Charge accumulation characteristic analysis method of polyimide material

Abstract

The invention relates to a charge accumulation characteristic analysis method for a polyimide material, and the method comprises the steps: applying a multi-stress synergistic effect to the polyimide material based on the multi-stress state of the polyimide material in the electric field, temperature, mechanical stress and irradiation in a deep space environment; a dynamic charge migration model of the polyimide material under the multi-stress synergistic effect is constructed, and the charge accumulation characteristic of the polyimide material is analyzed. According to the invention, based on the multi-stress state of electric field, temperature, mechanical stress and irradiation of the polyimide material in a deep space environment, a multi-stress synergistic effect is applied to the polyimide material, so that the problem of distortion of traditional single-stress or pairwise combined stress measurement is solved; through a dynamic charge migration model, charge accumulation characteristics of the polyimide material under the action of an electric field, temperature, mechanical stress and irradiation are analyzed, and accurate prediction, regulation and control for researching the electrical performance of the polyimide material are realized.

Description

Background Art

[0002] In the prior art research on polyimide materials, test platforms and methods for the characteristics of polyimide materials under various stress combinations such as electro-irradiation, electro-thermal, and thermal-irradiation have been established. The China Academy of Space Technology has found that electron radiation dominates in the deep space environment, and its electron absorption dose is 40,000 times the sum of the absorption doses of other types of irradiation, clarifying that the polyimide materials of flexible solar wings will mainly be affected by electron radiation in deep space. The National Aeronautics and Space Administration (NASA) has studied flexible solar wings based on the "Long Duration Exposure Facility" (LDEF) experimental platform and obtained that under the action of thermal radiation, the average temperature change rate of the polyimide materials constituting the flexible solar wings reaches 2°C / min, and the ambient temperature will have a major impact on the temperature rise of the flexible devices themselves, resulting in a decline in device performance. Since the dielectric properties of the polymer polyimide materials are very sensitive to temperature changes, the repeatedly rapidly changing temperature is extremely likely to cause charge accumulation in the polymer polyimide materials, thereby causing spacecraft failure accidents.

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

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

[0005] The purpose of the embodiments of the present disclosure is to provide a method for analyzing the charge accumulation characteristics of polyimide materials, so as to at least overcome one or more problems caused by the limitations and defects of the related technologies to a certain extent.

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

[0007] Based on the multi-stress state of electric field, temperature, mechanical stress, and irradiation of polyimide materials in the deep space environment, apply multi-stress synergistic action to the polyimide materials;

[0008] Measure and calculate the surface charge density, space charge distribution, and surface trap energy level of the polyimide materials by the surface potential decay method and atomic force microscopy;

[0009] Measure and calculate the conductivity and relative dielectric constant of the polyimide materials by the three-electrode method and the bridge method;

[0010] Measure and calculate the carrier mobility of the polyimide materials by the transit time algorithm and the electroacoustic pulse method;

[0011] Build a dynamic charge migration model for polyimide materials under the synergistic action of multiple stresses, determine the coefficients of the dynamic charge migration model through the measured and calculated parameters, and use the dynamic charge migration model to calculate and analyze the charge accumulation characteristics of polyimide materials.

[0012] In an exemplary embodiment of the present disclosure, a multi-stress synergistic loading platform is used to apply the multi-stress synergistic action to the polyimide material; 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, the support platform is used to place the sample of the polyimide material, the electric field loading module provides the field strength and pulse current to the sample of the polyimide material in the shielding box, the temperature control module includes an electric heating controller and a temperature sensor connected thereto, the temperature sensor is arranged at the bottom of the support platform, the mechanical force loading module is used to provide mechanical tension to the sample of the polyimide material placed on the support platform, and the irradiation simulation module is used to provide 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 the present disclosure, the expression of the conductivity is:

[0014]

[0015] where G 0 is the initial conductivity, coeff(T) is the correction coefficient related to temperature, q free (T) is the free charge density (C·m -3 ), P tr is the charge trapping probability (s -1 ), P de (T) is the charge detrapping probability (s -1 ), q e is the electronic charge, N t is the trap density (m -3 ), and t is the acting time.

[0016] In an exemplary embodiment of the present disclosure, the expression of the relative dielectric constant is:

[0017]

[0018] where C is the capacitance, ε is the relative dielectric constant, S is the plate area, k is the electrostatic constant, and d is the plate spacing.

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

[0020]

[0021] Among them, V(t) is the change value of the potential difference with time, Q 0 is the initial charge quantity, μ is the charge mobility, E is the electric field strength, τ is the carrier lifetime, L is the thickness of the polyimide material sample, C is the capacitance, t is the current time, t 0 is the transit time.

[0022] In an exemplary embodiment of the present disclosure, the steps of constructing the dynamic charge migration model of the polyimide material under the synergistic action of multiple stresses include:

[0023] According to the Fowler-Nordheim tunneling effect, calculate the coupling term of the electric field and temperature based on the influence of temperature on the barrier height;

[0024] According to the stress-induced lattice dislocation and the irradiation-induced chemical bond breakage, calculate the coupling term of stress and irradiation;

[0025] Combine the drift current and the diffusion current, and merge them into the migration-diffusion term through the Einstein relation.

[0026] In an exemplary embodiment of the present disclosure, the expression of the dynamic charge migration model is:

[0027]

[0028] Among them, ρ is the charge density, αE 2 e -β / T is the coupling term of the electric field and temperature, γσln(1 + δD) is the coupling term of stress and irradiation, is the migration-diffusion term; α is the coefficient of the coupling term of the electric field and temperature, E is the electric field strength, β is the temperature sensitivity coefficient, T is the temperature, γ is the coefficient of the coupling term of stress and irradiation, 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 the present disclosure, the electric field loading module can generate a variable voltage of 0 - ±20 kV and a current of 0 - 20 mA.

[0030] In an exemplary embodiment of the present disclosure, the temperature control range of the temperature control module is -100°C - 100°C.

[0031] In an exemplary embodiment of the present disclosure, the mechanical force loading module can apply a mechanical force of 0.1 N - 1000 N; the irradiation simulation module can generate an electron energy of 1 keV - 10 keV and an electron beam with a beam current density of 0 - 25 nA / cm 2 of the electron beam.

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

[0033] A method for analyzing the charge accumulation characteristics of a polyimide material provided by this application. On the one hand, based on the multi-stress state of the polyimide material 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 problem of distortion in traditional single-stress or two-by-two combined stress measurements. On the other hand, through a dynamic charge migration model, the charge accumulation characteristics of the polyimide material under the action of electric field, temperature, mechanical stress, and irradiation are analyzed, realizing accurate prediction and regulation of the electrical properties of the polyimide material.

[0034] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit this disclosure. Brief Description of the Drawings

[0035] The drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with this disclosure, and are used together with the specification to explain the principles of this disclosure. Obviously, the drawings in the following description are only some embodiments of this disclosure, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0036] Figure 1 A schematic diagram showing the steps of the method for analyzing the charge accumulation characteristics of the polyimide material in the exemplary embodiment of this disclosure;

[0037] Figure 2 A schematic diagram showing the structure of the solar wing and the charge accumulation process in the exemplary embodiment of this disclosure;

[0038] Figure 3 A schematic diagram showing the multi-stress synergistic loading experimental platform in the exemplary embodiment of this disclosure;

[0039] Figure 4 A schematic diagram showing electron irradiation and potential acquisition in the exemplary embodiment of this disclosure. Detailed Embodiments

[0040] Now, the exemplary embodiments will be described more fully with reference to the drawings. However, the exemplary embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The features, structures, or characteristics described can be combined in any suitable manner in one or more embodiments.

[0041] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0042] This exemplary embodiment provides a method for analyzing the charge accumulation characteristics of a polyimide material. As Figure 1 shown, it may include the following steps:

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

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

[0045] Step S103: Measure and calculate the conductivity and relative dielectric constant of the polyimide material by the three-electrode method and the bridge method.

[0046] Step S104: Measure and calculate the carrier mobility of the polyimide material by the transit time algorithm and the electroacoustic pulse method.

[0047] Step S105: Construct a dynamic charge migration model of the polyimide material under the multi-stress synergistic effect, determine the coefficients of the dynamic charge migration model through the measured and calculated parameters, and use the dynamic charge migration model to calculate and analyze the charge accumulation characteristics of the polyimide material.

[0048] A method for analyzing the charge accumulation characteristics of a polyimide material provided in the embodiment of the present disclosure, on the one hand, based on the multi-stress state of the polyimide material in the deep space environment, including electric field, temperature, mechanical stress, and irradiation, applies a multi-stress synergistic effect to the polyimide material to solve the problem of distortion in traditional single-stress or two-combination stress measurements; on the other hand, through the dynamic charge migration model, analyzes the charge accumulation characteristics of the polyimide material under the action of electric field, temperature, mechanical stress, and irradiation, and realizes accurate prediction and regulation of the electrical properties of the polyimide material.

[0049] Next, according to Figures 1 - 4 each step of the above method in this exemplary embodiment will be described in more detail.

[0050] As Figure 2As shown in the figure, under the combined action of electricity, heat, and irradiation, the charge accumulation amount of the polyimide material in the electrode structure of the traditional rigid solar wing increases compared with that under a single stress, and the surface insulation performance decreases significantly. Moreover, the electric field and mechanical stress borne by the flexible solar wing are more complex than those of the traditional rigid solar wing. On the one hand, under the combined action of the working electric field on the surface of the solar wing and the charged particles in space radiation, charges will be injected into the interior of the polyimide material. Compared with the vacuum / dielectric / electrode structure of the traditional solar wing, the vacuum / dielectric / electrode structure of the flexible solar wing makes it more difficult for the injected charges to be released. On the other hand, the flexible substrate bears a certain tension to maintain the stiffness required for the solar wing in space. Mechanical stress will cause changes in the local morphological structure 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 to damage the insulating medium, and in severe cases, it will lead to the scrapping of the spacecraft. It should be understood that this application analyzes the charge accumulation characteristics of the polyimide material of the flexible solar wing. When analyzing the charge accumulation characteristics of the polyimide material, a sample of the pre-treated polyimide material is used. The pretreatment of the sample of the polyimide material is prior art and will not be elaborated here.

[0051] Step S101: Apply a combined action of multiple stresses to the polyimide material based on the state of multiple stresses of the electric field, temperature, mechanical stress, and irradiation of the polyimide material in the deep space environment.

[0052] Specifically, based on the extremely complex space environment faced by the flexible solar wing of the deep space exploration spacecraft and its component structure, analyze the severe space radiation, rapid temperature cycling of hot and cold alternation, extremely high working field strength, and mechanical stress on the surface of the flexible solar wing. Build a combined loading platform for multiple stresses according to the potential field strength, temperature, tension, and irradiation (including electron energy and beam current density), such as Figure 3As shown in the figure, the multi-stress collaborative 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 the support platform includes a sample for placing the polyimide material. The electric field loading module provides an electric field strength and a pulsed current to the sample of the polyimide material inside the shielding box. The electric field loading module includes a high-voltage power supply module, a high-voltage pulsed power supply module, and a capacitance probe. The high-voltage power supply module is used to provide a stable DC electric field (voltage range 0 to ±20 kV, current range 0 to 20 mA) to meet the charge injection requirements of the sample of the polyimide material under a constant electric field. In the high-voltage pulsed power supply module and the capacitance probe, the high-voltage pulsed power supply module is used to apply a pulsed control voltage waveform (rise time > 350 V / μs), which is regulated by a signal generator and a power amplifier to meet the charge behavior test requirements under different test 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 capacitance probe is arranged above the support platform and is connected to the high-voltage pulsed power supply module; the electrostatic probe is arranged below the support platform and is connected to the electrometer; the data acquisition system is connected to the electrometer, and the data acquisition system is an oscilloscope and an upper computer. The temperature control module includes an electric heating controller and a temperature sensor connected thereto. The temperature sensor is arranged at the bottom of the support platform, and the temperature control range of the temperature control module is -100°C to 100°C, with a continuous temperature regulation rate reaching 2°C / min. The mechanical force loading module is used to provide a mechanical tensile force to the sample of the polyimide material placed on the support platform. The mechanical force loading module includes a high-precision force sensor to control a stepper motor to adjust the tensile force, and the mechanical force loading module can apply a mechanical force of 0.1 N to 1000 N. The irradiation simulation module is used to provide irradiation to the sample of the polyimide material placed on the support platform. The irradiation simulation module adopts the Schottky thermionic emission principle and realizes electron irradiation with different beam currents and energies by controlling the electron emitter current and the acceleration electrode voltage respectively. The irradiation simulation module can generate an electron beam with an electron energy of 1 keV to 10 keV and a beam current density of 0 to 25 nA / cm 2 2.

[0053] To prevent errors in measurement results caused by signal interference of the platform, the shielding box adopts a multi-layer insulation structure of impregnation with insulating paint and laminated wrapping with aluminum foil for shielding, to avoid interference of electron irradiation on the test results. The vacuum environment of the shielding box is realized by connecting the shielding box to a vacuum pump. In addition, the shielding box is also 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 using a surface potential decay method and an atomic force microscope.

[0055] It can be understood that a simulated deep space environment is established to make the flexible substrate polyimide material withstand field strength, temperature, tension and radiation stress, and the surface potential change is measured by the surface potential decay method.

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

[0057] After obtaining the initial surface potential of the sample, the electron irradiation module begins to preheat. 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 to just above the sample and start irradiation.

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

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

[0061] In the second stage, the acquisition system works. At this time, the capacitance probe is kept running at a relatively slow speed, and the potential acquisition work is started synchronously. In order to minimize the potential attenuation phenomenon during the acquisition process, the measurement is stopped when the capacitance probe acquires the irradiation center point;

[0062] In the third stage, the tester immediately and quickly returns to the initial position for the next irradiation stage. In order to avoid charge dissipation during the test, the total time of the entire test working potential measurement stage is less than 10s.

[0063] Through repeated experiments, we completed tests on the surface potential, charge accumulation density, dissipation and other parameters of polyimide materials under different field strengths, different temperatures, different tensions, and different radiation intensities, both individually and synergistically, as well as surface flashover.

[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 materials are studied by detecting the extremely weak atomic interaction force between the sample surface and a miniature force sensitive element.

[0066] Fix one end of a pair of micro-cantilevers that are extremely sensitive to weak forces, and bring the tiny needle tip at the other end close to the sample, where it will interact with the sample, causing the force to cause the micro-cantilever to deform or change its motion state.

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

[0068] Utilize the temperature control module to achieve real-time regulation of the specimen temperature, and measure the surface trap characteristics of polyimide materials and the variation laws of the barrier energy level distribution with electric field, temperature, mechanical stress, and irradiation.

[0069] Step S103: Measure and calculate the conductivity and relative permittivity of polyimide materials using the three-electrode method and the bridge method.

[0070] In the multi-stress collaborative loading scenario, measure the conductivity and relative permittivity of polyimide using the three-electrode method and the bridge method.

[0071] Dielectric properties refer to the response characteristics of the bound charges in the material molecules to the externally applied stress field, which are important parameters for describing the material properties and include conductivity, permittivity, dielectric loss, etc. Under the action of multi-stresses alone and in combination, the conductivity, relative permittivity, and charge mobility are obtained through the first formula, the second formula, and the third formula;

[0072] The first formula is:

[0073]

[0074] where G 0 is the initial conductivity, coeff(T) is the temperature-related correction coefficient, q free (T) is the free charge density (C·m -3 ), P tr is the charge trapping probability (s -1 ), P de (T) is the charge detrapping probability (s -1 ), q e is the electronic charge, N t is the trap density (m -3 ), and t is the acting time;

[0075] The second formula is:

[0076] where C is the capacitance, ε is the relative permittivity, S is the plate area, k is the electrostatic constant, and d is the plate spacing;

[0077] The third formula is:

[0078]

[0079] where V(t) is the voltage corresponding to the current time, Q 0is 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 material sample, C is the capacitance, t is the current time, t 0 For the crossing 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 external stress fields. They are important parameters for describing material performance, including conductivity, dielectric constant, dielectric loss, etc. On the basis of the multi-stress collaborative loading device, the three-electrode method and the bridge method are used to build a conductivity and relative dielectric constant measurement platform. The test sample of polyimide material is placed in the test cavity, and the test cavity is heated according to the test requirements. Using an electrometer, after pressurization, the first formula and the second formula are used to obtain the variation law of key dielectric characteristic parameters such as conductivity and relative dielectric constant of polyimide material with temperature, field strength, mechanical force and irradiation under the working conditions to be tested.

[0081] Step S104: measuring carrier mobility using a transit time algorithm and an electroacoustic pulse method.

[0082] Specifically, the transit time algorithm calculates mobility based on the time it takes for a carrier to travel a certain distance under the action of an electric field. After applying an electric field at both ends of the polyimide material and injecting charges, the transit time for the charges to migrate from one end of the material to the other is measured. The carrier mobility can be calculated by combining the measured material thickness, voltage, and transit time. The electroacoustic pulse method injects an electric pulse into the polyimide material to generate an acoustic pulse, which propagates in the material. The carrier mobility is calculated by detecting information such as the propagation time and amplitude of the acoustic pulse.

[0083] The transit time algorithm, the third formula and the electroacoustic pulse method are used to measure and calculate the mobility of carriers or ions (including positive and negative ions, holes, electrons, etc.) of materials with controllable temperature and field strength. The temperature of the polyimide material is reasonably regulated through real-time temperature feedback. The temperature control range is -100 to 100°C, and the control accuracy is 0.1°C. The mobility of carriers of different polarities is tested by measuring the charge accumulation rate, and the change law of the charge mobility of polyimide materials and other internal charge characteristics of the material under the action of multiple stresses alone and in combination is measured. Physical phenomena such as charge injection, trapping, detrapping, and migration determine the surface potential decay process. By analyzing the dynamic characteristics of surface potential decay through the dynamic change of surface potential over time, parameters such as the trap energy level distribution on the surface of the sample can be obtained.

[0084] Step S105: constructing a dynamic charge migration model of the polyimide material under the synergistic effect of multiple stresses, determining the coefficients of the dynamic charge migration model by measuring and calculating the parameters, and using the dynamic charge migration model to calculate and analyze the charge accumulation characteristics of the polyimide material.

[0085] Specifically, according to the Fowler-Nordheim (Fowler-Nordheim tunneling effect) tunneling effect, the coupling term of the electric field and temperature is calculated based on the influence of temperature on the barrier height; in the coupling term of the electric field and temperature, electrons tunnel through the barrier via quantum tunneling under a high electric field, resulting in non-linear conductance and a decrease in the barrier height due to the increase in temperature, enhancing the probability of carrier detrapping.

[0086] According to the Fowler-Nordheim formula, the field emission current density is: Where: A is a material constant, the charge q, mass m, and barrier height h represents Planck's constant, and E is the electric field strength; B is a parameter related to the barrier height. An increase in temperature will reduce the barrier height, and the modified barrier is: Where, represents the modified effective barrier height, is the initial barrier height without considering the influence of temperature, is the change in the barrier height caused by the temperature change; assuming, then the modified field emission formula: Where, k B represents the Boltzmann constant; after simplification (Taylor expansion retaining the first-order term): J FN (E,T)≈αE 2 e -β / T , where e represents the natural constant.

[0087] According to the stress-induced lattice dislocation and radiation-induced chemical bond breakage, the coupling term of stress and radiation is calculated. In the coupling term of stress and radiation, the coupling effect of stress and radiation affects charge migration. Applying tensile / compressive stress causes periodic damage to the material lattice, generating dislocations and microcracks. The increase in dislocation density forms charge trapping centers, and the measured trap density N t increases linearly with stress, and the proportionality coefficient k σ , high-energy electron irradiation induces the breakage of C-N bonds, generating free radicals and vacancy-type defects, and the 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 a uniaxial tensile test: Where, the increase in trap density caused by the applied stress is σ is the mechanical stress, and the radiation damage kinetic equation is obtained based on Monte Carlo simulation: Where, is the change rate of the defect density with time, Φ represents the incident particle flux, σ dis the irradiation damage cross-section, N d = N sat (1 - e -δD ), where N d is the defect density, δ is the damage coefficient, and at low doses N d ≈ δD; Solving for the steady-state defect density N d = N sat (1 - e -δD ), where N sat is the saturation defect density, and e -δD reflects the relationship between the irradiation dose D and the saturation defect density N sat ; At low doses N d ≈ δD; Assume that the synergistic effect of stress and irradiation is manifested as a multiplicative enhancement of the defect density: where is the initial trap density, is the increase in trap density due to the applied stress, is the defect density generated by irradiation, γ is the coefficient of the stress-irradiation coupling term, δ is the damage coefficient, D is the irradiation dose, and by fitting the multi-stress experimental data using the least squares method, the form of the coupling term is determined to be: G σ-D = γσln(1 + δD), where G σ-D represents the stress-irradiation coupling term, and γ is the coefficient of the stress-irradiation coupling term.

[0088] Combining the drift current and the diffusion current, they are merged into the migration-diffusion term through the Einstein relation. The motion of carriers in the electric field in the drift current: J drift = μρE, where J drift represents the drift current density, μ is the charge mobility, ρ is the charge density, and E is the electric field strength; The diffusion driven by the concentration gradient in the diffusion current: where J diffusion is the diffusion current density, is the charge density gradient, and M is the diffusion coefficient; According to the Einstein relation M = -μk B T / q, where T is the temperature, and the total current density can be merged as: k B is the Boltzmann constant. Taking the divergence of the total current density, where reflects the net outflow (or inflow) of the current density at a certain point in space. Under the steady-state assumption is simplified to: Because the charge decreases due to migration out of the region, the migration-diffusion term is

[0089] According to the physical mechanisms of the coupling of electric field and temperature, the coupling of stress and irradiation, and the migration and diffusion of charges, a dynamic charge migration model is constructed. Based on the principle of charge conservation, the change of charge density with time is described. Among them, ρ is the charge density; M is the carrier generation rate, R is the carrier recombination rate. is the total current density of taking the divergence. The carrier generation rate includes: the coupling term of electric field and temperature and the coupling term of stress and irradiation; in polyimide materials dominated by deep traps, the recombination rate can be ignored (trap capture is dominant), so: R≈0. Because charges decrease due to migration out of the region, the migration and diffusion term is

[0090] The expression of the dynamic charge migration model is:

[0091]

[0092] Among them, ρ is the charge density, αE 2 e -β / T is the coupling term of electric field and temperature, and the quadratic electric field reflects non-linear conduction. γσln(1 + δD) is the coupling term of stress and irradiation. is the migration and diffusion term; α is the coefficient of the coupling term of electric field and temperature, E is the electric field strength, β is the temperature sensitivity coefficient, T is the temperature, γ is the coefficient of the coupling term of stress and irradiation, σ is the mechanical stress, δ is the irradiation damage coefficient, D is the irradiation dose, and μ is the charge mobility.

[0093] It should be understood that in order to make the dynamic charge migration model more accurately describe the charge accumulation characteristics of polyimide materials, the coefficients in the model need to be determined. By measuring the conductivity and relative permittivity under different stress conditions, experimental data can be obtained. These data are closely related to the charge migration characteristics and can provide strong support for determining the coefficients related to charge migration. When determining the electric field-temperature coupling coefficients (α and β), experiments with different combinations of electric field strength and temperature are carried out, and the change of charge density with time is measured. The variation laws of conductivity and relative permittivity with temperature and electric field strength help to understand the charge migration process, and then make the measured data match the electric field-temperature coupling term in the model, so as to determine the values of α and β. When 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 can reflect the influence of stress and irradiation on charge capture 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 are carried out. The conductivity and relative permittivity of the polyimide material are measured using the three - electrode method and the bridge method respectively under various working conditions. At the same time, the data of the change of charge density with time are recorded. Under the conditions of setting different temperatures (such as - 100 °C, 0 °C, 100 °C, etc.) and electric field strengths (selecting multiple values within the range of 0 - ±20 kV), the material is tested to obtain the corresponding curves of conductivity, relative permittivity, and the change of charge density with time. The measured conductivity and relative permittivity data are combined with the charge density change data and fitted to the electric - field - temperature coupling term in the dynamic charge migration model. Since the conductivity and relative permittivity are affected by temperature and electric field, their variation laws reflect the effect of electric - field - temperature coupling on charge migration. By adjusting the values of α and β, the change of charge density calculated by the model is made to match the experimental measurement values as much as possible. First, fix the temperature and change the electric field strength, observe the difference between the change of charge density and the model calculation result, and adjust α and β; then fix the electric field strength and change the temperature and repeat the above operation. Finally, determine the values of α and β that can best fit the model and experimental data.

[0095] When determining the stress - irradiation coupling coefficients (γ and δ), experiments are carried out under different combinations of mechanical stress (0.1 N - 1000 N) and irradiation dose (electron energy of 1 keV - 10 keV, beam current density of 0 - 25 nA / cm 2 electron beam), and the conductivity and relative permittivity of the polyimide material are measured. During the experiment, data related to charge density, such as surface charge density and space charge distribution, are recorded synchronously. Gradually increase the mechanical stress and irradiation dose, and observe the changes in conductivity and relative permittivity, as well as the response of charge density. Using the measured conductivity, relative permittivity, and charge density data, fit the stress - irradiation coupling term. Stress and irradiation will affect the microstructure of the material, thereby changing the conductivity and relative permittivity, and these changes are related to charge capture and migration. By fitting methods such as the least - squares method, adjust the values of γ and δ so that the calculation result of the stress - irradiation coupling term in the model fits the experimental data, and thus determine the values of γ and δ.

[0096] Using a multi - stress collaborative loading platform, under different combinations of electric field (0~±20 kV), temperature (- 100~100 °C), mechanical stress (0.1~1000 N), and irradiation (electron energy of 1 keV - 10 keV, beam current density in 0 - 25 nA / cm 2 electron beam), measure the surface charge density (surface potential decay method); space charge distribution (atomic force microscope); conductivity (three - electrode method); permittivity (bridge method); carrier mobility (transit - time algorithm, electro - acoustic pulse method). Through non - linear regression or the least - squares method, determine the model coefficients (α, β, γ, δ) based on the experimental data.

[0097] The surface charge density, space charge distribution and surface trap energy level of polyimide materials are measured by surface potential decay method and atomic force microscope. Measurements are carried out under different combinations of electric field, temperature, mechanical stress and irradiation, and the corresponding charge distribution data are obtained. These data reflect the distribution of charges on the surface and inside the material, are related to the charge density, and provide basic data support for determining the coefficients.

[0098] The conductivity and relative permittivity of polyimide materials are measured by three - electrode method and bridge method. The conductivity and relative permittivity under different stress conditions are measured. These parameters are closely related to the charge migration characteristics and can assist in determining the coefficients related to charge migration.

[0099] The carrier mobility is measured by the transit - time algorithm and the electro - acoustic pulse method. The carrier mobility data are measured under various stress combinations, which directly provide a basis for determining the mobility (μ), and also help to determine other coefficients related to charge migration.

[0100] For the electric - field - temperature coupling coefficients (α and β), experiments with different combinations of electric - field intensity and temperature are carried out to measure the change of charge density with time. By fitting these data, the measured data are matched with the electric - field - temperature coupling term in the model, so as to determine the values of (α and β). Fix the temperature, change the electric - field intensity, measure the change of charge density, then fix the electric - field intensity and change the temperature for measurement, and use the measured data to fit out (α and β).

[0101] For the stress - irradiation coupling coefficients (γ and δ), experiments are carried out under different combinations of mechanical stress and irradiation dose to measure the charge - density - related data. By fitting the experimental data with the stress - irradiation coupling term, the values of γ and δ are determined. Gradually increase the stress and irradiation dose, and record the change of charge density for fitting and solving the coefficients.

[0102] The mobility (μ), the carrier mobility data directly measured by the transit - time algorithm and the electro - acoustic pulse method, can directly calibrate the value of the mobility (μ) after data processing and statistical analysis.

[0103] Numerical calculation methods such as the finite - difference method or the finite - element method are used to solve the partial - differential equations of the dynamic charge - migration model. The finite - difference method discretizes the continuous model equation into difference equations and obtains the charge density at different times and positions through iterative calculation; the finite - element method divides the material region into a finite number of elements, approximately solves each element, and then integrates to obtain the overall charge - density distribution. According to the actual experimental situation, ensure the accuracy and uniqueness of the model solution.

[0104] Measurements and calculations are carried out using a multi-stress collaborative loading platform and a dynamic charge migration model to obtain the data in Table 1; as shown in Table 1. The multi-stress collaborative effect significantly exacerbates charge accumulation. The charge density under the four-stress collaboration is 5.6 times that of a single electric field, verifying the effectiveness of the model for the dynamic charge migration model in a complex environment.

[0105] Table 1

[0106] Stress conditions <![CDATA[Charge density (C / m 3 )]]> <![CDATA[Accumulation rate (C / m 3 ·s)]]> Single electric field (10 kV) <![CDATA[1.2×10 -5 > <![CDATA[3.5×10 -7 > Electric field + temperature (10 kV, 80 °C) <![CDATA[2.8×10 -5 > <![CDATA[9.1×10 -7 > Electric field + irradiation (10 kV, 5 keV) <![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, the conductivity increases significantly, accelerating charge migration. However, high temperatures also reduce the barrier height, resulting in an increased probability of trap detrapping and faster charge dissipation. Tensile stress linearly increases the trap density, and the irradiation dose leads to defect accumulation. The combined effect of the two significantly enhances the charge capture ability and exacerbates charge accumulation. Under a high electric field, the migration term dominates, and charges rapidly migrate into the material interior, forming space charges.

[0108] Calculate the numerical solution of the dynamic charge migration model to evaluate the charge accumulation rate under different stress combinations. Analyze the spatial distribution of the charge density after long-term action to predict the dielectric breakdown risk of the material.

[0109] Through the dynamic charge migration model, analyze the charge accumulation characteristics of polyimide materials under the action of electric fields, temperatures, mechanical stresses, and irradiation, and achieve accurate prediction and regulation of the electrical properties of polyimide materials.

[0110] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated herein.

[0111] It should be noted that although several modules or units of a device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of the 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. The components shown as modules or units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present disclosure solution. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0112] In an exemplary embodiment of the present disclosure, an electronic device is further provided. The electronic device may include a processor and a memory for storing executable instructions of the processor. Among them, the processor is configured to execute the steps of the method for analyzing the charge accumulation characteristics of the polyimide material in any one of the above embodiments by executing the executable instructions.

[0113] Those skilled in the art of the present technology can understand that various aspects of the present invention can be implemented as a system, a method, or a program product. Therefore, various aspects of the present invention can be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to as "circuit", "module", or "system" here.

[0114] Through the description of the above embodiments, those skilled in the art can easily understand that the exemplary embodiments described here can be implemented by software or by a combination of software and necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, or a network device, etc.) to execute the method for analyzing the charge accumulation characteristics of the polyimide material according to the above embodiments of the present disclosure.

[0115] In an exemplary embodiment of the present disclosure, a computer storage medium is further provided, on which a computer program is stored. When the program is executed by, for example, a processor, the steps of the method for analyzing the charge accumulation characteristics of the polyimide material in any one of the above embodiments can be implemented.

[0116] In some possible implementation manners, various aspects of the present invention can also be implemented in the form of a computer program product, which includes a computer program or instructions. When the computer program product runs on a terminal device, the computer program code or instructions are used to enable the terminal device to execute the steps according to various exemplary embodiments of the present invention described in the part of the method for analyzing the charge accumulation characteristics of the polyimide material in this specification.

[0117] The above program product can be written in any combination of one or more programming languages for executing the operations of the present invention. The programming languages include object-oriented programming languages such as Java, C++, etc., and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, executed as a stand-alone 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 the case of a remote computing device, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (e.g., by using an Internet service provider to connect through the Internet).

[0118] The computer software product can be stored in a computer storage medium, which includes 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 memories, magnetic disk memories, tape memories, or any other computer-readable medium capable of carrying or storing data.

[0119] Those skilled in the art will readily conceive of other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include known common knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and examples are only considered exemplary, and the true scope and spirit of the present disclosure are pointed out by the appended claims.

Claims

1. A method for analyzing the charge accumulation characteristics of a polyimide material, characterized in that: The following steps are involved: Based on the multi-stress state of the polyimide material in the deep space environment, including electric field, temperature, mechanical stress and irradiation, a multi-stress synergistic effect is applied to the polyimide material; The surface charge density, spatial charge distribution and surface trap energy level of polyimide materials were calculated by surface potential decay method and atomic force microscopy. The three-electrode method and bridge method were used to measure and calculate the conductivity and relative dielectric constant of polyimide materials. The carrier mobility of polyimide materials was measured and calculated using the transit time algorithm and the electroacoustic pulse method. A dynamic charge migration model of polyimide material under the synergistic action of multiple stresses is constructed, the coefficients of the dynamic charge migration model are determined by measuring and calculating the parameters, and the dynamic charge migration model is used to calculate and analyze the charge accumulation characteristics of the polyimide material.

2. The method for analyzing the charge accumulation characteristics of a polyimide material according to claim 1, characterized in that: The multi-stress synergistic effect is applied to the polyimide material using a multi-stress synergistic loading platform; The multi-stress collaborative loading platform includes: a supporting 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 the support platform is used to place the sample of the polyimide material. The electric field loading module provides field strength and pulse current to the sample of the polyimide material in the shielding box. The temperature control module includes an electric heating controller and a temperature sensor connected thereto, and the temperature sensor is arranged at the bottom of the support platform. The mechanical force loading module is used to provide mechanical tension to the sample of the polyimide material placed on the support platform. The irradiation simulation module is used to provide 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.

3. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 1, characterized in that: The conductivity expression is: Where G0 is the initial conductivity, coeff(T) is the temperature-dependent correction factor, and q free (T) is the free charge density (C·m -3 ), P tr is the charge trapping probability (s -1 ), P de (T) is the charge trapping probability (s -1 ), q e is the electron charge, N t is the trap density (m -3 ), t is the action time.

4. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 1, characterized in that: The expression of the relative dielectric constant is: Among them, C is the capacitance, ε is the relative dielectric constant, S is the plate area, k is the electrostatic force constant, and d is the plate spacing.

5. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 1, characterized in that: The expression of the carrier mobility is: Among them, V(t) is the change of potential difference with 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 material sample, D is the capacitance, t is the current time, and t0 is the transit time.

6. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 1, characterized in that: The step of constructing a dynamic charge migration model of polyimide material under the synergistic effect of multiple stresses comprises: According to the Fowler-Nordheim tunneling effect, the coupling term between electric field and temperature is calculated based on the temperature effect on the barrier height. The stress and radiation coupling terms are calculated based on the lattice dislocation caused by stress and the chemical bond breaking caused by radiation; The drift current and diffusion current are combined into the migration diffusion term through the Einstein relationship.

7. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 1, characterized in that: The expression of the dynamic charge migration model is: Where ρ is the charge density, αE 2 e -β / T is the coupling term between electric field and temperature, γσln(1+δD) is the coupling term between stress and radiation, is the migration and diffusion term; α is the coefficient of the electric field and temperature coupling term, E is the electric field strength, β is the temperature sensitivity coefficient, T is the temperature, γ is the coefficient of the stress and radiation coupling term, σ is the mechanical stress, δ is the radiation damage coefficient, D is the radiation dose, and μ is the charge mobility.

8. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 2, characterized in that: The electric field loading module can generate a variable voltage of 0-±20 kV and a current of 0-20 mA.

9. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 8, characterized in that: The temperature control range of the temperature control module is -100°C to 100°C.

10. The method for analyzing charge accumulation characteristics of polyimide materials according to claim 9, characterized in that: The mechanical force loading module can apply a mechanical force of 0.1N-1000N; the irradiation simulation module can generate an electron energy of 1keV-10keV and a beam current density of 0-25nA / cm 2 of electron beam.

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