Temperature-dependent resistive switching statistics and mechanisms in nanoscale graphene–SiO₂–graphene memristors†

Yuwen Cai ^ab, Wei Yu ^ab, Qiuhao Zhu ^ab, Xiyuan Liu ^ab, Xiao Guo ^a and Wenjie Liang *^abc
aBeijing National Center for Condensed Matter Physics, Beijing Key Laboratory for Nanomaterials and Nanodevices, Institute of Physics, Chinese Academy of Sciences (CAS), Beijing 100190, China. E-mail: wjliang@iphy.ac.cn
^bSchool of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
^cSongshan Lake Materials Laboratory, Dongguan, Guangdong, China

First published on 29th May 2025

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Introduction

With the rapid development of artificial intelligence (AI),¹ traditional computing systems face significant challenges related to latency, integration and power consumption.² Memristors, also known as resistive random-access memory (RRAM), offer an innovative in-memory computing technology expected to play a crucial role in future electronics.^3–7 Among the various options, the silicon oxide memristor stands out due to its near-perfect interface, low manufacturing cost and excellent compatibility with complementary metal–oxide–semiconductor (CMOS) technology,⁸ making it a highly desirable material for RRAM devices,^9–16 and exhibits excellent on–off ratio, endurance, retention time and integration capabilities. However, switching uniformity and stability issues restrict the further utilization of silicon oxide RRAM memory chips, underlining the importance of understanding debatable switching mechanisms to overcome these limitations.

The switching mechanisms in silicon oxide RRAM devices have been broadly classified into intrinsic resistive switching (RS) of the oxide and extrinsic switching involving diffusive metal electrodes. Intrinsic switching is particularly promising because it avoids the potential instability in CMOS circuits caused by electrode ion diffusion during extrinsic switching. Transmission electron microscopy (TEM) studies have shown preliminary indications of Si nanocrystal crystallization and aggregation inside silicon oxide upon RS, suggesting that RS in intrinsic silicon oxide RRAM is primarily due to the formation and rupture of Si conductive filament (Si CF).^9,17,18 However, experimental studies of the mechanisms for the formation and dissociation of Si CF are still insufficient, leaving critical factors (such as detailed switching dynamics, temperature-dependent defect migration and size effects^16,19–25) affecting the switching process undefined. It is desirable to study the switching mechanisms of a pure and simple device, such as a nanoscale Si CF memristor with a single Si nanocrystal, to elucidate the intrinsic switching mechanisms.

In this article, we fabricate nanometer-sized (sub-2 nm) silicon oxide memristors in graphene–SiO₂–graphene nanogaps and investigate their switching behaviors at various temperatures. The ultimate device's size benefits our study in limiting switching events within a presumably single domain (Si single nanocrystal or filament typically sized 3–5 nm (ref. 17 and 18)), ruling out the complication of multi domain switching. As expected, the set and reset voltages of our devices vary with time, which is consistent with other reported silicon oxide memristors. The statistics of these values are examined utilizing a percolation model that includes the formation and rupture of defect-related conductive cells. We found that the formation of Si CF in the set process is thermally influenced by the diffusion of oxygen ions from oxygen vacancies, and the rupture of Si CF in the reset process is primarily driven by localized Joule heating, yet elevated environmental temperatures demand increased Joule heating to overcome thermally extended oxygen ion migration distances. Additionally, we demonstrate that the high local temperatures induced by graphene nanoconstriction electromigration generate initial oxygen vacancy clusters, significantly enhancing the electroforming efficiency of our devices. This comprehensive investigation provides key insights into refining the technology and improving the performance of silicon oxide RRAM.

Experimental

Device fabrication

The photoresist PMMA 950A5 was spin-coated at 4000 rpm, and the graphene pattern was obtained using a Raith e-line e-beam lithography system. The etching procedure of the graphene nanoconstriction was performed in a reactive ion etching system (PlasmaLab 80 plus, Oxford Instruments Company) using oxygen gas, with the plasma power, gas pressure and etching time being 100 W, 50 mTorr, and 10 s, respectively. Cr/Au metal electrodes were defined by a second EBL procedure and then by a metal deposition and lifting-off technique. To reduce the contact resistance of the device, the device was annealed at 350 °C for 1 h in an argon atmosphere.

Measurements

X-ray photoelectron spectroscopy (XPS) measurements were performed using a Thermo Scientific K-Alpha with a monochromated Al source at 10⁻⁸ Torr. An elliptical X-ray illumination spot with a major axis of 400 μm at 1486.6 eV was used to gather data, and the analyser pass energy was set at 20 eV. Spectral data were processed using Thermo Fisher Avantage v5.976. Electronic measurements were performed in a TTPX probe station with a data acquisition board (National Instruments, PCI 6289) together with a LABVIEW program, and a low-noise current amplifier (DL Instrument 1211) was used to convert the current to voltage.

Fitting the measured set/reset voltage with the Weibull distribution

The Weibull distribution is mainly used for reliability analysis in electronic devices and fits well with the set/reset distributions of our RS devices (Fig. 2b and c). The probability distribution function (PDF) of the Weibull distribution is

The cumulative probability function (CDF) of the Weibull distribution is defined as follows:

F = 1 − exp(−x/x63%)β

or in a linear form:
where β is the shape parameter called the Weibull slope and x_63% is the x value for F ≈ 63%. In the switching model, x can be the measurement data, such as V_set or V_reset, and F is the cumulative probability for the set or reset process.

Therefore, the set/reset Weibull distribution function is similarly defined by the set/reset cumulative probability: F_Vset/reset, as W(V_set/reset) ≡ ln(−Ln(1 − F_Vset/reset)) = β_Vset/resetln(V_set/reset/V_{set/reset, 63%}).

The mean value of the Weibull PDF is given by

The standard deviation is

The Weibull slope β ≫ 1 is found in our experiments. Therefore, with an increase in the Weibull slope, the mean value increases and the standard deviation decreases.

Results and discussion

Our previous work²⁶ demonstrated the successful creation of nanometer-sized graphene nanogap devices using feedback-controlled electromigration, achieving graphene breakdown at a critical current density. In this study, we aim to fabricate nanoscale SiO_x memristors by employing nanometer-sized graphene electrodes on a silicon oxide substrate.

Initially, graphene nanogap devices are prepared by mechanically exfoliating a few-layer graphene onto a SiO₂ substrate and patterning it into the nanoconstriction of width W = 1 μm and length L = 1 μm by electron beam lithography (EBL) and reactive ion etching (RIE) with oxygen gas. A second-step EBL is used to define electrical contacts to the graphene nanoconstriction, followed by the thermal evaporation of Cr/Au (3 nm/60 nm), as depicted in Fig. 1a. To create graphene nanogaps, we apply a feedback-controlled electromigration²⁶ DC voltage to the device at room temperature under vacuum conditions (10⁻⁶ mbar), as shown in Fig. 1b. A sudden decrease in current at an applied voltage of 8 V is observed, which is attributed to the sublimation of carbon atoms.^27–29 This phenomenon enables the device to reach a target resistance of over 1 MΩ, resulting in the controlled DC voltage dropping to zero. Thus, the formed graphene–SiO₂–graphene nanogap is estimated by measuring the tunneling current at a low bias (Fig. S1†). Fitting the low bias voltage tunneling current with the Simmons model³⁰ and atomic force microscopy (AFM) measurements revealed a sub-2 nm gap size (approximately 1.5 nm, as portrayed in Fig. S1†), providing clear evidence for the successful fabrication of graphene nanogap devices on a silicon oxide substrate.

Electroforming of SiO_x memristors is performed by multiple voltage ramps to the nanogap device. An insulating behavior is initially observed, followed by current jumps at a voltage around V_form = 3.3 V (called electroforming voltage), which is attributed to the dielectric soft breakdown and the concurrent generation of oxygen defects in silicon oxide.³¹ As the voltage ramping continues, an oscillatory current I (V) is observed, as depicted in Fig. 1c (red curve), likely owing to the stochastic migration of defects, leading to the formation of an unstable Si CF.^32–34 After over 10 cycles of voltage ramping between 0 V and 8 V, devices eventually showed a stable IV characteristic (Fig. 1c, blue curve), indicating that a stable Si CF is formed. The detailed evolution of conductance changes during voltage cycles is represented in Fig. S2a.† In contrast, no electroforming phenomenon is observed in graphene–Si₃N₄–graphene nanogap devices (Fig. S2b†), proving SiO_x memristor rather than the motion of carbon atoms³⁵ in the graphene nanogap.

A typical RS characteristic curve extracted from multiple cycles of our as-formed SiO_x memristor is shown in Fig. 1d, similar to other SiO_x memristor studies.^8–10,15,36 Initially, the device maintains a low resistance state (LRS) of the Si CF until the voltage reaches approximately 6 V. At this point, a decrease in current is detected, transitioning the device into a high resistance state (HRS), marking the reset process, with the corresponding voltage identified as the reset voltage V_reset. Notably, the HRS is retained as the voltage returns to zero. Upon ramping the voltage to 3 V, a current jump occurs, indicating the set process at set voltage V_set. This unipolar RS phenomenon, where set and reset occur at the same polarity with V_set < V_reset, is highlighted in Fig. 1d and aligns with previous studies on SiO_x RS.^9,15,37,38 The notably high reset voltage of approximately 6 V, while eliminating the need for current compliance, poses challenges for device power consumption, reliability, and system complexity.

The stability of our SiO_x memristor is evaluated through pulse cycling and retention time measurements. As illustrated in Fig. 1e, the device exhibits stable switching characteristics of over 10000 cycles under 0.1 V read voltage, with set and reset operations performed at 5 V and 10 V voltage pulses, respectively. Conductance measurements for both ON and OFF states reveal negligible degradation, confirming reliable cycle endurance. Furthermore, ON and OFF state resistances demonstrate excellent retention stability for over 10⁵ s at a read voltage of 0.1 V, as shown in Fig. 1f, underscoring the device's exceptional non-volatile data retention capability. These results align closely with the prior stability performance of SiO_x memristors,^8–10,15,36 reinforcing the reliability of our study. Moreover, ON state power consumption at a read voltage of 0.1 V is comparable across devices on the order of microwatts (∼0.1 μW), while the OFF-state power consumption ranges from picowatts to nanowatts (pw–nW). The related functions of neuromorphic computing, such as multilevel and synaptic plasticity, are also demonstrated in Fig. S7 of the ESI.† These results highlight the potential of our device for applications in neuromorphic computing.

A distinctive feature of our device is that set voltage V_set = 3 V is close to the electroforming voltage V_form = 3.3 V (red L-shaped arrow in Fig. 1c), unlike other studies where V_set ≪ V_form.^{9,11,15,17,37–39} In these studies, much larger electroforming voltage V_form is required to create a silicon conductive path between two electrodes (>10 nm), presumedly over several oxide domains. The reset process involves breaking only a small portion of this path. Therefore, their set process merely reconnects the broken section, influenced by the shape and location of the broken section, introducing stochasticity and failing to fully capture the intrinsic characteristics of the Si CF's intrinsic characteristics. In contrast, our device forms the Si CF within a very small nanogap (<2 nm), resulting in electroforming voltage V_form closely matching the set voltage V_set. This indicates that the set process in our device directly involves the formation and complete re-formation of the Si CF rather than merely bridging a pre-existing break.^9,17,18 Consequently, our devices encompass all the research conditions in unipolar SiO_x memristors; investigation of our nanogap devices could provide a clear picture of the intrinsic characteristics of unipolar SiO_x switching.

Switching uniformity issues of typical SiO_x memristor is repeated and confirmed in our study by operating those nanoscale devices over one hundred times under constant conditions to obtain the statistics. A stochastic variation in the switching threshold voltage of one device is illustrated in Fig. 2a for operation at room temperature. Set threshold voltages group around 3.2 V with a difference between cycles as large as 0.8. A similar pattern appears for the reset process, with the threshold voltages group around 6.3 V and a variation of 2.6 V. There is no clear correlation between variations in V_set and V_reset of the same trace, indicating random variation of the set and reset voltage. To further investigate this stochastic switching process, we primarily focus on analyzing the statistical distribution of these switching threshold voltages and their temperature dependence.

A ramping voltage is applied with a fixed ramping rate of 0.4 V s⁻¹ over 150 sweep cycles at temperatures ranging from 250 K to 350 K. The statistical distributions of the set/reset voltage at three distinct temperatures are presented in histograms, as depicted in Fig. 2b–g. A clear conclusion can be drawn that higher temperatures correspond to lower set voltage V_set (Fig. 2b–d), and an increase in reset voltage V_reset is consistent with previous studies.⁴⁰ Moreover, a narrower broadening of the set/reset voltage distribution is observed at higher temperatures. Our nano memristor devices cannot be operated below 250 K, indicating that thermal activation is involved in the process (see Fig. S4 in ESI†).

To quantitatively analyze these data, the Weibull distribution is utilized, which models the evolution of defects, leading to percolation path formation, consistent with the analysis of switching dynamics in RRAM devices.^41–43 Black curves illustrated in Fig. 2b–g are fittings of our data according to the Weibull distribution, which shows satisfying agreements, offering average values and standard deviation of V_set and V_reset for different experimental conditions.

Fig. 3 illustrates the extracted switching threshold voltages for the set/reset processes over a temperature range of 250 K to 350 K using the Weibull distribution model. Notably, the variability of set/reset voltages significantly increases as temperature decreases, indicating greater stochasticity in switching operations at lower temperatures, particularly near 250 K. Conversely, distinct trends are observed in the mean values of the set and reset voltages as the temperature varies. The mean set voltage decreases with increasing temperature, indicating a thermally activated process in which higher temperatures facilitate thermal activation. This thermal activation enables the transition from the HRS to the LRS more readily at elevated temperatures, leading to decreased set variability at higher temperatures. For the reset process transitioning from LRS to HRS, the formed Si CF is in a metastable state⁴⁴ influenced by thermal excitation. At higher temperatures, this metastable structure becomes more stable, requiring more energy to disrupt. Consequently, the mean reset voltage increases slightly as the temperature increases, whereas its variability diminishes. This suggests that the thermal stability of the silicon conductive filament in the LRS is enhanced at elevated temperatures, reducing susceptibility to rupture by external electric fields.

To understand temperature-related switching behavior, we model the set/reset process forming Si CF as a single path composed of N resistive switching cells, as described by the percolation model.⁴⁵ In this model, Si CF, spanning the nanogap length d_gap, is conceptualized as a chain with N cells of size a₀, as illustrated in Fig. 4a. Each cell has a switching probability λ from a normal insulating cell to a conductive defective cell when subjected to an electric field. Because a defective cell triggers more cells to switch, switching probability λ is proportional to the ratio of defected cells in the filament.

During the set process, with an applied voltage having a ramping rate R over time t such that V(t) = Rt, the time evolution of λ follows the relationship⁴⁵λ ∝ (t/τ_T)^α, where α is the voltage-independent exponent that models the nonlinearity of the defect generation and τ_T is the characteristic time for defect generation. τ_T corresponds to the power-law rate of the voltage:⁴⁶τ_T = τ_T0(V/d_gap)^−m, where τ_T0 and m are constants. We can expect the statistically Weibull function to evolve linearly with lnV_set,⁴¹ with a slope β_Vset is given by

βVset = (m + 1)αN.	(1)

Room temperature Weibull distribution function W(V_SET) is depicted in Fig. 4b, derived from 150 ramping voltage stress sweep cycles during the set process. The linearity observed in the Weibull plot substantiates the validity of the percolation model analysis.

As previously mentioned, the set process is thermally activated and fails to set operation stably at temperatures below 240 K (Fig. S3†). Thus, the defect switching rate adheres to the Arrhenius law, modeled as ∂λ/∂t ∝ exp(−E_a1/k_BT), where E_a1 is the activation energy of defect switching in a cell, k_B is the Boltzmann constant and T represents the environmental temperature. Consequently, the temperature dependence of the Weibull slope can be expressed as follows (details in ESI subsection 1.4†):

	(2)

where E_a1 is the activation energy of the set process and t_SET is the time required to reach the set voltage V_SET under ramp voltage stress, defined as t_SET = V_SET/R. The Weibull distribution function W(V_SET) at room temperature is depicted in Fig. 4b, derived from 150 ramping voltage stress sweep cycles during the set process. The linearity observed in the Weibull plot substantiates the validity of the Weibull distribution function analysis. Additionally, W(V_SET) at various temperatures, ranging from 255 K to 345 K, is plotted alongside their linear fits, as shown in Fig. 4c. It is evident from eqn (2) that the Weibull slope, representing the statistical dispersion rate, is a temperature-dependent parameter. The temperature-dependent Weibull slope is clearly shown in Fig. 4c, with the extracted Weibull slopes shown in Fig. 4d (red dots). The fitting curve from eqn (2) is also plotted in Fig. 4d (blue curve, detailed fitting method in section 4 in the ESI†). The fitting results in an activation energy (for defect switching in a cell) of E_a1 = 0.18 ± 0.06 eV, which matches 0.19 eV–0.25 eV oxygen ion diffusion energy barrier reported^47,48 in α-SiO₂. These findings enable a deeper discussion of the underlying mechanisms of the set process of Si CF, as follows.

During the set process, the formation of the Si CF involves the breaking of silicon–oxygen bonds, resulting in the generation of oxygen vacancies and oxygen ions.⁸ The accumulation of these oxygen vacancies ultimately leads to the formation of the conductive pathway. However, for effective defect formation, it is essential not only to generate oxygen vacancies and ions but also to ensure the effective separation of oxygen ions from oxygen vacancies. The separation of oxygen vacancies and ions, facilitating the creation of effective defect cells, and the migration of oxygen ions have been substantiated.^39,44 Before the set operation, the device is in HRS, and the Joule heating effect (∼nW) in HRS is negligible owing to the minimal current, ensuring that the temperature of the Si CF remains equivalent to the environmental temperature in HRS. The Arrhenius activation energy of 0.18 eV observed in this study, which matches the oxygen ion migration energy barrier, indicates that at lower temperatures, the generated oxygen ions cannot adequately separate from the oxygen vacancies to form effective defect sites. Consequently, the Si CF cannot form during the set process at low temperatures. The correspondence of the obtained activation energy with the oxygen ion migration energy barrier highlights the necessity for the effective separation of oxygen vacancies and ions for defect formation, explaining the inability of the device to undergo the set process at low temperatures and underscoring the validity of our results.

Based on our understanding of device operation, we now delve into the mechanisms driving the reset process. The silicon oxide intrinsic reset process can be influenced by several factors, including thermal effects,⁴⁹ electromigration,⁵⁰ and proton exchange reactions.⁵¹ In our device, the reset process is predominantly governed by thermal effects owing to unipolar resistive switching and a lack of hydrogen in the thermally oxidized silicon oxide substrate. Previous in situ TEM measurements showed non-crystallization of Si nanocrystals during the reset process.¹⁷ However, the role of oxygen migration could be overlooked. The reset process is fundamentally characterized by the rupture of the Si CF. This can be effectively described by the thermal dissolution model illustrated in Fig. 5a (inset). In this model, the rupture occurs as the conductive cells of the Si CF diffuse outward, driven by a temperature rise due to Joule heating⁴⁹ as follows:

	(3)

where T represents the temperature of the Si CF, T₀ denotes the environmental temperature, R_on denotes the resistance of CF in the LRS, and R_th denotes the equivalent thermal resistance of the Si CF. As we previously mentioned, breaking the Si CF during the reset process becomes more challenging at higher temperatures (higher V_reset with increasing temperature, as shown in Fig. 3). Consequently, the diffusion coefficient D conforms to the Arrhenius law with a negative activation energy expressed as

	(4)

where E_a2 is the silicon atom diffusion activation energy, which is negative (E_a2 < 0); T₀ is the temperature of the environment; R_on is the resistance of CF in the LRS; and R_th is the equivalent thermal resistance of CF. Given this assumption, the Weibull slope β_Vreset of the reset voltage is given by⁴²

βVreset = γn(M + 1),	(5)

where M = E_a2/2k_BT₀, γ is an exponent for reset evolution, and n is the number of cells diffused in the reset process.

The cumulative probability of reset voltage is measured over 150 cycles across a temperature range of 250 K–350 K. The Weibull distribution function against lnV_reset at different temperatures (from 250 K to 350 K) is also plotted in Fig. 5a. A clear piecewise linear behavior with different slopes becomes apparent, indicating that the number of cells n involved in the reset process is not fixed according to eqn (5). Fig. 5b shows the Weibull distribution function of reset voltage at 255 K, accompanied by a piecewise linear fit and corresponding Weibull slopes. These slopes reflect different diffusion quantized numbers: n = 1, 2 and 10, corresponding to β₀, 2.1β₀ and 9.9β₀, respectively, where β₀ represents the Weibull slope of a unit cell with n = 1. This non-controlled n in the reset process could be why the variation in V_reset is larger than V_set, suggesting importance of further control of n to achieve uniformity of SiO_x memristors. As illustrated in Fig. 5c, the piecewise Weibull slopes at temperatures from 250 K to 350 K divided by the unit cell Weibull slope (n = 1) for each temperature are plotted. These slopes converge into a single slope as the temperature rises above 330 K, indicating that diffusion is less active at higher temperatures. The piecewise linearity observed at relatively low temperatures corresponds to a greater diffusion of cells owing to the reduced stability of Si CF at these temperatures, thus making the reset process easier at lower temperatures.

Beyond the piecewise linear property, the minimum piecewise Weibull slope at each temperature, which is assumed to correspond to the unit diffusion number n = 1, is also found to be temperature dependent; it increases as the temperature increases (Fig. 5d blue dots), which is consistent with eqn (5). The fit (Fig. 5d red line) exponent for reset evolution is γ = 41 ± 8. Activation energy can be obtained from the fit parameter, with E_a2 = −37 ± 3 meV. The negative activation energy is consistent with the fact that more cells are active in the reset process and V_reset increase with temperature. In studies of the reset voltage dependence on environmental temperature in SiO_x memristors, planar unipolar silicon oxide memristors,⁵² which are similar to our configuration but with a larger 40 nm gap size, applied Fowler–Nordheim (FN) tunneling to initiate the reset process. However, FN tunneling is temperature independent, which implies that the reset voltage is independent of temperature variations. In contrast, our observations show that reset voltage varies with temperature. Consequently, FN tunneling as the reset mechanism may not be responsible for the reset process in our devices. Observations in unipolar 60 nm SiO_x memristor⁴⁰ have revealed a trend consistent with our findings: the reset voltage increases as environmental temperature increases. This behavior was attributed to the growth of Si CF at higher temperatures. However, in our resistive switching measurements across different temperatures, we do not observe a significant increase in the memristor's conductance with an increase in temperature (see Fig. S6 in ESI†). Moreover, our devices, with sizes below 2 nm, rule out the mechanism of Si CF constant growth at high temperatures. In contrast, a similar trend of increasing reset voltage with increasing temperature was reported in bipolar 2 nm SiO_x memristor,⁵³ comparable in size to ours.

In such bipolar systems, this phenomenon is attributed to thermally enhanced oxygen ion diffusion distances at higher environmental temperatures, necessitating a stronger electric field to retract oxygen ions toward the Si CF during the reset process. However, our unipolar devices operate in a unipolar mode. Despite the distinct switching mechanisms between bipolar and unipolar modes, enhanced oxygen ion diffusion distances at elevated temperatures are a shared phenomenon. Consequently, we propose that the thermally extended diffusion distance of oxygen ions under elevated environmental temperatures requires amplified Joule heating to facilitate silicon atom diffusion, enabling recombination with oxygen ions and ultimately leading to the rupture of the Si CF.

This mechanism is consistent with our observations under ambient conditions. The abundance of oxygen atoms in the air causes the Si CF to combine more readily with oxygen atoms, resulting in a lower reset voltage (Fig. S4†). However, once the device transitions to an HRS, the pervasive presence of oxygen atoms in the air prevents a further set transition to an LRS. It can only transition back to the LRS by returning the device to a vacuum environment.

Thus far, we have successfully explained the switching mechanism of the silicon oxide memristor at the nanoscale. However, the sudden current increase observed during the electroforming process (Fig. 1c) deviates from the gradual increase typically observed in conventional metal–insulator–metal (MIM) structures characterized by edge defects or silicon-rich SiO_x films.^9,10,19 Therefore, pre-existing oxygen vacancies in our device accelerate the generation of another oxygen vacancy nearby,⁵⁴ which is induced by the electromigration process of graphene nanoconstriction. In this context, the high local temperatures generated by electromigration within the graphene nanoconstriction may contribute to the formation of oxygen vacancies, thus causing a sudden increase in current during electroforming. To investigate the influence of high local temperatures on oxygen vacancy generation, similar graphene–SiO₂–graphene nanogap devices were fabricated under ambient conditions and subsequently transferred into a vacuum chamber. As shown in Fig. 6a, the electroforming process is only successful in devices undergoing electromigration in a vacuum (Fig. 6b, blue curve) but not in an ambient atmosphere (Fig. 6b, red curve). This phenomenon can be attributed to the significantly higher temperatures achieved in the graphene nanogap during vacuum sublimation compared to oxidation in air (noting that graphite's sublimation temperature is approximately six times higher than its oxidation temperature).⁵⁵ Therefore, a high local temperature appears to play a crucial role in facilitating the generation of oxygen vacancies, which in turn leads to an abrupt increase in the current observed during electroforming.

To estimate local temperature during the sublimation process in our device, we employed a one dimensional (1D) quasi-stable heat conduction model, as illustrated in Fig. 6a. This model assumes that the Au electrodes and the silicon wafer are held at a fixed room temperature T₀ = 300 K owing to their excellent thermal conductivity. Heat transfer is primarily mediated by graphene nanoconstriction and the silicon oxide substrate. The 1D quasi-steady heat equation is thus represented as follows:

AgKgd2T/dx2 + px − gox(T − T0) = 0,	(6)

where A_g is the cross-sectional area of graphene, K_g is the thermal conductivity of graphene, p_x is the Joule heat power of unit length, and g_ox = K_oxW/t_ox is the thermal conductance of silicon oxide per unit length. From eqn (6), the maximum central temperature is obtained as follows:

	(7)

where . The parameters used for the 1D quasi-steady thermal model are listed below (Table 1).

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For our devices, the required breakdown power is in the range of 8–10 mW. The central local high temperature is estimated to be between 1500 K and 1800 K. This is consistent with previous reports,⁵⁸ in which the graphene sublimation temperature is below 2500 K. To validate that high local temperatures induced by the sublimation of graphene nanoconstriction lead to the generation of oxygen vacancies, we check changes in the same silicon oxide substrate under heating conditions. The substrate is subjected to a rapid temperature annealing (RTA) process at 1000 °C in a nitrogen atmosphere for 10 s, followed by X-ray photoelectron spectroscopy (XPS) analysis. Fig. 6c illustrates the Si 2p signals of the silicon oxide substrate before and after the RTA process. The deconvolution of the Si 2p XPS peak reveals the presence of a silicon suboxide peak Si³⁺ and a fully oxidized peak Si⁴⁺, positioned at 102.7 eV and 103.7 eV,⁵⁹ respectively, after the RTA process. The emergence of the Si³⁺ valence state indicates a reduction in oxygen atoms following exposure to high local temperature for a short duration, confirming the formation of oxygen vacancies.⁶⁰ Therefore, the high local temperature induced by the sublimation of the graphene nanoconstriction leads to the generation of a few oxygen vacancies, which accelerates the electroforming of the Si CF.

Conclusions

In conclusion, to study the uniformity and stability issues of SiO_x memristors, we statically studied the switching mechanism of set and reset processes at different temperatures, using nanometer-sized (sub-2 nm) silicon oxide memristor devices within a graphene–SiO₂–graphene nanogap. Switching mechanisms match the Weibull distribution quantitatively, and influencing factors are identified. During the set process from HRS to LRS, the formation of the Si CF is facilitated by the generation and diffusion of oxygen vacancies and ions, and their effective separation allows the accumulation of oxygen vacancies to form the Si CF. The activation energy for the thermal diffusion of oxygen ions is extracted from our measurement to be 0.18 eV. Conversely, thermal effects also play a critical role in the reset process of SiO_x memristors, involving the rupture of the Si CF. The thermal dissolution of the Si CF is governed by localized Joule heating but requires increased Joule heat at elevated environmental temperatures, which increases the initial oxygen ion diffusion distance. This necessitates amplified Joule heating to enable silicon–oxygen recombination and rupture of the Si CF. Consequently, the thermal diffusion process during the reset process exhibits a negative activation energy, with a calculated value of −37 meV for the diffusion of a single Si atom.

In general, our results in this paper illustrate a quantitative experimental understanding of the switching mechanisms in silicon oxide memristors and provide important insights into reducing the stochastic nature of the switching voltage, which is crucial for developing silicon oxide memristors or neuromorphic systems.

Data availability

The data and simulation protocols supporting this article have been included as part of ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant no. 62404250), the National Basic Research Program of China (Grant No. 2016YFA0200800), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000 and XDB07030100), the Sinopec Innovation Scheme (Grant No. A-527) and the Synergetic Extreme Condition User Facility (SECUF, https://cstr.cn/31123.02.SECUF).

References

1. A. Szalay and J. Gray, Nature, 2006, 440, 413 CrossRef CAS PubMed .
2. J. V. Neumann, IEEE Ann. Hist. Comput., 1988, 10, 243–256 Search PubMed .
3. L. Chua, IEEE Trans. Circuit Theory, 1971, 18, 507–519 Search PubMed .
4. D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, Nature, 2008, 453, 80–83 CrossRef CAS PubMed .
5. J. J. Yang, M. D. Pickett, X. Li, D. A. A. Ohlberg, D. R. Stewart and R. S. Williams, Nat. Nanotechnol., 2008, 3, 429–433 CrossRef CAS PubMed .
6. H. Kim, M. R. Mahmoodi, H. Nili and D. B. Strukov, Nat. Commun., 2021, 12, 5198 CrossRef CAS PubMed .
7. F. Cai, J. M. Correll, S. H. Lee, Y. Lim, V. Bothra, Z. Zhang, M. P. Flynn and W. D. Lu, Nat. Electron., 2019, 2, 290–299 CrossRef CAS .
8. A. Mehonic, A. L. Shluger, D. Gao, I. Valov, E. Miranda, D. Ielmini, A. Bricalli, E. Ambrosi, C. Li, J. J. Yang, Q. Xia and A. J. Kenyon, Adv. Mater., 2018, 30, 1801187 CrossRef PubMed .
9. J. Yao, Z. Sun, L. Zhong, D. Natelson and J. M. Tour, Nano Lett., 2010, 10, 4105–4110 CrossRef CAS PubMed .
10. J. Yao, J. Lin, Y. Dai, G. Ruan, Z. Yan, L. Li, L. Zhong, D. Natelson and J. M. Tour, Nat. Commun., 2012, 3, 1101 CrossRef PubMed .
11. Y. Wang, Y.-T. Chen, F. Xue, F. Zhou, Y.-F. Chang, B. Fowler and J. C. Lee, Appl. Phys. Lett., 2012, 100, 083502 CrossRef .
12. A. Mehonic, S. Cueff, M. Wojdak, S. Hudziak, O. Jambois, C. Labbé, B. Garrido, R. Rizk and A. J. Kenyon, J. Appl. Phys., 2012, 111, 074507 CrossRef .
13. S. Tappertzhofen, I. Valov, T. Tsuruoka, T. Hasegawa, R. Waser and M. Aono, ACS Nano, 2013, 7, 6396–6402 CrossRef CAS PubMed .
14. S. Tappertzhofen, H. Mündelein, I. Valov and R. Waser, Nanoscale, 2012, 4, 3040–3043 RSC .
15. C. He, Z. Shi, L. Zhang, W. Yang, R. Yang, D. Shi and G. Zhang, ACS Nano, 2012, 6, 4214–4221 CrossRef CAS PubMed .
16. G. Wang, Y. Yang, J.-H. Lee, V. Abramova, H. Fei, G. Ruan, E. L. Thomas and J. M. Tour, Nano Lett., 2014, 14, 4694–4699 CrossRef CAS PubMed .
17. J. Yao, L. Zhong, D. Natelson and J. M. Tour, Sci. Rep., 2012, 2, 242 CrossRef PubMed .
18. C. He, J. Li, X. Wu, P. Chen, J. Zhao, K. Yin, M. Cheng, W. Yang, G. Xie, D. Wang, D. Liu, R. Yang, D. Shi, Z. Li, L. Sun and G. Zhang, Adv. Mater., 2013, 25, 5593–5598 CrossRef CAS PubMed .
19. M. Buckwell, L. Montesi, S. Hudziak, A. Mehonic and A. J. Kenyon, Nanoscale, 2015, 7, 18030–18035 RSC .
20. A. N. Mikhaylov, A. I. Belov, D. V. Guseinov, D. S. Korolev, I. N. Antonov, D. V. Efimovykh, S. V. Tikhov, A. P. Kasatkin, O. N. Gorshkov, D. I. Tetelbaum, A. I. Bobrov, N. V. Malekhonova, D. A. Pavlov, E. G. Gryaznov and A. P. Yatmanov, Mater. Sci. Eng., B, 2015, 194, 48–54 CrossRef CAS .
21. W. Sun, B. Gao, M. Chi, Q. Xia, J. J. Yang, H. Qian and H. Wu, Nat. Commun., 2019, 10, 3453 CrossRef PubMed .
22. M. S. Munde, A. Mehonic, W. H. Ng, M. Buckwell, L. Montesi, M. Bosman, A. L. Shluger and A. J. Kenyon, Sci. Rep., 2017, 7, 9274 CrossRef CAS PubMed .
23. A. Mehonic, T. Gerard and A. J. Kenyon, Appl. Phys. Lett., 2017, 111, 233502 CrossRef .
24. C. Li, L. Han, H. Jiang, M.-H. Jang, P. Lin, Q. Wu, M. Barnell, J. J. Yang, H. L. Xin and Q. Xia, Nat. Commun., 2017, 8, 15666 CrossRef CAS PubMed .
25. A. Mehonic, A. Vrajitoarea, S. Cueff, S. Hudziak, H. Howe, C. Labbe, R. Rizk, M. Pepper and A. Kenyon, Sci. Rep., 2013, 3, 1–8 Search PubMed .
26. W. Yu, X. Guo, Y. Cai, X. Yu and W. Liang, Chin. Phys. B, 2023, 32, 077202 CrossRef CAS .
27. C. Evangeli, S. Tewari, J. M. Kruip, X. Bian, J. L. Swett, J. Cully, J. Thomas, G. A. D. Briggs and J. A. Mol, Proc. Natl. Acad. Sci. U. S. A., 2022, 119, e2119015119 CrossRef CAS PubMed .
28. O. Schmuck, D. Beretta, R. Furrer, J. Oswald and M. Calame, AIP Adv., 2022, 12, 055312 CrossRef CAS .
29. A. Barreiro, F. Börrnert, M. Rümmeli, B. Büchner and L. Vandersypen, Nano Lett., 2012, 12, 1873–1878 CrossRef CAS PubMed .
30. J. G. Simmons, J. Appl. Phys., 2004, 34, 1793–1803 CrossRef .
31. H. S. P. Wong, H. Y. Lee, S. Yu, Y. S. Chen, Y. Wu, P. S. Chen, B. Lee, F. T. Chen and M. J. Tsai, Proc. IEEE, 2012, 100, 1951–1970 CAS .
32. E. Piros, M. Lonsky, S. Petzold, A. Zintler, S. U. Sharath, T. Vogel, N. Kaiser, R. Eilhardt, L. Molina-Luna, C. Wenger, J. Müller and L. Alff, Phys. Rev. Appl., 2020, 14, 034029 CrossRef CAS .
33. B. Sánta, Z. Balogh, A. Gubicza, L. Pósa, D. Krisztián, G. Mihály, M. Csontos and A. Halbritter, Nanoscale, 2019, 11, 4719–4725 RSC .
34. Y. Sun, X. Wang, J. Wang, S. Cheng, Y. Liu, T. Shen, X. Li, B. Gao and H. Qian, IEEE Trans. Electron Devices, 2023, 70, 1025–1028 CAS .
35. H. Zhang, W. Bao, Z. Zhao, J. W. Huang, B. Standley, G. Liu, F. Wang, P. Kratz, L. Jing, M. Bockrath and C. N. Lau, Nano Lett., 2012, 12, 1772–1775 CrossRef CAS PubMed .
36. L. Pósa, M. El Abbassi, P. Makk, B. Sánta, C. Nef, M. Csontos, M. Calame and A. Halbritter, Nano Lett., 2017, 17, 6783–6789 CrossRef PubMed .
37. Y. F. Chang, P. Y. Chen, B. Fowler, Y. T. Chen, F. Xue, Y. Wang, F. Zhou and J. C. Lee, J. Appl. Phys., 2012, 112, 729 Search PubMed .
38. Y. F. Chang, L. Ji, Z. J. Wu, F. Zhou, Y. Wang, X. Fei, B. Fowler, E. T. Yu, P. S. Ho and J. C. Lee, Appl. Phys. Lett., 2013, 103, 482 Search PubMed .
39. Y. Wang, X. Qian, K. Chen, Z. Fang, W. Li and J. Xu, Appl. Phys. Lett., 2013, 102, 042103 CrossRef .
40. Y. F. Chang, P. Y. Chen, B. Fowler, Y. T. Chen, F. Xue, Y. Wang, F. Zhou and J. C. Lee, Int. Symp. VLSI Technol., Syst., Appl. (VLSI-TSA), 2013, 1–2 Search PubMed .
41. S. Long, X. Lian, C. Cagli, L. Perniola, E. Miranda, M. Liu and J. Suñé, IEEE Electron Device Lett., 2013, 34, 999–1001 CAS .
42. S. Long, C. Cagli, D. Ielmini, M. Liu and J. Sune, J. Appl. Phys., 2012, 111, 074508 CrossRef .
43. W.-C. Luo, J.-C. Liu, Y.-C. Lin, C.-L. Lo, J.-J. Huang, K.-L. Lin and T.-H. Hou, IEEE Trans. Electron Devices, 2013, 60, 3760–3766 CAS .
44. A. Mehonic, M. Buckwell, L. Montesi, M. S. Munde, D. Gao, S. Hudziak, R. J. Chater, S. Fearn, D. McPhail, M. Bosman, A. L. Shluger and A. J. Kenyon, Adv. Mater., 2016, 28, 7486–7493 CrossRef CAS PubMed .
45. J. Sune, IEEE Electron Device Lett., 2001, 22, 296–298 CAS .
46. A. Conde, C. Martínez, D. Jiménez, E. Miranda, J. Rafí, F. Campabadal and J. Suñé, Solid-State Electron., 2012, 71, 48–52 CrossRef CAS .
47. D. Z. Gao, A.-M. El-Sayed and A. L. Shluger, Nanotechnology, 2016, 27, 505207 CrossRef PubMed .
48. D. Z. Gao, J. Strand, M. S. Munde and A. L. Shluger, Front. Phys., 2019, 7, 43 CrossRef .
49. U. Russo, D. Ielmini, C. Cagli and A. L. Lacaita, IEEE Trans. Electron Devices, 2009, 56, 193–200 CAS .
50. A. Mehonic, M. Buckwell, L. Montesi, L. Garnett, S. Hudziak, S. Fearn, R. Chater, D. McPhail and A. J. Kenyon, J. Appl. Phys., 2015, 117, 124505 CrossRef .
51. Y.-F. Chang, B. Fowler, Y.-C. Chen, F. Zhou, C.-H. Pan, T.-C. Chang and J. C. Lee, Sci. Rep., 2016, 6, 1–10 CrossRef CAS PubMed .
52. F. Zhou, Y. F. Chang, Y. C. Chen, X. Wu, Y. Zhang, B. Fowler and J. C. Lee, Phys. Chem. Chem. Phys., 2016, 18, 700–703 RSC .
53. C. C. Shih, W. J. Chen, K. C. Chang, T. C. Chang, T. M. Tsai, T. J. Chu, Y. T. Tseng, C. H. Wu, W. C. Su, M. C. Chen, H. C. Huang, M. H. Wang, J. H. Chen, J. C. Zheng and S. M. Sze, IEEE Electron Device Lett., 2016, 37, 1276–1279 CAS .
54. D. Z. Gao, J. Strand, A. M. El-Sayed, A. L. Shluger, A. Padovani and L. Larcher, IEEE Int. Reliab. Phys. Symp., 2018, 5A.2-1–5A.2-7 Search PubMed .
55. A. D. Liao, J. Z. Wu, X. Wang, K. Tahy, D. Jena, H. Dai and E. Pop, Phys. Rev. Lett., 2011, 106, 256801 CrossRef PubMed .
56. R. Murali, Y. Yang, K. Brenner, T. Beck and J. D. Meindl, Appl. Phys. Lett., 2009, 94, 243114 CrossRef .
57. J. O. Island, A. Holovchenko, M. Koole, P. F. A. Alkemade, M. Menelaou, N. Aliaga-Alcalde, E. Burzurí and H. S. J. van der Zant, J. Phys.: Condens. Matter, 2014, 26, 474205 CrossRef CAS PubMed .
58. J. Y. Huang, L. Qi and J. Li, Nano Res., 2010, 3, 43–50 CrossRef CAS .
59. A. Hohl, T. Wieder, P. A. van Aken, T. E. Weirich, G. Denninger, M. Vidal, S. Oswald, C. Deneke, J. Mayer and H. Fuess, J. Non-Cryst. Solids, 2003, 320, 255–280 CrossRef CAS .
60. Y. Wang, K. Chen, X. Qian and Z. Fang, Appl. Phys. Lett., 2014, 104, 2632 Search PubMed .

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5nr01019e

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