Resistive devices and methods of making the same

Abstract

The application provides a resistive device and a manufacturing method thereof, comprising: predicting an electrical resistance value of a phase change process caused by a phase change of a resistive material of the resistive device based on a tensor-based multi-dimensional model; and manufacturing the resistive device according to the prediction result. The method of the application can greatly reduce the calculation amount required for prediction by introducing a tensor to abstractly describe the material; meanwhile, the method can solve the problem that the channel behavior of the resistive device depending on the phase change material is complex, nonlinear and difficult to predict by sequentially changing the value of the tensor element to simulate the gradual phase change process of the material and tracking the change of the overall resistance of the material in the process to predict the behavior. The method is simple and easy to implement, the prediction is relatively effective, and the method has a wide application prospect.

Description

Technical Field

[0001] This invention relates to semiconductor devices and material simulation devices, and particularly to resistive devices and their fabrication methods. Background Technology

[0002] The modern semiconductor industry has established a relatively complete information storage system. To bridge the speed gap between volatile devices (DRAM, SRAM, register file) and non-volatile devices (SSD, HDD), and to obtain information storage media that balances non-volatility with speed and area, various approaches have been proposed, such as redox-based memory, ferroelectric RAM, magnetic RAM, phase-change RAM, and spin-transfer torque RAM. In addition to novel RAM devices, resistive devices such as memristors and synaptic transistors have also been widely developed and applied.

[0003] Compared to charge-based devices (such as DRAM / SRAM), resistive devices based on phase transitions (not limited to those involving physical, chemical, or electrochemical processes) offer numerous advantages, such as non-volatility and a large number of resolvable states. However, these phase transition processes are often complex. For example, some phase transitions involve intermediate transition phases, some rely on ion insertion / extraction, and some involve non-uniform and asynchronous reactions across the material. These issues lead to significant nonlinearities in the resistive switching behavior of resistive devices, which have been observed in various systems including LiCoO2, WO3, MoO3, and MoS2. The nonlinearity and complexity of phase transition-dependent resistive switching behavior make external control or encoding of the devices difficult, easily resulting in high information processing / storage error rates and high software design costs. These problems limit the application of these devices.

[0004] Other computational or simulation methods based on physical laws struggle to rapidly predict the electrical conductivity changes of specialized devices with dimensions of hundreds of micrometers or larger; the larger the size, the greater the computational burden. For example, a paper published in Advanced Functional Materials in 2019 (DOI: 10.1002 / adfm.201902821) calculated the electrical conductivity changes during phase transitions in nanoscale LCO polycrystalline materials based on density functional theory. While the original paper did not provide detailed parameters, it stated that the polycrystalline material calculated was "nanoscale," and the specific example in the paper calculated the electrical conductivity changes for a 100nm × 100nm × 70nm LCO material.

[0005] Since the aforementioned problems essentially stem from the intrinsic physical and chemical properties of the materials in the devices, they are difficult to completely eliminate. Therefore, a key issue is how to accurately and quickly predict the resistance change behavior of polycrystalline materials caused by phase transitions through simulation, calculation, and other methods. With prediction methods, on the one hand, it is possible to design various devices based on this material more conveniently and rationally; on the other hand, its behavior can be more accurately controlled in device applications. Summary of the Invention

[0006] One object of the present invention is to overcome at least one technical defect in the prior art and to provide a resistive device and a method for fabricating the same.

[0007] A further objective of this invention is to efficiently and accurately predict the resistive switching behavior of materials (and corresponding devices) in order to enable high-throughput, rapid screening or design of new materials and device structures, thereby manufacturing high-performance resistive devices.

[0008] Another further objective of this invention is to simplify the device manufacturing method, improve the consistency of the manufactured devices, and produce high-precision large-size resistive devices while ensuring device design accuracy.

[0009] Another further objective of this invention is to use a highly compatible resistive switching behavior prediction method to manufacture devices so that the manufactured devices can be applied to multiple fields such as electrochemistry, optics, and electronics.

[0010] Another further objective of this invention is to manufacture devices using a highly compatible resistive switching behavior prediction method, enabling them to have highly controllable resistive state switching performance. This allows them to be used in non-volatile information storage devices and non-von Neumann computing systems, thereby reducing error rates, coding complexity, and power consumption during information storage or processing in related devices (memristors, synapses, etc.) and related computing systems (neuromorphic computing, neuromorphic computing, etc.).

[0011] Another objective of this invention is to understand the possible causes of abnormal resistive switching behavior in resistive switching materials, so as to facilitate problem tracing and mechanism research.

[0012] In particular, according to one aspect of the present invention, a method for manufacturing a resistive device is provided, comprising:

[0013] Predict the resistance value of the phase transition process caused by the phase transition of the resistive switching material in the resistive device based on a tensor-based multidimensional model; and

[0014] The resistive device is manufactured based on the prediction results.

[0015] Optionally, the step of predicting the resistance value of the phase transition process caused by the phase transition of the resistive switching material of the resistive device based on a tensor-based multidimensional model includes:

[0016] Construct a third-order tensor T of N×M×P state And map each phase state of the resistive switching material to the third-order tensor T. state Among them, N, M,

[0017] The phase state of the resistive switching material is controlled at various points, and the third-order tensor T is iterated during each control. state This yields N×M×P updated third-order tensors T. state ;

[0018] Based on a preset mapping relationship, for each of the third-order tensors T state The tensor elements are reassigned, thereby resetting each of the third-order tensors T. state One-to-one mapping to N×M×P N×M×P third-order tensors T R N×M×P of the aforementioned third-order tensors T R Record the resistance values ​​of the phase transition process at various points along the resistive switching material; and

[0019] According to each of the aforementioned third-order tensors T R Calculate the equivalent resistance of each phase transition process of the resistive switching material to obtain the resistance value of each phase transition process of the resistive switching material.

[0020] Optionally, construct a third-order tensor T of N×M×P. state And map each phase state of the resistive switching material to the third-order tensor T. state The steps include:

[0021] The length, width, and height of the resistive switching material are measured and denoted as L, W, and H, respectively. A spatial precision of 'a' is preset. Then, N = round(L / a), M = round(W / a), and P = round(H / a), where 'a' is a unit of length, and a > 0.

[0022] Measure all phases that appear during the phase transition of the resistive switching material, and record them sequentially from the initial state to the final state as follows: Then the third-order tensor T state The tensor elements take values ​​of 0, 1, 2, ..., n, and the third-order tensor T... state The values ​​of each tensor element correspond sequentially to all phases of the resistive switching material, and the third-order tensor T... state The index of a tensor element represents the material location corresponding to that tensor element.

[0023] Optionally, regulate the phase states of each part of the resistive switching material, and iterate the third-order tensor T each time of regulation state , when the phase states of each part of the material reach the final phase state after N×M×P times of regulation, a total of N×M×P updated third-order tensors T are obtained state The steps include:

[0024] Among all the tensor elements of non-empty elements, randomly select a tensor element. If the value of the selected tensor element < n, increase its value by 1 to obtain an updated third-order tensor T state , if the value of the selected tensor element is n, randomly select another tensor element and make the above determination until a tensor element with a value other than n is selected; when the values of all tensor elements are n, end the regulation; and

[0025] In this step, an updated third-order tensor T is obtained respectively each time of regulation state , the N×M×P third-order tensors T state are respectively used to describe a series of states experienced by the resistive switching material from the initial state to the final state; the probability of each tensor element being selected is equal, or the probability of each tensor element being selected is inversely proportional to the resistivity of the phase of the resistive switching material it describes.

[0026] Optionally, the step of reassigning values to the tensor elements of each of the third-order tensors T state includes:

[0027] Obtain the resistance values of the resistive switching material in the shape of a cube with side length a in each phase state, which are denoted as the resistance values of each phase state of a single grain of the resistive switching material;

[0028] Reassign values to the tensor elements of each of the third-order tensors T state according to the resistance values of each phase state of a single grain of the resistive switching material, so as to obtain the values of the tensor elements in the third-order tensor T R .

[0029] Optionally, the values of the tensor elements in each of the third-order tensors T R are determined by the following method:

[0030] T R (i,j,k) = R0×δ Tstate(i,j,k),0 +R2×δ Tstate(i,j,k),1 +R3×δ Tstate(i,j,k),2 +…+R n ×δ Tstate(i,j,k),n .

[0031] Where δ i,j is the Kronecker product, and its value is 1 if and only if i = j, and 0 in other cases; R0, R1, …, Rn These represent the resistance values ​​of a single grain of each phase of the resistive switching material from the initial state to the final state.

[0032] Optionally, based on each of the third-order tensors T R The steps for calculating the equivalent resistance of each phase transition process of the resistive switching material include:

[0033] Each of the aforementioned third-order tensors T R The data is mapped to a netlist file and then used by calculation software to calculate the equivalent resistance.

[0034] Optionally, when each of the third-order tensors T is... R In the steps of mapping to a netlist file:

[0035] The resistance value between adjacent nodes in the netlist file is the third-order tensor T. R The values ​​of the tensor elements at corresponding positions in the tensor; the values ​​of each of the third-order tensors T. R Generate a netlist file and obtain an equivalent resistance value.

[0036] Optionally, when the resistive switching material undergoes a phase transition that leads to a metal-insulator phase transition, the phase state at various points of the resistive switching material is controlled, and the third-order tensor T is iterated during each control. state When the material is in its final state through N×M×P manipulations, a total of N×M×P updated third-order tensors T are obtained. state Following that, it also includes:

[0037] Detect each of the third-order tensors T state Whether there is a conductive path in it, wherein the conductive path refers to a group of adjacent low-resistivity phase grains;

[0038] Record each of the third-order tensors T state The number of conductive pathways and the depth of modulation when a conductive pathway first appears.

[0039] According to another aspect of the present invention, a resistive device is also provided, which is manufactured using the resistive device manufacturing method described in any of the preceding claims.

[0040] The resistive device and its manufacturing method of this invention predict the resistance change caused by the phase transition of the resistive switching material based on a tensor-based multidimensional model. This allows for continuous, progressive, and accurate recording of a series of continuous and progressive phase transition states and corresponding resistance values ​​at various points on the resistive switching material. Therefore, based on the efficient and accurate prediction of the resistive switching behavior of the resistive switching material (and corresponding device), the resistive device can be manufactured "targeted" according to the prediction results. In the context of the rapid development of related functional devices, the technical solution of this invention can be used for high-throughput, rapid screening or design of new materials and device structures. The resistive device only requires that the materials of the key components be screened or predicted using a tensor-based multidimensional model prediction method; the key components refer to the locations where the resistance regulation of the resistive device occurs, such as the active dielectric layer between the top and bottom electrodes of a two-terminal device, or the channel between the source and drain electrodes of a three-terminal device.

[0041] Furthermore, the resistive device and its manufacturing method of the present invention, due to the highly abstract nature of the relevant parameters and processes in the prediction model, do not involve specific physical laws or depend on the specific physical processes occurring during phase transitions. Therefore, the computational load is significantly reduced, resulting in advantages such as fast calculation speed and accurate results, facilitating the practical design and industrial application of the device. In addition, since specific basic information related to the phases (such as the number of phases and pure-phase resistance) still needs to be determined in advance, the computational accuracy of the technical solution of the present invention is not affected by the abstraction and simplification. Due to the fast calculation speed, based on the solution of the present invention, repeated simulation calculations can be performed on resistive switching materials, facilitating the examination of the consistency of the resistive switching behavior of the resistive switching materials. Moreover, the resistive switching materials or devices to be predicted are not limited to micro-nano sizes; efficient calculations can be performed on large-size materials or devices, resulting in a wide range of applications.

[0042] Furthermore, the resistive device and its manufacturing method of the present invention, because the prediction process uses a third-order tensor to reflect the phase state and resistance value at various points of the resistive switching material, can be easily adjusted according to different resistive switching materials and different control parameters when different resistive switching materials are needed to manufacture different devices, thus exhibiting high compatibility. Regarding resistive switching materials, the present invention can be applied to oxides, sulfides, or nitrides, as well as insulators, semiconductors, half-metals, semi-metals, or metals, or even metal-insulator phase transition materials (including but not limited to Wilson phase transitions, Anderson phase transitions, or Mott phase transitions), superconducting phase transition materials, or crystalline-amorphous phase transition materials. Regarding devices, the present invention can be applied to two-terminal devices (such as memristors), three-terminal devices (such as transistors), and multi-terminal devices (such as artificial synapses). In summary, the method of the present invention is widely applicable to various materials and devices in electrochemistry, optics, and electronics.

[0043] Furthermore, the resistive device and its manufacturing method of the present invention, because the resistive switching behavior prediction method relies on a series of progressively increasing material state record tensors, not only provides the equivalent resistance but also facilitates problem backtracking and mechanism research. This allows for the discovery of possible causes of abnormal resistive switching behavior and resistive switching phenomena related to certain special structures in the material. For example, for metallic insulator phase change materials, by analyzing the T... state Studies of the special structures in the material reveal that conductive pathways significantly influence the equivalent resistance of the material. Therefore, this invention can be applied not only to the mass production design of practical devices to guide their application, but also to scientific research.

[0044] The above and other objects, advantages and features of the present invention will become more apparent to those skilled in the art from the following detailed description of specific embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0045] The following sections will describe some specific embodiments of the invention in detail by way of example and not limitation, with reference to the accompanying drawings. The same reference numerals in the drawings denote the same or similar parts or portions. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings:

[0046] Figure 1 This is a schematic diagram of a method for manufacturing a resistive device according to an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram illustrating the segmentation and modeling of a material to be predicted according to an embodiment of the present invention;

[0048] Figure 3 It is a third-order tensor T according to an embodiment of the present invention. state A schematic diagram showing the correspondence between resistive switching materials;

[0049] Figure 4 The results of the changes in conductive clusters and conductive pathways in the material recorded in step (4) of Embodiment 1 of the present invention with the depth of modulation are shown;

[0050] Figure 5 Experimental and predicted results of the material resistance variation with modulation depth according to Embodiment 1 of the present invention are shown;

[0051] Figure 6 Experimental and predicted results of the material resistance variation with modulation depth according to Embodiment 2 of the present invention are shown;

[0052] Figure 7 The predicted results of the material resistance variation with modulation depth according to Embodiment 3 of the present invention are shown;

[0053] Figure 8The predicted results of the material resistance variation with the control depth according to Embodiment 4 of the present invention are shown. Detailed Implementation

[0054] Reference will now be made in detail to embodiments of the invention, one or more of which are illustrated in the accompanying drawings. The various embodiments provided are intended to explain the invention and not to limit it. In fact, various modifications and variations to the invention will be apparent to those skilled in the art without departing from the scope or spirit of the invention. For example, a feature illustrated or described as part of one embodiment may be used with another embodiment to produce yet another embodiment. Therefore, the invention is intended to cover such modifications and variations within the scope of the appended claims and their equivalents.

[0055] The following reference Figures 1 to 8 This invention describes resistive devices and methods for manufacturing the same, according to embodiments of the present invention. In the description of the invention, unless otherwise explicitly specified, when a feature “includes or comprises” one or more of the features it covers, this indicates that other features are not excluded and may be further included, unless otherwise specifically stated.

[0056] Figure 1 This is a schematic diagram of a method for manufacturing a resistive device according to an embodiment of the present invention. The method for manufacturing a resistive device generally includes the following steps:

[0057] Step S102: Predict the resistance value of the resistive switching material in the resistive device based on a tensor multidimensional model. In this step, the tensor multidimensional model can refer to a three-dimensional, four-dimensional, five-dimensional, or more-dimensional tensor model. The resistive switching material refers to a material whose resistance changes based on a phase transition; hereinafter, it can be simply referred to as "material".

[0058] For example, in predicting the resistance value of the phase transition process caused by the phase transition of the resistive switching material in a resistive device using a tensor-based multidimensional model, a multidimensional tensor model can be established first according to a preset rule to obtain a multidimensional tensor. Each tensor element of the established multidimensional tensor is then set to correspond to the position and phase of the resistive switching material. Then, the multidimensional tensor is iteratively transformed according to a preset control method to regulate the phase state of the resistive switching material, resulting in multiple updated multidimensional tensors reflecting different phase states of the resistive switching material. According to a preset mapping rule, the values ​​of the tensor elements of the obtained multidimensional tensors are converted into resistance values ​​reflecting different phase states of the resistive switching material. By analyzing the re-assigned multidimensional tensors, the equivalent resistance of each phase transition process of the resistive switching material can be calculated.

[0059] Of course, the method of predicting the resistance value of the phase transition process caused by the phase transition of the resistive switching material of the resistive device based on the tensor multidimensional model is not limited to this.

[0060] Step S104: Fabricate the resistive device based on the prediction results. After determining the resistance change caused by the phase transition of the resistive switching material in the resistive device, the device coding and / or other designs can be guided. Since the resistive switching behavior of the resistive switching material can be accurately obtained based on step S102, resistive devices with multiple excellent properties such as high precision and controllable behavior can be fabricated under the guidance of the prediction results.

[0061] Using the above method, the resistance change caused by the phase transition of the resistive switching material of the device can be predicted by a tensor-based multidimensional model. This method can continuously, progressively and accurately record the states of a series of continuous and progressive phase transitions and the corresponding resistance values ​​at various points in the resistive switching material. Thus, under the premise of efficiently and accurately predicting the resistive switching behavior of the resistive switching material (and the corresponding device), resistive devices can be manufactured "targeted" based on the prediction results. In the context of the rapid development of related functional devices, the technical solution of this invention can be used for high-throughput, rapid screening or design of new materials, device structures, etc.

[0062] It is worth emphasizing that, compared with many existing methods that predict material resistance based on physical laws through calculation or simulation and then manufacture devices based on the prediction results (such as prediction methods based on density functional theory), the present invention breaks through the ideological constraints of the prior art and creatively provides a new method for predicting the resistance value of material phase transition processes based on a tensor-based multidimensional model. It has the advantages of being novel and unique, highly accurate, widely applicable, computationally efficient, fast, and highly controllable in terms of product resistance switching behavior. It solves many problems existing in the current prediction methods, such as low accuracy, small applicable device size, large computational load, and slow computation speed. It provides a feasible solution for more convenient and rational design of various devices based on resistive switching materials and for more accurate control of their behavior in device applications.

[0063] In some optional embodiments, the step of predicting the resistance value of the phase transition process caused by the phase transition of the resistive switching material in a resistive device based on a tensor-based multidimensional model includes:

[0064] Step A: Construct a third-order tensor T of type N×M×P. state The phase states of the resistive switching material are mapped one by one to the third-order tensor T. state Among them, N, M,

[0065] Step B involves controlling the phase state of the resistive switching material at various points, and iterating the third-order tensor T during each control step. state This yields N×M×P updated third-order tensors T. state .

[0066] Step C, based on the preset mapping relationship, for each third-order tensor T stateThe tensor elements are reassigned, thereby resetting each third-order tensor T. state One-to-one mapping to N×M×P N×M×P third-order tensors T R Make N×M×P third-order tensors T R Record the resistance values ​​of the phase transition process at various points in the resistive switching material.

[0067] Step D, based on each third-order tensor T R Calculate the equivalent resistance of each phase transition process of the resistive switching material to obtain the resistance value of each phase transition process.

[0068] The above describes the most important core steps of predicting the resistance value of a resistive device caused by a phase transition of the resistive switching material based on a tensor-based multidimensional model according to an embodiment of the present invention. It should be understood that the prediction method provided by the present invention does not limit the specific mapping rules and correspondences in step AD, etc. In specific implementation, the physical and chemical properties of the material to be predicted should be analyzed to determine the appropriate methods, and transformations and extensions can be made based on the above step AD. All such transformations and extensions should fall within the protection scope of the present invention.

[0069] The method described above in this invention significantly reduces the computational load required for prediction by introducing tensors to abstractly describe the material. Simultaneously, by sequentially changing the values ​​of tensor elements to simulate the gradual phase transition process of the material and tracking the change in the overall resistance of the material during this process, its behavior is predicted. This solves the problem of complex, nonlinear, and difficult-to-predict channel behavior in resistive devices dependent on phase transition materials. The method is simple to implement and provides relatively effective predictions, showing broad application prospects.

[0070] Using the above prediction method, the computational load is significantly reduced because the relevant parameters and processes in the prediction model are highly abstract, do not involve specific physical laws, and do not depend on the specific physical processes of phase transitions. This results in advantages such as fast computation speed and accurate results, facilitating the practical design and industrial application of devices. Furthermore, since specific basic information related to the phases (such as the number of phases and pure-phase resistance) still needs to be determined in advance, the computational accuracy of the technical solution in this embodiment is not affected by the abstraction and simplification. Due to the fast computation speed, the solution in this embodiment can be used for repeated simulations of resistive switching materials, facilitating the examination of the consistency of the resistive switching behavior. Moreover, the resistive switching materials or devices to be predicted are not limited to micro- and nano-sized dimensions; efficient calculations can be performed on large-sized materials or devices, resulting in a wide range of applications.

[0071] Because the prediction process uses a third-order tensor to reflect the phase state and resistance value at various points in the resistive switching material, the technical solution of this embodiment allows for convenient adjustment based on different resistive switching materials and control parameters when different devices need to be manufactured using different resistive switching materials, exhibiting high compatibility. Regarding resistive switching materials, this embodiment can be applied to oxides, sulfides, or nitrides, as well as insulators, semiconductors, half-metals, semi-metals, or metals. It can also be applied to metal-insulator phase transition materials (including but not limited to Wilson phase transitions, Anderson phase transitions, or Mott phase transitions), superconducting phase transition materials, or crystalline-amorphous phase transition materials. Regarding devices, this embodiment can be applied to two-terminal devices (such as memristors), three-terminal devices (such as transistors), and multi-terminal devices (such as artificial synapses). In summary, the method of this embodiment is widely applicable to various materials and devices in electrochemistry, optics, and electronics.

[0072] In some further embodiments, an N×M×P third-order tensor T can be established based on the correspondence between the overall material size and the average size of individual grains and the tensor, as well as the correspondence between all phases appearing in the material phase transition and all possible values ​​of the tensor element. state To illustrate the method of the present invention in more detail, a possible detailed procedure will be given below with reference to embodiments. For ease of description, the following embodiments will describe the method of the present invention in detail with reference to the prediction process of the resistive switching behavior of an L×W×H cuboid resistive switching material (this shape of material is commonly found in the active part of memristors or transistors). The average diameter of the single crystal of the material to be predicted is preset to 'a', which can be determined experimentally. The test direction of the material's equivalent resistance is parallel to the long side of the cuboid. The test direction is only used to determine the current direction and does not refer to the actual test required in the simulation.

[0073] Specifically, we establish a third-order tensor T of N×M×P. state The phase states of the resistive switching material are mapped one by one to the third-order tensor T. state The steps include:

[0074] The length, width, and height of the resistive switching material are measured and denoted as L, W, and H, respectively. With a preset spatial accuracy of 'a', then N = round(L / a), M = round(W / a), and P = round(H / a), where 'a' is a unit of length, and a > 0. a

[0075] Measuring all phases that appear during the phase transition of a resistive switching material, from the initial state to the final state, and denoting them sequentially as follows: Then the third-order tensor T state The tensor elements take values ​​of 0, 1, 2, ..., n, and the third-order tensor T...state The values ​​of each tensor element correspond sequentially to all phases of the resistive switching material. The third-order tensor T... state The index of a tensor element represents the material location corresponding to that tensor element, while the value of the tensor element represents the phase of the material at that location.

[0076] The aforementioned resistive switching material refers to the resistive switching material to be predicted. This is based on establishing an N×M×P integer third-order tensor T. state At that time, its initial value can be set to 0. This third-order tensor T state Each part corresponds to a specific part of the resistive switching material; the correspondence can be found in the reference. Figures 2 to 3 The round function represents the rounding rule, such as round(5.5) = 6, round(5.4) = 5.

[0077] Figure 2 This is a schematic diagram illustrating the segmentation and modeling of a material to be predicted according to an embodiment of the present invention. Figure 2 In the diagram, the top image is a top view, and the bottom image is a front view. 1 represents the test electrode, and 2 represents the material to be predicted.

[0078] Figure 3 It is a third-order tensor T according to an embodiment of the present invention. state A schematic diagram showing the correspondence between the resistive switching materials. Figure 3 In the diagram, the left side shows a schematic of segmentation and modeling of the material to be predicted, while the right side shows the corresponding third-order tensor T. state The schematic diagram shows that 1 represents the test electrode, 2 represents the material to be predicted, and 3 represents T. state (·,·,1). For example... Figure 3 As shown, for example, T state (5,4,1) = 1 indicates that the material is not in its initial state at that location (dark marker), while the other tensor values ​​are 0, indicating that the material is in its initial state at these locations (light marker). For example, T state (1,1,1)=0 represents the cube region (denoted as O) with side length a at the lower left corner of the material, which is in the initial phase, while T state (1,1,2)=n represents the final state of a cubic region with side length a that is adjacent to and located on top of O.

[0079] Using the above method, a third-order tensor T of N×M×P is established. state And make the third-order tensor T state Each part of the resistive switching material corresponds one-to-one with another part of the resistive switching material, and each part of the resistive switching material can be mapped one-to-one to the third-order tensor T. state This greatly facilitates the continuous and progressive control of the phase state of materials, thereby calculating the resistance value of each phase state, and provides a basic model for simplifying the prediction process, reducing the amount of calculation, improving the calculation speed, and ensuring the prediction accuracy.

[0080] In step A above, all phases in the material phase transition can be obtained through experimental and theoretical analysis. For ease of description, it is assumed that the material to be predicted has three phases: P0 (initial state), P1 (intermediate state), and P2 (final state), where P0 and P1 are insulating phases, and P2 is a metallic phase. Therefore, T state All tensor elements in the model have possible values ​​of 0, 1, and 2, representing three phases. Specific embodiments described below will be based on this. state The value records the current phase state of the material, for example: T state (0,0,0) = 0 represents the initial state of a grain at one end of the material. T state (N,M,P)=2 represents the grain at the other end of the material being in its final state. In this embodiment, the material is exactly a cuboid, and its various positions can be T state The indices of all tensors in the code correspond one-to-one.

[0081] However, in practical applications, since the shape of the material may be irregular or arbitrary, L, W, and H can be the length, width, and height of the smallest cuboid that can just contain the material, while T... state This actually corresponds to the smallest cuboid that can just hold the material, therefore T state There are tensor elements that do not correspond to the material, which can be called "vacuum elements". In the subsequent simulation and control process, the "vacuum elements" are not changed and are not included in any statistical data in any form.

[0082] T state The initial values ​​of tensors are set as follows: "empty element" is set to empty value, and the rest of the tensors are set to 0.

[0083] Of course, in other embodiments, this can be applied to a third-order tensor T of N×M×P. state The method of establishing the tensor T can be modified, which will not be elaborated in this disclosure, as long as it can map each part of the material to the established third-order tensor T. state That's all.

[0084] For example, the minimum cuboid dimensions to accommodate the material to be predicted can be set as L (length), W (width), and H (height), and the spatial accuracy of the prediction method can be denoted as a. Preferably, N, M, and P are round(L / a), round(W / a), and round(H / a), respectively; alternatively, N, M, and P are round[L / (2×a)], round[W / (2×a)], and round[H / (2×a)], respectively; alternatively, N, M, and P are round[L / (m×a)], round[W / (m×a)], and round[H / (m×a)], respectively, where m>0 and The larger the m is, the lower the accuracy of the obtained prediction result, but the calculation and simulation speed can be increased. In applications, it can be determined according to the requirements of timeliness and accuracy.

[0085] For the spatial accuracy a of the above prediction method, preferably, a is the same as the average diameter of the single crystal grains of the material to be predicted. At this time, it can be denoted as a m ; optionally, 1μm > a ≥ 30nm; optionally, 10μm > a ≥ 1μm; optionally, 100μm > a ≥ 10μm.

[0086] In step B, by regulating the phase states of each part of the resistive switching material, and iterating the third-order tensor T each time of regulation state , after N×M×P times of regulation, each part of the material is in the final phase state. In some optional embodiments, regulate the phase states of each part of the resistive switching material, and iterate the third-order tensor T state , when each part of the material is in the final phase state after N×M×P times of regulation, a total of N×M×P updated third-order tensors T state are obtained, and the steps include:

[0087] Among all the non-empty tensor elements, randomly select one tensor element. If the value of the selected tensor element < n, then increase its value by 1 to obtain an updated third-order tensor T state , if the value of the selected tensor element is n, then randomly select another tensor element again and make the above determination until a tensor element with a value other than n is selected; when the values of all tensor elements are n, end the regulation; and

[0088] In this step, an updated third-order tensor T state is obtained respectively each time of regulation. After all regulations are completed, the N×M×P third-order tensors T state are respectively used to describe a series of states experienced by the resistive switching material from the initial state to the final state; the probability of each tensor element being selected is equal, or the probability of each tensor element being selected is inversely proportional to the resistivity of the phase of the resistive switching material it describes. In some other embodiments, optionally, the probability of each tensor element being selected is inversely proportional to the resistivity of the phase of the material represented by the adjacent tensor element.

[0089] In the above step B, the possibility of phase change at each part of the material can be analyzed first. According to the specific process of the material phase change, set the rule of sequential change of tensor elements during the simulation regulation process, and change all tensor elements according to the rule until no tensor element can change, then end this step. Preferably, after analyzing the specific process of the material phase change, design a change rule and corresponding operations that fit the specific process.

[0090] It can be assumed here that the phase transitions of grains everywhere in the material occur with equal probability and do not depend on processes such as mass transfer and heat transfer. After the simulation regulation process starts, each effective update of T state is called a regulation. After the update is completed, a total of N×M×P different third-order tensors T state are obtained, and their order can be defined according to the number of regulations (or in the order of regulation). Any T state differs from the previous or subsequent T state by only one tensor element. Here, the regulation depth value can be defined: the regulation depth corresponding to a certain T state is 100%×n / (N×M×P), where n is the number of regulations corresponding to this T state , that is, this T state is obtained after n regulations compared with the original T state . This step obtains a series of T state , corresponding to the material phase states in different states during the regulation, and describes a series of states experienced by the material from the initial state to the final state.

[0091] Taking the case where the material to be predicted has three phases, P0 (initial state), P1 (intermediate state), and P2 (final state), and all possible values of the tensor elements in T state are 0, 1, and 2 as an example, the update method of T state is as follows: randomly select a tensor element with equal probability. If its value is not equal to 2, increase its value by 1; if its value is 2, randomly select another tensor element with equal probability (the tensor element selected this time is still in the random pool). Repeat this step until all tensor element values are 2 and then stop.

[0092] The above example takes the case where the probability of each tensor element being selected is equal. In some other embodiments, the probability of each tensor element being selected can be inversely proportional to the resistivity of the phase of the resistive switching material it describes, or the probability of each tensor element being selected can be inversely proportional to the resistivity of the material phase represented by the adjacent tensor element.

[0093] Of course, in some other optional embodiments, another transformation can be performed on the regulation method in step B. The present invention does not specifically limit the rule of sequential change of tensor elements and the corresponding operations. Their optional forms are as follows: For example, optionally, in each state change of the material, among all non-"empty element" tensor elements, one tensor element is randomly selected (the probability of each tensor element being selected is equal). If the value of this tensor element ≤ n - q (q is any non-zero positive integer), increase its value by q; if the value of this tensor element < n and ≥ n - q, set its value to n; if the value of this tensor element is n, this selection is not counted, randomly select another tensor element, and make the above determination until a tensor element with a value other than n is selected. When all tensor element values are n, end this step.

[0094] In still some alternative embodiments, another transformation may be performed on the regulation method in step B. For example, optionally, in each state change of the material, among all tensor elements that are not "empty elements", one tensor element is randomly selected, and the probability of its being selected is inversely proportional to the resistivity of the material phase represented by the adjacent tensor elements. If the value of this tensor element < n, then its value is incremented by 1; if the value of this tensor element is n, then this selection is not counted, and another tensor element is randomly selected and the above determination is made until a tensor element with a value other than n is selected. When the values of all tensor elements are n, this step ends.

[0095] In some alternative embodiments, for example, when a phase change of the channel material causes a metal-insulator phase change, after the above step B and before step C, the step of predicting the resistance value of the phase change process caused by the phase change of the resistive material of the resistive device based on the multi-dimensional model of the tensor further includes:

[0096] Detecting whether there is a conductive path in each third-order tensor T state where a conductive channel refers to a group of adjacent low-resistance-phase grains; recording the number of conductive paths in each third-order tensor T state and the regulation depth when the conductive path first appears. This step aims to detect whether there is a conductive path in each third-order tensor T state and determine the number of conductive paths and the number of regulations when the conductive path appears, so as to facilitate the analysis of the possible reasons for abnormal resistive switching behavior and the resistive switching phenomena related to certain special structures in the material.

[0097] For example, after defining the measurement wiring for the material resistance, it can be checked whether a conductive path is formed on T state . At this time, a conductive path refers to a series of low-resistance-phase grains (the low-resistance-phase grains must be adjacent and cannot be separated by other high-resistance phases) connecting the measurement electrodes. Among them, the low-resistance phase refers to a phase with a room-temperature conductivity higher than 1×10 -2 S / m, and the high-resistance phase refers to a phase with a room-temperature conductivity higher than 1×10 -2 S / m.

[0098] Still taking the case where the material to be predicted has three material phases P0 (initial state), P1 (intermediate state), and P2 (final state), and all possible values of the tensor elements in T state are 0, 1, and 2 as an example, a conductive path can refer to a group of adjacent tensor elements with a value of 2. The formation of a conductive path can satisfy the following conditions: (a) Each tensor element in it is at least connected to another in the group, and being connected means that the difference between the three indices of the two tensor elements does not exceed 1. For example: T state (1, 2, 1) is connected to T state (1, 3, 1), while T state (1, 2, 1) is connected to T state(4,3,1) Not connected; (b) At least one tensor in the group has a first index of 1, such as T state (1,0,0), and there exists at least one tensor whose first index is N, such as T. state (N,2,1). The modulation depth at the first appearance of a conductive path can be denoted as D. crit .

[0099] Because the resistive switching behavior prediction method relies on a series of progressively increasing material state record tensors, it not only provides the equivalent resistance but also facilitates problem backtracking and mechanism research. This allows for the discovery of possible causes of abnormal resistive switching behavior and resistive switching phenomena related to certain special structures within the material. For example, for metallic insulator phase change materials, by analyzing the T... state Studies of special structures reveal that conductive pathways significantly influence the equivalent resistance of materials. Therefore, this embodiment can be applied not only to the mass production design of practical devices to guide their application, but also to scientific research.

[0100] In some optional embodiments, in step C, a third-order tensor T of N×M×P can be established. R The resistivity of a single grain in all phases during a material phase transition is given as a function of T. R The correspondence between the possible values ​​of a tensor element, through which T is... state Record the material state mapping to T R In other words, in step C, a cubic material with a side length of a (a single grain can be pre-defined as a cube with a side length of a) in various phases (i.e., the aforementioned P) can be obtained through theoretical calculations or actual tests. i The resistance value at which the resistance is measured is T. R The possible values ​​of the middle tensor are determined according to T. state The state values ​​of the material at various points are recorded in the medium to generate T. R For the series of T obtained in step B state A series of Ts can be obtained accordingly. R .

[0101] Specifically, based on a preset mapping relationship, for each third-order tensor T state The steps for reassigning tensors include:

[0102] Obtain the resistance values ​​of a cubic resistive switching material with side length a in each phase, and record them as the resistance values ​​of each phase of a single grain of the resistive switching material.

[0103] Based on the resistivity values ​​of each phase of a single grain of resistive switching material, and for each third-order tensor T... state The tensor elements are reassigned to obtain the third-order tensor T. R The value of the middle tensor.

[0104] Using the above method, the third-order tensor T, which reflects the phase state of the material at different control depths, can be mapped based on a preset mapping relationship. state Transformed into a third-order tensor T reflecting the resistance values ​​at different depths of material control. R The third-order tensor T is calculated using the resistivity values ​​of each phase in a single grain of a resistive switching material obtained through experimental measurement or theoretical calculation. R The values ​​of the middle tensor element can make the third-order tensor T R This accurately reflects the resistance value of the resistive switching material under various states. In this step, the side length 'a' is the same value as the spatial precision 'a' mentioned earlier. In other words, the spatial precision 'a' mentioned earlier is the side length or diameter of a single cubic grain of the resistive switching material.

[0105] In some further embodiments, the following method can be used to apply the resistance values ​​of each phase of a single grain of resistive switching material to each third-order tensor T. state The tensor elements are reassigned, that is, each third-order tensor T is reassigned. R The value of the middle tensor element is determined according to the following method:

[0106] T R (i,j,k)=R0×δ Tstate(i,j,k),0 +R2×δ Tstate(i,j,k),1 +R3×δ Tstate(i,j,k),2 +…+R n ×δ Tstate(i,j,k),n .

[0107] Where δ i,j The Kronecker product has a value of 1 if and only if i = j, and a value of 0 in all other cases; R0, R1, ..., R n These represent the resistance values ​​of a single grain of each phase of the resistive switching material from the initial state to the final state.

[0108] The material to be predicted still has three phases: P0 (initial state), P1 (intermediate state), and P2 (final state), and T... state Taking the case where all possible values ​​of tensors are 0, 1, and 2 as an example, in this step, let's assume that the grain resistance values ​​of the three phases of the material to be predicted are 10. 7 Ω, 10 6 Ω, 10 2 Ω. Construct N×M×P N×M×P tensors T R , with T state One-to-one correspondence. Each T R The value of T is determined as follows: R (i,j,k)=10 7 ×δ Tstate(i,j,k),0 +10 6 ×δTstate(i,j,k),1 +10 2 ×δ Tstate(i,j,k),2 This step yields a series of T... R This corresponds to the material resistance under different states during regulation.

[0109] In some alternative embodiments, based on each third-order tensor T R The steps for calculating the equivalent resistance of each phase transition process in a resistive switching material include: converting each third-order tensor T... R The data is mapped to a netlist file, which is then used by calculation software to calculate the equivalent resistance. For example, after defining the measurement wiring for the material resistance, T... R Calculate the equivalent resistance of the material. Based on T R The equivalent resistance of the material at various control depths can be calculated. Possible methods for obtaining the equivalent resistance include, but are not limited to, directly solving Kirchhoff's laws, directly solving for the electromagnetic field distribution, or using commercial computing software (such as COMSOL multiphysics or various EDA tools).

[0110] In some embodiments, when each T R After mapping to a netlist file, the equivalent resistance can be calculated using SPICE or other software. During mapping, the resistance of wires and metal electrodes can be set according to the specific materials. The resistance value between adjacent nodes in the netlist is T. R The value of the tensor element at the corresponding position in the T. For example, for all T... R (1,i,j) (corresponding to the materials connected to one side of the electrode), their resistance to the test electrode can be considered to be almost zero, T R (N,i,j) (corresponding to the material connected to the other electrode) is similar. For each T R It can generate a netlist file and obtain an equivalent resistance value.

[0111] In step D, preferably, if timeliness is critical, only the equivalent resistance at 0%, 10%, 20%, ..., 100% control depth needs to be calculated, and step D can be supplemented with calculation. crit The equivalent resistance in the vicinity can be linearly interpolated at other control depth values.

[0112] It should be noted that the prediction method of this invention mainly involves T state With T R The generation of T R The method for obtaining the equivalent resistance and the specific method for manufacturing the device based on the prediction results are not limited, and those skilled in the art can choose according to actual needs based on their understanding of this disclosure.

[0113] The above steps are some embodiments of the present invention. Other embodiments can be designed and determined after analyzing the physical and chemical properties of specific materials. The following will illustrate how the prediction method of the present invention can be applied to different types of materials using several more specific examples.

[0114] Example 1:

[0115] This embodiment predicts a cuboid Li4Ti5O with dimensions of 150 μm (length) × 4 mm (width) × 15 μm (height). 12 (Wide bandgap semiconductor phase, denoted as LTO-4) Polycrystalline materials undergo a phase transition induced by ion intercalation, transforming into Li7Ti5O. 12 The change in material resistivity caused by the process (metallic phase, denoted as LTO-7). Here, 150 μm is defined as the length of the material, and the direction of the resistance test current can be defined as parallel to this side (i.e., the distance between the test electrodes is 150 μm, with the target material in between). The prediction method includes the following steps:

[0116] (1) Construct a 60×1600×6 integer third-order tensor T state Let its initial value be 0. This represents that the smallest unit of phase transition during the prediction process is a cube LTO-4 with a side length of 2.5 μm. This third-order tensor corresponds one-to-one with all parts of the material. Since there are only two main phases in the phase transition process of the material to be predicted, T state The value can only be 0 or 1.

[0117] (2) Analyze the possibility of phase transitions occurring at various points in the material, that is, control the phase state at various points in the resistive switching material, and iterate the third-order tensor T during each control. state This yields N×M×P updated third-order tensors T. state The results of this embodiment need to be compared with the experiment, so the device characteristics in the experiment can be examined first. In the experiment, the two measuring electrodes are 150 μm apart and are in the same plane as the LTO-4 material (denoted as plane A). At the same time, there is a control electrode located about 20 μm outside plane A and parallel to plane A. This electrode can apply an electric field to control the lithium-ion extraction process, causing LTO-4 to undergo a phase transition. Due to the positional relationship between the electrode and the material, it can be assumed that the probability of phase transition occurring at all points along the direction parallel to plane A is similar (the electric field strength from the control electrode is similar); since the material thickness is only 15 μm, the field strength in the direction perpendicular to plane A is also similar, and it is almost unaffected by mass transfer rate limiting. After comprehensive analysis, it can be assumed that the probability of phase transition occurring at all points along the material is the same. Therefore, during the control process, T stateThe update method is as follows: Randomly select a tensor element with equal probability. If its value is 0, set it to 1; if its value is 1, randomly select another tensor element with equal probability (this selected tensor element remains in the random pool). Repeat this step until all tensor values ​​are 1. At this point, a total of 60 × 1600 × 6 different T values ​​are obtained. state Furthermore, their order can be defined according to the number of adjustments. Any T state With or after T state Only one tensor is different. This step yields a series of T... state This corresponds to the material phase state under different conditions during regulation.

[0118] (3) Check T state Special structures formed on the surface, such as conductive pathways and conductive clusters. A conductive cluster refers to a group of interconnected metallic phase particles, i.e., T... state Connected tensors are those with a value of 1. "Connected" means that the difference between the three indices of two tensors is no more than 1, for example: T state (1,2,1) and T state (1,3,1) are connected, and T state (1,2,1) and T state (4,3,1) are not connected. A conductive path is defined as a tensor element within a conductive cluster whose first index is 1, such as T. state (1, i, j), and at least one tensor element has a first index of 60, such as T state (60,i,j). Throughout the entire modulation process, the number of conductive pathways and conductive clusters changes with the depth of modulation as follows: Figure 4 As shown. Figure 4 The results of the changes in conductive clusters and conductive pathways in the material recorded in step (4) of Embodiment 1 of the present invention with the depth of modulation are shown. Based on this, the present invention provides a method for tracking special structures, which can help understand and explore resistive switching and phase transition behavior.

[0119] (4) Reasonable resistivity values ​​for a single 2.5μm side length cubic grain were obtained through experiments and theoretical methods. 576,000 tensors T of 60×1600×6 were established. R , with T state One-to-one correspondence. In this example, each T R The value of T is determined as follows: R (i,j,k)=10 7 ×δ Tstate(i,j,k),0 +10 2 ×δ Tstate(i,j,k),1 10 of them 7 10 2 These refer to the grain resistance values ​​of LTO-4 and LTO-7, respectively, in ohms. δ i,jThe Kronecker product has a value of 1 if and only if i = j, and a value of 0 otherwise. This step yields a series of T... R This corresponds to the material resistance under different states during regulation.

[0120] (5) Take the series of T obtained in step (4) R The data is converted to a netlist file, and the equivalent resistance is calculated using software such as HSPICE, with the voltage set to 1.0V. Based on the results provided by HSPICE, a constant contact resistance is considered to obtain the final result, such as... Figure 5 As shown. Figure 5 Experimental and predicted results of the material resistance variation with modulation depth according to Embodiment 1 of the present invention are shown. It can be seen that the predicted results using the technical solution of the present invention agree well with the experimental results, and the key trend of resistive switching behavior is clearly shown: in the modulation depth range of ~0-13%, the material resistance changes abruptly, while in the modulation depth range of ~13%-100%, the material resistance changes slowly or remains approximately constant. Although the predicted results agree well with the experiments, the computational load is very small: the entire process of this embodiment can be completed in only ~5 hours on a system with an i7 8700 CPU and 16GB of memory.

[0121] Based on the method of this invention, not only can relatively accurate resistance values ​​be obtained, but the causes or mechanisms of some key characteristics of resistive switching behavior can also be analyzed. For example, the two special structures examined in step (3), especially the conductive connections, are very helpful in analyzing and understanding the reasons for the abrupt changes in resistive switching behavior during the phase transition of LTO-4 material: the depth at which the first conductive connection appears is precisely where the inflection point occurs in both the experimental and the predicted values ​​of this invention, strongly suggesting a correlation between the two. In addition, the method provided by this invention can have other scientific research value, which will not be exemplified here.

[0122] Example 2:

[0123] This embodiment predicts that a cuboid LTO-7 polycrystalline material with dimensions of 150 μm (length) × 4 mm (width) × 15 μm (height) will undergo a phase transition caused by ion desorption, transforming into Li4Ti5O. 12 The change in material resistance caused during the process of (metallic phase, denoted as LTO-7).

[0124] In this embodiment, the simulation control process and experiment are the same as in Embodiment 1, except that T in step (4) of the prediction method is different. R The value of T is determined as follows: R (i,j,k)=10 2 ×δ Tstate(i,j,k),0 +10 7 ×δ Tstate(i,j,k),1 The result is as follows Figure 6As shown, the material is initially in a metallic phase, but it transforms into a semiconductor phase during the control process, thus increasing the equivalent resistance value. Figure 6 Experimental and predicted results of the material resistance variation with modulation depth according to Embodiment 2 of the present invention are shown. The experimental results and predicted values ​​are still in good agreement, which further proves the effectiveness of the technical solution of the present invention. In addition, compared with Embodiment 1, although the material to be predicted is different and the direction of resistance change is different, almost the same process can be used, only one pair of parameters needs to be modified (it is even possible that steps 1-3 do not need to be repeated, and all T values ​​generated in Embodiment 1 can be reused). state However, if density functional theory-based methods are used, different unit cell models are required when applying Example 1 and Example 2, taking into account many differences such as bond lengths, bond angles, and atomic occupancy. This is also the advantage of this invention: it does not require building a physical-based model for a specific material; only the key information of the material needs to be extracted, and certain individual steps or parameters in the method can be changed.

[0125] Example 3:

[0126] This embodiment mainly introduces a method for predicting the resistivity change of phase change materials involving intermediate phases and its application. This embodiment predicts the resistivity change of a 150μm (length) × 4mm (width) × 15μm (height) cuboid polycrystalline material during a phase transition. This virtual material has 10 phases, including an initial state, a final state, and 8 intermediate states. The prediction method includes the following steps:

[0127] (1) Same as step (1) in Example 1, except T state The value can be 0, 1, 2, ..., 9.

[0128] (2) Same as step (2) in Example 1, except that T is controlled. state The update method is as follows: Randomly select a tensor element with equal probability. If its value is not 9, increment its value by one; if its value is 9, randomly select another tensor element with equal probability (this selected tensor element remains in the random pool). Repeat this step until all tensor values ​​are 9. This step yields a total of 9 × 60 × 1600 × 6 distinct T0 values. state .

[0129] (3) Similar to step (4) in Example 1, except that 5,184,000 tensors T of size 60×1600×6 need to be created. R At the same time, T R The calculation process for the value of (i,j,k) needs to be modified to use the formula R0+(R9-R0)×T stateThe resistance is calculated as (i,j,k) / 9, where R0 is the initial resistance of a single crystal, and R9 is the final resistance of a single crystal. This rule assumes that the resistance of a single crystal changes linearly during the phase transition. For other specific materials, the resistance of each phase can be experimentally determined individually. In this embodiment, the initial resistance is 10. 7 The final resistance can be set to one of two values: 10 ohms. 2 Ohms, the second is 2 × 10 6 Ohms. Calculations can be performed based on these two settings separately.

[0130] (4) Same as step (5) in Example 1.

[0131] The results obtained can be found in Figure 7 . Figure 7 The predicted results of the material resistivity variation with the depth of modulation according to Embodiment 3 of the present invention are shown. Based on this embodiment, it can be demonstrated that the prediction method of the present invention can be widely used in two-phase or multi-phase reaction systems, requiring only the setting of corresponding parameters according to the actual phase transition process. This is also an advantage of the present invention compared to the prior art: the mapping rules, correspondences, and specific parameters in the prediction method of the present invention are easy to adjust, enabling the present invention to be widely used in various different material systems. Furthermore, Figure 7 The study also provides predictions for cases where the initial and final resistance values ​​are the same, but there is no intermediate transition phase.

[0132] Example 4:

[0133] This embodiment illustrates how the prediction method of the present invention is applied to predict the resistance changes of phase change materials with different shapes. Since the length of the channel material in transistor devices has a significant impact on performance, this embodiment predicts materials with the same height (15 μm) and width (4 mm), but different lengths (25 μm, 75 μm, 150 μm, and 225 μm, respectively). The required steps are the same as those in Embodiment 1, but the following differences exist:

[0134] Third-order tensor T state and T R The physical dimensions of the material to be predicted need to be set to 10×1600×6, 30×1600×6, 60×1600×6 and 90×1600×6 respectively, corresponding to the four different material dimensions mentioned above.

[0135] The results obtained are as follows Figure 8 As shown. Figure 8The predicted results of the material resistance variation with modulation depth according to Embodiment 4 of the present invention are shown. Based on this embodiment, on the one hand, it can be seen that the resistive switching behavior is related to the channel length; on the other hand, it can be seen that anomalous resistive switching behavior exists in the 25 μm long material: a sudden change occurs between 6% and 7% modulation depth. After careful analysis of the relevant data, it can be found that at ~6.8% modulation depth, a conductive path composed of low-resistivity states is established in the material, short-circuiting the material and causing its equivalent resistance to decrease significantly within 1% modulation depth. This further proves that the phase and resistance states of all locations in the material at different modulation depths can be traced throughout the resistive switching process. Based on this, the present invention provides convenience for analyzing anomalous resistive switching behavior in materials, which is also one of the advantages of the present invention.

[0136] Therefore, those skilled in the art should recognize that although numerous exemplary embodiments of the present invention have been shown and described in detail herein, many other variations or modifications conforming to the principles of the present invention can be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Thus, the scope of the present invention should be understood and construed as covering all such other variations or modifications.

Claims

1. A method for manufacturing a resistive device, comprising: The resistance value of the phase transition process caused by the phase transition of the resistive switching material of the resistive device is predicted based on a tensor-based multidimensional model. as well as The resistive device is manufactured based on the prediction results; wherein, The steps for predicting the resistance value of the phase transition process caused by the phase transition of the resistive switching material of the resistive device based on a tensor-based multidimensional model include: Construct a third-order tensor T of N×M×P state And map each phase state of the resistive switching material to the third-order tensor T. state Where N, M, P ∈ ℕ; The phase state of the resistive switching material is controlled at various points, and the third-order tensor T is iterated during each control. state This yields N×M×P updated third-order tensors T. state ; Based on a preset mapping relationship, for each of the third-order tensors T state The tensor elements are reassigned, thereby resetting each of the third-order tensors T. state One-to-one mapping to N×M×P N×M×P third-order tensors T R N×M×P of the aforementioned third-order tensors T R Record the resistance values ​​of the phase transition process at various points in the resistive switching material; and According to each of the aforementioned third-order tensors T R Calculate the equivalent resistance of the resistive switching material for each phase transition process to obtain the resistance value of the resistive switching material for each phase transition process; wherein, Construct a third-order tensor T of N×M×P state And map each phase state of the resistive switching material to the third-order tensor T. state The steps include: The length, width, and height of the resistive switching material are measured and denoted as L, W, and H, respectively. With a preset spatial accuracy a, N = round(L / a), M = round(W / a), and P = round(H / a), where a is a unit of length, a > 0, and a ∈ ℝ. The phases that appear during the phase transition of the resistive switching material are measured and denoted as P0, P1, ..., P2 in sequence from the initial state to the final state. n (n∈ℕ), then the third-order tensor T state The tensor elements take values ​​of 0, 1, 2, ..., n, and the third-order tensor T... state The values ​​of each tensor element correspond sequentially to all phases of the resistive switching material, and the third-order tensor T... state The index of a tensor element represents the material location corresponding to that tensor element. The phase state of the resistive switching material is controlled at various points, and the third-order tensor T is iterated during each control. state When the material is in its final state through N×M×P manipulations, a total of N×M×P updated third-order tensors T are obtained. state The steps include: Among all the tensor elements of non-empty elements, randomly select one tensor element. If the value of the selected tensor element < n, then increment its value by 1 to obtain an updated third-order tensor T state , if the value of the selected tensor element is n, then randomly select another tensor element and make the above determination until a tensor element with a value other than n is selected; when the values of all tensor elements are n, end the regulation; and In this step, each adjustment yields an updated third-order tensor T. state N×M×P of the aforementioned third-order tensors T state These are used to describe a series of states that the resistive switching material experiences from the initial state to the final state; each tensor element has an equal probability of being selected, or the probability of each tensor element being selected is inversely proportional to the resistivity of the phase of the resistive switching material it describes. Based on a preset mapping relationship, for each of the third-order tensors T state The steps for reassigning tensors include: Obtain the resistance values ​​of a cubic resistive switching material with side length a in each phase, and record them as the resistance values ​​of each phase of a single grain of the resistive switching material. Based on the resistance values ​​of each phase of a single grain of the resistive switching material, and for each of the third-order tensors T... state The tensor elements are reassigned to obtain the third-order tensor T. R The values ​​of the middle tensor; among which, Each of the third-order tensors T R The value of the middle tensor element is determined according to the following method: T R (i,j,k)=R0 × d Tstate(i,j,k),0 +R2 × d Tstate(i,j,k),1 +R3 × d Tstate(i,j,k),2 +…+ R n ×d Tstate(i,j,k),n Where d i,j The Kronecker product has a value of 1 if and only if i=j, and a value of 0 in all other cases; R0, R1, ..., R n These are the resistance values ​​of a single grain of each phase of the resistive switching material from the initial state to the final state; According to each of the aforementioned third-order tensors T R The steps for calculating the equivalent resistance of each phase transition process of the resistive switching material include: Each of the aforementioned third-order tensors T R The data is mapped to a netlist file and then used by calculation software to calculate the equivalent resistance.

2. The manufacturing method according to claim 1, wherein, In each of the aforementioned third-order tensors T R In the steps of mapping to a netlist file: The resistance value between adjacent nodes in the netlist file is the third-order tensor T. R The values ​​of the tensor elements at corresponding positions in the tensor; the values ​​of each of the third-order tensors T. R Generate a netlist file and obtain an equivalent resistance value.

3. The manufacturing method according to claim 1, wherein, When the resistive switching material undergoes a phase transition leading to a metal-insulator phase transition, the phase state at various points of the resistive switching material is controlled, and the third-order tensor T is iterated during each control. state When the material is in its final state through N×M×P manipulations, a total of N×M×P updated third-order tensors T are obtained. state Following that, it also includes: Detect each of the third-order tensors T state Does a conductive path exist in the structure, whereby a conductive path refers to a group of adjacent low-resistivity phase grains? Record each of the third-order tensors T state The number of conductive pathways and the depth of modulation when a conductive pathway first appears.

4. A resistive device manufactured using the resistive device manufacturing method as described in any one of claims 1-3.

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