A Modeling Method for a Threshold Transition Memristor Based on a Transmission Mechanism

Abstract

The present invention discloses a modeling method for a threshold switching memristor based on a transport mechanism, using the space charge limited current mechanism (SCLC) to model the threshold switching memristor; wherein, the threshold switching memristor includes memristors such as TaOx, VOx, and NbOx that have been experimentally proven to have threshold characteristics; using the direct tunneling to Fowler-Nordheim tunneling mechanism (DT-FNT) to model another type of threshold switching memristor; wherein, the another type of threshold switching memristor includes memristors such as HfOx:Ag, SiOxNy:Ag, and SiO2:Ag that have been experimentally proven to have threshold characteristics. The above method has the advantages of being complete and efficient, and can facilitate the flexible application of memristors in circuits.

Description

Technical Field

[0001] The present invention relates to the technical field of memristors, and particularly to a modeling method for a threshold switching memristor based on a transport mechanism. Background Art

[0002] As an emerging electronic component, the memristor was proposed by Leon Chua in 1971. It has low power consumption, high density, fast operation, high durability, and the ability to integrate with standard CMOS circuits, making memory technology the focus of attention. Constructing a suitable memristor model is of great significance for exploring the application scenarios of memristors.

[0003] Currently, the model research on threshold switching memristors is not yet mature, and there is a lack of corresponding modeling schemes. Summary of the Invention

[0004] The purpose of the present invention is to provide a modeling method for a threshold switching memristor based on a transport mechanism. This method is more complete and efficient compared to single modeling, and further explores the complete electrical characteristics of the threshold memristor, thus facilitating the flexible application of the memristor in circuits.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A modeling method for a threshold switching memristor based on a transport mechanism, the method comprising:

[0007] Step 1, modeling the threshold switching memristor using the space charge limited current mechanism (SCLC); wherein, the threshold switching memristor includes a memristor with a tantalum oxide, vanadium oxide, niobium oxide, or niobium oxide intermediate layer that has been experimentally proven to have threshold characteristics;

[0008] Step 2, modeling another type of threshold switching memristor using the direct tunneling to Fowler-Nordheim tunneling mechanism (DT-FNT); wherein, the another type of threshold switching memristor includes a memristor with a hafnium oxide doped with silver, silicon oxynitride doped with silver, or silicon dioxide doped with silver intermediate layer that has been experimentally proven to have threshold characteristics.

[0009] It can be seen from the technical solutions provided by the present invention described above that the above method is more complete and efficient compared to single modeling, and further explores the complete electrical characteristics of the threshold memristor, thus facilitating the flexible application of the memristor in circuits. Brief Description of the Drawings

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0011] Figure 1 Schematic flow diagram of the modeling method of the threshold switching memristor based on the transport mechanism provided by the embodiments of the present invention;

[0012] Figure 2 Schematic diagram of the Spice model designed by the embodiments of the present invention;

[0013] Figure 3 Schematic diagram of the Spice model designed based on DT-FNT by the embodiments of the present invention. Detailed implementation manners

[0014] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments, which does not constitute a limitation to the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0015] As Figure 1 shown is the schematic flow diagram of the modeling method of the threshold switching memristor based on the transport mechanism provided by the embodiments of the present invention, and the method includes:

[0016] Step 1: Model the threshold switching memristor using the space charge limited current mechanism SCLC;

[0017] Among them, the threshold switching memristor includes a memristor with a middle layer of tantalum oxide, vanadium oxide, niobium oxide or niobium oxide that has been experimentally proven to have threshold characteristics;

[0018] In this step, the space charge limited current mechanism SCLC usually occurs when charges are injected from a metal electrode into a dielectric such as an insulator, generating a space charge region at the interface to control the current passing through the dielectric. For low voltages and low charge injections, the current is mainly due to the free charges present in the dielectric and follows Ohmic behavior I~V (current-voltage relationship curve). Since the current density J conforms to the following formula through Ohm's law:

[0019] J~Eexp(-Eae / KT) (1)

[0020] In the formula, E is the electric field; Eae is the electron activation energy; K is the Boltzmann constant; T is the internal temperature of the threshold switching memristor;

[0021] In fact, the characteristics of a real dielectric are the presence of lattice defects, impurities, etc., and these defects will lead to the existence of electron traps. Considering the existence of electron traps, the relationship between current density and voltage depends on the energy distribution of the traps. When it is a shallow trap, that is, it follows Curve I-V 2 (shallow trap region), satisfying Equation 2:

[0022]

[0023] where θ represents the proportion of free electrons; Nc is the number of states at the bottom of the conduction band; Nt is the number of trap states; μ is the electron mobility; the thin-film dielectric constant; d is the film thickness; Ea describes the activation energy level of the energy trap below the conduction band;

[0024] When it is a deep trap, that is, it follows Curve I-V n n>2 (deep trap region), satisfying Equation 3:

[0025]

[0026] where Tt is the trap temperature; l + 1 is the current proportional to V n in the exponent n of, and the experimental logarithmic I-V curve of the TaOx memristor exactly coincides with the SCLC mechanism;

[0027] Through the above analysis, based on SCLC, a physical model of the threshold-switching memristor is established. Dividing both sides of Equations 1-3 by voltage, the following physical model is obtained:

[0028] R ohm =R 1 exp(E ae / KT) (4)

[0029]

[0030] R deep =R 3 4T n-1 V -(n-1) (6)

[0031]

[0032] where Rohm, R shollow 、R deep are the device resistances of the current-voltage of the threshold-switching memristor when following Ohm's law, Curve I-V 2 、Curve I-V n n>2 respectively; R1, R2, and R3 are the initial resistances in these three states;

[0033] To describe the self-heating effect, we use the heat transfer law Equation 7 to describe the energy exchange between the conductive region of the threshold switching memristor and the external environment. Similar to the thermal capacitance, its temperature change can be described by Joule heating and heat dissipation; R and i are the real-time resistance and current of the device respectively; Гth is the thermal conductivity; C is the thermal capacitance; ΔT=T-Tamb, which is between the ambient temperature Tamb and the temperature T of the fiber region;

[0034] The above Equations 1-4 are the physical models of the threshold switching memristor designed using the space charge limited current mechanism SCLC.

[0035] In addition, to explore the complete electrical characteristics of the threshold switching memristor, it is also necessary to simulate it in circuit software. Therefore, according to the physical model established above, the embodiment of the present invention also designs a Spice model, as Figure 2 Shown is the schematic diagram of the Spice model designed by the embodiment of the present invention:

[0036] Figure 2 The left side represents the complete threshold switching memristor. The three capacitors are the resistors of the above Equations (4)(5)(6) respectively. When the voltage is very small, Rohm is very small, and the resistance values of the other two resistors are very large, resulting in the basic non-conduction of the branch circuits of Rshollow and Rdeep. At this time, the Joule heat inside the device is basically provided by Rohm; similarly, when the voltage is slightly increased and very large, the Joule heat is provided by Rshallow and Rdeep respectively.

[0037] Figure 2 The right side is the equivalent circuit of Equation (7), that is, the thermal capacitance. According to Kirchhoff's nodal current law, the current flows into the node T from I=joule(), and flows out from the capacitor and resistor. It is equivalent to that as the voltage of the memristor increases, the current I is equivalent to the heat generated by the internal fiber temperature, but at the same time the device will also dissipate a part of the heat (represented by the current on R3). The generated heat minus the dissipated heat is equal to the net heat generated inside the device, that is, the current on the capacitor C1.

[0038] Step 2: Use the direct tunneling to Fowler-Nordheim tunneling (F-N) mechanism DT-FNT to model another type of threshold switching memristor;

[0039] Among them, the another type of threshold switching memristor includes memristors with hafnium oxide doped with silver (HfOx:Ag), silicon oxynitride doped with silver (SiOxNy:Ag), or silicon dioxide doped with silver (SiO2:Ag) in the intermediate layer, which have been experimentally proven to have threshold characteristics.

[0040] In this step, based on the direct tunneling to Fowler-Nordheim tunneling mechanism DT-FNT, in the initial stage of applying voltage to another type of threshold switching memristor, DT is the main transport mechanism. As the distance between silver clusters in the silver-doped oxide decreases, the increase in the internal electric field of the threshold switching memristor causes the potential barrier to change from a step potential barrier to a triangular potential barrier, and the transport mechanism also becomes dominated by FNT. Among them, the current density formulas of DT and FNT are respectively equations (8) and (9):

[0041]

[0042]

[0043] Among them, q is the electron charge; m * is the effective mass of the electron; φ B is the potential difference; k is the fitting coefficient; h is Planck's constant; t ox is the relative oxide thickness; E is the electric field;

[0044] Through the above analysis, based on DT-FNT, a physical model is established for another type of threshold switching memristor. Specifically, after taking the reciprocal of both sides of equations 8-9 and multiplying by the voltage V respectively, so that R DT =V / J DT , R FNT =V / J FNT , R FNT0 =8πhφ B / q 2 , by removing the approximate equal sign from R DT0 , the following physical model is obtained:

[0045]

[0046]

[0047]

[0048] Among them, R DT is the resistance generated by direct tunneling; R DT0 is the fitting parameter of DT; R FNT is the resistance generated by FNT; R FNT0 is the fitting parameter of FNT; h is the relative length of the growth of the conductive filament; tox is the oxide thickness; uv is the ionic mobility of the oxide; Dic is the number of diffusing ions per second;

[0049] At the same time, equation 12 is used to describe the dynamic change of the length of the silver conductive filament of the threshold switching memristor;

[0050] The above formula 10-12 is a physical model of another type of threshold switching memristor designed using the direct tunneling to Fowler-Nordheim tunneling (F-N) mechanism DT-FNT.

[0051] In addition, in order to explore the complete electrical characteristics of this other type of threshold switching memristor, it is also necessary to simulate it in circuit software. Based on the physical model designed in step 2, this embodiment designs a Spice model, as Figure 3 shown in the schematic diagram of the Spice model designed based on DT-FNT in the embodiment of the present invention:

[0052] Figure 3 On the left is the equivalent circuit of the memristor, Figure 3 and on the right is shown the growth rate relationship of the conductive filaments inside the memristor. When the voltage is small, R DT is small, and the memristor current is mainly provided by direct tunneling; as the electric field increases, R FNT is less than R DT , and the current is mainly provided by FNT.

[0053] It should be noted that the content not described in detail in the embodiment of the present invention belongs to the prior art well-known to those skilled in the art.

[0054] As described above, only the preferred specific embodiments of the present invention are given, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims. The information disclosed in the background art part of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or any form of suggestion that this information constitutes the prior art well-known to those skilled in the art.

Claims

1. A modeling method for a threshold-switching memristor based on a transport mechanism, characterized in that, the method includes: Step 1: Model the threshold-switching memristor using the space-charge-limited current mechanism SCLC; wherein, the threshold-switching memristor includes a memristor with a middle layer of tantalum oxide, vanadium oxide, niobium oxide, or niobium oxide that has been experimentally proven to have threshold characteristics; The process of Step 1 is specifically as follows: Based on the space-charge-limited current mechanism SCLC, the current density J of Ohm's law conforms to the following formula: J~Eexp(-Eae / KT) (1) In the formula, E is the electric field; Eae is the electron activation energy; K is the Boltzmann constant; T is the internal temperature of the threshold-switching memristor; Considering the existence of electron traps, the relationship between current density and voltage depends on the energy distribution of the traps. When the traps are shallow, it follows the curve I-V 2 , satisfying Equation 2: where, θ represents the proportion of free electrons; Nc is the number of states at the bottom of the conduction band; Nt is the number of trap states; μ is the electron mobility; the thin-film dielectric constant; d is the film thickness; Ea describes the activation energy level of the energy trap below the conduction band; When it is a deep trap, it follows curves I to V n n > 2, satisfying Equation 3: where Tt is the trap temperature; l + 1 is the exponent n in which the current is proportional to V n in; Through the above analysis, a physical model of the threshold-switching memristor is established based on SCLC. Divide both sides of equations 1-3 by voltage to obtain the following physical model: R ohm = R 1 exp(E ae / KT) (4) R deep = R 3 4T n-1 V -(n-1) (6) Among them, Rohm, R shollow , R deep are respectively the current-voltage of the threshold switching memristor when following Ohm's law, curve I-V 2 , curve I-V n when n>2; R1, R2, and R3 are respectively the initial resistances in these three states; Equation 7 is used to describe the energy exchange between the conductive region of the threshold-switching memristor and the external environment, which is similar to a thermal capacitance, and its temperature change can be described by Joule heating and heat dissipation; wherein, Гth is the thermal conductivity; C is the thermal capacitance; ΔT=T-Tamb, between the ambient temperature Tamb and the fiber region temperature T; The above equations 1-4 are the physical models of the threshold-switching memristor designed using the space-charge-limited current mechanism SCLC; Step 2: Model another type of threshold-switching memristor using the direct tunneling to Fowler-Nordheim tunneling mechanism DT-FNT; wherein, the another type of threshold-switching memristor includes a memristor with a middle layer of hafnium oxide doped with silver, silicon oxynitride doped with silver, or silicon dioxide doped with silver that has been experimentally proven to have threshold characteristics; The process of Step 2 is specifically as follows: Based on the direct tunneling to Fowler-Nordheim tunneling mechanism DT-FNT, in the initial stage of applying voltage to another type of threshold-switching memristor, DT is the main transport mechanism. As the distance between silver clusters in the silver-doped oxides becomes smaller, the increase in the internal electric field of the threshold-switching memristor causes the potential barrier to change from a step potential barrier to a triangular potential barrier, and the transport mechanism also becomes dominated by FNT; wherein, the current density formulas of DT and FNT are respectively formulas (8) and (9): where q is the electronic charge; m * is the effective mass of the electron; φ B is the potential difference; k is the fitting coefficient; h is Planck's constant; t ox is the relative oxide thickness; E is the electric field; Based on the above analysis, a physical model is established for another type of threshold-switching memristor on the basis of DT-FNT. Specifically, after taking the reciprocal of both sides of Equations (8-9) and then multiplying by the voltage V, we get R DT = V / J DT , R FNT = V / J FNT , R FNT0 = 8πhφ B / q 2 . By removing the approximate sign from R DT0 , the following physical model is obtained: Among them, R DT is the resistance generated by direct tunneling; R DT0 is the fitting parameter of DT; R FNT is the resistance generated by FNT; R FNT0 is the fitting parameter of FNT; h is the relative length of conductive filament growth; tox is the oxide thickness; uv is the ionic mobility of the oxide; Dic is the number of diffused ions per second; At the same time, equation 12 is used to describe the dynamic change of the silver conductive filament length of the threshold-switching memristor; The above equations 10-12 are the physical models of another type of threshold-switching memristor designed using the direct tunneling to Fowler-Nordheim tunneling mechanism DT-FNT.

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