Implementation method of a general compact model of metal oxide memristor

Abstract

This invention discloses a method for implementing a universal compact model of a metal-oxide-semiconductor (MOD) memristor, comprising: obtaining electric field gain parameters based on the resistance and length of a conductive filament; further obtaining the oxygen ion concentration entering the top electrode during the setting process and the oxygen ion concentration released during the reset process; and modeling the competitive process between the generation and recombination of oxygen holes during the setting and reset processes to construct a universal model of the memristor. This universal model can explain and reproduce various unconventional programming characteristics of MOD memristors during the reset process. Based on this universal model, a method is proposed to regulate the potential barrier for oxygen ions entering and leaving the electrodes by adjusting process parameters during device manufacturing, programming voltage and current parameters during operation, thereby controlling unipolar and bipolar memristors, as well as gradual and abrupt programming modes, thus improving the ability to control the programming characteristics of memristors.

Description

Technical Field

[0001] This invention belongs to the field of modeling technology, specifically relating to a method for implementing a general compact model of a metal oxide memristor. Background Technology

[0002] Resistive Random-Access Memory (RRAM), also known as memristor, is a novel type of memory device. It has been extensively studied due to its excellent compatibility with Complementary Metal-Oxide-Semiconductor (CMOS) processes, small size, low power consumption, non-volatility, and large capacity. It is a promising technology for next-generation high-density on-chip memory and in-memory computing. [1,2] .

[0003] Memristors store information using varying resistance values. The operation of decreasing the resistance (forming a conductive filament) is called setting, while the operation of increasing the resistance (breaking the filament) is called resetting. Setting and resetting operations are performed by applying a voltage across the memristor, thus changing the resistance and consequently altering the information stored within the device. If the required set and reset voltages have the same polarity, it is a unipolar device; if they have opposite polarities, it is a bipolar device. Typically, under DC operating voltage, the resistance value changes gradually or abruptly with increasing voltage during setting and resetting. Generally, a gradually changing resistance is advantageous for continuous resistance control, making it suitable for analog memory-based computations, while abrupt resistance results in a larger switching resistance ratio, making it more suitable for robust storage and computation. [3] .

[0004] To gain a deeper understanding of the intrinsic physical mechanisms of metal oxide memristors based on conductive filaments, several physical models have been established, and the basic operating characteristics of memristors have been reproduced. [4-6] However, some current memristor models are not yet perfect and have some unresolved issues:

[0005] (1) Existing models cannot uniformly explain the writing process of unipolar and bipolar memristors, nor can they uniformly explain the writing patterns of abrupt and gradual changes, and therefore lack universality.

[0006] (2) The various unconventional phenomena during the memristor reset process, including reverse setting, small-amplitude setting after reset, and setting during voltage retrace, cannot be well explained.

[0007] (3) It is not possible to provide control methods for different memristor writing processes, such as the control of unipolar and bipolar memristors, and the conversion process between abrupt and gradual writing modes.

[0008] Therefore, a universal, compact model of memristors is needed to uniformly explain various phenomena, thereby enabling better simulation of device circuits.

[0009] Existing literature reports compact models of memristors that can simulate basic memristor programming characteristics. [7] However, due to the lack of clarity and completeness of some of the underlying physical mechanisms, it is impossible to uniformly explain the gradual or abrupt programming modes of unipolar and bipolar devices, as well as some unconventional reset processes. At the same time, it is impossible to provide theoretical guidance for the direct control between different programming modes. The above problems still exist.

[0010] The shortcomings and deficiencies of existing implementation schemes:

[0011] 1. Existing models fail to uniformly explain the physical principles of the gradual or abrupt programming modes of unipolar / bipolar memristors;

[0012] 2. Existing models cannot adequately explain the unconventional characteristics of memristors during the reset process, including reverse setting, small-amplitude setting after reset, and setting during voltage flyback.

[0013] 3. Existing models are insufficient to provide effective theoretical guidance for the conversion between different writing modes.

[0014] References:

[0015] [1] H.-SPWong, HYLee, S.Yu, YSchen, Y.Wu, P.-S.Chen, B.Lee, FTChen, and M.-J.Tsai, “Metal–oxide RRAM,” Proc.IEEE, vol.100, no.6, pp.1951–1970, May2012.

[0016] [2] S. Yu, Neuro-Inspired Computing using Resistive SynapticDevices. Cham, Switzerland: Springer, 2017.

[0017] [3]W.Wu,H.Wu,B.Gao,N.Deng,S.Yu,and H.Qian,“Improving analog switchingin HfOx-based resistive memory with a thermal enhanced layer,”IEEE ElectronDevice Lett.,vol.38,no.8,pp.1019–1022,Aug.2017.

[0018] [4]B.Traoré,P.Blaise,E.Vianello,L.Perniola,B.De Salvo,and Y.Nishi,“HfO2-based RRAM:electrode effects,Ti / HfO2 interface,charge injection,andoxygen(O)defects diffusion through experiment and ab initio calculations,”IEEE Trans.Electron Devices,vol.63,no.1,pp.360–368,Jan.2016.

[0019] [5]Y.Liao,B.Gao,F.Xu,P.Yao,J.Chen,W.Zhang,J.Tang,H.Wu,and H.Qian,“Acompact model of analog RRAM with device and array nonideal effects forneuromorphic systems,”IEEE Trans.Electron Devices,vol.67,no.4,pp.1593–1599,Apr.2020.

[0020] [6]H.Li,P.Huang,B.Gao,B.Chen,X.Liu,and J.Kang,“A SPICE model ofresistive random access memory for large-scale memory array simulation,”IEEEElectron Device Lett.,vol.35,no.2,pp.211–213,Feb.2014.

[0021] [7] Z.Jiang, Y.Wu, S.Yu, L.Yang, K.Song, Z.Karim, and H.-SPWong, "A compactmodel for metal–oxide resistive random access memory with experimentverification," IEEE Trans.Electron Devices, vol.63, no.5, pp.1884–1892, May 2016. Summary of the Invention

[0022] In view of the above-mentioned deficiencies of the prior art, the present invention provides a method for implementing a universal compact model of a metal-oxide memristor, the method comprising:

[0023] For memristors based on conductive filaments, the resistance value of the memristor is obtained based on the resistance value and length of the conductive filaments, and the electric field gain parameter is obtained by modeling the relationship between electric field gain and resistance.

[0024] Based on the electric field gain parameters obtained from the above fitting and the potential barrier for oxygen ions to enter the electrode, the probability of oxygen ions entering the electrode under the conditions of an applied electric field E and a local temperature T is obtained, and then the concentration of oxygen ions entering the top electrode and the concentration of oxygen ions remaining in the oxide layer during the placement process are obtained.

[0025] Based on the electric field gain parameters obtained from the above fitting and the potential barrier for oxygen ions to migrate out of the electrode, the probability of oxygen ions being released from the top electrode during the reset process is obtained, and the concentration of oxygen ions released through diffusion in the oxide layer is calculated, thereby obtaining the total concentration of oxygen ions released during the reset process.

[0026] A general model for memristors is constructed by modeling the competition between the generation and recombination of oxygen holes during the setting and resetting processes.

[0027] Furthermore, the resistance value of the memristor is calculated using the following formula:

[0028]

[0029] in R0 is the resistance of the conductive filament determined based on the low-resistance state resistance of the device, d is the thickness of the oxide layer, gap is the length of the broken conductive filament, a0 is the lattice constant, and g0 is the fitting parameter extracted from the experimental data of the device resistance.

[0030] Furthermore, the electric field gain parameter k E The relationship model between the resistor R and the resistor is as follows:

[0031] kE =k E0 -αlnR,

[0032] Where, k E0 α and α are fitting parameters based on experimental data.

[0033] Furthermore, under the conditions of an applied electric field E and a local temperature T, the probability P of oxygen ions entering the electrode is... Absorb Calculated using the following formula:

[0034]

[0035] Among them, E ab Δt is the potential barrier for oxygen ions to enter the electrode, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field gain parameters are obtained through fitting.

[0036] Furthermore, the concentration of oxygen ions entering the top electrode during the placement process... for:

[0037]

[0038] Where t1 is the total writing cycle during the setting process, and n tot This represents the total concentration of oxygen ions generated during the placement process.

[0039] Furthermore, during the placement process, the concentration of oxygen ions remaining in the oxide layer... for:

[0040]

[0041] Furthermore, during the reset process, the probability P of oxygen ions being released from the top electrode... Rel,e Calculated using the following formula:

[0042]

[0043] Among them, E rel It is the potential barrier for oxygen ions to migrate out of the electrode, Δt is the unit time, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field gain parameters are obtained through fitting.

[0044] Furthermore, during the reset process, the oxygen ions remaining in the oxide layer are released mainly through thermal diffusion, and their release probability P Rel,o Comply with:

[0045]

[0046] Among them, P Rel,o ν represents the probability of releasing oxygen ions remaining in the oxide layer. D0 Here, a is the diffusion coefficient of oxygen ions, a0 is the lattice constant, Δt is the time per unit time, and E is the density coefficient. diff For diffusion barrier, k B Here, denoted as Boltzmann's constant, and T represents the local temperature.

[0047] Furthermore, the final concentration of oxygen ions released during the reset process... for:

[0048]

[0049] Where t2 is the total programming cycle during the reset process, P Rel,e This represents the probability of oxygen ions being released from the top electrode during the reset process. P represents the oxygen ion concentration entering the top electrode during the placement process. Rel,o This represents the probability of releasing oxygen ions remaining in the oxide layer. This represents the concentration of oxygen ions remaining in the oxide layer during the placement process.

[0050] Furthermore, during the placement process, under the influence of the applied electric field E, the probability P of oxygen hole generation within a unit time Δt is... G for:

[0051]

[0052] Among them, E a It is the potential barrier for generating oxygen holes, Δt is the unit time, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field gain parameters are obtained through fitting.

[0053] Furthermore, during the placement process, the concentration of oxygen ions generated, n tot for:

[0054]

[0055] Among them, P G t1 represents the probability of oxygen vacancies being generated per unit time Δt under the influence of an external electric field E during the setting process, and t1 represents the total writing period during the setting process.

[0056] Furthermore, the probability P of oxygen-hole recombination... R Calculated using the following formula:

[0057]

[0058] Among them, E r It is the potential barrier for oxygen-hole recombination, and Δt is the potential per unit time. The concentration of oxygen ions released during the reset process, k B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency of ).

[0059] Furthermore, during the setting or resetting process, there is a competing process between the generation and recombination of oxygen holes, and the change in the length gap of the broken conductive filament, Δgap, is:

[0060]

[0061] Where t3 is the total period, a0 is the lattice constant, and P Net·G,R The net generation or net recombination probability, i.e., the probability P of oxygen hole generation. G The probability P of recombination with oxygen holes R The difference between them, therefore P Net·G,R =P G -P R .

[0062] Furthermore, for reverse set, the relationship between the current I and the voltage V across the memristor during the device set and reset processes is as follows:

[0063]

[0064] Where V is the applied voltage, V0 is the fitting parameter representing the nonlinearity of the memristor's resistance as a function of voltage, and R is the calculated resistance value of the memristor.

[0065] The Joule heating generated by the current causes the temperature inside the memristor to rise, which is consistent with the following:

[0066] T = T0 + IV × R th ,

[0067] Where T0 is the ambient temperature, R th This represents the thermal resistance parameter of the oxide layer.

[0068] On the other hand, the present invention provides a general model for memristors constructed by the above method.

[0069] In another aspect, the present invention provides an application of a general model of the memristor, which is used to explain and reproduce the unconventional programming characteristics of metal oxide memristors during the reset process, the small-amplitude reset after reset, and the reset during the voltage flyback process.

[0070] Furthermore, by adjusting the process parameters during device manufacturing and the programming voltage and current parameters during operation, the barrier for oxygen ions to enter and exit the electrodes can be controlled, thereby regulating unipolar and bipolar memristors, as well as the programming methods of gradual and abrupt changes, thus improving the ability to control the programming characteristics of memristors.

[0071] Technical effect

[0072] The method for implementing the universal compact model of metal oxide memristors in this invention introduces a new physical mechanism into the internal mechanism of memristors, including the competition between the generation and recombination of oxygen holes during reset and set processes, the regulation of the potential barrier for oxygen ions to enter and exit the electrodes during set and reset processes, and the influence of oxygen hole concentration on the electric field gain. This solves the previous problem of lacking a unified memristor model, models and reproduces the physical mechanism of the gradual and abrupt resistance regulation of metal oxide memristors in unipolar and bipolar modes, and establishes a universal compact model of memristors.

[0073] By utilizing the aforementioned general model of memristors, the bottleneck of previous memristor models being unable to explain unconventional programming characteristics has been overcome. The unconventional programming characteristics of metal oxide memristors, such as reverse setting during the reset process, small-amplitude setting after reset, and reset during voltage flyback, have been successfully explained and reproduced.

[0074] The universal compact model of the metal oxide memristor of this invention can provide theoretical guidance for the conversion between different resistance control methods. Based on this universal model, a method is proposed to control the potential barrier for oxygen ions to enter and exit the electrode by adjusting the process parameters during device manufacturing and the programming voltage and current during operation. This method controls unipolar and bipolar memristors, as well as the programming methods of gradual and abrupt changes. The method has been experimentally verified and improves the ability to control the programming characteristics of memristors. Attached Figure Description

[0075] Figure 1 It is the basic modeling structure of a memristor based on conductive filaments;

[0076] Figure 2 The left side shows the different resistance modulation processes observed in experiments with unipolar and bipolar devices, and the corresponding model structures (right side).

[0077] Figure 3 It consists of various abnormal phenomena during the reset process obtained by experimental measurement and fitting using a general model of memristors, which are explained and verified by the competitive relationship between oxygen hole generation and recombination.

[0078] Figure 4 This is an experimental verification and model fitting of different resistance conversion methods based on the general model of memristors. Detailed Implementation

[0079] This invention provides a modeling method for a general compact model of a metal oxide memristor. The method includes: for a memristor based on a conductive filament, obtaining the resistance value of the memristor based on the resistance value and length of the conductive filament, and modeling the relationship between electric field gain and resistance to obtain electric field gain parameters.

[0080] Based on the electric field gain parameters obtained from the above fitting and the potential barrier for oxygen ions to enter the electrode, the probability of oxygen ions entering the electrode under the conditions of an applied electric field E and a local temperature T is obtained, and then the concentration of oxygen ions entering the top electrode and the concentration of oxygen ions remaining in the oxide layer during the placement process are obtained.

[0081] Based on the electric field gain parameters obtained from the above fitting and the potential barrier for oxygen ions to migrate out of the electrode, the probability of oxygen ions being released from the top electrode during the reset process is obtained, and the concentration of oxygen ions released through diffusion in the residual oxide layer is calculated, thereby obtaining the concentration of oxygen ions released during the reset process.

[0082] A general model for memristors is constructed by modeling the competition between the generation and recombination of oxygen holes during the setting and resetting processes.

[0083] 1. Modeling the effect of oxygen hole concentration on electric field gain.

[0084] For memristors based on conductive filaments, where the conductive filaments are based on oxygen holes (V0, V ... O The accumulation of oxygen holes creates a gap between the electrodes. In the low-resistance state, the memristor typically has relatively intact conductive filaments. However, in the high-resistance state, these filaments partially break and form a gap between the electrodes, increasing the internal resistance of the memristor. During the set and reset processes, oxygen holes are gradually generated or recombine, decreasing or increasing the value of the gap, thus altering the internal resistance of the memristor.

[0085] The basic structure of a memristor is as follows: Figure 1 As shown in the figure, the dashed line represents the conductive filament formed by the accumulation of oxygen vacancies. The conductive filament is partially broken and there is a certain gap between it and the electrode, the length of which is gap.

[0086] Different oxygen hole concentrations affect the resistivity of the conductive filament, ultimately influencing the electric field distribution within the device and thus the electric field gain. The oxygen hole concentration is directly reflected in the resistance of the conductive filament. Therefore, by establishing a relationship between the electric field gain and the device's resistance, the influence of oxygen hole concentration on the electric field gain can be successfully modeled.

[0087] In this model, the resistance calculation of the memristor follows:

[0088]

[0089] in

[0090] Where R0 is the resistance of the conductive filament determined based on the low-resistance state resistance of the device, d is the thickness of the oxide layer, gap is the distance between the partially broken conductive filament and the electrode, a0 is the lattice constant, and g0 is a fitting parameter extracted from the experimental data of the device resistance. The electric field gain parameter k... E The relationship between resistance and resistance is modeled as follows:

[0091] k E =k E0 -αlnR,

[0092] Where, k E0 α and α are fitting parameters based on experimental data. It can be seen that, under the same gap, R... CF The smaller the value, the higher the oxygen hole concentration, and the lower the resistance R, thus increasing k. E The larger the value, the greater the value. And the same R... CF At the same oxygen hole concentration, the larger the gap, the larger the resistance R, and thus k E The smaller the value, the better it matches the experimental results.

[0093] 2. Modeling the potential barriers for oxygen ions entering and exiting the electrode during the placement and reset process.

[0094] (1) Modeling the effect of electrode material on the potential barrier for oxygen ions to enter the electrode

[0095] For oxidizable electrode metals (such as titanium nitride and titanium), there is usually a smaller potential barrier, allowing oxygen ions to migrate more easily. Conversely, for inert metals (such as platinum and ruthenium), their greater stability typically results in a higher potential barrier, thus limiting oxygen ion migration. Therefore, in the model, the potential barrier for oxygen ions to enter the electrode is influenced by the electrode material, changing with the electrode material.

[0096] (2) Modeling the effect of electric field and heat on the potential barrier for oxygen ions to enter the electrode.

[0097] The diffusion and drift of oxygen ions are affected by heat and field. Oxygen ions generated during the placement process are more likely to enter the electrode under the combined influence of an electric field and heat. Under an applied electric field E and temperature T, the probability P of oxygen ions entering the electrode is... Absorb Comply with:

[0098]

[0099] Among them, E abΔt is the potential barrier for oxygen ions to enter the electrode, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field enhancement parameters are obtained through fitting. E Related to oxygen hole concentration: Higher oxygen hole concentration and stronger conductive filaments usually concentrate the electric field, thereby increasing k. E .

[0100] Therefore, the oxygen ion concentration entering the top electrode during the placement process for:

[0101]

[0102] Where t1 is the total writing cycle during the setting process, and n tot This represents the total oxygen ion concentration generated during the placement process. The oxygen ion concentration remaining in the oxide layer is the other value. for:

[0103]

[0104] (3) Modeling the effect of voltage and current on the potential barrier for oxygen ion migration out of the electrode during the placement process

[0105] During the placement process, the generated oxygen ions enter the electrode under the combined influence of the electric field and heat. Under higher temperatures and stronger electric fields, oxygen ions can more easily penetrate deeper into the electrode. Therefore, if a larger voltage is used during the placement process, it will provide a larger electric field and current, further increasing Joule heating and leading to higher temperatures. This further raises the barrier for oxygen ions to migrate out of the electrode, making it more difficult for oxygen ions to be released during the reset process. Figure 2 During the reset process, the probability of oxygen ion release from the top electrode follows:

[0106]

[0107] Among them, E rel It is the potential barrier for oxygen ions to migrate out of the electrode, Δt is the unit time, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field enhancement parameters are obtained through fitting. In the model, E... rel Set as a dynamic parameter that varies with the set voltage (V) and current (I): E rel ∝V·I, thus a higher set voltage and current have a larger potential barrier. Meanwhile, oxygen ions remaining in the oxide layer are released through thermal diffusion, and their release probability P...Rel,o Comply with:

[0108]

[0109] Where ν D0 Here, a is the diffusion coefficient of oxygen ions, a0 is the lattice constant, Δt is the time per unit time, and E is the density coefficient. diff For diffusion barrier, k B Let be the Boltzmann constant, and T be the local temperature. Therefore, the final concentration of oxygen ions released during the reset process is... for:

[0110]

[0111] Where t2 is the total programming cycle during the reset process, P Rel,e This represents the probability of oxygen ions being released from the top electrode during the reset process. P represents the oxygen ion concentration entering the top electrode during the placement process. Rel,o This represents the probability of releasing oxygen ions remaining in the oxide layer. This represents the concentration of oxygen ions remaining in the oxide layer during the placement process.

[0112] 3. Model the competitive process between the generation and recombination of oxygen holes during the placement and reset processes.

[0113] During the placement process, the generation of oxygen vacancies follows the same principle as the traditional soft breakdown of electrolytes. Under the influence of an applied electric field E, the probability of oxygen vacancies being generated per unit time Δt is:

[0114]

[0115] Among them, E a It is the potential barrier for generating oxygen holes, Δt is the unit time, q is the charge per unit electron, and k is the potential barrier. B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency, k E The electric field gain parameters are obtained through fitting. During the placement process, oxygen ions and oxygen holes appear in pairs; therefore, the concentration of oxygen ions generated during the placement process is:

[0116]

[0117] Among them, P G t1 represents the probability of oxygen vacancies being generated per unit time Δt under the influence of an external electric field E during the setting process, and t1 represents the total writing period during the setting process.

[0118] The probability of oxygen-hole recombination is positively correlated with the oxygen ion concentration, which can be expressed as:

[0119]

[0120] Among them, E r It is the potential barrier for oxygen-hole recombination, and Δt is the potential per unit time. The concentration of oxygen ions released during the reset process, k B Here, is Boltzmann's constant, T is the local temperature, and f is the oxygen ion concentration (O). 2- The vibration frequency of oxygen holes. During the entire setting and resetting process, the generation and recombination of oxygen holes should be a simultaneous and dynamically competitive process. Therefore, in the model, the competitive relationship between the generation and recombination of oxygen holes is considered: during the setting process, the net generation probability of oxygen holes is P. G -P R During the reset process, the net recombination probability of oxygen holes is P. R -P G Therefore, during the setting or resetting process, there is a competing process between the generation and recombination of oxygen holes, and the change in gap Δgap of the broken conductive filament is:

[0121]

[0122] Where t3 is the total period, a0 is the lattice constant, and P Net·G,R The net generation or net recombination probability, i.e., the probability P of oxygen hole generation. G The probability P of recombination with oxygen holes R The difference between them.

[0123] Figure 2 a, Figure 2 b、 Figure 2 Figure c shows the different resistance modulation processes observed experimentally for unipolar and bipolar devices (left), and the corresponding modeling methods (right). Figure (a) corresponds to the gradual reset process of the bipolar device, and a1-a3 in the figure correspond to the three physical processes on the right. Figures (b) and (c) correspond to the abrupt reset processes of the bipolar memristors in (b) and the unipolar memristors in (c), respectively, and the physical principle explanations corresponding to the right figures are in the same order as those in Figure (a).

[0124] 4. Construct a general model for memristors and explain the characteristics of unconventional programming.

[0125] Beyond conventional resistor-controlled operation, memristors exhibit several unconventional characteristics. These include various unusual phenomena during the reset process, such as reverse setting, small-amplitude setting after reset, and setting during voltage flyback. Modeling these characteristics can improve the accuracy and universality of the model, thereby constructing a general model for memristors.

[0126] For reverse placement, the competitive relationship between oxygen hole generation and recombination can be modeled. Figure 3 a) Under applied voltage, the current across the memristor exhibits a non-linear relationship with the voltage during device set and reset processes:

[0127]

[0128] Where V is the applied voltage, V0 is the fitting parameter representing the nonlinearity of the memristor's resistance as a function of voltage, and R is the calculated resistance value of the memristor.

[0129] The Joule heating generated by the current causes the temperature inside the memristor to rise, which is consistent with the following:

[0130] T = T0 + IV × R th ,

[0131] Where T0 is the ambient temperature, R th This represents the thermal resistance parameter of the oxide layer.

[0132] During the reset process, when the voltage is high and the oxygen ion concentration is sufficiently low, the probability of oxygen hole generation is greater than the probability of recombination, thus causing a reverse set. The small-amplitude set after reset is similar in principle to the reverse set, but because some oxygen ions are still present, it can suppress large-amplitude reverse set. Figure 3 b). The placement during voltage retracement can be modeled using a high oxygen ion release barrier and the competition between oxygen hole generation and recombination. Figure 3 c) When the oxygen ion release barrier is high, oxygen ions are gradually released under a higher voltage. At this time, the electric field is high, resulting in a higher probability of oxygen hole generation, which inhibits oxygen hole recombination and reset. However, as the voltage gradually decreases during the scanback process, the concentration of oxygen ions has already accumulated to a high level, and the probability of oxygen hole generation gradually decreases with the decrease of the electric field. Eventually, the recombination probability exceeds the generation probability, thus causing reset.

[0133] Figure 3 a, Figure 3 b、 Figure 3 c illustrates the measurement and modeling of unconventional programming characteristics during the reset process. Figure 3 (a) Reverse setting during the reset process. Figure 3 (b) Small-amplitude reset after reset. Figure 3 (c) Reset during voltage retracement. The unconventional characteristics during the reset process can be modeled by the competition between oxygen hole generation and recombination, and the modulation of the potential barrier for oxygen ions entering and leaving the electrode.

[0134] 5. The model provides theoretical guidance for the conversion between different resistance control methods.

[0135] (1) The effect of oxygen hole concentration on different resistance control methods

[0136] When the oxygen hole concentration is low, the electric field gain is low, causing memristor devices to tend to reset gradually. Conversely, when the oxygen hole concentration is high, the electric field gain is high, causing memristor devices to tend to reset abruptly. The reset mechanism of a memristor can be effectively controlled by adjusting the oxygen hole concentration. For example, using a high-temperature settling method results in a more uniform distribution of oxygen holes and a lower concentration, making the device easier to reset gradually. Increasing the set voltage and set current, by increasing the oxygen hole concentration and thus the electric field gain, makes the memristor device more prone to abrupt reset.

[0137] Based on this, the oxygen hole density or concentration can be controlled by adjusting the setting current, thereby regulating the reset method. Figure 4 ac).

[0138] (2) The effect of the potential barrier for oxygen ion migration out of the electrode on different resistance control methods

[0139] The impact of the oxygen ion migration barrier on the reset mechanism is mainly as follows: When the barrier is high, the required release voltage for oxygen ions is also high. At this high voltage, the probability of oxygen hole generation increases, thus inhibiting reset until the oxygen ion concentration reaches a certain level. At this point, the large accumulation of oxygen ions results in an abrupt reset. Conversely, if the oxygen ion release barrier is low and the release voltage is low, the probability of oxygen hole generation is low and has little impact on the reset process, resulting in a gradual reset.

[0140] Based on this, by adjusting the voltage during the setting process, the potential barrier for oxygen ion release can be controlled, thereby affecting its reset mechanism. Figure 4 ac).

[0141] (3) The influence of the competition between the generation and recombination of oxygen holes on different resistance modulation methods

[0142] The competition between oxygen hole generation and recombination ultimately determines the different reset mechanisms. In the absence of competition, oxygen ions are gradually released and recombine during the reset process, resulting in a smooth reset. However, the competition between oxygen hole generation and recombination leads to a more rapid reset, with oxygen hole generation inhibiting recombination. In the equivalent electric field (k... E • When E is large, reset will occur only when the oxygen ion concentration is released and accumulates to a certain concentration to overcome the inhibitory effect, and this is called a sudden reset.

[0143] Based on this, by comprehensively adjusting parameters such as oxygen hole concentration and the barrier height for oxygen ion migration, the competitive relationship between oxygen hole generation and recombination can be affected, ultimately controlling the reset mechanism.

[0144] (4) The effect of the potential barrier height for oxygen ions entering the electrode on different resistance control methods

[0145] Different electrode materials typically have different potential barrier heights. Generally, oxidizable electrode metals have lower potential barriers, while inert metals have higher barriers. These different barrier heights determine the difficulty for oxygen ions to enter the electrode, thus determining whether the oxygen ions ultimately enter the electrode or remain in the resistive switching layer. Oxygen ions entering the electrode require an external electric field to release, while oxygen ions in the resistive switching layer can drift to the vicinity of the conductive filament through thermal effects. Therefore, the electrode barrier height ultimately determines whether the device operates in a unipolar or bipolar resistance control mode.

[0146] Based on this theory and the experimentally fabricated asymmetric electrode structure, the polarity of the set voltage can be changed to alter the direction of oxygen ion movement towards the easily oxidized electrode or the inert electrode, ultimately determining the potential barrier for oxygen ions to enter the top electrode, thereby switching between unipolar or bipolar resistance control modes. Figure 4 df).

[0147] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for implementing a general compact model of a metal-oxide-semiconductor memristor, the method comprising: For memristors based on conductive filaments, the resistance value of the memristor is obtained based on the resistance value and length of the conductive filaments, and the electric field gain parameter is obtained by modeling the relationship between the electric field gain and the resistance value of the memristor. Based on the electric field gain parameters obtained by the above fitting and the potential barrier of oxygen ions entering the electrode, the probability of oxygen ions entering the electrode under the condition of an applied electric field E and local temperature T is obtained, and then the oxygen ion concentration entering the top electrode during the setting process and the oxygen ion concentration remaining in the oxide layer is obtained. Based on the electric field gain parameters obtained from the above fitting and the potential barrier for oxygen ions to migrate out of the electrode, the probability of oxygen ions being released from the top electrode during the reset process is obtained, and the concentration of oxygen ions released through diffusion in the oxide layer is calculated, thereby obtaining the total concentration of oxygen ions released during the reset process. A general model for memristors is constructed by modeling the competition between the generation and recombination of oxygen holes during the setting and resetting processes.

2. The method according to claim 1, characterized in that, The resistance value of the memristor R is calculated by the following equation: ， wherein , R 0 is the resistance value of the conduction filament determined based on the resistance value of the low resistance state of the device, d is the thickness of the oxide layer, gap is the length of the broken conduction filament, a 0 is the lattice constant, g 0 is the fitting parameter extracted from the device resistance experimental data, Further, the relationship model between the electric field gain parameter k E and the resistance value of the memristor is: R ​ ， wherein k E0 and α are fitting parameters based on experimental data.

3. The method according to claim 1, characterized in that, In the case of an applied electric field E and local temperature T the probability of oxygen ions entering the electrode P Absorb is calculated by the following equation: ， wherein, E ab is a potential barrier for oxygen ions to enter the electrode, Δt is a unit of time, E is an applied electric field, q is a charge amount per electron, a 0 is a lattice constant, k B is a Boltzmann constant, T is a local temperature, f is a vibration frequency of oxygen ions (O 2- ), k E is a fitting electric field gain parameter, Further, the concentration of oxygen ions entering the top electrode during the setting process is : ， wherein t 1 is the total cycle time for programming during the set process, n tot is the total oxygen ion concentration generated during the set process, During the setting process, the oxygen ion concentration remaining in the oxide layer is: 。 4. The method according to claim 1, characterized in that, The probability of oxygen ion release in the top electrode during the reset process P Rel,e This is calculated by the following equation: ， in, E rel It is the potential barrier for oxygen ions to migrate out of the electrode. Δt It is a unit of time. E It is an external electric field. q It is the charge per unit electron. a 0 is the lattice constant. k B Boltzmann's constant, T For local temperature, f oxygen ions (O 2- The vibration frequency of ) k E To fit the obtained electric field gain parameters, Furthermore, during the reset process, the probability of releasing oxygen ions remaining in the oxide layer... P Rel,o Comply with: ， in, ν D0 is the diffusion coefficient of oxygen ions. a 0 is the lattice constant. Δt It is a unit of time. E diff For diffusion barrier, k B Boltzmann's constant, T For local temperature, The final concentration of oxygen ions released during the reset process for: in, t 2 represents the total programming cycle during the reset process. P Rel,e This represents the probability of oxygen ions being released from the top electrode during the reset process. This represents the concentration of oxygen ions entering the top electrode during the placement process. P Rel,o This represents the probability of releasing oxygen ions remaining in the oxide layer. This represents the concentration of oxygen ions remaining in the oxide layer during the placement process.

5. The method according to claim 1, characterized in that, The competitive process between the generation and recombination of oxygen holes during the placement and reset processes is modeled. During the setting process, under the applied electric field E Under the influence of the unit time Δt The probability of oxygen hole generation inside. P G for: ， in, E a It is a potential barrier that generates oxygen holes. Δt It is a unit of time. E It is an external electric field. q It is the charge per unit electron. a 0 is the lattice constant. k B Boltzmann's constant, T For local temperature, f oxygen ions (O 2- The vibration frequency of ) k E To fit the obtained electric field gain parameters, During the placement process, the concentration of oxygen ions generated is: ， in, P G The electric field applied during the setting process E Under the influence of the unit time Δt The probability of oxygen vacancies being generated within the cavity. t 1 represents the total programming cycle during the bit-setting process. Probability of oxygen-hole recombination P R Calculated using the following formula: ， in, E r It is the barrier to oxygen-hole recombination. Δt It is a unit of time. It refers to the concentration of oxygen ions released during the reset process. k B Boltzmann's constant, T For local temperature, f oxygen ions (O 2- The vibration frequency of ) Throughout the setting and resetting process, the generation and recombination of oxygen holes coexist and dynamically compete, affecting the conductive filament. gap Change Δ gap for: in, t 3 is the total writing cycle, a 0 is the lattice constant. The net generation or net recombination probability, i.e., the probability of oxygen hole generation. P G Probability of recombination with oxygen holes P R The difference between them , Furthermore, as the gap in the conductive filament changes, the resistance value of the memristor... R The current across the memristor changes. I With voltage V The relationship is as follows: ， in, V For the applied voltage, V 0 is a fitting parameter representing the non-linearity of the memristor's resistance value as a function of voltage. R To calculate the resistance value of the memristor, The Joule heating generated by the current causes the temperature inside the memristor to rise, which is consistent with the following: ， in, T 0 represents the ambient temperature. R th This represents the thermal resistance parameter of the oxide layer.

6. A general model of a memristor constructed by the method according to any one of claims 1-5.

7. The application of the general model of the memristor of claim 6 is used to explain and reproduce the unconventional programming characteristics of the metal oxide memristor during the reset process, the small-amplitude reset after reset, and the reset during the voltage flyback process.

8. The application according to claim 7, characterized in that, By adjusting the process parameters during device manufacturing and the programming voltage and current parameters during operation, the potential barrier for oxygen ions to enter and exit the electrodes can be controlled, thereby regulating unipolar and bipolar memristors, as well as the programming methods of gradual and abrupt changes, thus improving the ability to control the programming characteristics of memristors.

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