Trap level measurement method for variable temperature rise rate thermally stimulated current

By employing a multi-heating-rate thermal stimulation current testing method, combined with linear fitting and least squares method, the problem of identifying overlapping peaks under a single heating rate was solved, enabling accurate characterization of trap energy levels and dipoles within insulating materials, and improving the reliability and accuracy of the test.

CN121453845APending Publication Date: 2026-02-03XI AN JIAOTONG UNIV +1
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Patent Information

Application Number
CN202511569083.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-10-30
Publication Date
2026-02-03

AI Technical Summary

Technical Problem

The existing thermal stimulation current test method with a single heating rate results in overlapping peaks of the depolarization current curve, making it difficult to accurately identify the trap energy level and dipole type inside the insulating material, and the calculation results have systematic biases.

Method used

A thermal stimulation current testing method with multiple heating rates was adopted. The relationship between heating rate and peak temperature was established by linear fitting and least squares method. The trap energy level was calculated, and the single relaxation process was separated by the peak temperature evolution law under multiple heating rates.

Benefits of technology

It enables accurate identification of trap energy levels and dipoles at different depths inside insulating materials, improves the reliability and repeatability of test results, and solves the problem of limited resolution of overlapping peaks in existing technologies.

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Abstract

The invention provides a trap level measurement method considering temperature rise rate thermal stimulation current, and belongs to the technical field of insulating materials. ET is calculated according to the change relation of the peak temperature Tm along with the heating rate beta. The TSDC curve often has overlapped peaks, the parameter of a single peak is difficult to accurately extract in the TSDC curve with a single heating rate, and the method of changing beta can effectively distinguish the peaks in different dynamic processes by tracking the change track of Tm of each peak along with beta, so that respective ET is calculated respectively. According to the method, the dependence on the current peak shape is remarkably reduced, the identification and analysis capability of overlapped peaks is improved, and whether the relaxation process has single activation energy or not can be judged, so that more reliable and more accurate characterization of the trap energy level is realized.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of insulating materials, and particularly relates to a trap energy level measurement method of variable heating rate thermal stimulated current. BACKGROUND

[0002] Thermal Stimulated Depolarization Current (TSDC) is a commonly used test method for bulk traps of insulating materials, and is widely used in scenes such as cross-linked polyethylene (XLPE) cable insulation, GIS basin insulator, electronic devices such as polymer dielectric film, etc. The principle is that the dipole moment generated by fully polarizing the insulating material at high temperature is quickly “frozen”, and then the dipole moment inside the sample is slowly released in the process of temperature rise, and accordingly the properties of traps, dipoles and movable ions in the dielectric material are studied. The internal dipole of the material gradually takes out the orientation with the increase of temperature, the trapped charge is activated by heat to escape from the bondage, and the released depolarization current changes with temperature to form a current-temperature curve, i.e. TSDC curve. Researchers and engineers can invert the trap energy level distribution, dipole activation energy and movable ion migration characteristics in the material through the curve characteristics such as current peak position, peak value and peak width, and provide key basis for performance optimization, aging evaluation and life prediction of insulating materials.

[0003] In the existing TSDC test technology, in order to test conveniently, a fixed single heating rate test mode is generally used in the process of temperature rise. The fixed heating rate is a certain value, and the obtained activation energy of the dipole or the trap depth of the trapped charge E T Calculation formula and heating rate βIrrelevant. However, the effect of heating rate on TSDC curve in actual test is far beyond the assumption of the simplified model, and the core contradiction lies in that TSDC is essentially a dynamic measurement process of charge release rate under thermal activation, and the heating rate directly determines the input rhythm of thermal activation energy, thereby changing the dynamic process of charge escaping from traps or dipole disorientation: when a slower heating rate is used, the thermal activation energy input is gentle, and shallow trap charges and weakly bound dipoles will be released slowly in a lower temperature interval, resulting in a broadened and reduced peak, and even overlapping with the deep trap charge release peak in the adjacent temperature interval; when a faster heating rate is used, the thermal activation energy input is rapid, and shallow trap charges may be released in a short time to form a sharp narrow peak, while deep trap charges may be delayed to a higher temperature interval due to insufficient accumulation of thermal activation energy, and may also overlap with the current peak of other relaxation processes in the high temperature zone. The single heating rate has very weak ability to analyze the overlapping peaks, and there are often multiple trap energy levels and multiple dipole types in the internal insulation of insulating materials, especially after aging. The current peaks of different relaxation processes under a single heating rate are easily overlapped and fused on the temperature axis, and it is impossible to distinguish the contribution of a single trap energy level or dipole, resulting in the inability to accurately identify the specific type of internal micro defects such as shallow traps corresponding to surface defects and deep traps corresponding to internal crosslinking defects; and it is difficult to accurately characterize the activation energy of the dipole and the trap depth. Under a fixed heating rate, the matching relationship between the charge release process and the temperature is simplified, and the calculation formula ignores the correlation between the heating rate and the thermal activation efficiency, resulting in systematic deviation of the derived ET value.

[0004] In addition, although some studies in the prior art mention the effect of heating rate, no systematic solution has been formed: most schemes only adjust the heating rate by experience, lack of unified theoretical model support, and a few methods that try to test multiple heating rates also do not establish a quantitative correlation logic between heating rate, peak temperature and trap depth, resulting in poor repeatability and comparability of test results, and failing to meet the demand for accurate characterization of insulating material properties in engineering practice. SUMMARY

[0005] The present application proposes a variable heating rate trap depth measurement method of thermally stimulated current to solve the technical problems of limited resolution of depolarization current curve to overlapping peaks and difficulty in accurately characterizing the activation energy of dipole or trap depth caused by single heating rate in the prior art.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows: A variable heating rate trap depth measurement method of thermally stimulated current, comprising the following steps: Polarizing the insulating material to obtain a polarized sample; The polarized sample is heated at different heating rates, and the depolarization current during the heating process is collected to obtain the depolarization current curves at different heating rates. The peak temperature on the depolarization current curve corresponding to each heating rate is obtained, and the linear fitting of the heating rate and the corresponding peak temperature is performed, and the trap energy level is calculated based on the linear fitting result.

[0007] Before the insulation material is polarized, the preparation of the insulation material is also included, and the preparation of the insulation material is specifically: a flat plate insulation material is prepared by a flat plate vulcanizing instrument, and an ion sputtering instrument is used to sputter metal on the a surface and the b surface of the flat plate insulation material, so as to complete the preparation of the insulation material.

[0008] The thickness of the flat plate insulation material prepared by the flat plate vulcanizing instrument is 50-1000 μm.

[0009] When the metal is sputtered on the a surface and the b surface of the flat plate insulation material, the diameter of the metal sputtered on the a surface in contact with the upper electrode is 10-30 cm, and the diameter of the metal sputtered on the b surface in contact with the lower electrode is 20-50 cm.

[0010] The ion sputtering instrument sputters metal on the a surface and the b surface of the flat plate insulation material, and the metal is one of Au or Ag.

[0011] The prepared insulation material is placed in a TSDC device, the lower electrode of the TSDC device covers the b surface metal, the upper electrode of the TSDC device is covered by the a surface metal, a direct current field is applied to the insulation material at a temperature of 70-100 ℃ to make it fully polarized, and then the voltage is removed after rapid cooling to freeze the polarization state, and a polarized sample is obtained.

[0012] The planned insulation material needs to be cooled to 100-250 K to freeze the polarization state.

[0013] The peak temperature on the depolarization current curve corresponding to each heating rate is obtained, and the linear fitting of the heating rate and the corresponding peak temperature is performed, and the trap energy level is calculated based on the linear fitting result.

[0014] The linear fitting of the heating rate and the corresponding peak temperature is specifically: X =1 / T mi is the abscissa, Y =ln( T mi 2 / β i is the ordinate, and T miobtaining the peak temperature on the depolarization current curve corresponding to each heating rate, β i The heating rate is linearly fitted with the peak temperature corresponding to the heating rate by using the least square method, and the fitting formula is as follows:

[0015] In the formula, is the trap energy level, is the least square linear fitting constant, is the Boltzmann constant.

[0016] Based on the linear fitting result, the peak temperature under different heating rates β The slope of the peak temperature under different heating rates T m is obtained, the evolution law of the characteristic relaxation peak temperature under different heating rates is analyzed, a calculation model related to the heating rate is established, and the trap energy level β E T

[0017] Compared with the prior art, the present application has the following beneficial effects: The present application carries out tests by using multiple different heating rates, and the current peak corresponding to the same trap energy level or dipole will show a specific peak temperature evolution law under different heating rates. The faster the heating rate, the higher the peak temperature. At the same time, the peak temperature of the same current peak under each heating rate can be accurately extracted. Even if the initial depolarization current curve has peak overlap, the single relaxation process corresponding peak can be clearly separated by means of the continuous evolution trajectory of the peak temperature under multiple heating rates, so as to accurately identify the trap energy level or different types of dipoles at different depths in the material, and completely solve the problem of limited overlap peak analysis capability in the prior art.

[0018] Further, the present application establishes a quantitative calculation model related to the heating rate, constructs a scatter plot with the reciprocal of the peak temperature as the abscissa and the correlation term of the heating rate and the peak temperature as the ordinate, and calculates the trap energy level by using the product of the fitting slope and the Boltzmann constant after linear fitting by using the least square method. The influence of the heating rate on the charge release is directly included in the calculation process, and the error caused by the simplified model is avoided. For example, for the same insulating material, the fitting of the test data of three or more heating rates can effectively offset the accidental error under a single rate, so that the deviation of the trap energy level calculation value is controlled in a smaller range, the accuracy of the dipole activation energy and trap depth representation is significantly improved, and the problem of difficult accurate representation in the prior art is solved.

[0019] ​​​Further, the present application standardizes the key test process, defines the sample thickness as 50-1000 microns, limits the sputtered metal diameter on the a surface contacting the upper electrode to 10-30 cm, the b surface contacting the lower electrode to 20-50 cm, and only selects Au or Ag for the sputtered metal to ensure consistent conductivity, and strictly cools the temperature to 100-250 K after polarization to freeze the polarization state and ensure stable polarization effect. This standardized operation reduces the interference caused by differences in sample preparation and test conditions, makes the test results of different batches and different personnel comparable, further improves the reliability of the method, and meets the demand for precise evaluation of the properties of insulating materials in engineering practice. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 FIG. 1 is a depolarization current curve of an insulating material at different heating rates in an embodiment of the present application; Figure 2 FIG. 2 is an analysis and calculation diagram of the depolarization current peak trap energy level in an embodiment of the present application; Figure 3 FIG. 3 is a flowchart of a trap energy level measurement method of a variable heating rate thermal stimulated current in an embodiment of the present application. DETAILED DESCRIPTION

[0021] In order to further understand the content of the present application, the present application will be described in detail below in combination with the drawings and specific embodiments. It should be understood that the embodiments are only used to explain the present application and are not limiting.

[0022] In this paper, all the characteristics defined in the form of numerical range or percentage range such as numerical value, quantity, content and concentration are only for the sake of brevity and convenience. Therefore, the description of the numerical range or percentage range should be considered to have covered and specifically disclosed all possible secondary ranges and individual numerical values in the range (including integers and fractions).

[0023] In this paper, unless otherwise specified, “comprising”, “including”, “containing”, “having” or similar terms cover the meaning of “consisting of” and “consisting essentially of”, for example, “A contains a” covers the meaning of “A contains a and other” and “A contains only a”.

[0024] In this paper, in order to make the description simple, all possible combinations of each technical feature in each embodiment or example are not described. Therefore, as long as the combination of these technical features does not exist, each technical feature in each embodiment or example can be combined arbitrarily, and all possible combinations should be considered as the scope disclosed in this specification.

[0025] The embodiments of the present application will be described in detail below in combination with the drawings.

[0026] Example 1 This embodiment proposes a method for measuring the trap energy level of a thermally stimulated current with a variable heating rate, such as... Figure 3 As shown, it includes the following steps: An insulating material is prepared and then polarized to obtain a polarized sample. By heating polarized samples at different heating rates and collecting the depolarization current during the heating process, depolarization current curves at different heating rates were obtained. The peak temperature on the depolarization current curve corresponding to each heating rate is obtained. A linear fit is performed on the heating rate and its corresponding peak temperature. Based on the linear fit result, the trap energy level is calculated.

[0027] Specifically, based on the above steps, this embodiment provides the following detailed description, and the specific implementation method includes the following steps: S1: Preparation and pretreatment of insulating materials. Flat plate samples with a thickness of 50–1000 μm were prepared using a flat plate vulcanizing apparatus. The flat insulating material was wiped with a lint-free cloth dampened with alcohol and then air-dried. It was then placed in an ion sputtering apparatus for double-sided metal sputtering. The diameter of the metal sputtered on the surface (a) in contact with the upper electrode was 10–30 cm, and the diameter of the metal sputtered on the surface (b) in contact with the lower electrode was 20–50 cm. To ensure good conductivity at the contact surfaces, the sputtered metal was either Au or Ag.

[0028] S2: Insulating Material Polarization. The insulating material processed in step S1 is placed in the TSDC device. The lower electrode must be covered by the metal on side b, while the upper electrode must be covered by the metal on side a. A DC electric field is applied to the insulating material at a high temperature to fully polarize it. Then, it is rapidly cooled to a low temperature, and the voltage is removed, "freezing" the polarization state. The low temperature varies depending on the insulating material being tested, typically ranging from 100 to 250 K.

[0029] S3: Measure the depolarization current curve. Short-circuit the sample and heat it at a constant rate. β 1. Heat the sample while precisely measuring the released depolarization current. I 1( T A current-temperature curve was obtained, which contained one or more current peaks.

[0030] S4: Repeat the measurement. For another identical sample, keeping the polarization conditions constant, only change the heating rate, and repeat steps S2 and S3. To ensure the accuracy of the test results, at least three different heating rates should be used for the TSDC test, i.e., heating rate... β 1 、β 2 and β 3. Finally, the heating rate was obtained as follows: β 1 、β 2 and β 3 depolarization current I1 T ), I 2 T ), I 3 T ).

[0031] In the specific implementation process, in the S3, S4 steps, the temperature rising rate β i The peak temperature of the same current peak on the corresponding depolarization current curve is, that is, β 1 T m1 , ( β 2 T m2 ), ( β 3 T m3 ). Let X =1 / T mi For the abscissa, Y =ln( T mi 2 / β i ) For the ordinate, the data is plotted on the scatter plot, and the slope is linearly fitted by the least square method. The product of the slope and the Boltzmann constant k is the activation energy of the current peak, that is, the trap energy level, and the fitting formula is as follows:

[0032] In the formula, is the trap energy level, is the least square linear fitting constant, is the Boltzmann constant.

[0033] Based on the linear fitting result, the slope of the peak temperature β under different temperature rising rates T m is obtained, the evolution law of the characteristic relaxation peak temperature under different temperature rising rates β is analyzed, a model for calculating the activation energy related to the temperature rising rate is established, and the trap energy level E T is calculated: .

[0034] In the above linear fitting process, ( β 1 T m1 ), ( β 2 T m2 ), ( β 3T m3 Three coordinate-drawn straight lines represent a single relaxation process, but in actual tests, the current peak can be the relaxation of a single trap level or the superposition of multiple trap levels. If a single fitting is directly calculated, the calculation result will be distorted. Therefore, the determination coefficient of linear fitting is introduced in this embodiment to determine whether the current peak is a single current peak or the superposition of multiple relaxation processes. Specifically, when the determination coefficient is greater than or equal to 0.95, it can be approximately considered that there is only a single current peak at the position, that is, the calculated activation energy is accurate, that is, the trap level is accurate. If the data points deviate from the straight line obviously, it can mean that the relaxation process contains a distributed activation energy, that is, the trap level is a distribution, or the kinetic mechanism is more complex. At this time, a more complex model is needed for analysis. R 2 Three coordinate-drawn straight lines represent a single relaxation process, but in actual tests, the current peak can be the relaxation of a single trap level or the superposition of multiple trap levels. If a single fitting is directly calculated, the calculation result will be distorted. Therefore, the determination coefficient of linear fitting is introduced in this embodiment to determine whether the current peak is a single current peak or the superposition of multiple relaxation processes. Specifically, when the determination coefficient is greater than or equal to 0.95, it can be approximately considered that there is only a single current peak at the position, that is, the calculated activation energy is accurate, that is, the trap level is accurate. If the data points deviate from the straight line obviously, it can mean that the relaxation process contains a distributed activation energy, that is, the trap level is a distribution, or the kinetic mechanism is more complex. At this time, a more complex model is needed for analysis. R 2 Three coordinate-drawn straight lines represent a single relaxation process, but in actual tests, the current peak can be the relaxation of a single trap level or the superposition of multiple trap levels. If a single fitting is directly calculated, the calculation result will be distorted. Therefore, the determination coefficient of linear fitting is introduced in this embodiment to determine whether the current peak is a single current peak or the superposition of multiple relaxation processes. Specifically, when the determination coefficient is greater than or equal to 0.95, it can be approximately considered that there is only a single current peak at the position, that is, the calculated activation energy is accurate, that is, the trap level is accurate. If the data points deviate from the straight line obviously, it can mean that the relaxation process contains a distributed activation energy, that is, the trap level is a distribution, or the kinetic mechanism is more complex. At this time, a more complex model is needed for analysis.

[0035] Embodiment 2 Based on the trap level measurement method of variable heating rate thermal stimulated current proposed in Embodiment 1, this embodiment combines specific data to measure the trap level, and the specific implementation method is as follows: Step 1: Preparation and pretreatment of insulating material A. Prepare completely identical sheet-shaped insulating materials A1, A2 and A5 with a thickness of 250 μm by means of a flat plate curing instrument. After wiping the flat plate insulating material with alcohol with a dust-free cloth and drying, it is placed in an ion sputtering instrument, and the two sides are sputtered with metal. The diameter of the sputtered metal on the a surface in contact with the upper electrode is 22 cm, and the diameter of the sputtered metal on the b surface in contact with the lower electrode is 40 cm. In order to make the contact surface conduct electricity well, the sputtered metal is Ag.

[0036] Step 2: Polarization of insulating material A1. The insulating material A1 treated in S1 is placed in a TSDC device. The lower electrode covers the b surface metal, and the upper electrode is covered with the a surface metal. A 250 V direct current voltage is applied to the insulating material A at 70°C, which is converted into an electric field of 1 kV / mm, and the polarization time is 30 min, so as to fully polarize it. Then it is rapidly cooled to-100°C and the electric field is removed, and the polarization state is "frozen".

[0037] Step 3: Measurement of depolarization current curve. After short-circuiting the sample, heat the sample at a rate of 1 ℃ / min until 120°C. The polarization charge frozen in the medium is gradually released, and the released depolarization current is measured with a precision I 1( T ). Figure 1 The blue square points describe the depolarization current-temperature curve at a heating rate of 1 ℃ / min.

[0038] Step 4: Repeated measurement. After taking another completely same insulation material A2 to take the pretreatment of step 1, changing the heating rate to 2℃ / min, repeating step 2 and step 3, the depolarization current I 2( T )。 Figure 1 of white triangle points describes the depolarization current-temperature curve of 2℃ / min heating rate. After taking insulation material A5 to take the pretreatment of step 1, changing the heating rate to 5℃ / min, repeating step 2 and step 3, the depolarization current I 5( T )。 Figure 1 of red circle points describes the depolarization current-temperature curve of 5℃ / min heating rate.

[0039] Step 5: Through step 3 and step 4, the depolarization current curves of heating rate of 1, 2, 5℃ / min are obtained, as shown in Figure 1 . The depolarization current curve has a current peak in the temperature range of 80~120℃. It is observed that in the current peak, different heating rates β i correspond to different peak temperatures, and three groups of β i , T mi ) are obtained: (1℃ / min, 90.80℃), (2℃ / min, 99.97℃), (5℃ / min, 108.28℃). Taking X =1 / T mi as the horizontal coordinate, Y =ln( T mi 2 / β i ) as the vertical coordinate, the above three groups of data are converted into Y - X coordinate system, and the corresponding three data points are: (0.00275, 11.79403), (0.00268, 11.15065) and (0.00262, 10.27842), as shown in Figure 2 . By least square linear fitting of 3 data points, the slope E T / k =11971.638 is obtained. The trap energy level E T of the current peak is the product of the slope and the Boltzmann constant, and the unit is eV. The trap energy level of the current peak is calculated as E T as follows:

[0040] The slope fitting of the current peak R 2 =0.967>0.95, indicating that the position of the current peak is single, or the trap energy level E T is 1.0326eV.

[0041] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that those skilled in the art can understand. The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made on the basis of the technical solutions according to the technical idea of the present application falls within the protection scope of the claims of the present application.

Claims

1. A method for measuring the trap energy level of a thermally stimulated current with a variable heating rate, characterized in that, Includes the following steps: Polarize the insulating material to obtain a polarized sample; By heating polarized samples at different heating rates, the depolarization current during the heating process was collected to obtain depolarization current curves at different heating rates. The peak temperature on the depolarization current curve corresponding to each heating rate is obtained. A linear fit is performed on the heating rate and its corresponding peak temperature. Based on the linear fit result, the trap energy level is calculated.

2. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 1, characterized in that, The preparation of insulating materials is also included before the planning of insulating materials. Specifically, the preparation of insulating materials involves: preparing flat insulating materials using a flat vulcanizer, and sputtering metal onto the a-side and b-side of the flat insulating materials using an ion sputtering instrument to complete the preparation of the insulating materials.

3. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 2, characterized in that, The thickness of the flat insulating material prepared by the flat vulcanizer is 50~1000μm.

4. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 2, characterized in that, When sputtering metal onto the a-side and b-side of the flat insulating material, the diameter of the metal sputtered on the a-side, which contacts the upper electrode, is 10-30 cm, and the diameter of the metal sputtered on the b-side, which contacts the lower electrode, is 20-50 cm.

5. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 4, characterized in that, The ion sputtering instrument sputters metal, either Au or Ag, onto the a-side and b-side of the flat insulating material.

6. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 2, characterized in that, The prepared insulating material is placed in a TSDC device. The lower electrode of the TSDC device is covered with the b-side metal, and the upper electrode of the TSDC device is covered with the a-side metal. A DC electric field is applied to the insulating material at a temperature of 70-100℃ to fully polarize it. After cooling, the voltage is removed, and the polarized state is frozen to obtain a polarized sample.

7. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 6, characterized in that, To freeze the polarization state, the planned insulating material needs to be cooled to 100~250K.

8. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 2, characterized in that, The method of obtaining the peak temperature on the depolarization current curve corresponding to each heating rate specifically involves obtaining the peak temperature of the same current peak on the depolarization current curve corresponding to each heating rate, since the depolarization current curve corresponding to each heating rate includes one or more current peaks.

9. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 1, characterized in that, A linear fit is performed on the heating rate and its corresponding peak temperature, specifically: X =1 / T mi The x-axis is... Y =ln( T mi 2 / β i Plot a scatter plot with y as the vertical axis, where y = y. T mi To obtain the peak temperature on the depolarization current curve corresponding to each heating rate, β i To determine the heating rate, the least squares method was used to perform a linear fit between the heating rate and its corresponding peak temperature. The fitting formula is as follows: In the formula, For trap energy level, These are the least squares linear fitting constants. is Boltzmann's constant.

10. The method for measuring the trap energy level of a thermally stimulated current with a variable heating rate according to claim 9, characterized in that, Based on the linear fitting results, different heating rates were obtained. β Peak temperature T m The slope of the curve is analyzed at different heating rates. β The evolution law of characteristic relaxation peak temperature was investigated, and an activation energy calculation model related to the heating rate was established to calculate the trap energy level. E T : 。