Multi-physics coupling modeling and verification method and system for gallium nitride radio frequency device

Abstract

The invention provides a gallium nitride radio frequency device multi-physics field coupling modeling and verification method and system, and relates to the technical field of modeling, and the method comprises the steps: carrying out the dynamic coupling calculation of physical parameters of a device through a temperature variation iterative algorithm, and building an electrothermal coupling field distribution function; constructing a self-adaptive iterative calculation equation to calculate high-frequency working state physical characteristic parameters; performing discretization processing by adopting a finite element method to obtain field distribution parameters; and correcting the coupling prediction equation based on the measured parameters of the low-frequency working state. According to the method, the model precision can be improved, and the calculation complexity of the gallium nitride radio frequency device model is reduced.

Description

Technical Field

[0001] The present invention relates to the field of modeling technology, and in particular to a method and system for modeling and verifying multi-physics coupling of gallium nitride radio frequency devices. Background Art

[0002] Gallium nitride (GaN) has become a key semiconductor material in the RF and microwave fields due to its excellent properties, including wide bandgap, high breakdown electric field, high saturation electron velocity, and good thermal stability. With the rapid development of 5G communications, satellite communications, radar systems, and other fields, the performance requirements for GaN RF devices are constantly increasing, especially in terms of reliability and stability under high-frequency and high-power operating conditions. During the operation of GaN RF devices, complex multi-field coupling effects occur, including interactions between various physical fields such as electric fields, thermal fields, and stress fields. These effects have a significant impact on the electrical performance and reliability of the devices.

[0003] Traditional GaN RF device modeling approaches typically consider each physical field separately, ignoring the mutual coupling between these fields. This results in significant discrepancies between model predictions and actual operating conditions. Especially under high-frequency and high-power operating conditions, the interactions between device internal temperature distribution, thermal stress, and electrical parameters are even more complex, making a single physical field model incapable of accurately reflecting the device's actual operating conditions.

[0004] Current multi-physics coupling modeling and verification methods for GaN RF devices suffer from the following deficiencies and shortcomings: The existing technology lacks an effective temperature variation iteration algorithm, making it impossible to accurately calculate the dynamic coupling of the physical parameters of GaN devices under high-frequency operating conditions, resulting in insufficient accuracy in the electrothermal coupling field distribution model. Conventional modeling methods also struggle to establish a correlation between high-frequency and low-frequency operating conditions, making it impossible to use measured data from low-frequency operating conditions to verify and correct models under high-frequency operating conditions, increasing verification costs and difficulty. Summary of the Invention

[0005] The embodiments of the present invention provide a gallium nitride radio frequency device multi-physics field coupling modeling and verification method and system, which can solve the problems in the prior art.

[0006] A first aspect of an embodiment of the present invention provides a multi-physics field coupling modeling and verification method for a gallium nitride radio frequency device, comprising: Obtaining physical parameters of the GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device; Constructing an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculating the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; Substituting the physical characteristic parameters into the electrothermal coupling field distribution function, performing discretization processing using the finite element method, and calculating the field distribution parameters under the high-frequency working state; Establishing a coupling prediction equation based on the field distribution parameters, substituting the physical characteristic parameters into the coupling prediction equation, and calculating the prediction parameters under the low-frequency working state; The measured parameters under the low-frequency working state are collected, and the multi-layer mathematical expression of the coupled prediction equation is corrected using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

[0007] Obtaining physical parameters of the GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device, including: Constructing an electron transport equation and an energy balance equation based on the physical parameters of the gallium nitride radio frequency device; constructing a variational iterative expression based on the electron transport equation and the energy balance equation, the variational iterative expression including a temperature-dependent term, calculating a carrier mobility value based on the variational iterative expression, correcting the carrier mobility value according to the temperature-dependent term, and substituting the corrected carrier mobility value into the variational iterative expression to solve the electric field distribution function; Establishing a grid coordinate axis for the device structure corresponding to the physical parameters of the gallium nitride radio frequency device, substituting the electric field distribution function into the grid coordinate axis to calculate a Joule heating value, substituting the Joule heating value into the energy balance equation to calculate a heat dissipation value, and constructing a thermal field distribution function based on the Joule heating value and the heat dissipation value; A temperature distribution function is constructed according to the Joule heat value and the heat dissipation value, the temperature distribution function is substituted into the temperature-related term, the carrier mobility value is recalculated, and the updated carrier mobility value is substituted into the variational iterative expression to obtain the electrothermal coupling field distribution function.

[0008] An adaptive iterative calculation equation is constructed according to the electrothermal coupling field distribution function, and physical characteristic parameters under high-frequency working state are calculated by the adaptive iterative calculation equation, including: Substituting the temperature field component and the electric field component in the electrothermal coupling field distribution function into the Lagrange equation to construct a variational expression, and establishing an adaptive iterative calculation equation based on the variational expression; Analyzing the carrier concentration threshold using the temperature field component to construct a carrier concentration correction factor, performing characteristic decomposition on the carrier concentration correction factor using the carrier concentration threshold to extract an iterative correction step size; Couple the iterative correction step size and the electric field component and map them to the adaptive iterative calculation equation to resolve the source current density and the drain current density; Substituting the source current density and the drain current density into the adaptive iterative calculation equation to calculate carrier mobility, and substituting the carrier mobility and the temperature field component into the adaptive iterative calculation equation to calculate thermal conductivity; A physical characteristic parameter is constructed according to the carrier mobility and the thermal conductivity, and the physical characteristic parameter is output as a calculation result of a high-frequency working state.

[0009] Utilizing the temperature field component to analyze the carrier concentration threshold, constructing a carrier concentration correction factor, performing characteristic decomposition on the carrier concentration correction factor through the carrier concentration threshold, and extracting an iterative correction step size, including: Establishing a carrier drift velocity equation based on the spatial temperature distribution value in the temperature field component, and establishing a carrier scattering equation based on the time temperature change rate in the temperature field component; The carrier drift velocity equation and the carrier scattering equation are coupled and mapped to the Boltzmann transport equation space to solve the carrier concentration threshold; Constructing a carrier concentration correction factor, and using the carrier concentration threshold to perform dynamic characteristic analysis on the collision frequency term and the transport loss term in the carrier concentration correction factor to obtain a collision correction coefficient and a loss correction coefficient; constructing an iterative step calculation matrix according to the collision correction coefficient and the loss correction coefficient, performing eigendecomposition on the spatial temperature distribution value and the iterative step calculation matrix, and extracting a temperature correction factor; The carrier concentration threshold is corrected and mapped using the temperature correction factor, and the iterative step length is analyzed and iterated by calculating the iterative step length matrix.

[0010] Substituting the physical characteristic parameters into the electrothermal coupling field distribution function, performing discretization processing using the finite element method, and calculating the field distribution parameters under the high-frequency working state include: Establishing a state equation group of the gallium nitride radio frequency device according to the physical characteristic parameters, and calculating correction coefficients of the physical characteristic parameters as they change with temperature and frequency based on the state equation group; multiplying the physical characteristic parameter by the correction coefficient to obtain a corrected physical characteristic parameter, substituting the corrected physical characteristic parameter into an electrothermal coupling field distribution function to construct a corrected electrothermal coupling field distribution function; constructing an initial finite element calculation grid based on the modified electrothermal coupling field distribution function, initializing the electric field intensity and temperature field at the grid nodes according to the modified physical characteristic parameters to obtain an initial field distribution; Using an adaptive grid refinement algorithm, the grid regions in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold are subdivided to construct a discretized set of equations; Solve the discretized equation group, calculate the electric field distribution and temperature distribution of each grid node based on the solution of the discretized equation group, correct the electric field distribution and the temperature distribution according to the correction coefficient, and obtain the field distribution parameters under the high-frequency working state.

[0011] The grid regions in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold are subdivided using an adaptive grid refinement algorithm to construct a discretized set of equations, including: constructing a grid encryption indicator function based on the electric field gradient and the temperature gradient, comparing the grid encryption indicator function with a preset gradient threshold, and determining a grid unit to be encrypted; Constructing a local encryption hierarchy tree based on the grid cells to be encrypted, calculating the encryption hierarchy depth of the local encryption hierarchy tree using the grid encryption indicator function, and performing binary splitting processing on the grid cells to be encrypted whose encryption hierarchy depth is greater than a first preset threshold; constructing transition units for the mesh area after the binary splitting process, calculating geometric features of the transition units, calculating a mesh quality factor based on the geometric features, and performing mesh smoothing on the transition units whose mesh quality factor is less than a second preset threshold; The degree of distortion of the encrypted mesh cells is evaluated using the mesh quality factor and the geometric features, and the mesh cells with a degree of distortion greater than a third preset threshold are subjected to a binary splitting process and a mesh smoothing process again, and the process is repeated until the mesh quality factor is greater than the second preset threshold; Based on the grid quality factor, encrypted grid cells that meet the grid quality requirement are screened, and a discretized set of equations is constructed using the geometric features of the encrypted grid cells.

[0012] A coupling prediction equation is established based on the field distribution parameters, and the physical characteristic parameters are substituted into the coupling prediction equation to calculate the prediction parameters under the low-frequency working state, including: Performing time domain decomposition and frequency domain decomposition on the field distribution parameters to obtain a time domain eigenvector and a frequency domain eigenvector; constructing a state transfer matrix based on the time domain eigenvector and the frequency domain eigenvector, and combining the state transfer matrix with the field distribution parameter to establish a coupling prediction equation; Extracting principal component features of the time domain eigenvector and the frequency domain eigenvector, constructing a feature mapping function, and performing dimensionality reduction processing on the coupling prediction equation using the feature mapping function to obtain a coupling prediction equation after dimensionality reduction; Calculating a feature weight coefficient based on the principal component feature, and performing a weighted combination of the feature weight coefficient and the physical characteristic parameter to obtain a weighted physical characteristic parameter; Utilizing the weighted physical characteristic parameters to perform parameter correction on the coupling prediction equation after dimensionality reduction, optimizing the coefficients of the coupling prediction equation, and obtaining an optimized coupling prediction equation; The optimized coupling prediction equation is substituted into the boundary conditions of the low-frequency working state, and the coupling prediction equation is solved to obtain the prediction parameters under the low-frequency working state.

[0013] A second aspect of an embodiment of the present invention provides a multi-physics field coupling modeling and verification system for gallium nitride radio frequency devices, including: The first unit is used to obtain physical parameters of the GaN RF device, perform dynamic coupling calculation on the physical parameters of the GaN RF device through a temperature variation iterative algorithm, and establish an electrothermal coupling field distribution function of the GaN RF device; The second unit is used to construct an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculate the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; The third unit is configured to substitute the physical characteristic parameters into the electrothermal coupling field distribution function, perform discretization processing using a finite element method, and calculate the field distribution parameters under the high-frequency working state; A fourth unit is configured to establish a coupling prediction equation based on the field distribution parameters, substitute the physical characteristic parameters into the coupling prediction equation, and calculate the prediction parameters under the low-frequency working state; The fifth unit is used to collect the measured parameters under the low-frequency working state, and correct the multi-layer mathematical expression of the coupled prediction equation using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

[0014] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0015] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0016] The beneficial effects of this application are as follows: The present invention uses a temperature variation iterative algorithm to perform dynamic coupling calculations on the physical parameters of GaN RF devices, establishes an electrothermal coupling field distribution function, and calculates the physical characteristic parameters under high-frequency operating conditions through adaptive iterative calculation equations. This method can accurately simulate the complex electrothermal coupling effects of GaN RF devices in actual operating environments, thereby improving the accuracy and reliability of the model.

[0017] The present invention uses the finite element method to discretize the electrothermal coupling field distribution function, calculates the field distribution parameters under the high-frequency working state, and establishes a coupling prediction equation based on these parameters, realizing parameter prediction from high-frequency to low-frequency working states, solving the problem of insufficient accuracy of traditional methods in cross-band characteristic prediction, and greatly reducing the modeling complexity.

[0018] This invention innovatively uses the comparison between measured parameters and predicted parameters to correct the multi-layer mathematical expression of the coupled prediction equation, realizing the self-correction and optimization functions of the model, significantly improving the prediction accuracy, and reducing the workload and cost of experimental verification, providing more reliable theoretical support and technical guidance for the design and application of gallium nitride RF devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a multi-physics field coupling modeling and verification method for gallium nitride radio frequency devices according to an embodiment of the present invention; Figure 2 This is the distribution diagram of the electrothermal coupling field of the GaN RF device; Figure 3 Schematic diagram of the system architecture for calculating the field distribution parameters of GaN RF devices under high-frequency working conditions. DETAILED DESCRIPTION

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0021] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0022] Figure 1 FIG. 1 is a flow chart of a multi-physics coupling modeling and verification method for a gallium nitride radio frequency device according to an embodiment of the present invention. Figure 1 As shown, the method includes: Obtaining physical parameters of the GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device; Constructing an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculating the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; Substituting the physical characteristic parameters into the electrothermal coupling field distribution function, performing discretization processing using the finite element method, and calculating the field distribution parameters under the high-frequency working state; Establishing a coupling prediction equation based on the field distribution parameters, substituting the physical characteristic parameters into the coupling prediction equation, and calculating the prediction parameters under the low-frequency working state; The measured parameters under the low-frequency working state are collected, and the multi-layer mathematical expression of the coupled prediction equation is corrected using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

[0023] In an optional embodiment, obtaining physical parameters of a GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device include: Constructing an electron transport equation and an energy balance equation based on the physical parameters of the gallium nitride radio frequency device; constructing a variational iterative expression based on the electron transport equation and the energy balance equation, the variational iterative expression including a temperature-dependent term, calculating a carrier mobility value based on the variational iterative expression, correcting the carrier mobility value according to the temperature-dependent term, and substituting the corrected carrier mobility value into the variational iterative expression to solve the electric field distribution function; Establishing a grid coordinate axis for the device structure corresponding to the physical parameters of the gallium nitride radio frequency device, substituting the electric field distribution function into the grid coordinate axis to calculate a Joule heating value, substituting the Joule heating value into the energy balance equation to calculate a heat dissipation value, and constructing a thermal field distribution function based on the Joule heating value and the heat dissipation value; A temperature distribution function is constructed according to the Joule heat value and the heat dissipation value, the temperature distribution function is substituted into the temperature-related term, the carrier mobility value is recalculated, and the updated carrier mobility value is substituted into the variational iterative expression to obtain the electrothermal coupling field distribution function.

[0024] In this embodiment, the physical parameters of the GaN RF device are first obtained. These parameters include but are not limited to: device geometry (gate length is 0.25 μm, gate width is 100 μm, source-drain spacing is 2.5 μm), material properties (such as the thermal conductivity of GaN is 130 W / (m·K), the specific heat capacity is 490 J / (kg·K), and the density is 6150 kg / m³), and doping concentration (typical value is 1×10¹ 8 cm⁻³), dielectric constant (8.9 for gallium nitride), carrier mobility (about 1500 cm² / (V·s) at room temperature), etc.

[0025] Based on the acquired physical parameters, the electron transport equation and energy balance equation are constructed. The electron transport equation describes the movement of carriers within the device, taking into account factors such as carrier drift, diffusion, and potential barriers. The energy balance equation describes the energy transfer and conversion process within the device, taking into account the generation of heat sources and the transfer of heat.

[0026] A variational iterative expression is constructed based on the electron transport equation and the energy balance equation. This expression includes a temperature-dependent term to describe the effect of temperature changes on carrier mobility. In practical applications, the relationship between carrier mobility and temperature can be expressed as follows: as the temperature increases, the carrier mobility decreases. For example, at room temperature (300K), the electron mobility of gallium nitride is approximately 1500 cm² / (V·s), but when the temperature rises to 400K, the electron mobility drops to approximately 1000 cm² / (V·s).

[0027] The variational iterative calculation process is as follows: The initial temperature is set to ambient temperature (300K), and the initial carrier mobility values ​​are calculated based on this temperature. For example, under the conditions of a gate voltage of -3V and a drain voltage of 10V, the initial mobilities in the gate-source-drain region are 1450cm² / (V·s), 1480cm² / (V·s), and 1350cm² / (V·s), respectively. These initial mobility values ​​are substituted into the variational iterative expression to solve for the electric field distribution function.

[0028] After the electric field distribution is solved, a grid coordinate system is established for the GaN RF device. In this example, a 100×100×50 three-dimensional grid is established, with the x-axis corresponding to the width of the device, the y-axis corresponding to the length of the device, and the z-axis corresponding to the depth of the device. The grid spacing is 0.05μm. The electric field distribution function is substituted into this grid coordinate system, and the Joule heating value at each grid point is calculated. For example, in the area below the gate, the Joule heating value can reach 1.2×10¹ 0 W / m³, while in the area near the drain, the Joule heat value is about 8.5×10 9 W / m³.

[0029] Substitute the calculated Joule heat value into the energy balance equation to calculate the heat dissipation value. Heat dissipation is mainly carried out through three ways: conduction, convection and radiation. In this embodiment, conduction is the main way of heat dissipation. Heat is transferred outward through the bottom substrate of the device. The thermal conductivity coefficient is set to 130W / (m·K). According to calculations, the heat dissipation rate in the gate area is about 9.8×10 9 W / m³, the drain region is approximately 7.2×10 9 W / m³.

[0030] A thermal field distribution function (TDF) was constructed based on the Joule heating and heat dissipation values. This function describes the heat distribution at various points within the device. The TDF shows that heat is primarily concentrated in the region between the gate and drain, particularly near the gate edge, which is consistent with the hotspot distribution in actual devices.

[0031] Based on the thermal field distribution function, a temperature distribution function is constructed. This temperature distribution function shows the temperature distribution at various points within the device during operation. For example, the temperature in the region below the gate can reach 375K, 75K higher than the ambient temperature; the temperature in the drain region is approximately 350K, 50K higher than the ambient temperature; and the temperature in the source region is approximately 325K, 25K higher than the ambient temperature.

[0032] Substituting the temperature distribution function into the temperature-dependent term, we recalculate the carrier mobility values. As the temperature increases, the carrier mobility decreases accordingly. For example, the mobility in the gate region decreases from an initial 1450 cm² / (V·s) to approximately 1100 cm² / (V·s), a decrease of approximately 24%. The mobility in the drain region decreases from an initial 1350 cm² / (V·s) to approximately 1050 cm² / (V·s), a decrease of approximately 22%.

[0033] Substitute the updated carrier mobility value into the variational iterative expression and recalculate the electric field distribution function. Repeat this process until the electric field and temperature distributions reach a stable state, that is, the difference between the results of the previous and next iterations is less than a preset threshold (such as 1%). Typically, convergence is achieved after 5-10 iterations.

[0034] The resulting electrothermal coupled field distribution function comprehensively considers the mutual influence of electric field and temperature distribution, and can more accurately describe the performance characteristics of GaN RF devices under actual operating conditions. This function can be used to analyze device hotspot distribution, reliability assessment, and performance optimization.

[0035] Figure 2This diagram shows the electrothermal coupling field distribution of a GaN RF device, clearly showing the gradient of the device's internal temperature distribution from 300K (blue) to 375K (red). The device structure shows the three key electrodes: source (S), gate (G), and drain (D). The source-drain spacing is 2.5μm, and the gate length is 0.25μm.

[0036] The thermal field distribution shows two distinct hotspots: Hotspot 1 at the gate edge and Hotspot 2 between the gate and drain. This is consistent with theoretical expectations, as the high electric field intensity at the gate edge leads to energy accumulation, while the impact ionization effect caused by electron drift in the region between the gate and drain generates significant Joule heating. Temperatures in these two regions can reach 370-375K, 70-75K higher than the ambient temperature (300K). These high temperatures reduce carrier mobility, further affecting the electric field distribution and creating an electrothermal coupling effect.

[0037] In an optional embodiment, an adaptive iterative calculation equation is constructed according to the electrothermal coupling field distribution function, and the physical characteristic parameters under the high-frequency working state are calculated by the adaptive iterative calculation equation, including: Substituting the temperature field component and the electric field component in the electrothermal coupling field distribution function into the Lagrange equation to construct a variational expression, and establishing an adaptive iterative calculation equation based on the variational expression; Analyzing the carrier concentration threshold using the temperature field component to construct a carrier concentration correction factor, performing characteristic decomposition on the carrier concentration correction factor using the carrier concentration threshold to extract an iterative correction step size; Couple the iterative correction step size and the electric field component and map them to the adaptive iterative calculation equation to resolve the source current density and the drain current density; Substituting the source current density and the drain current density into the adaptive iterative calculation equation to calculate carrier mobility, and substituting the carrier mobility and the temperature field component into the adaptive iterative calculation equation to calculate thermal conductivity; A physical characteristic parameter is constructed according to the carrier mobility and the thermal conductivity, and the physical characteristic parameter is output as a calculation result of a high-frequency working state.

[0038] In this embodiment, an adaptive iterative calculation equation is first constructed based on the electrothermal coupling field distribution function, and the physical characteristic parameters under the high-frequency working state are calculated using the equation.

[0039] When constructing the electrothermal coupling field distribution function, both the temperature field and the electric field components must be considered. The temperature field component, represented by T(x, y, z), describes the temperature distribution at each point in three-dimensional space. The electric field component, represented by E(x, y, z), describes the electric field intensity distribution at each point in three-dimensional space. These two components influence each other through physical property parameters, forming a coupled relationship.

[0040] Based on the temperature field components T(x, y, z) and the electric field components E(x, y, z), a variational expression can be constructed using the Lagrange equation. This variational expression takes into account the thermal and electrical energy of the system and is expressed as the integral of the system's total energy in the spatial and temporal domains. Specifically, the expression includes temperature gradient terms, electric field intensity terms, heat source terms, and power supply terms, which are interconnected through material parameters such as thermal conductivity and electrical conductivity. Based on this variational expression, an adaptive iterative calculation equation can be established. This equation is discretized using the finite element method to form a calculation equation in matrix form.

[0041] In a real-world case, for a semiconductor device with dimensions of 100 microns x 50 microns x 2 microns, the grid is divided into 10,000 cells, the initial value of the temperature field is set to the ambient temperature of 300 Kelvin, and the initial value of the electric field is calculated based on the applied voltage distribution, for example, the electric field distribution when the gate voltage is 5 volts and the drain voltage is 20 volts.

[0042] Using the temperature field component to analyze the carrier concentration threshold is a key step. In semiconductor devices, carrier concentration is exponentially related to temperature. When the temperature exceeds a certain threshold, the carrier concentration changes dramatically, affecting device performance. In this embodiment, the carrier concentration threshold is set as a function related to the material's bandgap. For silicon materials, when the temperature reaches 450 Kelvin, the carrier concentration increases by an order of magnitude, and this temperature point is set as the threshold point.

[0043] When constructing the carrier concentration correction factor, the influence of the temperature field on carrier concentration is taken into account. This correction factor is expressed as a function of temperature, reflecting the effect of temperature changes on carrier concentration. This correction factor is subjected to eigendecomposition, extracting the main eigenvalues ​​and eigenvectors, and determining the iterative correction step size. In actual calculations, for silicon-based devices, when the temperature increases from 300 Kelvin to 400 Kelvin, the carrier concentration correction factor changes from 1.0 to 1.8, corresponding to an iterative correction step size of 0.05.

[0044] The obtained iterative correction step size is coupled with the electric field component and mapped to the adaptive iterative calculation equation. By solving this set of equations, the source current density and drain current density can be analytically obtained. In the above device case, when the gate voltage is 5 volts and the drain voltage is 20 volts, the source current density is calculated to be 2.5×10^5 amperes per square centimeter, and the drain current density is 2.3×10^5 amperes per square centimeter. The difference between the two represents the current loss caused by thermal effects.

[0045] Substituting the source and drain current densities into the adaptive iterative calculation equations, the carrier mobility is calculated. In silicon-based semiconductors, carrier mobility decreases with increasing temperature, ranging from approximately 1400 square centimeters per volt-second at room temperature to 900 square centimeters per volt-second at 400 Kelvin. Substituting the carrier mobility and the temperature field components into the adaptive iterative calculation equations, the thermal conductivity is further calculated. The thermal conductivity of silicon is approximately 150 watts per meter per Kelvin at room temperature and gradually decreases with increasing temperature, dropping to approximately 120 watts per meter per Kelvin at 400 Kelvin.

[0046] Based on the carrier mobility and thermal conductivity calculated above, a physical property parameter matrix was constructed. This matrix contains key parameters of the device under high-frequency operation, such as effective thermal conductivity, effective electrical conductivity, maximum current density, and heat source distribution. In the test case, when the device operates at a frequency of 2 GHz, the effective thermal conductivity is 112 watts per meter Kelvin, the effective electrical conductivity is 3.5×10^5 Siemens per meter, the maximum current density is 2.8×10^5 amperes per square centimeter, and the maximum heat source power density is 15 watts per square millimeter. These physical property parameters are output as calculation results for high-frequency operation and can be used to guide device design and performance optimization.

[0047] Through the above technical solution, the electrothermal coupling effect under high-frequency working conditions can be accurately calculated, providing reliable parameter support for semiconductor device design and effectively improving the device's thermal management strategy and electrical performance optimization solution.

[0048] In an optional embodiment, the temperature field component is used to analyze the carrier concentration threshold, construct a carrier concentration correction factor, perform characteristic decomposition on the carrier concentration correction factor through the carrier concentration threshold, and extract the iterative correction step size, including: Establishing a carrier drift velocity equation based on the spatial temperature distribution value in the temperature field component, and establishing a carrier scattering equation based on the time temperature change rate in the temperature field component; The carrier drift velocity equation and the carrier scattering equation are coupled and mapped to the Boltzmann transport equation space to solve the carrier concentration threshold; Constructing a carrier concentration correction factor, and using the carrier concentration threshold to perform dynamic characteristic analysis on the collision frequency term and the transport loss term in the carrier concentration correction factor to obtain a collision correction coefficient and a loss correction coefficient; constructing an iterative step calculation matrix according to the collision correction coefficient and the loss correction coefficient, performing eigendecomposition on the spatial temperature distribution value and the iterative step calculation matrix, and extracting a temperature correction factor; The carrier concentration threshold is corrected and mapped using the temperature correction factor, and the iterative step length is analyzed and iterated by calculating the iterative step length matrix.

[0049] The present invention provides a carrier concentration threshold analysis method that achieves high-precision carrier concentration correction through temperature field component analysis. In actual application scenarios, when a semiconductor device is working, its internal temperature distribution and changes have a significant impact on carrier behavior. Collecting temperature field components is the first step in implementing this method. The spatial temperature distribution value can be obtained through a high-precision infrared thermal imaging system with a sampling accuracy of 0.01K and a spatial resolution of up to 5μm. At the same time, a fast-response thermocouple array is used to capture the temperature change rate in real time with a sampling frequency of 10kHz to ensure that transient temperature change characteristics are captured.

[0050] Based on the acquired spatial temperature distribution values, an equation for the carrier drift velocity is established. Specifically, data points are selected from a temperature range of 250K to 400K. The temperature value T(x,y,z) at each spatial location (x,y,z) is processed to calculate the carrier drift velocity v(T). For example, for silicon materials, when the temperature is 300K, the electron drift velocity is approximately 1.35×10^5 m / s. When the temperature rises to 350K, the drift velocity decreases to 1.20×10^5 m / s. By establishing a mapping table between temperature and drift velocity, accurate drift velocity calculation can be achieved.

[0051] A carrier scattering equation is established based on the time-temperature rate of change. The temperature rate of change, dT / dt, directly affects carrier scattering mechanisms, including phonon scattering, impurity scattering, and intercarrier scattering. Based on the collected temperature rate of change data, a model is established to determine the relationship between the scattering frequency and the temperature rate of change. For example, when the temperature rate of change is 2 K / μs, the phonon scattering frequency increases by approximately 15%, while the impurity scattering frequency changes little. This scattering equation accurately reflects the impact of dynamic temperature changes on the carrier scattering process.

[0052] The key step in resolving the carrier concentration threshold is to couple the carrier drift velocity equation with the carrier scattering equation to the Boltzmann transport equation space. This process uses a discrete grid method to divide the space into cells of 0.5 μm × 0.5 μm × 0.5 μm, and establishes a local carrier distribution function within each cell. Through iterative calculations, the effects of drift and scattering processes are comprehensively considered, ultimately resulting in a steady-state solution. For a typical MOSFET device, the threshold carrier concentration calculated using this method is 5.8 × 10^16 cm^-3 at a gate voltage of 1.2 V. This is very close to the experimentally measured value of 5.7 × 10^16 cm^-3, with a relative error of only 1.75%.

[0053] Constructing the carrier concentration correction factor involves processing the collision frequency term and the transport loss term. For the collision frequency term, a piecewise linearization is performed using the carrier concentration threshold calculated above. When the carrier concentration is below the threshold, the collision frequency is approximately constant; when the carrier concentration exceeds the threshold, the collision frequency increases nonlinearly. The collision correction factor α is obtained through dynamic characteristic analysis. In practical applications, the value of α typically varies between 0.85 and 1.15, depending on the specific temperature distribution. For example, for GaN devices in power amplifiers, when the hotspot temperature reaches 175°C, the α value is 1.12, indicating a 12% increase in the collision frequency.

[0054] For the transport loss term, we also use a carrier concentration threshold for characterization to obtain the loss correction factor β. The β value reflects the extent to which thermal effects affect energy loss during carrier transport. In a real-world example, a silicon-based power device operating at high temperature had a β value of 0.92, indicating that thermal effects increased transport loss by 8%. This method allows for precise quantification of the impact of temperature effects on carrier transport characteristics.

[0055] The iterative step calculation matrix M is constructed based on the collision correction factor α and the loss correction factor β. The M matrix is ​​typically n×n in size, where n is the number of spatial grids. Each element M(i,j) in the M matrix represents the carrier transfer probability from grid i to grid j, modulated by both α and β. The spatial temperature distribution and the iterative step calculation matrix are subjected to eigendecomposition, and the principal eigenvector is extracted as the temperature correction factor γ. For a 3×3×3 grid calculation area, γ is typically represented as a 27-dimensional vector, with each component corresponding to the correction factor for a grid point.

[0056] The temperature correction factor γ is used to correct the carrier concentration threshold and obtain the corrected threshold n' that takes the temperature effect into account. The correction mapping adopts a piecewise function form. In the area with a temperature below 300K, the deviation of n' from the original threshold n is less than 3%; while in the hot spot area with a temperature above 350K, the correction can reach more than 15%. Finally, the iterative step size δ is calculated by the iterative step size matrix analysis. In practical applications, the value of δ is usually between 0.05 and 0.2. A smaller δ value means a more stable but slower convergence iterative process, while a larger δ value may lead to faster convergence but with the risk of numerical instability. For complex three-dimensional device structures, δ = 0.1 is usually selected as the initial value and dynamically adjusted according to the convergence situation.

[0057] In an optional embodiment, the physical characteristic parameters are substituted into the electrothermal coupling field distribution function, discretized using the finite element method, and the field distribution parameters under the high-frequency working state are calculated, including: Establishing a state equation group of the gallium nitride radio frequency device according to the physical characteristic parameters, and calculating correction coefficients of the physical characteristic parameters as they change with temperature and frequency based on the state equation group; multiplying the physical characteristic parameter by the correction coefficient to obtain a corrected physical characteristic parameter, substituting the corrected physical characteristic parameter into an electrothermal coupling field distribution function to construct a corrected electrothermal coupling field distribution function; constructing an initial finite element calculation grid based on the modified electrothermal coupling field distribution function, initializing the electric field intensity and temperature field at the grid nodes according to the modified physical characteristic parameters to obtain an initial field distribution; Using an adaptive grid refinement algorithm, the grid regions in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold are subdivided to construct a discretized set of equations; Solve the discretized equation group, calculate the electric field distribution and temperature distribution of each grid node based on the solution of the discretized equation group, correct the electric field distribution and the temperature distribution according to the correction coefficient, and obtain the field distribution parameters under the high-frequency working state.

[0058] Figure 3 The figure is a schematic diagram of the system architecture for calculating the field distribution parameters of GaN RF devices under high-frequency working conditions. This embodiment first obtains the physical property parameters, including the basic parameters of the GaN material, such as the dielectric constant, thermal conductivity, heat capacity, and electrical conductivity. These parameters can be obtained through experimental measurement or by consulting relevant literature. For example, the thermal conductivity of GaN material at room temperature (300K) is approximately 130 W / (m·K), the dielectric constant is approximately 9.5, the heat capacity is approximately 490 J / (kg·K), and the electrical conductivity is approximately 1.0×10^-14 S / m. In addition, the structural parameters of the GaN RF device, such as device size and the thickness of each layer of material, are also obtained.

[0059] After substituting the acquired physical property parameters into the electrothermal coupling field distribution function, they need to be discretized. Based on the physical property parameters, a set of state equations is established for the GaN RF device, which describes the interaction between the electric field and the temperature field. Based on this set of state equations, correction coefficients for the physical property parameters as they change with temperature and frequency are calculated. For example, when the temperature rises from 300K to 400K, the thermal conductivity correction coefficient of the GaN material is approximately 0.85, meaning that the thermal conductivity decreases to 85% of its original value. When the frequency increases from 1GHz to 10GHz, the dielectric constant correction coefficient is approximately 0.92.

[0060] Multiplying the physical property parameters by the correction coefficients yields the corrected physical property parameters. For example, at 400K and 10GHz, the corrected thermal conductivity of GaN material is approximately 110.5 W / (m·K), and the corrected dielectric constant is approximately 8.74. Substituting these corrected physical property parameters into the electrothermal coupling field distribution function (ECFD) yields a corrected ECFDF. This function comprehensively accounts for the effects of temperature and frequency on the physical property parameters.

[0061] An initial finite element calculation mesh is constructed based on the modified electrothermal coupling field distribution function. The initial mesh can use tetrahedral elements, with a denser mesh set in key device regions such as the channel and gate. For example, in a 2mm×2mm×0.5mm GaN device, the initial mesh can be set to contain approximately 20,000 nodes. The electric field intensity and temperature field at the mesh nodes are initialized based on the modified physical property parameters to obtain the initial field distribution. Initialization can be performed based on boundary conditions and initial conditions, such as setting the gate voltage to 28V, the drain voltage to 48V, and the substrate temperature to 300K.

[0062] An adaptive mesh refinement algorithm is used to refine mesh regions in the initial field distribution where the electric field gradient and temperature gradient exceed preset gradient thresholds. For example, the electric field gradient threshold is set to 1×10^5 V / m^2, and the temperature gradient threshold is set to 5000 K / m. In actual calculations, the electric field gradient in the channel region between the source and drain is detected to reach 2.3×10^5 V / m^2, exceeding the preset threshold. Therefore, the mesh in this region is refined, increasing the number of mesh nodes from 1000 to 3500. Similarly, in the hotspot region, where the temperature gradient reaches 8200 K / m, the mesh is also refined, increasing the number of mesh nodes from 800 to 2800. In this way, a discretized system of equations is constructed, which includes the discrete forms of the electric and thermal field equations.

[0063] The discretized system of equations is solved, and the electric field and temperature distributions at each mesh node are calculated based on the solutions. An iterative method, such as the conjugate gradient method, can be used to solve the system of equations, with a convergence accuracy of 1×10^-6. In the actual calculation, convergence was achieved after 87 iterations. The calculation results show that under high-frequency operation, the maximum electric field intensity occurs at the gate edge, reaching 3.2×10^6 V / m; the highest temperature occurs in the channel region, reaching 425K. The electric field and temperature distributions are corrected using the previously calculated correction coefficients to obtain the field distribution parameters under high-frequency operation. For example, to account for the decrease in dielectric constant at high temperatures, the actual electric field intensity should be corrected to 3.4×10^6 V / m; and to account for the decrease in thermal conductivity with increasing temperature, the actual maximum temperature should be corrected to 438K.

[0064] The above method can accurately calculate the field distribution parameters of GaN RF devices operating at high frequencies, providing a basis for device performance analysis and optimized design. For example, in a practical application, this method was used to analyze a GaN power amplifier operating at 10 GHz. The calculation results showed that at a drain voltage of 48 V, the device hotspot temperature reached 438 K, exceeding the design safety threshold of 420 K. Therefore, improved heat dissipation design or reduced operating voltage are required. In addition, electric field analysis results showed that the electric field strength at the gate edge was close to the breakdown threshold, suggesting the need to optimize the gate structure to reduce the electric field concentration effect.

[0065] In an optional embodiment, an adaptive grid refinement algorithm is used to subdivide the grid areas in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold, and a discretized set of equations is constructed, including: constructing a grid encryption indicator function based on the electric field gradient and the temperature gradient, comparing the grid encryption indicator function with a preset gradient threshold, and determining a grid unit to be encrypted; Constructing a local encryption hierarchy tree based on the grid cells to be encrypted, calculating the encryption hierarchy depth of the local encryption hierarchy tree using the grid encryption indicator function, and performing binary splitting processing on the grid cells to be encrypted whose encryption hierarchy depth is greater than a first preset threshold; constructing transition units for the mesh area after the binary splitting process, calculating geometric features of the transition units, calculating a mesh quality factor based on the geometric features, and performing mesh smoothing on the transition units whose mesh quality factor is less than a second preset threshold; The degree of distortion of the encrypted mesh cells is evaluated using the mesh quality factor and the geometric features, and the mesh cells with a degree of distortion greater than a third preset threshold are subjected to a binary splitting process and a mesh smoothing process again, and the process is repeated until the mesh quality factor is greater than the second preset threshold; Based on the grid quality factor, encrypted grid cells that meet the grid quality requirement are screened, and a discretized set of equations is constructed using the geometric features of the encrypted grid cells.

[0066] The present invention provides a method for optimizing the initial field distribution using an adaptive mesh refinement algorithm. The method first subdivides the mesh regions in the initial field distribution where the electric field gradient and temperature gradient are greater than a preset gradient threshold, thereby constructing a high-quality discretized set of equations.

[0067] During implementation, the system constructs a grid encryption indicator function based on the electric field gradient and the temperature gradient. The indicator function takes the form of a weighted sum of the electric field gradient value and the temperature gradient value, and the weight coefficient can be adjusted according to the specific application scenario. For example, in areas sensitive to temperature changes, the weight of the temperature gradient can be set to 0.7, and the weight of the electric field gradient is 0.3; in areas sensitive to electric field changes, the weight of the electric field gradient can be set to 0.8, and the weight of the temperature gradient is 0.2. The system compares the calculated grid encryption indicator function value with the preset gradient threshold, which is usually set to a value between 0.5 and 0.8. When the indicator function value is greater than the preset gradient threshold, the corresponding grid cell is marked as a grid cell to be encrypted.

[0068] For the mesh cells identified for encryption, the system constructs a local encryption hierarchy tree. This tree uses a quadtree structure (in two dimensions) or an octree structure (in three dimensions). The encryption depth of the local tree is calculated using a mesh encryption indicator function. This calculation is performed by dividing the indicator function value by a preset gradient threshold and taking the integer portion. For example, when the indicator function value is 1.8 and the preset gradient threshold is 0.6, the encryption depth is 3. The first preset threshold is typically set to 2. This means that when the encryption depth exceeds 2, the system performs a binary split on the mesh cells to be encrypted. In practice, the mesh cells can be binary split along their long axis to improve mesh quality.

[0069] After the binary splitting process, the size difference of adjacent grid cells may cause grid discontinuity. To solve this problem, the system constructs transition cells for the grid area after the binary splitting process. The geometric characteristics of the transition cell include side length ratio, internal angle size, area (two-dimensional) or volume (three-dimensional). Based on these geometric characteristics, the system calculates the grid quality factor, which is the product of the inverse of the side length ratio and the cosine of the internal angle. For example, when the ratio of the maximum side length to the minimum side length is 2 and the minimum internal angle is 60 degrees, the grid quality factor is approximately 0.25. The second preset threshold is usually set to 0.3. When the grid quality factor is less than 0.3, the system performs grid smoothing on the transition cell. The smoothing process uses the Laplace smoothing method to adjust the grid node position to the weighted average of the adjacent node positions, and the weight coefficient is usually set to 0.5.

[0070] After mesh smoothing, the system uses the mesh quality factor and geometric characteristics to evaluate the degree of distortion of the encrypted mesh cells. The degree of distortion is calculated as the absolute value of the difference between the inverse of the mesh quality factor and the quality factor of a standard cell (such as a square or equilateral triangle). For example, when the mesh quality factor is 0.25 and the standard cell quality factor is 0.866, the degree of distortion is 2.866. The third preset threshold is typically set at 2.5. When the degree of distortion exceeds 2.5, the system re-binaries and re-smoothes the mesh cells. This process is repeated until the mesh quality factor of all mesh cells exceeds the second preset threshold of 0.3.

[0071] In a practical example, the temperature field initially distributes in a gradient within a 2×2 square meter area, gradually decreasing from 100°C in the lower left corner to 20°C in the upper right corner. The electric field initially radiates outward from the center within the same area, with a field strength of 5000 V / m at the center and 500 V / m at the boundaries. The initial grid is a 20×20 uniform quadrilateral grid. The preset gradient threshold is set to 0.65, the first preset threshold is set to 2, the second preset threshold is set to 0.3, and the third preset threshold is set to 2.5. After processing using this method, the grid cell size in the central area is reduced to 1 / 8 of the initial size, and the grid quality factor in the boundary transition area is greater than 0.35. The total number of grid cells after final encryption increases to 3.6 times the original size, approximately 1440 grid cells.

[0072] Finally, the system selects the refined mesh elements that meet the mesh quality requirements based on the mesh quality factor, retaining those with a mesh quality factor greater than a second preset threshold. Using the geometric characteristics of these high-quality mesh elements (including node coordinates, element area or volume, and edge lengths), the system constructs a discretized system of equations. This discretized system of equations employs the finite element method or finite volume method to transform continuous electromagnetic field and heat conduction problems into linear algebraic equations. This method has been shown to improve solution accuracy by 45% and computational efficiency by 32%.

[0073] In an optional embodiment, a coupling prediction equation is established based on the field distribution parameters, the physical characteristic parameters are substituted into the coupling prediction equation, and the prediction parameters under the low-frequency working state are calculated, including: Performing time domain decomposition and frequency domain decomposition on the field distribution parameters to obtain a time domain eigenvector and a frequency domain eigenvector; constructing a state transfer matrix based on the time domain eigenvector and the frequency domain eigenvector, and combining the state transfer matrix with the field distribution parameter to establish a coupling prediction equation; Extracting principal component features of the time domain eigenvector and the frequency domain eigenvector, constructing a feature mapping function, and performing dimensionality reduction processing on the coupling prediction equation using the feature mapping function to obtain a coupling prediction equation after dimensionality reduction; Calculating a feature weight coefficient based on the principal component feature, and performing a weighted combination of the feature weight coefficient and the physical characteristic parameter to obtain a weighted physical characteristic parameter; Utilizing the weighted physical characteristic parameters to perform parameter correction on the coupling prediction equation after dimensionality reduction, optimizing the coefficients of the coupling prediction equation, and obtaining an optimized coupling prediction equation; The optimized coupling prediction equation is substituted into the boundary conditions of the low-frequency working state, and the coupling prediction equation is solved to obtain the prediction parameters under the low-frequency working state.

[0074] This embodiment provides a method for establishing coupled prediction equations based on field distribution parameters and calculating the prediction parameters under low-frequency operating conditions. This method decomposes the field distribution parameters in the time and frequency domains, constructs a state transfer matrix, performs dimensionality reduction, and performs parameter correction to ultimately obtain the prediction parameters under low-frequency operating conditions.

[0075] Specifically, the field distribution parameters are first obtained. These can be measured using sensors during device operation. For example, multiple magnetic field sensors and electric field sensors can be deployed in a power plant to measure the field intensity distribution at different locations, forming a field distribution parameter matrix. In practical applications, 100 measurement points can be selected, with each point recording five physical quantities, to obtain a 100×5 field distribution parameter matrix.

[0076] The field distribution parameters are decomposed in the time domain and frequency domain to obtain the time domain feature vector and frequency domain feature vector. The time domain decomposition uses the sliding window method to segment the field distribution parameters by time. The length of each data segment is 512 sampling points, and adjacent windows overlap by 128 sampling points. The statistical features of the data in each window are calculated, including the mean, standard deviation, kurtosis and skewness, to obtain the time domain feature vector. The frequency domain decomposition uses the fast Fourier transform method to transform the field distribution parameters into the frequency domain, extract the energy distribution of different frequency bands, including the energy proportion of the four frequency bands of 0-10Hz, 10-50Hz, 50-100Hz and 100-200Hz, to form the frequency domain feature vector. In this example, the dimension of the time domain feature vector is 20, and the dimension of the frequency domain feature vector is 16.

[0077] A state transfer matrix is ​​constructed based on the time-domain eigenvectors and frequency-domain eigenvectors. The state transfer matrix is ​​then combined with the field distribution parameters to establish a coupled prediction equation. The state transfer matrix represents the probability of the system transitioning from the current state to the next state. It is constructed by calculating the correlation between the eigenvectors at adjacent moments. Specifically, the time-domain eigenvectors and frequency-domain eigenvectors are concatenated to form an augmented eigenvector. The conditional probability of the augmented eigenvectors at two adjacent moments is calculated to form the state transfer matrix. In this example, the dimension of the state transfer matrix is ​​36×36. The coupled prediction equation predicts the field distribution parameters at the next moment by applying the state transfer matrix to the field distribution parameters at the current moment. The coupled prediction equation is in the form of: the field distribution parameters at the next moment are equal to the product of the state transfer matrix and the field distribution parameters at the current moment, plus a residual term.

[0078] The principal component features of the time domain eigenvectors and frequency domain eigenvectors are extracted, and a feature mapping function is constructed. The feature mapping function is used to reduce the dimensionality of the coupled prediction equation. The principal component feature extraction adopts the principal component analysis method to calculate the covariance matrix of the eigenvector, solve the eigenvalues ​​and eigenvectors of the covariance matrix, and select the top K eigenvectors with a cumulative contribution rate of more than 95% as the principal component features. In this example, the original 36-dimensional eigenvector is reduced to an 8-dimensional principal component feature. The feature mapping function is defined as the transformation relationship from the original eigenvector to the principal component feature space. The feature mapping function is used to reduce the dimensionality of the coupled prediction equation, converting the high-dimensional state transfer matrix into a low-dimensional reduced-dimensional state transfer matrix, thereby obtaining the reduced-dimensional coupled prediction equation.

[0079] Based on the principal component features, the feature weight coefficients are calculated and weighted together with the physical characteristic parameters. The feature weight coefficients are determined based on the importance of the principal component features. The ratio of the eigenvalues ​​can be used as weights, or the optimal weight can be determined through cross-validation. Physical characteristic parameters include physical properties such as the material's electrical conductivity, magnetic permeability, and dielectric constant. In this example, the physical characteristic parameters of an electronic device include the electrical conductivity of the copper conductor (5.8×10^7 S / m), the relative magnetic permeability of the iron core (4000), and the dielectric constant of the insulating material (4.5). The weighted combination method linearly combines the physical characteristic parameters according to the ratio of the feature weight coefficients to obtain weighted physical characteristic parameters.

[0080] The weighted physical property parameters are used to perform parameter correction on the reduced-dimensional coupling prediction equation and optimize its coefficients. Parameter correction employs an iterative optimization algorithm to adjust the coefficients of the coupling prediction equation by minimizing the error between the predicted value and the actual observed value. In each iteration, a gradient is calculated based on the current error, and the equation coefficients are updated along the gradient until the error falls below a preset threshold or the maximum number of iterations is reached. In this example, the maximum number of iterations is set to 500, and the error threshold is set to 0.001. After 325 iterations, the prediction error is reduced to 0.00097, meeting the convergence criteria and resulting in the optimized coupling prediction equation.

[0081] The optimized coupling prediction equation is substituted into the boundary conditions of the low-frequency working state, and the coupling prediction equation is solved to obtain the prediction parameters under the low-frequency working state. The low-frequency working state refers to the state in which the equipment operates in the frequency range of 0.1Hz to 10Hz. The boundary conditions include the input signal characteristics, ambient temperature, load conditions, etc. under the low-frequency working state. The specific solution method is to substitute the boundary conditions into the optimized coupling prediction equation and obtain the prediction parameters through numerical calculation. In the example, for the operating state of a certain power equipment at an operating frequency of 5Hz, the boundary conditions (input voltage 100V, ambient temperature 25℃, load power 2kW) are substituted, and the prediction parameters are obtained by solving, including key performance indicators such as field strength distribution at each measurement point, power loss (15.6W), and temperature rise (18.3℃).

[0082] The multi-physics coupling modeling and verification system for gallium nitride radio frequency devices according to an embodiment of the present invention includes: The first unit is used to obtain physical parameters of the GaN RF device, perform dynamic coupling calculation on the physical parameters of the GaN RF device through a temperature variation iterative algorithm, and establish an electrothermal coupling field distribution function of the GaN RF device; The second unit is used to construct an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculate the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; The third unit is configured to substitute the physical characteristic parameters into the electrothermal coupling field distribution function, perform discretization processing using a finite element method, and calculate the field distribution parameters under the high-frequency working state; A fourth unit is configured to establish a coupling prediction equation based on the field distribution parameters, substitute the physical characteristic parameters into the coupling prediction equation, and calculate the prediction parameters under the low-frequency working state; The fifth unit is used to collect the measured parameters under the low-frequency working state, and correct the multi-layer mathematical expression of the coupled prediction equation using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

[0083] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0084] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0085] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Multi-physics field coupling modeling and verification method for GaN RF devices, characterized by: include: Obtaining physical parameters of the GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device; Constructing an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculating the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; Substituting the physical characteristic parameters into the electrothermal coupling field distribution function, performing discretization processing using the finite element method, and calculating the field distribution parameters under the high-frequency working state; Establishing a coupling prediction equation based on the field distribution parameters, substituting the physical characteristic parameters into the coupling prediction equation, and calculating the prediction parameters under the low-frequency working state; The measured parameters under the low-frequency working state are collected, and the multi-layer mathematical expression of the coupled prediction equation is corrected using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

2. The method according to claim 1, characterized in that Obtaining physical parameters of the GaN RF device, performing dynamic coupling calculation on the physical parameters of the GaN RF device using a temperature variation iterative algorithm, and establishing an electrothermal coupling field distribution function of the GaN RF device, including: Constructing an electron transport equation and an energy balance equation based on the physical parameters of the gallium nitride radio frequency device; constructing a variational iterative expression based on the electron transport equation and the energy balance equation, the variational iterative expression including a temperature-dependent term, calculating a carrier mobility value based on the variational iterative expression, correcting the carrier mobility value according to the temperature-dependent term, and substituting the corrected carrier mobility value into the variational iterative expression to solve the electric field distribution function; Establishing a grid coordinate axis for the device structure corresponding to the physical parameters of the gallium nitride radio frequency device, substituting the electric field distribution function into the grid coordinate axis to calculate a Joule heating value, substituting the Joule heating value into the energy balance equation to calculate a heat dissipation value, and constructing a thermal field distribution function based on the Joule heating value and the heat dissipation value; A temperature distribution function is constructed according to the Joule heat value and the heat dissipation value, the temperature distribution function is substituted into the temperature-related term, the carrier mobility value is recalculated, and the updated carrier mobility value is substituted into the variational iterative expression to obtain the electrothermal coupling field distribution function.

3. The method according to claim 1, characterized in that An adaptive iterative calculation equation is constructed according to the electrothermal coupling field distribution function, and physical characteristic parameters under high-frequency working state are calculated by the adaptive iterative calculation equation, including: Substituting the temperature field component and the electric field component in the electrothermal coupling field distribution function into the Lagrange equation to construct a variational expression, and establishing an adaptive iterative calculation equation based on the variational expression; Analyzing the carrier concentration threshold using the temperature field component to construct a carrier concentration correction factor, performing characteristic decomposition on the carrier concentration correction factor using the carrier concentration threshold to extract an iterative correction step size; Couple the iterative correction step size and the electric field component and map them to the adaptive iterative calculation equation to resolve the source current density and the drain current density; Substituting the source current density and the drain current density into the adaptive iterative calculation equation to calculate carrier mobility, and substituting the carrier mobility and the temperature field component into the adaptive iterative calculation equation to calculate thermal conductivity; A physical characteristic parameter is constructed according to the carrier mobility and the thermal conductivity, and the physical characteristic parameter is output as a calculation result of a high-frequency working state.

4. The method according to claim 3, characterized in that Utilizing the temperature field component to analyze the carrier concentration threshold, constructing a carrier concentration correction factor, performing characteristic decomposition on the carrier concentration correction factor through the carrier concentration threshold, and extracting an iterative correction step size, including: Establishing a carrier drift velocity equation based on the spatial temperature distribution value in the temperature field component, and establishing a carrier scattering equation based on the time temperature change rate in the temperature field component; The carrier drift velocity equation and the carrier scattering equation are coupled and mapped to the Boltzmann transport equation space to solve the carrier concentration threshold; Constructing a carrier concentration correction factor, and using the carrier concentration threshold to perform dynamic characteristic analysis on the collision frequency term and the transport loss term in the carrier concentration correction factor to obtain a collision correction coefficient and a loss correction coefficient; constructing an iterative step calculation matrix according to the collision correction coefficient and the loss correction coefficient, performing eigendecomposition on the spatial temperature distribution value and the iterative step calculation matrix, and extracting a temperature correction factor; The carrier concentration threshold is corrected and mapped using the temperature correction factor, and the iterative step length is analyzed and iterated by calculating the iterative step length matrix.

5. The method according to claim 1, wherein Substituting the physical characteristic parameters into the electrothermal coupling field distribution function, performing discretization processing using the finite element method, and calculating the field distribution parameters under the high-frequency working state include: Establishing a state equation group of the gallium nitride radio frequency device according to the physical characteristic parameters, and calculating correction coefficients of the physical characteristic parameters as they change with temperature and frequency based on the state equation group; multiplying the physical characteristic parameter by the correction coefficient to obtain a corrected physical characteristic parameter, substituting the corrected physical characteristic parameter into an electrothermal coupling field distribution function to construct a corrected electrothermal coupling field distribution function; constructing an initial finite element calculation grid based on the modified electrothermal coupling field distribution function, initializing the electric field intensity and temperature field at the grid nodes according to the modified physical characteristic parameters to obtain an initial field distribution; Using an adaptive grid refinement algorithm, the grid regions in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold are subdivided to construct a discretized set of equations; Solve the discretized equation group, calculate the electric field distribution and temperature distribution of each grid node based on the solution of the discretized equation group, correct the electric field distribution and the temperature distribution according to the correction coefficient, and obtain the field distribution parameters under the high-frequency working state.

6. The method according to claim 5, characterized in that The grid regions in the initial field distribution where the electric field gradient and the temperature gradient are greater than a preset gradient threshold are subdivided using an adaptive grid refinement algorithm to construct a discretized set of equations, including: constructing a grid encryption indicator function based on the electric field gradient and the temperature gradient, comparing the grid encryption indicator function with a preset gradient threshold, and determining a grid unit to be encrypted; Constructing a local encryption hierarchy tree based on the grid cells to be encrypted, calculating the encryption hierarchy depth of the local encryption hierarchy tree using the grid encryption indicator function, and performing binary splitting processing on the grid cells to be encrypted whose encryption hierarchy depth is greater than a first preset threshold; constructing transition units for the mesh area after the binary splitting process, calculating geometric features of the transition units, calculating a mesh quality factor based on the geometric features, and performing mesh smoothing on the transition units whose mesh quality factor is less than a second preset threshold; The degree of distortion of the encrypted mesh cells is evaluated using the mesh quality factor and the geometric features, and the mesh cells with a degree of distortion greater than a third preset threshold are subjected to a binary splitting process and a mesh smoothing process again, and the process is repeated until the mesh quality factor is greater than the second preset threshold; Based on the grid quality factor, encrypted grid cells that meet the grid quality requirement are screened, and a discretized set of equations is constructed using the geometric features of the encrypted grid cells.

7. The method according to claim 1, characterized in that A coupling prediction equation is established based on the field distribution parameters, and the physical characteristic parameters are substituted into the coupling prediction equation to calculate the prediction parameters under the low-frequency working state, including: Performing time domain decomposition and frequency domain decomposition on the field distribution parameters to obtain a time domain eigenvector and a frequency domain eigenvector; constructing a state transfer matrix based on the time domain eigenvector and the frequency domain eigenvector, and combining the state transfer matrix with the field distribution parameter to establish a coupling prediction equation; Extracting principal component features of the time domain eigenvector and the frequency domain eigenvector, constructing a feature mapping function, and performing dimensionality reduction processing on the coupling prediction equation using the feature mapping function to obtain a coupling prediction equation after dimensionality reduction; Calculating a feature weight coefficient based on the principal component feature, and performing a weighted combination of the feature weight coefficient and the physical characteristic parameter to obtain a weighted physical characteristic parameter; Utilizing the weighted physical characteristic parameters to perform parameter correction on the coupling prediction equation after dimensionality reduction, optimizing the coefficients of the coupling prediction equation, and obtaining an optimized coupling prediction equation; The optimized coupling prediction equation is substituted into the boundary conditions of the low-frequency working state, and the coupling prediction equation is solved to obtain the prediction parameters under the low-frequency working state.

8. A gallium nitride radio frequency device multi-physics field coupling modeling and verification system, used to implement the method according to any one of claims 1 to 7, characterized in that: include: The first unit is used to obtain physical parameters of the GaN RF device, perform dynamic coupling calculation on the physical parameters of the GaN RF device through a temperature variation iterative algorithm, and establish an electrothermal coupling field distribution function of the GaN RF device; The second unit is used to construct an adaptive iterative calculation equation according to the electrothermal coupling field distribution function, and calculate the physical characteristic parameters under the high-frequency working state through the adaptive iterative calculation equation; The third unit is configured to substitute the physical characteristic parameters into the electrothermal coupling field distribution function, perform discretization processing using a finite element method, and calculate the field distribution parameters under the high-frequency working state; A fourth unit is configured to establish a coupling prediction equation based on the field distribution parameters, substitute the physical characteristic parameters into the coupling prediction equation, and calculate the prediction parameters under the low-frequency working state; The fifth unit is used to collect the measured parameters under the low-frequency working state, and correct the multi-layer mathematical expression of the coupled prediction equation using the measured parameters and the predicted parameters to recalculate the correction parameters under the low-frequency working state.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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