Method and System for Establishing a Refined Model of Polyimide Charge Behavior under Multiple Stress Actions

Abstract

This application relates to a method and system for establishing a refined model of polyimide charge behavior under multiple stress actions, belonging to the technical field of material analysis. The method includes: performing a bias thermal stimulation current test on the polyimide material to be tested to obtain trap characteristics; differentiating trap charges at different energy levels according to the thermal stimulation current curve and the dielectric spectroscopy test results to obtain charge peaks of different properties; fitting the trap current according to the trap charge detrapping peak to obtain a trap current fitting curve, and then obtaining the trap energy level through the Arrhenius formula and the trap density by integrating the trap current fitting curve; obtaining the electron incident trajectory and electron energy deposition distribution through the Monte Carlo method, and calculating the electron deposition depth distribution; constructing a refined model of polyimide charge behavior based on the trap parameters and the electron deposition depth distribution. This application can accurately simulate the charge behavior inside the polyimide material.

Description

Technical Field

[0001] The present application relates to the technical field of material analysis, and particularly to a method and system for establishing a refined model of the charge behavior of polyimide under multi-stress action. Background Technique

[0002] Polyimide materials are widely used in the fields of electronics, electrical, and aerospace. As an insulating dielectric material, under the combined action of multi-stresses, a large amount of electron accumulation will occur inside it. When the accumulation reaches a certain level, a discharge process will be triggered, which will affect the insulation effect of the polyimide material. At the same time, the effects of electricity, heat, force, and irradiation will significantly change the morphology and potential barrier of the polyimide material. Therefore, accurately describing the charge behavior inside the polyimide is the key to studying the degradation mechanism of the polyimide material.

[0003] In the prior art, for example, the patent with the publication number CN118607290A and the patent name of a simulation method for the space charge distribution of a solid-solid insulation structure under high-frequency stress establishes a one-dimensional model of the polyimide-epoxy resin composite insulation structure and its interface under high-frequency stress to obtain the internal space charge distribution structure, thus providing some help for the research on the insulation degradation of the material to a certain extent. However, this technical solution cannot accurately judge the key parameters of mesoscopic parameters such as activation energy, relaxation time, trap density, and trap filling speed, cannot accurately simulate the internal charge behavior of the polyimide material, and it is difficult to ensure the performance of the polyimide material in applications.

[0004] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that the information disclosed in the above background section is only used to enhance the understanding of the background of the present disclosure, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The purpose of the embodiments of the present disclosure is to provide a method for establishing a refined model of the charge behavior of polyimide under multi-stress action, and thus at least to a certain extent overcome one or more problems caused by the limitations and defects of the related art.

[0007] In a first aspect, the present application provides a method for establishing a refined model of the charge behavior of polyimide under multi-stress action, including:

[0008] Performing a bias thermal stimulation current test on the polyimide material to be measured to obtain trap characteristics, where the trap characteristics include the thermal stimulation current curve and the dielectric spectrum test results;

[0009] According to the results of the thermally stimulated current curve and the dielectric spectroscopy test, trap charges at different energy levels are distinguished to obtain charge peaks of different properties, and the charge peaks of different properties include a dipole rotation polarization peak, a thermal ion polarization peak, and a trap charge detrapping peak;

[0010] The detrapping current is fitted according to the trap charge detrapping peak to obtain a fitted curve of the detrapping current, and then the trap energy level is obtained through the Arrhenius formula, and the trap density is obtained by integrating the fitted curve of the detrapping current;

[0011] The electron incident trajectory and the electron energy deposition distribution are obtained by the Monte Carlo method, and the electron deposition depth distribution is calculated;

[0012] According to the trap parameters and the electron deposition depth distribution, a refined model of the charge behavior of polyimide is constructed through the basic laws of charge motion, the law of conservation of charge, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion speed, trap parameters, and capture cross-section; the trap parameters include the trap energy level and the trap density.

[0013] In a possible implementation manner, the step of obtaining trap characteristics by performing a biased thermally stimulated current test on the polyimide material to be tested, where the trap characteristics include the results of the thermally stimulated current curve and the dielectric spectroscopy test, includes:

[0014] Biased voltages with different polarities and amplitudes are applied to both ends of the polyimide material to be tested;

[0015] Data of the thermally stimulated current changing with temperature are continuously collected and recorded to obtain thermally stimulated current curves under voltages with different polarities and amplitudes;

[0016] The dielectric spectroscopy test is performed by the planar capacitance method to obtain the capacitance value and the dielectric constant of the polyimide material to be tested.

[0017] In a possible implementation manner, the step of distinguishing trap charges at different energy levels according to the results of the thermally stimulated current curve and the dielectric spectroscopy test to obtain charge peaks of different properties, where the charge peaks of different properties include a dipole rotation polarization peak, a thermal ion polarization peak, and a trap charge detrapping peak, includes:

[0018] According to the results of the dielectric spectroscopy test, the thermally stimulated current curve is peak-fitted by Origin software;

[0019] The released charge amounts of each charge peak after peak-fitting are calculated to obtain the released charge amounts of each charge peak under different bias voltages;

[0020] According to the released charge amounts of each charge peak under different bias voltages, the change relationship of the released charge amount of each charge peak with the bias voltage is obtained;

[0021] According to the variation relationship between the released charge amount of each charge peak and the bias voltage, the charge properties corresponding to each charge peak are obtained.

[0022] In a possible implementation manner, the steps of fitting the trap current according to the trap charge detrapping peak to obtain a trap current fitting curve, and then obtaining the trap energy level through the Arrhenius formula and obtaining the trap density by integrating the trap current fitting curve include:

[0023] According to the trap charge detrapping peak, trap current data is selected from the thermally stimulated current curve, and the current formula is fitted through the first formula to obtain a trap current fitting curve; the first formula is , where is the variation function of the trap current with time, is the initial trap current, is the trap time constant;

[0024] Change the temperature to conduct multiple thermally stimulated current experiments to obtain the maximum trap current at different temperatures, and obtain the maximum trap current function at different temperatures through the Arrhenius formula. Among them, the maximum trap current formula is: , where is the maximum trap current, is the frequency factor, is the relaxation activation energy, is the gas constant, is the absolute temperature;

[0025] After taking the natural logarithm of both ends of the maximum trap current formula, and are linearly fitted, and the relaxation activation energy is calculated through the slope of the fitting straight line, and then the trap energy level is obtained through the relaxation activation energy; among them, the slope of the fitting straight line is ;

[0026] Integrate the trap current fitting curve, and obtain the trap density through the second formula. The second formula is , where is the natural constant, is the integral of the trap current fitting curve, is the volume, is the electronic charge.

[0027] In a possible implementation manner, the steps of obtaining the electron incident trajectory and the electron energy deposition distribution by the Monte Carlo method and calculating the electron deposition depth distribution include:

[0028] The two-body collision is used to describe the collision between the incident electron and the atomic nucleus of the material target; wherein, the energy of the incident electron is continuously and uniformly lost during the interaction with the electrons in the material between the two two-body collisions.

[0029] Set the simulation parameters of the polyimide material to be measured and the incident electrons in the Geant4 simulation software; wherein, the simulation parameters of the polyimide material to be measured include the atomic species, density, and lattice structure, and the simulation parameters of the incident electrons include the initial energy and the incident angle.

[0030] Simulate the motion of the incident electrons in the polyimide material to be measured through the Geant4 simulation software, and obtain the electron incident trajectory and the electron energy deposition distribution in the polyimide material to be measured.

[0031] Divide the polyimide material to be measured into depth intervals along the depth direction, judge the energy deposition amount or charge amount of the electrons in each depth interval, establish a coordinate system, and obtain the electron deposition depth distribution.

[0032] In a possible implementation manner, the step of constructing a refined polyimide charge behavior model according to the trap parameters and the electron deposition depth distribution through the basic motion law of charges, the law of conservation of charge, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion velocity, trap parameters, and capture cross-section includes:

[0033] According to the basic motion law of charges in the electric field, obtain the basic relationship between the charge current density and the electric field, charge concentration, and mobility. Then, through the fact that the mobility changes due to the influence of temperature, mechanical stress, and irradiation dose rate, obtain the dynamic charge transport equation, and the dynamic charge transport equation is ; wherein, is the charge current density, is the electron charge, is the electron concentration, is the charge mobility, is the electric field strength, is the absolute temperature, is the mechanical stress, is the irradiation dose rate;

[0034] In any infinitesimal volume element inside the material, obtain the electron concentration change rate equation according to the law of conservation of charge, and the electron concentration change rate equation is ; wherein, , ; is the rate of thermally excited electron-hole pair generation, is the irradiation ionization generation rate, is the dynamic recombination rate, is the electron concentration, is the hole concentration, is the electric field strength, is the carrier lifetime, is the room temperature bandgap, is the temperature coefficient, is the change in absolute temperature, is the Boltzmann constant, is the electron deposition depth distribution;

[0035] According to the hole generation and recombination mechanism, the hole concentration change rate equation is obtained. The hole concentration change rate equation is ;

[0036] Based on the change in thermal stress causing a change in thermal motion velocity, mechanical stress and irradiation changing the trap density and capture cross-section, and the electric field causing a change in trap energy levels to promote charge detrapping, a charge capture and release dynamic equation is established. The charge capture and release dynamic equation includes an electron capture rate dynamic equation and an electron release rate dynamic equation. Among them, the electron capture rate dynamic equation is , and the electron release rate dynamic equation is ; where is the electron capture rate, is the thermal motion velocity, is the trap density, is the capture cross-section, is the electron release rate, is the release cross-section, is the trap energy level;

[0037] Construct a refined model of the charge behavior of polyimide; the refined model of the charge behavior of polyimide includes:

[0038] .

[0039] In one possible implementation, the bias thermal stimulated current test is performed through a combined test platform. The combined test platform includes a temperature control module, an electrode module, a capacitance module, a signal acquisition module, and an analysis module; among them, the temperature control module is used to control the temperature, the electrode module is used to apply a bias voltage and measure the thermal stimulated current; the capacitance module is used to collect capacitance data; the signal acquisition module is used to collect current data, temperature data, capacitance data, plate area, and plate spacing, and transmit them to the analysis module; the analysis module is used to calculate the thermal stimulated current curve under different polarities and amplitudes of voltage according to the current and temperature data, and is used to calculate the dielectric constant according to the capacitance data, plate area, and plate spacing.

[0040] In one possible implementation, the trap energy level is calculated according to the third formula. The third formula is: ; where is the kinetic order, is the initial temperature, is the frequency factor, is the heating rate.

[0041] In a possible implementation manner, the trap parameters further include trap distribution and trap filling speed; wherein, the trap distribution is obtained by electron energy loss spectroscopy or secondary ion mass spectrometry, and the trap filling speed is calculated by the trap time constant of the detrapping current fitting curve.

[0042] In a second aspect, the present application provides a polyimide degradation analysis system under the synergistic action of multiple stresses. The system is used to execute the above-mentioned method for establishing a refined model of the charge behavior of polyimide under the action of multiple stresses. The system includes:

[0043] A bias thermal stimulation module, configured to perform a bias thermal stimulation current test on the polyimide material to be tested to obtain trap characteristics, where the trap characteristics include a thermal stimulation current curve and a dielectric spectroscopy test result;

[0044] A charge peak discrimination module, configured to distinguish trap charges at different energy levels according to the thermal stimulation current curve and the dielectric spectroscopy test result to obtain charge peaks of different properties, where the charge peaks of different properties include a dipole rotation polarization peak, a thermal ion polarization peak, and a trap charge detrapping peak;

[0045] A detrapping current fitting module, configured to fit the detrapping current according to the trap charge detrapping peak to obtain a detrapping current fitting curve, and further obtain trap energy levels through the Arrhenius formula and obtain trap density by integrating the detrapping current fitting curve;

[0046] A motion simulation module, configured to obtain electron incident trajectories and electron energy deposition distributions by the Monte Carlo method and calculate the electron deposition depth distribution;

[0047] A model establishment module, configured to construct a refined model of the charge behavior of polyimide according to the trap parameters and the electron deposition depth distribution through the basic motion law of charges, the law of conservation of charges, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion speed, trap parameters, and capture cross-section; the trap parameters include trap energy levels and trap density.

[0048] The technical solution provided by the present application may include the following beneficial effects:

[0049] Through the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in this application, trap characteristics can be obtained through the bias thermal stimulated current test, and trap charges at different energy levels can be distinguished to obtain charge peaks of different properties. Then, trap parameters can be obtained by processing the trap charge detrapping peaks, and the electron deposition depth distribution can be obtained through the Monte Carlo method. A refined model of the charge behavior of polyimide can be constructed to accurately simulate the charge behavior inside the polyimide material, providing assistance for analyzing the performance of polyimide materials in practical applications.

[0050] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. Brief Description of the Drawings

[0051] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0052] Figure 1 A flowchart showing the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0053] Figure 2 A detailed flowchart showing step S100 of the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0054] Figure 3 A detailed flowchart showing step S200 of the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0055] Figure 4 A detailed flowchart showing step S300 of the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0056] Figure 5 A detailed flowchart showing step S400 of the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0057] Figure 6 A detailed flowchart showing step S500 of the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure;

[0058] Figure 7Schematic diagram of the HFWT-TSC-PEA joint test system for establishing a refined model of the charge behavior of polyimide under multi-stress in an exemplary embodiment of the present disclosure;

[0059] Figure 8 Schematic diagram of the test method for the dynamic evolution law of space charge in the method for establishing a refined model of the charge behavior of polyimide under multi-stress in an exemplary embodiment of the present disclosure;

[0060] Figure 9 Schematic diagram of the refined description model of the charge behavior in the method for establishing a refined model of the charge behavior of polyimide under multi-stress in an exemplary embodiment of the present disclosure;

[0061] Figure 10 Schematic diagram of the structure of the system for establishing a refined model of the charge behavior of polyimide under multi-stress in an exemplary embodiment of the present disclosure. Detailed implementation manners

[0062] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments.

[0063] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repeated description will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0064] In the present example embodiment, a method for establishing a refined model of the charge behavior of polyimide under multi-stress is first provided. This method can be applied to a terminal device, such as a mobile terminal like a mobile phone, a desktop computer, a personal digital assistant, a laptop computer, a tablet computer, a smart watch, etc. Referring to Figure 1 as shown, this method may include the following steps:

[0065] Step S100: Perform a bias thermal stimulated current test on the polyimide material to be tested to obtain trap characteristics, where the trap characteristics include the thermal stimulated current curve and the dielectric spectrum test results.

[0066] Step S200: According to the thermally stimulated current curve and the dielectric spectroscopy test results, trap charges at different energy levels are distinguished to obtain charge peaks of different properties, and the charge peaks of different properties include dipole rotation polarization peaks, thermionic polarization peaks, and trap charge detrapping peaks.

[0067] Step S300: Fit the detrapping current according to the trap charge detrapping peak to obtain a detrapping current fitting curve, and then obtain the trap energy level through the Arrhenius formula and the trap density by integrating the detrapping current fitting curve.

[0068] Step S400: Obtain the electron incident trajectory and electron energy deposition distribution through the Monte Carlo method, and calculate the electron deposition depth distribution.

[0069] Step S500: According to the trap parameters and the electron deposition depth distribution, construct a refined model of the charge behavior of polyimide through the basic laws of charge motion, the law of conservation of charge, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion speed, trap parameters, and capture cross-section; the trap parameters include trap energy level and trap density.

[0070] Through the above method, the trap characteristics can be obtained through the biased thermally stimulated current test, and the trap charges at different energy levels are distinguished to obtain dipole rotation polarization peaks, thermionic polarization peaks, and trap charge detrapping peaks. Then, the detrapping current is fitted according to the trap charge detrapping peak to obtain a detrapping current fitting curve; according to the detrapping current fitting curve, the trap parameters are obtained through the Arrhenius formula and integration, and then the electron incident trajectory and electron energy deposition distribution are obtained through the Monte Carlo method, so as to calculate the electron deposition depth distribution; finally, a refined model of the charge behavior of polyimide is constructed through the trap parameters and the electron deposition depth distribution, so as to accurately simulate the charge behavior inside the polyimide material and provide help for analyzing the performance of the polyimide material in practical applications.

[0071] Next, reference will be made to Figures 1 to 6 to describe each step of the above method in the exemplary embodiment in more detail.

[0072] In step S100, the polyimide material to be tested is subjected to a biased thermally stimulated current test to obtain trap characteristics, and the trap characteristics include the thermally stimulated current curve and the dielectric spectroscopy test results.

[0073] It can be understood that under the action of electric field strength, temperature, tension, and irradiation alone or in combination, charges will be injected into the material and trapped by the traps existing in the material, and impurities in the material will also generate traps.

[0074] In one embodiment, such as Figure 2As shown, step S100 may include the following sub-steps:

[0075] In step S110, bias voltages with different polarities and amplitudes are applied to both ends of the polyimide material to be measured.

[0076] It can be understood that by applying bias voltages with different polarities and amplitudes to both ends of the material, using the thermally stimulated current theory, that is, during the heating process of the material, the charges in the traps will obtain sufficient energy to escape from the traps, generating a thermally stimulated current.

[0077] In step S120, the data of the thermally stimulated current changing with temperature are continuously collected and recorded to obtain the thermally stimulated current curves under different polarities and amplitudes of voltage.

[0078] In step S130, dielectric spectroscopy tests are carried out by the parallel-plate capacitance method to obtain the capacitance value and dielectric constant of the polyimide material to be measured.

[0079] It should be noted that the parallel-plate capacitance method is implemented based on a parallel-plate capacitor. The parallel-plate capacitor consists of two parallel plates that are very close to each other. When a voltage is applied to the two metal plates, positive charges will accumulate on one plate and negative charges will accumulate on the other plate, forming an electric field between the two metal plates. According to the parallel-plate capacitance formula (where is the capacitance, is the dielectric constant of the medium between the plates, is the area of the plates ， is the distance between the plates), when the area and distance of the plates are known, the dielectric constant can be calculated by measuring the capacitance.

[0080] Furthermore, the bias voltage thermally stimulated current test is carried out through the combined test platform as shown in Figure 7 . The combined test platform includes a temperature control module, an electrode module, a capacitance module, a signal acquisition module, and an analysis module; wherein, the temperature control module is used to control the temperature, the electrode module is used to apply a bias voltage and measure the thermally stimulated current; the capacitance module is used to collect capacitance data; the signal acquisition module is used to collect current data, temperature data, capacitance data, the area of the plates and the distance between the plates, and transmit them to the analysis module; the analysis module is used to calculate the thermally stimulated current curves under different polarities and amplitudes of voltage according to the current and temperature data, and is used to calculate the dielectric constant according to the capacitance data, the area of the plates and the distance between the plates.

[0081] In step S200, according to the thermally stimulated current curves and the results of the dielectric spectroscopy tests, the trap charges at different energy levels are distinguished to obtain different property charge peaks, and the different property charge peaks include a dipole rotation polarization peak, a thermal ion polarization peak, and a trap charge escape peak.

[0082] It can be understood that by means of the curve of current varying with temperature, the changing trends of the thermally stimulated current curves at different bias voltages are compared, and combined with the results of dielectric spectroscopy tests, three different types of charges, namely the dipole rotation polarization peak, the thermionic polarization peak, and the trapped charge detrapping peak, in the thermally stimulated current curve are distinguished. Using the Origin software, the curve is subjected to peak separation fitting in combination with the results of dielectric spectroscopy tests. After peak separation, the amount of charge released by each charge peak is calculated respectively. By comparing the relationship between the amount of charge released by each charge peak and the bias voltage at different bias voltages, the charge nature corresponding to each current peak is identified, so as to determine information such as the trap energy level distribution and trap density.

[0083] In one embodiment, as Figure 3 shown, step S200 may include the following sub-steps:

[0084] In step S210, according to the results of dielectric spectroscopy tests, the thermally stimulated current curve is subjected to peak separation fitting by the Origin software.

[0085] It can be understood that charges of different natures, such as dipole rotation polarization charges, thermionic polarization charges, and trapped charges, have different detrapping behaviors under thermal stimulation, and the characteristics such as the peak shape, peak position, and peak value reflected in the thermally stimulated current curve also vary. By comparing the changing trends of the thermally stimulated current curves at different bias voltages, different types of charge peaks can be preliminarily distinguished. For example, the dipole rotation polarization peak usually appears at a relatively low temperature and is related to the molecular structure and polarization characteristics of the material; the temperature range and variation law of the thermionic polarization peak are related to ion migration in the material; the trapped charge detrapping peak is closely related to the trap depth and the distribution of charges in the trap, and its peak position and peak value will change with the change of trap energy level and trap density.

[0086] In step S220, the amount of charge released by each charge peak after peak separation fitting is calculated to obtain the amount of charge released by each charge peak at different bias voltages.

[0087] In step S230, according to the amount of charge released by each charge peak at different bias voltages, the relationship between the amount of charge released by each charge peak and the change of bias voltage is obtained.

[0088] In step S240, according to the relationship between the amount of charge released by each charge peak and the change of bias voltage, the charge nature corresponding to each charge peak is obtained.

[0089] It is understandable that, optionally, when the charge release amount of a charge peak has a linear relationship with the electric field strength and increases with the increase in temperature within a certain temperature range, it is determined that this charge peak is a dipole rotation polarization peak; when the charge release amount of a charge peak increases sharply with the increase in temperature and is related to the concentration and mobility of ions in the material, it is determined that this charge peak is a thermal ion polarization peak; if the charge release amount of a charge peak shows an exponential growth trend with the increase in temperature and is related to the trap density in the material, it is determined that this charge peak is a trap charge detrapping peak.

[0090] In step S300, the detrapping current is fitted according to the trap charge detrapping peak to obtain a detrapping current fitting curve, and then the trap energy level is obtained through the Arrhenius formula, and the trap density is obtained by integrating the detrapping current fitting curve.

[0091] In one embodiment, as Figure 4 shown, step S300 may include the following sub-steps:

[0092] In step S310, according to the trap charge detrapping peak, detrapping current data is selected from the thermally stimulated current curve, and the current formula is fitted through the first formula to obtain a detrapping current fitting curve; the first formula is , where is the variation function of the detrapping current with time, is the initial detrapping current, is the detrapping time constant.

[0093] In step S320, through the above-mentioned variable temperature, multiple thermally stimulated current experiments are carried out to obtain the maximum detrapping current at different temperatures, and the maximum detrapping current function at different temperatures is obtained through the Arrhenius formula. Among them, the maximum detrapping current formula is: , where is the maximum detrapping current, is the frequency factor, is the relaxation activation energy, is the gas constant, is the absolute temperature. Among them, the gas constant is 8.314 J / (mol•K).

[0094] In step S330, after taking the natural logarithm of both ends of the maximum detrapping current formula, and are linearly fitted, and the relaxation activation energy is calculated through the slope of the fitting straight line, and then the trap energy level is obtained through the relaxation activation energy; among them, the slope of the fitting straight line is .

[0095] Further, the trap energy level is calculated according to the third formula, and the third formula is: ; where is the kinetic series, is the initial temperature, is the frequency factor, is the heating rate.

[0096] It can be understood that the basic formula for calculating the trap energy level is obtained, and the deformation formula , where is the number of traps, is the initial number of traps; during the thermal stimulation process, when the heating rate is , the relationship between the current caused by the detrapping of charged particles and the detrapping rate is , and the rate formula for the detrapping of charged particles from the trap is integrated, combined with the initial conditions , , to obtain , which is substituted into the deformation formula and simplified to obtain .

[0097] In step S340, the detrapping current fitting curve is integrated, and the trap density is obtained through the second formula. The second formula is , where is the natural constant, is the integral of the detrapping current fitting curve, is the volume, is the electron charge.

[0098] It can be understood that the integral of the fitting curve of the detrapping current is performed in the time interval to obtain the value of .

[0099] In one embodiment, the trap parameters further include trap distribution and trap filling speed; among them, the trap distribution is obtained through electron energy loss spectroscopy or secondary ion mass spectrometry, and the trap filling speed is calculated through the detrapping time constant of the detrapping current fitting curve.

[0100] It can be understood that the trap filling speed is calculated through the fourth formula, and the fourth formula is ; where is the trap filling speed, is the charge injection speed, is the change in the charge in the trap over time, is the detrapping time constant.

[0101] In step S400, the electron incident trajectory and the electron energy deposition distribution are obtained by the Monte Carlo method, and the electron deposition depth distribution is calculated.

[0102] It should be noted that, as Figure 8 shown, in the Geant4 simulation software, the Monte Carlo method is used to simulate the electron irradiation of the dielectric material to track the movement of the incident electrons, and the finite element electrodynamics is combined.

[0103] In one embodiment, as Figure 5 shown, step S400 may include the following sub-steps:

[0104] In step S410, the two-body collision is used to describe the collision between the incident electron and the atomic nucleus of the material target; wherein, the incident electron continuously and uniformly loses energy during the interaction with the electrons in the material between the two two-body collisions.

[0105] It should be noted that through the description of the two-body collision, the incident electron continuously and uniformly loses energy during the interaction with the electrons in the material.

[0106] In step S420, the simulation parameters of the polyimide material to be measured and the incident electrons are set in the Geant4 simulation software; wherein, the simulation parameters of the polyimide material to be measured include the atomic species, density and lattice structure, and the simulation parameters of the incident electrons include the initial energy and the incident angle.

[0107] It should be noted that when studying the polyimide material, the initial parameters of the electrons need to be set first. In the Geant4 simulation software, information such as the atomic species, density and lattice structure of the polyimide material to be measured needs to be clarified. These parameters determine the basic environment for the electrons to move in the material. At the same time, the initial energy and the incident angle of the incident electrons need to be set, which have a crucial impact on the subsequent movement trajectory of the electrons.

[0108] In step S430, the movement of the incident electrons in the polyimide material to be measured is simulated by the Geant4 simulation software, and the electron incident trajectory and the electron energy deposition distribution in the polyimide material to be measured are obtained.

[0109] It should be noted that after obtaining the basic motion information of electrons, the electron scattering trajectories of electrons incident on polyimide materials are further studied in combination with finite element electrodynamics. Finite element electrodynamics can accurately analyze factors such as the electric field distribution inside the material. By discretizing the material using the finite element method, it is divided into multiple small units, and the distribution of physical quantities such as the electric field is solved on each unit. During the electron incidence process, according to the electric field distribution of the material, the electrons will be affected by the electric field force, thereby changing their motion trajectories. This combination can more comprehensively consider the influence of various physical factors inside the material on the electron motion, making the simulation results closer to the actual situation. When analyzing the electron energy deposition distribution, factors such as electron-nucleus collisions, the motion of electrons in the electric field, and the interaction between electrons and other electrons in the material are comprehensively considered. During the electron-nucleus collision process, the electrons will lose part of their energy and change their motion directions, and this energy will be deposited near the collision position. The existence of the electric field will accelerate or change the motion path of the electrons, affecting the residence time and energy loss position of the electrons in the material, thereby affecting the energy deposition distribution. Through the detailed analysis and simulation of these processes, the electron energy deposition distribution in the polyimide material to be measured is finally obtained.

[0110] In step S440, the polyimide material to be measured is divided into depth intervals along the depth direction, the energy deposition amount or charge amount of electrons in each depth interval is judged, a coordinate system is established, and the electron deposition depth distribution is obtained.

[0111] It can be understood that according to the thickness of the material and the accuracy requirements of the research, the material is divided into several small intervals along the depth direction. For example, the polyimide material is divided into multiple intervals of equal thickness from the surface to the inside, and the thickness of each interval is ; for each electron incidence trajectory, according to its energy deposition distribution, the energy deposition amount of electrons in each depth interval is judged. When electrons have energy deposition in a certain depth interval, the deposited energy or the corresponding charge amount is accumulated into the deposition amount statistics of this interval. Traverse all electron incidence trajectories to complete the statistical calculation of the electron deposition amount in each depth interval, and obtain the total electron deposition amount in each depth interval (or the total charge amount ), where is the th depth interval; with the depth as the abscissa and the electron deposition amount as the ordinate, an electron deposition depth distribution curve is plotted. Discrete data points can be used to represent the deposition amount of each depth interval, or appropriate fitting can be performed according to the data characteristics to obtain a continuous electron deposition depth distribution function .

[0112] In step S500, according to the trap parameters and the electron deposition depth distribution, a refined polyimide charge behavior model is constructed through the basic laws of charge motion, the law of conservation of charge, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion velocity, trap parameters, and capture cross-section; the trap parameters include trap energy levels and trap densities.

[0113] In one embodiment, as Figure 6 shown, step S500 may include the following sub-steps:

[0114] In step S510, according to the basic law of charge motion in an electric field, the basic relationship between charge current density and electric field, charge concentration, and mobility is obtained. Then, considering that the mobility changes due to the influence of temperature, mechanical stress, and irradiation dose rate, the dynamic charge transport equation is obtained. The dynamic charge transport equation is ; where is the charge current density, is the electron charge, is the electron concentration, is the charge mobility, is the electric field strength, is the absolute temperature, is the mechanical stress, is the irradiation dose rate.

[0115] In step S520, within any infinitesimal volume element inside the material, the electron concentration change rate equation is obtained according to the law of conservation of charge. The electron concentration change rate equation is ; where , ; is the rate of electron-hole pair generation by thermal excitation, is the ionization generation rate by irradiation, is the dynamic recombination rate, is the electron concentration, is the hole concentration, is the electric field strength, is the carrier lifetime, is the room temperature bandgap, is the temperature coefficient, is the absolute temperature change, is the Boltzmann constant, is the electron deposition depth distribution.

[0116] In step S530, according to the generation and recombination mechanism of holes, the hole concentration change rate equation is obtained. The hole concentration change rate equation is .

[0117] In step S540, based on the fact that the thermal motion speed changes due to the change in thermal stress, the mechanical stress and irradiation change the trap density and capture cross-section, and the electric field changes the trap energy level to promote charge detrapping, a dynamic equation for charge capture and release is established. The dynamic equation for charge capture and release includes a dynamic equation for electron capture rate and a dynamic equation for electron release rate. Among them, the dynamic equation for electron capture rate is and the dynamic equation for electron release rate is ; where is the electron capture rate, is the trap density, is the capture cross-section, is the electron release rate, is the release cross-section, is the trap energy level, is the thermal motion speed, , is the effective mass of the carrier.

[0118] In step S550, a refined model of the charge behavior of polyimide is constructed; the refined model of the charge behavior of polyimide includes:

[0119] .

[0120] It can be understood that the relationship between charge current density and electric field, charge concentration and mobility is . The mobility under multi-stress will change, thus obtaining the dynamic charge transport equation ( is the absolute temperature, is the mechanical stress, is the irradiation dose rate), which reflects the coupling law of charge transport under the drive of multi-stress electric field by multiple factors.

[0121] According to the Boltzmann distribution, the rate of electron-hole pair generation by thermal excitation , under thermal stress , will change, obtaining the rate of electron-hole pair generation by thermal excitation , which is an important source of charge generation, especially dominating charge generation at high temperatures. The charge generation by irradiation ionization Rate , is the irradiation dose rate, is the ionization efficiency, which is related to the irradiation type, energy and material interaction. Considering the depth distribution of electron deposition , a depth-variable irradiation generation term is constructed to reflect the charge generation distribution characteristics under irradiation. According to the case where the Shockley-Reed-Hall recombination dominates, the recombination rate ( is the electron lifetime, is the hole lifetime, determined according to the trap energy level, determined according to the Fermi energy level, is the intrinsic carrier concentration). Charge accumulation induces an electric field, and the change in carrier concentration affects recombination. The increase in the electric field promotes recombination. According to Poisson's equation ( is the dielectric constant) and the charge continuity equation are solved simultaneously to obtain the dynamic recombination rate , which accurately describes the process of charge dynamic balance being disturbed by multiple factors. Thermal stress changes ( is the effective mass of the carrier), and mechanical stress and irradiation will change and , and the electric field will make change to promote charge detrapping, thereby establishing a dynamic equation for charge capture and release, indicating the interaction between charge and trap evolving with the environment, as shown in Figure 9 .

[0122] Furthermore, in this exemplary embodiment, a polyimide degradation analysis system under the synergistic action of multiple stresses is also provided. As shown in reference Figure 10 , the system may include:

[0123] A bias thermal stimulation module for performing a bias thermal stimulation current test on the polyimide material to be tested to obtain trap characteristics, where the trap characteristics include the thermal stimulation current curve and the dielectric spectroscopy test results;

[0124] A charge peak discrimination module for discriminating trap charges of different energy levels according to the thermal stimulation current curve and the dielectric spectroscopy test results to obtain charge peaks of different properties, where the charge peaks of different properties include dipole rotation polarization peaks, thermionic polarization peaks, and trap charge detrapping peaks;

[0125] A detrapping current fitting module for fitting the detrapping current according to the trap charge detrapping peak to obtain a detrapping current fitting curve, and then obtaining the trap energy level through the Arrhenius formula and obtaining the trap density by integrating the detrapping current fitting curve;

[0126] A motion simulation module for obtaining the electron incident trajectory and electron energy deposition distribution by the Monte Carlo method and calculating the electron deposition depth distribution;

[0127] A model establishment module, configured to construct a refined polyimide charge behavior model according to trap parameters and the electron deposition depth distribution, through the basic laws of charge motion, the law of conservation of charge, the generation and recombination mechanism of holes, and the influence mechanism of multi-stress changes on the thermal motion velocity, trap parameters, and capture cross-section; the trap parameters include trap energy levels and trap density, and the refined polyimide charge behavior model.

[0128] Optionally, the refined polyimide charge behavior model includes:

[0129] ;

[0130] Among them, , ;

[0131] is the charge current density, is the electron charge, is the electron concentration, is the charge mobility, is the electric field strength, is the absolute temperature, is the mechanical stress, is the irradiation dose rate, is the rate of thermally excited electron-hole pair generation, is the irradiation ionization generation rate, is the carrier lifetime, is the room temperature bandgap, is the temperature coefficient, is the Boltzmann constant, is the electron deposition depth distribution, is the dynamic recombination rate, is the electron concentration, is the hole concentration, is the electric field strength, is the trap density, is the electron capture rate, is the thermal motion velocity, is the capture cross-section, is the electron release rate, is the release cross-section, is the trap energy level.

[0132] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0133] It should be noted that although several modules or units of a device for action execution are mentioned in the above detailed description, such a division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more of the above-described modules or units can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units. The components shown as modules or units may or may not be physical units, that is, they may be located in one place or may be distributed over multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present disclosure. A person of ordinary skill in the art can understand and implement it without creative work.

[0134] Those skilled in the art will readily conceive of other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include known common knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and examples are only regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the appended claims.

Claims

1. A method for establishing a refined model of charge behavior of polyimide under multiple stresses, characterized in that: include: Conducting a biased thermal stimulation current test on the polyimide material to be tested to obtain trap characteristics, wherein the trap characteristics include a thermal stimulation current curve and a dielectric spectrum test result; According to the thermal stimulation current curve and the dielectric spectrum test results, the trapped charges at different energy levels are distinguished to obtain charge peaks with different properties, wherein the charge peaks with different properties include dipole steering polarization peak, thermal ion polarization peak and trapped charge detrapping peak; Fitting the trap current according to the trap charge trap peak to obtain a trap current fitting curve, and then obtaining the trap energy level through the Arrhenius formula, and obtaining the trap density by integrating the trap current fitting curve; According to the trap charge detrapping peak, detrapping current data is selected from the thermal stimulation current curve, and the current formula is fitted by the first formula to obtain a detrapping current fitting curve; the first formula is: ,in, is the function of the detrapping current changing with time, is the initial detrapping current, is the escape time constant; The temperature was changed to conduct multiple thermal stimulation current experiments to obtain the maximum detrapping current at different temperatures. The maximum detrapping current function at different temperatures was obtained by the Arrhenius formula, where the maximum detrapping current formula is: ,in, is the maximum dropout current, is the frequency factor, is the relaxation activation energy, is the gas constant, is the absolute temperature; After taking the natural logarithm of both ends of the maximum de-entrapment current formula, and Perform linear fitting, calculate the relaxation activation energy by the slope of the fitting line, and then obtain the trap energy level by the relaxation activation energy; wherein the slope of the fitting line is ; The trap current fitting curve is integrated to obtain the trap density by a second formula, wherein the second formula is: ,in, is a natural constant, is the integral of the trap current fitting curve, is the volume, is the electron charge; The electron incident trajectory and electron energy deposition distribution are obtained by Monte Carlo method, and the electron deposition depth distribution is calculated; According to the trap parameters and the electron deposition depth distribution, a refined model of polyimide charge behavior is constructed through the basic laws of charge movement, the law of charge conservation, the generation and recombination mechanism of holes, and the influence mechanism of multiple stress changes on thermal motion speed, trap parameters and capture cross-section; the trap parameters include trap energy level and trap density.

2. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The step of subjecting the polyimide material to be tested to a biased thermal stimulation current test to obtain trap characteristics, wherein the trap characteristics include a thermal stimulation current curve and a dielectric spectrum test result, comprises: Apply bias voltages of different polarities and amplitudes to both ends of the polyimide material to be tested; Continuously collect and record the data of thermal stimulation current changing with temperature, and obtain thermal stimulation current curves under different polarities and amplitude voltages; The dielectric spectrum test is carried out by the flat plate capacitance method to obtain the capacitance value and dielectric constant of the polyimide material to be tested.

3. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The step of distinguishing the trapped charges at different energy levels according to the thermal stimulation current curve and the dielectric spectrum test results to obtain charge peaks with different properties, wherein the charge peaks with different properties include a dipole steering polarization peak, a thermal ion polarization peak and a trapped charge detrapping peak, comprises: According to the dielectric spectrum test results, the thermal stimulation current curve was peak-fitted using Origin software; Calculate the released charge amount of each charge peak after peak fitting, and obtain the released charge amount of each charge peak under different bias voltages; According to the released charge amount of each charge peak under different bias voltages, the relationship between the released charge amount of each charge peak and the change of bias voltage is obtained; According to the relationship between the amount of charge released from each charge peak and the change of the bias voltage, the charge properties corresponding to each charge peak are obtained.

4. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The step of obtaining the electron incident trajectory and the electron energy deposition distribution by the Monte Carlo method and calculating the electron deposition depth distribution comprises: Two-body collision is used to describe the collision between the incident electron and the target nucleus of the material; wherein, between two two-body collisions, the incident electron continuously and evenly loses energy through interaction with the electrons in the material; The simulation parameters of the polyimide material to be tested and the incident electrons are set in the Geant4 simulation software; wherein the simulation parameters of the polyimide material to be tested include the atomic type, density and lattice structure, and the simulation parameters of the incident electrons include the initial energy and the incident angle; The movement of incident electrons in the polyimide material to be tested is simulated by using Geant4 simulation software to obtain the electron incident trajectory and the electron energy deposition distribution in the polyimide material to be tested; The polyimide material to be tested is divided into depth intervals along the depth direction, the energy deposition amount or charge amount of the electrons in each depth interval is determined, a coordinate system is established, and the electron deposition depth distribution is obtained.

5. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The step of constructing a refined model of polyimide charge behavior according to the trap parameters and the electron deposition depth distribution, through the basic laws of charge movement, the law of charge conservation, the generation and recombination mechanism of holes, and the influence mechanism of multiple stress changes on thermal motion speed, trap parameters and capture cross section, includes: According to the basic movement law of charge in the electric field, the basic relationship between charge current density and electric field, charge concentration and mobility is obtained. Then, the mobility will change due to the influence of temperature, mechanical stress and irradiation dose rate, and the dynamic charge transport equation is obtained. The dynamic charge transport equation is: ;in, is the charge current density, is the electron charge, is the electron concentration, is the charge mobility, is the electric field strength, is the absolute temperature, is the mechanical stress, is the irradiation dose rate; In any small volume element inside the material, the electron concentration change rate equation is obtained according to the law of conservation of charge. The electron concentration change rate equation is: ;in, , ; is the rate of electron-hole pair generation by thermal excitation, is the radiation ionization rate, is the dynamic recombination rate, is the electron concentration, is the hole concentration, is the electric field strength, is the carrier lifetime, is the room temperature band gap, is the temperature coefficient, is the absolute temperature change, is the Boltzmann constant, is the electron deposition depth distribution; According to the hole generation and recombination mechanism, the hole concentration change rate equation is obtained, which is: ; According to the change of thermal stress causing the change of thermal motion speed, the change of trap density and capture cross section by mechanical stress and irradiation, and the change of trap energy level by electric field to promote charge detrapping, a charge capture and release dynamic equation is established, which includes the electron capture rate dynamic equation and the electron release rate dynamic equation, wherein the electron capture rate dynamic equation is: , the electron release rate dynamic equation is ;in, is the electron capture rate, is the speed of thermal motion, is the trap density, To capture the cross section, is the electron release rate, To release the cross section, is the trap energy level; Constructing a refined model of polyimide charge behavior; the refined model of polyimide charge behavior includes: 。 6. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The biased thermal stimulation current test is carried out through a joint test platform, which includes a temperature control module, an electrode module, a capacitor module, a signal acquisition module and an analysis module; wherein the temperature control module is used to control the temperature, the electrode module is used to apply a bias voltage, and to measure the thermal stimulation current; the capacitor module is used to collect capacitance data; the signal acquisition module is used to collect current data, temperature data, capacitance data, plate area and plate spacing, and transmit them to the analysis module; the analysis module is used to calculate the thermal stimulation current curve under different polarities and amplitude voltages according to the current and temperature data, and to calculate the dielectric constant according to the capacitance data, plate area and plate spacing.

7. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The trap energy level is calculated according to a third formula, which is: ;in, is the kinetic series, is the initial temperature, is the frequency factor, is the heating rate.

8. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 1, characterized in that: The trap parameters also include trap distribution and trap filling speed; wherein the trap distribution is obtained by electron energy loss spectrum or secondary ion mass spectrum, and the trap filling speed is calculated by the trap time constant of the trap current fitting curve.

9. A polyimide degradation analysis system under multi-stress synergistic action, characterized in that: The system is used to execute the method according to any one of claims 1 to 8, and the system comprises: A biased thermal stimulation module is used to perform a biased thermal stimulation current test on the polyimide material to be tested to obtain trap characteristics, wherein the trap characteristics include a thermal stimulation current curve and a dielectric spectrum test result; A charge peak differentiation module is used to differentiate trapped charges of different energy levels to obtain charge peaks of different properties according to the thermal stimulation current curve and the dielectric spectrum test results. The charge peaks of different properties include dipole steering polarization peaks, thermal ion polarization peaks and trapped charge detrapping peaks; A trap current fitting module is used to fit the trap current according to the trap charge trap peak to obtain a trap current fitting curve, and then obtain the trap energy level through the Arrhenius formula and obtain the trap density by integrating the trap current fitting curve; Motion simulation module, used to obtain electron incident trajectory and electron energy deposition distribution through Monte Carlo method, and calculate electron deposition depth distribution; The model building module is used to construct a refined model of polyimide charge behavior based on the trap parameters and the electron deposition depth distribution, through the basic law of charge movement, the law of charge conservation, the generation and recombination mechanism of holes, and the influence mechanism of multiple stress changes on thermal motion speed, trap parameters and capture cross-section; the trap parameters include trap energy level and trap density.

Images