Bipolar transistor reliability analysis method and system, electronic device

Abstract

The application provides a bipolar transistor reliability analysis method and system and electronic equipment, and belongs to the field of semiconductor device reliability analysis. The method comprises the following steps: based on a boundary model of a bipolar transistor device, performing initial mesh division on the boundary model; performing mesh encryption on the junction surface of the emitter and the base of the bipolar transistor device and the junction surface of the base and the collector, and performing mesh reconstruction; defining a simulation physical model and a defect evolution model, introducing related terms of defect concentration and carrier recombination rate through defects into the control equation of the simulation physical model, and coupling the defect reaction rate of the defect evolution model with the current intensity of the device; determining an application area of the defect evolution model, and assigning the defect evolution model to the application area; and performing analysis based on the simulation physical model and the defect evolution model to obtain reliability degradation data. The application can restore the reliability state of the bipolar transistor device in the actual application scenario, and perform efficient and accurate reliability analysis.

Description

Technical Field

[0001] This invention relates to the field of semiconductor device reliability analysis, and more specifically to a bipolar transistor reliability analysis method and system, and electronic equipment. Background Technology

[0002] Modern integrated circuit systems consist of hundreds of millions of transistors, whose arrangements and combinations constitute logic, arithmetic, amplification, and other functions, enabling complex transformations of electrical signals. The operating state of transistors determines the stability of the circuit system, and the reliability of transistor devices is a key focus for integrated circuit researchers. Bipolar junction transistors (BJTs) are formed entirely by ion implantation of substrate materials in layers, belonging to homogeneous devices. Their reliability depends on the impact of the active current at the PN junction on the lattice atoms. When a device fails, the BJT material lattice is damaged, defects accumulate in large numbers, and charge carriers are severely annihilated, making it difficult to achieve current conduction and regulation functions.

[0003] Existing research lacks reliability analysis models specifically for BJT devices. Current techniques typically rely on modifying key parameters (semiconductor ideality factor, recombination rate, etc.) in compact equations such as SPICE to study the impact of device degradation on integrated circuit performance. However, this process requires researchers to update model information in real time, limiting its predictive ability for device performance. Therefore, there is an urgent need to develop an efficient and accurate reliability analysis method for BJT devices. Summary of the Invention

[0004] To address one of the shortcomings of existing technologies, this invention provides a bipolar transistor reliability analysis method, system, and electronic device to achieve efficient and accurate reliability analysis of bipolar transistor devices.

[0005] The first aspect of this invention provides a method for reliability analysis of bipolar transistors, comprising: Based on the boundary model of a bipolar transistor device, the regions of emitter, base, and collector are divided according to actual process information, and the boundary model is initially meshed. The mesh of the emitter-base interface and the base-collector interface of the bipolar transistor device is refined and then rebuilt. Based on the boundary model after mesh reconstruction, a simulation physical model and a defect evolution model for bipolar transistor devices are defined. The control equations of the simulation physical model introduce terms related to defect concentration and carrier recombination rate through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. Determine the application region of the defect evolution model for the bipolar transistor device, and assign the defect evolution model to the application region; The reliability of bipolar transistors is analyzed based on the simulation physical model and defect evolution model to obtain device reliability degradation data.

[0006] In this embodiment of the invention, the initial mesh generation of the boundary model includes: Initial mesh generation is performed for different material regions in the boundary model. High-density mesh generation is performed for regions corresponding to materials that participate in the conduction process, while sparse mesh generation is performed for regions corresponding to materials that do not participate in the conduction process.

[0007] In this embodiment of the invention, the bipolar transistor reliability analysis method further includes: After initial meshing of the boundary model, ion doping is performed, with the doping concentration varying from the device boundary to the interior in a Gaussian gradient, forming the emitter region, base region, and collector region of the concentration gradient.

[0008] In this embodiment of the invention, the emitter region and the collector region are N-type doped, the base region is P-type doped, and the N-type doping concentration in the emitter region is higher than that in the collector region.

[0009] In this embodiment of the invention, the mesh refinement of the interface between the emitter and base, and the interface between the base and collector of the bipolar transistor device, includes: In the process of mesh refinement of the interface between the emitter and base, and the interface between the base and collector of a bipolar transistor device, high-concentration gradient regions are determined by dynamically adjusting the mesh topology and node positions, and only the high-concentration gradient regions are refined.

[0010] In this embodiment of the invention, determining the high concentration gradient region by dynamically adjusting the grid topology and node positions includes: dynamically splitting or merging grid cells according to a concentration gradient threshold to determine the high concentration gradient region, and moving the position of the grid node to make the grid node gather towards the high concentration gradient region.

[0011] In this embodiment of the invention, the step of dynamically splitting or merging grid cells according to a concentration gradient threshold includes: dynamically splitting grid cells when the concentration gradient density of the grid is greater than a first concentration gradient threshold and less than a second concentration gradient threshold.

[0012] In this embodiment of the invention, the step of moving the position of the grid node to gather the grid node towards the high concentration gradient region includes: when the concentration gradient density of the grid is greater than the second concentration gradient threshold, gradually shifting and adjusting the grid node to move it closer to the high concentration gradient region until the concentration gradient density of the grid is less than or equal to the first concentration gradient threshold.

[0013] In this embodiment of the invention, the concentration gradient density is a logarithmic value, and both the first concentration gradient threshold and the second concentration gradient threshold are logarithmic values.

[0014] In this embodiment of the invention, the concentration gradient density of doped regions with different polarities of ions takes the opposite sign, and the concentration gradient density of transpolar regions takes the absolute value.

[0015] In this embodiment of the invention, the governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and the carrier lifetime equation introduce terms related to defect concentration, and the continuity equation and the defect recombination equation introduce terms related to the recombination rate of carriers through defects.

[0016] In this embodiment of the invention, the expression for the Poisson equation is: ; in, For the Laplace operator, For electric potential, For elementary charge, Where is the dielectric constant. Hole concentration, For electron concentration, Donor concentration, Hole concentration This represents the defect concentration.

[0017] In this embodiment of the invention, the expression for the continuity equation is: ; ; in, For time, This represents the rate of change of electron concentration over time. This represents the rate of change of hole concentration over time. For elementary charge, For gradient operators, It is an electron current. Hole current, For electron production rate, Hole generation rate , The intrinsic recombination rate, The recombination rate of charge carriers through defects.

[0018] In this embodiment of the invention, the expression for the defect composite equation is: ; in, This represents the recombination rate of charge carriers through defects. For electron concentration, Hole concentration Intrinsic carrier concentration, For electronic lifetime, For hole lifetime, For trap energy level, K Boltzmann's constant, T is the lattice temperature.

[0019] In this embodiment of the invention, the expression for the carrier lifetime equation is: ; ; in, For electronic lifetime, For hole lifetime, For electron capture cross section, For hole capture cross section, For carrier velocity, This represents the defect concentration.

[0020] In this embodiment of the invention, the expression for the defect evolution model is: ; ; in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, For device current, and This is a constant in the degenerate equation.

[0021] In this embodiment of the invention, determining the application region of the defect evolution model for a bipolar transistor device includes: defining the depletion region of the device based on doping concentration and grid density, and defining the application region of the defect evolution model within the depletion region.

[0022] In this embodiment of the invention, the depletion region of the device is defined based on doping concentration and grid density, including: The reconstructed grid is sorted by density, and high-density grid regions are determined based on the density sort. The intersection region of the local minimum absolute value region of doping concentration and the high grid density region above the grid density threshold is defined as the depletion region of the bipolar transistor device.

[0023] In this embodiment of the invention, determining high grid density regions based on density sorting includes: calculating the reciprocal of the size of each grid cell as a density index, wherein the reciprocal of the surface base is taken for two-dimensional grids and the reciprocal of the volume is taken for three-dimensional grids; arranging the density indices from largest to smallest, and determining the grid cells with the highest sorting as high grid density regions.

[0024] In this embodiment of the invention, the depletion region of the bipolar transistor device is the depletion region of the emitter junction and the collector junction; the emitter junction is the depletion region corresponding to the boundary between the emitter and the base, and the collector junction is the depletion region corresponding to the boundary between the base and the collector.

[0025] In this embodiment of the invention, assigning the defect evolution model to the applied region includes: assigning the defect evolution model to the depletion regions of the emitter junction and the collector junction, and setting different initial reaction rates for the emitter junction and the collector junction respectively.

[0026] In this embodiment of the invention, the reliability of the bipolar transistor is analyzed based on the simulation physical model and the defect evolution model, including: Define the parameters of the simulation physical model and the defect evolution model, and perform transient solutions; Define the simulation analysis duration and obtain the reliability degradation simulation curve based on the solution results; The reliability degradation simulation curves were analyzed to obtain reliability degradation data for bipolar transistors.

[0027] A second aspect of the present invention provides a bipolar transistor reliability analysis system, comprising: Mesh generation unit is used to divide the emitter, base, and collector regions based on the boundary model of a bipolar transistor device according to actual process information, and to perform initial mesh generation on the boundary model; The mesh reconstruction unit is used to refine the mesh at the interface between the emitter and base, and the interface between the base and collector of a bipolar transistor device, and to reconstruct the mesh. The simulation model construction unit is used to define the simulation physical model and defect evolution model of the bipolar transistor device based on the boundary model after mesh reconstruction. The control equation of the simulation physical model introduces terms related to defect concentration and carrier recombination rate through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. The reliability analysis unit is used to determine the application area of ​​the defect evolution model of the bipolar transistor device, assign the defect evolution model to the application area, analyze the reliability of the bipolar transistor based on the simulation physical model and the defect evolution model, and obtain device reliability degradation data.

[0028] In this embodiment of the invention, during the process of refining the mesh at the interface between the emitter and base and the interface between the base and collector of the bipolar transistor device, the mesh reconstruction unit determines the high-concentration gradient region by dynamically adjusting the mesh topology and node positions, and only refines the high-concentration gradient region.

[0029] In this embodiment of the invention, high concentration gradient regions are determined by dynamically adjusting the grid topology and node positions, including: dynamically splitting or merging grid cells according to a concentration gradient threshold to determine high concentration gradient regions, and moving the positions of grid nodes to make the grid nodes cluster towards the high concentration gradient regions.

[0030] In this embodiment of the invention, the governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and the carrier lifetime equation introduce terms related to defect concentration, and the continuity equation and the defect recombination equation introduce terms related to the recombination rate of carriers through defects.

[0031] In this embodiment of the invention, the expression for the defect evolution model is: ; ; in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, For device current, and This is a constant in the degenerate equation.

[0032] In this embodiment of the invention, the reliability analysis unit is specifically used for: The reconstructed grid is sorted by density, and high-density grid regions are determined based on the density sort. The intersection region of the local minimum absolute value region of doping concentration and the high grid density region above the grid density threshold is defined as the depletion region of the bipolar transistor device, and the depletion region is used as the application region of the defect evolution model.

[0033] In this embodiment of the invention, the reliability analysis unit is specifically used for: Define the parameters of the simulation physical model and the defect evolution model, and perform transient solutions; Define the simulation analysis duration and obtain the reliability degradation simulation curve based on the solution results; The reliability degradation simulation curves were analyzed to obtain reliability degradation data for bipolar transistors.

[0034] A third aspect of the present invention provides an electronic device, comprising: Memory, which stores computer programs; A processor is used to execute the computer program to implement the bipolar transistor reliability analysis method described above.

[0035] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the above-described bipolar transistor reliability analysis method.

[0036] The above technical solution involves initial mesh generation for the boundary model of a bipolar transistor device, followed by refined mesh reconstruction for key regions such as the emitter-base interface and the base-collector interface. Terms related to defect concentration and carrier recombination rate via defects are introduced into the control equations of the simulation physical model. Furthermore, a correction factor based on device current intensity is introduced into the defect evolution model to correct the defect response rate, coupling the defect response rate with the device current. Based on the aforementioned simulation physical model and defect evolution model, realistic electro-thermal coupling degradation simulation can be achieved, obtaining accurate reliability degradation data for bipolar transistor devices. This invention can recreate the reliable state of bipolar transistor devices in real-world application scenarios, enabling efficient and accurate reliability analysis.

[0037] Other features and advantages of the technical solution of the present invention will be described in detail in the following detailed embodiments section. Attached Figure Description

[0038] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the bipolar junction transistor (BJT) reliability analysis method provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of the simulation process model of an NPN type BJT device in one example of the present invention; Figure 3 This is a detailed mesh diagram of the simulation process model of an NPN type BJT device in one example of the present invention. Figure 4 This is a partial schematic diagram of the fine mesh of the simulation process model of the NPN type BJT device in an example of the present invention. Figure 5 This is a reliability simulation data curve of an NPN type BJT device in an example of the present invention; Figure 6 This is a block diagram of the bipolar transistor reliability analysis system provided in an embodiment of the present invention. Detailed Implementation

[0039] To make the technical solutions and advantages of the embodiments of the present invention clearer, the exemplary embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0040] Figure 1 This is a flowchart of the bipolar transistor reliability analysis method provided in an embodiment of the present invention. Figure 1 As shown, the bipolar transistor reliability analysis method provided in this embodiment includes the following steps: S100, based on the boundary model of a bipolar transistor device, divides the regions of emitter, base and collector according to actual process information, and performs initial mesh division on the boundary model; S200 refines the mesh at the interface between the emitter and base, and the interface between the base and collector of a bipolar transistor device, and then rebuilds the fine mesh. S300 defines a simulation physical model and a defect evolution model for bipolar transistor devices based on the boundary model reconstructed by a refined mesh. The control equations of the simulation physical model introduce terms related to defect concentration and recombination rate of carriers through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. S400, Determine the application region of the defect evolution model for the bipolar transistor device, and assign the defect evolution model to the application region; S500, based on the simulation physical model and defect evolution model, analyzes the reliability of the bipolar transistor and obtains device reliability degradation data.

[0041] The fabrication model of a bipolar junction transistor (BJT) device comprises two parts: a boundary model and a doping model. The doping model includes the emitter region, base region, and collector region. The emitter and base regions are homogeneous structures, forming a PN junction through different types of ion doping. The collector region forms a PN junction with the base region via the substrate. The boundary model defines the overall simulation range of the device.

[0042] In step S100 above, the initial meshing of the boundary model is performed. Specifically, the initial meshing is performed for different material regions in the boundary model. The region (active region) corresponding to the material that participates in the conduction process (conductive material) is meshed with high density, and the region (dielectric isolation region) corresponding to the material that does not participate in the conduction process (dielectric material) is meshed with sparse mesh to reduce subsequent computational resources.

[0043] After initial mesh generation of the boundary model, ion doping is performed using the Gaussian doping analytical method. The doping concentration varies with a Gaussian gradient from the device boundary inwards, forming concentration gradients in the emitter, base, and collector regions, achieving a continuous distribution of doping concentration in the active region. Specifically, the emitter and collector regions use N-type doping, while the base region uses P-type doping. The N-type doping concentration in the emitter region is higher than that in the collector region. The emitter and base regions are homogeneous structures, forming a PN junction through different types of ion doping. The collector region forms a PN junction with the base region through the substrate.

[0044] In step S200 above, the algorithm seeks regions with high concentration gradient density for densification. The h / r adaptive hybrid method based on gradient detection is used to densify the grid in key regions such as the interface between the emitter and base and the interface between the base and collector of the bipolar transistor device. During the mesh densification process, the grid topology (h-adaptive) and node positions (r-adaptive) are dynamically adjusted to maintain the overall gradient density logarithmic threshold within a preset threshold range, thereby identifying high concentration gradient regions. Only high concentration gradient regions are densified to improve calculation accuracy and reduce computational redundancy.

[0045] During mesh refinement, the mesh topology (h-adaptive) and node positions (r-adaptive) are dynamically adjusted. Mesh cells are dynamically split or merged based on a concentration gradient threshold to identify high-concentration gradient regions. Mesh nodes are then moved to cluster within these regions. Specifically, "h-adaptive" involves dynamically splitting or merging mesh cells based on the concentration gradient threshold to identify high-concentration gradient regions, where mesh refinement is performed while maintaining the mesh topology. "r-adaptive" involves moving mesh nodes to cluster them in high-density regions, reducing redundancy and ensuring subsequent solution convergence.

[0046] Specifically, the dynamic splitting or merging of grid cells based on a concentration gradient threshold is as follows: when the concentration gradient density of the grid is greater than the first concentration gradient threshold (>10 ... And the concentration gradient density is less than the second concentration gradient threshold (< When ( ), the mesh elements are dynamically split. Among them, Indicates the concentration gradient threshold. This represents the logarithm of the concentration gradient threshold. The exponent of the concentration gradient density is calculated for the carrier dopant ion concentration; positive values ​​are taken for P-type boron doping concentrations, and negative values ​​are taken for N-type phosphorus doping concentrations. The dopant ion concentration range is 10¹² cm⁻¹. - ³~10² 0 cm - ³.

[0047] Specifically, the grid nodes are moved to cluster towards regions with high concentration gradients, where the concentration gradient density of the grid is greater than the second concentration gradient threshold (>). When the concentration gradient density of a grid node is less than or equal to the first concentration gradient threshold, the grid node is gradually shifted and adjusted to move closer to the high concentration gradient region until the concentration gradient density of the grid is less than or equal to the first concentration gradient threshold (≤ The concentration gradient density is logarithmic, and both the first and second concentration gradient thresholds are logarithmic. , This avoids excessive densification in certain areas under linear coordinates. A concentration gradient threshold can be set. The value is 4 to 5, which achieves effective mesh refinement while avoiding excessive computational burden. In addition, the concentration gradient density of different polarity ion doping regions takes the opposite sign, and the concentration gradient density of cross-polarity regions takes the absolute value, so as to ensure that the gradient density is effectively obtained in the depletion region of the PN junction.

[0048] In step S300 above, the governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and carrier lifetime equation introduce terms related to defect concentration, while the continuity equation and defect recombination equation introduce terms related to the recombination rate of carriers through defects. These additions modify the governing equations. Based on the modified governing equations, the simulation physical model includes: a mobility model (doped scattering model, high-field saturation model), a recombination generation model (SRH indirect recombination model, Auger recombination model), and a bandgap model (bandgap narrowing model).

[0049] The expression for the Poisson equation is: ; in, For the Laplace operator, For electric potential, For elementary charge, Where is the dielectric constant. Hole concentration For electron concentration, Donor concentration, Hole concentration This represents the defect concentration.

[0050] The expression for the continuity equation is: ; ; in, For time, This represents the rate of change of electron concentration over time. This represents the rate of change of hole concentration over time. For elementary charge, For gradient operators, It is an electron current. Hole current, For electron production rate, Hole generation rate , The intrinsic recombination rate, The recombination rate of charge carriers through defects.

[0051] The expression for the defect composite equation is: ; in, This represents the recombination rate of charge carriers through defects. For electron concentration, Hole concentration Intrinsic carrier concentration, For electronic lifetime, For hole lifetime, For trap energy level, K Boltzmann's constant, T is the lattice temperature.

[0052] The carrier lifetime equations (electron lifetime and hole lifetime) are expressed as follows: ; ; For electronic lifetime, For hole lifetime, For electron capture cross section, For hole capture cross section, For carrier velocity, This represents the defect concentration.

[0053] The modified governing equations define the quantitative relationship between carrier lifetime and defect concentration, trapping cross section, and carrier velocity: higher defect concentration and larger trapping cross section result in shorter carrier lifetime and more significant device degradation. The reaction rate in the defect evolution model... With device current Coupling, defect concentration The lifespan increases dynamically with stress time and current intensity. , Continuous decay, eventually through defect recombination rate This manifests as device performance degradation, reflecting the logical relationship between device current and defect generation, carrier lifetime decay, and device degradation.

[0054] The expression for the defect evolution model is: ; ; in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, This indicates the effect of thermal activation energy on the reaction rate; For device current, and This is a constant in the degenerate equation.

[0055] The defect evolution model introduces a correction factor. High-energy carrier collisions via current-mechanism and thermal activation via temperature-mechanism are combined. Superposition, jointly driving defect evolution, can achieve more realistic electro-thermal coupling degradation simulation.

[0056] In step S400 above, the depletion region of the device is defined based on doping concentration and mesh density, and the application area of ​​the defect evolution model is defined within the depletion region. Specifically, the reconstructed mesh is density-sorted, and high mesh density regions are determined based on the density sorting. The intersection of the local minimum absolute value region of doping concentration and the high mesh density region above the mesh density threshold is determined as the depletion region of the device. Specifically, the reciprocal of the size of each mesh cell can be calculated; for two-dimensional meshes, the reciprocal of the plane base is used, and for three-dimensional meshes, the reciprocal of the volume is used as the density index (the reciprocal of the size of the refined mesh cells is used as the density index). The magnitude of the density value indicates the degree of density. The density indices are arranged from largest to smallest, and the mesh cells at the top of the sort are determined as high mesh density regions. Then, the local minimum absolute value region of doping concentration is determined, and the intersection of the local minimum absolute value region of doping concentration and the high mesh density region above the mesh density threshold is determined as the depletion region of the device. Specifically, the depletion regions of a bipolar transistor device are the emitter junction and the collector junction. The emitter junction is the depletion region corresponding to the boundary between the emitter and the base, and the collector junction is the depletion region corresponding to the boundary between the base and the collector.

[0057] The defect evolution model is assigned to the depletion regions of the emitter and collector junctions, and different initial response rates are set for the emitter and collector junctions respectively. By assigning the defect evolution model only to the depletion regions of the emitter and collector junctions, the numerical convergence problem and computational resource redundancy caused by applying the defect model globally can be avoided.

[0058] In step S500 above, the reliability transient solution of the bipolar transistor is performed based on the simulation physical model and the defect evolution model. Specifically, the parameters of the simulation physical model and the defect evolution model are defined, and a transient solution is performed. The simulation analysis duration is defined, and the reliability degradation simulation curve is obtained based on the solution results. The reliability degradation simulation curve is analyzed to obtain the reliability degradation data of the bipolar transistor.

[0059] Typically, bipolar junction transistor (BJT) devices are modeled using TCAD (Technology Computer-Aided Design) tools for semiconductor device simulation. In a specific example, the complete modeling steps are as follows: 1) Boundary modeling of bipolar junction transistor (BJT) devices: Construct a BJT device model framework and divide the emitter, base, and collector regions according to actual process information; 2) Initial mesh generation: Perform material-guided meshing on the overall boundary model to achieve a consistent mesh; 3) Definition of process doping information: Doping is defined at the boundary of the BJT device using analytical methods to achieve Gaussian-like doping in the active region of the device. Taking an NPN BJT device as an example, N-type doping is implemented on the emitter and collector electrodes, and P-type doping is implemented on the base electrode; 4) Refined Mesh Reconstruction: Targeted mesh refinement is performed on the key regions of the BJT device solution to ensure solution accuracy; among them, the key regions of the BJT device are the emitter-base and base-collector interfaces; 5) Additional basic control equations and physical models: Define the basic control equations and models for simulation, including mobility models (doped scattering model, high field saturation model), recombination models (SRH indirect recombination model, Auger recombination model), and band structure models (bandgap narrowing model). 6) Custom Defect Evolution Model: Define a defect evolution model in the depletion region of the BJT device to increase the current recombination probability and achieve device degradation effect; 7) Transient reliability solution: Perform transient solution on BJT device, define simulation duration, and obtain reliability degradation data.

[0060] Taking NPN bipolar junction transistor (BJT) devices as an example, Figure 2 This is a cross-sectional view of the simulation process model of the doping distribution of an NPN bipolar transistor (BJT) device. Figure 2 The device structure and doping concentration distribution are shown. The model, from top to bottom, includes the collector, emitter, and base metal contact regions, with the corresponding semiconductor doping regions below: the emitter region has a high concentration of N-type doping, the base region has P-type doping, and the collector region has a medium concentration of N-type doping, exhibiting an overall Gaussian-like distribution. The light-colored stripes represent the depletion regions at the emitter-base and base-collector interfaces, where the doping concentration is the local minimum absolute value. Combined with the high grid density characteristics after adaptive grid refinement, the application areas of the defect evolution model (emitter junction and collector junction) can be accurately located, providing a physical basis for setting differentiated initial reaction rates.

[0061] Based on the process model, a refined mesh is reconstructed. Figure 3 This is a detailed mesh diagram of the simulation process model of an NPN-type BJT device in one example of the present invention. For example... Figure 3 As shown, the regions at the junction of the emitter and base, and the regions at the junction of the base and collector, are the critical solution regions, where the carrier concentration gradient is large. To ensure solution convergence, mesh refinement is performed on these junction regions.

[0062] The densification of the junction region is generated using an adaptive meshing method. Specifically, the algorithm seeks regions with high concentration gradient density for densification, and the densification process is based on the gradient detection-based h / r adaptive hybrid method. The gradient detection-based h / r adaptive hybrid method is an efficient mesh optimization technique for regions with abrupt changes in concentration gradient. By dynamically adjusting the mesh topology (h-adaptive) and node positions (r-adaptive), it ensures improved simulation accuracy and computational efficiency. Specifically, h-adaptive dynamically splits or merges mesh cells based on the concentration gradient threshold, densifying where the gradient is high while maintaining the mesh topology; r-adaptive moves mesh node positions, causing nodes to cluster towards high-density regions, reducing redundancy. The process sets a local concentration gradient threshold. Distinguish between grid partitioning trigger mechanisms: such as when the concentration gradient exponent > And the concentration gradient < When h-adaptive method is used for grid fission; if concentration gradient > At this time, the r-adaptive method is used to shift and adjust the grid points, moving them closer to the high gradient region; this process is repeated 3-5 times until the gradient density is ≤ .

[0063] During the coordinated adjustment process, the following operations can be performed: 1) For semiconductor devices, the concentration gradient exhibits an exponential change law, and the density gradient changes drastically in the PN junction region. During the process, the above threshold and concentration gradient are both taken in logarithmic form to ensure that the threshold adjustment is within a reasonable range and to prevent the condition of concentration gradient ≤ 0.5 in linear coordinates from being met. 1) Excessive densification in some areas; 2) For ion doping regions of different polarities, the concentration gradient density takes the opposite sign, and the absolute value is taken for cross-polarity calculation to ensure that the gradient density is effectively taken in the depletion region of the PN junction.

[0064] Taking a conventional bipolar junction transistor (BJT) device as an example, the carrier doping ion concentration is 10 12 cm -3 ~10 20 cm -3 The discussion focuses on P-type boron doping with positive concentration values ​​and N-type phosphorus doping with negative concentration values. In the transition region, the logarithm of the device concentration gradient density changes rapidly between -20 and 12. To effectively refine the mesh without excessively increasing the computational burden, the following settings are employed: To meet encryption requirements. The device model for mesh encryption using the above algorithm is as follows: Figure 3 As shown, the junction region is effectively encrypted.

[0065] The electrical characteristics of semiconductor devices are typically derived theoretically based on the intrinsic material properties. In semiconductors, the motion of charge carriers is mainly determined by finite element analysis using three fundamental governing equations. The conventional governing equations are: 1) Poisson equation: ; 2) Drift-diffusion equation: ; ; 3) Continuity equation: ; ; In the above formula, For electric potential, For elementary charge, Where is the dielectric constant. Hole concentration For electron concentration, Donor concentration, Hole concentration It is an electron current. Hole current, For mobility, For electric field, The diffusion coefficient is... For time, For generation rate, The composite rate is denoted as .

[0066] migration rate The generation rate is determined by the mobility model. With composite rate The subscript is determined by the generation of the composite model. and These represent differentiating the electron and hole, respectively.

[0067] Device-level reliability calculation theory is updated based on the premise of accurate electrical simulation. Essentially, device performance degradation stems from the continuous accumulation of internal defects. This invention considers the impact of defect evolution on device reliability degradation, and firstly, modifies the control equations. The new control equations are as follows: 1) Poisson equation: ; 2) Drift-diffusion equation: ; ; 3) Continuity equation: ; ; The above equation introduces two new terms: defect concentration. and the recombination rate of charge carriers through defects , This represents the rate at which electrons are captured by defect traps and recombine with holes, reflecting the attenuation effect of defects on carrier lifetime.

[0068] 4) Defect equation: ; In the above formula, and This refers to the carrier concentration parameter related to the trap energy level. The defect equation is a key equation in semiconductor devices used to describe the dynamic process of carriers being trapped and released by defect states (traps). The kinetic equation is constructed based on the parameterized definition of defects. The parameterized definition includes semiconductor material properties, such as defining the energy level positions of the traps. (e.g., conduction band / valence band offset), concentration distribution (Volume trap or interface trap). The kinetic equations are constructed by establishing a trap-assisted carrier generation-recombination rate equation, including an extension term to the SRH model, introducing a trap occupancy probability function, and the defect recombination equation is: ; The above formula involves electronic lifetime parameters. Hole lifetime parameters The carrier lifetime is derived from the defect concentration equation, and we have: 5) Carrier lifetime equation: , In the formula To capture the cross section, denoted as carrier velocity.

[0069] Under the premise of updating the control equations, a global definition of the conventional physical model is performed, completing the basic control equations and physical model additions for device simulation. The models covered include mobility models (doped scattering model, high-field saturation model), recombination models (SRH indirect recombination model, Auger recombination model), and bandgap models (bandgap narrowing model), meeting the simulation requirements of conventional semiconductor devices.

[0070] Bipolar transistor reliability models need to consider the time-dependent evolution of device defects to describe the impact of active currents at the PN junction on lattice atoms. In a specific embodiment, the device defect evolution model is constructed based on the empirical formula for the growth exponential of interface trap charge: ; in, It is the initial interface state concentration. It is the concentration of the trap over time. It is the quantity of defects. It is the total amount of unbroken bonds. For time, For the reaction rate, The reaction index, and These are experimental parameters. In first-order dynamics, the defect increment satisfies: ; ; In the formula, For trap energy level, For lattice temperature, The initial reaction rate is given.

[0071] By defining the initial interface state concentration of the defect Total number of unbroken bonds Response index Trap energy level Basic reliability simulations are performed, at which point the device degenerates into a spontaneous process, unaffected by external electric field stress.

[0072] The degradation of bipolar devices is affected by high-energy carrier collisions in the depletion region of the PN junction; therefore, the device degradation response rate should be coupled with the current intensity. This invention deeply considers the causes of real device degradation, innovates the model of the influence of coupled current on device defects, and introduces a correction factor based on device current intensity to correct the defect response rate constant (device defect evolution has an exponential dependence on current, consistent with the common sense of electron collisions under avalanche breakdown), namely: ; ; in, and For degenerate equation constants, This represents the device current.

[0073] The above defines a reliability model for bipolar transistor devices. Combining this model with conventional models yields a complete theoretical model for reliability simulation. Conventional simulation models only consider thermal activation (temperature T, trap energy level). The influence of the device's operating current on defect response rate is considered, as is the impact of the device's operating current intensity on defect evolution. The simulation physical model of this invention adds terms related to defect concentration and carrier recombination rate via defects to the governing equations. The defect evolution model, based on thermal activation, further introduces a correction factor based on current intensity. defect reaction rate constant The defect reaction rate constant is corrected. With device current Direct coupling demonstrates the accelerating effect of current on defect evolution.

[0074] In theory, semiconductor device defects are distributed throughout the entire active region. However, based on experimental experience, device degradation mainly accumulates in the depletion region of the PN junction. Complex global device models present global convergence challenges. This invention addresses this by setting up a dedicated region (application region) for device defect evolution.

[0075] In this embodiment of the invention, during the reconstruction of the refined mesh, an adaptive mesh algorithm was used to locally refine the device depletion region, maintaining the overall gradient density logarithmic threshold to ≤ At this point, setting defect regions based on density gradients becomes difficult. Device region selection is based on dopant ion concentration, combined with a grid density function, to define the device defect evolution model region. The specific process includes: 1) Sort the constructed grid by density, calculating the reciprocal of the size for each grid cell (reciprocal of the surface area for 2D grids, reciprocal of the volume for 3D grids) as a density index. The magnitude of the value represents the density, and the density index is arranged from largest to smallest to find high grid density regions; 2) Combine the dopant concentration value to find device depletion regions, where the device dopant concentration is the local minimum absolute value. Simultaneously considering the local minimum dopant concentration and high grid density (setting a grid density threshold to only locate device regions with a density higher than this threshold), device depletion regions can be located, such as... Figure 4 The defect evolution models for Region 1 and Region 2 are shown in the figure. Based on the defined device boundary model, the emitter junction and collector junction can be located. Region 1 represents the emitter junction, and Region 2 represents the collector junction. The defect evolution models are assigned to these two grid regions. Considering that the emitter doping concentration is higher than the collector doping concentration in the process device, the electric field strength at the emitter-base interface is stronger than that at the base-collector interface. Therefore, the defect accumulation process at the emitter-base interface plays a dominant role in device degradation. Different initial reaction rates can be discussed separately for the two types of device regions. , And there are The actual degradation curve of the device is fitted to meet the simulation accuracy requirements.

[0076] Based on the complete construction of the device mesh and physical model, relevant model parameters are defined, and transient solutions are performed on the BJT device. By defining the simulation duration, reliability degradation simulation data curves are obtained. Specifically, timing solutions can be performed using the TCAD software solver, and the device reliability degradation simulation curves can be analyzed using a visualization software module. A reliability simulation data curve for an NPN BJT device is shown below. Figure 5 As shown, the collector current of the device exhibits significant degradation over time.

[0077] Figure 6 This is a block diagram of a bipolar transistor reliability analysis system provided in an embodiment of the present invention. Figure 6As shown, the bipolar transistor reliability analysis system provided in this embodiment includes: a mesh generation unit, a mesh reconstruction unit, a simulation model construction unit, and a reliability analysis unit. The mesh generation unit is used to divide the emitter, base, and collector regions based on the boundary model of the bipolar transistor device according to actual process information, and performs initial mesh generation on the boundary model. The mesh reconstruction unit is used to refine the mesh at the interface between the emitter and base, and the interface between the base and collector of the bipolar transistor device, and perform mesh reconstruction. The simulation model construction unit is used to define a simulation physical model and a defect evolution model of the bipolar transistor device based on the boundary model after mesh reconstruction. The control equations of the simulation physical model introduce terms related to defect concentration and carrier recombination rate through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. The reliability analysis unit is used to determine the application area of ​​the defect evolution model of the bipolar transistor device, assign the defect evolution model to the application area, and analyze the reliability of the bipolar transistor based on the simulation physical model and the defect evolution model to obtain device reliability degradation data.

[0078] In a specific embodiment, the mesh generation unit performs initial mesh generation for different material regions in the boundary model. The regions (active regions) corresponding to materials that participate in the conduction process (conductive materials) are meshed with high density, while the regions (dielectric isolation regions) corresponding to materials that do not participate in the conduction process (dielectric materials) are meshed with sparse density to reduce subsequent computational resources.

[0079] After initial mesh generation of the boundary model, ion doping is performed using the Gaussian doping analytical method. The doping concentration varies with a Gaussian gradient from the device boundary inwards, forming concentration gradients in the emitter, base, and collector regions, achieving a continuous distribution of doping concentration in the active region. Specifically, the emitter and collector regions use N-type doping, while the base region uses P-type doping. The N-type doping concentration in the emitter region is higher than that in the collector region. The emitter and base regions are homogeneous structures, forming a PN junction through different types of ion doping. The collector region forms a PN junction with the base region through the substrate.

[0080] In a specific embodiment, during the process of refining the mesh at the interface between the emitter and base and the interface between the base and collector of the bipolar transistor device, the mesh reconstruction unit determines the high-concentration gradient region by dynamically adjusting the mesh topology and node positions, and only refines the high-concentration gradient region to improve computational accuracy and reduce computational redundancy.

[0081] Specifically, high-concentration gradient regions are determined by dynamically adjusting the mesh topology and node positions. This includes dynamically splitting or merging mesh cells based on a concentration gradient threshold to identify high-concentration gradient regions, and moving mesh nodes to cluster them towards these regions. When the mesh concentration gradient density is greater than a first concentration gradient threshold (>10 ... And the concentration gradient density is less than the second concentration gradient threshold (< When ( ), the mesh elements are dynamically split. Among them, Indicates the concentration gradient threshold. This represents the logarithm of the concentration gradient threshold.

[0082] Specifically, moving the grid node to cluster it towards a high-concentration gradient region involves ensuring that the grid's concentration gradient density is greater than a second concentration gradient threshold (>). When the concentration gradient density of a grid node is less than or equal to the first concentration gradient threshold, the grid node is gradually shifted and adjusted to move closer to the high concentration gradient region until the concentration gradient density of the grid is less than or equal to the first concentration gradient threshold (≤ The concentration gradient density is logarithmic, and both the first and second concentration gradient thresholds are logarithmic. , This avoids excessive densification in certain areas under linear coordinates. A concentration gradient threshold can be set. The value is 4 to 5, which achieves effective mesh refinement while avoiding excessive computational burden. In addition, the concentration gradient density of different polarity ion doping regions takes the opposite sign, and the concentration gradient density of cross-polarity regions takes the absolute value, so as to ensure that the gradient density is effectively obtained in the depletion region of the PN junction.

[0083] In a specific embodiment, the governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and carrier lifetime equation introduce terms related to defect concentration, while the continuity equation and defect recombination equation introduce terms related to the recombination rate of carriers via defects. These additions modify the governing equations. Based on the modified governing equations, the simulation physical model includes: a mobility model (doped scattering model, high-field saturation model), a recombination generation model (SRH indirect recombination model, Auger recombination model), and a bandgap model (bandgap narrowing model).

[0084] The expression for the Poisson equation is: ; in, For the Laplace operator, For electric potential, For elementary charge, Where is the dielectric constant. Hole concentration For electron concentration, Donor concentration, Hole concentration This represents the defect concentration.

[0085] The expression for the continuity equation is: ; ; in, For time, This represents the rate of change of electron concentration over time. This represents the rate of change of hole concentration over time. For elementary charge, For gradient operators, It is an electron current. Hole current, For electron production rate, Hole generation rate , The intrinsic recombination rate, The recombination rate of charge carriers through defects.

[0086] The expression for the defect composite equation is: ; in, This represents the recombination rate of charge carriers through defects. For electron concentration, Hole concentration Intrinsic carrier concentration, For electronic lifetime, For hole lifetime, For trap energy level, K Boltzmann's constant, T is the lattice temperature.

[0087] The carrier lifetime equations (electron lifetime and hole lifetime) are expressed as follows: ; ; For electronic lifetime, For hole lifetime, For electron capture cross section, For hole capture cross section, For carrier velocity, This represents the defect concentration.

[0088] The modified governing equations define the quantitative relationship between carrier lifetime and defect concentration, trapping cross section, and carrier velocity: higher defect concentration and larger trapping cross section result in shorter carrier lifetime and more significant device degradation. The reaction rate in the defect evolution model... With device current Coupling, defect concentration The lifespan increases dynamically with stress time and current intensity. , Continuous decay, eventually through defect recombination rate This manifests as device performance degradation, reflecting the logical relationship between device current and defect generation, carrier lifetime decay, and device degradation.

[0089] The expression for the defect evolution model is: ; ; in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, This indicates the effect of thermal activation energy on the reaction rate; For device current, and This is a constant in the degenerate equation.

[0090] The defect evolution model introduces a correction factor. High-energy carrier collisions via current-mechanism and thermal activation via temperature-mechanism are combined. Superposition, jointly driving defect evolution, can achieve more realistic electro-thermal coupling degradation simulation.

[0091] In a specific embodiment, the reliability analysis unit sorts the reconstructed mesh by density and determines high mesh density regions based on the density sorting. The intersection of the region with the local minimum absolute value of doping concentration and the high mesh density region above the mesh density threshold is determined as the depletion region of the bipolar transistor device, and this depletion region is used as the application region for the defect evolution model. Specifically, the reciprocal of the size of each mesh cell can be calculated, with the reciprocal of the face size for two-dimensional meshes and the reciprocal of the volume for three-dimensional meshes, as a density index (the reciprocal of the size of the refined mesh cells is used as the density index). The magnitude of the density value indicates the degree of density, and the density indices are arranged from largest to smallest, with the mesh cells at the top of the sorting determined as high mesh density regions. Then, the region with the local minimum absolute value of doping concentration is determined, and the intersection of this region with the high mesh density region above the mesh density threshold is determined as the depletion region of the device. That is, the depletion region of the bipolar transistor device is the depletion region of the emitter junction and the collector junction. The emitter junction is the depletion region corresponding to the boundary between the emitter and base, and the collector junction is the depletion region corresponding to the boundary between the base and collector. The defect evolution model is assigned to the depletion regions of the emitter and collector junctions, and different initial response rates are set for the emitter and collector junctions respectively. By assigning the defect evolution model only to the depletion regions of the emitter and collector junctions, the numerical convergence problem and computational resource redundancy caused by applying the defect model globally can be avoided.

[0092] In a specific embodiment, the reliability analysis unit performs transient reliability calculations on the bipolar transistor based on a simulation physical model and a defect evolution model. Specifically, this includes: defining the parameters of the simulation physical model and the defect evolution model, performing transient calculations, defining the simulation analysis duration, obtaining the reliability degradation simulation curve based on the calculation results, analyzing the reliability degradation simulation curve, and obtaining the reliability degradation data of the bipolar transistor.

[0093] The bipolar transistor reliability analysis system provided in this embodiment is the same as the bipolar transistor reliability analysis method in the above embodiments in terms of specific technical details and technical effects. It can be understood by referring to the details and examples of the bipolar transistor reliability analysis method described above.

[0094] The present invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the bipolar transistor reliability analysis method of the above embodiments.

[0095] The present invention also provides a machine-readable storage medium storing computer program instructions thereon, which, when executed by a processor, implement the bipolar transistor reliability analysis method of the above embodiments.

[0096] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0097] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0098] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0099] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0100] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention. Furthermore, it should be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. As long as such combination does not violate the spirit of the embodiments of the present invention, it should also be considered as the content disclosed in the embodiments of the present invention.

Claims

1. A method for reliability analysis of bipolar transistors, characterized in that, include: Based on the boundary model of a bipolar transistor device, the regions of emitter, base, and collector are divided according to actual process information, and the boundary model is initially meshed. The mesh of the emitter-base interface and the base-collector interface of the bipolar transistor device is refined and then rebuilt. Based on the boundary model after mesh reconstruction, a simulation physical model and a defect evolution model for bipolar transistor devices are defined. The control equations of the simulation physical model introduce terms related to defect concentration and carrier recombination rate through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. Determine the application region of the defect evolution model for the bipolar transistor device, and assign the defect evolution model to the application region; The reliability of bipolar transistors is analyzed based on the simulation physical model and defect evolution model to obtain device reliability degradation data.

2. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The initial mesh generation of the boundary model includes: Initial mesh generation is performed for different material regions in the boundary model. High-density mesh generation is performed for regions corresponding to materials that participate in the conduction process, while sparse mesh generation is performed for regions corresponding to materials that do not participate in the conduction process.

3. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The method further includes: After initial meshing of the boundary model, ion doping is performed, with the doping concentration varying from the device boundary to the interior in a Gaussian gradient, forming the emitter region, base region, and collector region of the concentration gradient.

4. The bipolar transistor reliability analysis method according to claim 3, characterized in that, The emitter region and the collector region are N-type doped, the base region is P-type doped, and the N-type doping concentration in the emitter region is higher than that in the collector region.

5. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The mesh refinement of the emitter-base interface and the base-collector interface of the bipolar transistor device includes: In the process of mesh refinement of the interface between the emitter and base, and the interface between the base and collector of a bipolar transistor device, high-concentration gradient regions are determined by dynamically adjusting the mesh topology and node positions, and only the high-concentration gradient regions are refined.

6. The bipolar transistor reliability analysis method according to claim 5, characterized in that, The method of determining high-concentration gradient regions by dynamically adjusting the grid topology and node positions includes: Dynamically split or merge grid cells based on concentration gradient thresholds to identify high concentration gradient regions, and move the position of grid nodes to make them cluster towards high concentration gradient regions.

7. The bipolar transistor reliability analysis method according to claim 6, characterized in that, The dynamic splitting or merging of grid cells based on a concentration gradient threshold includes: The grid cells are dynamically split when the concentration gradient density of the grid is greater than the first concentration gradient threshold and less than the second concentration gradient threshold.

8. The bipolar transistor reliability analysis method according to claim 6, characterized in that, The step of moving the grid node to cluster towards a high-concentration gradient region includes: When the concentration gradient density of the grid is greater than the second concentration gradient threshold, the grid nodes are gradually shifted and adjusted to move the grid nodes closer to the high concentration gradient region until the concentration gradient density of the grid is less than or equal to the first concentration gradient threshold.

9. The bipolar transistor reliability analysis method according to claim 7 or 8, characterized in that, The concentration gradient density is a logarithmic value, and both the first concentration gradient threshold and the second concentration gradient threshold are logarithmic values.

10. The bipolar transistor reliability analysis method according to claim 7 or 8, characterized in that, The concentration gradient density of ions doped with different polarities takes the opposite sign, while the concentration gradient density of ions doped with transpolarities takes the absolute value.

11. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and the carrier lifetime equation introduce terms related to defect concentration, and the continuity equation and the defect recombination equation introduce terms related to the recombination rate of carriers through defects.

12. The bipolar transistor reliability analysis method according to claim 11, characterized in that, The expression for the Poisson equation is: ； in, For the Laplace operator, For electric potential, For elementary charge, Where is the dielectric constant. Hole concentration For electron concentration, Donor concentration, Hole concentration This represents the defect concentration.

13. The bipolar transistor reliability analysis method according to claim 11, characterized in that, The expression for the continuity equation is: ； ； in, For time, This represents the rate of change of electron concentration over time. This represents the rate of change of hole concentration over time. For elementary charge, For gradient operators, For electron current, Hole current, For electron production rate, Hole generation rate , The intrinsic recombination rate, The recombination rate of charge carriers through defects.

14. The bipolar transistor reliability analysis method according to claim 11, characterized in that, The expression for the defect composite equation is: ； in, This represents the recombination rate of charge carriers through defects. For electron concentration, Hole concentration Intrinsic carrier concentration, For electronic lifetime, For hole lifespan, For trap energy level, K Boltzmann's constant, T is the lattice temperature.

15. The bipolar transistor reliability analysis method according to claim 14, characterized in that, The expression for the carrier lifetime equation is: ； ； in, For electronic lifetime, For hole lifespan, For electron capture cross section, For hole capture cross section, For carrier velocity, This represents the defect concentration.

16. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The expression for the defect evolution model is: ； ； in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, For device current, and This is a constant in the degenerate equation.

17. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The application region for determining the defect evolution model of the bipolar transistor device includes: The depletion region of the device is defined based on doping concentration and mesh density, and the application region of the defect evolution model is defined within the depletion region.

18. The bipolar transistor reliability analysis method according to claim 17, characterized in that, The depletion region of the device, defined based on doping concentration and grid density, includes: The reconstructed grid is sorted by density, and high-density grid regions are determined based on the density sort. The intersection region of the local minimum absolute value region of doping concentration and the high grid density region above the grid density threshold is defined as the depletion region of the bipolar transistor device.

19. The bipolar transistor reliability analysis method according to claim 18, characterized in that, The step of determining high grid density regions based on density sorting includes: For each grid cell, the reciprocal of the size is calculated as a density index, where the reciprocal of the surface base is used for two-dimensional grids and the reciprocal of the volume is used for three-dimensional grids. The density indices are arranged from largest to smallest, and the grid cells at the top of the list are identified as high-density areas.

20. The bipolar transistor reliability analysis method according to claim 18, characterized in that, The depletion region of the bipolar transistor device is the depletion region of the emitter junction and the collector junction; The emitter junction is the depletion region corresponding to the boundary between the emitter and the base, and the collector junction is the depletion region corresponding to the boundary between the base and the collector.

21. The bipolar transistor reliability analysis method according to claim 20, characterized in that, Assigning the defect evolution model to the application region includes: The defect evolution model is assigned to the depletion regions of the emitter junction and collector junction, and different initial reaction rates are set for the emitter junction and collector junction respectively.

22. The bipolar transistor reliability analysis method according to claim 1, characterized in that, The reliability analysis of the bipolar transistor based on the simulation physical model and defect evolution model includes: Define the parameters of the simulation physical model and the defect evolution model, and perform transient solutions; Define the simulation analysis duration and obtain the reliability degradation simulation curve based on the solution results; The reliability degradation simulation curves were analyzed to obtain reliability degradation data for bipolar transistors.

23. A bipolar transistor reliability analysis system, characterized in that, include: Mesh generation unit is used to divide the emitter, base, and collector regions based on the boundary model of a bipolar transistor device according to actual process information, and to perform initial mesh generation on the boundary model; The mesh reconstruction unit is used to refine the mesh at the interface between the emitter and base, and the interface between the base and collector of a bipolar transistor device, and to reconstruct the mesh. The simulation model construction unit is used to define the simulation physical model and defect evolution model of the bipolar transistor device based on the boundary model after mesh reconstruction. The control equation of the simulation physical model introduces terms related to defect concentration and carrier recombination rate through defects. The defect response rate of the defect evolution model is coupled to the device current intensity, and the defect response rate is corrected by introducing a correction factor based on the device current intensity. The reliability analysis unit is used to determine the application area of ​​the defect evolution model of the bipolar transistor device, assign the defect evolution model to the application area, analyze the reliability of the bipolar transistor based on the simulation physical model and the defect evolution model, and obtain device reliability degradation data.

24. The bipolar transistor reliability analysis system according to claim 23, characterized in that, In the process of refining the mesh at the interface between the emitter and base, and the interface between the base and collector of the bipolar transistor device, the mesh reconstruction unit determines the high-concentration gradient region by dynamically adjusting the mesh topology and node positions, and only refines the high-concentration gradient region.

25. The bipolar transistor reliability analysis system according to claim 24, characterized in that, The method of determining high-concentration gradient regions by dynamically adjusting the grid topology and node positions includes: Dynamically split or merge grid cells based on concentration gradient thresholds to identify high concentration gradient regions, and move the position of grid nodes to make them cluster towards high concentration gradient regions.

26. The bipolar transistor reliability analysis system according to claim 23, characterized in that, The governing equations of the simulation physical model of the bipolar transistor device include one or more of the following: Poisson equation, drift-diffusion equation, continuity equation, defect recombination equation, and carrier lifetime equation. The Poisson equation and the carrier lifetime equation introduce terms related to defect concentration, and the continuity equation and the defect recombination equation introduce terms related to the recombination rate of carriers through defects.

27. The bipolar transistor reliability analysis system according to claim 23, characterized in that, The expression for the defect evolution model is: ； ； in, For the reaction rate, The initial reaction rate, For trap energy level, Boltzmann's constant, For lattice temperature, As a reaction rate correction factor, For device current, and This is a constant in the degenerate equation.

28. The bipolar transistor reliability analysis system according to claim 23, characterized in that, The reliability analysis unit is specifically used for: The reconstructed grid is sorted by density, and high-density grid regions are determined based on the density sort. The intersection region of the local minimum absolute value region of doping concentration and the high grid density region above the grid density threshold is defined as the depletion region of the bipolar transistor device, and the depletion region is used as the application region of the defect evolution model.

29. The bipolar transistor reliability analysis system according to claim 23, characterized in that, The reliability analysis unit is specifically used for: Define the parameters of the simulation physical model and the defect evolution model, and perform transient solutions; Define the simulation analysis duration and obtain the reliability degradation simulation curve based on the solution results; The reliability degradation simulation curves were analyzed to obtain reliability degradation data for bipolar transistors.

30. An electronic device, characterized in that, include: Memory, which stores computer programs; A processor for executing the computer program to implement the bipolar transistor reliability analysis method according to any one of claims 1-22.

31. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is executed by a processor to implement the bipolar transistor reliability analysis method according to any one of claims 1-22.

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