A method and system for predicting the reliability of a field effect transistor based on instantaneous power

Abstract

The application provides a kind of MOSFET reliability prediction method and system based on instantaneous power, it is related to MOSFET life prediction technical field, method includes: through sensor acquisition instantaneous voltage and instantaneous current of the field effect transistor to be predicted;According to instantaneous voltage and instantaneous current, calculate instantaneous power;Based on instantaneous power, calculate internal transient temperature distribution by lattice boltzmann method;According to internal transient temperature distribution, calculate defect generation rate;In combination with defect generation rate and non-homogeneous Poisson process, determine the spatial defect distribution of the field effect transistor to be predicted;Extract the fractal structure feature of spatial defect distribution, and calculate the fractal dimension of the field effect transistor to be predicted;According to fractal dimension and critical defect density, judge whether the field effect transistor to be predicted forms the conductive path from top to bottom;If yes, determine that the field effect transistor to be predicted occurs oxide layer breakdown;Otherwise, continue to monitor;Output the comprehensive reliability prediction result of the field effect transistor to be predicted.

Description

Technical Field

[0001] This invention relates to the field of MOSFET lifetime prediction technology, and in particular to a method and system for predicting the reliability of field-effect transistors based on instantaneous power. Background Technology

[0002] As power electronic devices continue to evolve towards higher frequencies, higher power densities, and smaller sizes, field-effect transistors (MOSFETs, GaN FETs, and SiC FETs) play a crucial role in energy conversion in applications such as new energy vehicles, data centers, power conversion, and industrial control. During rapid dynamic switching, these devices generate strong transient thermal effects. The formation of localized hotspots subjects the oxide layer, electrode interfaces, and other micro / nano structures to severe thermo-electric coupling stress, leading to increasingly prominent reliability issues.

[0003] Reliability prediction of MOSFETs can accurately reflect the transient thermal stress generated by the device under high-speed switching and dynamic load conditions, which is of great significance for the safe operation of high power density devices in fields such as new energy vehicles, power conversion and industrial control.

[0004] However, existing MOSFET reliability prediction methods mainly rely on steady-state thermal models, average power methods, or empirical lifetime curves, such as those based on the Arrhenius formula, power cycling tests, and the TDDB (Time Dependent Dielectric Breakdown) lifetime model. These methods typically assume that the device operates under stable thermal conditions, neglecting instantaneous power fluctuations under rapid switching conditions and the resulting non-uniform temperature distribution. This makes it impossible to accurately determine when a penetrating flow path will appear in the oxide layer from top to bottom, and also prevents real-time, dynamic reliability prediction. Consequently, their reliability is insufficient in high-power, high-frequency, and high-stress applications, limiting the safety and predictability of modern power electronic systems. Summary of the Invention

[0005] To address the technical problem that existing methods typically assume devices operate under stable thermal conditions, neglecting instantaneous power fluctuations under rapid switching conditions and the resulting non-uniform temperature distribution, which leads to the inability to accurately determine when a penetrating flow path will appear in the oxide layer from top to bottom, and the inability to perform real-time, dynamic reliability prediction, resulting in insufficient reliability in high-power, high-frequency, and high-stress applications, thus limiting the safety and predictability of modern power electronic systems, this invention provides a method and system for predicting the reliability of MOSFETs based on instantaneous power.

[0006] The technical solutions provided by the embodiments of the present invention are as follows:

[0007] A first aspect of this invention provides a method for predicting the reliability of a field-effect transistor based on instantaneous power, comprising:

[0008] S1: Acquire the instantaneous voltage and instantaneous current of the field-effect transistor to be predicted through a sensor;

[0009] S2: Calculate the instantaneous power based on the instantaneous voltage and instantaneous current;

[0010] S3: Based on instantaneous power, the internal transient temperature distribution of the field-effect transistor to be predicted is calculated using the lattice Boltzmann method;

[0011] S4: Based on the internal transient temperature distribution, the defect generation rate of the field-effect transistor to be predicted is calculated using the Arrhenius model;

[0012] S5: Combine the defect generation rate and the non-homogeneous Poisson process to determine the spatial defect distribution of the field-effect transistor to be predicted, where the spatial defect distribution includes the defect location and the number of defects;

[0013] S6: Extract the fractal structure features of the spatial defect distribution, and calculate the fractal dimension of the field-effect transistor to be predicted based on the fractal structure features;

[0014] S7: Based on the fractal dimension and the preset critical defect density, determine whether the field-effect transistor to be predicted has formed a conductive path from top to bottom using the spherical base permeation model; if so, determine that the field-effect transistor to be predicted has experienced oxide layer breakdown and proceed to step S8; otherwise, use the spatial defect distribution as historical data and return to step S1 to continue monitoring.

[0015] S8: Output the comprehensive reliability prediction result of the field-effect transistor to be predicted.

[0016] Optionally, S3 specifically includes:

[0017] S301: Calculate the equivalent volumetric heat source density based on the instantaneous power and the effective heating volume of the field-effect transistor to be predicted;

[0018] S302: Construct a D2Q8 lattice model based on the actual two-dimensional geometry of the field-effect transistor to be predicted;

[0019] S303: Determine the discrete phonon energy transport equation based on the D2Q8 lattice model and the equivalent volumetric heat source density;

[0020] S304: Perform a propulsion process on the lattice Boltzmann using the discrete phonon energy transport equation;

[0021] S305: Based on the propulsion processing results, sum the phonon energy distribution functions in all discrete directions to determine the macroscopic phonon energy;

[0022] S306: The temperature distribution is determined by inverting the macroscopic phonon energy using the Debye model;

[0023] S307: Set the thermal boundary conditions required for the lattice Boltzmann method solution;

[0024] S308: Under the constraints of the thermal boundary conditions, repeat steps S304-S306 until the change in the temperature field is less than the temperature threshold, and determine the internal transient temperature distribution.

[0025] Optionally, the thermal boundary conditions in S307 include: isothermal boundary conditions, adiabatic boundary conditions, and temperature jump boundary conditions.

[0026] Optionally, S4 specifically includes:

[0027] S401: Based on the material properties and defect type of the field-effect transistor to be predicted, initialize the key parameters of the Arrhenius model, wherein the key parameters include: activation energy and pre-exponential factor;

[0028] S402: Based on the initialized Arrhenius model and combined with the gradient penetration mechanism, establish a spatially relevant defect generation rate model;

[0029] S403: Based on the defect generation rate model, the active region of the field-effect transistor to be predicted is integrated by volume to determine the defect generation rate.

[0030] Optionally, S5 specifically includes:

[0031] S501: Construct a temperature-driven spatial defect intensity function based on the defect generation rate and gradient weight function;

[0032] S502: Calculate the local expected number of defects in the oxide layer region using the non-homogeneous Poisson process based on the spatial defect intensity function.

[0033] S503: Combining the aforementioned local expected defect number, a non-homogeneous Poisson point field is generated using the envelope-sparse algorithm;

[0034] S504: Map each Poisson point in the non-homogeneous Poisson point field to a defect entity;

[0035] S505: Statistically analyze the defective entities to determine the spatial defect distribution of the field-effect transistor to be predicted.

[0036] Optionally, S6 specifically includes:

[0037] S601: Based on the spatial defect distribution, construct a set of defect cluster structures;

[0038] S602: Select the largest defect cluster in the defect cluster structure set as the representative defect cluster;

[0039] S603: Based on the representative defect clusters, perform multi-scale counting of the number of defects within the radius sphere;

[0040] S604: Based on the multi-scale counting results, and according to the power-law characteristics of the fractal structure of the field-effect transistor to be predicted, an approximate power-law relationship is constructed for the number of defects as a function of the counting radius.

[0041] S605: Map the approximate power-law relationship and the multi-scale counting results to a logarithmic coordinate system to construct a linear relationship;

[0042] S606: By using the least squares algorithm, straight lines are fitted to the data points in the linear relationship to obtain the fractal structure characteristics of the spatial defect distribution;

[0043] S607: Based on the fractal structure characteristics, calculate the fractal dimension related to the oxide layer thickness of the field-effect transistor to be predicted.

[0044] Optionally, S7 specifically includes:

[0045] S701: Calculate the average defect density of the current space based on the oxide layer volume region and the spatial defect distribution;

[0046] S702: Based on the fractal dimension, using the spherical-based permeation model, all defects are divided into a predetermined number of connected clusters, wherein the connected clusters are candidate conductive clusters;

[0047] S703: Based on each of the candidate conductive clusters, determine whether there is a through-flow path from top to bottom; if yes, proceed to step S704; otherwise, return to step S1 to continue monitoring.

[0048] S704: Based on the critical defect density, the conductive path of the field-effect transistor to be predicted is determined using a dual-criteria decision rule;

[0049] S705: If the field-effect transistor to be predicted forms a conductive path from top to bottom, proceed to step S8; if the field-effect transistor to be predicted does not form a conductive path from top to bottom, return to step S1 to continue monitoring.

[0050] Optionally, the dual-criteria decision rule specifically includes:

[0051] If the defect density is greater than the critical defect density and the oxide layer has a through-flow path from top to bottom, or if the defect density is equal to the critical defect density and the oxide layer has a through-flow path from top to bottom, the predicted field-effect transistor is determined to have oxide layer breakdown.

[0052] If the defect density is less than the critical defect density or there is no through-flow path from top to bottom, it is determined that the field-effect transistor to be predicted has not experienced oxide layer breakdown.

[0053] Optionally, the comprehensive reliability prediction results include: the health status, failure probability curve, remaining service life, and maintenance recommendations of the field-effect transistor to be predicted.

[0054] A second aspect of the present invention provides a field-effect transistor reliability prediction system based on instantaneous power, comprising:

[0055] processor;

[0056] The memory stores computer-readable instructions, which, when executed by a processor, implement the MOSFET reliability prediction method based on instantaneous power as described in the first aspect.

[0057] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the field-effect transistor reliability prediction method based on instantaneous power as described in the first aspect.

[0058] The beneficial effects of the technical solutions provided by the embodiments of the present invention include at least the following:

[0059] In this embodiment of the invention, by introducing the unsteady-state thermal effect driven by instantaneous power into the reliability prediction process, and combining it with lattice Boltzmann temperature field calculation, Arrhenius defect generation model, non-homogeneous Poisson point field, fractal structure analysis and spherical basis percolation criterion, the complete evolution process of defects from generation and aggregation to the formation of a conductive path can be characterized from the microscopic mechanism level. This significantly improves the failure prediction accuracy and lead time of field-effect transistors under dynamic operating conditions, not only improving the reliability of oxide layer breakdown determination, but also enabling accurate assessment of the remaining life of the device, effectively supporting the safe operation and preventive maintenance of high-power electronic systems. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0061] Figure 1 This is a flowchart illustrating a field-effect transistor reliability prediction method based on instantaneous power, provided as an embodiment of the present invention.

[0062] Figure 2This is a schematic diagram of a field-effect transistor reliability prediction system based on instantaneous power, provided as an embodiment of the present invention. Detailed Implementation

[0063] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0064] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0065] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0066] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0067] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0068] Reference manual attached Figure 1 The diagram shows a flowchart of a field-effect transistor reliability prediction method based on instantaneous power provided by an embodiment of the present invention.

[0069] This invention provides a method for predicting the reliability of field-effect transistors (FETs) based on instantaneous power. This method can be implemented by a device for predicting the reliability of FETs based on instantaneous power, which can be a terminal or a server. The processing flow of the method for predicting the reliability of FETs based on instantaneous power may include the following steps:

[0070] S1: The instantaneous voltage and instantaneous current of the field-effect transistor to be predicted are collected by the sensor.

[0071] Among them, the sensor is a measuring device used to acquire voltage and current signals in real time. It may include a high-speed current probe, voltage probe, Hall sensor or integrated on-chip electrical parameter monitoring module, and is required to have high bandwidth and fast response capability.

[0072] Instantaneous voltage refers to the device port voltage value measured within a very short period of time, used to reflect the transient voltage changes of the MOSFET under rapid switching or dynamic load conditions. Instantaneous current refers to the actual current value passing through the MOSFET channel or pin at the same instant, used to characterize the device's true current response under switching action or pulsed load conditions.

[0073] It should be noted that by acquiring instantaneous voltage and current in real time, the most realistic electro-thermal excitation input of the MOSFET under high-speed switching conditions can be obtained. This allows subsequent power and temperature field calculations to be based on actual operating conditions rather than average values ​​or assumptions, thereby significantly improving the accuracy of reliability prediction and dynamic response capability.

[0074] S2: Calculate the instantaneous power based on the instantaneous voltage and instantaneous current.

[0075] Instantaneous power refers to the power value obtained by directly multiplying instantaneous voltage and instantaneous current at a specific moment. It is used to reflect the transient energy input intensity of the device under fast switching or pulsed load and is the core physical quantity describing the internal heating rate of the device.

[0076] It should be noted that by calculating instantaneous power based on real-time acquired instantaneous voltage and instantaneous current, the actual heat source intensity of the MOSFET under dynamic operating conditions can be accurately characterized. This makes the power calculation no longer dependent on average values ​​or steady-state assumptions, thereby significantly improving the authenticity and accuracy of subsequent thermal field solutions, defect generation rate calculations, and reliability predictions.

[0077] S3: Based on instantaneous power, the internal transient temperature distribution of the field-effect transistor to be predicted is calculated using the lattice Boltzmann method.

[0078] Among them, the Lattice Boltzmann Method (LBM) is a numerical method based on the evolution of microscopic particle distribution to solve macroscopic transport behavior. It simulates the heat conduction process through the collision and streaming of discrete phonon energy distribution functions, and is particularly suitable for solving transient temperature fields at the nanoscale, non-Fourier heat conduction and under complex boundary conditions.

[0079] Among them, the internal transient temperature distribution refers to the temperature field distribution at various locations inside the field-effect transistor as time changes. It can reflect the formation of hot spots, the dynamics of heat diffusion, and local overheating areas, and is the direct driving force for the generation of thermally activated defects.

[0080] It should be noted that by using the lattice Boltzmann method to solve the internal transient temperature distribution based on instantaneous power, it is possible not only to capture the unsteady thermal effects generated by the device under high-speed switching, but also to accurately describe local overheating, temperature gradient and non-uniform thermal diffusion characteristics. This provides a high-resolution, physically consistent temperature field basis for subsequent defect generation rate modeling, and significantly improves the accuracy of reliability prediction and mechanism explanation capabilities.

[0081] In one possible implementation, S3 specifically includes:

[0082] S301: Calculate the equivalent volumetric heat source density based on the instantaneous power and the effective heating volume of the field-effect transistor to be predicted.

[0083]

[0084] Where, q v V(t) represents the equivalent volumetric heat source density at time t, P(t) represents the instantaneous power at time t, and V act Indicates the effective heat generation volume.

[0085] The effective heat generation volume refers to the effective volume of the channel region and parasitic resistance region that actually participate in heat generation during the switching process, and is the physical source of heat generated inside the power device.

[0086] Among them, the equivalent volume heat source density represents the instantaneous heat source intensity within a unit effective heat-generating volume, which is the direct input quantity driving transient heat transfer.

[0087] S302: Construct a D2Q8 lattice model based on the actual two-dimensional geometry of the field-effect transistor to be predicted.

[0088]

[0089] Among them, c i This represents the lattice velocity in the i-th discrete direction. Indicates the x-axis direction. Indicates the y-axis direction. Indicates the diagonal direction.

[0090] Specifically, by dividing the propagation direction of phonons in the two-dimensional lattice into 8 types and numbering them 1 to 8 respectively, with numbers 1 to 4 corresponding to horizontal / vertical propagation and numbers 5 to 8 corresponding to diagonal propagation, LBM will propagate the phonon energy along these 8 directions during the solution process.

[0091] Among them, the D2Q8 lattice model refers to the two-dimensional eight-velocity discrete model of LBM (D=2, Q=8), which contains discrete velocities in four orthogonal directions and four diagonal directions on a two-dimensional plane, and is suitable for simulating planar heat conduction problems.

[0092] S303: Based on the D2Q8 lattice model and equivalent volumetric heat source density, the discrete phonon energy transport equation is determined:

[0093]

[0094] in, This represents the phonon energy density at position x at time t, along the i-th discrete direction. Indicates the time step. express The phonon energy density at position x along the i-th discrete direction at time x. Indicates the distance between the space and the walking distance. Let represent the equilibrium phonon energy distribution at position x at time t along the i-th discrete direction. q represents the relaxation time. v This represents the equivalent volumetric heat source density, i.e., the internal volumetric heat source term. express Always in position At point i, the phonon energy density along the i-th discrete direction.

[0095] Among them, the discrete phonon energy transport equation refers to the mathematical expression of the entire process of instantaneous power being converted into volumetric heat source, further driving phonon migration and relaxation processes, and finally forming macroscopic temperature distribution after spatiotemporal discretization. Essentially, it describes the physical process of "heat being carried by phonons and moving, colliding, and relaxing in the lattice" using the discretized Boltzmann transport equation. It is the core governing equation of the Lattice Boltzmann Method (LBM) for simulating heat conduction.

[0096] S304: Performing a propagation process on the lattice Boltzmann using the discrete phonon energy transport equation:

[0097]

[0098] .

[0099] S305: Based on the propulsion processing results, the phonon energy distribution functions in all discrete directions are summed to determine the macroscopic phonon energy:

[0100]

[0101] in, denoted by t, represents the macroscopic phonon energy of the field-effect transistor at position x at time t, and 8 represents the total number of discrete propagation directions.

[0102] Among them, the macroscopic phonon energy is obtained by summing the phonon energy densities in all directions, and is used to invert the temperature.

[0103] S306: The temperature distribution is determined by inverting the macroscopic phonon energy using the Debye model.

[0104]

[0105] Where T(x,t) represents the local temperature of the field-effect transistor at position x at time t, i.e., the temperature distribution result obtained by inversion. This represents the inversion function of the Debye model.

[0106] The Debye model points out that there is a definite relationship between energy and temperature, and the corresponding temperature can be obtained from energy through inversion.

[0107] S307: Set the thermal boundary conditions required for solving the lattice Boltzmann method.

[0108] Thermal boundary conditions are used to describe the thermal behavior of device boundaries, including isothermal boundaries, adiabatic boundaries, and temperature jump boundaries. They are necessary constraints for solving the temperature field.

[0109] S308: Under the constraint of thermal boundary conditions, repeat steps S304-S306 until the change in temperature field is less than the temperature threshold, and determine the internal transient temperature distribution.

[0110] It should be noted that those skilled in the art can set the temperature threshold according to actual needs, and this invention does not limit it.

[0111] It should be noted that by converting instantaneous power into volumetric heat source density and solving the phonon energy transport equation using the D2Q8 lattice Boltzmann method, this step can accurately characterize the unsteady-state heat conduction characteristics inside the field-effect transistor at the microscopic scale. At the same time, by obtaining a high-precision temperature field distribution through Debye model inversion, the calculation process has both a physical mechanism basis and numerical stability and high resolution, thereby significantly improving the accuracy of temperature field prediction and providing a reliable thermal field input for subsequent defect generation, spatial evolution, and seepage path determination.

[0112] In one possible implementation, the thermal boundary conditions in S307 include: isothermal boundary conditions, adiabatic boundary conditions, and temperature jump boundary conditions.

[0113] The isothermal boundary conditions are as follows:

[0114]

[0115] in, Let x represent the phonon energy density of the field-effect transistor to be predicted at time step 0, at position x on the isothermal boundary, along the i-th discrete direction. The equilibrium phonon energy distribution at position x of the isothermal boundary of the field-effect transistor at time step 0.

[0116] The specific adiabatic boundary conditions are as follows:

[0117]

[0118] in, Let represent the phonon energy density at position y of the field-effect transistor to be predicted at time step 0, along the i-th discrete direction. Let represent the phonon energy density at position y of the field-effect transistor to be predicted at time step 1, along the i-th discrete direction. Let represent the phonon energy density of the field-effect transistor to be predicted at position y on the isothermal boundary at time step n, along the i-th discrete direction. Let denot represent the phonon energy density at position y of the field-effect transistor to be predicted at time step n-1, along the i-th discrete direction.

[0119] The specific temperature jump boundary conditions are as follows:

[0120]

[0121] in, L represents the phonon energy density along the i-th discrete direction at the interface boundary node (x,m). c This represents the characteristic length of the field-effect transistor to be predicted. u represents the lattice space step size along the normal (y-direction). w Represents the wall phonon energy density. This represents the adjustable coefficient, and Kn represents the Knudsen number. This represents the phonon energy density at adjacent nodes m-1 within the interface along the i-th discrete direction.

[0122] The larger Kn is, the more pronounced the nonlocal effect becomes, thus making the temperature jump effect more significant.

[0123] It should be noted that by simultaneously introducing three types of thermal boundary conditions—isothermal, adiabatic, and temperature jump—it is possible to accurately model the real physical characteristics of field-effect transistors in different packaging, electrode, interface, and oxide layer regions. This allows the temperature field solved by the lattice Boltzmann method to satisfy both macroscopic heat conduction laws and reflect nonlocal thermal effects at micro- and nanoscale interfaces, thereby significantly improving the accuracy and physical consistency of transient temperature distribution and providing a more realistic thermal field basis for defect generation rate and subsequent reliability prediction.

[0124] S4: Based on the internal transient temperature distribution, the defect generation rate of the field-effect transistor to be predicted is calculated using the Arrhenius model.

[0125] The Arrhenius model is a physical model that describes the rate of thermal activation as a function of temperature. This model is suitable for describing thermally driven mechanisms such as defect formation, trap generation, and bond breaking in the oxide layer of MOSFETs.

[0126] Among them, the defect generation rate refers to the number of defects that may be generated inside the oxide layer per unit time under a given temperature condition. It is the basic input for subsequent defect spatial distribution modeling, statistical evolution analysis and seepage path formation judgment.

[0127] It should be noted that by utilizing the internal transient temperature distribution and combining it with the Arrhenius model to calculate the defect generation rate, the local temperature rise, hotspot effect, and thermal activation mechanism of micro-defects in the device can be directly correlated, achieving a precise mapping from the thermal field to defect dynamics. This method not only reflects the impact of temperature differences at different locations and times on the defect generation rate, but also effectively describes the significantly accelerated defect accumulation process in high-power-density MOSFETs as operating conditions change. This provides more realistic, physically consistent, and dynamically responsive foundational data for subsequent defect spatial distribution modeling and reliability prediction.

[0128] In one possible implementation, S4 specifically includes:

[0129] S401: Initialize the key parameters of the Arrhenius model based on the material properties and defect type of the field-effect transistor to be predicted. The key parameters include the activation energy and the pre-exponential factor.

[0130] Among them, material properties refer to the physical parameters of the oxide layer of the field-effect transistor and its surrounding materials, including bond energy, crystal structure, thermal stability, defect formation energy, etc. These properties determine the ease with which the material forms defects under thermal excitation.

[0131] Among them, defect type refers to the microstructural damage that may occur inside the oxide layer, such as oxygen vacancies, silicon-oxygen bond breakage, charge traps, interface states, etc. Different defect types correspond to different activation energies and generation mechanisms.

[0132] The activation energy is the minimum energy barrier that must be overcome for defect formation, determining the sensitivity of temperature to the defect formation rate. The pre-exponential factor represents the frequency of defect formation attempts and is the fundamental rate factor for thermal activation events.

[0133] S402: Based on the initialized Arrhenius model and combined with the gradient permeation mechanism, establish a spatially relevant defect generation rate model:

[0134]

[0135] in, Let A represent the spatially correlated defect generation rate at location (x,y) and temperature T, where A represents the pre-exponential factor of the Arrhenius model, exp() represents the exponential function, and E represents the spatially correlated defect generation rate at location (x,y) and temperature T. a k represents the activation energy. B Let represent the Boltzmann constant, and T(x,y) represent the instantaneous temperature of the field-effect transistor to be predicted at position (x,y).

[0136] Among them, the gradient penetration mechanism refers to the fact that the spatial distribution of defect generation is affected not only by local temperature, but also by the internal temperature gradient of the material or the energy penetration characteristics in the depth direction, which makes the defect generation rate spatially non-uniform.

[0137] Among them, the spatially correlated defect generation rate model is used to describe the defect generation rate at different spatial locations inside the device under different temperature conditions, and serves as a bridge between the local temperature field and the dynamics of microscopic defects.

[0138] S403: Based on the defect generation rate model, the active region of the field-effect transistor to be predicted is integrated by volume to determine the defect generation rate.

[0139] The active region refers to the core area in a MOSFET where current mainly flows and heat is concentrated. It typically includes the channel region, drift region, and related dielectric structures, and is the region where defects are most likely to form.

[0140] Specifically, the defect generation rate is the average defect generation rate. First, based on the physical mechanism that defect generation belongs to a thermal activation process, we introduce the Arrhenius expression. Subsequently, considering that defect generation mainly occurs in high-temperature regions, in order to obtain the overall average defect generation rate... Replace the temperature in the formula with the maximum temperature T in the temperature field. max Therefore, by substituting the exponential decay term consisting of the activation energy and the Boltzmann constant into the maximum temperature, the approximate average defect generation rate of the device under the current thermal state can be quickly calculated, i.e., the defect generation rate, thus realizing accelerated lifetime assessment based on the most unfavorable temperature.

[0141] It should be noted that by initializing the key parameters of the Arrhenius model based on material properties and defect types, and establishing a spatially relevant defect generation rate model in conjunction with the gradient permeation mechanism, this method can accurately reflect the defect formation behavior at different locations within the device under transient thermal excitation. Furthermore, by integrating the volume over the active region, the local thermal activation process can be transformed into the overall defect generation rate, achieving a quantitative mapping from microscopic defect dynamics to macroscopic reliability indicators. This method not only improves the accuracy and physical consistency of defect generation prediction but also effectively captures the impact of spatial non-uniformity on reliability evolution, providing high-quality input for subsequent defect spatial distribution modeling and permeation path determination.

[0142] S5: Combine the defect generation rate and the non-homogeneous Poisson process to determine the spatial defect distribution of the field-effect transistor to be predicted, where the spatial defect distribution includes the defect location and the number of defects.

[0143] The non-homogeneous Poisson process is a statistical model used to describe the non-uniform random distribution of events in space or time. In this scenario, it means that the probability of defect formation varies in different regions, changing with temperature, material properties, and depth location; therefore, the occurrence of defects exhibits significant spatial variability.

[0144] The spatial defect distribution represents the location and number of defects within the oxide layer or active region in three-dimensional space, and is a set of defect points obtained by sampling a non-homogeneous Poisson process. This distribution directly reflects the spatial density, aggregation trend, and random characteristics of defects.

[0145] It should be noted that by combining the defect generation rate calculated based on the temperature field with a non-homogeneous Poisson process, the defect generation mechanism can be elevated from a macroscopic average description to a stochastic process model with spatial resolution. This method can realistically reflect the non-uniform distribution characteristics of defects under different thermal stimuli at different locations, thereby generating a complete defect map containing the number of defects and their spatial coordinates. Compared with traditional methods that use uniform assumptions or empirical distributions, this step not only captures the randomness of defect generation driven by temperature, but also reveals the formation trends of defect clusters and potential penetration paths, providing physically meaningful and high-precision input data for subsequent fractal analysis and seepage determination.

[0146] In one possible implementation, S5 specifically includes:

[0147] S501: Construct a temperature-driven spatial defect intensity function based on the defect generation rate and gradient weight function:

[0148]

[0149]

[0150] in, Let represent the spatial defect intensity function of the field-effect transistor to be predicted at position (x,y). This represents the position-dependent gradient weight function, exp() represents the exponential function, and y represents the vertical coordinate. This indicates the gradient decay length.

[0151] The gradient weight function represents a weighting factor that indicates the decreasing energy or defect generation capacity of the oxide layer in the vertical direction with depth, and is used to describe the difference in defect generation intensity with depth.

[0152] Among them, the temperature-driven spatial defect intensity function is a "defect generation intensity field" obtained by combining the temperature-driven defect generation rate and the influence of the depth gradient, which is used to characterize the probability of defects appearing at different locations.

[0153] Specifically, the defect generation intensity at any location in the oxide layer is driven by the local temperature, which affects the generation rate. With gradient weight function that decays exponentially with depth A joint decision.

[0154] S502: Calculate the local expected number of defects in the oxide layer region using a non-homogeneous Poisson process based on the spatial defect intensity function.

[0155] Among them, the local expected defect number refers to the expected number of defects calculated according to the defect intensity function in a certain small spatial region, which is the target statistic when generating the point field.

[0156] S503: Combine the local expected defect number and generate a non-homogeneous Poisson point field using the envelope-sparse algorithm.

[0157] Among them, the envelope-sparse algorithm refers to the sampling method used to convert a homogeneous Poisson point field into a non-homogeneous Poisson point field.

[0158] Specifically, after obtaining the local expected number of defects in each sub-region within the oxide layer region, the upper bound of the defect intensity function for the entire region is first determined. Using this upper bound as the envelope intensity, a homogeneous Poisson point field is generated on the oxide layer volume, ensuring that the number of events in any sub-region follows a Poisson distribution. Subsequently, for each candidate defect location in this homogeneous Poisson point field, the retention probability is calculated based on the ratio between the actual defect intensity value and the envelope intensity at that location. A Bernoulli trial is performed independently for each point, retaining it with a preset probability and deleting it with a probability of 1 minus a preset probability. After this spatial sparsification process, the final point set precisely satisfies the non-homogeneous Poisson process distribution corresponding to the intensity function, which is the non-homogeneous Poisson point field. This field simultaneously reflects the spatial variability of the local expected defect number and the temperature-driven non-uniform generation characteristics.

[0159] S504: Map each Poisson point in a non-homogeneous Poisson point field to a defect entity.

[0160] Among them, the defect entity is a three-dimensional spherical defect structure obtained by assigning actual physical meaning to the points in the point field. Each defect has attributes such as location, size (radius), and quantity.

[0161] Specifically, after obtaining the non-homogeneous Poisson point field, each Poisson point in the field is physically interpreted as "a potential defect center location." Furthermore, a corresponding spherical defect region is constructed in three-dimensional space with this point as the center and a preset defect radius *r* as the scale. Through this mapping operation, the non-homogeneous Poisson point field, which was originally just an abstract "point," is concretized into a set of three-dimensional defect entities. Each entity has both a defined geometric volume and precise spatial location attributes. Simultaneously, the number of Poisson points within the finite region of the entire oxide layer is counted to obtain the total number of defects at the current time step. The correspondence between "defect center coordinates and defect geometric entities" serves as a complete description of the spatial defect distribution. This spatial defect distribution not only provides the precise location of each defect within the oxide layer but also explicitly characterizes the size and quantity of defects, thus providing a complete three-dimensional input data foundation for subsequent cluster structure identification, fractal feature extraction, and spherical base seepage path determination.

[0162] S505: Statistically analyze defective entities to determine the spatial defect distribution of the field-effect transistor to be predicted.

[0163] It should be noted that by combining the temperature-driven defect generation rate with the depth gradient weighting function and constructing a spatial defect point field using a non-homogeneous Poisson process and an envelope-sparse algorithm, this step can realistically reproduce the non-uniform, random, and temperature-sensitive generation mechanism of defects within the oxide layer. Furthermore, mapping the abstract point field to defect entities with actual geometric dimensions gives the defect distribution not only statistical significance but also spatial structural significance, providing physically reliable three-dimensional input for subsequent defect cluster identification, fractal dimension extraction, and seepage path determination. Compared to traditional uniform distribution or empirical assumption methods, this scheme significantly improves the realism, resolution, and interpretability of defect spatial modeling, and is a key step in achieving microscopic reliability prediction.

[0164] S6: Extract the fractal structure features of the spatial defect distribution, and calculate the fractal dimension of the field-effect transistor to be predicted based on the fractal structure features.

[0165] Fractal structure features are used to describe the geometric properties of defect sets in space, including self-similarity, clustering patterns, and growth patterns. Typical features include multi-scale counting results, power-law relation parameters, and cluster density, which are important indicators for measuring defect clustering behavior.

[0166] Among them, fractal dimension is used as an index to quantify the filling ability of spatial defect clusters, and is used to describe whether the defect structure is sparse, dendritic or dense.

[0167] It should be noted that by extracting fractal structural features from the spatial defect distribution and calculating the fractal dimension, the evolutionary behavior of defect clustering can be characterized from both geometric and statistical dimensions. This elevates defects from simple random point sets to interpretable models with structural properties. The fractal dimension, as a key indicator revealing the complexity and spatial filling capacity of defect clusters, directly reflects the trend of defects evolving from scattered distribution to connected clustering, and is an important precursor to the formation of seepage paths. Compared to traditional methods that only count the number of defects, this step can capture the spatial correlation and clustering patterns between defects, improving the sensitivity and prediction accuracy of breakdown risk, and providing a more in-depth and physically consistent structural basis for subsequent seepage determination.

[0168] In one possible implementation, S6 specifically includes:

[0169] S601: Based on the spatial defect distribution, construct a set of defect cluster structures.

[0170] The defect cluster structure set is a collection of multiple defect clusters obtained by classifying defect entities in the spatial defect distribution according to connectivity rules (such as the distance between defects ≤ 2r). Each cluster represents a group of defects that are close to each other and may co-evolve.

[0171] S602: Select the largest defect cluster in the defect cluster structure set as the representative defect cluster.

[0172] S603: Perform multi-scale counting of the number of defects within a radius sphere based on representative defect clusters:

[0173]

[0174] in, Indicates a radius of r m The number of defects contained within the sphere, where j represents the defect index, and C... max x represents the representative defect cluster, i.e., the largest defect cluster. j Let x represent the spatial coordinates of the j-th defect. c r represents the center point (usually the centroid) of a representative defect cluster. m This represents the radius of the sphere at the m-th scale. The spatial coordinates x of the j-th defect are represented by [x]. j to cluster center x c Euclidean distance, The cardinality (number of elements) of a set. Condition qualifiers for sets.

[0175] Specifically, the radius sphere is defined by the center point x of the representative defect cluster. c Centered on the sphere, with scale r mA three-dimensional spherical region is constructed using the radius of the sphere. The radius of the sphere is used to characterize the filling ability of the defect cluster at different spatial scales.

[0176] S604: Based on multi-scale counting results, and according to the power-law characteristics of the fractal structure of the field-effect transistor to be predicted, an approximate power-law relationship is constructed for the number of defects as a function of the counting radius:

[0177]

[0178] in, Let represent the expected number of defects contained in a sphere of radius r, i.e., the desired value; and let k0 represent the scaling constant of the fractal cluster size, i.e., the baseline size of the defect cluster at the smallest reference scale. The power-law scaling factor represents the spatial expansion behavior of defect clusters. Fractal dimension (a metric for measuring the ability of a cluster of defects to fill space) represents the fractal dimension. The larger the cluster, the denser it is, and the closer it is to a three-dimensional uniform filling. The smaller the cluster, the sparser and more dendritic the structure. d represents the Euclidean dimension of the space (d=3 in this scenario).

[0179] Specifically, E[N(r)] is obtained by statistical averaging or smoothing the multi-scale counting results.

[0180] S605: Map the approximate power-law relationship and multi-scale counting results to a logarithmic coordinate system to construct a linear relationship:

[0181]

[0182] Where ln represents the logarithmic function, This represents a sphere centered at the center of a representative defect cluster, with a radius of... The number of defects expected to be included within the sphere.

[0183] Specifically, by mapping the power-law relationship between the number of defects and the radius to a logarithmic coordinate system, we can obtain a law derived from... and The linear relationship formed by the composition. Among them, the fractal dimension... The slope of the corresponding line and the proportionality constant k0 correspond to the intercept of the corresponding line, thus the fractal structure features of the defect cluster can be extracted through linear fitting.

[0184] S606: By using the least squares algorithm to fit straight lines to the data points in the linear relationship, the fractal structure characteristics of the spatial defect distribution are obtained.

[0185]

[0186]

[0187]

[0188] Among them, lnr m Let represent the natural logarithm of the counting radius at the m-th scale. This represents the average of the logarithmic values ​​of all radii.

[0189] Specifically, by performing a logarithmic linear transformation on the power-law relationship between radius and number of defects, and using the least squares method to obtain the slope and intercept, the fractal dimension and proportionality constant of the spatial defect distribution can be obtained respectively. The fractal dimension reflects the self-similar filling ability of the defect cluster in three-dimensional space, and the proportionality constant is used to characterize the scale characteristics of the defect structure at the initial scale.

[0190] S607: Based on the fractal structure characteristics, calculate the fractal dimension related to the oxide layer thickness of the field-effect transistor to be predicted:

[0191]

[0192] in, Indicates the relationship with oxide layer thickness The relevant fractal dimension, d f ( ) represents the functional relationship between fractal dimension and oxide layer thickness.

[0193] Among them, fractal dimension is a core indicator that characterizes the spatial self-similarity and structural complexity of defect clusters. The larger the value, the denser the defects tend to be, the stronger the connectivity, and the higher the risk of penetration.

[0194] Specifically, by mapping the extracted fractal structure features to an oxide layer thickness-related model, the fractal dimension corresponding to the oxide layer thickness is obtained.

[0195] It should be noted that by constructing a set of defect clusters from the spatial defect distribution and selecting the largest defect cluster for multi-scale counting, the complex spatial structure of defects can be transformed into a quantifiable fractal dimension through a power-law model and log-linear fitting, clearly revealing the degree of cluster aggregation, self-similarity, and expansion trend of defect clusters. This method can not only capture the key geometric features of defect evolution from random distribution to connected structures, but also establish a correlation between fractal dimension and oxide layer thickness, making reliability evaluation more consistent with actual device size and structural characteristics. Compared with traditional simple defect count statistics or uniform distribution assumptions, this step significantly improves the accuracy of judging defect structural complexity, connectivity, and potential seepage risk, providing a more predictive structural basis for subsequent determination of conductive path formation.

[0196] S7: Based on the fractal dimension and the preset critical defect density, determine whether the field-effect transistor to be predicted has formed a conductive path from top to bottom using the spherical base permeation model; if so, determine that the field-effect transistor to be predicted has experienced oxide layer breakdown and proceed to step S8; otherwise, use the spatial defect distribution as historical data and return to step S1 to continue monitoring.

[0197] Critical defect density refers to the minimum defect volume fraction required for a material to undergo through-hole breakdown or percolation. This threshold is determined based on material properties, oxide layer thickness, and experimental data, and is a crucial criterion for determining whether a conductive path has formed.

[0198] Among them, the spherical-based seepage model is a seepage model used to determine whether a through-channel has formed in three-dimensional space. It treats each defect as a sphere, determines whether the spheres are spatially connected, and further determines whether the connected clusters span the entire oxide layer. This model is particularly suitable for characterizing the formation of electrical breakdown paths caused by random defect aggregation.

[0199] It should be noted that those skilled in the art can set the critical defect density according to actual needs, and this invention does not limit it.

[0200] It should be noted that by utilizing fractal dimension and critical defect density, and employing a spherical-based permeation model to assess defect connectivity, a potential breakdown path from top to bottom can be accurately identified from both geometric and statistical physics perspectives. This step not only avoids the limitations of simply judging breakdown risk based on the number of defects but also significantly improves the sensitivity and accuracy of determining the formation of conductive chains. Simultaneously, the introduction of historical defect data enables dynamic monitoring, continuously tracking the defect evolution process and providing early warnings before breakdown occurs, thus enhancing the real-time performance and predictive depth of the entire reliability prediction system.

[0201] In one possible implementation, S7 specifically includes:

[0202] S701: Calculate the average defect density of the current space based on the volume region of the oxide layer and the spatial defect distribution.

[0203] Among them, the oxide layer volume region refers to the three-dimensional space actually occupied by the MOSFET gate oxide layer or gate dielectric, which is the main area for defect generation, diffusion and seepage path formation.

[0204] Specifically, the average defect density is calculated as the ratio of the total number of defects within the oxide layer volume to the oxide layer volume area.

[0205] S702: Based on the fractal dimension, using the spherical-based permeation model, all defects are divided into a predetermined number of connected clusters, where the connected clusters are candidate conductive clusters.

[0206] Among them, candidate conductive clusters refer to defect clusters obtained through connectivity analysis that have the potential to form conductive channels in three-dimensional space, and are the direct objects for determining seepage paths.

[0207] Specifically, any two defective spheres are considered connected when the distance between them is less than or equal to twice the defect radius.

[0208] It should be noted that those skilled in the art can set the preset number of items according to actual needs, and this invention does not limit this.

[0209] S703: Based on each candidate conductive cluster, determine whether a through-flow path exists from top to bottom. If yes, proceed to step S704. Otherwise, return to step S1 to continue monitoring.

[0210] Among them, the through-flow path is a continuous path that spans the entire thickness of the oxide layer, formed by interconnected defects. Once formed, it indicates that the gate oxide layer has broken down or is about to break down.

[0211] Specifically, it is determined whether any connected cluster contains both a defect that contacts the top of the oxide layer and a defect that contacts the bottom of the oxide layer; if a connected cluster that satisfies the above conditions exists, it is determined that a through-flow path has been formed in the oxide layer.

[0212] S704: Combining critical defect density, the conductive path of the field-effect transistor to be predicted is determined through a dual-criteria decision rule.

[0213] Among them, the dual-criteria decision rule refers to using two conditions—whether a seepage path has formed and whether the defect density exceeds a critical value—to jointly determine the risk of electronic conduction, thereby improving the reliability and robustness of the determination.

[0214] In one possible implementation, the dual-criteria decision rule specifically includes:

[0215] If the defect density is greater than the critical defect density and the oxide layer has a through-flow path from top to bottom, or if the defect density is equal to the critical defect density and the oxide layer has a through-flow path from top to bottom, the oxide layer breakdown of the field-effect transistor to be predicted is determined.

[0216] If the defect density is less than the critical defect density or there is no through-flow path from top to bottom, it is determined that the oxide layer of the field-effect transistor to be predicted has not broken down.

[0217] S705: If the field-effect transistor to be predicted forms a conductive path from top to bottom, proceed to step S8; if the field-effect transistor to be predicted does not form a conductive path from top to bottom, return to step S1 to continue monitoring.

[0218] It should be noted that by calculating the average defect density, constructing connected clusters, and determining the existence of penetration paths based on a spherical flow model, a comprehensive and multi-faceted assessment of oxide layer breakdown risk can be achieved by combining defect quantity, defect structural characteristics, and spatial connectivity. Simultaneously, a dual-criteria decision mechanism based on fractal dimension and critical defect density is introduced, ensuring that the judgment process possesses both statistical physical accuracy and structural geometric sensitivity, significantly improving the early warning capability for conductive path formation. This step also possesses real-time capability, dynamically providing breakdown trend judgments during the continuous evolution of defects, offering powerful predictive capabilities and practical engineering value for reliability monitoring.

[0219] S8: Output the comprehensive reliability prediction result of the field-effect transistor to be predicted.

[0220] Oxide layer breakdown refers to the failure phenomenon in which internal defects in the gate oxide layer of a MOSFET gradually accumulate under long-term electrical and thermal stress, eventually forming a conductive channel from the top electrode to the bottom electrode, causing the dielectric to lose its insulating ability. Breakdown can be divided into soft breakdown and hard breakdown. This step mainly focuses on through-through hard breakdown, which leads to device failure.

[0221] It should be noted that by performing the S8 step based on prior thermal field calculations, defect generation models, defect spatial distribution, fractal structure analysis, and percolation path determination, accurate determination of oxide layer breakdown can be achieved at the physical mechanism level, and comprehensive reliability prediction results with engineering value can be output. S8 not only integrates multi-source model outputs into diagnostic information that can be directly used for device health management, but also provides future failure trend predictions and remaining lifetime estimates, significantly improving the safety and predictability of system-level operation. Compared to traditional data-driven methods that rely on empirical rules or are based solely on average temperature, this step has higher accuracy, interpretability, and practicality, and can effectively support the development of preventative maintenance and reliable operation strategies for high-power electronic devices.

[0222] In one possible implementation, the comprehensive reliability prediction results include: the health status of the field-effect transistor to be predicted, the failure probability curve, the remaining service life, and maintenance recommendations.

[0223] In this embodiment of the invention, by introducing the unsteady-state thermal effect driven by instantaneous power into the reliability prediction process, and combining it with lattice Boltzmann temperature field calculation, Arrhenius defect generation model, non-homogeneous Poisson point field, fractal structure analysis and spherical basis percolation criterion, the complete evolution process of defects from generation and aggregation to the formation of a conductive path can be characterized from the microscopic mechanism level. This significantly improves the failure prediction accuracy and lead time of field-effect transistors under dynamic operating conditions, not only improving the reliability of oxide layer breakdown determination, but also enabling accurate assessment of the remaining life of the device, effectively supporting the safe operation and preventive maintenance of high-power electronic systems.

[0224] Reference manual attached Figure 2 The diagram shows a schematic of the structure of a field-effect transistor reliability prediction system based on instantaneous power provided by the present invention.

[0225] The present invention also provides a field-effect transistor reliability prediction system 20 based on instantaneous power, applied to the above-mentioned field-effect transistor reliability prediction method based on instantaneous power, comprising:

[0226] Processor 201.

[0227] The memory 202 stores computer-readable instructions. When the computer-readable instructions are executed by the processor 201, they implement the MOSFET reliability prediction method based on instantaneous power as described in the method embodiment.

[0228] The instantaneous power-based MOSFET reliability prediction system 20 provided by this invention can execute the above-described instantaneous power-based MOSFET reliability prediction method and achieve the same or similar technical effects. To avoid repetition, this invention will not elaborate further.

[0229] It should be understood that the processor in the embodiments of the present invention can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0230] It should also be understood that the memory in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0231] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0232] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0233] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0234] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0235] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0236] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0237] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0238] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0239] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0240] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0241] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the field-effect transistor reliability prediction method based on instantaneous power as described in the method embodiment.

[0242] The present invention provides a computer-readable storage medium that can implement the steps and effects of the field-effect transistor reliability prediction method based on instantaneous power in the above-described method embodiments. To avoid repetition, the present invention will not elaborate further.

[0243] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0244] The following points need to be explained:

[0245] (1) The accompanying drawings of the embodiments of the present invention only involve the structures involved in the embodiments of the present invention. Other structures can refer to the general design.

[0246] (2) For clarity, the thickness of layers or regions is enlarged or reduced in the drawings used to describe embodiments of the invention, i.e., these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being “above” or “below” another element, the element may be “directly” located “above” or “below” the other element or there may be intermediate elements.

[0247] (3) Where there is no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0248] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the reliability of a field-effect transistor based on instantaneous power, characterized in that, include: S1: Acquire the instantaneous voltage and instantaneous current of the field-effect transistor to be predicted through a sensor; S2: Calculate the instantaneous power based on the instantaneous voltage and the instantaneous current; S3: Based on the instantaneous power, calculate the internal transient temperature distribution of the field-effect transistor to be predicted using the lattice Boltzmann method; S4: Based on the internal transient temperature distribution, calculate the defect generation rate of the field-effect transistor to be predicted using the Arrhenius model; S5: Combine the defect generation rate and the non-homogeneous Poisson process to determine the spatial defect distribution of the field-effect transistor to be predicted, wherein the spatial defect distribution includes the defect location and the number of defects; S6: Extract the fractal structure features of the spatial defect distribution, and calculate the fractal dimension of the field-effect transistor to be predicted based on the fractal structure features; S7: Based on the fractal dimension and the preset critical defect density, determine whether the field-effect transistor to be predicted has formed a conductive path from top to bottom using the spherical base permeation model; if so, determine that the field-effect transistor to be predicted has experienced oxide layer breakdown and proceed to step S8; otherwise, use the spatial defect distribution as historical data and return to step S1 to continue monitoring. S8: Output the comprehensive reliability prediction result of the field-effect transistor to be predicted.

2. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, S3 specifically includes: S301: Calculate the equivalent volumetric heat source density based on the instantaneous power and the effective heating volume of the field-effect transistor to be predicted; S302: Construct a D2Q8 lattice model based on the actual two-dimensional geometry of the field-effect transistor to be predicted; S303: Determine the discrete phonon energy transport equation based on the D2Q8 lattice model and the equivalent volumetric heat source density; S304: Perform a propulsion process on the lattice Boltzmann using the discrete phonon energy transport equation; S305: Based on the propulsion processing results, sum the phonon energy distribution functions in all discrete directions to determine the macroscopic phonon energy; S306: The temperature distribution is determined by inverting the macroscopic phonon energy using the Debye model; S307: Set the thermal boundary conditions required for the lattice Boltzmann method solution; S308: Under the constraints of the thermal boundary conditions, repeat steps S304-S306 until the change in the temperature field is less than the temperature threshold, and determine the internal transient temperature distribution.

3. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 2, characterized in that, The thermal boundary conditions in S307 include: isothermal boundary conditions, adiabatic boundary conditions, and temperature jump boundary conditions.

4. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, S4 specifically includes: S401: Based on the material properties and defect type of the field-effect transistor to be predicted, initialize the key parameters of the Arrhenius model, wherein the key parameters include: activation energy and pre-exponential factor; S402: Based on the initialized Arrhenius model and combined with the gradient penetration mechanism, establish a spatially relevant defect generation rate model; S403: Based on the defect generation rate model, the active region of the field-effect transistor to be predicted is integrated by volume to determine the defect generation rate.

5. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, S5 specifically includes: S501: Construct a temperature-driven spatial defect intensity function based on the defect generation rate and gradient weight function; S502: Calculate the local expected number of defects in the oxide layer region using the non-homogeneous Poisson process based on the spatial defect intensity function. S503: Combining the aforementioned local expected defect number, a non-homogeneous Poisson point field is generated using the envelope-sparse algorithm; S504: Map each Poisson point in the non-homogeneous Poisson point field to a defect entity; S505: Statistically analyze the defective entities to determine the spatial defect distribution of the field-effect transistor to be predicted.

6. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, S6 specifically includes: S601: Based on the spatial defect distribution, construct a set of defect cluster structures; S602: Select the largest defect cluster in the defect cluster structure set as the representative defect cluster; S603: Based on the representative defect clusters, perform multi-scale counting of the number of defects within the radius sphere; S604: Based on the multi-scale counting results, and according to the power-law characteristics of the fractal structure of the field-effect transistor to be predicted, an approximate power-law relationship is constructed for the number of defects as a function of the counting radius. S605: Map the approximate power-law relationship and the multi-scale counting results to a logarithmic coordinate system to construct a linear relationship; S606: By using the least squares algorithm, straight lines are fitted to the data points in the linear relationship to obtain the fractal structure characteristics of the spatial defect distribution; S607: Based on the fractal structure characteristics, calculate the fractal dimension related to the oxide layer thickness of the field-effect transistor to be predicted.

7. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, Specifically, S7 includes: S701: Calculate the average defect density of the current space based on the oxide layer volume region and the spatial defect distribution; S702: Based on the fractal dimension, using the spherical-based permeation model, all defects are divided into a predetermined number of connected clusters, wherein the connected clusters are candidate conductive clusters; S703: Based on each of the candidate conductive clusters, determine whether there is a through-flow path from top to bottom; if yes, proceed to step S704; otherwise, return to step S1 to continue monitoring. S704: Based on the critical defect density, the conductive path of the field-effect transistor to be predicted is determined by a dual-criteria decision rule; S705: If the field-effect transistor to be predicted forms a conductive path from top to bottom, proceed to step S8; if the field-effect transistor to be predicted does not form a conductive path from top to bottom, return to step S1 to continue monitoring.

8. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 7, characterized in that, The dual-criteria decision rule specifically includes: If the average defect density is greater than the critical defect density and the oxide layer has a through-flow path from top to bottom, or if the average defect density is equal to the critical defect density and the oxide layer has a through-flow path from top to bottom, the predicted field-effect transistor is determined to have oxide layer breakdown. If the average defect density is less than the critical defect density or there is no through-flow path from top to bottom, it is determined that the field-effect transistor to be predicted has not experienced oxide layer breakdown.

9. The method for predicting the reliability of a field-effect transistor based on instantaneous power according to claim 1, characterized in that, The comprehensive reliability prediction results include: the health status, failure probability curve, remaining service life, and maintenance recommendations of the field-effect transistor to be predicted.

10. A field-effect transistor reliability prediction system based on instantaneous power, characterized in that, include: processor; A memory storing computer-readable instructions, which, when executed by the processor, implement the MOSFET reliability prediction method based on instantaneous power as described in any one of claims 1 to 9.

Images