Simulation Method and System for Dielectric Transient Current and Conductance Entropy-Enthalpy Compensation Characteristics

Abstract

The present invention discloses a simulation method and system for the transient current and conductance entropy-enthalpy compensation characteristics of dielectrics, proposes an inverse power function form of the attempt-to-jump frequency of charge carriers, and obtains the carrier migration rate based on the hopping transport of charge carriers and the carrier resonance effect. A two-step charge transfer model at the electrode-dielectric interface is proposed, and the injection current density based on the filling of surface traps and hopping transport in the dielectric is obtained. Considering comprehensively the charge injection, charge migration and diffusion, charge conservation, and Poisson's equation at the electrode-dielectric interface, a bipolar charge transport model of the nanocomposite dielectric is established. Finally, a simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric is established by integrating the bipolar charge transport and Fourier heat conduction.

Description

Technical Field

[0001] The invention belongs to the technical field of computational high voltage engineering, and in particular relates to a method and system for simulating transient current and conductivity entropy-enthalpy compensation characteristics of nanocomposite dielectrics. Background Art

[0002] Dielectric energy storage capacitors have the advantages of high power density, high working field strength, long charge and discharge cycle life, easy processing, and environmental protection. They have been widely used in the fields of new energy power generation, pulse power technology, and electromagnetic energy equipment. However, compared with energy storage devices such as electrochemical capacitors and lithium-ion batteries, the energy density of dielectric energy storage capacitors is relatively low, which limits their application to a certain extent. Therefore, the development of high-energy-density capacitors urgently requires the research and development of high-performance electrical insulation materials.

[0003] Nanocomposite dielectrics are known as the third generation of electrical insulation materials. They have many excellent properties and are the preferred materials for high energy density capacitors. The conductivity of nanocomposite dielectrics determines the high temperature breakdown strength, high temperature energy storage density, and charge and discharge efficiency of capacitors. The structure and properties of the interface region in nanocomposite dielectrics determine the trap distribution characteristics in the nanocomposite dielectrics, and then determine the transport characteristics and conductivity characteristics of charge carriers. In order to establish the relationship between the structure and properties of the interface region and the macroscopic conductivity characteristics, it is urgent to develop a charge carrier transport simulation method that considers the trap distribution characteristics of the interface region. In order to clarify the influence of the trap distribution characteristics of the interface region on the macroscopic conductivity, the essential connection of the conductivity characteristics of nanocomposite dielectrics can be found. Then, the relationship between the structure and properties of the interface region and the macroscopic conductivity characteristics is established using the interface region traps as a bridge, providing theoretical and methodological support for the development of high-performance nanocomposite dielectrics. Summary of the invention

[0004] The present invention provides a method and system for simulating transient current and conductivity entropy-enthalpy compensation characteristics of dielectrics, establishes the relationship between the structure and properties of the interface region and the macroscopic conductivity characteristics, and provides theoretical and methodological support for the research and development of high-performance nanocomposite dielectrics.

[0005] To achieve the above object, the method for simulating transient current and conductivity entropy-enthalpy compensation characteristics of nanocomposite dielectrics of the present invention comprises the following steps:

[0006] Step 1: Establish an inverse power function of the attempted hopping frequency of charge carriers in the nanocomposite dielectric, and obtain the transient charge carrier attempted escape frequency according to the inverse power function; obtain the electron migration rate and hole migration rate based on hopping transport and carrier resonance effect according to the attempted hopping frequency of charge carriers;

[0007] Step 2: Calculate the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface according to the transient charge carrier attempted escape frequency obtained in step 1;

[0008] Step 3: Establish the charge migration and diffusion equations at the electrode-dielectric interface of the nanocomposite dielectric. Based on the charge migration and diffusion equations at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, and the electron migration rate and hole migration rate obtained in Step 1, establish the bipolar charge transport model of the nanocomposite dielectric;

[0009] Step 4: Establish the Fourier heat conduction equation. Based on the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface, the Fourier heat conduction equation, the transient current calculation formula of the dielectric material, the steady-state conductivity calculation formula of the dielectric material, and the bipolar charge transport model of the nanocomposite dielectric, establish the simulation model of the transient current and the conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric. Use the simulation model to simulate the transient current and the conductance entropy-enthalpy compensation characteristics of the dielectric, and obtain the conductive characteristics of the nanocomposite dielectric at different temperatures.

[0010] Further, in Step 1, the inverse power function of the charge carrier's attempted jump frequency is:

[0011] υ ATE (t) = υ0(αt -β +1) (1);

[0012] Where: υ ATE (t) is the transient charge carrier's attempted escape frequency, υ0 is the charge carrier's attempted escape frequency at steady state, t represents the time when the electric field is applied, α is the pre-factor of the inverse power function, and β is the exponent of the power function; α and β are coefficients related to the electric field E and the test temperature T, i.e., α(E,T) and β(E,T).

[0013] Further, in Step 1, the calculation formulas for the electron migration rate and the hole migration rate are:

[0014]

[0015]

[0016] Where: v e (x,t) and v h (x,t) are the electron and hole migration rates respectively, λ e and λ h are the average jump distances of electrons and holes respectively, u T(e) and u T(h) are the trap energy levels of electrons and holes respectively, e is the electron charge, k B is the Boltzmann constant, T MNis the Meyer-Neldel temperature, x represents the position in the dielectric, E(x,t) is the externally applied electric field strength, and T is the test temperature.

[0017] Furthermore, in step 2,

[0018] The calculation formulas for the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface are:

[0019]

[0020]

[0021] Where: j in(e) (0,t) and j in(h) (d,t) are the charge injection densities at the cathode-dielectric and anode-dielectric interfaces respectively, n MD(e) and n MD(h) are the surface trap electron and surface trap hole densities formed by charge transfer at the interface between the nanocomposite dielectric and the electrode respectively.

[0022] Furthermore, in step 3, the established charge migration and diffusion equations are:

[0023]

[0024]

[0025] Among them, j D(e) (x,t) and j D(h) (x,t) are the conduction current densities formed by electrons and holes respectively, D e and D h are the diffusion coefficients of electrons and holes respectively.

[0026] Furthermore, in step 3, the bipolar charge transport model of the nanocomposite dielectric includes the charge injection density at the electrode-dielectric interface, the charge migration and diffusion equations at the electrode-dielectric interface, the charge conservation equation, and the Poisson equation.

[0027] Furthermore, in step 4, the Fourier heat conduction equation is:

[0028]

[0029] Where: ρ is the mass density of the nanocomposite dielectric, Cs is the specific heat capacity, and κ is the thermal conductivity of the nanocomposite dielectric.

[0030] A simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric includes a migration rate calculation module, a charge injection density calculation module, a charge migration and diffusion equation module, and a simulation module;

[0031] A migration rate calculation module, which is used to establish an inverse power function of the attempted jump frequency of charge carriers in the nanocomposite dielectric, and obtain the attempted escape frequency of transient charge carriers according to the inverse power function; obtain the electron migration rate and hole migration rate based on the jump transport and carrier resonance effect according to the attempted jump frequency of charge carriers.

[0032] A charge injection density calculation module, which is used to calculate the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface according to the attempted escape frequency of transient charge carriers.

[0033] A charge migration and diffusion equation module, which is used to establish a charge migration and diffusion equation at the electrode-dielectric interface of the nanocomposite dielectric, and establish a bipolar charge transport model of the nanocomposite dielectric according to the charge migration and diffusion equation at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, the electron migration rate and the hole migration rate.

[0034] A simulation module, which is used to establish a Fourier heat conduction equation, and establish a simulation model of the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric according to the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface, the Fourier heat conduction equation, the transient current calculation formula of the dielectric material, the steady-state conductivity calculation formula of the dielectric material and the bipolar charge transport model of the nanocomposite dielectric, and simulate the transient current and conductance entropy-enthalpy compensation characteristics of the dielectric with the simulation model to obtain the conductive characteristics of the nanocomposite dielectric at different temperatures.

[0035] A simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric, comprising:

[0036] A processor;

[0037] A memory for storing instructions executable by the processor;

[0038] Wherein, the processor is configured to execute the above-mentioned simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the nanocomposite dielectric.

[0039] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0040] (1) After the nano-composite dielectric contacts the electrode, the charges in the electrode are first transferred to the surface traps of the nano-composite dielectric. After an electric field is applied, the amount of charge in the surface traps of the nano-composite dielectric enters the interior of the dielectric in the form of hopping transport. Based on the above characteristics, the present invention establishes an inverse power function form of the attempted hopping frequency of charge carriers, and obtains the carrier migration rate based on the hopping transport of charge carriers and the carrier resonance effect. A two-step charge transfer model is proposed to obtain the injection current density based on the surface trap filling and hopping transport of the nano-composite dielectric. And a bipolar charge transport model of the nano-composite dielectric is established by comprehensively considering charge injection, charge migration and diffusion, charge conservation and Poisson's equation at the electrode-dielectric interface. Finally, a simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling of the nano-composite dielectric is established by integrating bipolar charge transport and Fourier heat conduction. The structure and properties of the interface region determine the trap distribution characteristics, and thus determine the transport characteristics and conductance characteristics of charge carriers. The present invention can establish the correlation between the structure and properties of the interface region and the macroscopic conductance characteristics, obtain the conductance characteristics of the polymer nano-composite dielectric, and develop high-performance electrical insulation materials by studying the conductance characteristics of different polymer nano-composite dielectrics, and then develop capacitors with high energy density.

[0041] (2) The present invention uses the weighted essentially non-oscillatory method and the implicit method to solve the charge conservation equation, the implicit method to solve the charge migration and diffusion equation and the Fourier heat conduction equation, and the finite element method to solve Poisson's equation. It integrates the advantages of the weighted essentially non-oscillatory method, the implicit method, the finite element method, etc., and numerically solves the bipolar charge transport model and the Fourier heat conduction equation. The solution process is fast, efficient, accurate and stable, realizing the stable, efficient and high-precision numerical solution of the generalized Poisson's equation. Description of the Drawings

[0042] Figure 1 is the overall flow chart of the present invention;

[0043] Figure 2 is the charge injection and hopping transport model in the nano-composite dielectric;

[0044] Figure 3 is the temperature dependence of the steady-state conductivity of six polyetherimide nano-composite dielectric specimens; (a) is the temperature dependence of the conductivity of polyetherimide nano-composite dielectrics with different doping contents at 20 kV / mm, and (b) is the analysis of the steady-state conductivity test results of PEI nano-composite dielectric specimens at different temperatures using the Meyer compensation formula;

[0045] Figure 4Transient current characteristics of six polyetherimide nanocomposite dielectric specimens at different temperatures. (a) shows the transient current characteristics of specimen 1, (b) shows those of specimen 2, (c) shows those of specimen 3, (d) shows those of specimen 4, (e) shows those of specimen 5, and (f) shows those of specimen 6;

[0046] Figure 5 Variation characteristics of space charge distribution with time for six polyetherimide nanocomposite dielectric specimens at a temperature of 350K. (a) shows the variation characteristics of specimen 1, (b) shows those of specimen 2, (c) shows those of specimen 3, (d) shows those of specimen 4, (e) shows those of specimen 5, and (f) shows those of specimen 6;

[0047] Figure 6 Variation characteristics of electric field distribution with time for six polyetherimide nanocomposite dielectric specimens at a temperature of 350K. (a) shows the variation characteristics of specimen 1, (b) shows those of specimen 2, (c) shows those of specimen 3, (d) shows those of specimen 4, (e) shows those of specimen 5, and (f) shows those of specimen 6;

[0048] Figure 7 Steady-state conductivity temperature dependence of six polyimide nanocomposite dielectric specimens. (a) is the Arrhenius plot, and (b) is the entropy-enthalpy compensation characteristic plot;

[0049] Figure 8 Transient current characteristics of six polyimide nanocomposite dielectric specimens at different temperatures. (a) shows the transient current characteristics of specimen 1, (b) shows those of specimen 2, (c) shows those of specimen 3, (d) shows those of specimen 4, (e) shows those of specimen 5, and (f) shows those of specimen 6;

[0050] Figure 9 Variation characteristics of space charge distribution with time for six polyimide nanocomposite dielectric specimens at a temperature of 350K. (a) shows the variation characteristics of specimen 1, (b) shows those of specimen 2, (c) shows those of specimen 3, (d) shows those of specimen 4, (e) shows those of specimen 5, and (f) shows those of specimen 6;

[0051] Figure 10The variation characteristics of the electric field distribution of six polyimide nanocomposite dielectric specimens with time at a temperature of 350K, where (a) shows the variation characteristics of specimen 1, (b) shows the variation characteristics of specimen 2, (c) shows the variation characteristics of specimen 3, (d) shows the variation characteristics of specimen 4, (e) shows the variation characteristics of specimen 5, and (f) shows the variation characteristics of specimen 6;

[0052] Figure 11 Schematic diagram of the dielectric transient current and conductance entropy-enthalpy compensation characteristic simulation system provided by the present invention. Specific implementation manners

[0053] In order to make the objectives and technical solutions of the present invention clearer and easier to understand, the following further details the present invention with reference to the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0054] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation of the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise stated, the meaning of "plurality" is two or more. In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "mounted", "connected" and "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the internal communication of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0055] Referring to Figure 1 , a method for simulating the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric includes the following steps:

[0056] Step 1: Establish the inverse power function of the attempted hopping frequency of charge carriers, and obtain the transient attempted escape frequency of charge carriers from the inverse power function; obtain the electron migration rate and hole migration rate based on hopping transport and carrier resonance effects; specifically:

[0057] The process of establishing the inverse power function form of the attempted hopping frequency of charge carriers is as follows:

[0058] The frequency-domain response characteristics of the transient current indicate that when the voltage is just applied, the charge carriers in the nanocomposite dielectric will resonate with the applied external electric field, resulting in the vibration frequency of the charge carriers being much greater than that in the steady state. As the voltage application time extends, the resonance between the charge carriers and the applied external electric field gradually weakens and finally approaches the vibration frequency under thermal action. The resonance under the action of the transient electric field will cause the attempted escape frequency of the charge carriers to increase. As the electric field application time extends, the resonance effect weakens, and the attempted escape frequency of the charge carriers will tend to the steady-state value. The inverse power function form of the attempted hopping frequency of charge carriers can be expressed as follows:

[0059] υ ATE (t) = υ0(αt -β + 1)(1)

[0060] In the formula: υ ATE (t) is the transient attempted escape frequency of charge carriers, υ0 is the attempted escape frequency of charge carriers in the steady state, t represents the time of applying the electric field, α is the pre-factor of the inverse power function, and β is the exponent of the power function. α and β are coefficients related to the electric field E and the test temperature T, i.e., α(E,T) and β(E,T).

[0061] The migration rate of charge carriers based on hopping transport and carrier resonance effects. Under the action of the applied external electric field, the charge carriers inside the nanocomposite dielectric will undergo directional migration, forming a charge transport process microscopically and a current macroscopically. There are generally many traps or localized states in the nanocomposite dielectric, which may be formed by polar groups, folding of molecular chains, energy band discontinuities between molecular chains, etc. The charge carriers are transported in the form of hopping between the traps or localized states. Considering the influence of the resonance effect on the attempted escape frequency of the carriers, i.e., Equation (1), the calculation formula for the migration rate of charge carriers can be obtained as:

[0062]

[0063]

[0064] In the formula: v e (x,t) and v h (x,t) are the migration rates of electrons and holes respectively, λ e and λh are the average hopping distances of electrons and holes, respectively, u T(e) and u T(h) are the trap energy levels of electrons and holes, respectively, e is the electron charge, k B is the Boltzmann constant, T MN is the Meyer-Neldel temperature, x represents the position in the dielectric, E(x,t) is the applied electric field strength, and T is the test temperature.

[0065] Step 2: Establish a two-step charge transfer model at the electrode-dielectric interface. The two-step charge transfer model is used to represent the process of trap filling on the dielectric surface. According to the two-step charge transfer model and Step 1, calculate the charge injection density at the cathode-dielectric and the charge injection density at the anode-dielectric interface for the transient charge carriers attempting to escape frequency, which specifically includes the following steps:

[0066] There are many surface traps on the surface of the nanocomposite dielectric. After the nanocomposite dielectric contacts the electrode, the charges in the electrode first transfer to the surface traps of the nanocomposite dielectric. Since the charge density in the electrode is very large and the electrode can provide sufficient charges, the charge amount in the surface traps of the nanocomposite dielectric can be kept at a constant value. After applying an electric field, the charge amount in the surface traps of the nanocomposite dielectric will enter the interior of the dielectric in the form of hopping transport, as Figure 2 shown. Figure 2 It shows that the charges in the electrode will first transfer to the surface traps of the nanocomposite dielectric and then jump from the surface traps into the interior of the dielectric. This process is called the two-step charge transfer model. From the two-step charge transfer model, the injection current density at the electrode-dielectric interface is related to the charge amount, trap energy level, and average hopping distance of the carriers in the surface traps of the nanocomposite dielectric. The charge injection density at the electrode-dielectric interface can be expressed by the following formula:

[0067]

[0068]

[0069] In the formula: j in(e) (0,t) and j in(h) (d,t) are the charge injection densities at the cathode-dielectric and anode-dielectric interfaces, respectively, n MD(e) and n MD(h) are the surface trap electron and surface trap hole densities formed by charge transfer at the interface between the nanocomposite dielectric and the electrode, respectively.

[0070] Step 3: Establish the charge migration and diffusion equations at the electrode-dielectric interface. Based on the charge injection density at the electrode-dielectric interface, the charge migration and diffusion equations at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, and the electron migration rate and hole migration rate obtained in Step 1, establish a bipolar charge transport model for the nanocomposite dielectric. The bipolar charge transport model includes the charge injection density at the electrode-dielectric interface, the charge migration and diffusion equations at the electrode-dielectric interface, the charge conservation equation, and the Poisson equation; calculate the conduction current density formed by electrons and holes according to the charge migration and diffusion equations; and use the Poisson equation to solve the potential and electric field distributions inside the nanocomposite dielectric, including the following steps:

[0071] Construct the constitutive equation of the microscopic form of the conduction current density: When the densities of electrons and holes inside the nanocomposite dielectric are given, n D(e) and n D(h) , the expressions for the conduction current densities of electrons and holes can be obtained from the product of the densities of electrons and holes and their migration rates. Combining with the diffusion process of charge carriers, the charge migration and diffusion equations are obtained, namely:

[0072]

[0073]

[0074] j D(e) (x, t) and j D(h) (x, t) are the conduction current densities formed by electrons and holes respectively, D e and D h are the diffusion coefficients of electrons and holes respectively.

[0075] Charge conservation equation: When electrons and holes are transported in the nanocomposite dielectric, they satisfy the charge conservation equation, that is, the sum of the charge inflow and outflow at a certain position is equal to the change in the charge density at that position over time, reflecting the transport process of charge carriers. Since there is a certain probability of recombination of electrons and holes, the recombination process will lead to a decrease in the densities of electrons and holes. Therefore, the positive and negative charge recombination kinetic equations also need to be considered in the charge conservation equation. The charge conservation equations for electrons and holes are as follows:

[0076]

[0077]

[0078] According to the two-step charge transfer model, when x = 0, the charge injection density j in(e) (0, t) at the cathode-dielectric interface is equal to the conduction current density j D(e) (x, t) formed by electrons. When x = d, the charge injection density jin(h) (d, t) is equal to the conduction current density j formed by holes D(h) (x, t).

[0079] Take the charge injection density j in(e) (0, t) of the cathode-dielectric as the conduction current density j formed by electrons D(e) (x, t) as the boundary condition;

[0080] Take the charge injection density j in(h) (d, t) of the anode-dielectric interface as the conduction current density j formed by holes D(h) (x, t) as the boundary condition, and solve the charge conservation equations for electrons and holes.

[0081] R e,h is the recombination coefficient of electrons and holes, which can be calculated by the Langevin recombination model. R e,h = e(v e + v h ) / ε0ε r E. Here, ε0 and ε r are the vacuum permittivity and the relative permittivity of the nanocomposite dielectric, respectively.

[0082] Poisson's equation: After there is charge inside the nanocomposite dielectric, its electric field will be distorted. It is necessary to use Poisson's equation to solve the potential and electric field distribution inside the nanocomposite dielectric.

[0083]

[0084] In the formula: φ is the potential inside the nanocomposite dielectric. The electric field can be calculated from the negative gradient of the potential.

[0085]

[0086] Then, the transient current j ext (t) of the dielectric material can be calculated using formula (11):

[0087]

[0088] After obtaining the relationship between the transient current and time, the steady-state transient current j ext_st can be obtained. Dividing by the applied average electric field, the steady-state conductivity of the dielectric material can be obtained:

[0089]

[0090] Step 4: Establish the Fourier heat conduction equation, and fuse the Fourier heat conduction equation and the bipolar charge transport model obtained in Step 3 to establish a simulation model for the transient current and the conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric.

[0091] Step 4 is specifically as follows:

[0092] Establish the Fourier heat conduction equation. Under the action of an electric field, the current inside the nanocomposite dielectric will generate Joule heat, resulting in a local temperature increase. When a temperature difference is formed inside the nanocomposite dielectric, energy carriers are transported under the drive of a negative temperature gradient, making the temperature inside the dielectric tend to be balanced. The transport process of energy carriers can be described by the Fourier heat conduction equation.

[0093]

[0094] In the formula: ρ is the mass density of the nanocomposite dielectric, C s is the specific heat capacity, and κ is the thermal conductivity of the nanocomposite dielectric.

[0095] Substitute the results of equations (6), (7), and simultaneously solve equations (8), (9), (10), (11), (12), (13), and (14) to establish a simulation model for the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric.

[0096] The bipolar charge transport model obtained in step 3 mainly reflects the transport process of charge carriers, and the Fourier heat conduction equation mainly reflects the transport process of energy carriers, that is, this model considers both charge carriers and energy carriers.

[0097] The present invention comprehensively considers processes such as charge injection at the electrode-dielectric interface, migration and diffusion of charges inside the dielectric, charge conservation, and electric field distortion caused by space charges, etc., to establish a bipolar charge transport model of the nanocomposite dielectric. It includes calculating the charge injection rate at the electrode-dielectric interface using formulas (4) and (5), calculating the current density formed by the migration and diffusion of charges inside the dielectric using formulas (6) and (7), calculating the change in charge density caused by charge migration, diffusion, recombination, etc. using formulas (8) and (9), calculating the electric field distribution under the combined action of the applied voltage and space charges using formula (10), to obtain the evolution laws of charge density, electric field strength, and current density inside the dielectric. By integrating the bipolar charge transport model and the Fourier heat conduction equation (14), a simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric is established.

[0098] The weighted essentially non-oscillatory method and the implicit method are used to solve the charge conservation equations (8) and (9), the implicit method is used to solve the charge migration and diffusion equations and the Fourier heat conduction equation, the finite element method is used to solve the Poisson equation (10), the transient current of the nanocomposite dielectric is obtained from Equation (12), and the numerical solution of the steady-state conductivity is obtained from Equation (13). By adjusting the temperature in the simulation model established in Step 4, the steady-state conductivity under different temperature conditions can be calculated, and then the law of the change of the steady-state conductivity with temperature, that is, the entropy-enthalpy compensation characteristic, can be obtained.

[0099] Referring to Figure 11 , a simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric, including a migration rate calculation module, a charge injection density calculation module, a charge migration and diffusion equation module, and a simulation module;

[0100] The migration rate calculation module is used to establish an inverse power function of the attempt-to-jump frequency of charge carriers in the nanocomposite dielectric, and obtain the attempt-to-escape frequency of transient charge carriers according to the inverse power function; obtain the electron migration rate and the hole migration rate based on the jump transport and carrier resonance effect according to the attempt-to-jump frequency of charge carriers.

[0101] The charge injection density calculation module is used to calculate the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface according to the attempt-to-escape frequency of transient charge carriers.

[0102] The charge migration and diffusion equation module is used to establish the charge migration and diffusion equation at the electrode-dielectric interface of the nanocomposite dielectric, and establish a bipolar charge transport model of the nanocomposite dielectric according to the charge migration and diffusion equation at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, the electron migration rate, and the hole migration rate.

[0103] The simulation module is used to establish the Fourier heat conduction equation, and establish a simulation model of the transient current and conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric according to the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface, the Fourier heat conduction equation, the transient current calculation formula of the dielectric material, the steady-state conductivity calculation formula of the dielectric material, and the bipolar charge transport model of the nanocomposite dielectric, and simulate the transient current and conductance entropy-enthalpy compensation characteristics of the dielectric with the simulation model to obtain the conductive characteristics of the nanocomposite dielectric at different temperatures.

[0104] A simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric, including:

[0105] A processor;

[0106] A memory for storing instructions executable by the processor;

[0107] Wherein, the processor is configured to execute the above-mentioned simulation method of transient current and conductivity entropy-enthalpy compensation characteristics of nanocomposite dielectrics.

[0108] The invention is described below in conjunction with a simulation example.

[0109] Example 1: Transient current and conductivity entropy-enthalpy compensation characteristics of polyetherimide nanocomposite dielectrics

[0110] (1) Basic data. The sample thickness d is 15 μm and the density ρ is 1270 kgm -3 , specific heat capacity C S 1200Jkg -1 K -1 , thermal conductivity κ is 0.21WK -1 m -1 , relative dielectric constant ε r is 3.17, and the charge carrier attempt escape frequency υ0 in the steady state is 1×10 10 Hz, Meyer-Neldel temperature T MN It is 925K.

[0111] Surface trapped electron and hole charge density at the electrode-dielectric interface MD(e) and MD(h) All 3cm -3 , the inverse power function prefactor α is 100, the power function exponent β is 0.8, and the average jump distance between electrons and holes λ e and λ h All are 1.3nm. Test electric field E: 20kV / mm. Temperature varies between 360 and 400K.

[0112] Since the trap energy level of polyetherimide nanocomposite dielectrics changes with the doping content, the difference in trap energy level values is used to reflect the change in doping content. T(e) and u T(h) It varies between 0.70eV and 0.95eV, the trap energy level of sample 1 is 0.70eV, the trap energy level of sample 2 is 0.75eV, the trap energy level of sample 3 is 0.80eV, the trap energy level of sample 4 is 0.85eV, the trap energy level of sample 5 is 0.90eV, and the trap energy level of sample 6 is 0.95eV.

[0113] (2) According to the method described above, a simulation program was written to calculate the steady-state conductivity of six polyetherimide nanocomposite dielectric samples at different temperatures. The relationship between the steady-state conductivity and temperature is the conductivity entropy-enthalpy compensation characteristic, as shown in Table 1.

[0114] Table 1. Steady-state conductivity of six polyetherimide nanocomposite dielectric specimens at different temperatures

[0115]

[0116] The temperature dependence analysis was carried out on the conductivity of polyetherimide nanocomposite dielectrics with different doping contents at 20 kV / mm, and the obtained results are as Figure 3 (a) shown. As can be seen from Figure 3 (a), the conductivity of PEI nanocomposite dielectric specimens with different doping contents all satisfies the Arrhenius equation. The conductance activation energy of each specimen was obtained through fitting calculation, and it was found that the activation energy increases with the increase of doping content. In PEI, the activation energy of specimen 1 is about 0.67 eV, and the activation energy of specimen 6 is about 0.92 eV. This indicates that doping nanoparticles increases the trap depth of the nanocomposite dielectric and inhibits the transport of carriers inside the specimen.

[0117] The Mayer compensation formula was used to analyze the steady-state conductivity test results of PEI nanocomposite dielectric specimens at different temperatures, as Figure 3 (b) shown. As can be seen from the figure, the extended lines of the Arrhenius fitting curves of the temperature-dependent conductivity of the PEI nanocomposite dielectric can all intersect at one point, and the intersection coordinates are (T MN , σ 00 ) are given in the figure. The temperature dependence of the conductivity follows the Mayer compensation rule, indicating that when the activation energy E T of electron transition increases, the pre-exponential factor σ 00 will be compensated, hindering the decrease of the specimen conductivity.

[0118] The transient current characteristics of PEI nanocomposite dielectric materials with different doping concentrations at different temperatures are as Figure 4 shown. It can be seen that as the temperature increases, the current density increases. The attenuation rate of the current density gradually slows down and tends to be stable.

[0119] The space charge distribution of nanocomposite dielectric materials with different nanoparticle concentrations is as Figure 5 shown. As can be seen from Figure 5 , for specimens with each doping concentration, as the external electric field action time prolongs, the amount of space charge accumulation inside the dielectric shows an increasing trend. The space charge mainly accumulates at the interface where the electrode contacts the dielectric material, and the accumulation amount gradually decreases from this interface to the middle position of the dielectric material. The pressurization time of specimen 6 is longer than that of other specimens.

[0120] Figure 6 respectively represent the electric field distributions of PEI nanocomposite dielectric specimens with different doping concentrations. As can be seen from Figure 6It can be seen that for specimens with any doping concentration, the local electric field strength increases with the increase of the applied electric field action time. The relationship between the magnitude of the local field strength and the relative position of the space charge accumulation amount is opposite. At any moment, the local field strength gradually decreases from the middle position of the dielectric to the interface where the electrode contacts the dielectric. This is because a large amount of like-polarity space charges accumulate at the interface, resulting in the establishment of a weakening electric field opposite to the external field strength at the interface, while the weakening electric field strength in the middle of the dielectric is relatively weak. From the process of the formation of the local electric field, it is the accumulation of space charges that leads to the formation of the local electric field. When the accumulation degree of space charges increases, the local field strength also increases. After the space charges accumulate to a certain extent, the local electric field will also undergo a large degree of distortion.

[0121] Example 2: Transient current and conductance entropy-enthalpy compensation characteristics of polyimide nanocomposite dielectrics

[0122] (1) Fixed parameters. Specimen thickness d: 15 μm, density ρ: 1420 kg / m³ -3 , specific heat capacity C S : 1090 J / (kg·K) -1 K -1 , thermal conductivity κ: 0.12 W / (K·m) -1 m -1 , relative permittivity ε r : 3.4, the attempt-to-escape frequency υ0 of charge carriers at steady state: 1×10⁹ Hz, Meyer-Neldel temperature T 10 : 955 K. MN

[0123] The surface trap electron and hole charge densities en MD(e) and en MD(h) at the electrode-dielectric interface are both 5 C / m² -3 , the inverse power function pre-factor α: 200, the exponent β of the power function: 0.8, the average hopping distances λ e and λ h of electrons and holes are both 1.6 nm.

[0124] Test electric field and temperature. Electric field E: 20 kV / mm. The temperature varies between 360 and 400 K.

[0125] The trap levels of polyimide nanocomposite dielectrics change with the doping content, and the change of the doping content is reflected by the different trap level values. The trap levels u T(e) and u T(h)It varies between 0.75 eV and 1.00 eV. For example, the trap energy level of sample 1 is 0.75 eV, that of sample 2 is 0.80 eV, that of sample 3 is 0.85 eV, that of sample 4 is 0.90 eV, that of sample 5 is 0.95 eV, and that of sample 6 is 1.00 eV.

[0126] (2) According to the simulation program, the steady-state conductivities of six polyimide nanocomposite dielectric samples at different temperatures were calculated, as shown in Table 2.

[0127] Table 2. Steady-state conductivities of six polyimide nanocomposite dielectric samples at different temperatures

[0128]

[0129] The temperature dependence of the conductivity of polyimide nanocomposite dielectrics with different doping contents at 20 kV / mm was analyzed, and the results are as Figure 7 (a) shown. As can be seen from Figure 7 (a), the conductivities of PI nanocomposite dielectric samples with different doping contents all satisfy the Arrhenius equation. By fitting and calculating, the activation energy of conduction for each sample was obtained, and it was found that it increases with the increase of doping content. In PI, the activation energy of sample 1 is about 0.72 eV, and that of sample 6 is about 0.96 eV. This indicates that doping nanoparticles increases the trap depth of the nanocomposite dielectric and inhibits the transport of carriers inside the sample.

[0130] The Mayer compensation formula was used to analyze the test results of the steady-state conductivity of PI nanocomposite dielectric samples at different temperatures, as Figure 7 (b) shown. As can be seen from the figure, the extended lines of the Arrhenius fitting curves of the temperature-dependent conductivity of PI nanocomposite dielectrics can all intersect at one point, and the intersection coordinates are (T MN , σ 00 ) which are given in the figure. The temperature dependence of the conductivity obeys the Mayer compensation rule, indicating that when the activation energy E T of electron transition increases, the pre-exponential factor σ 00 of the conductivity will be compensated, hindering the decrease of the sample conductivity.

[0131] The transient current characteristics of PI nanocomposite dielectric materials with different doping concentrations at different temperatures are as Figure 8 shown. It can be seen that as the temperature increases, the current density increases. The attenuation rate of the current density gradually slows down and tends to be stable.

[0132] The space charge distributions of nanocomposite dielectric materials with different nanoparticle concentrations are as Figure 9 shown. As can be seen from Figure 9It can be seen that for each sample with a doping concentration, as the action time of the external electric field prolongs, the amount of space charge accumulation inside the dielectric shows an increasing trend. The space charge mainly accumulates at the interface where the electrode contacts the dielectric material, and the accumulation amount gradually decreases from this interface to the middle position of the dielectric material. The pressurization time of sample 6 is longer than that of other samples.

[0133] Figure 10 respectively represent the electric field distributions of PI nanocomposite dielectric samples with different doping concentrations. From Figure 10 it can be seen that for any sample with a doping concentration, the local electric field strength increases with the increase of the action time of the applied electric field. The relationship between the magnitude of the local field strength and the relative position of the space charge accumulation amount is opposite. At any moment, the local field strength gradually decreases from the middle position of the dielectric to the interface where the electrode contacts the dielectric. This is because a large amount of like-polarity space charge accumulates at the interface, resulting in the establishment of a weakening electric field opposite to the external field strength at the interface, while the weakening electric field strength in the middle of the dielectric is relatively weak. From the process of forming the local electric field, it is the accumulation of space charge that leads to the formation of the local electric field. When the accumulation degree of space charge increases, the local field strength also increases accordingly. After the space charge accumulates to a certain extent, the local electric field will also undergo a large degree of distortion.

[0134] The above content is only to illustrate the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of nanocomposite dielectrics, characterized in that, It includes the following steps: Step 1: Establish the inverse power function of the attempt-to-hop frequency of charge carriers in the nanocomposite dielectric, and obtain the attempt-to-escape frequency of transient charge carriers according to the inverse power function; obtain the electron migration rate and hole migration rate based on hopping transport and carrier resonance effects according to the attempt-to-hop frequency of charge carriers; Step 2: Calculate the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface according to the attempt-to-escape frequency of transient charge carriers obtained in Step 1; Step 3: Establish the charge migration and diffusion equation at the electrode-dielectric interface of the nanocomposite dielectric, and establish the bipolar charge transport model of the nanocomposite dielectric according to the charge migration and diffusion equation at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, and the electron migration rate and hole migration rate obtained in Step 1; Step 4: Establish the Fourier heat conduction equation, and establish the simulation model of the transient current and the conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric according to the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface, the Fourier heat conduction equation, the transient current calculation formula of the dielectric material, the steady-state conductivity calculation formula of the dielectric material, and the bipolar charge transport model of the nanocomposite dielectric. Use the simulation model to simulate the transient current and the conductance entropy-enthalpy compensation characteristics of the dielectric, and obtain the conductive characteristics of the nanocomposite dielectric at different temperatures.

2. The simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the nanocomposite dielectric according to claim 1, characterized in that In Step 1, the inverse power function of the attempt-to-hop frequency of charge carriers is: υ ATE (t) = υ0(αt -β + 1) (1); where: υ ATE (t) is the transient charge carrier attempt-to-escape frequency, υ0 is the charge carrier attempt-to-escape frequency at steady state, t represents the time when the electric field is applied, α is the pre-factor of the inverse power function, and β is the exponent of the power function; α and β are coefficients related to the electric field E and the test temperature T, i.e., α(E,T) and β(E,T).

3. The simulation method of the transient current and conductance entropy-enthalpy compensation characteristics of the nano-composite dielectric according to claim 1, characterized in that, In Step 1, the calculation formulas for the electron migration rate and hole migration rate are: where: v e (x, t) and v h (x, t) are the migration rates of electrons and holes respectively, λ e and λ h are the average hopping distances of electrons and holes respectively, u T(e) and u T(h) are the trap levels of electrons and holes respectively, e is the electron charge, k B is the Boltzmann constant, T MN is the Meyer-Neldel temperature, x represents the position in the dielectric, E(x, t) is the applied electric field strength, and T is the test temperature.

4. The simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the nano-composite dielectric according to claim 1, wherein In Step 2, The calculation formulas for the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface are: where: j in(e) (0, t) and j in(h) (d, t) are the charge injection densities at the cathode-dielectric and anode-dielectric interfaces respectively, and n MD(e) and n MD(h) are the surface trap electron and surface trap hole densities formed by charge transfer at the interfaces between the nanocomposite dielectric and the electrodes respectively.

5. The simulation method of the transient current and conductance entropy-enthalpy compensation characteristics of the nanocomposite dielectric according to claim 1, wherein In Step 3, the established charge migration and diffusion equation is: where j D(e) (x, t) and j D(h) (x, t) are the conduction current densities formed by electrons and holes respectively, D e and D h are the diffusion coefficients of electrons and holes respectively.

6. The simulation method for the transient current and conductance entropy-enthalpy compensation characteristics of the nano-composite dielectric according to claim 1 or 5, characterized in that, In Step 3, the bipolar charge transport model of the nanocomposite dielectric includes the charge injection density at the electrode-dielectric interface, the charge migration and diffusion equation at the electrode-dielectric interface, the charge conservation equation, and the Poisson equation.

7. The simulation method of the transient current and conductance entropy-enthalpy compensation characteristics of the nano-composite dielectric according to claim 1, characterized in that In Step 4, the Fourier heat conduction equation is: Where: ρ is the mass density of the nanocomposite dielectric, C s is the specific heat capacity, and κ is the thermal conductivity of the nanocomposite dielectric.

8. A simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric, characterized in that, It includes a migration rate calculation module, a charge injection density calculation module, a charge migration and diffusion equation module, and a simulation module; The migration rate calculation module is used to establish the inverse power function of the attempt-to-hop frequency of charge carriers in the nanocomposite dielectric, obtain the attempt-to-escape frequency of transient charge carriers according to the inverse power function; obtain the electron migration rate and hole migration rate based on hopping transport and carrier resonance effects according to the attempt-to-hop frequency of charge carriers; The charge injection density calculation module is used to calculate the charge injection density at the cathode-dielectric interface and the charge injection density at the anode-dielectric interface according to the attempt-to-escape frequency of transient charge carriers; The charge migration and diffusion equation module is used to establish the charge migration and diffusion equation at the electrode-dielectric interface of the nanocomposite dielectric, and establish the bipolar charge transport model of the nanocomposite dielectric according to the charge migration and diffusion equation at the electrode-dielectric interface, the charge conservation equation, the Poisson equation, the electron migration rate, and the hole migration rate; A simulation module, which is used to establish the Fourier heat conduction equation, and establish a simulation model for the transient current and the conductance entropy-enthalpy compensation characteristics of the electro-thermal coupling effect of the nanocomposite dielectric according to the charge injection density at the cathode-dielectric interface, the charge injection density at the anode-dielectric interface, the Fourier heat conduction equation, the transient current calculation formula of the dielectric material, the steady-state conductivity calculation formula of the dielectric material, and the bipolar charge transport model of the nanocomposite dielectric. The simulation model is used to simulate the transient current and the conductance entropy-enthalpy compensation characteristics of the dielectric, and obtain the conductive characteristics of the nanocomposite dielectric at different temperatures.

9. A simulation system for the transient current and conductance entropy-enthalpy compensation characteristics of a nanocomposite dielectric, characterized in that, It includes: A processor; A memory for storing processor-executable instructions; Wherein, the processor is configured to execute the method for simulating the transient current and the conductance entropy-enthalpy compensation characteristics of the nanocomposite dielectric according to any one of the above claims 1-7.

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