Simulation method of polarization intensity of ferroelectric, simulation equipment and computer program product

Abstract

The invention belongs to the technical field of simulation, and relates to a simulation method and simulation equipment for polarization intensity of a ferroelectric and a computer program product. The method comprises the following steps: uniformly dispersing the ferroelectric into N ferroelectric blocks, and initializing each ferroelectric block through an initial polarization parameter; in each simulation step length, applying a target voltage to the ferroelectric block according to the voltage time sequence signal; according to the absolute value and the polarity of the target voltage, the polarization parameter of each ferroelectric block at the current moment is updated in combination with the polarization direction of the ferroelectric block at the previous moment; and calculating the polarization intensity of the ferroelectric according to the polarization parameters of all the ferroelectric blocks at the current moment and the saturation polarization value corresponding to the ferroelectric material used by the ferroelectric. According to the method, the polarization intensity of the ferroelectric during repeated polarization overturning is simulated, and the effective use time of the ferroelectric is conveniently calculated.

Description

[0001] This application claims priority to Chinese Patent Application No. 202510036806.4, filed January 09, 2025, the contents of which are incorporated by reference in their entirety. TECHNICAL FIELD

[0002] The present application relates to the technical field of simulation, in particular to a simulation method, simulation device and computer program product for polarization strength of ferroelectric. BACKGROUND

[0003] Ferroelectric materials are a class of functional materials with spontaneous polarization, and the spontaneous polarization can be reversed by applying an external electric field greater than the coercive field. They also have important characteristics such as dielectricity, piezoelectricity, pyroelectricity, etc. and are widely used in information storage, photoelectric sensing and other fields of electronic devices. Traditional perovskite ferroelectric oxide materials are limited by the critical size effect. When the thickness is less than 100 nm, the ferroelectric properties significantly deteriorate, which restricts the miniaturization and high-density integration development of future devices.

[0004] AlScN (aluminum scandium nitride) is a new type of ferroelectric material with strong electromechanical coupling coefficient, high Curie temperature, and a high residual polarization strength of 140 μC / cm, which is 3-5 times that of traditional oxide ferroelectric materials. It still has macroscopic ferroelectricity below 10 nm. In addition to its superior ferroelectric and piezoelectric properties, AlScN is also more compatible with CMOS technology. Its polarization characteristics are crucial to device performance.

[0005] However, traditional experimental methods cannot simulate the failure caused by repeated polarization reversal of ferroelectric materials. Therefore, it is of great significance to develop an efficient simulation algorithm to understand and optimize the performance of AlScN ferroelectric materials. SUMMARY

[0006] The present application aims to provide a simulation method, simulation device and computer program product for polarization strength of ferroelectric, which can simulate the polarization strength of ferroelectric when polarization is repeatedly reversed.

[0007] According to a first aspect of an embodiment of the present application, a simulation method for polarization strength of ferroelectric is provided, comprising: Discretizing the ferroelectric into N ferroelectric blocks, N being an integer greater than 1; Initializing each ferroelectric block by an initial polarization parameter, the initial polarization parameter including an initial polarization direction, an initial number of reversals, an initial polarization loss degree and an initial applied voltage; In each simulation step, applying a target voltage to the ferroelectric block according to a voltage time sequence signal, the simulation step being a specified time length; updating the polarization parameters of each ferroelectric block at the current time according to the absolute value and polarity of the target voltage and the polarization direction of the ferroelectric block at the previous time, the polarization parameters including the polarization direction, the number of flips and the polarization loss degree; calculating the polarization intensity of the ferroelectric body according to the polarization parameters of all the ferroelectric blocks at the current time and the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body.

[0008] In an embodiment, the value of N is associated with the target simulation accuracy and hardware computing power; the material of the ferroelectric body is aluminum scandium nitrogen.

[0009] In an embodiment, the initialization of each ferroelectric block by the initial polarization parameters includes: randomly configuring the initial polarization direction of each ferroelectric block using a binary distribution with a probability of 0.5; configuring the initial number of flips of each ferroelectric block as zero; configuring the initial polarization loss degree of each ferroelectric block according to the simulation fitting parameters of the ferroelectric body, the simulation fitting parameters including the flip influence coefficient; configuring the initial applied voltage of each ferroelectric block as zero.

[0010] In an embodiment, the initial polarization loss degree is loss 初 , ; wherein a represents the flip influence coefficient and n represents the number of flips.

[0011] In an embodiment, updating the polarization parameters of each ferroelectric block at the current time according to the absolute value and polarity of the target voltage and the polarization direction of the ferroelectric block at the previous time includes: when the absolute value of the target voltage at the current time is greater than the absolute value of the target voltage change amount at the previous time or the polarity of the target voltage at the current time is different from the polarity of the target voltage at the previous time, if the polarization direction of the ferroelectric block at the previous time is the same as the electric field direction indicated by the target voltage at the current time, the polarization parameters of the ferroelectric block at the previous time are taken as the polarization parameters at the current time; if the polarization direction of the ferroelectric block at the previous time is opposite to the electric field direction indicated by the target voltage at the current time, it is determined whether the polarization direction of the ferroelectric block flips based on the current polarization flip probability, and the corresponding polarization parameters are updated when the flip is determined; when the absolute value of the target voltage at the current time is less than or equal to the absolute value of the target voltage change amount at the previous time and the polarity of the target voltage at the current time is the same as the polarity of the target voltage at the previous time, the polarization parameters of all the ferroelectric blocks at the previous time are taken as the polarization parameters at the current time.

[0012] In an embodiment, the method further comprises determining whether the polarization direction of the ferroelectric block is flipped based on a current polarization flipping probability, updating the corresponding polarization parameter when the flipping is determined, including: calculating a probability value p of the ferroelectric block flipping polarization, wherein c1 represents a time influence coefficient, c1 is greater, and the steady-state simulation is closer; c2 represents an activation energy influence coefficient, c2 is greater, and the polarization flipping is slower; E represents a target voltage; a represents an electric field influence coefficient, a is greater, and the polarization response speed to the electric field is faster; taking a probability random number in the interval [0, 1]; when the probability random number is greater than the probability value p, determining that the ferroelectric block does not flip, and taking the polarization parameter of the ferroelectric block at the last time as the polarization parameter at the current time; when the probability random number is less than or equal to the probability value p, determining that the ferroelectric block flips, and updating the corresponding polarization parameter.

[0013] In an embodiment, the method further comprises determining whether the polarization direction of the ferroelectric block is flipped based on a current polarization flipping probability, updating the corresponding polarization parameter when the flipping is determined, including: an updated polarization direction d', d' = -d, wherein d is the polarization direction of the ferroelectric block at the last time; an updated flipping number n', n' = n + 1, wherein n is the flipping number of the ferroelectric block at the last time; an updated polarization loss degree loss, wherein a represents a flipping influence coefficient, and n' represents the flipping number of the ferroelectric block at the current time.

[0014] In an embodiment, the method further comprises calculating the polarization intensity of the ferroelectric body according to the polarization parameters of all the ferroelectric blocks at the current time and the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body, including: calculating the average polarization intensity P of all the ferroelectric blocks of the ferroelectric body as the polarization intensity of the ferroelectric body, wherein, ; P s represents the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body, N represents the number of ferroelectric blocks, i is the number of ferroelectric blocks, and loss i represents the polarization loss degree of the ferroelectric block numbered i.

[0015] According to a second aspect of the embodiments of the present application, a kind of including processor and memory;The memory is used to store the computer program executable in the processor;The processor is used to execute the computer program in the memory, to realize the simulation method described above.

[0016] According to a third aspect of the embodiments of the present application, a computer program product is provided, comprising a computer program which, when executed by a processor, implements the simulation method described above.

[0017] Compared with the prior art, the present application has the beneficial effect that by discretizing the ferroelectric into N ferroelectric blocks for representing ferroelectric domains, after initialization is completed, in each simulation step, a corresponding target voltage is applied to all ferroelectric blocks of the ferroelectric according to the voltage time sequence signal until the simulation corresponding to the simulation step ends, thereby realizing simulation of the ferroelectric according to the voltage time sequence signal within a specified time length. The voltage time sequence signal is used to control the external field of the ferroelectric, so as to realize the corresponding polarization reversal of each ferroelectric block in the ferroelectric under repeated loading of the external field, thereby facilitating quantification of the polarization intensity of the ferroelectric through the polarization loss of each ferroelectric block.

[0018] In the simulation step, the polarization direction of the previous time, the absolute value and polarity of the target voltage of the current time affect the polarization direction of the ferroelectric block under the target voltage of the next time, thereby accurately simulating whether the polarization direction of each ferroelectric block is reversed, obtaining the polarization parameter of each ferroelectric block at the current time, and further obtaining the polarization intensity of the ferroelectric. Therefore, the present application can accurately simulate the overall polarization intensity of the ferroelectric under the applied voltage of the voltage time sequence signal, judge the influence of the polarization loss on the performance of the ferroelectric, and facilitate calculation of the effective use time length of the ferroelectric, thereby providing a new method and tool for research and application of ferroelectric materials. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a flowchart of a simulation method of polarization intensity of a ferroelectric according to an exemplary embodiment.

[0020] Figure 2 is a discrete schematic diagram of a ferroelectric according to an exemplary embodiment.

[0021] Figure 3 is Figure 1 a flowchart of step 102 in

[0022] Figure 4 is Figure 1 a flowchart of step 104 in

[0023] Figure 5 is Figure 4 a flowchart of step 104-5 in

[0024] Figure 6 is a block diagram of a simulation device of polarization intensity of a ferroelectric according to an exemplary embodiment.

[0025] Figure 7 is a block diagram of a simulation device according to an exemplary embodiment. DETAILED DESCRIPTION

[0026] Unless otherwise defined, technical and scientific terms used in this specification and claims shall have the meaning commonly understood by one of ordinary skill in the art to which this application pertains. In the following description, specific embodiments of the application are described in connection with the appended drawings, in which it is noted that the drawings provide merely examples of the application and therefore should not be considered as limiting its scope. It will be apparent to those skilled in the art that numerous modifications and variations can be made without departing from the spirit and scope of the application.

[0027] An embodiment of the application provides a simulation method of polarization strength of ferroelectric. The simulation method of polarization strength of ferroelectric can be applied to a simulation device installed with simulation software.

[0028] Reference Figure 1 As shown in the figure, the simulation method of polarization strength of ferroelectric can include the following steps 101-105: Step 101, uniformly disperse the ferroelectric into N ferroelectric blocks, N is an integer greater than 1.

[0029] Reference Figure 2 As shown in the figure, in the simulation software, the ferroelectric device to be tested is algorithmically modeled into a ferroelectric 1 in the simulation software. The ferroelectric 1 is prismatic, and the ferroelectric 1 includes an upper bottom surface S1 and a lower bottom surface (not shown), and the upper bottom surface S1 and the lower bottom surface are rectangular.

[0030] This step uniformly disperses the ferroelectric 1 in the simulation software, and the ferroelectric 1 is divided into N ferroelectric blocks, each ferroelectric block representing a ferroelectric domain, and the ferroelectric block is set as a microscopic region with the same polarization direction or magnetization direction in the ferroelectric material. The number of N is determined according to the calculation accuracy required by simulation and the hardware computing power used by simulation. The higher the number of N, the higher the calculation accuracy of simulation, and the higher the computing power required by simulation.

[0031] In one example, reference Figure 2 As shown in the figure, a space rectangular coordinate system O-XYZ is established, which includes a horizontal axis OX, a vertical axis OY, and a vertical axis OZ, the horizontal axis OX extends to the right along the horizontal direction, the vertical axis OY extends upward along the vertical direction, and the vertical axis OZ extends outward perpendicular to the paper; the ferroelectric 1 is located in the above-mentioned space rectangular coordinate system, and the three edges intersecting at the same vertex of the ferroelectric 1 are parallel to the horizontal axis OX, the vertical axis OY, and the vertical axis OZ. The space rectangular coordinate system is convenient for determining the polarization direction of each ferroelectric block.

[0032] Step 102, initialize each ferroelectric block by initial polarization parameters, the initial polarization parameters including initial polarization direction, initial flip count, initial polarization loss degree and initial applied voltage.

[0033] This step aims to initialize each ferroelectric block, refer to Figure 3 The process of initialization includes: Step 102-1, randomly configure the initial polarization direction of each ferroelectric block using a binary distribution with a probability of 0.5, the initial polarization direction of each ferroelectric block being +1 or -1.

[0034] Step 102-2, configure the initial flip count n of each ferroelectric block as zero value, that is, when t=0, the initial flip count n of the ferroelectric block is 0.

[0035] Step 102-3, according to the simulation fitting parameters of the ferroelectric body, configure the initial polarization loss degree loss 初 of each ferroelectric block, that is, when t=0, ; a represents the flip impact coefficient, n represents the flip count of the ferroelectric block. When t=0, n is the initial flip count of the ferroelectric block, n=0, so the initial polarization loss degree . The flip impact coefficient is one of the simulation fitting parameters corresponding to the ferroelectric material used by the ferroelectric body 1.

[0036] Step 102-4, configure the initial applied voltage of each ferroelectric block as zero value, that is, when t=0, E=0V.

[0037] Step 103, within each simulation step, apply the target voltage to the ferroelectric block according to the voltage time sequence signal, the simulation step being a specified time length.

[0038] In this step, the simulation step is a specified time length, meaning the single time length allowed for each simulation. The voltage time sequence signal can be generated according to the voltage waveform given by the user, can be imported through third-party software, can be generated by an electronic device, or can be generated according to the wavelength, wave crest, frequency and other waveform characteristics.

[0039] When the simulation software runs, the target voltage corresponding to the current time is applied to each ferroelectric block according to the voltage time sequence signal, specifically, the time sequence starting point of the voltage time sequence signal is aligned with the time when the initialization of the ferroelectric block is completed, and then the corresponding voltage of the ferroelectric block is applied according to the time sequence of the voltage time sequence signal, which is regarded as the target voltage at the current time.

[0040] Step 104, update the polarization parameters of each ferroelectric block at the current time according to the absolute value and polarity of the target voltage, combined with the polarization direction of the ferroelectric block at the last time, the polarization parameters including polarization direction, flip count and polarization loss degree.

[0041] In this step, for each ferroelectric block, the polarization parameters of the ferroelectric block at the current time are updated according to the absolute value and polarity of the target voltage at the current time t, combined with the polarization direction of the ferroelectric block at the last time t-1. Referring to Figure 4 As shown in the figure, the implementation of step 104 specifically includes: Step 104-1, judge whether the absolute value of the target voltage at the current time increases, if yes, execute step 104-3, if not, execute 104-4.

[0042] Specifically, the absolute value of the target voltage E at each time is collected, and the absolute value |E(t)| of the target voltage at the current time t is compared with the absolute value |E(t-1)| of the target voltage at the last time t-1. When |E(t)|>|E(t-1)|, step 104-3 is executed, and when |E(t)|≤|E(t-1)|, step 104-4 is executed.

[0043] Step 104-2, judge whether the polarity of the target voltage at the current time is different from the polarity of the target voltage at the last time, if yes, execute step 104-3, if not, execute 104-4.

[0044] Specifically, the polarity of the target voltage E at each time is collected, and the polarity is positive or negative. The target voltage at the last time is negative, and the target voltage at the current time is positive, and the target voltage at the last time is positive, and the target voltage at the current time is negative, which are all determined as the polarity of the target voltage at the current time is different from the polarity of the target voltage at the last time, and step 104-3 is executed. The target voltage at the last time is negative, and the target voltage at the current time is negative, and the target voltage at the last time is positive, and the target voltage at the current time is positive, which are all determined as the polarity of the target voltage at the current time is the same as the polarity of the target voltage at the last time, and step 104-4 is executed.

[0045] Step 104-3, judge whether the direction of the electric field indicated by the target voltage at the current time is the same as the polarization direction of the ferroelectric block at the last time, if yes, execute step 104-4, if not, execute step 104-5.

[0046] Specifically, the electric field direction generated by each ferroelectric block affected by the target voltage is calculated, for example, the electric field intensity = target voltage / ferroelectric material thickness; again, for example, the direction of the electric field intensity corresponding to the target voltage is obtained by simulation calculation using simulation software (such as COMSOL Multiphysics, ANSYS, etc.).

[0047] Step 104-4, the polarization parameters of the ferroelectric block at the last time are taken as the polarization parameters at the current time, and the polarization parameters include the polarization direction, the number of flips and the polarization loss degree.

[0048] Specifically, it is determined that the polarization direction of the ferroelectric block does not flip, and the polarization parameter of the ferroelectric block will not change. The polarization parameter at the current time is directly set as the polarization parameter at the last time. For example, in this step, the polarization parameter of the ferroelectric block at t=1 is set as the polarization parameter at t=0, that is, the polarization parameter initialized and configured in step 102.

[0049] Step 104-5, determining whether the polarization direction of the ferroelectric block flips based on the current polarization flip probability, and updating the corresponding polarization parameter when the flip is determined.

[0050] In this step 104-5, refer to Figure 5 as shown, including: Step 104-5-1, calculating the probability value p of the polarization flip of the ferroelectric block at the current time, , c1 represents the time influence coefficient, the larger c1 is, the closer to the steady-state simulation; c2 represents the activation energy influence coefficient, the larger c2 is, the slower the polarization flip is; E represents the target voltage; a represents the electric field influence coefficient, the larger a is, the faster the polarization responds to the electric field. Among them, the time influence coefficient c1, the activation energy influence coefficient c2, and the electric field influence coefficient a are one of the simulation fitting parameters corresponding to the ferroelectric material used by the ferroelectric body 1.

[0051] Step 104-5-2, taking a probability random number radom in the interval [0, 1].

[0052] Step 104-5-3, when radom>p, executing step 104-4; Step 104-5-4, when radom≤p, determining that the ferroelectric block flips, and updating the polarization direction, the flip number and the polarization loss degree loss, specifically, the updated polarization direction d', d'=-d, where d is the polarization direction of the ferroelectric block at the last time; the updated flip number n', n'=n+1, where n is the flip number of the ferroelectric block at the last time; the updated polarization loss degree loss, , where a represents the flip influence coefficient, and n' represents the flip number of the ferroelectric block at the current time.

[0053] This step 104 fully simulates that under the control of the voltage time sequence signal in the simulation duration, each ferroelectric block in the ferroelectric body is affected by the target voltage corresponding to the current time, and the polarization direction, the flip number and the polarization loss degree of the ferroelectric block are obtained, so that the user can directly determine the polarization loss degree of each ferroelectric block at the current time.

[0054] Step 105, calculating the polarization intensity of the ferroelectric body according to the polarization parameters of all ferroelectric blocks at the current time and the saturation polarization value corresponding to the ferroelectric material used by the ferroelectric body.

[0055] In this step 105, the saturation polarization value Ps The simulation fitting parameters (including time influence coefficient c1, activation energy influence coefficient c2, and electric field influence coefficient a) are determined by the ferroelectric material used by the ferroelectric body, and these values are related to the ferroelectric material used by the ferroelectric body. In the present application, the ferroelectric material of the ferroelectric body supports aluminum scandium nitrogen AlScN.

[0056] The average polarization intensity P of the ferroelectric body corresponding to all ferroelectric blocks is calculated as the polarization intensity of the whole ferroelectric body, wherein, ; wherein P s represents the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body, N represents the number of ferroelectric blocks, i is the number of ferroelectric blocks, i is in the range of [1, N], loss i represents the polarization loss degree of the ferroelectric block numbered i, d i represents the polarization direction of the ferroelectric block numbered i.

[0057] In one example, after the simulation is completed, a polarization intensity curve corresponding to the voltage time sequence signal is generated. Through graphical representation, the polarization intensity of the ferroelectric body changing over time under the influence of the voltage time sequence signal is shown.

[0058] In the embodiment of the present application, at the end of each simulation step, the polarization parameters of each ferroelectric block changing over time are obtained according to the voltage time sequence signal, and then the polarization intensity of the ferroelectric body changing over time is obtained, and finally it is displayed through a curve. The polarization intensity indicates that the polarization of each ferroelectric block is reversed under the influence of the voltage time sequence signal, so that the polarization intensity of the ferroelectric body also changes correspondingly. The polarization intensity indicates the strength of the ferroelectric characteristics of the ferroelectric body.

[0059] In actual application, the ferroelectric device is modeled in the simulation software to obtain the ferroelectric body, and the polarization intensity of the ferroelectric body is less than or equal to the corresponding value required by the ferroelectric device, which is determined that the ferroelectric device indicated by the ferroelectric body cannot be effectively used. When the polarization intensity is equal to the corresponding value required by the ferroelectric device, the current time is the time when the ferroelectric device indicated by the ferroelectric body cannot be used, and then the effective use time length of the ferroelectric device under the simulated voltage time sequence signal is obtained.

[0060] The simulation and simulation method of the present application supports the polarization intensity curve simulation of the ferroelectric body with different ferroelectric materials, supports the polarization intensity curve simulation of the ferroelectric body with different simulation time lengths (i.e. simulation step), and supports the polarization intensity simulation of the ferroelectric body with different voltage time sequence signals. It is convenient to judge the influence of polarization loss on the performance of the ferroelectric device indicated by the ferroelectric body, and then calculate the effective use time length of the ferroelectric device indicated by the ferroelectric body, which provides a new method and tool for the research and application of ferroelectric materials.

[0061] Another example embodiment of the present application also provides a simulation device for polarization strength of ferroelectric. In the simulation software, referring to Figure 2 As shown in the figure, the ferroelectric device includes a ferroelectric, the ferroelectric is prismatic, and the ferroelectric includes an upper bottom surface and a lower bottom surface, the upper bottom surface and the lower bottom surface are rectangular. Referring to Figure 6 As shown in the figure, the simulation device for polarization strength of the ferroelectric in the embodiment includes: The discretization module 61 is configured to uniformly discretize the ferroelectric into N ferroelectric blocks, N is an integer greater than 1.

[0062] The initialization module 62 is configured to initialize each ferroelectric block by an initial polarization parameter, the initial polarization parameter includes an initial polarization direction, an initial flip count, an initial polarization loss degree and an initial applied voltage.

[0063] The simulation module 63 includes a power supply simulation unit 631 and a simulation operation unit 632, the power supply simulation unit 631 is configured to apply a target voltage to the ferroelectric block according to a voltage time sequence signal in each simulation step, the simulation operation unit 632 is configured to update the polarization parameter of each ferroelectric block at the current time according to the absolute value and polarity of the target voltage, combined with the polarization direction of the ferroelectric block at the last time, the simulation step is a specified time length, and the polarization parameter includes the polarization direction, the flip count and the polarization loss degree.

[0064] The calculation module 64 is configured to calculate the polarization strength of the ferroelectric according to the polarization parameter of all ferroelectric blocks at the current time and the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric.

[0065] The generation module 65 is configured to generate a polarization strength curve corresponding to the voltage time sequence signal based on the polarization strength of the ferroelectric changing with time after the simulation is completed.

[0066] The embodiment of the present application also proposes a simulation device, including a processor and a memory; the memory is used to store a computer program executable by the processor; the processor is used to execute the computer program in the memory to realize the simulation method in any of the above embodiments.

[0067] The embodiment of the present application also proposes a computer readable storage medium, when the executable computer program in the storage medium is executed by the processor, the simulation method in any of the above embodiments can be realized.

[0068] The embodiment of the present application also proposes a computer program product, including a computer program, the computer program is executed by the processor to realize the simulation method in any of the above embodiments.

[0069] As to the apparatus in the above embodiments, the specific manner in which the processor performs operations has been described in detail in the embodiments of the method, and thus will not be described in detail here.

[0070] Embodiments of the present application also provide a simulation device 700. Referring to FIG. 7, the simulation device 700 includes a memory 701 and a processor 702, the memory 701 being configured to store a computer program executable in the processor 702, and the processor 702 being configured to execute the computer program in the memory 701 to implement the simulation method of the polarization strength of the ferroelectric provided in any one of the above embodiments. Figure 7

[0071] The simulation device 700 further includes a communication interface 703. The processor 702, the memory 701 and the communication interface 703 are connected through a communication bus and complete communication with each other.

[0072] The processor 702 can be a general central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the execution of programs of the above solutions.

[0073] The communication interface 703 is configured to communicate with other devices or communication networks, such as Ethernet, a radio access network (RAN), a wireless local area network (WLAN), etc.

[0074] The memory 701 can be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disk storage, a magneto-optical disk, a magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer, but is not limited to this. The memory can exist independently and be connected to the processor through a bus. The memory can also be integrated with the processor.

[0075] ​In the present disclosure, the terms "first", "second", etc. are used only for descriptive purposes and not to be understood as indicating or implying relative importance. The term "plurality" means two or more, unless otherwise expressly specified.

[0076] The above description of the embodiments is for facilitating an understanding of and application of the present invention by those having ordinary skills in the art. Those skilled in the art will readily perceive various modifications to the embodiments, and apply the general principles described herein to other embodiments without inventing creative labors. Therefore, the present invention is not limited to the embodiments described herein, and the improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope and spirit of the present invention are within the scope of the present invention.

Claims

1. A method of simulating the polarization strength of a ferroelectric, characterized by, The application relates to a method for simulating a ferroelectric body, and belongs to the technical field of ferroelectric simulation. The uniform discrete ferroelectric body is composed of N ferroelectric blocks, and N is an integer greater than 1. Each ferroelectric block is initialized by an initial polarization parameter, and the initial polarization parameter includes an initial polarization direction, an initial flip number, an initial polarization loss degree and an initial applied voltage. In each simulation step, a target voltage is applied to the ferroelectric block according to a voltage time sequence signal, and the simulation step is a specified time length. According to the absolute value and polarity of the target voltage, the polarization parameter of each ferroelectric block at the current time is updated in combination with the polarization direction of the ferroelectric block at the last time, and the polarization parameter includes a polarization direction, a flip number and a polarization loss degree. The polarization intensity of the ferroelectric body is calculated according to the polarization parameter of all the ferroelectric blocks at the current time and the corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body.

2. The simulation method of claim 1, wherein, The value of N is related to the target simulation accuracy and hardware computing power; and the material of the ferroelectric body is aluminum scandium nitrogen.

3. The simulation method of claim 1, wherein, The initialization of each ferroelectric block by the initial polarization parameter includes the following steps. The initial polarization direction of each ferroelectric block is randomly configured by using a binary distribution with a probability of 0.

5. The initial flip number of each ferroelectric block is configured as zero. The initial polarization loss degree of each ferroelectric block is configured according to the simulation fitting parameter of the ferroelectric body, and the simulation fitting parameter includes a flip influence coefficient. The initial applied voltage of each ferroelectric block is configured as zero.

4. The simulation method of claim 3, wherein, The initial polarization loss degree is loss 初 , ； Wherein, a represents the flip influence coefficient, and n represents the flip number.

5. The simulation method of claim 1, wherein, According to the absolute value and polarity of the target voltage, the polarization parameter of each ferroelectric block at the current time is updated in combination with the polarization direction of the ferroelectric block at the last time, and the polarization parameter includes a polarization direction, a flip number and a polarization loss degree. When the absolute value of the target voltage at the current time is greater than the absolute value of the target voltage variation at the last time, or the polarity of the target voltage at the current time is different from that of the target voltage at the last time, if the polarization direction of the ferroelectric block at the last time is the same as the electric field direction indicated by the target voltage at the current time, the polarization parameter of the ferroelectric block at the last time is taken as the polarization parameter at the current time; if the polarization direction of the ferroelectric block at the last time is opposite to the electric field direction indicated by the target voltage at the current time, whether the polarization direction of the ferroelectric block is flipped is determined based on the current polarization flip probability, and the corresponding polarization parameter is updated when the flip is determined; When the absolute value of the target voltage at the current time is less than or equal to the absolute value of the target voltage variation at the last time, and the polarity of the target voltage at the current time is the same as that of the target voltage at the last time, the polarization parameter of all the ferroelectric blocks at the last time is taken as the polarization parameter at the current time.

6. The simulation method of claim 5, wherein, Whether the polarization direction of the ferroelectric block is flipped is determined based on the current polarization flip probability, and the corresponding polarization parameter is updated when the flip is determined, including the following steps. The probability value p of the polarization flip of the ferroelectric block is calculated, wherein, cl represents a time influence coefficient, the larger cl is, the closer to the steady-state simulation; c2 represents an activation energy influence coefficient, the larger c2 is, the slower the polarization flip is; E represents the target voltage; a represents an electric field influence coefficient, the larger a is, the faster the response speed of the polarization to the electric field is; a probability random number in the interval [0, 1] is taken; When the probability random number is greater than the probability value p, it is determined that the ferroelectric block does not appear flip, and the polarization parameter of the ferroelectric block at the last time is taken as the polarization parameter at the current time; When the probability random number is less than or equal to the probability value p, it is determined that the ferroelectric block appears flip, and the corresponding polarization parameter is updated.

7. The emulation method of claim 5, wherein, The determining that the ferroelectric block appears a flip, updating a corresponding polarization parameter, comprises: An updated polarization direction d', d'=-d, wherein d is a polarization direction of the ferroelectric block at a previous moment; An updated flip number n', n' = n + 1, wherein n is a flip number of the ferroelectric block at the previous moment; an updated polarization loss degree loss, wherein a represents a flip influence coefficient, and n' represents the number of flips of the ferroelectric block at the current moment.

8. The emulation method of claim 1, wherein, According to the polarization parameters of all the ferroelectric blocks at the current moment and a corresponding saturation polarization value of the ferroelectric material used by the ferroelectric body, the polarization intensity of the ferroelectric body is calculated, comprising: An average polarization intensity P of the ferroelectric body corresponding to all the ferroelectric blocks is calculated as the polarization intensity of the ferroelectric body, wherein, ； P s represents the saturation polarization value of the ferroelectric material used for the ferroelectric body, N represents the number of ferroelectric blocks, i is the number of the ferroelectric block, loss i represents the polarization loss degree of the ferroelectric block numbered i, d i represents the polarization direction of the ferroelectric block numbered i.

9. An emulation device, comprising: The computer program is executed by the processor to realize the simulation method of any one of claims 1-8.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the simulation method of any one of claims 1-8.

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