadd-d361-4505-b79a-c9620daadb5d","added_by":"auto","created_at":"2026-04-08 09:14:34","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":452414,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Representative SEM images of four regions (Regions 1–4) used for structural quantification, with the number of analyzed particles (n) indicated for each area. (b, c) Particle size distribution shown via (b) regional histograms and (c) a cumulative average histogram (\u003cem\u003eμ\u003c/em\u003e = 10.22 nm, \u003cem\u003eσ\u003c/em\u003e = 0.67 nm). (d) Plot of the mean (\u003cem\u003eμ\u003c/em\u003e) and coefficient of variation (CV) for particle size across the analyzed regions. (e, f) Interparticle gap distribution shown via (e) regional histograms and (f) a cumulative average histogram (\u003cem\u003eμ\u003c/em\u003e = 2.84 nm, \u003cem\u003eσ\u003c/em\u003e = 0.64 nm). (g) Plot of the mean (\u003cem\u003eμ\u003c/em\u003e) and CV for the interparticle gap across regions. (h) Radial distribution function, \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e), showing periodic peaks corresponding to a square lattice configuration. (i) Bond-orientational correlation function, \u003cem\u003eg\u003c/em\u003e\u003csub\u003eorient\u003c/sub\u003e(\u003cem\u003er\u003c/em\u003e), exhibiting a long-range plateau that confirms global orientational order.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/005517c9f188320831a977c6.png"},{"id":106244839,"identity":"041afe6e-9fb1-4722-9f6d-efd68811ac02","added_by":"auto","created_at":"2026-04-06 15:48:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":335592,"visible":true,"origin":"","legend":"\u003cp\u003eFabrication and volatile memristive behavior of Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC array devices. (a) Schematic illustration of the device fabrication process. (b) Optical and microscopic images of the fabricated single crossbar and crossbar array devices, with magnified views of the active-region trenches. (c) Representative I–V characteristics of the NC array device after activation, showing volatile switching at an operating current of ~10 nA. (d) Initial forming behavior of the NC array device, followed by stable volatile hysteresis. (e) Cumulative probability plots of V\u003csub\u003eset\u003c/sub\u003e and V\u003csub\u003ereset\u003c/sub\u003e extracted from 100 consecutive cycles. (f) Distribution histograms with Gaussian fitting for V\u003csub\u003eset\u003c/sub\u003e and V\u003csub\u003ereset\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/6f8cc015544c515d43832412.png"},{"id":106244840,"identity":"26a25566-5f26-4548-a0e7-ccccc748a436","added_by":"auto","created_at":"2026-04-06 15:48:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":97784,"visible":true,"origin":"","legend":"\u003cp\u003eConduction mechanisms and relaxation dynamics of the NC array device. (a) Log–log I–V characteristics under positive bias, showing Ohmic conduction, Schottky emission, and Fowler–Nordheim tunneling regimes. (b) Schottky emission fitting in the intermediate voltage range. (c) Fowler–Nordheim tunneling fitting in the high-field region. (d) Transient current responses of the NC array and thin film under pulse operation. (e) Fast relaxation behavior fitted with an exponential decay model on the μs timescale. (f) Slow relaxation behavior measured at different read biases after LRS initialization.\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/98bb442510fdae995a9f9907.png"},{"id":106405823,"identity":"faf8085f-3fac-4c1f-b5d1-e2e655457015","added_by":"auto","created_at":"2026-04-08 09:28:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2067717,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/89a6f4bc-ee6b-4a2e-b3a0-8ac5ed35629b.pdf"},{"id":106404017,"identity":"edbb687a-f162-4494-8ae9-a3d199b868bf","added_by":"auto","created_at":"2026-04-08 09:15:22","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":6156355,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-9079219/v1/ad628857ba910cffc4aa6505.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Engineering Structural Discontinuity in Ordered Co3O4 Nanocube Arrays for Volatile Memristive Dynamics","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe precise engineering of nanoscale gaps between discrete building blocks offers a powerful strategy for defining new charge transport regimes in functional materials. Unlike continuous media, where electronic properties are often limited by stochastic bulk processes, architectures with deliberate structural discontinuity allow for the confinement of active conduction volumes to localized interfaces. This level of structural determinism is particularly critical for modulating memristive behavior, the dynamic evolution of resistance in response to external electrical stimuli [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], which is often unstable or irreversible in conventional thin-film systems. While continuous oxide films are effective for non-volatile switching [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], the inherent structural continuity often stabilizes filamentary pathways even after the bias is removed [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], leading to a gradual drift toward non-volatility. This phenomenon is fundamentally linked to energetically demanding bulk transport through the lattice and redox-driven structural changes [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn contrast, the creation of a non-percolated network of nanoscale junctions prioritizes shallow energy pathways at localized interfaces, facilitating volatile memristive behavior where conductance spontaneously returns to its initial state [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Such behavior is generally governed by interfacial processes, including rapid detrapping from shallow states or ion migration along grain boundaries [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], providing a distinct pathway for emulating biological temporal dynamics in logic-in-memory circuits [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and signal processing [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Spinel-type Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e provides a rich landscape for such investigations due to its mixed-valence states of Co\u003csup\u003e2+\u003c/sup\u003e and Co\u003csup\u003e3+\u003c/sup\u003e, which are conducive to intricate charge transport and trapping dynamics. However, the dominance of bulk-governed conduction in conventional Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin films often masks these subtle interface-mediated phenomena, necessitating device geometries that can suppress persistent filament formation [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this study, we investigate the emergence of unique conduction physics enabled by structural discontinuity in a network of self-assembled Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanocubes (NCs). By engineering a non-percolated architecture in which NCs are separated by well-defined nanogaps, we induce a transition in the dominant transport behavior from bulk-dominated percolation to interface-mediated tunneling and localized trapping. Unlike continuous Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin films which exhibit negligible memory effects, our NC array reveals a stable and highly reliable volatile response. This structural determinism achieves an ultralow operating current of 10 nA with exceptional statistical uniformity, yielding a coefficient of variation below 9%. Our findings demonstrate that leveraging nanogap-driven transport physics in discontinuous nanoscale architectures provides a robust pathway for developing energy-efficient electronic functionalities unattainable in conventional continuous media [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Experimental Section","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Materials\u003c/h2\u003e \u003cp\u003eThe following chemicals were used in this study: cobalt(II) perchlorate hexahydrate (Co(ClO\u003csub\u003e4\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO, 99.5%), cobalt(II) chloride hexahydrate (CoCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO, 98%), 1-octanol (CH\u003csub\u003e3\u003c/sub\u003e(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e7\u003c/sub\u003eOH, 99%), oleylamine (CH\u003csub\u003e3\u003c/sub\u003e(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e7\u003c/sub\u003eCH\u0026thinsp;=\u0026thinsp;CH(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e7\u003c/sub\u003eCH\u003csub\u003e2\u003c/sub\u003eNH\u003csub\u003e2\u003c/sub\u003e, 70%), oleic acid (CH\u003csub\u003e3\u003c/sub\u003e(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e7\u003c/sub\u003eCH\u0026thinsp;=\u0026thinsp;CH(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e7\u003c/sub\u003eCOOH, 90%), all purchased from Sigma-Aldrich. \u003cem\u003en\u003c/em\u003e-Hexane (CH\u003csub\u003e3\u003c/sub\u003e(CH\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e4\u003c/sub\u003eCH\u003csub\u003e3\u003c/sub\u003e, 95%) and toluene (C\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e5\u003c/sub\u003eCH\u003csub\u003e3\u003c/sub\u003e, 99.8%) were obtained from Daejung Chemicals \u0026amp; Metals. All reagents were used as received without further purification. AZ GXR-601 positive photoresist (Merck Performance Materials), LOR lift-off resist (MicroChem/Kayaku Advanced Materials), and APOL-LO 3200 negative lift-off photoresist (KemLab Inc.) were employed for i-line (365 nm) photolithography. p-type Si (100) wafers with a 100 nm SiO\u003csub\u003e2\u003c/sub\u003e layer grown by dry oxidation were used as substrates. A 2-inch Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e sputtering target (TASCO, 99.9%) was used for Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin film deposition, and 1.5-inch Pt and Ti sputtering targets (TASCO, 99.99%) were used for the electrode deposition.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Device fabrication\u003c/h2\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Si substrates were sequentially cleaned with acetone, ethanol, and deionized water, followed by photolithographic patterning and lift-off to define the electrode geometry. A 5 nm Ti adhesion layer and a 20 nm Pt bottom electrode were deposited using an RF magnetron sputtering system equipped with multiple targets. Photolithography was then used to define 25 \u0026times; 25 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e square trenches in the photoresist, into which the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC arrays were subsequently assembled.\u003c/p\u003e \u003cp\u003eMonodisperse Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NCs were synthesized via a colloidal method [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Cobalt(II) perchlorate hexahydrate (370 mg) was dissolved in 15 mL of 1-octanol containing 3.32 mL of oleylamine. The mixture was gradually heated to 120\u0026deg;C under magnetic stirring, and 0.7 mL of distilled water was added prior to reaching the target temperature. The reaction was maintained for 2 h to promote NC growth, then cooled to room temperature. The products were collected by adding acetone and ethanol followed by centrifugation and washing.\u003c/p\u003e \u003cp\u003eTo form Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC arrays inside the pre-defined trenches, the synthesized NCs were redispersed in a 1:1 (v/v) mixture of hexane and toluene containing oleic acid (18 \u0026micro;L\u0026middot;mL\u003csup\u003e-1\u003c/sup\u003e). The dispersion was ultrasonicated for 10 min to ensure homogeneity, and the patterned substrates were immersed in the dispersion. During natural solvent evaporation at 25\u0026deg;C, convective flow induced lateral assembly of NCs into ordered two-dimensional arrays within the trench regions. After drying, the assembled layers were annealed at 400\u0026deg;C in air for 30 min to remove residual organic ligands and achieve well-ordered Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC arrays. The photoresist surrounding the trenches was then removed by lift-off, leaving the NC arrays only inside the patterned regions. After this process, Pt top electrodes with 25 \u0026times; 25 \u0026micro;m\u003csup\u003e2\u003c/sup\u003e square geometry were patterned by photolithography and defined by a lift-off process to complete the Pt/Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e/Pt device structure.\u003c/p\u003e \u003cp\u003eCo\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin films were subsequently deposited under identical conditions using a 2-inch Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e ceramic target (99.9%, TASCO) at a substrate temperature of 400\u0026deg;C. During sputtering, Ar (40 sccm) and O\u003csub\u003e2\u003c/sub\u003e (10 sccm) were introduced to maintain a total pressure of 5 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Torr, with an RF power of 70 W and a base pressure of 5.8 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e Torr. Top Pt electrodes for the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin film devices were fabricated using the same photolithography and lift-off process as for the NC-array devices.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Material characterization\u003c/h2\u003e \u003cp\u003eThe structural properties such as crystallinity and crystalline phase were analyzed by XRD (SmartLab diffractometer, Rigaku, λ\u0026thinsp;=\u0026thinsp;1.5418 \u0026Aring;). The surface morphology of as-prepared samples was analyzed by scanning electron microscope (SEM, JSM-7500F, JEOL). The chemical properties were estimated using X-ray photoelectron spectroscopy (XPS, NEXAS, Thermo Fisher Scientific). To calculate the valence band maximum and work function of Co3O4 on Pt, UPS (KRATOS AXIS Supra model) was employed with a UV source He I (21.2 eV) under a sample bias\u0026thinsp;\u0026minus;\u0026thinsp;9 eV. The TEM samples were prepared by focused ion beam (FIB) system (NX5000, Hitachi) using a Ga\u0026thinsp;+\u0026thinsp;ion beam source. A carbon protection layer was deposited to prevent specimen degradation and protect the surface of the TEM samples. The elemental mapping across the cross-section and structural information were obtained with a TEM apparatus (Tecnai G2 F30 S-Twin, FEI) operated at 300 kV and equipped with an energy-dispersive spectrometer (EDS). All characterizations were performed at the GIST Advanced Institute of Instrumental Analysis (GAIA).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Device test\u003c/h2\u003e \u003cp\u003eA probe station connected to a Keithley 4200A-SCS parameter analyzer (Tektronix Inc., USA) was used for all electrical measurements. To ensure high signal integrity at low current levels, Keithley 4200-PA remote preamplifiers were employed, effectively reducing the system noise floor from the nA range to below 1 pA. This enhancement provided a high signal-to-noise ratio (SNR\u0026thinsp;\u0026gt;\u0026thinsp;10\u003csup\u003e5\u003c/sup\u003e) for accurately capturing the volatile switching characteristics of the NC array, which operates at an ultralow current level of ~\u0026thinsp;100 nA. Measurements were performed at room temperature under ambient conditions, with the bottom electrode used for voltage bias and the top electrode grounded.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Structural and Crystallographic Characterization of Co3O4 Thin Film and NC Array\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo systematically investigate the influence of structural configuration on memristive behavior, we established two distinct model systems: a continuous thin film and discontinuous NC arrays. As detailed in the Experimental Section, the continuous Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin films were deposited via radio frequency (RF) magnetron sputtering, whereas the discontinuous NC arrays were constructed through a Marangoni flow-driven self-assembly process (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The internal structural integrity of the NC active layer within the device environment was first verified. Cross-sectional analysis via focused ion beam (FIB) reveals that the NC layer is well-confined between the electrode interfaces (\u003cb\u003eFig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e), while energy dispersive X-ray spectroscopy (EDS) mapping confirms the precise spatial distribution of Co and O without interlayer diffusion (\u003cb\u003eFig. S2\u003c/b\u003e). The crystalline integrity and orientation of the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e layers were characterized using X-ray diffraction (XRD). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC powder displays diffraction peaks consistent with the standard spinel cubic phase (JCPDS #42-1467) [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. While the sputtered thin film exhibits multiple reflections such as (111), (222), and (511), indicating a polycrystalline nature, the NC array shows an exclusive and intense reflection at the (004) plane. The magnified XRD view in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec further confirms this strong out-of-plane orientation, suggesting that the NCs are precisely aligned with their {100} facets parallel to the substrate. The surface morphology, captured via top-view scanning electron microscopy (SEM) in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed, reveals that the self-assembled NCs form a long-range ordered, densely packed two-dimensional (2D) array over a large area. Such high structural uniformity and reproducibility of the NC arrays ensure a reliable platform for subsequent integration into memristive devices. The chemical state and purity of the self-assembled Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC array were further verified using X-ray photoelectron spectroscopy (XPS). As presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef, the O 1s and Co 2p spectra exhibit the characteristic features of a conventional spinel Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e phase [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The Co 2p spectrum shows the typical 2p\u003csub\u003e3/2\u003c/sub\u003e and 2p\u003csub\u003e1/2\u003c/sub\u003e doublets along with their respective satellite peaks, confirming the expected mixed-valence states of Co\u003csup\u003e2+\u003c/sup\u003e and Co\u003csup\u003e3+\u003c/sup\u003e. Similarly, the O 1s spectrum reflects the presence of lattice oxygen and surface-adsorbed species consistent with standard oxide surfaces. These results confirm that the NCs maintain high chemical integrity throughout the self-assembly process without the formation of secondary phases or detectable impurities. Finally, the atomic-scale crystalline structure was further characterized via high-resolution transmission electron microscopy (HR-TEM). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg shows a clear lattice fringe pattern of the assembled NCs. The corresponding Fast Fourier Transform (FFT) patterns from the grain interior (Area 1, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eh) and the interfacial region (Area 2, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ei) both exhibit well-defined diffraction spots along the [110] zone axis. These two well-defined systems, a continuous thin film and a discontinuous NC array, were therefore selected as representative structural models for subsequent electrical characterization.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Quantitative Structural Analysis of the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC Array\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo establish a rigorous structural model, we optimized the assembly process to yield a discrete monolayer of Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NCs for statistical characterization. This intentional single-layer configuration was essential to prevent overlapping particle images, thereby ensuring the pixel-resolved boundaries required for precise automated analysis. The quantitative evaluation was performed using an automated segmentation framework based on the Segment Anything Model (SAM), as detailed in \u003cb\u003eSupplementary Note 1\u003c/b\u003e [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, instance-level binary masks were generated for four representative regions (Regions 1\u0026ndash;4), with original SEM images and exhaustive labeled masks provided in \u003cb\u003eFig. S3\u003c/b\u003e and \u003cb\u003eS4\u003c/b\u003e, respectively.\u003c/p\u003e \u003cp\u003eUsing this framework, we extracted the critical parameters including physical dimensions, in-plane orientation (\u003cem\u003eθ\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e, \u003cb\u003eSupplementary Note 2\u003c/b\u003e and \u003cb\u003eFig. S5\u003c/b\u003e), and positional coordinates for every identified particle. To evaluate the structural uniformity across the large-area assembly, we analyzed the distribution of particle sizes (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed) and interparticle gaps (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg). The cumulative analysis revealed a highly monodisperse size distribution with a mean of 10.22 nm (\u003cem\u003eσ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.67 nm) and a precisely controlled interparticle gap of 2.84 nm (\u003cem\u003eσ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.64 nm). These gaps, which serve as fundamental tunneling junctions, were resolved at the pixel level using a robust contour-resolved method (\u003cb\u003eSupplementary Notes 3\u003c/b\u003e, \u003cb\u003e4\u003c/b\u003e and \u003cb\u003eFig. S6\u003c/b\u003e, \u003cb\u003eS7\u003c/b\u003e). The exceptionally low coefficient of variation for both parameters confirms that the array possesses high structural determinism.\u003c/p\u003e \u003cp\u003eThe long-range ordering was further quantified by computing the radial distribution function, \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh. The prominent periodic peaks correspond precisely to the characteristic distance to a square lattice, including \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{d}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt{2}\\varvec{d}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(2\\varvec{d}\\)\u003c/span\u003e\u003c/span\u003e (\u003cb\u003eSupplementary Notes 5\u003c/b\u003e, \u003cb\u003e6\u003c/b\u003e and \u003cb\u003eFig. S8\u003c/b\u003e, \u003cb\u003eS9\u003c/b\u003e). Notably, the first peak is observed at 13.04 nm, which shows an exceptional agreement with the theoretical center-to-center distance of 13.06 nm calculated from the sum of the mean particle size (10.22 nm) and the interparticle gap (2.84 nm). This numerical consistency confirms that the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NCs form a well-defined, non-percolated network with high geometric fidelity. This translational order is complemented by the bond-orientational correlation function, \u003cem\u003eg\u003c/em\u003e\u003csub\u003eorient\u003c/sub\u003e(\u003cem\u003er\u003c/em\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ei), which exhibits a long-range plateau. This result confirms the preservation of global orientational alignment across the entire assembly (\u003cb\u003eSupplementary Note 7\u003c/b\u003e and \u003cb\u003eFig. S10\u003c/b\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Fabrication and Electrical Characterization of Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC Array Devices\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo investigate the influence of nanoscale architecture on electrical switching performance, we fabricated Pt/Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC array/Pt and a Pt/Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e thin film/Pt device. The detailed fabrication sequence, involving the selective deposition of the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e active layer within pre-defined trenches, is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. Optical and microscopic imaging in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb confirms the structural integrity and precise alignment of these NC-assembled active regions. Initial characterization revealed a striking disparity in the switching mechanisms between the two configurations. The architectural impact on switching behavior is clearly evidenced by the contrasting electrical responses of the two systems. While the NC array device achieves stable volatile memristive switching at a low operating current of ~\u0026thinsp;10 nA (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec), its continuous thin film counterpart fails to exhibit any functional switching, presenting only a featureless and nearly linear I\u0026ndash;V response without discernible hysteresis (\u003cb\u003eFig. S11a\u003c/b\u003e). This disparity indicates that the bulk-like environment of the continuous film facilitates non-selective charge transport [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], which prevents the formation of the localized, reversible switching paths uniquely enabled by the discontinuous, NC-assembled geometry.\u003c/p\u003e \u003cp\u003eThe structural robustness of the NC array was further validated during the initial activation process. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed, the NC array requires an initial forming step (indicated by the arrow), where the current significantly drops at high bias (\u0026gt;\u0026thinsp;10 V), signifying an irreversible transition to a high-resistance state (HRS) [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Notably, even after this breakdown-like event, the NC array immediately establishes a stable and repeatable volatile hysteresis loop within the nA range. When the same electrical sequence was applied to the thin film (\u003cb\u003eFig. S11b\u003c/b\u003e), a similar irreversible increase in resistance occurred; however, the thin film failed to exhibit any subsequent memory effect. Instead, the thin film exhibited unstable current fluctuations and a featureless I\u0026ndash;V curve lacking any repeatable hysteresis, suggesting that the catastrophic bulk failure [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] completely suppressed the charge dynamics. These findings demonstrate that while high bias causes irreversible modifications in both systems, the discontinuous NC-gap-NC geometry maintains its interfacial integrity even after the initial HRS transition. This allows the NC array to preserve localized charge trapping or ionic displacement within the gaps, thereby maintaining electrically reversible switching that is unattainable in the homogenized, failed bulk material. The reliability and uniformity of the switching parameters were statistically validated through a rigorous analysis of 100 consecutive cycles. As shown in the cumulative probability plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee), the transition voltages for both V\u003csub\u003eset\u003c/sub\u003e and V\u003csub\u003ereset\u003c/sub\u003e exhibit a steep and linear slope, indicating a highly predictable switching behavior within a well-defined voltage window. This is further supported by the distribution histograms (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef), where the operating voltages exhibit exceptional uniformity, characterized by a mean set voltage (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003eset\u003c/sub\u003e) of 8.75 V (with a standard deviation, \u003cem\u003eσ\u003c/em\u003e\u003csub\u003eset\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.54 V) and a mean reset voltage (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003ereset\u003c/sub\u003e) of 4.38 V (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003ereset\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.39 V). To further evaluate the device's stability, we calculated the coefficient of variation (\u003cem\u003eσ\u003c/em\u003e/\u003cem\u003e\u0026micro;\u003c/em\u003e), which yielded remarkably low values of 6.17% for V\u003csub\u003eset\u003c/sub\u003e and 8.90% for V\u003csub\u003ereset\u003c/sub\u003e. The narrow Gaussian distributions and consistent alignment in the cumulative plots reflect a high degree of reproducibility, which can be attributed to the localized switching occurring within the NC-assembled architecture. This statistical consistency suggests that the NC-based geometry helps to regulate the stochastic nature of charge dynamics and ionic motion. By providing a more controlled environment for these processes, the NC array achieves the level of uniformity necessary for reliable memristive applications [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Conduction Mechanisms and Relaxation Dynamics of the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC Array\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo understand the physical origin of the reliable volatile switching observed in our NC array, we examined the I\u0026ndash;V characteristics using log\u0026ndash;log plots under positive bias [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). The device shows distinct transport regimes, shifting from low-voltage Ohmic conduction to field-assisted emission as the bias increases [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. In the intermediate (0.7~-5.8 V) and high-field (\u0026gt;\u0026thinsp;5.8 V) regions, the conduction is well-described by Schottky emission (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and Fowler\u0026ndash;Nordheim (FN) tunneling (Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) models [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], respectively:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\text{J}}_{\\text{S}\\text{E}}\\propto{\\text{T}}^{2}\\text{e}\\text{x}\\text{p}(\\text{A}\\frac{\\sqrt{\\text{E}}}{\\text{T}}-\\text{B})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\text{J}}_{\\text{F}\\text{N}}\\propto{\\text{E}}^{2}\\text{e}\\text{x}\\text{p}\\left(\\frac{-\\text{A}}{\\text{E}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eJ\u003c/em\u003e represents the current density, \u003cem\u003eE\u003c/em\u003e is the electric field, and \u003cem\u003eT\u003c/em\u003e is the temperature. Constants A and B are material-specific parameters related to the interface barrier and dielectric properties. The excellent linear fits in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9964) and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9846) confirm that charge transport is primarily limited by the potential barriers at the NC interfaces rather than bulk conduction [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. This conclusion is supported by the clear distinction from bulk-dominated transport; if the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e bulk were the governing factor, the I\u0026ndash;V characteristics would typically remain confined to ohmic (\u003cem\u003eJ\u003c/em\u003e\u0026prop;\u003cem\u003eE\u003c/em\u003e) or trap-limited space-charge-limited current (SCLC, \u003cem\u003eJ\u003c/em\u003e\u0026prop;\u003cem\u003eE\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] regimes. Notably, the high-electric field data in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec exhibit a clear linear relationship with a characteristic negative slope in the ln(I/V\u003csup\u003e2\u003c/sup\u003e) vs. 1/V plot, which is a definitive signature of FN tunneling. This confirms that under strong electric fields, the interface barrier narrows into a triangular shape, allowing carriers to tunnel through the junction [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Given the discontinuous nature of the NC array, where each NC is physically separated by nanoscale gaps, these results validate that the interfacial junctions act as the primary structural determinants of the electrical response of NC array device [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The volatile nature of this switching is further clarified by time-dependent measurements. Unlike the continuous thin film, which shows high mA-range currents and abrupt failure, the NC array operates at an ultralow nA level and exhibits a gradual, analog relaxation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). Such a contrast is consistent with the fact that resistive switching in continuous oxide stacks is often dominated by filamentary conduction, where localized conductive paths can concentrate Joule heating and accelerate irreversible degradation under large current stress [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. In comparison, the discontinuous NC-gap-NC geometry effectively confines the active conduction volume to nanoscale junctions, which can mitigate uncontrolled filament overgrowth and help preserve interfacial integrity even after irreversible high-bias perturbations [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. This relaxation follows an exponential decay [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\text{I}\\left(\\text{t}\\right)\\propto\\text{A}\\text{e}\\text{x}\\text{p}(-\\text{t}/{\\tau})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere A is the initial current amplitude and \u003cem\u003eτ\u003c/em\u003e represents the characteristic decay time constant. Following a short 1 ms pulse, we observe fast relaxation with \u003cem\u003eτ\u003c/em\u003e\u003csub\u003efast\u003c/sub\u003e values between 1.20 and 1.95 \u0026micro;s (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee). Given the short timescale, this transient relaxation is most plausibly dominated by electronic processes, such as rapid detrapping or interfacial charge redistribution, which are widely observed as the origin of short-term plasticity in volatile memristive systems [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. To further investigate the long-term dynamics under maximum stimulus, a prolonged bias (10 V for 60 s) was applied. This intense stimulus can induce pronounced ionic redistribution within the NC network, driving the device into a distinct HRS [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. While similar high-bias conditions in continuous thin films can lead to permanent failure modes accompanied by electrode/oxide damage and loss of switching functionality, the NC array uniquely maintains its dynamic recovery even in this regime [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Under subsequent read biases, the device exhibits a slow relaxation component with \u003cem\u003eτ\u003c/em\u003e\u003csub\u003eslow\u003c/sub\u003e values ranging from 67.63 to 175.8 s (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef). The stark difference in these timescales suggests a dual-process model where short-term relaxation originates from electronic processes and long-term recovery is controlled by the stochastic back-diffusion of localized ionic species within the interfacial gaps [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Notably, as the read bias increases, \u003cem\u003eτ\u003c/em\u003e\u003csub\u003eslow\u003c/sub\u003e also increases; this trend is consistent with an external electric field that can bias ionic drift and oppose spontaneous relaxation toward equilibrium [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eUltimately, these dual-mode dynamics underpin the exceptional functional uniformity observed in our device. It is particularly intriguing that the NC array exhibits intrinsic leaky integrate-and-fire (LIF)-like behavior within a single-device architecture, as evidenced by the biomimetic neuronal firing responses [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] in \u003cb\u003eFig. S12\u003c/b\u003e. While the Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e NC array currently operates at relatively high voltages, this could be further optimized by engineering the interfacial gaps during the self-assembly process, for instance, by tailoring the length and chemical nature of the organic surfactants to reduce the effective tunneling barrier and strengthen inter-NC coupling [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. Importantly, the ultralow operating current and reproducible relaxation observed here suggest that the NC-gap-NC junction can serve as a controllable physical motif to program volatile memristive dynamics. In this sense, nanoscale gaps provide a fundamental design handle to access and tune interface-mediated transport regimes that are often masked in continuous films, offering useful guidance for constructing energy-conscious neuromorphic primitives.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn summary, we have established a deterministic design rule for modulating charge transport by engineering the structural dimensionality of Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e architectures. Our comparative study demonstrates that the transition from irreversible hard breakdown in continuous thin films to reliable, low-power switching in self-assembled NC arrays is fundamentally driven by the deliberate introduction of structural discontinuity. The rigorous statistical framework, integrating SAM-based segmentation and spatial correlation functions, proves that the high translational and orientational ordering of the NC lattice is the key determinant of reproducibility and functional uniformity. Specifically, the formation of an ordered array with an average particle size of 10.22 nm and a precisely controlled interparticle gap of 2.84 nm effectively localizes charge trapping and tunneling processes at the nanoscale junctions. This structural determinism enables stable volatile memristive switching at an ultralow operating current of 10 nA with exceptional statistical uniformity, yielding coefficient of variation values for switching voltages below 9%. Furthermore, the identification of dual-mode relaxation dynamics, which encompass rapid microsecond electronic and slow long-term ionic processes, enables the emulation of complex temporal dynamics essential for biomimetic signal processing. By bridging the gap between automated image-based metrology and macroscopic electronic functionality, this work provides a scalable and predictable platform for the development of robust, next-generation functional hardware. Ultimately, leveraging the unique transport physics of discontinuous nanoscale architectures offers a versatile pathway for engineering energy-conscious electronic systems with high structural and functional determinism.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eInhyeok Oh and Jun Beom Hwang contributed equally to this work. This research was supported by the program of Future Hydrogen Original Technology Development (RS-2021-NR057808), through the National Research Foundation of Korea (NRF), funded by the Korean government (Ministry of Science and ICT (MSIT)). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-00563779).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI. Oh: Writing \u0026ndash; original draft, Formal analysis, Visualization, Conceptualization. J. B. Hwang: Writing \u0026ndash; original draft, Formal analysis, Visualization, Conceptualization. M. Kang: Formal analysis, Writing\u0026ndash;review \u0026amp; editing. D. Kim: Formal analysis. S. Kim: Investigation. J. Lee: Validation. H. Kim: Investigation. D. Lee: Validation. M. H. Oh: Writing \u0026ndash; review \u0026amp; editing, Supervision, Project administration. S. Lee: Writing \u0026ndash; review \u0026amp; editing, Supervision, Validation, Project administration, Funding acquisition.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the program of Future Hydrogen Original Technology Development (RS-2021-NR057808), through the National Research Foundation of Korea (NRF), funded by the Korean government (Ministry of Science and ICT (MSIT)). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-00563779).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eStrukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. 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Nano Lett Am Chem Soc 10:1960\u0026ndash;1969. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nl101284k\u003c/span\u003e\u003cspan address=\"10.1021/nl101284k\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"advanced-composites-and-hybrid-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"achm","sideBox":"Learn more about [Advanced Composites and Hybrid Materials](https://link.springer.com/journal/42114)","snPcode":"42114","submissionUrl":"https://submission.nature.com/new-submission/42114/3","title":"Advanced Composites and Hybrid Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Nanocube array, Interparticle gap, Automated metrology, Volatile memristive behavior, Fowler-Nordheim tunneling, Conduction mechanism","lastPublishedDoi":"10.21203/rs.3.rs-9079219/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9079219/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe precise engineering of nanoscale gaps between discrete building blocks offers a deterministic pathway to govern charge transport physics in functional materials. Here, we demonstrate a fundamental transition from stochastic bulk conduction to reliable interface-mediated volatile switching by deliberately introducing structural discontinuity in spinel-type Co\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e nanocube (NC) arrays. While continuous oxide thin films suffer from irreversible breakdown and featureless transport, our self-assembled NC architecture enables a stable and low-power functional response. Utilizing an automated metrology framework based on the Segment Anything Model (SAM), we confirm the formation of a highly ordered, non-percolated square lattice with sub-nanometer precision in interparticle spacing. This structural determinism confines the active conduction volume to nanoscale junctions, achieving an ultralow operating current of 10 nA and exceptional statistical uniformity (coefficient of variation\u0026thinsp;\u0026lt;\u0026thinsp;9%). Quantitative analysis identifies Schottky emission and Fowler-Nordheim tunneling at NC-gap-NC interfaces as the dominant mechanisms. Furthermore, time-resolved measurements reveal dual-mode relaxation dynamics characterized by microsecond electronic detrapping and long-term ionic back-diffusion, which facilitate complex temporal dynamics for biomimetic signal processing. Our findings suggest that nanogap-driven tunneling, rather than bulk percolation, can serve as a useful design principle for energy-efficient electronic primitives beyond conventional continuous media.\u003c/p\u003e","manuscriptTitle":"Engineering Structural Discontinuity in Ordered Co3O4 Nanocube Arrays for Volatile Memristive Dynamics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-06 15:48:33","doi":"10.21203/rs.3.rs-9079219/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-22T08:24:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-22T07:53:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"144042898393403852582057362650026814043","date":"2026-04-03T21:33:40+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-02T17:04:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-01T21:52:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"132877768331792138138812257991841398184","date":"2026-04-01T17:14:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"1329528142015986431021591051833769173","date":"2026-04-01T08:47:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"58985346513718337096742592310130477102","date":"2026-04-01T08:40:12+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-01T08:30:28+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-13T11:10:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-11T01:41:25+00:00","index":"","fulltext":""},{"type":"submitted","content":"Advanced Composites and Hybrid Materials","date":"2026-03-10T04:53:11+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"advanced-composites-and-hybrid-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"achm","sideBox":"Learn more about [Advanced Composites and Hybrid Materials](https://link.springer.com/journal/42114)","snPcode":"42114","submissionUrl":"https://submission.nature.com/new-submission/42114/3","title":"Advanced Composites and Hybrid Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"b65c4e41-e588-4aa0-a990-317386bd5861","owner":[],"postedDate":"April 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-04-22T08:42:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-06 15:48:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9079219","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9079219","identity":"rs-9079219","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}

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