Method for analyzing charge accumulation characteristics of a polyimide material

Abstract

The application relates to a method for analyzing the charge accumulation characteristics of a polyimide material, which comprises the following steps: based on the multi-stress state of the electric field, temperature, mechanical stress and irradiation of the polyimide material in a deep space environment, applying multi-stress synergy to the polyimide material; constructing a dynamic charge migration model of the polyimide material under the multi-stress synergy, and analyzing the charge accumulation characteristics of the polyimide material. Based on the multi-stress state of the electric field, temperature, mechanical stress and irradiation of the polyimide material in a deep space environment, multi-stress synergy is applied to the polyimide material, so that the distortion problem of traditional single stress or two-by-two combined stress measurement is solved; through the dynamic charge migration model, the charge accumulation characteristics of the polyimide material under the action of the electric field, temperature, mechanical stress and irradiation are analyzed, and accurate prediction and regulation of the electric performance of the polyimide material are realized.

Description

Technical Field

[0001] This application relates to the field of materials analysis technology, and in particular to a method for analyzing the charge accumulation characteristics of polyimide materials. Background Technology

[0002] Research on polyimide materials has established testing platforms and methods for assessing their properties under various stress combinations, including electro-irradiation, electro-thermal, and thermal-irradiation. Research by the China Academy of Space Technology has revealed that electron radiation dominates in deep space, with the absorbed electron dose being 40,000 times the sum of other types of radiation. This clarifies that the polyimide material in flexible solar arrays is primarily subjected to electron radiation in deep space. NASA's research on flexible solar arrays using the Long Term Exposure Facility (LDEF) experimental platform shows that under thermal radiation, the average temperature change rate of the polyimide material constituting the flexible solar array reaches 2°C / min. Ambient temperature has a major impact on the temperature rise of the flexible device itself, leading to a decline in device performance. Because the dielectric properties of polymer polyimide materials are highly sensitive to temperature changes, repeated rapid temperature changes can easily cause charge accumulation in the polymer polyimide material, potentially leading to spacecraft malfunctions.

[0003] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this disclosure is to provide a method for analyzing the charge accumulation characteristics of polyimide materials, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] This application provides a method for analyzing the charge accumulation characteristics of polyimide materials, including:

[0007] Based on the multi-stress state of polyimide materials under electric field, temperature, mechanical stress and irradiation in deep space environment, a multi-stress synergistic effect is applied to polyimide materials;

[0008] The surface charge density, space charge distribution, and surface trap energy levels of polyimide materials were calculated using the surface potential decay method and atomic force microscopy.

[0009] The conductivity and relative permittivity of polyimide materials were measured and calculated using the three-electrode method and the bridge method.

[0010] The carrier mobility of polyimide materials was measured and calculated using the transit-time algorithm and the electroacoustic pulse method.

[0011] A dynamic charge transfer model for polyimide materials under the synergistic effect of multiple stresses was constructed. The coefficients of the dynamic charge transfer model were determined by measuring and calculating the parameters. The charge accumulation characteristics of polyimide materials were calculated and analyzed using the dynamic charge transfer model.

[0012] In an exemplary embodiment of this disclosure, the application of multi-stress synergistic effects to the polyimide material utilizes a multi-stress synergistic loading platform. The multi-stress synergistic loading platform includes: a support platform, an electric field loading module, a temperature control module, a mechanical force loading module, an irradiation simulation module, a detection module, and a shielding box. The support platform is placed at the bottom of the shielding box and is used to place a sample of the polyimide material. The electric field loading module provides an electric field strength and pulsed current to the sample of the polyimide material inside the shielding box. The temperature control module includes an electric heating controller and a temperature sensor connected thereto, the temperature sensor being located at the bottom of the support platform. The mechanical force loading module provides mechanical tension to the sample of the polyimide material placed on the support platform. The irradiation simulation module provides irradiation to the sample of the polyimide material placed on the support platform. The detection module is used to detect and analyze the collected data of the polyimide material.

[0013] In an exemplary embodiment of this disclosure, the expression for the conductivity is:

[0014]

[0015] Where G0 is the initial conductivity, coeff(T) is the temperature-dependent correction factor, and q free (T) represents the free charge density (C·m). -3 ), P tr The probability of charge trapping (s) -1 ), P de (T) represents the charge trapping probability (s) -1 ), q e N represents the electron charge. t Traps density (m -3 ), where t is the duration of action.

[0016] In an exemplary embodiment of this disclosure, the expression for the relative permittivity is:

[0017]

[0018] Where C is capacitance, ε is relative permittivity, S is plate area, k is electrostatic constant, and d is plate spacing.

[0019] In an exemplary embodiment of this disclosure, the expression for the carrier mobility is:

[0020]

[0021] Where V(t) is the change of potential difference over time, Q0 is the initial charge, μ is the charge mobility, E is the electric field strength, τ is the carrier lifetime, L is the thickness of the polyimide sample, C is the capacitance, t is the current time, and t0 is the transit time.

[0022] In an exemplary embodiment of this disclosure, the step of constructing a dynamic charge transfer model of polyimide materials under multi-stress synergy includes:

[0023] Based on the Fowler-Nordheim tunneling effect, the coupling term between electric field and temperature is calculated based on the effect of temperature on barrier height;

[0024] The stress-irradiation coupling term is calculated based on stress-induced lattice dislocations and irradiation-induced chemical bond breakage.

[0025] The drift current and the diffusion current are combined and merged into a migration-diffusion term through the Einstein relation.

[0026] In an exemplary embodiment of this disclosure, the expression for the dynamic charge transfer model is:

[0027]

[0028] Where ρ is the charge density, αE 2 e -β / T For electric field and temperature coupling terms, γσln(1+δD) is for stress and radiation coupling terms. α is the migration and diffusion term; E is the electric field strength; β is the temperature sensitivity coefficient; T is the temperature; γ is the stress and irradiation coupling term coefficient; σ is the mechanical stress; δ is the irradiation damage coefficient; D is the irradiation dose; and μ is the charge mobility.

[0029] In an exemplary embodiment of this disclosure, the electric field loading module can generate a variable voltage of 0-±20kV and a current of 0-20mA.

[0030] In an exemplary embodiment of this disclosure, the temperature control module has a temperature control range of -100℃ to 100℃.

[0031] In an exemplary embodiment of this disclosure, the mechanical force loading module can apply a mechanical force of 0.1N-1000N; the irradiation simulation module can generate electron energies of 1keV-10keV and beam current densities of 0-25nA / cm². 2 The electron beam.

[0032] The technical solution provided in this application may include the following beneficial effects:

[0033] This application provides a method for analyzing the charge accumulation characteristics of polyimide materials. On the one hand, based on the multi-stress state of polyimide materials under electric field, temperature, mechanical stress, and irradiation in the deep space environment, the method applies a synergistic effect of multiple stresses to the polyimide material, solving the distortion problem of traditional single stress or pairwise stress measurements. On the other hand, through a dynamic charge migration model, the method analyzes the charge accumulation characteristics of polyimide materials under the action of electric field, temperature, mechanical stress, and irradiation, thereby achieving accurate prediction and control of the electrical properties of polyimide materials.

[0034] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0036] Figure 1 This diagram illustrates the steps of a method for analyzing the charge accumulation characteristics of polyimide materials in an exemplary embodiment of this disclosure.

[0037] Figure 2 This diagram illustrates the solar array structure and charge accumulation process in an exemplary embodiment of the present disclosure.

[0038] Figure 3 This diagram illustrates a multi-stress coordinated loading experimental platform in an exemplary embodiment of this disclosure.

[0039] Figure 4 A schematic diagram of electron irradiation and potential acquisition in an exemplary embodiment of this disclosure is shown. Detailed Implementation

[0040] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary 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.

[0041] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some 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, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0042] This example embodiment provides a method for analyzing the charge accumulation characteristics of polyimide materials, such as... Figure 1 As shown, the following steps may be included:

[0043] Step S101: Based on the multi-stress state of the polyimide material under electric field, temperature, mechanical stress and irradiation in the deep space environment, apply a multi-stress synergistic effect to the polyimide material.

[0044] Step S102: Calculate the surface charge density, space charge distribution, and surface trap energy level of the polyimide material by measuring the surface potential decay method and atomic force microscopy.

[0045] Step S103: The conductivity and relative permittivity of the polyimide material are measured and calculated using the three-electrode method and the bridge method.

[0046] Step S104: The carrier mobility of the polyimide material is measured and calculated using the transit time algorithm and the electroacoustic pulse method.

[0047] Step S105: Construct a dynamic charge transfer model for polyimide materials under the synergistic effect of multiple stresses, determine the coefficients of the dynamic charge transfer model by measuring and calculating the parameters, and use the dynamic charge transfer model to calculate and analyze the charge accumulation characteristics of polyimide materials.

[0048] The present disclosure provides a method for analyzing the charge accumulation characteristics of polyimide materials. On the one hand, based on the multi-stress state of polyimide materials in the deep space environment, including electric field, temperature, mechanical stress, and irradiation, a multi-stress synergistic effect is applied to the polyimide material to solve the distortion problem of traditional single stress or pairwise stress measurements. On the other hand, through a dynamic charge migration model, the charge accumulation characteristics of polyimide materials under the action of electric field, temperature, mechanical stress, and irradiation are analyzed, thereby achieving accurate prediction and control of the electrical properties of polyimide materials.

[0049] Below, according to Figures 1-4 The steps of the method described above in this example embodiment will be explained in more detail.

[0050] like Figure 2As shown, the electrode structure of a traditional rigid solar array exhibits increased charge accumulation in the polyimide material under the combined effects of electricity, heat, and radiation compared to single stress, and its surface insulation performance is significantly reduced. The electric field and mechanical stress experienced by a flexible solar array are more complex than those of a traditional rigid solar array. On one hand, under the combined effect of the working electric field on the solar array surface and charged particles radiated from space, charge is injected into the interior of the polyimide material. Compared to the vacuum / dielectric / electrode structure of a traditional solar array, the vacuum / dielectric / electrode structure of a flexible solar array makes it more difficult to release the injected charge. On the other hand, the flexible substrate bears a certain tension to maintain the required stiffness of the solar array in space. Mechanical stress leads to changes in the local morphology and trap distribution characteristics of the polyimide material, accelerating the charge accumulation process. The electric field distortion caused by charge accumulation will induce electrostatic discharge, damaging the insulating medium, and in severe cases, leading to the scrapping of the spacecraft. It should be understood that this application analyzes the charge accumulation characteristics of the polyimide material in a flexible solar array. When analyzing the charge accumulation characteristics of polyimide materials, samples of pretreated polyimide materials were used. Pretreatment of polyimide samples is a prior art technique and will not be elaborated upon here.

[0051] Step S101: Based on the multi-stress state of the polyimide material under electric field, temperature, mechanical stress and irradiation in the deep space environment, apply a multi-stress synergistic effect to the polyimide material.

[0052] Specifically, given the extremely complex space environment and component structure faced by flexible solar arrays in deep space exploration spacecraft, this study analyzes the harsh space radiation, rapid temperature cycling, extremely high operating field strength, and mechanical stress that the flexible solar array surface needs to withstand in deep space. Based on the potential field strength, temperature, tension, and irradiance (including electron energy and beam density), a multi-stress collaborative loading platform is constructed, such as... Figure 3As shown, the multi-stress co-loading platform includes: a support platform, an electric field loading module, a temperature control module, a mechanical force loading module, an irradiation simulation module, a detection module, and a shielding box. The support platform is placed at the bottom of the shielding box and includes a sample of the polyimide material for placement. The electric field loading module provides an electric field and pulsed current to the polyimide material sample inside the shielding box. The electric field loading module includes a high-voltage power supply module, a high-voltage pulse power supply module, and a capacitor probe. The high-voltage power supply module provides a stable DC electric field (voltage range 0~±20kV, current range 0~20mA) to meet the charge injection requirements of the polyimide material sample under a constant electric field. The high-voltage pulse power supply module and the capacitor probe apply a pulse-controlled voltage waveform (rise time >350V / us), which is controlled by a signal generator and a power amplifier to meet the charge behavior testing requirements under different testing scenarios (such as surface potential decay, space charge mobility measurement, etc.). The detection module is used to detect and analyze the collected data of the polyimide material. The detection module includes an electrometer, an electrostatic probe, an atomic force microscope, and a data acquisition system. The capacitive probe is positioned above the support platform and connected to a high-voltage pulse power supply module; the electrostatic probe is positioned below the support platform and connected to the electrometer; the data acquisition system is connected to the electrometer and comprises an oscilloscope and a host computer. The temperature control module includes an electric heating controller and a connected temperature sensor, which is located at the bottom of the support platform. The temperature control module has a temperature control range of -100℃ to 100℃ and a continuous temperature adjustment rate of 2℃ / min. The mechanical force loading module provides mechanical tension to the polyimide sample placed on the support platform. The mechanical force loading module includes a high-precision force sensor controlling a stepper motor to adjust the tensile force, and can apply a mechanical force of 0.1N-1000N. The irradiation simulation module is used to irradiate the polyimide material sample placed on the support platform. The module employs the Schottky thermal emission principle, controlling the electron emitter current and accelerating electrode voltage to achieve electron irradiation with different beam currents and energies. The irradiation simulation module can generate electron energies of 1keV-10keV and beam current densities of 0-25 nA / cm². 2 The electron beam.

[0053] To prevent signal interference from the platform from causing measurement errors, the shielding box employs a multi-layered insulating structure consisting of insulating varnish impregnation and aluminum foil wrapping, avoiding interference from electron irradiation on the test results. A vacuum environment is achieved by connecting the shielding box to a vacuum pump; additionally, the shielding box is connected to a liquid nitrogen device.

[0054] Step S102: Calculate the surface charge density, space charge distribution, and surface trap energy level of the polyimide material by measuring the surface potential decay method and atomic force microscopy.

[0055] Understandably, a simulated deep space environment is established, subjecting the flexible substrate polyimide material to electric field strength, temperature, tension, and irradiation stress, and the surface potential change is measured using the surface potential decay method.

[0056] Before the test begins, the capacitance probe is moved to the surface of the polyimide sample to measure the initial potential.

[0057] After obtaining the initial surface potential of the sample, the electron irradiation module begins preheating. After 10 minutes of preheating, the potentials of the accelerating electrode and the confinement electrode are adjusted to the set values.

[0058] Move the irradiation simulation module directly above the sample to begin irradiation.

[0059] like Figure 4 As shown, the potential acquisition stage is divided into three stages.

[0060] In the first stage, the capacitive probe is quickly moved to the edge of the polyimide material sample.

[0061] In the second stage, the data acquisition system operates. During this stage, the capacitance probe is kept running at a relatively slow speed while simultaneously starting potential acquisition. To minimize potential decay during acquisition, the measurement stops when the capacitance probe reaches the exact center of the irradiation point.

[0062] In the third stage, the device immediately and quickly returns to its initial position for the next irradiation phase. To avoid charge dissipation during the test, the total time for the entire working potential measurement phase is less than 10 seconds.

[0063] Through repeated experiments, the surface potential, charge accumulation density, dissipation and other parameters of polyimide materials under different field strengths, temperatures, tensions and irradiation intensities, both individually and synergistically, were tested.

[0064] Atomic force microscopy (AFM) is used to analyze changes in the surface structure of solid materials, including insulators.

[0065] The surface structure and properties of a material are studied by detecting the extremely weak interatomic interaction forces between the sample surface and a micro force-sensitive element.

[0066] Fix one end of a pair of microcantilever arms that are extremely sensitive to weak forces, and bring the tiny needle tip of the other end close to the sample. The needle tip will then interact with the sample, and the force will cause the microcantilever arm to deform or change its motion state.

[0067] Obtaining surface morphology and roughness information at nanoscale resolution helps improve our understanding of the internal charge distribution and trap information of polyimide materials.

[0068] The temperature control module was used to achieve real-time temperature regulation of the sample in order to measure the surface trap characteristics of polyimide materials and the variation of barrier energy level distribution with electric field, temperature, mechanical stress and irradiation.

[0069] Step S103: The conductivity and relative permittivity of the polyimide material are measured and calculated using the three-electrode method and the bridge method.

[0070] In multi-stress synergistic loading scenarios, the conductivity and relative permittivity of polyimide were measured using the three-electrode method and the bridge method.

[0071] Dielectric properties refer to the response of bound charges in a material's molecules to an applied stress field. They are important parameters describing material performance, including conductivity, dielectric constant, and dielectric loss. Under the individual and synergistic effects of multiple stresses, conductivity, relative dielectric constant, and charge mobility are obtained using the first, second, and third formulas.

[0072] The first formula is:

[0073]

[0074] Where G0 is the initial conductivity, coeff(T) is the temperature-dependent correction factor, and q free (T) represents the free charge density (C·m). -3 ), P tr The probability of charge trapping (s) -1 ), P de (T) represents the charge trapping probability (s) -1 ), q e N represents the electron charge. t Traps density (m -3 ), where t is the duration of action;

[0075] The second formula is:

[0076] Where C is capacitance, ε is relative permittivity, S is plate area, k is electrostatic constant, and d is plate spacing.

[0077] The third formula is:

[0078]

[0079] Where V(t) is the voltage at the current time, Q0 is the initial charge, μ is the charge mobility, E is the electric field strength, τ is the carrier lifetime, L is the thickness of the polyimide sample, C is the capacitance, t is the current time, and t0 is the transit time.

[0080] It should be noted that the correction coefficient coeff(T) can be determined through experimental measurement and data fitting. Dielectric properties refer to the response characteristics of bound charges in material molecules to an applied stress field, and are important parameters describing material performance, including conductivity, dielectric constant, and dielectric loss. Based on a multi-stress co-loading device, a measurement platform for conductivity and relative dielectric constant is built using the three-electrode method and the bridge method. The polyimide sample to be tested is placed in the test chamber, and the test chamber is heated according to the test requirements. Using an electrometer, after pressurization, the changes of key dielectric properties parameters such as conductivity and relative dielectric constant of the polyimide material with temperature, field strength, mechanical force, and irradiation are obtained under the test conditions using the first and second formulas.

[0081] Step S104: Measure carrier mobility using the transit time algorithm and the electroacoustic pulse method.

[0082] Specifically, the transit-time algorithm calculates mobility based on the time it takes for charge carriers to travel a certain distance under the influence of an electric field. By applying an electric field to both ends of a polyimide material, injecting charge, and measuring the transit time of the charge from one end to the other, the carrier mobility can be calculated by combining the measured material thickness, voltage, and transit time. The electroacoustic pulse method involves injecting an electrical pulse into the polyimide material, generating an acoustic pulse. This acoustic pulse propagates within the material, and the carrier mobility is calculated by detecting information such as the propagation time and amplitude of the acoustic pulse.

[0083] The mobility of charge carriers or ions (including positive and negative ions, holes, and electrons) in a material with controllable temperature and field strength is measured and calculated using a transit-time algorithm, a third formula, and an electroacoustic pulse method. Real-time temperature feedback allows for reasonable temperature control of the polyimide material, with a control range of -100 to 100℃ and a control accuracy of 0.1℃. The mobility of charge carriers of different polarities is tested by measuring the charge accumulation rate, and the changes in charge mobility and other internal charge characteristics of the polyimide material under individual and synergistic effects of multiple stresses are measured. Physical phenomena such as charge injection, trapping, detrapping, and migration determine the surface potential decay process. Dynamic analysis of the surface potential decay characteristics over time yields parameters such as the trap energy level distribution on the sample surface.

[0084] Step S105: Construct a dynamic charge transfer model for polyimide materials under the synergistic effect of multiple stresses, determine the coefficients of the dynamic charge transfer model by measuring and calculating the parameters, and use the dynamic charge transfer model to calculate and analyze the charge accumulation characteristics of polyimide materials.

[0085] Specifically, based on the Fowler-Nordheim tunneling effect, the coupling term between electric field and temperature is calculated based on the effect of temperature on the barrier height. The electric field-temperature coupling term is based on the fact that electrons pass through the barrier through quantum tunnels under a high electric field, which generates nonlinear conductivity and the temperature rise reduces the barrier height, thereby increasing the probability of carrier detrapping.

[0086] According to the Fowler-Nordheim formula, the field emission current density is: in: A is a material constant, and the charge q, mass m, and barrier height are also given. h represents Planck's constant, and E is the electric field strength; B is a parameter related to the barrier height. Increased temperature decreases the barrier height; the corrected barrier height is: in, This indicates the corrected effective barrier height. Initial barrier height without considering the effect of temperature This is the change in barrier height due to temperature changes; assuming, The corrected field emission formula is as follows: Where, k B Represents the Boltzmann constant; simplified treatment (Taylor expansion retains first-order terms): J FN (E,T)≈αE 2 e -β / T , where e represents the natural constant.

[0087] Based on the stress-induced lattice dislocations and irradiation-induced chemical bond breaking, the stress-irradiation coupling term is calculated. In this term, the coupling effect of stress and irradiation influences charge migration. Applying tensile / compressive stress leads to the periodic disruption of the material's lattice, generating dislocations and microcracks. Increased dislocation density forms charge trapping centers, and the measured trap density N... t As stress increases linearly, the proportionality constant k σ High-energy electron irradiation induces CN bond breaking, generating free radicals and vacancy-type defects, with a defect density N. d =δD, where δ is the damage coefficient and D is the radiation dose. The stress-trap density relationship is established through uniaxial tensile testing: The increase in trap density due to applied stress is... σ represents mechanical stress. The irradiation damage kinetic equation is obtained based on Monte Carlo simulation: in, σ represents the rate of change of defect density over time, Φ represents the incident particle flux, and σ represents the rate of change of defect density over time. d It is the irradiation damage section, N d =N sat (1-e -δD ), where N d Let N be the defect density, δ be the damage coefficient, and N be approximately equal to N at low doses. d ≈δD; Solving for the steady-state defect density N d =N sat (1-e -δD ), where N sat It is the saturation defect density, e -δD This reflects the relationship between the irradiation dose D and the saturation defect density N. sat The relationship between the two; low dose approximation N d ≈δD; Assuming the synergistic effect of stress and irradiation manifests as an enhancement of the product of defect density: in, It is the initial trap density. The increase in trap density due to applied stress. G is the defect density caused by irradiation, γ is the coefficient of the stress-irradiation coupling term, δ is the damage coefficient, and D is the irradiation dose. By fitting the multi-stress experimental data using the least squares method, the coupling term is determined to be in the form of: G σ-D =γσln(1+δD), where G σ-D γ represents the coupling term of stress and irradiation, and γ is the coefficient of the stress-irradiation coupling term.

[0088] Combining drift current and diffusion current, and integrating them into a migration-diffusion term using Einstein's relation, the motion of charge carriers in the drift current within the electric field is: J drift =μρE, where J drift The drift current density is represented by μ, the charge mobility is ρ, the charge density is E, and the electric field strength is E; diffusion driven by the concentration gradient in the diffusion current: Among them, J diffusion For diffusion current density, It is the charge density gradient, and M is the diffusion coefficient; according to Einstein's relation, M = -μk B T / q, where T is the temperature, and the total current density can be combined as: k B Let be the Boltzmann constant, and take the divergence with respect to the total current density. in, It reflects the net outflow (or net inflow) of current density at a certain point in space, under the steady-state assumption. Simplified to: Because the charge decreases as it migrates out of the region, the migration-diffusion term is:

[0089] Based on the physical mechanisms of electric field-temperature coupling, stress-irradiation coupling, and charge migration and diffusion, a dynamic charge migration model is constructed. Based on the principle of charge conservation, it describes the change of charge density over time. Where ρ is the charge density; M is the carrier generation rate; and R is the carrier recombination rate. Let R be the total current density with divergence. Carrier generation rate includes: electric field-temperature coupling term and stress-irradiation coupling term; in deep-trapping-dominated polyimide materials, recombination rate is negligible (trapping is dominant), therefore: R≈0, because charge decreases due to migration out of the region, hence the migration-diffusion term is...

[0090] The expression for the dynamic charge transfer model is:

[0091]

[0092] Where ρ is the charge density, αE 2 e -β / T The electric field and temperature are coupled terms, the secondary electric field reflects nonlinear conduction, and γσln(1+δD) is a stress-irradiation coupled term. α is the migration and diffusion term; E is the electric field strength; β is the temperature sensitivity coefficient; T is the temperature; γ is the stress and irradiation coupling term coefficient; σ is the mechanical stress; δ is the irradiation damage coefficient; D is the irradiation dose; and μ is the charge mobility.

[0093] It is important to understand that in order for the dynamic charge transfer model to more accurately describe the charge accumulation characteristics of polyimide materials, the coefficients in the model need to be determined. Experimental data can be obtained by measuring the conductivity and relative permittivity under different stress conditions. These data are closely related to charge transfer characteristics and provide strong support for determining the coefficients associated with charge transfer. In determining the electric field-temperature coupling coefficients (α and β), experiments are conducted with different combinations of electric field strength and temperature, measuring the change in charge density over time. The changes in conductivity and relative permittivity with temperature and electric field strength help to understand the charge transfer process, thus matching the measured data with the electric field-temperature coupling term in the model, thereby determining the values ​​of α and β. In determining the stress-irradiation coupling coefficients (γ and δ), the measured data of conductivity and relative permittivity under different combinations of mechanical stress and irradiation dose reflect the influence of stress and irradiation on charge trapping and migration. By fitting the experimental data with the stress-irradiation coupling term, the values ​​of γ and δ can be determined.

[0094] It is also necessary to understand that experiments with different combinations of electric field strength and temperature were conducted, using the three-electrode method and the bridge method to measure the conductivity and relative permittivity of polyimide materials under various operating conditions. Simultaneously, the charge density variation over time was recorded. Under different temperature conditions (e.g., -100℃, 0℃, 100℃, etc.) and electric field strengths (e.g., multiple values ​​selected within the range of 0-±20kV), the material was tested, and the corresponding curves of conductivity, relative permittivity, and charge density variation over time were obtained. The measured conductivity and relative permittivity data were combined with the charge density variation data and fitted to the electric field-temperature coupling term in the dynamic charge migration model. Since conductivity and relative permittivity are affected by temperature and electric field, their variation reflects the effect of electric field-temperature coupling on charge migration. By adjusting the values ​​of α and β, the charge density variation calculated by the model was made to match the experimental measurements as closely as possible. First, fix the temperature, change the electric field strength, observe the difference between the change in charge density and the model calculation results, and adjust α and β; then fix the electric field strength, change the temperature and repeat the above operation, and finally determine the α and β values ​​that best fit the model with the experimental data.

[0095] To determine the stress-irradiation coupling coefficients (γ and δ), under different mechanical stresses (0.1N-1000N) and irradiation doses (1keV-10keV electron energy, beam current density 0-25nA / cm²), 2 Experiments were conducted using an electron beam combination to measure the electrical conductivity and relative permittivity of polyimide materials. During the experiments, charge density data, such as surface charge density and space charge distribution, were recorded simultaneously. Mechanical stress and irradiation dose were gradually increased, and changes in conductivity and relative permittivity, as well as the response of charge density, were observed. Using the measured conductivity, relative permittivity, and charge density data, a stress-irradiation coupling term was fitted. Stress and irradiation affect the microstructure of the material, thereby altering conductivity and relative permittivity; these changes are related to charge trapping and migration. Using fitting methods such as least squares, the values ​​of γ and δ were adjusted to ensure that the calculated results of the stress-irradiation coupling term in the model matched the experimental data, thus determining the values ​​of γ and δ.

[0096] Using a multi-stress synergistic loading platform, electron energies and beam current densities ranging from 0 to ±20 kV, temperatures from -100 to 100 °C, mechanical stresses from 0.1 to 1000 N, and irradiation from 1 keV to 10 keV were applied under different combinations of electric fields (0 to ±20 kV), temperatures from -100 to 100 °C, mechanical stresses from 0.1 to 1000 N, and irradiation from 1 keV to 10 keV, with a range of 0 to 25 nA / cm². 2 Under electron beam conditions, surface charge density (surface potential decay method); space charge distribution (atomic force microscopy); conductivity (three-electrode method); dielectric constant (electric bridge method); and carrier mobility (transit time algorithm, electroacoustic pulse method) were measured. Model coefficients (α, β, γ, δ) were determined based on experimental data using nonlinear regression or least squares methods.

[0097] The surface charge density, space charge distribution, and surface trap energy levels of polyimide materials were measured using the surface potential decay method and atomic force microscopy. Measurements were performed under different combinations of electric fields, temperatures, mechanical stresses, and irradiation to obtain corresponding charge distribution data. These data reflect the distribution of charge on and within the material surface and are related to charge density, providing fundamental data support for determining coefficients.

[0098] The electrical conductivity and relative permittivity of polyimide materials were measured using the three-electrode method and the bridge method. The electrical conductivity and relative permittivity were measured under different stress conditions. These parameters are closely related to charge migration characteristics and can help determine the coefficients associated with charge migration.

[0099] Carrier mobility was measured using a transit-time algorithm and an electroacoustic pulse method. Measurements of carrier mobility under various stress combinations directly provided a basis for determining mobility (μ), and also helped to determine other coefficients related to charge migration.

[0100] The electric field-temperature coupling coefficients (α and β) are determined by conducting experiments with different combinations of electric field strength and temperature, measuring the change in charge density over time. These data are then fitted to match the measured data with the electric field-temperature coupling terms in the model, thus determining the values ​​of (α and β). The method involves fixing the temperature, changing the electric field strength, measuring the change in charge density, then fixing the electric field strength again, changing the temperature, and using the measured data to fit (α and β).

[0101] The stress-irradiation coupling coefficients (γ and δ) were determined experimentally under different combinations of mechanical stress and irradiation dose, measuring charge density-related data. The values ​​of γ and δ were determined by fitting the experimental data to the stress-irradiation coupling term. The changes in charge density were recorded as stress and irradiation dose were gradually increased and used to fit and solve the coefficients.

[0102] Mobility (μ) is the carrier mobility data directly measured by the transit time algorithm and the electroacoustic pulse method. After data processing and statistical analysis, the value of mobility (μ) can be directly determined.

[0103] Numerical methods such as the finite difference method or the finite element method are used to solve the partial differential equations of the dynamic charge transfer model. The finite difference method discretizes the continuous model equations into difference equations and obtains the charge density at different times and locations through iterative calculations. The finite element method divides the material region into a finite number of elements, performs approximate solutions for each element, and then integrates them to obtain the overall charge density distribution. Based on actual experimental conditions, the accuracy and uniqueness of the model solution are ensured.

[0104] Measurements and calculations were performed using a multi-stress synergistic loading platform and a dynamic charge transfer model, and the data are shown in Table 1. The synergistic effect of multiple stresses significantly exacerbates charge accumulation; the charge density under four-stress synergy is 5.6 times that under a single electric field, verifying the effectiveness of the model for dynamic charge transfer in complex environments.

[0105] Table 1

[0106] Stress conditions <![CDATA[Charge density (C / m 3 )]]> <![CDATA[Accumulation rate (C / m 3 ·s)]]> Single electric field (10kV) <![CDATA[1.2×10 -5 ]]> <![CDATA[3.5×10 -7 ]]> Electric field + temperature (10kV, 80℃) <![CDATA[2.8×10 -5 ]]> <![CDATA[9.1×10 -7 ]]> Electric field + irradiation (10kV, 5keV) <![CDATA[3.5×10 -5 ]]> <![CDATA[1.2×10 -6 ]]> Four-stress synergy <![CDATA[6.7×10 -5 ]]> <![CDATA[2.8×10 -6 ]]>

[0107] At high temperatures, electrical conductivity increases significantly, accelerating charge migration. However, high temperatures also reduce the potential barrier height, leading to an increased probability of trap escaping and faster charge dissipation. Tensile stress linearly increases trap density, while irradiation dose causes defect accumulation. The combined effect of these two factors significantly enhances charge trapping capability and exacerbates charge accumulation. Under high electric fields, the migration term dominates, causing charges to rapidly migrate into the material interior, forming space charges.

[0108] Numerical solutions to the dynamic charge transfer model are calculated to assess the charge accumulation rate under different stress combinations. The spatial distribution of charge density after long-term exposure is analyzed to predict the dielectric breakdown risk of the material.

[0109] By using a dynamic charge transfer model, the charge accumulation characteristics of polyimide materials under electric field, temperature, mechanical stress and irradiation are analyzed, so as to achieve accurate prediction and control of the electrical properties of polyimide materials.

[0110] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0111] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above 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. Components shown as modules or units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without any inventive effort.

[0112] In exemplary embodiments of this disclosure, an electronic device is also provided, which may include a processor and a memory for storing executable instructions of the processor. The processor is configured to perform the steps of the charge accumulation characteristic analysis method for the polyimide material described in any of the above embodiments by executing the executable instructions.

[0113] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely hardware implementations, entirely software implementations (including firmware, microcode, etc.), or implementations combining hardware and software aspects, collectively referred to herein as “circuits,” “modules,” or “systems.”

[0114] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the above-described method for analyzing the charge accumulation characteristics of polyimide materials according to the embodiments of this disclosure.

[0115] In an exemplary embodiment of this disclosure, a computer storage medium is also provided, on which a computer program is stored, which, when executed by, for example, a processor, can implement the steps of the charge accumulation characteristic analysis method for polyimide materials described in any of the above embodiments.

[0116] In some possible implementations, various aspects of the present invention may also be implemented as a computer program product comprising a computer program or instructions which, when run on a terminal device, cause the terminal device to perform the steps described in the section on the method for analyzing the charge accumulation characteristics of polyimide materials described in this specification, according to various exemplary embodiments of the present invention.

[0117] The aforementioned program products can be written in any combination of one or more programming languages ​​to perform the operations of this invention. These programming languages ​​include object-oriented programming languages—such as Java and C++—and conventional procedural programming languages—such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0118] The computer software product may be stored in a computer storage medium, including read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0119] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method of analyzing a charge accumulation property of a polyimide material, characterized by, The method comprises the following steps: Based on the multi-stress state of the electric field, temperature, mechanical stress and radiation of the polyimide material in the deep space environment, the polyimide material is subjected to multi-stress synergy; The surface charge density, space charge distribution and surface trap energy level of the polyimide material are measured and calculated by surface potential decay method and atomic force microscope; The conductivity and relative dielectric constant of the polyimide material are measured and calculated by three-electrode method and bridge method; The carrier mobility of the polyimide material is measured and calculated by time-of-flight algorithm and electroacoustic pulse method; A dynamic charge migration model of the polyimide material under multi-stress synergy is constructed, the coefficients of the dynamic charge migration model are determined by the measured and calculated parameters, and the charge accumulation characteristics of the polyimide material are calculated and analyzed by using the dynamic charge migration model. The dynamic charge migration model of the polyimide material under multi-stress synergy comprises: According to the Fowler-Nordheim tunneling effect, the coupling term of electric field and temperature is calculated based on the influence of temperature on barrier height; According to the stress-induced lattice dislocation and the radiation-induced chemical bond rupture, the stress and radiation coupling term is calculated; The drift current and diffusion current are combined into a migration-diffusion term through Einstein relationship; The expression of the dynamic charge migration model is: ； wherein, is the charge density, is the electric field and temperature coupling term, is the stress and irradiation coupling term, is the migration and diffusion term; is the coefficient of the electric field and temperature coupling term, is the electric field intensity, temperature sensitivity coefficient, temperature, is the coefficient of the stress and irradiation coupling term, is the mechanical stress, is the irradiation damage coefficient, is the irradiation dose, is the charge mobility.

2. The method of claim 1, wherein the method is a method of analyzing charge accumulation characteristics of a polyimide material, characterized by, The multi-stress synergy loading platform is used to apply multi-stress synergy to the polyimide material. The multi-stress synergy loading platform comprises a support platform, an electric field loading module, a temperature control module, a mechanical force loading module, a radiation simulation module, a detection module and a shielding box. The support platform is placed at the bottom of the shielding box, and is used to place the sample of the polyimide material.

3. The method of claim 1, wherein the method is a method of analyzing charge accumulation characteristics of a polyimide material, characterized by, The electric field loading module provides field strength and pulse current to the sample of the polyimide material in the shielding box. ； wherein, is the initial conductivity, is a temperature-dependent correction factor, is the free charge density, is the charge trapping probability, is the charge detrapping probability, is the electron charge, is the trap density, is the action time.

4. The method of claim 1, wherein the polyimide material is a polyimide film. The temperature control module comprises an electric heating controller and a temperature sensor connected thereto. ； wherein, is the capacitance, is the relative dielectric constant, is the plate area, is the electrostatic force constant, is the plate separation.

5. The method of claim 1, wherein the polyimide material is a polyimide film. The temperature sensor is arranged at the bottom of the support platform. ； wherein, is a value of the potential difference as a function of time, is an initial charge quantity, is a charge mobility, is an electric field strength, is a carrier lifetime, is a thickness of the sample of the polyimide material, is a capacitance, is a current time, is a transit time.

6. The method of claim 2, wherein the method is a method of analyzing charge accumulation characteristics of a polyimide material, characterized by, The mechanical force loading module is used to provide mechanical tension to the sample of the polyimide material placed on the support platform.

7. The method according to claim 6, wherein the method is a method for analyzing the charge accumulation characteristics of a polyimide material, characterized by, The radiation simulation module is used to provide radiation to the sample of the polyimide material placed on the support platform.

8. The method according to claim 7, wherein the method is a method for analyzing the charge accumulation characteristics of a polyimide material, characterized by, The detection module is used to detect and analyze the collected data of the polyimide material. The expression of the conductivity is: The expression of the relative dielectric constant is: The expression of the carrier mobility is: The electric field loading module can generate variable voltage of 0-±20kV and current of 0-20mA. The temperature control range of the temperature control module is -100℃-100℃. The mechanical force loading module can apply mechanical force of 0.1N-1000N. The radiation simulation module can generate electron energy of 1keV-10keV and electron beam with beam current density of 0-25nA / cm².

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