Multi-stress polyimide charge behavior refined model establishment method and system

Abstract

The invention relates to a multi-stress polyimide charge behavior refined model establishment method and system, and relates to the technical field of material analysis, and the method comprises the steps: carrying out a bias thermally stimulated current test on a to-be-tested polyimide material to obtain trap characteristics; according to a thermally stimulated current curve and a dielectric spectrum test result, the trapped charges of different energy levels are distinguished to obtain charge peaks of different properties; fitting the trap removal current according to the trap charge trap removal peak to obtain a trap removal current fitting curve, further obtaining a trap energy level through an Arrhenius formula, and integrating the trap removal current fitting curve to obtain trap density; an electron incidence track and electron energy deposition distribution are obtained through a Monte Carlo method, and electron deposition depth distribution is calculated; and according to the trap parameters and the electron deposition depth distribution, constructing a polyimide charge behavior refined model. According to the invention, the charge behavior in the polyimide material can be accurately simulated.

Description

Technical Field

[0001] The present application relates to the technical field of material analysis, and in particular to a method and system for establishing a refined model of charge behavior of polyimide under multiple stresses. Background Art

[0002] Polyimide materials are widely used in electronics, electrical engineering, aerospace and other fields. As insulating dielectric materials, a large amount of electrons will accumulate inside them under the synergistic effect of multiple stresses. When the accumulation reaches a certain level, it will trigger a discharge process, thereby affecting the insulation effect of the polyimide material. At the same time, electricity, heat, force and radiation will significantly change the morphology and potential barriers of polyimide materials. Therefore, accurately describing the charge behavior inside polyimide is the key to studying the degradation mechanism of polyimide materials.

[0003] In the prior art, for example, the patent publication number CN118607290A, entitled "A method for simulating spatial charge distribution in solid-solid insulating structures under high-frequency stress", establishes a one-dimensional model of a polyimide-epoxy composite insulating structure and its interface under high-frequency stress to obtain the internal spatial charge distribution structure, thereby providing assistance to the study of the insulation degradation of the material to a certain extent. However, this technical solution cannot accurately determine 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 polyimide materials, and is difficult to guarantee the performance of polyimide materials 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 technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. 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 charge behavior of polyimide under multiple stresses, thereby overcoming one or more problems caused by limitations and defects of related technologies at least to a certain extent.

[0007] In a first aspect, the present application provides a method for establishing a refined model of charge behavior of polyimide under multiple stresses, comprising: 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; 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.

[0008] In a possible implementation, 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.

[0009] In a possible implementation, the step of distinguishing 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, wherein the charge peaks of 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.

[0010] In a possible implementation, the step of 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 by the Arrhenius formula, and obtaining the trap density by integrating the trap current fitting curve includes: 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 time-varying function of the detrapping current, 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.

[0011] In a possible implementation, 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.

[0012] In a possible implementation, 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 law of charge motion, 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 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: .

[0013] In a possible embodiment, the biased thermal stimulation current test is performed 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 based on the current and temperature data, and to calculate the dielectric constant based on the capacitance data, plate area and plate spacing.

[0014] In a possible implementation manner, the trap energy level is calculated according to a third formula, and the third formula is: ;in, is the kinetic series, is the initial temperature, is the frequency factor, is the heating rate.

[0015] In a possible implementation, the trap parameters further include trap distribution and trap filling speed; wherein the trap distribution is obtained by electron energy loss spectrum or secondary ion mass spectrometry, and the trap filling speed is calculated by the trap time constant of the trap current fitting curve.

[0016] In a second aspect, the present application provides a polyimide degradation analysis system under the synergistic action of multiple stresses, the system being used to execute the above-mentioned method for establishing a refined model of polyimide charge behavior under multiple stresses, the system comprising: 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.

[0017] The technical solution provided by this application may have the following beneficial effects: Through the method for establishing a refined model of the charge behavior of polyimide under multiple stresses in the present application, it is possible to obtain trap characteristics through a bias thermal stimulation current test, and distinguish trapped charges at different energy levels to obtain charge peaks of different properties. The trap parameters are then obtained by processing the trap charge detrapping peaks, and the electron deposition depth distribution is obtained through the Monte Carlo method, thereby constructing a refined model of the charge behavior of polyimide, thereby accurately simulating the charge behavior inside the polyimide material, and providing assistance for analyzing the performance of the polyimide material in practical applications.

[0018] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0020] Figure 1 A flow chart showing a method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure; Figure 2 A detailed flow chart of step S100 of the method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown; Figure 3 A detailed flow chart of step S200 of the method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown; Figure 4 A detailed flow chart of step S300 of the method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown; Figure 5 A detailed flow chart of step S400 of the method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown; Figure 6 A detailed flow chart of step S500 of the method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown; Figure 7 A schematic diagram of a HFWT-TSC-PEA joint testing system showing a method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure; Figure 8 A schematic diagram showing a method for testing the dynamic evolution law of space charge of a method for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure; Fig. 9 A schematic diagram of a charge behavior refinement description model of a method for establishing a multi-stress polyimide charge behavior refinement model in an exemplary embodiment of the present disclosure is shown; Fig.10 A schematic diagram of the structure of a system for establishing a refined model of charge behavior of polyimide under multiple stresses in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0021] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0022] 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 figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0023] In this exemplary embodiment, a method for establishing a refined model of charge behavior of polyimide under multiple stresses is first provided. The method can be applied to a terminal device, such as a mobile phone, a desktop computer, a personal digital assistant, a laptop computer, a tablet computer, a smart watch, or other mobile terminal. Figure 1 As shown in , the method may include the following steps: Step S100: performing 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.

[0024] Step S200: 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 a dipole steering polarization peak, a thermal ion polarization peak and a trapped charge detrapping peak.

[0025] Step S300: 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.

[0026] Step S400: obtaining the electron incident trajectory and the electron energy deposition distribution by using the Monte Carlo method, and calculating the electron deposition depth distribution.

[0027] Step S500: 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 charge conservation, the generation and recombination mechanism of holes, and the influence mechanism of multiple stress changes on the thermal motion speed, trap parameters and capture cross-section; the trap parameters include trap energy levels and trap density.

[0028] Through the above method, the trap characteristics can be obtained through the biased thermal stimulation current test, and the trapped charges of different energy levels can be distinguished to obtain the dipole steering polarization peak, thermionic polarization peak and the trapped charge detrapping peak, and then the detrapping current is fitted through the trapped charge detrapping peak to obtain the detrapping current fitting curve; according to the trap 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 polyimide charge behavior 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 polyimide materials in practical applications.

[0029] Next, we will refer to Figures 1 to 6 Each step of the above method in this example implementation is described in more detail.

[0030] In step S100, a biased thermal stimulation current test is performed 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.

[0031] It can be understood that under the action of field strength, temperature, tension and radiation alone or in combination, charges will be injected into the material and bound by traps existing in the material, and impurities in the material will also produce traps.

[0032] In one embodiment, Figure 2 As shown, step S100 may include the following sub-steps: In step S110, bias voltages of different polarities and amplitudes are applied to two ends of the polyimide material to be tested.

[0033] It can be understood that by applying bias voltages of different polarities and amplitudes to both ends of the material, using the theory of thermally stimulated current, that is, when the material is heated, the charges in the traps will gain enough energy to be released, generating thermally stimulated current.

[0034] In step S120, data of thermal stimulation current changing with temperature is continuously collected and recorded to obtain thermal stimulation current curves under different polarities and amplitude voltages.

[0035] In step S130, a dielectric spectrum test is performed using a flat plate capacitance method to obtain a capacitance value and a dielectric constant of the polyimide material to be tested.

[0036] It should be noted that the flat plate capacitor method is based on the flat plate capacitor, which consists of two parallel plates close to each other. When a voltage is applied to the two metal plates, positive charge accumulates on one plate and negative charge accumulates on the other plate, forming an electric field between the two metal plates. (in is the capacitance, is the dielectric constant of the medium between the plates, The plate area ， is the plate spacing), the dielectric constant can be calculated by measuring the capacitance when the plate area and spacing are known.

[0037] Furthermore, by Figure 7 The combined test platform shown in the figure performs the biased thermal stimulation current test, and the combined test platform 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.

[0038] In step S200, according to the thermal stimulation current curve and the dielectric spectrum test results, the trapped charges of different energy levels are distinguished to obtain charge peaks of different properties, wherein the charge peaks of different properties include dipole steering polarization peaks, thermal ion polarization peaks and trapped charge detrapping peaks.

[0039] It can be understood that by comparing the change trend of the thermal stimulation current curve under different bias voltages through the curve of current change with temperature, and combining the dielectric spectrum test results, the three different types of charges in the thermal stimulation current curve, namely the dipole steering polarization peak, the hot ion polarization peak, and the trap charge decapping peak, are distinguished. Combined with the dielectric spectrum test results, the Origin software is used to perform peak fitting on the curve, and the amount of charge released by each charge peak is calculated after peak separation. Compare the relationship between the amount of charge released by each charge peak under different bias voltages and the bias voltage, so as to identify the charge properties corresponding to each current peak, and thus determine information such as the trap energy level distribution and trap density.

[0040] In one embodiment, Figure 3As shown, step S200 may include the following sub-steps: In step S210, the thermal stimulation current curve is peak-fitted using Origin software according to the dielectric spectrum test results.

[0041] It is understandable that charges of different properties, such as dipole steering polarization charge, thermoionic polarization charge and trapped charge, have different detrapping behaviors under thermal stimulation, which are reflected in the peak shape, peak position and peak value of the thermal stimulation current curve. By comparing the changing trends of the thermal stimulation current curve under different bias voltages, charge peaks of different properties can be preliminarily distinguished. For example, the dipole steering polarization peak usually appears at lower temperatures and is related to the molecular structure and polarization characteristics of the material; the temperature range and variation law of the thermoionic polarization peak are related to the ion migration in the material; the trap charge detrapping peak is closely related to the trap depth and the distribution of charge in the trap, and its peak position and peak value will change with the changes in the trap energy level and trap density.

[0042] In step S220, the released charge amount of each charge peak after peak fitting is calculated to obtain the released charge amount of each charge peak under different bias voltages.

[0043] In step S230, according to the released charge amount of each charge peak under different bias voltages, the variation relationship between the released charge amount of each charge peak and the change of the bias voltage is obtained.

[0044] In step S240, the charge properties corresponding to each charge peak are obtained according to the variation relationship between the amount of charge released from each charge peak and the variation of the bias voltage.

[0045] It can be understood that, optionally, if the amount of charge released from a charge peak is linearly related to the electric field strength and increases with increasing temperature within a certain temperature range, then this charge peak is judged to be a dipole steering polarization peak; if the amount of charge released from a charge peak increases sharply with increasing temperature and is related to the concentration and mobility of ions in the material, then this charge peak is judged to be a thermal ion polarization peak; if the amount of charge released from a charge peak shows an exponential growth trend with increasing temperature and is related to the trap density in the material, then this charge peak is judged to be a trapped charge detrapping peak.

[0046] In step S300, the trap current is fitted according to the trap charge trap peak to obtain a trap current fitting curve, and then the trap energy level is obtained by using the Arrhenius formula, and the trap density is obtained by integrating the trap current fitting curve.

[0047] In one embodiment, Figure 4 As shown, step S300 may include the following sub-steps: In step S310, 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 a first formula to obtain a detrapping current fitting curve; the first formula is: ,in, is the time-varying function of the detrapping current, is the initial detrapping current, is the detrapping time constant.

[0048] In step S320, multiple thermal stimulation current experiments are performed by varying the temperature to obtain the maximum detrapping current at different temperatures, and the maximum detrapping current function at different temperatures is obtained by the Arrhenius formula, wherein 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. Among them, the gas constant It is 8.314J / (mol•K).

[0049] In step S330, after taking the natural logarithm of both ends of the maximum detrapping 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 .

[0050] Further, the trap energy level is calculated according to a third formula, and the third formula is: ;in, is the kinetic series, is the initial temperature, is the frequency factor, is the heating rate.

[0051] It can be understood that the basic formula for calculating the trap energy level is Get, the deformation formula ,in, is the number of traps, is the initial number of traps; during the thermal stimulation process, when the heating rate is When the charged particle detrapping current and the detrapping rate are , the rate formula for the escape of charged particles from the trap is Integrate and combine the initial conditions , ,get , substitute into the deformation formula In the simplification, we get .

[0052] In step S340, the trap current fitting curve is integrated to obtain the trap density using a second formula, where 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.

[0053] It is understandable that the de-entrapment current The fitting curve of Integrate on The value of .

[0054] In one embodiment, 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 trap current fitting curve.

[0055] It is understood that the trap filling rate is calculated by the fourth formula, which is ;in, is the trap filling speed, is the charge injection rate, is the change of charge in the trap over time, is the detrapping time constant.

[0056] In step S400, the electron incident trajectory and the electron energy deposition distribution are obtained by using the Monte Carlo method, and the electron deposition depth distribution is calculated.

[0057] It should be noted that if Figure 8 As shown, in the Geant4 simulation software, the Monte Carlo method is used to simulate the electron irradiation dielectric material to track the motion of the incident electrons, and combined with finite element electrodynamics.

[0058] In one embodiment, Figure 5 As shown, step S400 may include the following sub-steps: In step S410, 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 due to the interaction with the electrons in the material.

[0059] It should be noted that, through the description of two-body collision, the incident electrons interact with the electrons in the material and lose energy continuously and uniformly.

[0060] In step S420, simulation parameters of the polyimide material to be tested and incident electrons are set in Geant4 simulation software; wherein the simulation parameters of the polyimide material to be tested include atomic species, density and lattice structure, and the simulation parameters of the incident electrons include initial energy and incident angle.

[0061] It should be noted that when studying polyimide materials, the initial parameters of the electrons must be set first. In the Geant4 simulation software, it is necessary to clarify the atomic type, density, and lattice structure of the polyimide material to be tested. These parameters determine the basic environment for the movement of electrons in the material. At the same time, the initial energy and incident angle of the incident electrons must be set, which has a key impact on the subsequent movement trajectory of the electrons.

[0062] In step S430, 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 of the electrons in the polyimide material to be tested.

[0063] It should be noted that after obtaining the basic motion information of electrons, the electron scattering trajectory of the incident polyimide material is further studied in combination with finite element electrodynamics. Finite element electrodynamics can accurately analyze factors such as the electric field distribution inside the material. The material is discretized by the finite element method and divided into multiple small units. The distribution of physical quantities such as the electric field is solved on each unit. During the electron incident process, the electron will be affected by the electric field force according to the electric field distribution of the material, thereby changing its motion trajectory. 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 the collision between electrons and atomic nuclei, the motion of electrons in the electric field, and the interaction between electrons and other electrons in the material are comprehensively considered. During the collision between electrons and atomic nuclei, electrons will lose part of their energy and change their direction of motion, and this energy will be deposited near the collision position. The presence 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 detailed analysis and simulation of these processes, the electron energy deposition distribution in the polyimide material to be tested is finally obtained.

[0064] In step S440, 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.

[0065] It is understandable 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 incident trajectory, the energy deposition amount of the electron in each depth interval is determined according to its energy deposition distribution. When the electron deposits energy in a certain depth interval, its deposited energy or corresponding charge is added to the deposition amount statistics of the interval. All electron incident trajectories are traversed to complete the statistical calculation of the electron deposition amount in each depth interval, and the total electron deposition amount in each depth interval is obtained. (or total charge ),in For the depth interval; The electron deposition depth distribution curve is plotted with the electron deposition amount as the horizontal axis and the electron deposition amount as the vertical axis. Discrete data points can be used to represent the deposition amount in each depth interval, or appropriate fitting can be performed according to the characteristics of the data to obtain a continuous electron deposition depth distribution function. .

[0066] In step S500, 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.

[0067] In one embodiment, Figure 6 As shown, step S500 may include the following sub-steps: In step S510, 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, and then the dynamic charge transport equation is obtained by considering that the mobility will change due to the influence of temperature, mechanical stress and irradiation dose rate. 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.

[0068] In step S520, 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 irradiation 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 Boltzmann constant, is the electron deposition depth distribution.

[0069] In step S530, the hole concentration change rate equation is obtained according to the hole generation and recombination mechanism. The hole concentration change rate equation is: .

[0070] In step S540, according to the change of thermal stress causing the change of thermal motion speed, the change of trap density and capture cross section caused by mechanical stress and irradiation, and the change of trap energy level caused by electric field to promote charge detrapping, a charge capture and release dynamic equation is established, wherein the charge capture and release dynamic equation includes an electron capture rate dynamic equation and an 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 trap density, To capture the cross section, is the electron release rate, To release the cross section, is the trap level, is the speed of thermal motion, , is the effective mass of the carrier.

[0071] In step S550, a refined model of polyimide charge behavior is constructed; the refined model of polyimide charge behavior includes: .

[0072] It can be understood that the charge current density is related to the electric field, charge concentration and mobility as follows: . Mobility under multiple stresses will change, thus obtaining the dynamic charge transport equation ( is the absolute temperature, For mechanical stress, is the irradiation dose rate), reflecting that the charge transport driven by multi-stress electric field is subject to the multi-factor coupling law.

[0073] According to the Boltzmann distribution, the rate of electron-hole pairs generated by thermal excitation is , under thermal stress , will change, and the rate of electron-hole pairs generated by thermal excitation is obtained , which is an important source of charge generation, especially at high temperatures. Rate , is the irradiation dose rate, is the ionization efficiency, which is related to the irradiation type, energy and material interaction, and takes into account the electron deposition depth distribution , construct the irradiance generation term with depth variable , reflecting the charge generation distribution characteristics under irradiation. According to the dominant Shockley-Read-Hall recombination, the recombination rate ( is the electron lifetime, is the hole lifetime, Determined by the trap energy level, According to the Fermi level, is the intrinsic carrier concentration). Charge accumulation induces electric field, carrier concentration changes affect recombination, electric field promotes recombination, according to Poisson's equation ( is the dielectric constant) and the charge continuity equation Solve the equations together to get the dynamic compound rate , accurately describe the process of charge dynamic balance being disturbed by multiple factors. ( is the effective mass of the carriers), mechanical stress and irradiation will change and , the electric field will The variable promotes charge detrapping, thus establishing the dynamic equation of charge capture and release, which expresses that the interaction between charge and trap evolves with the environment, such as Fig. 9 shown.

[0074] Furthermore, in this exemplary embodiment, a polyimide degradation analysis system under the synergistic effect of multiple stresses is also provided. Fig.10 As shown in , the system may include: 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 according to 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, and the refined model of polyimide charge behavior.

[0075] Optionally, the polyimide charge behavior refinement model comprises: ; 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, is the rate of electron-hole pair generation by thermal excitation, is the radiation ionization rate, is the carrier lifetime, is the room temperature band gap, 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 speed of thermal motion, To capture the cross section, is the electron release rate, To release the cross section, is the trap level.

[0076] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0077] It should be noted that although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiment of the present disclosure, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of a module or unit described above can be further divided into multiple modules or units for concretization. The components displayed as modules or units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the disclosed solution. Those of ordinary skill in the art can understand and implement it without paying creative work.

[0078] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated 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; 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 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 by the Arrhenius formula, and obtaining the trap density by integrating the trap current fitting curve includes: 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.

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 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.

6. 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 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: 。 7. 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.

8. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 4, 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.

9. The method for establishing a refined model of charge behavior of polyimide under multiple stresses according to claim 4, 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.

10. 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 9, 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.

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