IGBT (Insulated Gate Bipolar Translator) chip layer multi-physical field dynamic numerical calculation method and system

Abstract

The invention discloses an IGBT chip layer multi-physical field dynamic numerical calculation method and system. The method comprises the steps that a partial differential equation set of an IGBT chip layer multi-physical field evolution process is established; and a PINN numerical calculation model embedded with the partial differential equation set is established, and IGBT chip layer multi-physical field dynamic process numerical calculation is realized. According to the method, firstly, a partial differential equation set of multi-physics field coupling in an IGBT is established, and an IGBT chip layer coupling physics field dynamic numerical calculation method based on ETM-PINN is provided accordingly, so that embedding of a data driving algorithm by an analytic physical model can be realized, the optimization solving process of the algorithm is standardized, and the reliability of the algorithm is improved. Therefore, accurate numerical calculation under various data model configuration conditions can be flexibly handled.

Description

Technical Field

[0001] This application relates to the field of semiconductor numerical simulation technology, and particularly relates to a multi-physical field dynamic numerical calculation method and system for IGBT chip layers, mainly used for predicting and calculating the numerical values of key physical quantities inside semiconductor power devices such as IGBTs (Insulated Gate Bipolar Transistors). Background Art

[0002] The reliability and remaining service life of semiconductor devices are strongly correlated with state physical quantities such as junction temperature and electric potential. Affected by the power cycling process and the Arrhenius equation, there are a large number of chip junction temperatures and electrical parameters in the analytical life models and failure physics models of semiconductor power devices such as IGBTs. However, the difficult accurate monitoring of these physical quantities in actual engineering severely restricts the application of these life models, bringing difficulties to the reliability and life assessment of power devices. Traditional measurement and monitoring methods require the destruction of the packaging structure of the device module to obtain accurate values, which are often difficult to achieve in engineering applications. Considering the complex coupling and time-varying of multi-physical processes inside semiconductor devices, how to accurately calculate the evolution process of the internal state physical quantities of IGBTs non-destructively and non-invasively has gradually become a research hotspot in this field. The dynamic numerical calculation of the state physical quantities of semiconductor power devices such as IGBTs can not only be used for mechanism revelation, state monitoring and failure prediction of chips, but also for reliability analysis and packaging optimization in the chip design stage, with important research value and broad application prospects.

[0003] At present, the basic methods for numerical calculation, prediction or monitoring of key physical quantities of semiconductor power devices such as IGBTs can be mainly divided into two categories: (1) Model-based methods, such as relevant electrical models, finite element method, finite difference method, network topology method, thermal circuit equivalent method, etc. The models adopted by these methods essentially transform the problem of finding the definite solution of partial differential equation systems in the continuous domain into the problem of solving large algebraic equation systems. For more complex three-dimensional multi-physical field problems, the scale of such discrete algebraic equation systems is extremely large, and various order reduction algorithms are often required for post-processing. Their modeling and solving processes are very complex. Such model methods have limitations for a single physical field. For coupled multi-physical field calculation problems, usually multiple model methods need to be combined and dynamically jointly solved to achieve multi-field coverage. Due to problems such as mismatches in time scales and grids of various models and their one-way coupling simplification of physical processes, there may be errors in the joint transmission of different data. Therefore, such calculation processes still have limitations of their respective methods and calculation gaps in cross-method joint calculations. (2) Data-based methods, such as least squares method, polynomial method, neural network, support vector machine, etc. Since there is a mapping relationship between electrical parameters such as IGBT collector current, saturation voltage drop, and base voltage and the internal chip layer state variables, the change curves of key physical quantities with externally measurable parameters can be obtained by using a large amount of experimental monitoring data and relevant fitting algorithms, so as to achieve indirect measurement and calculation. Such methods essentially ignore the complex coupled physical system and expect to directly find the functional relationship between different physical quantities through data analysis. The performance of their algorithms strongly depends on the quantity, quality, and breadth of data, and the dynamic calculation ability is poor in the case of poor data. And such methods still have black box models and it is difficult to adaptively adjust the algorithm architecture and relevant parameters. Summary of the Invention

[0004] In order to solve the limitations, complexity, reliability and other problems existing in the existing model-based methods and data-based methods, the present application proposes a multi-physical field dynamic numerical calculation method and system for IGBT chip layers. The present application introduces measured data as a specification and constraint condition in the model-driven method to achieve deep integration of the model and data, so that the multi-physical field dynamic numerical calculation technology of semiconductor devices such as IGBTs has the ability to solve complex nonlinear problems and cope with multiple coupled systems.

[0005] The present application is realized through the following technical solutions:

[0006] A multi-physical field dynamic numerical calculation method for IGBT chip layers, the method includes:

[0007] Establish a partial differential equation system for the evolution process of the multi-physical field of the IGBT chip layer;

[0008] Establish a PINN numerical calculation model embedded with the partial differential equation system to achieve numerical calculation of the multi-physical field dynamic process of the IGBT chip layer.

[0009] In some embodiments, the partial differential equation system of the multi-physical field evolution process of the IGBT chip layer is as follows:

[0010]

[0011] Among them, σ is the conductivity, V is the electric potential, ε0 and ε r are the vacuum permittivity and relative permittivity respectively, x, y, and z are the X, Y, and Z directions of the chip layer respectively, T is the temperature, ρ is the density, C p is the constant-pressure heat capacity, k is the thermal conductivity, t is the time, ΔT is the temperature difference between the current and initial moments, a is the thermal expansion coefficient, and E is the elastic modulus.

[0012] In some embodiments, the calculation formulas for the conductivity and thermal conductivity are:

[0013] σ = 78.847×(1 - 1.3534×10 -3 ×(T - 273.15))

[0014] k = 131 - 0.4129×(T - 298.15).

[0015] In some embodiments, the establishment of the PINN numerical calculation model embedded with the partial differential equation system specifically includes:

[0016] Consider an arbitrary integer-order partial differential equation system, which includes multiple partial differential equation zero terms with parameters, as well as initial conditions and boundary conditions;

[0017] Construct a multi-input multi-output neural network as the initial solution vector, and specify corresponding training sets for the arbitrary integer-order partial differential equation system, initial conditions, and boundary conditions respectively. If there is additional available data, specify a data training set to strengthen the training;

[0018] Establish a loss function that includes multiple partial differential equation residual terms, initial condition and boundary condition residual terms, and data residual terms;

[0019] Train the neural network, minimize the loss function through the gradient descent algorithm, and find the optimal neural network weight coefficients;

[0020] Substitute the partial differential equations in the partial differential equation system of the multi-physical field evolution process of the IGBT chip layer into the loss function of the neural network through the corresponding weight coefficients respectively;

[0021] Considering the Dirichlet boundary conditions and initial conditions of the chip junction temperature and electric potential, as well as the error terms between the target values and the actual estimated values, and substituting them into the loss function of the neural network through the corresponding weight coefficients, so as to obtain a neural network that embeds the multi-physics field evolution process and constraints of the IGBT chip layer.

[0022] In some embodiments, the considered arbitrary integer-order partial differential equation system is:

[0023]

[0024] u(x,t0) = I(x,t0), x ∈ Ω

[0025] where u is the solution vector of the above partial differential equation system, and f i [x,t,u(x,t),...; λ] is the zero-term of i partial differential equations with parameter λ, and Ω is a subset of R D , is the boundary of Ω, t0 is the initial time, and t T is the terminal time, I(x,t0) is the zero initial condition of the equation system, and B(x,t) is the boundary condition of the equation system.

[0026] In some embodiments, the established loss function is:

[0027]

[0028] where is the residual term of the partial differential equation, and are the residual terms of the boundary condition and the initial condition respectively, is the data residual term, u * (x,t) is the true value of the additional data, w fi , w b , w i , w d are the weight coefficients of each residual term respectively, n(x,t; θ) is the neural network, is the training set of the partial differential equation, is the training set of the initial boundary, is the training set of the boundary condition, is the data training set.

[0029] In some embodiments, the Dirichlet boundary conditions and initial conditions are:

[0030] T - B T (x,y,z,t) = 0

[0031] V - B v (x,y,z,t) = 0

[0032] T - I T (x, y, z, t0) = 0

[0033] V - I v (x, y, z, t0) = 0

[0034] The error term between the target value and the actual estimated value is as follows:

[0035] T - T * (x, y, z, t) = 0

[0036] V - V * (x, y, z, t) = 0

[0037] where B T B(x, y, z, t) and B v B(x, y, z, t) respectively represent the Dirichlet boundary conditions of the chip junction temperature and the electric potential; I T I(x, y, z, t0) and I v I(x, y, z, t0) respectively represent the Dirichlet initial conditions of the chip junction temperature and the electric potential; T * T(x, y, z, t) represents the actual estimated value of the junction temperature; V * V(x, y, z, t) represents the actual estimated value of the electric potential.

[0038] In some embodiments, the weight coefficient of each residual term is composed of the reciprocal of the arithmetic mean of the loss function values at the zero - step of this term.

[0039] In some embodiments, establishing the PINN numerical calculation model incorporating the partial differential equation system further includes:

[0040] Performing linear normalization processing on each input and output of the neural network;

[0041] Substituting each normalization coefficient into the partial differential equation system of the multi - physical - field evolution process of the IGBT chip layer to obtain a normalized partial differential equation system, and establishing a PINN numerical calculation model based on this normalized partial differential equation system.

[0042] On the other hand, the present application also proposes a multi - physical - field dynamic numerical calculation system for the IGBT chip layer, and the system includes:

[0043] A coupling analysis module, which is used to establish the partial differential equation system of the multi - physical - field evolution process of the IGBT chip layer;

[0044] And an iterative solution module, which is used to establish a PINN numerical calculation model incorporating the partial differential equation system to realize the numerical calculation of the multi - physical - field dynamic process of the IGBT chip layer.

[0045] An IGBT chip layer multi-physical field dynamic numerical calculation method and system proposed in this application first established a partial differential equation system for multi-physical field coupling inside the IGBT, and based on this, proposed an IGBT chip layer coupled physical field dynamic numerical calculation method based on ETM-PINN, which can realize the embedding of an analytical physical model into a data-driven algorithm and standardize the optimization solution process of the algorithm, so as to flexibly handle accurate numerical calculations in various data model configuration situations;

[0046] An IGBT chip layer multi-physical field dynamic numerical calculation method and system proposed in this application can achieve accurate numerical solution of the multi-physical fields of the IGBT chip layer by using the laws of relevant physical models in the absence of data; this application can also complete the dynamic numerical calculation of the multi-physical coupling field with reduced accuracy in the case of incomplete physical models or missing key parameters; this application can also flexibly and fully utilize relevant data and models for fusion calculation in the case of additional data in the physical field, comprehensively improving the calculation and solution accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The drawings described herein are used to provide a further understanding of the embodiments of the present application, form a part of the present application, and do not limit the embodiments of the present application. In the drawings:

[0048] Figure 1 is the method flow chart proposed in the embodiment of the present application;

[0049] Figure 2 is a schematic diagram of the multi-physical field coupling principle inside the IGBT;

[0050] Figure 3 is a schematic diagram of the ETM-PINN numerical calculation model architecture established in the embodiment of the present application;

[0051] Figure 4 is the system principle block diagram proposed in the embodiment of the present application;

[0052] Figure 5 is the dynamic numerical solution result of the junction temperature and electric potential without data;

[0053] Figure 6 is the prediction calculation result of the reduced accuracy of the junction temperature and electric potential when key parameters of the model are missing;

[0054] Figure 7 is the data-model fusion calculation result when there is electric potential data;

[0055] Figure 8 is the data-model fusion calculation result when there are temperature and electric potential data. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] To make the objectives, technical solutions, and advantages of this application clearer and more understandable, the following further elaborates on this application in combination with embodiments and the accompanying drawings. The illustrative embodiments of this application and their descriptions are only used to explain this application and do not limit this application.

[0057] Embodiment 1:

[0058] Currently, the numerical calculation methods for key physical quantity values of semiconductor power devices such as IGBT mainly include model-based methods and data-based methods. However, the model-based methods have certain limitations and the calculation gap problem of multi-model joint calculation. The performance of data-based methods strongly depends on the performance of the data and is less adaptable to complex coupled physical systems. In response to this, this embodiment proposes a multi-physical field dynamic numerical calculation method for IGBT chip layers. The method proposed in this embodiment realizes the embedding of an analytical physical model into a data-driven algorithm and standardizes the optimization solution process of the algorithm by establishing a mathematical model of relevant multi-physical field coupling and the ETM-PINN algorithm, so as to flexibly handle accurate numerical calculations in various data model configuration situations, providing data and model support for the health management and fault prediction of semiconductor power devices such as IGBT, reducing the operation risk and maintenance cost of the system, and improving the safe operation level and guarantee ability.

[0059] As Figure 1 shown, the method proposed in this embodiment includes the following steps:

[0060] Step 100, establish a partial differential equation system for the multi-physical field evolution process of the IGBT chip layer.

[0061] In semiconductor power devices such as IGBT, a multi-physical coupling field mainly composed of electricity-thermal-mechanics widely exists, which dominates the evolution of each key state quantity inside the component. Affected by the thermal effect caused by the electric field power loss, the conductivity and thermal conductivity of the encapsulation material inside the IGBT will change and evolve with the temperature, and due to the differences in the thermal expansion processes of different materials, the contact resistance and contact thermal resistance inside the device will be changed. The principle of this multi-physical field coupling is as Figure 2 shown.

[0062] In this multi-physical coupling field, the electric field is mainly restricted by the charge conservation equation, the total current density equation, the electric field distribution equation, and the electric displacement formula, as shown in Equations (1)-(4).

[0063]

[0064] D = ε0ε r E (4)

[0065] Among them, is the Nabla operator, J is the current density vector, ρ eρ is the volume charge density, σ is the conductivity, E is the electric field strength vector, D is the electric displacement vector, t is the time, J e is the induced current density vector, V is the electric potential, ε0 and ε r are the vacuum permittivity and the relative permittivity, respectively.

[0066] The thermal field is mainly restricted by the heat conduction equation, the heat flux distribution equation and the electric field loss equation, as shown in Eqs. (5)-(7).

[0067]

[0068] Q e =J·E(7)

[0069] where ρ is the density, C p is the constant-pressure heat capacity, T is the temperature, u is the convection velocity vector, q is the heat flux vector, k is the thermal conductivity, Q e is the electric field heat source.

[0070] The mechanical field is mainly restricted by the deformation displacement equation, the solid thermal expansion and the thermal stress equation, as shown in Eqs. (8)-(11).

[0071]

[0072] S i =a i ΔTl0 (9)

[0073] F s,i =Ea i ΔT (10)

[0074]

[0075] where S is the solid deformation displacement vector, F s is the thermal stress vector, v is the deformation displacement velocity vector, a i is the thermal expansion coefficient in the i direction, ΔT is the temperature difference between the current and the initial moments, l0 is the initial length, and E is the elastic modulus.

[0076] Considering that the IGBT is in a fixed state in the simulation model, the convection term in the heat conduction equation and the acceleration term in the deformation displacement equation can be ignored; considering that the electromagnetic induction effect is weak when the IGBT is constantly energized, the induced current density term can be ignored; considering that the change rate of the charge density of the IGBT chip layer is very small under a constant current, the current flux through any closed surface can be approximated as 0 (especially in the steady-state process); at the same time, considering the isotropic material coefficients, Eqs. (1)-(11) can be further simplified.

[0077] Substituting Eqs. (2)-(4) into Eq. (1) and expanding, the electric field governing equation can be obtained, as shown in Eq. (12).

[0078]

[0079] Substituting equations (6)-(7) into equation (5) and expanding them, we can obtain the thermal field governing equation, as shown in equation (13).

[0080]

[0081] Substituting equations (9)-(11) into equation (8) and expanding them, we can obtain the mechanical field governing equation, as shown in equation (14).

[0082]

[0083] By combining equations (12) to (14), we can obtain the set of partial differential equations that govern the evolution of the IGBT electric-thermal-mechanical coupling field.

[0084] Step 200, establishing a PINN numerical calculation model with an embedded partial differential equation group to realize numerical calculation of multi-physical field dynamic process at the IGBT chip layer.

[0085] Taking into account the temperature effect of material coefficients, the conductivity and thermal conductivity in the equation group are functions that change with temperature. For the silicon chip layer of the IGBT, considering the physical properties in the on state, after correction and conversion of the measured data, the calculation formulas for conductivity and thermal conductivity are:

[0086] σ=78.847×(1-1.3534×10 -3 ×(T-273.15))(15)

[0087] k=131-0.4129×(T-298.15) (16)

[0088] Consider an arbitrary system of integer-order partial differential equations:

[0089]

[0090] Where u is the solution vector of the above partial differential equations, f i [x, t, u(x, t), ...; λ] are i partial differential equations with parameter λ and always zero terms, Ω is R D A subset of is the boundary of Ω, t0 is the initial time, t T is the terminal moment, I(x,t0) is the zero initial condition of the equation system, and B(x,t) is the boundary condition of the equation system.

[0091] First, construct a multi-input multi-output neural network n(x, t; θ) as the initial solution vector u, specify the corresponding training set for the partial differential equation and the initial and boundary conditions If there is additional available data, a data training set can also be specified to strengthen the training. Then, a loss function is defined that includes the residual terms of the PDEs, the residual terms of the initial and boundary conditions, and the data residual terms This loss function is defined as:

[0092]

[0093] where is the residual term of the partial differential equation, and are the residual terms of the boundary conditions and the initial conditions, is the data residual term, u * (x,t) is the true value of the additional data, w f , w b , w i , w d are the weight coefficients of each residual term respectively. The partial derivative calculation here uses the automatic differentiation technique, and the physical laws are embedded into the neural network by introducing the regularization residual terms of the partial differential equation system and its initial and boundary conditions.

[0094] Then, the above neural network is trained to find the optimal neural network weight configuration by minimizing the loss function through the gradient descent algorithm.

[0095]

[0096] The neural network trained to convergence through Equation (23) is the approximate solution of the partial differential equation system (Equation (17)).

[0097] In this embodiment, a PINN numerical calculation model is established for the complex coupled multi-physical fields existing inside the IGBT. The partial differential equation systems (Equations (12) - (14)) of the electro-thermal-mechanical coupling field evolution process of the IGBT chip layer obtained above are respectively substituted into the loss function of the neural network through the weight coefficients . The temperature effect functions of the material coefficients (Equations (15) - (16)) are introduced for the conductivity σ and the thermal conductivity k, and the Dirichlet boundary conditions and initial conditions of the chip junction temperature and the electric potential are considered:

[0098]

[0099] where B T (x,y,z,t) and B v (x,y,z,t) respectively represent the Dirichlet boundary conditions of the chip junction temperature and the electric potential; I T (x,y,z,t0) and I v (x,y,z,t0) respectively represent the Dirichlet initial conditions of the chip junction temperature and the electric potential.

[0100] and the error term between the target value and the actual estimated value:

[0101]

[0102] where T * (x, y, z, t) represents the actual estimated value of the junction temperature, and V * (x, y, z, t) represents the actual estimated value of the electric potential.

[0103] Substitute each equation from Equation (24) to Equation (25) into the inner term of the Euclidean norm of Equation (20) to Equation (21), and through the weight coefficients w b , w i , w d Substitute into the loss function of the neural network. Thus, a dedicated neural network for embedding the electro-thermal-mechanical coupling field evolution mechanism and constraints of the silicon chip layer is obtained, and the training process of the neural network is adjusted to automatically conform to the embedded physical laws.

[0104] To balance the influence of residuals of different orders of magnitude on the optimization process, each weight coefficient is composed of the reciprocal of the arithmetic mean of the loss function values at the zero-th step of each item:

[0105]

[0106] Since the neural network of this problem is a multi-input multi-output system, and the numerical differences between the input and output items are significant, in this embodiment, linear normalization processing is performed on each input and output:

[0107]

[0108] x i = [max(x i ) - min(x i )]x i ' + min(x i ) = a i x i ' + b i (28)

[0109] Considering that the normalization process itself performs a linear transformation on the variables, it will have an impact on the partial derivative coefficients in the partial differential equation system, and its impact process is shown in Equation (29):

[0110]

[0111] Substitute each normalization coefficient Substituting into the partial differential equation system (Equations (12)-(14)) gives the partial differential equation system after variable normalization. The scaling transformation caused by physical units is exactly canceled out in the normalization transformation and can be ignored. The schematic diagram of the principle of the PINN algorithm (ETM-PINN) that incorporates the electro-thermal-mechanical coupling field law of IGBT is as Figure 3 shown.

[0112] The PINN algorithm transforms the traditional numerical calculation problem into an iterative optimization problem. The trained neural network itself is a particular solution of the partial differential equation system. Compared with other optimization algorithms, the key to its ability to handle partial differential equations well lies in its full utilization of the automatic differentiation technology in the gradient descent process of the BP algorithm, making the partial derivative calculation process in this algorithm symbolic differentiation based on the chain rule, thus eliminating the error of the difference operation, and enabling the deep combination of the two fields. Compared with traditional numerical calculation methods, it has the advantages of being meshless and the data model information can be flexibly applied for solution.

[0113] In this embodiment, aiming at the problem that it is difficult to monitor the key physical variables inside the IGBT at present, first, a partial differential equation system for the electro-thermal-mechanical coupling field evolution process inside the IGBT is integrated and established, and then a PINN numerical calculation model incorporating the electro-thermal-mechanical coupling field evolution law of the IGBT chip layer is established. It can not only numerically solve the chip layer junction temperature and potential field in the absence of data, but also perform multi-physical field prediction calculations with reduced accuracy in the case of missing key coefficients of the partial differential equation system, and perform data-model fusion calculations in the case of additional data in the physical field to further improve the solution accuracy.

[0114] Based on the same technical concept as above, this embodiment also proposes a multi-physical field dynamic numerical calculation system for the IGBT chip layer, as Figure 4 shown. The system proposed in this embodiment includes:

[0115] A coupling analysis module, which is used to establish a partial differential equation system for the multi-physical field evolution process of the IGBT chip layer.

[0116] And an iterative solution module, which is used to establish a PINN numerical calculation model incorporating the partial differential equation system to realize the numerical calculation of the multi-physical field dynamic process of the IGBT chip layer.

[0117] It should be noted that the specific implementation process of the above functional modules is as described in the above method and will not be elaborated here.

[0118] Embodiment 2

[0119] In this embodiment, the silicon chip layer of the IGBT module 2MBIVA-20-50 is selected for numerical simulation calculation to verify the effectiveness of the method proposed in the above-mentioned Embodiment 1 in the dynamic numerical calculation of the internal state variables of the IGBT.

[0120] All the neural network architectures used for verification calculation in this embodiment adopt the fully connected method. From the finite element model established by Comsol, it is observed that the temperature and electric potential solutions of this problem are relatively smooth. Considering the convergence speed problem, the activation function Tanh with continuous high-order derivatives is selected, and the initial weight θ0 of the network is randomly sampled using Glorot uniform with a uniform distribution. Table 1 shows the main simulation parameters in the ETM-PINN algorithm, and the relevant parameters of the material are all the material coefficients of silicon.

[0121] Table 1 Main simulation parameters in the ETM-PINN algorithm

[0122]

[0123] The Comsol model simulates the heating process of a 1200V / 75A IGBT at room temperature of 298.15K for 0-30 seconds through finite element calculation. The collector and emitter are in a constantly conducting state. Considering that the heat transfer coefficient between the IGBT surface and air is almost negligible compared with that between the copper substrate and the radiator, only the bottom surface of the copper substrate is set as the boundary of convective heat dissipation. The relevant material coefficients of the IGBT chip layer in the Comsol simulation process are the same as those in Table 1, and some of the simulation results are used for neural network training and numerical calculation accuracy comparison.

[0124] (1) Traditional data-driven algorithms strongly depend on the quantity and quality of data. Since the ETM-PINN embeds the partial differential equation group of the electro-thermal-mechanical field evolution process of the IGBT, it can reduce the dependence on data to a certain extent. First, considering the case without internal data of the IGBT chip layer, only the partial differential equation group (Equations (12)-(14)) and the point boundary and initial conditions (Equation (24)) are used for numerical solution of the dynamic processes of the junction temperature and electric potential. 30,000 points are randomly taken in the four-dimensional Euclidean space of the chip layer from 0 to 30s, and other parameters and hyperparameters are set according to Table 1.

[0125] After training, the total average residual converges to 2.5618×10 -4 , compared with the Comsol model, the global RMSE of the temperature field from 0 to 30s is 0.3526, and the MAPE is 0.07636%. The global RMSE of the electric potential field from 0 to 30s is 0.003967, and the MAPE is 0.09565%. The transient numerical calculation results of the temperature and electric potential fields at 5s, 15s, and 30s and the errors at this moment are as Figure 5As shown in the figure. From this, it can be observed that the dynamic numerical calculation results of the two fields are relatively balanced and have high precision.

[0126] (2) Considering the temperature effect and semiconductor effect of the silicon chip layer material, the thermal conductivity and electrical conductivity of IGBT in actual operation are greatly affected by variables such as driving voltage and temperature. The experimental and fitting costs of the measured functions of these two material coefficients (Equations (15)-(16)) are relatively high. The lack of such key coefficients brings difficulties to traditional numerical calculation methods. Since PINN is essentially an iterative optimization algorithm that embeds physical laws, it has a relatively high compatibility with the integrity and accuracy of the model. It can follow complete physical laws during the training process, and can also obey the basic differential relations of the physical field in the case of missing key coefficients of the model, so as to reduce the accuracy and realize the prediction calculation of the dynamic numerical values of multiple physical fields.

[0127] Similarly, considering the case without internal data of the IGBT chip layer, only use the incomplete partial differential equations (Equations (12)-(14)) and point boundary and initial conditions (Equation (24)) to predict and calculate the dynamic process of the junction temperature and potential field. Randomly select 30,000 points in the four-dimensional Euclidean space of the chip layer from 0 to 30 s. The thermal conductivity and electrical conductivity are set to the rough values of 100 W / (m·K) and 100 S / m when the general semiconductor is conducting. Other parameters and hyperparameters are still set according to Table 1.

[0128] After the training is completed, the total average residual converges to 2.7838×10 -4 , compared with the Comsol model, the global RMSE of the temperature field from 0 to 30 s is 0.7662, and the MAPE is 0.1886%. The global RMSE of the potential field from 0 to 30 s is 0.01649, and the MAPE is 0.5203%. The transient prediction calculation results of the temperature and potential fields at 5 s, 15 s, and 30 s and the errors at this moment are as Figure 6 shown. It can be observed that in the case of an incomplete physical model, ETM-PINN can still complete the prediction calculation of the dynamic numerical values of the coupled physical fields with reduced accuracy.

[0129] (3) Considering the situation where there may be certain IGBT electric field data in the actual working conditions, the numerical solutions of unknown physical fields can be predicted and calculated across fields by using relevant coupled physical field data and coupling relationships. In the case of no internal data of the IGBT chip layer temperature field, partial data of the electric potential field (Equation (25)), partial differential equation sets (Equations (12)-(14)), and point boundary and initial conditions (Equation (24)) are used for numerical calculations of the dynamic processes of the junction temperature and electric potential. 30,000 points are randomly selected in the four-dimensional Euclidean space of the chip layer from 0 to 30 s. The training set has labels of electric potential field data. The weight coefficients wj of each residual term of the loss function are adjusted accordingly according to Equation (Equation (26)), and other parameters and hyperparameters are set according to Table 1.

[0130] After training, the total average residual converges to 2.0085×10 -4 , compared with the Comsol model, the global RMSE of the temperature field from 0 to 30 s is 0.2837, the MAPE is 0.06159%, the global RMSE of the electric potential field from 0 to 30 s is 0.002414, and the MAPE is 0.05959%. The transient numerical calculation results of the temperature and electric potential fields at 5 s, 15 s, and 30 s and the errors at this moment are as Figure 7 shown. It can be seen that in the case of having partial solution field data, the dynamic numerical calculation accuracy of this field of ETM-PINN has been improved to a certain extent, and through the coupling relationship of partial differential equations, the calculation accuracy of adjacent physical fields has also been improved to a certain extent.

[0131] (4) If there is still temperature field data, the solution accuracy of multiple physical fields can be further improved. Only add partial data of the temperature field (Equation (25)) under the conditions of (3) above.

[0132] After training, the total average residual converges to 1.9136×10 -4 , compared with the Comsol model, the global RMSE of the temperature field from 0 to 30 s is 0.1853, the MAPE is 0.04011%, the global RMSE of the electric potential field from 0 to 30 s is 0.001788, and the MAPE is 0.04483%. The transient numerical calculation results of the temperature and electric potential fields at 5 s, 15 s, and 30 s and the errors at this moment are as Figure 6 shown. It can be seen that in the case of having more solution field data, the dynamic numerical calculation accuracy of the coupled field of ETM-PINN has been comprehensively improved.

[0133] It can be verified through the above simulation tests that the method proposed in the embodiments of the present invention can not only achieve the numerical solution of the chip layer junction temperature and potential field in the case of no data, but also perform predictive calculations of multi-physical fields with reduced accuracy in the case of missing key coefficients of partial differential equations, and perform data-model fusion calculations in the case of additional data in the physical field, further improving the solution accuracy.

[0134] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application 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.

[0135] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the specified functions in one Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0136] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implement the specified functions in one Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the specified functions in one Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0138] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of this application. It should be understood that the above description is only the specific embodiments of this application and is not used to limit the protection scope of this application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this application shall be included within the protection scope of this application.

Claims

1. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer, characterized in that, The method includes: Establishing a partial differential equation system for the multi-physical field evolution process of the IGBT chip layer; Establishing a PINN numerical calculation model embedded with the partial differential equation system to achieve numerical calculation of the multi-physical field dynamic process of the IGBT chip layer.

2. The multi-physical field dynamic numerical calculation method for an IGBT chip layer according to claim 1, wherein The partial differential equation system for the multi-physical field evolution process of the IGBT chip layer established is: where σ is the conductivity, V is the electric potential, ε0 and ε r are the permittivity of free space and the relative permittivity respectively, x, y and z are the X, Y, Z directions of the chip layer respectively, T is the temperature, ρ is the density, C p is the heat capacity at constant pressure, k is the thermal conductivity, t is the time, ΔT is the temperature difference between the current and initial times, a is the coefficient of thermal expansion, and E is the elastic modulus.

3. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer according to claim 2, characterized in that, The calculation formulas for the conductivity and thermal conductivity are: σ = 78.847×(1 - 1.3534×10 -3 ×(T - 273.15)) k = 131 - 0.4129×(T - 298.15).

4. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer according to any one of claims 1-3, characterized in that The establishment of the PINN numerical calculation model embedded with the partial differential equation system specifically includes: Considering an arbitrary integer-order partial differential equation system, which includes multiple partial differential equation zero-term with parameters, as well as initial conditions and boundary conditions; Constructing a multi-input multi-output neural network as the initial solution vector, and specifying corresponding training sets for the arbitrary integer-order partial differential equation system, initial conditions, and boundary conditions respectively. If there is additional available data, specify a data training set to strengthen the training; Establishing a loss function that includes multiple partial differential equation residual terms, initial condition and boundary condition residual terms, and data residual terms; Training the neural network, minimizing the loss function through the gradient descent algorithm to find the optimal neural network weight coefficients; Substituting the partial differential equations in the partial differential equation system for the multi-physical field evolution process of the IGBT chip layer into the loss function of the neural network through the corresponding weight coefficients; Considering the Dirichlet boundary conditions and initial conditions of the chip junction temperature and electric potential, as well as the error terms between the target value and the actual estimated value, and substituting them into the loss function of the neural network through the corresponding weight coefficients, so as to obtain a neural network embedded with the multi-physical field evolution process and constraints of the IGBT chip layer.

5. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer according to claim 4, characterized in that, The considered arbitrary integer-order partial differential equation system is: u(x,t0) = I(x,t0), x ∈ Ω where \(u\) is the solution vector of the above partial differential equations, \(f\) i [x,t,u(x,t),...;\(\lambda\)] is the zero term of \(i\) partial differential equations with parameter \(\lambda\), \(\Omega\) is a subset of \(R\) D , is the boundary of \(\Omega\), \(t_0\) is the initial time, \(t\) T is the terminal time, \(I(x,t_0)\) is the zero initial condition of the equations, and \(B(x,t)\) is the boundary condition of the equations.

6. The multi-physical field dynamic numerical calculation method for an IGBT chip layer according to claim 5, wherein The established loss function is: Among them, is the residual term of the partial differential equation, and are the residual terms of the boundary condition and the initial condition respectively, is the data residual term, u * (x,t) is the true value of the additional data, w fi ,w b ,w i ,w d are the weight coefficients of each residual term respectively, n(x,t;θ) is the neural network, is the training set of the partial differential equation, is the training set of the initial boundary, is the training set of the boundary condition, is the data training set.

7. A method for dynamic numerical calculation of multi-physical fields of an IGBT chip layer according to claim 6, characterized in that, The Dirichlet boundary conditions and initial conditions are: T-B T (x, y, z, t) = 0 V-B v (x, y, z, t) = 0 T-I T (x, y, z, t0) = 0 V-I v (x, y, z, t0) = 0 The error terms between the target value and the actual estimated value are: T-T * (x, y, z, t) = 0 V-V * (x, y, z, t) = 0 Among them, B T (x, y, z, t) and B v (x, y, z, t) represent the Dirichlet boundary conditions of the chip junction temperature and electric potential respectively; I T (x, y, z, t0) and I v (x, y, z, t0) represent the Dirichlet initial conditions of the chip junction temperature and electric potential respectively; T * (x, y, z, t) represents the actual estimated value of the junction temperature; V * (x, y, z, t) represents the actual estimated value of the electric potential.

8. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer according to claim 6, characterized in that The weight coefficients of each residual term are composed of the reciprocal of the arithmetic mean of the loss function values of the term at the zero step.

9. A dynamic numerical calculation method for multi-physical fields of an IGBT chip layer according to claim 4, characterized in that, The establishment of the PINN numerical calculation model embedded with the partial differential equation system further includes: Performing linear normalization processing on the input and output of each item of the neural network; Substituting the normalization coefficients into the partial differential equation system for the multi-physical field evolution process of the IGBT chip layer to obtain a normalized partial differential equation system, and establishing a PINN numerical calculation model based on the normalized partial differential equation system.

10. An IGBT chip layer multi-physical field dynamic numerical calculation system, characterized in that, The system includes: A coupling analysis module, which is used to establish a partial differential equation system for the multi-physical field evolution process of the IGBT chip layer; And an iterative solution module, which is used to establish a PINN numerical calculation model embedded with the partial differential equation system to achieve numerical calculation of the multi-physical field dynamic process of the IGBT chip layer.

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