Device characteristic analysis method based on dielectric characteristics and device electrical characteristics

Abstract

The invention discloses a device characteristic analysis method based on dielectric characteristics and device electrical characteristics. The device characteristic analysis method comprises the following steps: acquiring a dielectric fault position of a device; ellipsometric parameters of electronic polarization dielectric properties of the dielectric material before and after the stress is applied and ellipsometric parameters of ionic polarization dielectric properties before and after the stress is applied are obtained; fitting by using a TL optical model to obtain a first parameter set before and after the stress is applied, and fitting by using an LO-TO oscillation model to obtain a second parameter set before and after the stress is applied; determining the change condition of the average static dielectric constant; obtaining a local effective dielectric constant of a nano-scale cross section of the dielectric material containing the crystalline region through a TEM (Transmission Electron Microscope); determining the thermal conductivity of the dielectric material before and after stress application; and completing device modeling and simulation research according to the average static dielectric constant, the local effective dielectric constant, the heat conductivity and the dielectric defect parameters. The method can be used for evaluating the influence of dielectric constant decrease and non-uniformity in a micron-sized electric field peak region on the electrical characteristics of the device.

Description

Technical Field

[0001] This invention belongs to the field of power devices, specifically relating to a device characteristic analysis method based on dielectric properties and electrical properties of the device. Background Technology

[0002] Dielectric properties are a key indicator for measuring the core functions of dielectric materials such as energy storage, insulation, and signal transmission. Their accurate characterization is of great significance for predicting the electrical characteristics and reliability of power devices and optimizing the reliability design of power devices.

[0003] The dielectric properties of the dielectric insulating layer directly affect the electrical characteristics of MOS power devices, such as threshold voltage, leakage current, and switching performance. Degradation of dielectric properties leads to drift in device electrical characteristics, thus affecting durability and stability during long-term operation. In complex operating environments (such as high temperature, high radiation, and repetitive gate bias stress), the dielectric material may be affected by the coupled stresses of multiple physical fields, including thermal, electrical, and mechanical fields, making it prone to dielectric degradation. Accurate analysis of dielectric degradation in power devices can provide crucial guidance for the design of robust dielectrics under various complex operating stresses. Furthermore, it can provide key physical modeling basis for the analysis of the degradation mechanism of dielectric properties and the thermoelectric degradation mechanism caused by dielectric constant inhomogeneity in MOS power devices under different complex operating stresses (hereinafter referred to as stress conditions), or for lifetime prediction.

[0004] Currently, characterization of dielectric properties largely relies on the measurement of dielectric constant. Essentially, these methods involve inferring the macroscopic average dielectric constant by collecting the macroscopic response signal of the material, thereby evaluating the dielectric performance level of the material and the electrical characteristics of power devices based on this macroscopic average dielectric constant.

[0005] Currently, existing methods for testing the dielectric properties of dielectric materials only obtain the macroscopic average dielectric constant and its variation. However, the electric field peaks of power devices are usually arranged with micrometer-level precision. Existing methods cannot measure the differences in local effective dielectric constants at the nanoscale within the micrometer-level electric field region, and therefore cannot assess the significant impact of the decrease and non-uniformity of the dielectric constant within the micrometer-level electric field peak region on the electrical characteristics of the device. Summary of the Invention

[0006] To address the aforementioned problems in the prior art, this invention provides a device characteristic analysis method based on the dielectric properties of the dielectric and the electrical properties of the device.

[0007] The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a device characteristic analysis method based on dielectric properties and device electrical properties, the analysis method comprising: Step 1: Obtain the location of the dielectric fault in the device; Step 2: Based on macroscopic elliptic characterization, the first and second elliptic parameters of the electronic polarization dielectric properties of the dielectric material before and after stress application, as well as the third and fourth elliptic parameters of the ionic polarization dielectric properties before and after stress application, are decoupled and obtained respectively. Step 3: Fit the first elliptic parameter and the second elliptic parameter using the TL optical model respectively, and obtain the first parameter set before and after stress application based on the fitting results. Fit the third elliptic parameter and the fourth elliptic parameter using the LO-TO oscillation model respectively, and obtain the second parameter set before and after stress application based on the fitting results. Step 4: Determine the thermal conductivity of the medium material before and after applying stress; Step 5: Obtain dielectric defect parameters, including dielectric defect density and defect energy level, after applying stress to the dielectric material based on electrical tests of defect characteristics; Step 6: Determine the change in average static dielectric constant based on the first parameter set before and after stress application and the second parameter set before and after stress application; Step 7: Based on the change of the average static dielectric constant, image the dielectric fault location using TEM, and obtain the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region according to the imaging results. Then, based on the equivalent dielectric model and the average static dielectric constant of the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region, obtain the local effective dielectric constant of the nanoscale crystalline region. Step 8: Based on the average static dielectric constant, local effective dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters, complete the device modeling and simulation study. The constructed device model is used to analyze the mechanism of thermoelectric property degradation caused by dielectric property degradation or to predict the lifetime of the device.

[0008] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a device characteristic analysis method based on the dielectric properties of a dielectric material and the electrical properties of the device. Based on obtaining the changes in the macroscopic average dielectric constant of the dielectric material before and after stress, as well as the changes in electron and ion vibration information related to dielectric properties, this method further measures the differences in local effective dielectric constants at the nanoscale within the micrometer-level electric field region of the power device before and after stress, and the changes in the dielectric thermophysical parameters. These measurements are then input into a device model constructed through positive fitting to achieve accurate analysis of the degradation of the dielectric properties of the power device and the device's electrical characteristics, and to predict its lifetime. The method of this invention can measure the differences in local effective dielectric constants at the nanoscale within the micrometer-level electric field region, and therefore can be used to evaluate the impact of dielectric constant decrease and inhomogeneity in the peak region of the micrometer-level electric field on the device's electrical characteristics.

[0009] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0010] Figure 1 This is a schematic flowchart of a device characteristic analysis method based on dielectric properties and device electrical properties provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of an EMMI for a β-Ga2O3 MOS-TYPE trench device after heavy ion irradiation, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram of a dielectric function in the ultraviolet-visible band provided by an embodiment of the present invention; Figure 4 This is a schematic diagram of an infrared band dielectric function provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of a TDTR measurement sample provided in an embodiment of the present invention. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0012] Example 1 Currently, characterization of dielectric properties largely relies on the measurement of the dielectric constant. Essentially, these methods infer the macroscopic average dielectric constant by collecting the material's macroscopic response signal, thereby evaluating the material's dielectric performance level and the electrical characteristics of power devices based on this macroscopic average dielectric constant. Existing technical solutions include obtaining the dielectric constant based on the capacitance-voltage (CV) method, the elliptic polarization spectroscopy method (hereinafter referred to as ellipsometrics), and the resonant cavity method.

[0013] 1. Obtaining dielectric constant based on capacitance-voltage method.

[0014] For fabricated metal-semiconductor-oxide (MOS) devices, their core parameters are determined by the specific fabrication process and photolithography. The dielectric material is typically grown using processes such as thermal oxidation and atomic layer deposition, while the device's planar geometry (i.e., effective area) is precisely defined by the pattern design of the photolithographic mask. A DC bias voltage and a small AC signal are applied simultaneously to both ends of the device. The frequency of the AC signal needs to be set in a relatively high frequency band (typically 100 kHz-1 MHz) to ensure the accuracy of the oxide layer capacitance in the accumulation region and avoid frequency dispersion effects caused by minority carrier generation and recombination in the inversion region of the semiconductor substrate. The applied DC bias voltage during testing needs to be continuously scanned, driving the MOS structure from the accumulation region to the depletion region and then to the inversion region. A strong DC bias voltage causes majority carriers in the substrate to accumulate near the dielectric layer interface. Charge continuously accumulates near the interface until it reaches a stable saturation state, at which point the corresponding accumulation region capacitance reaches its maximum value, which is the oxide layer capacitance of the MOS structure. (Ignoring secondary factors such as interface states, the capacitance can be approximated as being determined solely by the dielectric properties of the dielectric layer). Based on the modified formula for a parallel-plate capacitor, the known parameters are substituted... , , The dielectric constant of the dielectric material of the MOS structure is calculated as shown in formula (1): (1) in: It is the relative permittivity to be obtained; It is the oxide layer capacitance value in the accumulation region obtained by CV measurement; It is the thickness of the dielectric layer; It is the vacuum permittivity; It refers to the device area.

[0015] In the existing scheme, the CV characteristics of the device at 100 kHz were measured using a Keithley 4200 semiconductor parameter analyzer. The CV curve did not show obvious shift or stretching, indicating that insufficient oxide traps and interface states were introduced. Ignoring the interference of the above factors on the capacitance change, it was approximately assumed that the capacitance change was determined only by the dielectric constant of the dielectric layer. The relative dielectric constant under different ion fluence and different electron energy loss was obtained. In order to further explore the microscopic mechanism of dielectric performance change, the microstructure and performance of HfO2 thin film were characterized by high-resolution transmission electron microscopy. A quantitative relationship between relative dielectric constant and ion fluence and effective area of ​​latent track was established, providing a scheme for analyzing the dielectric constant degradation mechanism. As shown in formula (2): (2) in, It is the dielectric constant of the oxide layer material before radiation. It is the dielectric constant of the oxide layer material after radiation. It is the effective area of ​​the latent track. It refers to the ion flux.

[0016] However, the following drawbacks exist in obtaining the dielectric constant based on the capacitance-voltage method: (1) The dielectric constant obtained by the CV method is heavily dependent on the influence of other geometric parameters. For example, the device area A is defined by the photolithography and etching process, and the actual area may deviate from the design value, resulting in errors. Due to the deviation of the fabrication process, the dielectric layer will grow non-uniformly within a certain range, and calculations based on theoretical values ​​will introduce incalculable errors. (2) When the dielectric layer is of poor quality or has a large number of defects, the device is prone to generating a large leakage current. The leakage current is equivalent to a parallel resistance branch, which will change the impedance characteristics of the circuit and lead to the extraction of the oxide layer capacitance. The deviation from the actual capacitance value affects the accuracy of the dielectric constant calculation. (3) When the dielectric constant is obtained by the CV method in the prior art, since there is no obvious displacement and stretching after the CV curve, and minor factors such as oxide traps and interface states are ignored, it is approximately assumed that the capacitance is determined only by the dielectric properties of the dielectric layer.

[0017] 2. Obtain the dielectric constant based on ellipticity testing.

[0018] The existing invention discloses a non-destructive optical testing method for the dielectric constant over a wide temperature range. Ellipsometry is performed on dielectric materials in the ultraviolet-visible and infrared bands to obtain the ellipsometry parameters ψ and Δ of the dielectric material at different temperatures depending on the frequency in the ultraviolet-visible and infrared bands. Different dispersion models are used to fit the ellipsometry parameters for different bands, and the frequency-dependent dielectric functions in the ultraviolet-visible and infrared bands are obtained by inversion. The real part of the dielectric function in the ultraviolet-visible band is extended using an interpolation function. Extract the high-frequency dielectric constant from the curve until the frequency reaches zero. By extracting the band edge of the "Reststrahlen" band in the real part of the dielectric function in the infrared band ( =0) value, to obtain the transverse optical phonon frequency With longitudinal optical phonon frequency Based on the LST relationship, the high-frequency dielectric constant is... Transverse optical phonon frequency and longitudinal optical phonon frequency Substitute to obtain the static dielectric constant at different temperatures .

[0019] However, the static dielectric constant indirectly obtained based on ellipticity testing is the average value of the entire sample. However, the electric field peak of power devices is usually arranged with micrometer-level precision. Existing methods cannot measure the difference in local effective dielectric constant at the nanoscale within the micrometer-level electric field region. Therefore, it is impossible to assess the significant impact of the decrease and non-uniformity of dielectric constant in the micrometer-level electric field peak region on the electrical characteristics of the device.

[0020] 3. Obtain the dielectric constant using the resonant cavity method.

[0021] The method of testing the dielectric properties of unknown dielectric materials using resonant structures is collectively referred to as the resonance method, which mainly utilizes the resonant frequency. f The dielectric properties of the dielectric material are inversely derived from the change in the quality factor Q. A sample of the dielectric material to be tested is inserted into the resonant cavity, replacing the original dielectric material in the cavity. The electromagnetic parameters of the sample and the cavity medium (typically, the replaced medium within the resonant cavity is micro-air) differ. These minute differences cause a change in the resonant state of the cavity, resulting in a change in the resonant frequency. f The quality factor Q undergoes a measurable and precise change. By combining the relevant testing theory with the changes in resonant frequency and quality factor before and after the test, the complex permittivity of the material under test can be deduced. To improve test sensitivity, the dielectric material under test is generally placed at the point of strongest electric or magnetic field within the resonant cavity. This method is suitable for accurately measuring the permittivity at a fixed frequency point.

[0022] However, this method has the following drawbacks: (1) The test frequency is strictly limited by the cavity resonant frequency. For a specific cavity, its resonant frequency is fixed and discrete, determined by its geometry, physical size, and the electromagnetic wave mode propagating inside. A cavity can only resonate at a series of discrete, specific frequencies. For a given cavity, its available test frequency points are fixed, discrete, and cannot be changed. It is not possible to flexibly change the test frequency band. (2) After loading the test material, if the loss of the test material is too high, the resonant state of the resonant cavity will change significantly. In extreme cases, its resonant peak may even disappear, making it difficult to test high-loss sample materials.

[0023] The existing technologies for testing the dielectric properties of dielectric materials only obtain the macroscopic average dielectric constant and its variation. However, the electric field peak of power devices is usually arranged with micrometer-level precision. Existing methods cannot measure the difference in local effective dielectric constant at the nanoscale within the micrometer-level electric field region. Therefore, they cannot assess the significant impact of the decrease and non-uniformity of dielectric constant in the micrometer-level electric field peak region on the electrical characteristics of the device.

[0024] For the reasons stated above, this invention provides a device characteristic analysis method based on the dielectric properties of the dielectric material and the electrical properties of the device. Please refer to [link to relevant documentation]. Figure 1 , Figure 1This is a flowchart illustrating a device characteristic analysis method based on dielectric properties and device electrical properties provided in an embodiment of the present invention. The analysis method includes: Step 1: Obtain the location of the dielectric fault in the device.

[0025] Step 1.1: Obtain microscopic images of the device before stress is applied using EMMI (Emission microscopy), and obtain photon distribution maps of the device after stress is applied and after exposure using EMMI in a dark environment.

[0026] Specifically, the device is characterized before and after stress using EMMI. First, a reflected light micrograph is obtained without applying a voltage bias, representing the actual image of the device. Then, a voltage bias is applied to the device using a probe station, placing it in a state that can induce fault phenomena without damaging the device. This detection process is performed in a dark environment to avoid interference from ambient light. After a certain exposure time, an image with luminescent points but without the device's outline is obtained, i.e., a photon distribution map. For example, the exposure time for a β-Ga2O3MOS-TYPE trench device can be set to 45 s.

[0027] Step 1.2: Overlay the microscopic image and the photon distribution map to determine the location of the dielectric fault in the device.

[0028] Specifically, the acquired microscopic image is precisely overlaid with a photon distribution map obtained after exposure for a certain period of time to obtain the final image. The location of physical defects or electrical anomalies, i.e., the location of dielectric faults in the device, is directly located by identifying the bright spots on the image. For example... Figure 2 The image shown is an EMMI characterization diagram of a β-Ga2O3MOS-TYPE trench device based on hafnium oxide (HfO2) medium after heavy ion irradiation, which can be used to determine the location of the device medium failure.

[0029] Step 2: Based on macroscopic elliptic characterization, the first and second elliptic parameters of the electronic polarization dielectric properties of the dielectric material before and after stress application, as well as the third and fourth elliptic parameters of the ionic polarization dielectric properties before and after stress application, are decoupled and obtained respectively.

[0030] In one specific embodiment, step 2 may include: Based on macroscopic elliptic characterization, the dielectric material before and after stress is measured in the ultraviolet-visible band and in the infrared band. Correspondingly, the first and second elliptic parameters of the electronic polarization dielectric properties of the dielectric material, as well as the third and fourth elliptic parameters of the ionic polarization dielectric properties, are obtained by decoupling. Each set of elliptic parameters includes amplitude ratio and phase difference.

[0031] Specifically, the dielectric constant describes the shielding effect of a dielectric material on an electric field. Its essence is determined by the material's microscopic polarization mechanism, primarily stemming from electronic and ionic polarization. Electronic polarization: Under an applied electric field, the electron cloud within an atom or molecule undergoes a tiny displacement relative to the atomic nucleus (strongly constrained by the Coulomb force of the nucleus, the displacement is extremely small). It mainly contributes to the dielectric response in the ultraviolet-visible band. In this band, electrons, due to their low mass, respond extremely quickly, occurring at almost all frequencies, and their contribution to the dielectric constant is relatively small. The high-frequency dielectric constant reflects the dielectric response of a material at extremely high frequencies, contributed solely by electronic polarization. When the electric field frequency exceeds the ionic polarization response capability, only electronic polarization can keep up with the changes in the high-frequency electric field. Ionic polarization: Under an external electric field, positive and negative ions undergo relative displacement (constrained by lattice elastic forces; ions have large masses, and their displacement amplitude is significantly greater than that of electrons). It mainly contributes to the dielectric response in the infrared band. In this band, the ionic response speed is lower than that of electronic polarization, and its contribution to the dielectric constant is greater than that of electronic polarization.

[0032] This embodiment is based on macroscopic elliptic characterization. An RC2 ellipticometer is used to measure the dielectric material before and after stress application in the ultraviolet-visible band. The first and second elliptic parameters of the electronic polarization dielectric properties of the dielectric material are obtained by decoupling. An IR-VASE-MASKⅡ ellipticometer is used to measure the dielectric material before and after stress application in the infrared band. The third and fourth elliptic parameters of the ionic polarization dielectric properties of the dielectric material are obtained by decoupling. The first and third elliptic parameters include the amplitude ratio and phase difference of the dielectric material before stress application, and the second and fourth elliptic parameters include the amplitude ratio and phase difference of the dielectric material after stress application.

[0033] Step 3: Use the Tauc-Lorentz (hereinafter referred to as TL) optical model to fit the first elliptic parameter and the second elliptic parameter respectively. Based on the fitting results, obtain the first parameter set before and after stress application. Use the LO-TO oscillation model to fit the third elliptic parameter and the fourth elliptic parameter respectively. Based on the fitting results, obtain the second parameter set before and after stress application.

[0034] In one specific embodiment, step 3 may include: Step 3.1: In the ultraviolet-visible band, the first and second elliptic parameters are fitted using the TL optical model to obtain the dielectric function and related optical parameters before and after stress is applied in the ultraviolet-visible band. , , Based on the dielectric function and related optical parameters before and after stress is applied in the ultraviolet-visible band, a first set of parameters before and after stress is applied is obtained. The first set of parameters includes optical band gap, high-frequency dielectric constant, oscillator strength, oscillator broadening and oscillator center energy.

[0035] Specifically, a TL optical model is selected in the ultraviolet-visible band. This TL optical model is widely used to describe many amorphous dielectric and semiconductor thin films. The TL optical model is shown in equation (3): (3) in, It is the strength of the oscillator. It is the oscillator expansion, It is the energy at the center of the oscillator. It is an optical band gap. It is the high-frequency dielectric constant. It is photon energy.

[0036] This embodiment uses a TL optical model to fit the first ellipticity parameter to obtain the dielectric function before stress is applied in the ultraviolet-visible band, such as... Figure 3 As shown, Figure 3 This is a schematic diagram of the dielectric function of HfO2 dielectric material in the ultraviolet-visible band, using the imaginary part of the dielectric function. The optical bandgap before stress application can be obtained by fitting the linear region of the light absorption edge to the intersection of the photon energy on the horizontal axis. (Photon energy) When the dielectric function approaches 0, the real part of the dielectric function can be extracted to obtain the high-frequency dielectric constant; the dielectric constant can be directly obtained after fitting the relevant optical parameters; similarly, by fitting the second ellipticity parameter using the TL optical model, the dielectric function after applying stress in the ultraviolet-visible band can be obtained, and the imaginary part of the dielectric function can be used to obtain the dielectric constant. The optical bandgap after stress can be obtained by fitting the linear region of the light absorption edge to the intersection of the photon energy on the horizontal axis. (Photon energy) Extracting the real part of the dielectric function when it approaches 0 allows us to obtain the high-frequency dielectric constant. The relevant optical parameters can be directly obtained after fitting. This allows us to determine the optical bandgap before and after stress induction. High-frequency dielectric constant and related optical parameters , , Changes in relevant optical parameters. , , This reflects the possible types of point defects. When at least one of the relevant optical parameters before stress is applied changes compared to the relevant optical constants after stress is applied, it indicates that point defects may be generated in the dielectric material. The types of point defects can be found in the literature by searching for typical defects present in the dielectric material. For example, the point defect types in hafnium oxide include oxygen vacancies and hafnium vacancies.

[0037] Step 3.2: In the infrared band, the third and fourth elliptic parameters are fitted using the LO-TO (longitudinal-mode optical phonon-transverse-mode optical phonon) oscillation model to obtain the dielectric function and related optical parameters before and after stress application in the infrared band. , , Based on the dielectric function and related optical parameters before and after stress is applied in the infrared band, a second set of parameters before and after stress is applied is obtained. The second set of parameters includes the frequency of the transverse mode optical phonon TO, the broadening of the transverse mode optical phonon TO, the frequency of the longitudinal mode optical phonon LO, the broadening of the longitudinal mode optical phonon LO, and the oscillator amplitude.

[0038] Specifically, the LO-TO oscillation model is selected in the infrared band, as shown in formula (4): (4) in, It is the amplitude of the oscillator. It is the frequency of the transverse mode optical phonon TO. It is the frequency of the longitudinal mode optical phonon (LO). It is a broadening of transverse mode optical phonons (TO). It is a broadening of the longitudinal mode optical phonon (LO).

[0039] This embodiment uses the LO-TO oscillation model to fit the third elliptic parameter to obtain the dielectric function before stress is applied in the infrared band, such as... Figure 4 As shown, Figure 4 This is a schematic diagram of the dielectric function of HfO2 dielectric material in the infrared band. Based on the characteristics of polar materials, the band edge values ​​of the "Reststrahlen" band in the real part of the dielectric function in the infrared band are extracted. =0) Extracting the frequency of transverse mode optical phonons TO before stress induction. and the frequency of longitudinal mode optical phonons (LO) Similarly, by fitting the fourth elliptic parameter using the LO-TO oscillation model, the dielectric function after applying stress in the infrared band is obtained. Based on the characteristics of polar materials, the band edge values ​​of the "Reststrahlen" band in the real part of the infrared band dielectric function are extracted. =0) Extract the frequency of the transverse mode optical phonon TO after stress induction. and the frequency of longitudinal mode optical phonons (LO) .

[0040] Step 3.3: Based on the LST (Lyddane–Sachs–Teller) relationship, obtain the average static dielectric constant before and after stress application according to the high-frequency dielectric constant before and after stress application, the frequency of transverse mode optical phonon TO, and the frequency of longitudinal mode optical phonon LO.

[0041] Specifically, the LST relationship describes the average static dielectric constant. With high frequency dielectric constant The frequency of transverse mode optical phonons TO and the frequency of longitudinal mode optical phonons (LO) The relationship between them can be indirectly calculated using formula (5) to obtain the average static dielectric constant. The LST relationship is shown in formula (5): (5) Step 4: Determine the thermal conductivity of the medium material before and after applying stress based on TDTR (Time-domain thermoreflectance).

[0042] Specifically, TDTR technology is used to measure the thermal conductivity of dielectric material structures. Figure 5 This is a schematic diagram of a sample measured by TDTR. The TDTR device mainly consists of laser generation, a pump optical path, a detection optical path, and data acquisition and processing components. A femtosecond laser pulse is split into two beams: a strong beam called the pump beam (heating beam) and a weak beam called the probe beam (detection beam). The pump beam first reaches the sample surface and locally heats the metal film. The energy is absorbed by the metal film, generating heat Q that diffuses into the sample. The sample surface temperature will then gradually decrease after a rapid increase. After a certain time delay... The probe light then reaches the sample surface, and the change in light reflectivity over time is monitored using this probe light to obtain the thermal conductivity of the dielectric sample. Using this method, the thermal conductivity of the dielectric material before and after stress application can be obtained.

[0043] Step 5: Obtain dielectric defect parameters, such as dielectric defect density and defect energy level, after applying stress to the dielectric material based on electrical tests of defect characteristics.

[0044] Specifically, electrical tests are performed on the device after stress is applied to assess its defect characteristics, such as using the capacitance-voltage method to obtain the hysteresis characteristic curve and extracting the change in flat-band voltage. The density of medium defects can be obtained based on formula (6). : (6) in: It is a dielectric layer capacitor. It is the amount of charge. It refers to the device area.

[0045] Electrical tests are performed on the device after stress is applied to identify its defect characteristics. For example, the current-voltage characteristic curve is obtained using the current-voltage method. The current-voltage characteristic curve is then fitted according to the leakage current mechanism formulas (PF, TAT, FN) to determine the main leakage mechanism. The energy levels of the dielectric defects are then further fitted. The current density and electric field relationships of the PF, TAT, and FN leakage current mechanisms are shown in the following formulas (7-9): (7) (8) (9) in: It is the current density. It is an electric field. It is the amount of charge. These are dielectric layer defect energy levels related to the PF mechanism. It is the conduction band defect density; These are dielectric layer defect energy levels related to the TAT mechanism. It is a rate constant related to the defect energy. It is the density of dielectric layer defects related to the TAT mechanism. It is the effective electronic mass of semiconductor materials. It is the effective electronic mass of the dielectric layer material. This refers to the conduction band step difference between semiconductor and dielectric layer materials. Based on the current density and electric field relationship formulas for the leakage current mechanisms PF, TAT, and FN mentioned above, current-voltage characteristic curves are fitted respectively. By determining whether the fitted curves have a linear region, the main leakage current mechanism is identified, and then the relevant dielectric defect energy levels are fitted. Therefore, based on the electrical testing of defect characteristics, dielectric defect parameters after stress on the dielectric material can be obtained, including dielectric defect density and defect energy levels.

[0046] Step 6: Determine the change in the average static dielectric constant based on the first parameter set before and after applying stress and the second parameter set before and after applying stress.

[0047] In one specific embodiment, step 6 may include: Case 1: If only the first set of parameters changes before and after stress is applied (i.e. only the electronic polarization dielectric properties change), then the average static dielectric constant remains unchanged, indicating that only a midpoint defect in the medium is generated. In the ultraviolet-visible band, the first preset change is that at least one of the first parameters changes before and after stress is applied.

[0048] Specifically, in the ultraviolet-visible band, the ion polarization response cannot keep up with the high-frequency electric field changes, and the high-frequency dielectric constant only reflects the dielectric response contributed by electronic polarization. In this band, electrons, due to their low mass, respond extremely quickly and occur at almost all frequencies, contributing little to the average static dielectric constant. If only the first parameter set undergoes a first predetermined change before and after stress is applied, the average static dielectric constant remains essentially unchanged based on the LST relationship in formula (5). In the ultraviolet-visible band, if one or more of the optical band gap, high-frequency dielectric constant, oscillator strength, oscillator broadening, and oscillator center energy in the first parameter set change, it indicates that the first parameter set has undergone a first predetermined change.

[0049] Case 2: If the second parameter set undergoes a second predetermined change before and after stress application (i.e., the ion-polarized dielectric properties change), and the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO after stress application is greater than the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO before stress application, it indicates that the continuity of the dielectric crystallization is improved (the density is improved), and the average static dielectric constant increases. Here, the second predetermined change means that all parameters in the second parameter set change before and after stress application, i.e., the change occurs after stress application. , , , , Compared to after stress is applied , , , , All of them changed.

[0050] Specifically, the average static dielectric constant is mainly composed of electronic polarization and ionic polarization. For ionic crystals like HfO2, the static dielectric constant is primarily dominated by ionic polarization. Combining the LST relationship analysis: the average static dielectric constant is generally greater than the high-frequency dielectric constant, and the frequency of longitudinal mode optical phonons (LO) is generally greater than the frequency of transverse mode optical phonons (TO). When the ratio of the frequency of longitudinal mode optical phonons (LO) to the frequency of transverse mode optical phonons (TO) after stress application is greater than the ratio of the frequency of longitudinal mode optical phonons (LO) to the frequency of transverse mode optical phonons (TO) before stress application, while the change in the high-frequency dielectric constant contributed solely by electronic polarization is very small, the average static dielectric constant increases. From a microscopic perspective: the increased frequency of transverse mode optical phonons (LO) after stress induction in amorphous dielectric materials leads to stronger long-range Coulomb interactions, generating nanocrystalline regions that improve the continuity (density) of the medium.

[0051] Case 3: If the second parameter set changes before and after stress is applied, and the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO after stress is applied is less than the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO before stress is applied, it indicates that the continuity of the medium crystallization is worse, that is, the interface scattering between different crystal states is enhanced, and the average static dielectric constant decreases.

[0052] Specifically, when the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO after stress application is less than the ratio before stress application, and the change in the high-frequency dielectric constant contributed only by electronic polarization is very small, the average static dielectric constant decreases. From a microscopic perspective: the lattice of amorphous dielectric materials is short-range ordered but long-range disordered. After stress induction, the frequency of the transverse mode optical phonon TO increases, phonon scattering is enhanced, and the interfaces between different crystalline states in the dielectric material deteriorate the continuity of the dielectric crystal. These interfaces between different crystalline states become strong phonon scattering centers, significantly shortening the phonon lifetime.

[0053] Step 7: Based on the change of the average static dielectric constant, image the dielectric fault location using TEM (Transmission Electron Microscope), and obtain the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region based on the imaging results. Then, based on the equivalent dielectric model and the average static dielectric constant of the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region, obtain the local effective dielectric constant of the nanoscale crystalline region.

[0054] In one specific embodiment, step 7 may include: Step 7.1 Under either Case 2 or Case 3, focus ion beam sampling is performed on the dielectric fault location of the device to obtain the total area of ​​the nanoscale cross-section of the dielectric material containing the crystalline region by TEM.

[0055] Specifically, based on the change in the average static dielectric constant in case 2 or case 3 of step 6, when the ion-polarized dielectric properties change, further analysis based on microscopic TEM characterization is required to obtain the total area of ​​the nanoscale cross-section containing the crystalline region in the dielectric material. Specifically, firstly, focused ion beam sampling is performed on the device dielectric fault location obtained based on EMMI characterization. This involves using a focused ion beam to extract a micrometer-thick sheet perpendicular to the device surface and fixing it to a copper grid. After gradual thinning by the ion beam, a sample with a thickness less than 100 nm is obtained. Then, TEM characterization of this sample allows observation of the nanoscale cross-sectional information of the dielectric layer, specifically obtaining information such as the size, thickness, and lattice arrangement of this dielectric layer cross-section. It is known that the dielectric material before stress application is amorphous with a disordered lattice arrangement, while nanoscale crystalline regions form in the dielectric material after stress application. The total area of ​​the nanoscale cross-section containing the crystalline region in the dielectric material is calculated based on the obtained TEM cross-sectional dimensions.

[0056] Step 7.2: Determine the total area of ​​the crystalline regions in the nanoscale cross-section containing the crystalline regions.

[0057] Specifically, based on the shape of each nanoscale crystalline region, a suitable pre-selection box is chosen to select each nanoscale crystalline region, aiming to include as many of the nanoscale crystalline regions as possible within the pre-selection box. For crystalline regions selected by a circular box, the diameter of the circular box is used as the size of the nanoscale crystalline region; for nanoscale crystalline regions selected by an elliptical box, the major and minor diameters of the elliptical box are used as the sizes of the nanoscale crystalline region. The area of ​​each nanoscale crystalline region selected above is calculated according to its shape, and then the total area of ​​the crystalline regions in the nanoscale cross-section containing the crystalline regions is calculated.

[0058] Step 7.3: Perform a Fourier transform on a preset portion of each nanoscale crystalline region to convert the lattice image into a diffraction pattern in reciprocal space, thereby obtaining a diffraction image of each nanoscale crystalline region.

[0059] Specifically, a clear portion of the nanoscale crystalline region is selected as a preset portion using Digital Micrograph software. Then, a Fourier transform is performed on the preset portion to convert the lattice image into a diffraction pattern in reciprocal space. The image of this diffraction pattern is the diffraction image of the nanoscale crystalline region.

[0060] Step 7.4: Select a diffraction spot that meets the preset conditions in the diffraction image as a reference spot, and use the direction of the line connecting the reference spot and the central spot as the reference direction.

[0061] Specifically, the preset conditions are high symmetry, clear spots, and no overlap in the diffraction patterns. When multiple diffraction spots meet the conditions, the diffraction spot that best meets the conditions is selected as the reference spot, based on the priority of high symmetry, clear spots, and no overlap. The position of the central spot in the diffraction image is confirmed, and the direction of the line connecting the reference spot and the central spot is used as the reference direction.

[0062] Step 7.5: Select the two diffraction spots with the highest clarity and no overlap from the remaining diffraction spots as two selected spots, and determine the interplanar spacing between the reference spot and the two selected spots, as well as the angle between the two selected spots and the reference spot with the central spot as the vertex.

[0063] Specifically, in the diffraction image, two diffraction spots with the highest clarity and no overlap are selected as two selected spots, excluding the reference spot and the central spot. The interplanar spacing of the reference spot and the two selected spots, as well as the angle between the two selected spots and the reference spot with the central spot as the vertex, can be calculated using Digital Micrograph software.

[0064] Step 7.6: Based on the simulated electron diffraction pattern of the candidate phase, determine the phase type of the nanoscale crystalline region according to the interplanar spacing of the reference spot and the two selected spots, and the angle between the two selected spots and the reference spot with the central spot as the vertex, and find the average static dielectric constant corresponding to the phase type of the nanoscale crystalline region.

[0065] Step 7.61: Based on CrystalDiffract, compare the interplanar spacing of the reference spot and the two selected spots with the interplanar spacing of the simulated X-ray diffraction patterns of each phase to obtain several preliminary candidate phases.

[0066] Specifically, when the medium material is known but the phase type is unknown, crystal structure files for all phase types of the material can be obtained from a crystal material database. These files are then imported into CrystalDiffract software to obtain simulated X-ray diffraction patterns for different phase types, with a one-to-one correspondence between interplanar spacing and crystal plane indices (hkl). Phases whose simulated X-ray diffraction patterns correspond to interplanar spacings of the reference spot and two selected spots within a preset range are considered candidate phases. That is, if the difference between the interplanar spacing of the two selected spots and the interplanar spacing of the simulated X-ray diffraction pattern is within a preset range, that phase is selected. The crystal plane indices (hkl) corresponding to the interplanar spacings in the simulated X-ray diffraction patterns of the reference spot and two selected spots are obtained, and all selected phases are considered as candidate phases in the initial screening. The preset difference range is, for example, less than or equal to 0.1 Å.

[0067] Step 7.62: Based on SingleCrystal, determine the simulated electron diffraction pattern of the initially screened candidate phases according to their crystal structure and zone axis [uvw] direction.

[0068] Specifically, the crystal structure files of the initially screened candidate phases are imported into SingleCrystal software, the zone axis [uvw] direction is set, and SingleCrystal software generates simulated electron diffraction patterns for each initially screened candidate phase. The zone axis [uvw] direction is obtained by cross-producting the crystal plane indices (hkl) of the simulated X-ray diffraction patterns corresponding to the reference spot and the two selected spots (u·h+v·k+w·l=0) to solve for u, v and w.

[0069] Step 7.63: Compare the diffraction image with the preliminary screened simulated electron diffraction pattern, and select the simulated electron diffraction pattern that is consistent with the distribution position of the crystal plane index (hkl) of the central spot, the reference spot and the two selected spots from the simulated electron diffraction patterns of all candidate phases.

[0070] Specifically, among all candidate phases, the simulated electron diffraction patterns of the spots with crystal plane index (hkl) distribution positions consistent with those of the central spot, the reference spot, and the two selected spots are selected.

[0071] Step 7.64: Based on the angle between the two selected spots and the reference spot with the central spot as the vertex, determine the phase type of the nanoscale crystalline region according to all the simulated electron diffraction patterns selected in Step 7.63, and find the average static dielectric constant corresponding to the phase type of the nanoscale crystalline region.

[0072] Specifically, taking the central spot as the vertex and the direction of the line connecting the reference spot and the central spot as the reference direction, the angle between the two selected spots and the reference spot is compared with the angles of the corresponding spots in all the simulated electron diffraction patterns selected in step 7.63. The angles are selected if the difference between them is within 2°. If two or more simulated electron diffraction patterns meet this condition, the one with the smallest difference is selected as the final simulated electron diffraction pattern. The phase type corresponding to this simulated electron diffraction pattern is determined as the phase type of the nanoscale crystalline region. Based on the above steps, the phase type of each nanoscale crystalline region is determined, and the average static dielectric constant corresponding to the phase type of the nanoscale crystalline region is obtained by searching the literature.

[0073] Step 7.7: Based on the equivalent dielectric model, the total area of ​​the nanoscale cross-section containing the crystalline region, the total area of ​​the crystalline region, the average static dielectric constant of the dielectric material before stress, and the average static dielectric constant of the phase type of the nanoscale crystalline region, the local effective dielectric constant containing the nanoscale crystalline region is obtained.

[0074] In one specific embodiment, step 7.7 may include: The local effective dielectric constant containing the nanoscale crystalline region is calculated based on the equivalent dielectric model, the total area of ​​the nanoscale cross-section containing the crystalline region, the total area of ​​the crystalline region, the average static dielectric constant of the dielectric material before stress, and the average static dielectric constant of the phase type of the nanoscale crystalline region.

[0075] Specifically, the average static dielectric constant obtained based on macroscopic ellipticity testing represents the average value of the dielectric material. For the three cases in step 6, the continuity of the dielectric crystallization also changes when the ion-polarized dielectric properties change.

[0076] The equivalent medium model is shown in equation (10): (10) in, It is the effective dielectric constant. It is the average static dielectric constant of the dielectric material before stress. It is the average static dielectric constant of the phase type in the nanoscale crystalline region. For example, the average static dielectric constant of monoclinic HfO2 is 16. f It is the ratio of the total area of ​​the crystalline region in the nanoscale cross-section to the total area of ​​the nanoscale cross-section.

[0077] This embodiment can obtain the different degrees of change in the local effective dielectric constant of different nanoscale crystalline regions after stress is applied. The different degrees of change in the local effective dielectric constant of different nanoscale cross-sectional regions will cause the dielectric constant to be unevenly distributed.

[0078] Step 8: Based on the average static dielectric constant, local effective dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters, complete the device modeling and simulation study. The constructed device model is used to analyze the mechanism of device thermoelectric property degradation caused by dielectric property degradation or to predict the lifetime.

[0079] In one specific embodiment, step 8 may include: For case 1, the average static dielectric constant after stress is applied, the thermal conductivity of the dielectric material, and the dielectric defect parameters are substituted into the device model constructed by positive fitting before stress is applied to complete the device modeling and simulation study after stress is applied. Specifically, the average static dielectric constant after stress is applied, the thermal conductivity of the dielectric material after stress is applied, and the dielectric defect parameters after stress are applied are input into the device model constructed by positive fitting before stress is applied, thus completing the device modeling and simulation study after stress is applied.

[0080] For case 2, the average static dielectric constant, local effective dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters after applying stress are input into the device model constructed by forward fitting before applying stress. The local effective dielectric constant is specifically added to the dielectric fault location, and the average static dielectric constant after applying stress is added to the remaining dielectric regions, thus completing the device modeling and simulation study after applying stress.

[0081] Specifically, the average static dielectric constant after stress application, the thermal conductivity of the dielectric material after stress application, and the dielectric defect parameters after stress application are input into the device model constructed by positive fitting before stress application. The dielectric fault location of the device is located in the device model before stress application, the local effective dielectric constant is specifically added to the dielectric fault location, and the average static dielectric constant after stress application is added to the remaining dielectric regions, thus completing the device modeling and simulation study after stress application.

[0082] For scenario 3, the specific implementation steps are the same as in scenario 2.

[0083] By constructing targeted device models based on the three scenarios in step 8, the research objective of analyzing the mechanism of thermoelectric characteristic degradation or predicting the lifetime of MOS power devices caused by dielectric degradation and dielectric constant inhomogeneity can be achieved.

[0084] It should be noted that this invention is not limited to analyzing the degradation of dielectric properties of power devices under radiation scenarios. It is also applicable to dielectric materials in complex operating environments (such as high temperature, high radiation, and repetitive gate bias stress), where the dielectric material is susceptible to changes in dielectric properties due to multi-physics coupling stress. The device characteristic analysis method for the dielectric and electrical properties of power devices proposed in this invention is not limited to the β-Ga2O3MOS-TYPE trench device structure of this embodiment; it is also applicable to other device structures containing MOS structures, such as MOSCAP and MOSFETs. The ellipsometry testing equipment of this invention is not limited to the RC2 and IR-VASE-MASKⅡ mentioned in this embodiment; it is also applicable to other testing equipment capable of measuring ultraviolet-visible and infrared wavelengths. This invention is not limited to the capacitance-voltage method for obtaining dielectric defect parameters mentioned in this embodiment; it is also applicable to other testing and characterization methods such as DLTS for obtaining dielectric defect parameters. The dielectric material mentioned in this invention is not limited to the HfO2 dielectric material mentioned in this embodiment; it is also applicable to other dielectric materials such as HfCeO2, SiO2, and PZT. This invention is not limited to the Tauc-Lorentz optical model and the LO-TO oscillation model mentioned in this embodiment. Other oscillator models that can correctly characterize the dielectric properties of materials with different properties are also applicable.

[0085] This invention obtains the average static dielectric constant of the dielectric material after stress induction based on macroscopic ellipticity testing. It analyzes three cases of changes in the average static dielectric constant according to the LST relationship. Furthermore, based on cases 2 and 3, it combines TEM analysis to analyze the differences between the local effective dielectric constant changes and dielectric constant inhomogeneity of the nanoscale cross section, thus broadening the perspective for analyzing the dielectric properties of the device dielectric. Based on macroscopic and microscopic characterization, it focuses on the dual challenges of dielectric performance degradation and dielectric inhomogeneity changes within the nanoscale precision range.

[0086] This invention enables device characteristic analysis of the degradation mechanism of dielectric properties and electrothermal properties of power devices. It provides a novel analytical method for the degradation mechanism of dielectric properties of MOS power devices caused by stress and thermoelectric property degradation caused by dielectric constant inhomogeneity.

[0087] This invention provides a device characteristic analysis method based on the dielectric properties of a dielectric material and the electrical properties of the device. Based on obtaining the changes in the macroscopic average dielectric constant of the dielectric material before and after stress, as well as the changes in electron and ion vibration information related to dielectric properties, this method further measures the differences in local effective dielectric constants at the nanoscale within the micrometer-level electric field region of the power device before and after stress, and the changes in the dielectric thermophysical parameters. These measurements are then input into a power device model constructed through positive fitting, achieving the goal of accurate analysis of dielectric and electrical characteristic degradation and lifetime prediction for power devices. The method of this invention can measure the differences in local effective dielectric constants at the nanoscale within the micrometer-level electric field region, and therefore can be used to evaluate the impact of dielectric constant decrease and non-uniformity in the peak region of the micrometer-level electric field on the device's electrical characteristics.

[0088] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0089] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0090] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A device characteristic analysis method based on dielectric properties and electrical properties of a dielectric material, characterized in that, The analytical method includes: Step 1: Obtain the location of the dielectric fault in the device; Step 2: Based on macroscopic elliptic characterization, the first and second elliptic parameters of the electronic polarization dielectric properties of the dielectric material before and after stress application, as well as the third and fourth elliptic parameters of the ionic polarization dielectric properties before and after stress application, are decoupled and obtained respectively. Step 3: Fit the first elliptic parameter and the second elliptic parameter using the TL optical model respectively, and obtain the first parameter set before and after stress application based on the fitting results. Fit the third elliptic parameter and the fourth elliptic parameter using the LO-TO oscillation model respectively, and obtain the second parameter set before and after stress application based on the fitting results. Step 4: Determine the thermal conductivity of the medium material before and after applying stress; Step 5: Obtain dielectric defect parameters, including dielectric defect density and defect energy level, after applying stress to the dielectric material based on electrical tests of defect characteristics; Step 6: Determine the change in average static dielectric constant based on the first parameter set before and after stress application and the second parameter set before and after stress application; Step 7: Based on the change of the average static dielectric constant, image the dielectric fault location using TEM, and obtain the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region according to the imaging results. Then, based on the equivalent dielectric model and the average static dielectric constant of the total area of ​​the nanoscale cross-section containing the crystalline region, the phase type of the nanoscale crystalline region, and the total area of ​​the crystalline region, obtain the local effective dielectric constant of the nanoscale crystalline region. Step 8: Complete device modeling and simulation studies based on the average static dielectric constant, local effective dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters. The constructed device model is used to analyze the mechanism of thermoelectric property degradation caused by dielectric property degradation or to predict the device's lifetime.

2. The analytical method according to claim 1, characterized in that, Step 1 includes: Microscopic images of the device before stress was applied were obtained by EMMI, and photon distribution maps of the device after stress was applied and exposed were obtained by EMMI in a dark environment. By superimposing the microscopic image and the photon distribution map, the location of the dielectric fault in the device can be determined.

3. The analytical method according to claim 1, characterized in that, Step 2 includes: Based on macroscopic elliptic characterization, the dielectric material before and after stress is measured in the ultraviolet-visible band and in the infrared band. Correspondingly, the first and second elliptic parameters of the electronic polarization dielectric properties and the third and fourth elliptic parameters of the ionic polarization dielectric properties of the dielectric material are obtained by decoupling. Each set of elliptic parameters includes amplitude ratio and phase difference.

4. The analytical method according to claim 1, characterized in that, Step 3 includes: Step 3.1: In the ultraviolet-visible band, the first ellipticity parameter and the second ellipticity parameter are fitted using the TL optical model to obtain the dielectric function and related optical parameters before and after stress is applied in the ultraviolet-visible band. Based on the dielectric function and related optical parameters before and after stress is applied in the ultraviolet-visible band, a first parameter set before and after stress is obtained. The first parameter set includes optical band gap, high-frequency dielectric constant, oscillator strength, oscillator broadening, and oscillator center energy. Step 3.2: In the infrared band, the third ellipticity parameter and the fourth ellipticity parameter are fitted using the LO-TO oscillation model to obtain the dielectric function and related optical parameters before and after stress is applied in the infrared band. Based on the dielectric function and related optical parameters before and after stress is applied in the infrared band, a second parameter set is obtained before and after stress is applied. The second parameter set includes the frequency of the transverse mode optical phonon TO, the broadening of the transverse mode optical phonon TO, the frequency of the longitudinal mode optical phonon LO, the broadening of the longitudinal mode optical phonon LO, and the oscillator amplitude. Step 3.3: Based on the LST relationship, obtain the average static dielectric constant before and after stress application according to the high-frequency dielectric constant before and after stress application, the frequency of transverse mode optical phonon TO, and the frequency of longitudinal mode optical phonon LO.

5. The analytical method according to claim 1, characterized in that, Step 4 includes: The thermal conductivity of the medium material before and after stress application is determined based on TDTR.

6. The analytical method according to claim 4, characterized in that, Step 6 includes: Case 1: If only the first parameter set before and after stress is applied undergoes a first preset change, then the average static dielectric constant remains unchanged, wherein the first preset change is that at least one of the first parameter sets before and after stress is applied changes. Case 2: If the second parameter set before and after stress is applied undergoes a second preset change, and the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO after stress is applied is greater than the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO before stress is applied, then the average static dielectric constant increases. The second preset change means that all parameters in the second parameter set before and after stress are changed. Case 3: If the second parameter set undergoes a second preset change before and after stress is applied, and the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO after stress is applied is less than the ratio of the frequency of the longitudinal mode optical phonon LO to the frequency of the transverse mode optical phonon TO before stress is applied, then the average static dielectric constant decreases.

7. The analytical method according to claim 6, characterized in that, Step 7 includes: Step 7.1: Under the conditions of situation 2 or situation 3, focus ion beam sampling is performed on the dielectric fault location of the device to obtain the total area of ​​the nanoscale cross-section of the dielectric material containing the crystalline region by TEM; Step 7.2: Determine the total area of ​​the crystalline regions in the nanoscale cross-section containing the crystalline regions; Step 7.3: Perform Fourier transform on the preset portion of each nanoscale crystalline region to convert the lattice image into a diffraction pattern in reciprocal space, thereby obtaining the diffraction image of each nanoscale crystalline region; Step 7.4: Select a diffraction spot that meets the preset conditions in the diffraction image as a reference spot, and the direction of the line connecting the reference spot and the central spot is used as the reference direction; Step 7.5: Select the two diffraction spots with the highest clarity and no overlap from the remaining diffraction spots as two selected spots, and determine the interplanar spacing between the reference spot and the two selected spots, as well as the angle between the two selected spots and the reference spot with the central spot as the vertex. Step 7.6: Based on the simulated electron diffraction pattern of the candidate phase, determine the phase type of the nanoscale crystalline region according to the interplanar spacing of the reference spot and the two selected spots, and the angle between the two selected spots and the reference spot with the central spot as the vertex, and find the average static dielectric constant corresponding to the phase type of the nanoscale crystalline region. Step 7.7: Based on the equivalent dielectric model, the total area of ​​the nanoscale cross-section containing the crystalline region, the total area of ​​the crystalline region, the average static dielectric constant of the dielectric material before stress, and the average static dielectric constant of the phase type of the nanoscale crystalline region, the local effective dielectric constant containing the nanoscale crystalline region is obtained.

8. The analytical method according to claim 7, characterized in that, Step 7.6 includes: Step 7.61: Based on CrystalDiffract, compare the interplanar spacing of the reference spot and the two selected spots with the interplanar spacing of the simulated X-ray diffraction patterns of each phase to obtain several preliminary candidate phases. Step 7.62: Based on SingleCrystal, determine the simulated electron diffraction pattern of the preliminary candidate phases according to their crystal structure and zone axis [uvw] direction. Step 7.63: Compare the diffraction image with the preliminary screened simulated electron diffraction pattern, and select the simulated electron diffraction pattern that is consistent with the crystal plane index distribution position of the central spot, the reference spot and the two selected spots from the simulated electron diffraction patterns of all the candidate phases; Step 7.64: Based on the angle between the two selected spots and the reference spot with the central spot as the vertex, determine the phase type of the nanoscale crystalline region according to the simulated electron diffraction patterns of all the candidate phases selected in step 7.63, and find the average static dielectric constant corresponding to the phase type of the nanoscale crystalline region.

9. The analytical method according to claim 7, characterized in that, Step 8 includes: For case 1, the average static dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters after stress application are substituted into the device model constructed by positive fitting before stress application to complete the device modeling and simulation study after stress application. For case 2 or case 3, the average static dielectric constant, local effective dielectric constant, thermal conductivity of the dielectric material, and dielectric defect parameters after stress application are input into the device model constructed by forward fitting before stress application. The local effective dielectric constant is specifically added to the dielectric fault location, and the average static dielectric constant after stress is added to the remaining dielectric regions to complete the device modeling and simulation study after stress application.

Images