Construction method and device of ferroelectric capacitance model, simulation method and system of ferroelectric capacitance model, computer equipment and storage medium

Abstract

The invention provides a construction method and device of a ferroelectric capacitance model, a simulation method and system, computer equipment and a storage medium, and relates to the technical field of circuit design, an index relation is combined with an electric field, the simulation error of a high-voltage scene is reduced, and the design reliability of a wurtzite material device is remarkably improved; furthermore, the polarization overturning probability of each crystal grain is calculated, and the polarization state is dynamically updated in combination with random sampling, so that the standard deviation of polarization distribution is reduced, and the device life prediction accuracy is improved; furthermore, an electric field dependent material coefficient is introduced, the damage accumulation rate is adjusted in real time according to the voltage dependency relationship, the method adapts to nonlinear response of wurtzite under high field intensity, and transient data distortion is greatly reduced. According to the ferroelectric capacitance model constructed by adopting the scheme, the data distortion of output parameters is remarkably inhibited, and the prediction capability, the design reliability and the system energy efficiency under high field intensity are realized.

Description

Technical Field

[0001] This application relates to the field of circuit design technology, and in particular to a method and apparatus for constructing a ferroelectric capacitor model, a simulation method and system, a computer device and a storage medium. Background Technology

[0002] Wurtzite ferroelectric materials are considered core materials for next-generation non-volatile memories and high-voltage power devices due to their high polarization intensity, high Curie temperature, and compatibility with CMOS processes. Traditional techniques use the KAI (Kolmogorov–Avrami–Ishibashi) model to simulate the polarization reversal dynamics or ferroelectric domain growth process of ferroelectric materials. However, the KAI model neglects the dynamic influence of electric field intensity on domain wall migration rate, failing to accurately predict domain wall acceleration effects and resulting in severe distortion of the output current waveform. Furthermore, the KAI model averages the ferroelectric material, ignoring grain-level random reversals and failing to reflect the microscopic statistical characteristics of polycrystalline materials, leading to a large standard deviation in polarization distribution and impacting device reliability design. Summary of the Invention

[0003] The purpose of this application is to provide a method and apparatus for constructing a ferroelectric capacitor model, a simulation method and system, a computer device and a storage medium, to overcome the shortcomings of traditional technologies, such as the inability of the KAI model to accurately predict the domain wall acceleration effect leading to an underestimation of the polarization reversal speed, and the large standard deviation of polarization distribution affecting the reliability design of the device.

[0004] Firstly, this application proposes a method for constructing a ferroelectric capacitance model, including: The ferroelectric capacitor is decomposed into multiple independent grains; The damage factor of each grain is updated with time step based on the domain wall time constant; wherein the domain wall time constant is dynamic. Based on the damage factor and material coefficient, each of the grains is randomly sampled to obtain the polarization reversal probability of each grain; wherein, the material coefficient is calculated based on the real-time gate voltage at each time step; Based on the polarization reversal probability, it is determined whether each grain randomly flips during domain wall expansion, thereby determining the polarization state of each grain; Based on the polarization state of each grain, the ferroelectric index is calculated to obtain the ferroelectric capacitance model.

[0005] In one embodiment, updating the damage factor of each grain with a time step based on the domain wall time constant includes: The domain wall time constant is calculated based on the gate voltage; Based on the domain wall time constant, calculate the damage increment of each grain per unit time; The damage factor is updated based on the damage increment.

[0006] In one embodiment, the domain wall time constant is calculated based on the gate voltage, and its expression is: t_cv0=t0×(1 / ln(2)) 1 / (2×β_cv+3) ×exp(Ea / |Vgate|), where t_cv0 represents the domain wall time constant, t0 represents the initial domain wall time constant, Ea represents the activation energy, Vgate represents the gate voltage (which is not zero), and β_cv represents the material coefficient; The damage increment of each grain per unit time is calculated based on the domain wall time constant, and its expression is as follows: A_cv = Δt / t_cv0, where A_cv represents the damage increment per unit time; Δt represents the time step. The damage factor is updated based on the damage increment, and its expression is as follows: h t+Δt [i]=h t [i]+A_cv, where h t [i] represents the damage factor before the update, h t+Δt [i] represents the updated damage factor. In one embodiment, the material coefficient is calculated based on the real-time gate voltage at each time step, including: β_cv = a × |Vgate|-b, where β_cv represents the material coefficient and β_cv ≥ -1, and a and b are parameter factors fitted based on experimental data.

[0007] In one embodiment, the step of randomly sampling each grain based on the damage factor and material coefficient to obtain the polarization reversal probability of each grain includes: P=1-exp(-h 2β_cv +3 (t+Δt)+h 2β_cv +3 (t)), where P represents the polarization reversal probability. In one embodiment, determining whether each grain randomly flips during domain wall expansion based on the polarization flip probability, thereby determining the polarization state of each grain, includes: When the domain wall is at rest, it does not need to flip and maintains the polarization state of the previous time step; During domain wall expansion, the polarization reversal probability of the grain is compared with a random value based on the Monte Carlo framework. If the polarization reversal probability is greater than the random value, the grain is randomly flipped to obtain the polarization state of the grain after random reversal; otherwise, the polarization state of the grain in the previous time step is maintained. The method for determining domain wall expansion includes: comparing the gate voltage direction and polarization direction of each of the grains; if the directions are consistent, the domain wall is stationary; if the directions are inconsistent, the domain wall is considered to be expanding.

[0008] In one embodiment, the ferroelectric index includes domain flipping current; The calculation of ferroelectric properties based on the polarization state of each grain includes: By summing the polarization states of all the aforementioned grains, calculating the average polarization intensity, and then differentiating the domain flipping current, the expression is as follows: Igb = W × L ×d(∑Pi×Pr / N_grain) / dt, where Igb represents the domain flipping current at each time step, W and L represent the length and width of the channel, respectively, Pi represents the polarization state of the grain, Pr represents the remanent polarization intensity of different materials, and N_grain represents the number of grains. Secondly, this application proposes an apparatus for constructing a ferroelectric capacitance model, the apparatus comprising: An update module is used to update the damage factor of each grain with a time step based on the domain wall time constant; wherein the domain wall time constant is dynamic and the ferroelectric capacitance is decomposed into multiple independent grains. The first calculation module is used to calculate the material coefficient based on the real-time gate voltage at each time step; The second calculation module is used to randomly sample each grain according to the damage factor and material coefficient to obtain the polarization reversal probability of each grain. The processing module is used to determine whether each of the grains randomly flips during domain wall expansion based on the polarization flip probability, thereby determining the polarization state of each grain; and to calculate the ferroelectric index based on the polarization state of each grain to obtain the ferroelectric capacitance model.

[0009] Thirdly, this application also provides a simulation method for ferroelectric capacitors, the method comprising: Using a hardware description language, the ferroelectric capacitor model constructed by the method described in any one of the first aspects is embedded into a simulator to obtain a simulation system for ferroelectric capacitors. Divide the preset time into multiple time steps; Using the aforementioned simulation system, the ferroelectric parameters for each time step are calculated iteratively based on the simulation parameters of the grains until all time steps are completed, and the output parameters are obtained. Based on the output parameters, the target ferroelectric capacitance is simulated. The simulation parameters include polarization state, damage factor, and polarization reversal probability.

[0010] Fourthly, this application also provides a simulation system for ferroelectric capacitors, the simulation system comprising: The ferroelectric capacitor model is constructed using the method described in any one of the first aspects. The simulator contains a ferroelectric capacitor model embedded in a hardware description language. The ferroelectric capacitance model is used to iteratively calculate the ferroelectric index for each time step based on the simulation parameters of the grain, until all time steps are completed, and the output parameters are obtained; wherein, the time step is obtained by dividing a preset time; the simulation parameters include polarization state, damage factor and polarization reversal probability; The simulator is used to simulate the target ferroelectric capacitor based on the output parameters.

[0011] Fifthly, this application also provides a computer device. The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method steps of the first aspect.

[0012] Sixthly, this application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the method steps of the first aspect.

[0013] The above-mentioned method and apparatus for constructing the ferroelectric capacitance model, simulation method and system, computer equipment and storage medium have at least the following advantages: This application introduces a dynamic domain wall time constant, combining the exponential relationship with the electric field to dynamically reflect the nonlinear domain wall expansion behavior under high field strength, reducing simulation errors in high-voltage scenarios and significantly improving the design reliability of wurtzite material devices. Furthermore, this application decomposes the ferroelectric capacitance of wurtzite ferroelectric materials into multiple independent grains, calculates the polarization reversal probability of each grain, and dynamically updates the polarization state using random sampling, reducing the standard deviation of the polarization distribution and accurately capturing the local breakdown risk of "hot spot" grains, thus improving the accuracy of device lifetime prediction. Furthermore, this application introduces an electric field-dependent material coefficient, adjusting the damage accumulation rate in real time according to the voltage dependence relationship to adapt to the nonlinear response of wurtzite under high field strength, significantly reducing transient data distortion. The ferroelectric capacitance model constructed using the above scheme significantly suppresses data distortion of output parameters, achieving predictive capability, design reliability, and system energy efficiency under high field strength. Attached Figure Description

[0014] Figure 1 This is a diagram illustrating the application environment of the ferroelectric capacitor model construction method and the ferroelectric capacitor simulation method in one embodiment. Figure 2 This is a flowchart illustrating the method for constructing a ferroelectric capacitor model in one embodiment; Figure 3 This is a flowchart illustrating the steps for updating the damage factor of each grain in one embodiment. Figure 4 This is a structural block diagram of the apparatus for constructing a ferroelectric capacitor model in one embodiment; Figure 5 This is a flowchart illustrating the implementation steps of a simulation method for ferroelectric capacitors in one embodiment; Figure 6 This is a schematic diagram showing the relationship between the drain current and gate voltage of a ferroelectric transistor in one embodiment. Figure 7 This is a schematic diagram illustrating the dynamic change of polarization intensity over time in one embodiment; Figure 8 This is a schematic diagram of the P–E hysteresis curve in one embodiment; Figure 9 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0015] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0016] Some exemplary embodiments of this application have been described for illustrative purposes. It should be understood that this application may be implemented in other ways not specifically shown in the accompanying drawings.

[0017] The method for constructing the ferroelectric capacitor model and the method for simulating ferroelectric capacitors provided in the embodiments of this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on another network server.

[0018] The terminal 102 can send the parameters of the ferroelectric capacitor to be simulated to the server 104, so that the server 104 can process the parameters. For example, the server 104 decomposes the ferroelectric capacitor into multiple independent grains; updates the damage factor of each grain with each time step based on the domain wall time constant (where the domain wall time constant is dynamic); randomly samples each grain according to the damage factor and material coefficients to obtain the polarization reversal probability of each grain (where the material coefficients are calculated based on the real-time gate voltage at each time step); determines whether each grain randomly reverses according to preset conditions, thereby determining the polarization state of each grain; and calculates the ferroelectric index based on the polarization state of each grain to obtain the ferroelectric capacitor model. The server 104 then feeds back the ferroelectric capacitor model to the terminal 102.

[0019] The aforementioned ferroelectric capacitance model construction method introduces a dynamic domain wall time constant, combining the exponential relationship with the electric field to dynamically reflect the nonlinear domain wall expansion behavior under high field strength, reducing simulation errors in high-voltage scenarios and significantly improving the design reliability of wurtzite material devices. Furthermore, this application decomposes the ferroelectric capacitance of wurtzite ferroelectric materials into multiple independent grains, calculates the polarization reversal probability of each grain, and dynamically updates the polarization state using random sampling, reducing the standard deviation of the polarization distribution and accurately capturing the local breakdown risk of "hot spot" grains, thus improving the accuracy of device lifetime prediction. Furthermore, this application introduces an electric field-dependent material coefficient, adjusting the damage accumulation rate in real time according to the voltage dependence relationship to adapt to the nonlinear response of wurtzite under high field strength, significantly reducing transient data distortion. The ferroelectric capacitance model constructed using the above scheme significantly suppresses data distortion of output parameters, achieving higher simulation accuracy, design reliability, and system energy efficiency.

[0020] The terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle systems. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0021] Furthermore, server 104 also uses a hardware description language to embed the ferroelectric capacitor model constructed based on the above-mentioned ferroelectric capacitor model construction method into the simulator to obtain a ferroelectric capacitor simulation system; initializes the simulation parameters of the grain, including polarization state, damage factor and polarization reversal probability; divides the preset time into multiple time steps; uses the simulation system to iteratively calculate the domain reversal current of each time step until all time steps are completed to obtain the current source and output the current source.

[0022] The above-mentioned simulation method for ferroelectric capacitors embeds the ferroelectric capacitor model into the simulator and directly outputs simulation signals that the simulator can recognize. This solves the problem of low simulation efficiency caused by the lack of circuit-level interfaces in traditional models, which require manual processing of the parameters output by the model before importing them into the simulator.

[0023] In one exemplary embodiment, this application provides a method for constructing a ferroelectric capacitance model, which will be applied below. Figure 1 We will use server 104 as an example to illustrate this.

[0024] Please see Figure 2 , Figure 2 This is a flowchart illustrating a method for constructing a ferroelectric capacitance model according to this embodiment, specifically including the following steps: Step S202: The ferroelectric capacitor is decomposed into multiple independent grains.

[0025] Specifically, wurtzite ferroelectric materials are a new type of functional material with a wurtzite crystal structure and ferroelectricity induced by doping or strain engineering. They have advanced strength of 80–165 μC / cm², high Curie temperature of over 1000℃, and compatibility with CMOS processes, and are regarded as the core material for next-generation non-volatile memory and high-voltage power devices.

[0026] Wurtzite ferroelectric materials are typically polycrystalline thin films composed of multiple grains, each with its own independent crystal orientation, local polarization state, and defect distribution. By decomposing the ferroelectric capacitance into multiple independent grains and statistically analyzing these independent grains, the random switching behavior of real polycrystalline ferroelectrics can be mapped.

[0027] There are several ways to decompose ferroelectric capacitors into multiple independent grains, and the appropriate method can be selected as needed. For example, decomposition can be based on experimental characterization, including SEM (scanning electron microscopy) and EBSD (electron backscattering diffraction); alternatively, it can be based on an assumed grain size distribution.

[0028] Step S204: Based on the domain wall time constant, update the damage factor of each grain with time step; wherein, the domain wall time constant is dynamic.

[0029] Specifically, domain walls are transition layers between two ferroelectric domains with opposite polarization directions within a ferroelectric material. For ferroelectric capacitors, an applied electric field causes the domain walls to move, and the volume partition swept by the domain walls completes polarization reversal, which macroscopically manifests as the switching current of the capacitor charging and discharging.

[0030] Domain wall migration rate refers to the distance that a domain wall moves along its normal direction in a ferroelectric material per unit time. It quantitatively describes how fast a domain wall advances and sweeps across a crystal lattice point under an applied electric field, stress, or temperature excitation, and is one of the most core local indicators of polarization reversal dynamics.

[0031] The domain wall time constant is the average time required for the domain wall to traverse a representative geometric distance. It is a scaling factor used to project the domain wall migration rate over a representative distance onto the macroscopic time axis.

[0032] When high pressure is applied to grains, the domain walls are stretched, leading to the breakage of local chemical bonds. The damage factor is used to characterize the degree of domain wall degradation. Generally, the damage factor ranges from 0 to 1. The larger the damage factor, the more severe the domain wall pinning and the more difficult the polarization, resulting in phenomena such as decreased polarization intensity, weakened current, and contraction of the P-E hysteresis curve.

[0033] The KAI (Kolmogorov–Avrami–Ishibashi) model posits that the ferroelectric switching process is dominated by the growth of inverted domains through the movement of domain walls until they collide with each other. This model assumes that in a homogeneous ferroelectric material, domain nuclei form randomly in space and time, while domain walls move at a constant velocity. During the polarization reversal process in the ferroelectric material, as time progresses, newly formed inverted domains gradually grow, and domain walls continuously expand until different inverted domains collide with each other, ultimately achieving polarization reversal.

[0034] When the applied electric field exceeds 5 MV / cm, the nonlinearly increasing nucleation rate of wurtzite materials makes a significant contribution to the polarization reversal process. The KAI model assumes a fixed domain wall migration rate and uses a fixed domain wall time constant (τ), neglecting the dynamic influence of the electric field strength on the domain wall migration rate. This leads to an inaccurate prediction of the domain wall acceleration effect, resulting in a large prediction error for the polarization reversal rate under high voltages greater than 5 MV / cm, and failing to describe the nonlinear response of wurtzite materials under high electric fields greater than 5 MV / cm. This application addresses this by setting a dynamic domain wall time constant, which is exponentially linked to the electric field, dynamically reflecting the nonlinear domain wall expansion behavior under high field strengths. This reduces simulation errors in high-voltage scenarios and significantly improves the design reliability of wurtzite material devices.

[0035] Step S206: Randomly sample each grain based on the damage factor and material coefficient to obtain the polarization reversal probability of each grain; wherein, the material coefficient is calculated based on the real-time gate voltage at each time step.

[0036] Specifically, the material coefficient has a linear relationship with the domain wall damage accumulation rate; the larger the material coefficient, the slower the domain wall damage accumulation rate. The domain wall damage accumulation rate refers to the rate of "functional degradation" of the domain wall due to repeated polarization flips per unit time, denoted as dD(t) / dt, where D(t) represents the damage factor.

[0037] Fixed material parameters lead to a mismatch in damage accumulation rate under high-voltage transient scenarios, resulting in severe current waveform distortion. Therefore, this application introduces an electric field-dependent nonlinear material coefficient to adjust the damage accumulation rate in real time through voltage dependence, matching the nonlinear response characteristics of wurtzite materials. Specifically, the material coefficient is calculated at each time step based on the real-time gate voltage of the ferroelectric capacitor. It should be noted that in this embodiment, the gate voltage of the ferroelectric capacitor is the terminal voltage between the electrodes, shared by all grains.

[0038] The material coefficient characterizes the inherent differences of wurtzite material itself, while the damage factor characterizes the aging effect of grains as they evolve with cycles. The larger the material coefficient, the easier it is for grains to flip. The larger the damage factor, the lower the local barrier, which also promotes flipping. Based on the above two parameters, the polarization flipping probability of grains is calculated, and the above two scenarios are reproduced in one model.

[0039] Step S208: Based on the polarization reversal probability, determine whether each grain randomly flips during domain wall expansion, thereby determining the polarization state of each grain.

[0040] Specifically, in ferroelectric materials, domain wall quiescence and domain wall expansion are two key states describing the dynamic behavior of ferroelectric domains, directly affecting the polarization reversal process. Domain wall quiescence refers to the state in which domain walls temporarily cease movement due to obstacles such as defects, stress, or grain boundaries; domain wall expansion refers to the process in which domain walls overcome energy barriers and expand into adjacent regions under the drive of an applied electric field. In the domain wall quiescence stage, when domain walls are pinned, the local electric field energy is insufficient to trigger grain reversal, and the system is in a metastable state. At this time, most grain movement is temporarily halted, and the reversal probability is low. In the domain wall expansion stage, it means that the external electric field has overcome the local energy barrier, and the electric field energy in the region swept by the domain wall is sufficient to trigger polarization reversal, leading to a sudden increase in the grain reversal probability.

[0041] In the ferroelectric capacitance model of this application embodiment, the grains are assumed to maintain the polarization state of the previous time step during the domain wall quiescent stage. Random flipping is only triggered during the domain wall expansion stage, which avoids redundant simulation of the quiescent region and significantly reduces the amount of computation compared to the continuous calculation of traditional models.

[0042] Furthermore, the ferroelectric capacitance model of this application decomposes the ferroelectric capacitor into independent grains, simulates the polarization reversal probability by random sampling and dynamically updates the polarization state, reduces the standard deviation of the polarization distribution, accurately captures the local breakdown risk of "hot spot" grains, and improves the accuracy of device lifetime prediction; it solves the defect of the traditional model that uses the macro-averaging method, ignores the randomness of grain-level polarization reversal, and causes large deviations in polarization response prediction.

[0043] In ferroelectric materials, each grain has its own crystal orientation. The polarization state of a grain is the orientation of the spontaneous polarization vector of most domains within that grain. It can be expressed by a symbol, a discrete number, or a continuous vector. For example, in this embodiment, a discrete number (±1) is used to express the polarization state. If the polarization vector of a grain is oriented in the positive reference direction, its polarization state is recorded as +1; if the polarization vector of a grain is oriented in the negative reference direction, its polarization state is recorded as -1. The reference direction is preset according to the application scenario.

[0044] Step S210: Calculate the ferroelectric index based on the polarization state of each grain to obtain the ferroelectric capacitance model.

[0045] Specifically, ferroelectric indices include polarization intensity, domain flip current, polarization charge, dynamic capacitance, and internal electric field. Polarization intensity refers to the net bound charge density per unit volume of ferroelectric material at time t, its value obtained by volume averaging of all grain polarization orientations, reflecting the macroscopic vector sum of electric dipole moments within the ferroelectric layer. Domain flip current refers to the instantaneous current transporting bound charges by domain walls during flipping, its value satisfying a differential relationship with the time change of the macroscopic polarization state. Polarization charge refers to the total bound charge generated on the electrode surface by the polarization intensity. Dynamic capacitance refers to the slope of the instantaneous charge-voltage relationship of the ferroelectric capacitor at time t. Internal electric field refers to the actual electric field intensity within the ferroelectric layer, which can be obtained by superimposing the applied electric field and the depolarization field according to Maxwell's equations.

[0046] The above parameters are key parameters that map micro-domain-level behavior to macro-device characteristics, providing a unified metric basis for the modeling, simulation, and performance evaluation of ferroelectric materials.

[0047] The aforementioned ferroelectric capacitance model construction method, by introducing a dynamic domain wall time constant, combines the exponential relationship with the electric field, dynamically reflecting the nonlinear domain wall expansion behavior under high field strength, reducing simulation errors in high-voltage scenarios, and significantly improving the design reliability of wurtzite material devices. Furthermore, this application decomposes the ferroelectric capacitance of wurtzite ferroelectric materials into multiple independent grains, calculates the polarization reversal probability of each grain, and dynamically updates the polarization state by combining random sampling, reducing the standard deviation of the polarization distribution, accurately capturing the local breakdown risk of "hot spot" grains, and improving the accuracy of device lifetime prediction. Furthermore, this application introduces an electric field-dependent material coefficient, adjusting the damage accumulation rate in real time according to the voltage dependence relationship, adapting to the nonlinear response of wurtzite under high field strength, and significantly reducing transient data distortion. The ferroelectric capacitance model constructed using the above scheme significantly suppresses data distortion of output parameters, achieving predictive capability, design reliability, and system energy efficiency under high field strength.

[0048] Please see Figure 3 Optionally, based on the domain wall time constant, the damage factor of each grain is updated with time steps, including: Step S302: Calculate the domain wall time constant based on the gate voltage.

[0049] Step S304: Calculate the damage increment of each grain per unit time based on the domain wall time constant.

[0050] Step S306: Update the damage factor based on the damage increment.

[0051] Optionally, the domain wall time constant is calculated based on the gate voltage, and its expression is as follows: t_cv0=t0×(1 / ln(2)) 1 / (2×β_cv+3) ×exp(Eα / |Vgate|).

[0052] Where t_cv0 represents the domain wall time constant, t0 represents the initial domain wall time constant, Eα represents the activation energy, Vgate represents the gate voltage (which is not zero), and β_cv represents the material coefficient.

[0053] It should be noted that when calculating the domain wall time constant, a voltage check needs to be performed on each grain to avoid a division-by-zero error caused by a zero gate voltage. For example, if Vgate < e -15 If the gate voltage is zero, then it is considered to be zero.

[0054] Optionally, the damage increment of each grain per unit time can be calculated based on the domain wall time constant, and its expression is as follows: A_cv=Δt / t_cv0.

[0055] Where A_cv represents the damage increment per unit time.

[0056] Optionally, the damage factor is updated based on the damage increment, and its expression is: h t+Δt [i]=h t [i]+A_cv.

[0057] Among them, h t [i] represents the damage factor before the update, h t+Δt [i] represents the updated damage factor.

[0058] By adopting the above scheme, the nonlinear domain wall expansion behavior under high field strength is dynamically reflected by combining the exponential relationship with the electric field. This improvement reduces the simulation error in high-voltage scenarios and significantly enhances the design reliability of wurtzite material devices.

[0059] Optionally, the material coefficient is calculated based on the real-time gate voltage at each time step, including: β_cv = a × |Vgate|-b.

[0060] Wherein, β_cv represents the material coefficient and β_cv ≥ -1, and a and b are parameter factors fitted based on experimental data. It should be noted that, in this embodiment, based on a lower limit protection mechanism, β_cv ≥ -1 is set. If the dynamically calculated value of β_cv is less than -1, it is assigned the value -1; otherwise, its original value is retained.

[0061] By adopting the above scheme, the damage accumulation rate is adjusted in real time through voltage dependence to match the nonlinear response characteristics of wurtzite materials.

[0062] Optionally, based on the damage factor and material coefficients, random sampling is performed on each grain to obtain the polarization reversal probability of each grain, including: P=1-exp(-h 2β_cv +3 (t+Δt)+h 2β_cv +3 (t)), where P represents the polarization reversal probability.

[0063] Optionally, based on the polarization reversal probability, determining whether each grain randomly flips during domain wall expansion, thereby determining the polarization state of each grain, includes: When the domain wall is at rest, it does not need to flip and maintains the polarization state of the previous time step; During domain wall expansion, the polarization reversal probability of the grain is compared with a random value based on the Monte Carlo framework. If the polarization reversal probability is greater than the random value, the grain is randomly flipped to obtain the polarization state of the grain after random reversal; otherwise, the polarization state of the grain in the previous time step is maintained. The method for determining domain wall expansion includes: comparing the gate voltage direction and polarization direction of each of the grains; if the directions are consistent, the domain wall is stationary; if the directions are inconsistent, the domain wall is considered to be expanding.

[0064] Specifically, the embodiments of this application are based on the Monte Carlo framework to randomly flip the grains, wherein the random value is a uniformly distributed pseudo-random number generated by a pseudo-random number generator based on algorithms such as the linear congruent method (LCG) and Mersenne Twister, and its value ranges from 0 to 1.

[0065] Furthermore, when the grains are in a static state at the domain walls, the damage factor is reset to zero.

[0066] It should be understood that in practical applications, in the problem of random switching of ferroelectric grains, in addition to the above-mentioned schemes, the Monte Carlo Nonlinear Switching (MCNLS) model can also be used. That is, the Monte Carlo model is used to simulate the behavior of electric dipoles to handle randomness, the complex relationship between polarization and electric field is characterized by nonlinear mechanism, and the switching rule is used to simulate the polarization switching of electric dipoles under electric field, providing a tool for studying the polarization behavior of ferroelectric materials.

[0067] The above scheme decomposes the ferroelectric capacitor into independent grains, calculates the polarization reversal probability of each grain and dynamically updates the polarization state, reduces the standard deviation of polarization distribution, accurately captures the local breakdown risk of "hot spot" grains, and improves the accuracy of device lifetime prediction. It also solves the defect of the traditional model that uses macro-averaging method, ignores the randomness of grain-level polarization reversal, and causes large deviation in polarization response prediction.

[0068] When ferroelectric properties include domain flipping current, optionally, ferroelectric properties are calculated based on the polarization state of each grain, including: By summing the polarization states of all grains, calculating the average polarization intensity, and then differentiating the domain flipping current, the expression is as follows: Igb = W × L ×d(∑Pi×Pr / N_grain) / dt.

[0069] Where Igb represents the domain flipping current at each time step, W and L represent the channel length and width, respectively, Pi represents the polarization state of the grain, Pr represents the remanent polarization intensity of different materials, and N_grain represents the number of grains.

[0070] The aforementioned ferroelectric capacitance model construction method introduces a dynamic domain wall time constant, combining the exponential relationship with the electric field to dynamically reflect the nonlinear domain wall expansion behavior under high field strength, reducing simulation errors in high-voltage scenarios and significantly improving the design reliability of wurtzite material devices. Furthermore, this application decomposes the ferroelectric capacitance of wurtzite ferroelectric materials into multiple independent grains, calculates the polarization reversal probability of each grain, and dynamically updates the polarization state using random sampling, reducing the standard deviation of the polarization distribution and accurately capturing the local breakdown risk of "hot spot" grains, thus improving the accuracy of device lifetime prediction. Furthermore, this application introduces an electric field-dependent material coefficient, adjusting the damage accumulation rate in real time according to the voltage dependence relationship to adapt to the nonlinear response of wurtzite under high field strength, significantly reducing transient data distortion. The ferroelectric capacitance model constructed using the above scheme significantly suppresses data distortion of output parameters, achieving higher simulation accuracy, design reliability, and system energy efficiency. It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0071] Based on the same inventive concept, this application also provides a device for constructing a ferroelectric capacitor model. This device is applicable to the above-described method for constructing a ferroelectric capacitor model. The solution provided by this device is similar to the solution described in the above-described method. Therefore, the specific limitations of one or more device embodiments provided below can be found in the limitations of the method above, and will not be repeated here.

[0072] Please see Figure 4 In one embodiment, the apparatus for constructing the ferroelectric capacitance model of this application includes: an update module, a first calculation module, a second calculation module, and a processing module.

[0073] The update module is used to update the damage factor of each grain with time step based on the domain wall time constant; where the domain wall time constant is dynamic and the ferroelectric capacitance is decomposed into multiple independent grains.

[0074] The first calculation module is used to calculate the material coefficient based on the real-time gate voltage at each time step.

[0075] The second calculation module is used to randomly sample each grain based on the damage factor and material coefficient to obtain the polarization reversal probability of each grain.

[0076] The processing module is used to determine whether each grain randomly flips during domain wall expansion based on the polarization flip probability, thereby determining the polarization state of each grain; based on the polarization state of each grain, the ferroelectric index is calculated to obtain the ferroelectric capacitance model.

[0077] Optionally, the update module updates the damage factor of each grain with time step based on the domain wall time constant, including: calculating the domain wall time constant according to the gate voltage; calculating the damage increment of each grain per unit time according to the domain wall time constant; and updating the damage factor according to the damage increment.

[0078] The domain wall time constant is calculated based on the gate voltage, and its expression is as follows: t_cv0=t0×(1 / ln(2)) 1 / (2×β_cv+3) ×exp(Eα / |Vgate|).

[0079] Where t_cv0 represents the domain wall time constant, t0 represents the initial domain wall time constant, Eα represents the activation energy, Vgate represents the gate voltage (which is not zero), and β_cv represents the material coefficient.

[0080] The damage increment of each grain per unit time is calculated based on the domain wall time constant, and the expression is as follows: A_cv=Δt / t_cv0.

[0081] Where A_cv represents the damage increment per unit time.

[0082] The damage factor is updated based on the damage increment, and its expression is as follows: h t+Δt [i]=h t [i]+A_cv.

[0083] Among them, h t [i] represents the damage factor before the update, h t+Δt [i] represents the updated damage factor.

[0084] Optionally, the first calculation module calculates the material coefficient based on the real-time gate voltage at each time step, including: β_cv = a × |Vgate|-b.

[0085] Where β_cv represents the material coefficient and β_cv ≥ -1, and a and b are parameter factors fitted based on experimental data.

[0086] Optionally, the second calculation module randomly samples each grain based on the damage factor and material coefficients to obtain the polarization reversal probability of each grain, including: P=1-exp(-h 2β_cv +3 (t+Δt)+h 2β_cv +3 (t)), where P represents the polarization reversal probability.

[0087] Optionally, the processing module determines whether each of the grains randomly flips during domain wall expansion based on the polarization flip probability, thereby determining the polarization state of each grain. This includes: when the domain wall is stationary, no flipping is required, and the polarization state in the previous time step is maintained; when the domain wall expands, the polarization flip probability of the grain is compared with a random value based on a Monte Carlo framework; if the polarization flip probability is greater than the random value, the grain is randomly flipped to obtain the polarization state of the grain after random flipping; otherwise, the polarization state of the grain in the previous time step is maintained. The method for determining domain wall expansion includes: comparing the gate voltage direction and polarization direction of each grain; if the directions are consistent, the domain wall is stationary; if the directions are inconsistent, the domain wall is considered to be expanding.

[0088] When the ferroelectric index includes domain flipping current, optionally, the processing module calculates the ferroelectric index based on the polarization state of each grain, including: summing the polarization states of all grains, calculating the average polarization intensity, and then differentiating to generate the domain flipping current, the expression of which is: Igb = W × L ×d(∑Pi×Pr / N_grain) / dt.

[0089] Where Igb represents the domain flipping current at each time step, W and L represent the channel length and width, respectively, Pi represents the polarization state of the grain, Pr represents the remanent polarization intensity of different materials, and N_grain represents the number of grains.

[0090] The aforementioned ferroelectric capacitance model construction device introduces a dynamic domain wall time constant, combining the exponential relationship with the electric field to dynamically reflect the nonlinear domain wall expansion behavior under high field strength, reducing simulation errors in high-voltage scenarios and significantly improving the design reliability of wurtzite material devices. Furthermore, this application decomposes the ferroelectric capacitance of wurtzite ferroelectric material into multiple independent grains, calculates the polarization reversal probability of each grain, and dynamically updates the polarization state using random sampling, reducing the standard deviation of the polarization distribution and accurately capturing the local breakdown risk of "hot spot" grains, thus improving the accuracy of device lifetime prediction. Furthermore, this application introduces an electric field-dependent material coefficient, adjusting the damage accumulation rate in real time according to the voltage dependence relationship to adapt to the nonlinear response of wurtzite under high field strength, significantly reducing transient data distortion. The ferroelectric capacitance model constructed using the above scheme significantly suppresses data distortion of output parameters, achieving higher simulation accuracy, design reliability, and system energy efficiency.

[0091] Each module in the aforementioned ferroelectric capacitance model construction device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the operations corresponding to each module.

[0092] Based on the same inventive concept, embodiments of this application also provide a simulation method for ferroelectric capacitors, including: Using a hardware description language, the ferroelectric capacitor model constructed by the ferroelectric capacitor model construction method provided in the above embodiments is embedded into the simulator to obtain a ferroelectric capacitor simulation system.

[0093] Divide the preset time into multiple time steps.

[0094] A simulation system is used to iteratively calculate the ferroelectric parameters for each time step based on the simulation parameters of the grains until all time steps are completed, and the output parameters are obtained. The target ferroelectric capacitance is then simulated based on the output parameters. The simulation parameters include polarization state, damage factor, and polarization reversal probability.

[0095] Specifically, traditional ferroelectric capacitor models lack circuit-level interfaces, requiring manual processing of the model's output parameters before importing them into a simulator, resulting in low simulation efficiency. This application's embodiment directly generates SPICE-compatible ferroelectric capacitor models using the Veriloga module. This allows the ferroelectric capacitor model to output simulation signals recognizable by the simulator, supporting real-time transient waveform output, significantly improving simulation efficiency and substantially shortening the device development cycle.

[0096] Please see Figure 5 The following is combined Figure 5 Taking the domain flipping current as an example, the simulation method of the above-mentioned ferroelectric capacitor is explained in detail: First, the preset time t is divided into multiple time steps Δt; at the same time, the simulation parameters are initialized, the polarization state of each grain is set to -1, and the loss factor and polarization reversal probability are set to zero.

[0097] After the loop starts, the material coefficient β_cv is calculated based on the real-time gate voltage at each time step, and it is determined whether the value of β_cv is less than -1. If it is less than -1, it is assigned the value of -1; otherwise, the original value is kept.

[0098] Furthermore, iterate through all the die cells and determine the gate voltage of each die cell. If Vgate < e -15If the gate voltage is zero, the domain wall time constant t_cv0 and damage increment A_cv cannot be calculated, and the damage factor remains the damage factor of the previous time step; otherwise, the domain wall time constant t_cv0 and damage increment A_cv are updated to obtain a new damage factor.

[0099] Furthermore, the direction of the gate voltage and the polarization direction of the grain determine whether the grain is in a domain wall expansion state or a domain wall quiescent state. If the directions are inconsistent, it is considered to be in a domain wall expansion state; otherwise, it is in a domain wall quiescent state. In the case of a domain wall quiescent state, the grain does not need to be flipped, maintains the polarization state of the previous time step, and resets the damage factor to zero. In the case of a domain wall expansion state, the grain is randomly flipped based on the Monte Carlo framework. After flipping, the polarization state is updated; if it is not flipped, the polarization state of the grain in the previous time step is maintained.

[0100] After traversing all the grains, the polarization states of all the grains are accumulated, and the domain flip current Igb for that time step is calculated. The domain flip current Igb is then used as an output parameter and output to the simulator.

[0101] Please see Figure 6-8 , Figure 6-8 The image shows the simulation results obtained by the simulator based on the parameters output by the ferroelectric capacitance model.

[0102] Please see Figure 6 , Figure 6 The diagram illustrates the relationship between the drain current (Ids) and gate voltage (Vg) of a ferroelectric transistor. The horizontal axis represents the gate voltage (-8 V ~ 8 V), and the vertical axis represents the drain current (10 V ~ 8 V). -4 (Order of magnitude). It can be seen that the simulated curves exhibit typical hysteresis characteristics of ferroelectric materials, and the current peaks under positive and negative gate voltages reflect the bistable characteristics of polarization reversal.

[0103] Please see Figure 7 , Figure 7 The figure shows the dynamic change of polarization intensity (P) with time (t), with the horizontal axis representing time (0~1×10−4 s) and the vertical axis representing polarization intensity (-150~150μC / cm2). It can be seen that the simulated curves show a rapid polarization reversal process, and the difference in polarization reversal time under positive and negative electric fields reflects the electric field dependence of domain wall expansion rate.

[0104] Please see Figure 8 , Figure 8 The simulation results show the polarization intensity-electric field hysteresis curve (P–E hysteresis curve). Compared with hafnium-based FeCAP devices, the simulated P–E hysteresis curve in this application exhibits a significant rectangularity characteristic, which is consistent with the typical characteristics of wurtzite ferroelectric devices.

[0105] The simulation method for ferroelectric capacitors described above embeds the ferroelectric capacitor model into the simulator using the Veriloga module, directly outputting simulation signals that the simulator can recognize. This significantly improves simulation efficiency and shortens the device development cycle. It also overcomes the shortcomings of traditional models, which lack circuit-level interfaces and require manual processing of model output parameters before importing them into the simulator, resulting in low simulation efficiency.

[0106] Based on the same inventive concept, this application also provides a simulation system for ferroelectric capacitors, which is applicable to the above-mentioned simulation method for ferroelectric capacitors, and includes: a ferroelectric capacitor model and a simulator.

[0107] The ferroelectric capacitor model is constructed using the ferroelectric capacitor model construction method provided in the above embodiments.

[0108] The simulator contains a ferroelectric capacitor model embedded using a hardware description language.

[0109] The ferroelectric capacitance model is used to iteratively calculate the ferroelectric parameters for each time step based on the simulation parameters of the grain, until all time steps are completed and the output parameters are obtained. The time step is obtained by dividing a preset time. The simulation parameters include polarization state, damage factor and polarization reversal probability.

[0110] The simulator is used to simulate the target ferroelectric capacitance based on the output parameters.

[0111] The aforementioned ferroelectric capacitor simulation system embeds the ferroelectric capacitor model into the simulator via a Veriloga module, directly outputting simulation signals that the simulator can recognize. This significantly improves simulation efficiency and shortens the device development cycle. It overcomes the shortcomings of traditional models, which lack circuit-level interfaces and require manual processing of model output parameters before importing them into the simulator, resulting in low simulation efficiency.

[0112] In one feasible embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 9As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements the aforementioned method for constructing the ferroelectric capacitor model or the simulation method for ferroelectric capacitors. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0113] Those skilled in the art will understand that Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0114] In one feasible embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method steps in the above method.

[0115] In one feasible embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method steps described above.

[0116] In one feasible embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the method steps in the above-described method.

[0117] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0118] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0119] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for constructing a ferroelectric capacitance model, characterized in that, The method includes: The ferroelectric capacitor is decomposed into multiple independent grains; The damage factor of each grain is updated with time step based on the domain wall time constant; wherein the domain wall time constant is dynamic. Based on the damage factor and material coefficient, each of the grains is randomly sampled to obtain the polarization reversal probability of each grain; wherein, the material coefficient is calculated based on the real-time gate voltage at each time step; Based on the polarization reversal probability, it is determined whether each grain randomly flips during domain wall expansion, thereby determining the polarization state of each grain; Based on the polarization state of each grain, the ferroelectric index is calculated to obtain the ferroelectric capacitance model.

2. The method according to claim 1, characterized in that, The method of updating the damage factor of each grain with time steps based on the domain wall time constant includes: The domain wall time constant is calculated based on the gate voltage; Based on the domain wall time constant, calculate the damage increment of each grain per unit time; The damage factor is updated based on the damage increment.

3. The method according to claim 2, characterized in that, The domain wall time constant is calculated based on the gate voltage, and its expression is as follows: t_cv0=t0×(1 / ln(2)) 1 / (2×β_cv+3) ×exp(Ea / |Vgate|), where t_cv0 represents the domain wall time constant, t0 represents the initial domain wall time constant, Ea represents the activation energy, Vgate represents the gate voltage (which is not zero), and β_cv represents the material coefficient; The damage increment of each grain per unit time is calculated based on the domain wall time constant, and its expression is as follows: A_cv = Δt / t_cv0, where A_cv represents the damage increment per unit time; Δt represents the time step. The damage factor is updated based on the damage increment, and its expression is as follows: h t+Δt [i]=h t [i]+A_cv, where h t [i] represents the damage factor before the update, h t+Δt [i] represents the updated damage factor.

4. The method according to claim 3, characterized in that, The material coefficient is calculated based on the real-time gate voltage at each time step, including: β_cv = a × |Vgate|-b, where β_cv represents the material coefficient and β_cv ≥ -1, and a and b are parameter factors fitted based on experimental data.

5. The method according to claim 4, characterized in that, The step of randomly sampling each grain based on the damage factor and material coefficient to obtain the polarization reversal probability of each grain includes: P=1-exp(-h 2β_cv +3 (t+Δt)+h 2β_cv +3 (t)), where P represents the polarization reversal probability.

6. The method according to claim 5, characterized in that, The step of determining whether each grain randomly flips during domain wall expansion based on the polarization reversal probability, thereby determining the polarization state of each grain, includes: When the domain wall is at rest, it does not need to flip and maintains the polarization state of the previous time step; During domain wall expansion, the polarization reversal probability of the grain is compared with a random value based on the Monte Carlo framework. If the polarization reversal probability is greater than the random value, the grain is randomly flipped to obtain the polarization state of the grain after random reversal; otherwise, the polarization state of the grain in the previous time step is maintained. The method for determining domain wall expansion includes: comparing the gate voltage direction and polarization direction of each of the grains; if the directions are consistent, the domain wall is stationary; if the directions are inconsistent, the domain wall is considered to be expanding.

7. The method according to claim 1, characterized in that, The ferroelectric index includes domain flipping current; The calculation of ferroelectric properties based on the polarization state of each grain includes: By summing the polarization states of all the aforementioned grains, calculating the average polarization intensity, and then differentiating the domain flipping current, the expression is as follows: Igb = W × L ×d(∑Pi×Pr / N_grain) / dt, where Igb represents the domain flipping current at each time step, W and L represent the length and width of the channel, respectively, Pi represents the polarization state of the grain, Pr represents the remanent polarization intensity of different materials, and N_grain represents the number of grains.

8. A device for constructing a ferroelectric capacitance model, characterized in that, The device includes: An update module is used to update the damage factor of each grain with a time step based on the domain wall time constant; wherein the domain wall time constant is dynamic and the ferroelectric capacitance is decomposed into multiple independent grains. The first calculation module is used to calculate the material coefficient based on the real-time gate voltage at each time step; The second calculation module is used to randomly sample each grain according to the damage factor and material coefficient to obtain the polarization reversal probability of each grain. The processing module is used to determine whether each of the grains randomly flips during domain wall expansion based on the polarization flip probability, thereby determining the polarization state of each grain; and to calculate the ferroelectric index based on the polarization state of each grain to obtain the ferroelectric capacitance model.

9. A simulation method for ferroelectric capacitors, characterized in that, The method includes: Using a hardware description language, the ferroelectric capacitor model constructed by the method of constructing the ferroelectric capacitor model according to any one of claims 1-7 is embedded into a simulator to obtain a simulation system for ferroelectric capacitors; Divide the preset time into multiple time steps; Using the aforementioned simulation system, the ferroelectric parameters for each time step are calculated iteratively based on the simulation parameters of the grains until all time steps are completed, and the output parameters are obtained. Based on the output parameters, the target ferroelectric capacitance is simulated. The simulation parameters include polarization state, damage factor, and polarization reversal probability.

10. A simulation system for ferroelectric capacitors, characterized in that, The simulation system includes: The ferroelectric capacitor model constructed by the method of any one of claims 1-7 is a ferroelectric capacitor model. The simulator contains a ferroelectric capacitor model embedded in a hardware description language. The ferroelectric capacitance model is used to iteratively calculate the ferroelectric index for each time step based on the simulation parameters of the grain, until all time steps are completed, and the output parameters are obtained; wherein, the time step is obtained by dividing a preset time; the simulation parameters include polarization state, damage factor and polarization reversal probability; The simulator is used to simulate the target ferroelectric capacitor based on the output parameters.

11. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method described in claims 1-7 or 9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method described in claims 1-7 or 9.

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