Stochastic resonance in 2D materials based memristors

The paper investigates whether and how stochastic resonance (SR)—the constructive role of noise improving detectability and processing of weak signals—emerges in solid-state memristive devices based on hexagonal boron nitride (h-BN). SR has been widely studied in biology and sensory systems and has been observed in various electronic systems. Memristors, which replicate synaptic functions and are central to neuromorphic hardware, offer natural thresholding and nonlinearity necessary for SR. However, traditional memristive materials suffer from variability and reliability issues. The authors aim to fabricate scalable h-BN memristors and determine, through controlled noise injection and analysis of state transitions, whether SR can be demonstrated, quantified, and potentially leveraged to enhance neuromorphic and memory applications.

The introduction reviews SR from its origins (Benzi et al.) to applications in biology and medicine, highlighting sensory neurobiology examples (paddlefish, crickets) and prior electronic demonstrations (Schmitt triggers, tunnel diodes, phase-change materials, photodetectors). It discusses memristors as promising elements for neuromorphic systems due to thresholding and multilevel non-volatile behavior, contrasting advantages with variability and reliability challenges in conventional materials (metal-oxides, phase-change). Prior work on h-BN memristors and their switching mechanisms is cited, along with literature on SR analyses using cumulative distribution functions and power spectral density/SNR methods in other devices.

• Device fabrication: Industry-compatible, wafer-scalable process to form cross-point Au/Ti/h-BN/Au memristors (5 µm × 5 µm). Bottom electrodes: Ti (10 nm)/Au (40 nm) by e-beam evaporation. Multilayer h-BN (~6 nm, ~18 layers) grown by CVD on Cu and transferred via wet transfer onto SiO2/Si with bottom electrodes. Top electrodes: Ti/Au deposited orthogonally to form the cross-point. TEM and optical microscopy characterized the stacks (polycrystalline CVD h-BN vs. exfoliated h-BN). Exfoliated h-BN control devices were also prepared.
• Electrical characterization: Quasi-static ramped voltage stress (RVS) sequences applied to the top electrode with bottom grounded, measuring I–V and resistance states at VREAD = 0.1 V. Forming, SET (positive RVS), and RESET (negative RVS) operations were characterized. Set and reset voltages were extracted using numerical techniques (Supplementary Note 1).
• Noise injection: Exponential and Gaussian voltage noise (zero-mean) were superimposed on the RVS pulses. Noise standard deviation (SD) was swept from 50 to 150 mV in 25 mV steps. Time-domain input voltage and output current were recorded for consecutive SET cycles.
• SR assessment, approach 1 (state ratio analysis): For each noise condition, whether switching occurred per cycle was recorded, and RHRS, RLRS, and their ratio RHRS/RLRS (ROFF/RON) were statistically analyzed. Cumulative distribution functions (CDFs) were constructed for exponential and Gaussian noise. The median ROFF/RON versus noise SD was used to identify resonance-like enhancement relevant to memory applications.
• SR assessment, approach 2 (spectral SNR analysis): Power spectral densities (PSDs) of the input voltage and output current time series were computed for different Gaussian noise SDs. A main power peak at f0 ≈ 0.02–0.03 Hz (set-phase periodicity ~30–50 s) was identified along with harmonics. Signal-to-noise ratio (SNR) was quantified as the prominence of the main peak over surrounding noise frequencies within a band around f0, evaluating different counts of noisy frequencies (e.g., n = 20 or 30) to test robustness.
• Instrumentation: Keysight B1500A parameter analyzer with B1511B MPSMU and Karl Suss PSM6 probe station; microscopy and TEM via Leica DM400 and FEI JEM-2100; PSD/SNR computed from the measured time series.

• CVD-grown h-BN devices exhibited stable non-volatile bipolar resistive switching (RS); exfoliated h-BN devices did not show RS and instead underwent irreversible breakdown at high stress.
• Typical resistances at VREAD = 0.1 V: RHRS ≈ 575.5 MΩ; RLRS ≈ 156.7 Ω; RHRS/RLRS > 1000 across cycles enabling robust state discrimination.
• Switching voltages and variability: VSET ≈ 2.52 V with CV.SET ≈ 0.16; VRESET ≈ −0.49 V with CV.RESET ≈ 0.3. RESET involved sharp current drop attributed to Joule heating; currents during SET/RESET reached ~10 mA, occasionally ~100 mA.
• Mechanism: Filamentary RS via Ti x+ ion motion and conductive nanofilament (CNF) formation/rupture in polycrystalline CVD h-BN regions with higher defect density; Joule-assisted filament rupture during RESET.
• SR via state ratio method: Median ROFF/RON versus noise SD showed a clear peak at ~80 mV SD for both exponential and Gaussian noise, evidencing constructive effects of noise on switching contrast; CDFs of ROFF/RON shifted accordingly.
• SR via spectral SNR: PSD-based SNR of the output current displayed a pronounced enhancement at ~125 mV SD (robust to choice of noisy frequency count), and a possible secondary enhancement near ~60 mV SD.
• Implications: Noise can enhance memory-relevant metrics (e.g., resistance ratio, potential BER improvements), aligning with SR theory and indicating practical utility in memristive neuromorphic systems.

The study demonstrates that h-BN-based memristors, fabricated with scalable processes, exhibit stochastic resonance when biased with controlled noisy stimuli. The two complementary analyses confirm SR: a median ROFF/RON maximum at moderate noise (≈80 mV SD) and a spectral SNR optimum at higher noise (≈125 mV SD), with indications of a secondary resonance near 60 mV SD. These findings address the central question of whether noise can constructively improve memristor performance and signal detectability, analogous to biological systems. The ROFF/RON enhancement is directly relevant for memory reliability and read margin, while SNR optimization reflects improved periodic signal extraction in the presence of noise. Differences in optimal noise levels between the two methods likely arise from distinct metrics (quasi-static resistance ratio vs. frequency-domain SNR optimization), suggesting multiple SR regimes or a double SR phenomenon, as reported in other systems. Overall, the results support leveraging controlled noise in neuromorphic circuits and non-volatile memories to improve performance metrics and robustness.

This work fabricates and characterizes Au/Ti/h-BN/Au memristors that show clear non-volatile bipolar RS and unambiguously exhibit stochastic resonance under injected Gaussian and exponential voltage noise. Two independent methodologies reveal SR: (1) a peak in the median ROFF/RON at ~80 mV noise SD and (2) a PSD-based SNR peak at ~125 mV SD, with a possible secondary resonance at ~60 mV. The devices achieve large resistance contrast (RHRS/RLRS > 1000), reasonable variability in VSET/VRESET, and a filamentary mechanism consistent with Ti ion dynamics in polycrystalline h-BN. These findings bridge neurobiological SR concepts with memristive hardware and indicate opportunities to harness noise to enhance memory margins and neuromorphic functionality. Future research could explore: systematic mapping of SR regimes (including potential double SR), optimization of noise type and statistics, device-to-device and wafer-scale variability impacts, higher-speed/array-level demonstrations, and integration into functional neuromorphic circuits.

• The secondary SNR enhancement (~60 mV SD) and its relation to the ROFF/RON peak require further investigation to confirm a double SR phenomenon.
• SR characterization focused on specific noise distributions (Gaussian/exponential) and a limited SD range (50–150 mV); broader noise statistics and amplitudes were not explored.
• Measurements emphasize quasi-static RVS and low-frequency dynamics (set phase ~30–50 s); SR behavior at higher speeds/frequencies or in large arrays was not assessed.
• Inherent cycle-to-cycle variability and stochastic filament dynamics remain and may impact generalizability across devices and process corners.
• Exfoliated h-BN devices did not exhibit RS, underscoring material/defect-structure dependence; conclusions may not transfer to all h-BN implementations.