Gallium nitride HEMT packaging stress detection method

Abstract

The invention provides a gallium nitride HEMT (high electron mobility transistor) packaging stress detection method, which belongs to the technical field of chip manufacturing, and comprises the following steps of: determining a stress sensitive area by constructing a device mechanical basic matrix, and measuring a scattering parameter matrix without stress and under various stress loads in a frequency range of 1GHz to 40GHz by using a microwave network analyzer; a multi-channel pressure loading clamp is designed to realize accurate stress control, a frequency sensitive stress increasing and expanding matrix is established to improve detection sensitivity, Pearson's correlation coefficients are applied to screen characteristic frequency points to construct a frequency stress sparse matrix, and a high-precision stress prediction model is established based on a multi-head attention neural network. Accurate mapping from high-frequency scattering parameters to internal stress distribution is realized, and accurate detection of packaging stress in an actual working frequency range of a device is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of chip manufacturing, and more specifically, relates to a method for detecting the packaging stress of gallium nitride HEMT. Background Art

[0002] Gallium nitride high electron mobility transistors (GaN HEMT) have been widely used in fields such as 5G communication base stations, millimeter-wave radars, and high-frequency power electronics due to their excellent high-frequency characteristics, high power density, and high breakdown voltage. These devices usually operate in the high-frequency range of several GHz to dozens of GHz, and their performance and reliability are closely related to the residual stress generated during the packaging process. Traditional packaging stress detection methods mainly include X-ray diffraction analysis, Raman spectroscopy measurement, photoelasticity technology, and finite element numerical simulation, etc. These methods can provide certain stress distribution information under static or low-frequency conditions.

[0003] However, when GaN HEMT operates under high-frequency conditions, traditional measurement methods face severe challenges. First, technologies such as X-ray diffraction and Raman spectroscopy cannot perform real-time measurements under the actual working state of the device, making it difficult to capture the dynamic stress changes under high-frequency working conditions; second, photoelastic measurement has high requirements for the transparency of materials and is difficult to apply to GaN devices with multi-layer composite structures; third, although finite element simulation can predict the stress distribution, it often ignores the coupling effect between the high-frequency electric field and mechanical stress, resulting in a deviation between the simulation results and the actual situation. In addition, these methods are expensive, complex to operate, and have a high time cost, making it difficult to meet the requirements of industrial applications.

[0004] That is to say, there is a technical problem in the prior art that it is difficult to accurately detect the packaging stress distribution of gallium nitride HEMT under high-frequency working conditions (several GHz to dozens of GHz). Summary of the Invention

[0005] In view of this, the present invention provides a method for detecting the packaging stress of gallium nitride HEMT, which can solve the technical problem in the prior art that it is difficult to accurately detect the packaging stress distribution of gallium nitride HEMT under high-frequency working conditions (several GHz to dozens of GHz).

[0006] The present invention is implemented as follows: The present invention provides a method for detecting the stress of a gallium nitride HEMT package, including: constructing a mechanical basic matrix of the device to determine the stress-sensitive region; measuring the scattering parameter matrix of the gallium nitride HEMT in the frequency range from 1 GHz to 40 GHz in a stress-free state; designing and fabricating a multi-channel pressure loading fixture to apply precisely controlled mechanical stress to the gallium nitride HEMT; measuring the high-frequency scattering parameter matrix of the gallium nitride HEMT under different stress load conditions and recording the change values of electrical parameters; establishing a frequency-sensitive stress amplification matrix to establish a mathematical correspondence between the scattering parameter matrix and the stress load; calculating and constructing a frequency-stress sparse matrix using the Pearson correlation coefficient to screen out the characteristic frequency points most sensitive to the stress load; establishing a stress distribution matrix based on the stress response curve of the characteristic frequency points for back-inferring the unknown stress distribution; and using a stress prediction model for prediction, with the input being the scattering parameter matrix and the output being the stress distribution matrix of the key region of the gallium nitride HEMT.

[0007] Among them, the construction of the mechanical basic matrix of the device is to establish a geometric model and material parameters of the gallium nitride HEMT package structure through finite element analysis to determine the stress-sensitive region.

[0008] Among them, the mechanical basic matrix of the device refers to a mathematical expression describing the stress distribution of the gallium nitride HEMT under different stress load conditions established through finite element analysis, including material elastic modulus, Poisson's ratio, and geometric dimensions as key parameters.

[0009] Among them, the scattering parameter matrix refers to a complex matrix describing the signal relationship between the input and output ends of a microwave network, usually expressed as S parameters, including the S11 reflection coefficient and the S21 transmission coefficient.

[0010] Among them, the frequency-sensitive stress amplification matrix refers to a matrix establishing an amplification relationship between the change in electrical parameters and the change in mechanical stress of the gallium nitride HEMT at the characteristic frequency points, used to improve the detection sensitivity of small stress changes.

[0011] Among them, the frequency-stress sparse matrix refers to a matrix composed of a small number of discrete frequency points selected in the frequency range that are most sensitive to the change in stress load. Most of the frequency point elements are zero, and only the frequency point data with high sensitivity is retained.

[0012] Among them, the stress distribution matrix refers to a two-dimensional or three-dimensional numerical array representing the stress values at each point inside the gallium nitride HEMT device, used to completely describe the stress field distribution state inside the device.

[0013] Among them, the specific structure of the stress prediction model is a multi-head attention neural network based on deep learning, which includes an input layer for receiving normalized scattering parameter matrix data, multiple self-attention layers for capturing the correlations between scattering parameter matrices of different frequencies, a sparse attention mechanism layer for screening key feature frequency point information, a fully connected layer for mapping feature vectors to the stress distribution space, and an output layer for giving the predicted stress distribution matrix.

[0014] Among them, the sparse attention mechanism parameters are determined according to the frequency stress sensitivity index, the frequency sampling interval, and the transmission line characteristic impedance.

[0015] Among them, the steps for establishing the training data set in the training process of the stress prediction model include collecting data samples of the scattering parameter matrix of gallium nitride HEMT under known stress loads, using finite element simulation to obtain the internal stress distribution of gallium nitride HEMT under different packaging stresses, establishing data pairs of the mapping relationship between the scattering parameter matrix and the stress distribution matrix, using data augmentation technology to expand the number of training samples, and using the cross-validation method to divide the training set and the validation set.

[0016] Among them, the steps for training the stress prediction model include initializing the weight parameters of the multi-head attention neural network, using the mini-batch stochastic gradient descent optimization algorithm to input the training data batch by batch, calculating the mean square error loss between the predicted stress distribution matrix and the true stress distribution matrix, using the backpropagation algorithm to update the network weights, dynamically adjusting the learning rate to avoid overfitting, evaluating the model performance on the validation set until convergence, adjusting the weight coefficients of the sparse attention mechanism for the feature frequency points with high frequency sensitivity, and saving the optimal model parameters for actual stress prediction.

[0017] Among them, the described feature frequency points refer to the discrete frequency points that are most sensitive to the change of stress load screened by calculating the Pearson correlation coefficient.

[0018] Among them, the described mechanical stress refers to the internal stress caused by the external force applied to the surface of gallium nitride HEMT through a multi-channel pressure loading fixture.

[0019] Among them, the described stress-sensitive region refers to the region in the gallium nitride HEMT where the electrical performance changes significantly due to stress changes, which is determined by device mechanical basis matrix analysis.

[0020] Among them, the described multi-channel pressure loading fixture refers to a device used to apply precisely controlled mechanical stress to gallium nitride HEMT, which includes multiple independently controlled pressure channels, precision force sensors, a micro-displacement control system, and a high-frequency circuit interface, and is used for measuring high-frequency electrical parameters while applying pressures in different directions and magnitudes.

[0021] The key areas mentioned here refer to specific locations inside the GaN HEMT device that are particularly sensitive to stress changes and will significantly affect the electrical performance of the device. These typically include the gate metal and semiconductor interface, the two-dimensional electron gas channel layer, the transition interface between the epitaxial layer and the substrate, and the connection between the package solder joints and the chip.

[0022] This method accurately characterizes package stress under high-frequency operating conditions by measuring and analyzing the changes in the device's scattering parameter matrix over a frequency range of 1 GHz to 40 GHz. This method cleverly exploits the close correlation between the electrical properties and internal stress distribution of GaN HEMTs during high-frequency operation, establishing an electro-mechanical coupling detection mechanism.

[0023] Compared to traditional technologies, the method presented in this paper offers significant advantages. First, it can perform stress detection within the actual operating frequency range of GaN HEMTs, overcoming the limitation of traditional methods in capturing stress distribution under high-frequency conditions. Second, by constructing a frequency-sensitive stress augmentation matrix and applying the Pearson correlation coefficient to screen characteristic frequency points, it significantly improves detection sensitivity and can capture subtle stress changes. Third, a stress prediction model constructed using a multi-head attention neural network effectively addresses the technical issue of accurately detecting GaN HEMT package stress distribution under high-frequency operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flow chart of the method of the present invention.

[0025] Figure 2 Schematic diagram of the overall structure of the multi-channel pressure loading fixture in Example 2.

[0026] Figure 3 Schematic diagram of the local structure of the multi-axis pressure loading mechanism in Example 2.

[0027] Figure 4 This is a schematic diagram of the high-frequency probe system structure in Example 2. DETAILED DESCRIPTION

[0028] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0029] like Figure 1 FIG. 1 is a flow chart of a stress detection method for a gallium nitride HEMT package provided by the present invention. The method comprises the following steps:

[0030] S01. Construct the basic mechanical matrix of the device, establish the geometric model and material parameters of the GaN HEMT package structure through finite element analysis, and determine the stress-sensitive area;

[0031] S02. Use a microwave network analyzer to measure the scattering parameter matrix of GaN HEMT in the frequency range of 1 GHz to 40 GHz in the unstressed state;

[0032] S03. Design and manufacture a multi-channel pressure loading fixture to subject the gallium nitride HEMT to precisely controlled uniaxial or multiaxial mechanical stress;

[0033] S04. measuring the high-frequency scattering parameter matrix of the gallium nitride HEMT under different stress load conditions and recording the change value of the electrical parameters;

[0034] S05. Establish a frequency-sensitive stress augmentation matrix, and establish a mathematical correspondence between the scattering parameter matrix and the stress load;

[0035] S06. Calculate and construct a frequency-stress sparse matrix using the Pearson correlation coefficient to screen out the characteristic frequency points that are most sensitive to the stress load;

[0036] S07. Based on the characteristic frequency stress response curve, a stress distribution matrix is established to infer the unknown stress distribution;

[0037] S08. Use a pre-trained stress prediction model to perform prediction, with the scattering parameter matrix as input and the stress distribution matrix of the key area of the gallium nitride HEMT as output.

[0038] The device mechanical basic matrix refers to a mathematical expression established by finite element analysis to describe the stress distribution of the gallium nitride HEMT under different stress load conditions, including the material elastic modulus, Poisson's ratio and geometric dimensions as key parameters.

[0039] The scattering parameter matrix refers to a complex matrix that describes the relationship between the input and output signals of a microwave network, and is usually expressed as S parameters, including the S11 reflection coefficient and the S21 transmission coefficient.

[0040] The frequency-sensitive stress augmentation matrix refers to an amplification relationship matrix established between the electrical parameter variation and the mechanical stress variation of the gallium nitride HEMT at the characteristic frequency point, and is used to improve the detection sensitivity of small stress changes.

[0041] The frequency stress sparse matrix refers to a matrix composed of a small number of discrete frequency points that are most sensitive to the stress load change within the frequency range, most of the frequency point elements are zero, and only frequency point data with high sensitivity is retained.

[0042] The stress distribution matrix refers to a two-dimensional or three-dimensional numerical array representing the stress values at each point inside the gallium nitride HEMT device, and is used to fully describe the stress field distribution state inside the device.

[0043] Among them, the specific structure of the stress prediction model is a multi-head attention neural network based on deep learning, which includes an input layer for receiving and normalizing the scattering parameter matrix data, multiple self-attention layers for capturing the correlations between the scattering parameter matrices at different frequencies, a sparse attention mechanism layer for screening the key feature frequency point information, a fully connected layer for mapping the feature vectors to the stress distribution space, and an output layer for giving the predicted stress distribution matrix. Among them, the sparse attention mechanism parameters are determined according to the frequency stress sensitivity index, the frequency sampling interval, and the transmission line characteristic impedance.

[0044] Among them, the steps for establishing the training data set in the training process of the stress prediction model specifically include collecting the scattering parameter matrix data samples of the gallium nitride HEMT under known stress loads, using finite element simulation to simulate the internal stress distribution of the gallium nitride HEMT under different packaging stresses, establishing the mapping relationship data pairs between the scattering parameter matrix and the stress distribution matrix, using data augmentation technology to expand the number of training samples, and using the cross-validation method to divide the training set and the validation set.

[0045] Among them, the steps for training the stress prediction model specifically include initializing the weight parameters of the multi-head attention neural network, using the mini-batch stochastic gradient descent optimization algorithm to input the training data batch by batch, calculating the mean square error loss between the predicted stress distribution matrix and the true stress distribution matrix, using the backpropagation algorithm to update the network weights, dynamically adjusting the learning rate to avoid overfitting, evaluating the model performance on the validation set until convergence, adjusting the sparse attention mechanism weight coefficients for the feature frequency points with high frequency sensitivity, and saving the optimal model parameters for actual stress prediction.

[0046] Among them, the feature frequency points refer to the discrete frequency points screened out by calculating the Pearson correlation coefficient and being the most sensitive to the change of the stress load. The mechanical stress refers to the internal stress caused by the external force applied to the surface of the gallium nitride HEMT through the multi-channel pressure loading fixture. The stress-sensitive region refers to the region inside the gallium nitride HEMT where the electrical properties change significantly due to stress changes, which is determined by the device mechanical basis matrix analysis. The stress value refers to the stress magnitude at each point inside the gallium nitride HEMT, with the unit of Pascal. The change value of the electrical parameter refers to the change amount of the scattering parameter matrix of the gallium nitride HEMT before and after applying the mechanical stress. The stress response curve of the feature frequency point refers to the function relationship curve of the scattering parameter matrix at the feature frequency point changing with the stress load.

[0047] Among them, the multi-channel pressure loading fixture refers to a device used to apply precisely controlled mechanical stress to the gallium nitride HEMT, including multiple independently controlled pressure channels, a precision force sensor, a micro-displacement control system, and a high-frequency circuit interface, which is used to measure high-frequency electrical parameters while applying pressures in different directions and magnitudes.

[0048] Among them, the multi-head attention neural network refers to a neural network structure containing multiple parallel attention operation units, and each attention unit focuses on different features of the scattering parameter matrix. The sparse attention mechanism refers to an attention calculation mechanism in the multi-head attention neural network that only focuses on a small number of important feature frequency points.

[0049] Among them, the frequency stress sensitivity index refers to a dimensionless index that measures the response degree of the scattering parameter matrix to the change of the stress load, and is calculated by the Pearson correlation coefficient.

[0050] The key area refers to a specific position inside the gallium nitride HEMT device that is particularly sensitive to stress changes and will significantly affect the electrical performance of the device. Typically, it includes the interface between the gate metal and the semiconductor, the two-dimensional electron gas channel layer, the transition interface between the epitaxial layer and the substrate, and the connection between the package solder joint and the chip. Due to material property differences or structural discontinuities in these areas, stress concentration occurs, and local high stress or even micro-cracks are likely to occur under the action of external mechanical loads, resulting in electrical property offsets such as changes in electron mobility, enhancement or weakening of the piezoelectric polarization effect, and change of the carrier scattering mechanism. It is the primary target area for stress detection and analysis.

[0051] The following will describe the specific implementation manners of the above steps in detail.

[0052] Step S01: Construct the device mechanical basis matrix. Establish the geometric model and material parameters of the GaN HEMT package structure through finite element analysis, and determine the stress-sensitive regions. In this step, first use computer-aided design software to construct a three-dimensional geometric model of the GaN HEMT device, including the substrate layer, epitaxial layer, active region, gate, source, drain structure, and packaging materials, with a model accuracy of not less than 1μm. Then set the material parameters, including the elastic modulus (about 330GPa), Poisson's ratio (about 0.23), and anisotropic thermal expansion coefficient of the GaN material; the elastic modulus (about 15 - 25GPa), Poisson's ratio (about 0.35 - 0.45), and thermal expansion coefficient of the packaging material. Next, establish a grid model, refine the grid size to less than 0.1μm in key areas such as the two-dimensional electron gas channel region and the gate-semiconductor interface, and other areas can be appropriately relaxed to 0.5 - 5μm. Use a partial differential equation solver to calculate the stress distribution under predefined stress load conditions, such as uniaxial pressure from 0MPa to 100MPa, temperature from 25°C to 200°C, etc. By analyzing the stress distribution contour map, determine the stress-sensitive regions. Typical stress-sensitive regions include the gate metal-semiconductor interface, two-dimensional electron gas channel layer, transition interface between the epitaxial layer and the substrate, and the connection between the packaging solder joint and the chip. The von Mises stress gradient in these regions is usually greater than 10MPa / μm. Finally, construct the device mechanical basis matrix, which describes the relationship between stress and strain in each direction. Using Hooke's law in general form, organize parameters such as elastic modulus and Poisson's ratio into the form of a stiffness matrix for subsequent stress analysis. The purpose of this step is to establish a mechanical model of the GaN HEMT device, provide a theoretical basis and guidance for subsequent experimental measurements, and determine the key measurement regions.

[0053] Step S02: Use a microwave network analyzer to measure the scattering parameter matrix of the GaN HEMT in the frequency range from 1GHz to 40GHz in a stress-free state. In this step, first prepare the test environment, including a shielded room with the temperature controlled at 25±1°C and the humidity controlled at 45%±5% to eliminate the interference of environmental factors on high-frequency measurements. Then connect the standard calibration components to the vector network analyzer and perform full two-port calibration, including open circuit, short circuit, load, and through calibration (SOLT calibration method), to ensure that the measurement error is less than ±0.1dB and ±1°. Next, fix the GaN HEMT device to be measured on the test fixture to ensure that the device is in a state without external force and thermal stress, and monitor and confirm that the device temperature is uniform and maintained at 25±0.5°C through an infrared thermal imager. Set the scanning parameters of the vector network analyzer, with the frequency range from 1GHz to 40GHz, the frequency step of 0.1GHz, the intermediate frequency bandwidth set to 1kHz to improve the signal-to-noise ratio, and the input power controlled below -20dBm to avoid device nonlinear effects. Collect the scattering parameter matrix in the stress-free state, including S 11 、S 12 、S21 and S 22 Four complex parameters. Each frequency point is measured at least 10 times and the average value is taken, and the standard deviation is kept within ±0.05 dB. The measured reference scattering parameter matrix data is stored as a reference standard for subsequent comparison with the measurement results under the stressed state. The purpose of this step is to obtain the high-frequency electrical characteristic data of the device in the stress-free reference state and establish a reference benchmark for stress monitoring.

[0054] Step S03: Design and fabricate a multi-channel pressure loading fixture to apply precisely controlled uniaxial or multiaxial mechanical stress to the GaN HEMT. This step first designs a multi-channel pressure loading fixture based on the finite element analysis results. The fixture material is selected as invar alloy with a low coefficient of thermal expansion (≤5×10 -6 / °C) to minimize the influence of thermal stress caused by temperature changes. The fixture includes at least four independently controlled pressure channels, which can apply precise mechanical stress to the X, Y, and Z principal axes and the torsion direction of the device respectively. Each pressure channel is equipped with a precision piezoelectric ceramic actuator with a displacement resolution better than 0.01 μm and a maximum stroke of not less than 100 μm; at the same time, a high-precision force sensor is integrated, with a measurement accuracy better than 0.1 N and a range of 0 to 50 N. The microwave test interface is integrated in the fixture design, and low-loss coaxial connectors are used, with a working frequency covering DC to 40 GHz and an insertion loss less than 0.5 dB. Each component of the fixture is machined and manufactured, with the surface roughness controlled below Ra0.4 μm and the tolerance of each key dimension controlled within ±0.01 mm. The fixture system is assembled and connected to the computer control system, and the control software is developed to achieve precise control of stress loading, with a stress control accuracy better than ±0.1 MPa and the stress loading rate adjustable in the range of 0.01 to 10 MPa / s. The fixture is calibrated, and a standard strain gauge is used to verify the linearity and repeatability of stress loading in each direction, ensuring that the linear error is less than 1% and the repeatability error is less than 0.5%. The purpose of this step is to construct an experimental platform that can apply precisely controllable mechanical stress to the GaN HEMT device and provide the necessary conditions for studying the influence of stress on the high-frequency characteristics of the device.

[0055] Step S04: Measure the high-frequency scattering parameter matrix of the GaN HEMT under different stress load conditions and record the change values of electrical parameters. In this step, the GaN HEMT device is first installed in a multi-channel pressure loading fixture to ensure that the main axis direction of the device is precisely aligned with the loading direction of the fixture, and the deviation angle is controlled within ±0.5°. Then, a stress loading scheme is set, including uniaxial stress tests (from 0 MPa to 50 MPa in the X, Y, and Z directions respectively, with a step of 5 MPa) and combined stress tests (including at least 5 typical stress combination modes). For each stress load condition, the set stress is stably applied using the control system for no less than 30 seconds, and the stress fluctuation is controlled within ±0.5% of the set value. After each stress load condition is stabilized, the scattering parameter matrix of the device in the frequency range of 1 GHz to 40 GHz is measured using a microwave network analyzer with the same measurement settings and accuracy requirements as in Step S02. To eliminate random errors, each stress load condition is measured at least 5 times, and the average value is taken as the effective measurement result under this condition. Calculate the change amount of the scattering parameter matrix relative to the stress-free state under each stress load condition, including the amplitude change (unit: dB) and the phase change (unit: degree). Establish a corresponding database of stress load and scattering parameter changes, including high-frequency scattering parameter change data under at least 100 different stress load conditions. The purpose of this step is to obtain the high-frequency electrical characteristic change data of the GaN HEMT device under different stress load conditions and provide an experimental basis for establishing the corresponding relationship between stress and electrical characteristics in the subsequent steps.

[0056] Step S05: Establish a frequency-sensitive stress augmentation matrix to establish a mathematical correspondence between the scattering parameter matrix and the stress load. In this step, the experimental data obtained in Step S04 is first preprocessed, including outlier detection and rejection (using the 3σ criterion, that is, data deviating from the average value by more than 3 times the standard deviation is regarded as an outlier) and data smoothing (using the Savitzky-Golay filtering algorithm, with a window width set to 5 data points and a polynomial order of 2). Then, the relationship between the change amount of the scattering parameter (amplitude and phase) and the stress load is calculated for each frequency point (from 1 GHz to 40 GHz, with an interval of 0.1 GHz), and a preliminary mapping relationship is established using the multiple linear regression method. Sensitivity analysis is performed on the scattering parameter components at each frequency point to calculate the stress sensitivity coefficient K s , which is defined as the ratio of the change amount of the scattering parameter to the change amount of the stress, with the unit of dB / MPa or degree / MPa. Based on the sensitivity analysis results, a frequency-sensitive stress augmentation matrix M amp is constructed. Each element M ij of this matrix represents the stress sensitivity coefficient corresponding to the jth scattering parameter component at the ith frequency point. Considering the non-linear effect of the scattering parameter, a second-order term correction is introduced, and the mapping relationship is improved using a multiple polynomial regression model. The regression determination coefficient R2 It should be greater than 0.95. The generalization ability of the model is evaluated using the cross-validation method (K-fold cross-validation, K = 5) to ensure that the model still has good prediction accuracy under unseen stress load conditions, and the prediction error is controlled within ±5%. The purpose of this step is to establish a quantitative correspondence between the change in scattering parameters and the stress load, laying a mathematical foundation for subsequent stress prediction.

[0057] Step S06: Calculate and construct a frequency-stress sparse matrix using the Pearson correlation coefficient to screen out the characteristic frequency points that are most sensitive to the stress load. This step first performs statistical analysis on the frequency-sensitive stress augmented matrix data obtained in step S05, and calculates the Pearson correlation coefficient between the change in scattering parameters and the change in stress load for each frequency point. The calculation of the Pearson correlation coefficient uses standard statistical methods. For frequency point f and scattering parameter component s, the correlation coefficient r f，s represents the degree of linear correlation between the change in scattering parameters and the change in stress load at this frequency point, and its value range is [-1, 1]. According to the absolute value of the correlation coefficient, all frequency points are sorted from high to low according to sensitivity, and the frequency points with the absolute value of the correlation coefficient greater than the threshold (usually taken as 0.8) are selected as candidate characteristic frequency points. Considering the distribution characteristics of the frequency points, cluster analysis (such as the K-means clustering algorithm, the value of K is determined according to the data distribution characteristics, usually 5 - 10) is applied to group the candidate characteristic frequency points, and the frequency point with the largest absolute value of the correlation coefficient is selected from each group as the final characteristic frequency point to ensure the dispersion of the characteristic frequency points in the frequency domain. Construct a frequency-stress sparse matrix M sparse , and only the elements corresponding to the characteristic frequency points are retained in this matrix, and the rest of the elements are set to zero. The effectiveness of the frequency-stress sparse matrix is verified through reconstruction experiments to ensure that the stress prediction accuracy using the sparse matrix is not lower than 95% of the accuracy using the complete matrix. The number of finally selected characteristic frequency points is usually 10 - 20, and these characteristic frequency points should be distributed throughout the frequency range from 1 GHz to 40 GHz. The purpose of this step is to reduce the data dimension, extract the most informative characteristic frequency points, reduce redundant information, and improve the efficiency and robustness of stress prediction.

[0058] Step S07: Based on the stress response curves of the characteristic frequency points, establish a stress distribution matrix for back-calculating the unknown stress distribution. This step first plots a stress response curve for each characteristic frequency point, that is, a function relationship curve of the change in scattering parameters with respect to the change in stress load. The stress response curve is mathematically expressed using the polynomial fitting method, and the order of the fitting polynomial is usually 2 - 3, and the goodness of fit R 2Not less than 0.98. Then, an inverse function relationship between the scattering parameter change and the stress distribution is established, and the inverse mapping method is used to map the scattering parameter change amount into the stress distribution space. Considering the ill-posedness of the inverse problem (i.e., multiple stress distributions may lead to similar scattering parameter changes), the Tikhonov regularization method is introduced to stabilize the solution, and the regularization parameter λ is usually selected in the range of 10 -3 to 10 -5 . A stress distribution matrix σ dist is constructed. This matrix represents the stress values at each key point inside the GaN HEMT device, and the matrix dimension depends on the spatial resolution requirements of the stress analysis, usually 10×10×5 (representing the number of discrete points in the three-dimensional space of X, Y, and Z). The iterative optimization algorithm (such as the Levenberg-Marquardt algorithm) is applied to perform the stress distribution inversion calculation, and the convergence condition is set as the change amount of the stress distribution between adjacent iterative steps is less than 0.1 MPa or the number of iterations reaches 100 times. The rationality of the inversion result is verified by finite element to ensure that the consistency error between the inverted stress distribution and the finite element simulation result is less than 10%. The purpose of this step is to establish an inversion method from the electrical parameter change to the stress distribution to realize the indirect measurement and evaluation of the internal stress state of the device.

[0059] Step S08: Prediction is performed using a pre-trained stress prediction model, with the scattering parameter matrix as input and the stress distribution matrix of the GaN HEMT's key regions as output. This step first loads a pre-trained multi-head attention neural network model, which comprises an input layer, multiple self-attention layers, a sparse attention mechanism layer, a fully connected layer, and an output layer. The measured scattering parameter matrix data is pre-processed, including normalization (using the Z-score method to normalize the data to a mean of 0 and a standard deviation of 1) and dimensionality transformation (reorganizing the data into a data format suitable for network input). The pre-processed scattering parameter matrix data is input into the neural network model. The forward propagation of the neural network first captures the correlation between scattering parameters at different frequencies through a multi-head self-attention layer. The number of attention heads is typically set to 8, and the hidden layer dimension is 256. The data then passes through a sparse attention mechanism layer, which sparsifies the attention weights based on the characteristic frequency information determined in step S06. The sparsity is typically controlled to above 90%, meaning that most attention weights are approximately zero. The feature vectors are then mapped to the stress distribution space through a fully connected layer, where the number of neurons typically decreases from 1024, 512, and 256 layer by layer. Finally, the output layer produces a predicted stress distribution matrix, which represents the stress distribution state in key regions of the device (such as the gate metal-semiconductor interface and the two-dimensional electron gas channel layer). The reliability of the prediction results is evaluated, including prediction error analysis (compared with finite element simulations) and uncertainty quantification (using the Monte Carlo method to estimate the confidence interval of the prediction results). The purpose of this step is to use deep learning models to quickly and accurately predict the internal stress distribution of GaN HEMT devices, providing an important basis for device reliability assessment and failure analysis.

[0060] The stress prediction model uses a multi-head attention neural network structure based on deep learning. The model is used to predict the internal stress distribution of GaN HEMT from the high-frequency scattering parameter matrix. The model structure includes the following key components: the input layer receives the normalized scattering parameter matrix data with the dimension [batch size × number of frequency points × 4], where 4 represents S 11 , S 12 , S 21 , S 22The amplitude and phase of the image are a total of 8 features, which are reduced to 4 complex parameters; the encoding layer uses a 1D convolutional neural network for feature extraction, which includes 3 convolution layers with convolution kernel sizes of 5, 3, and 3, and the number of channels is 64, 128, and 256 respectively. Each layer is followed by batch normalization and ReLU activation function; the multi-layer self-attention layer captures the correlation between scattering parameters of different frequencies, including 4 attention layers, each with 8 attention heads, an embedding dimension of 256, and a feedforward network dimension of 1024; the sparse attention mechanism layer distributes weights according to the frequency stress sensitivity index, and the weight coefficient corresponding to the important frequency point is significantly increased. The Top-K sparsification method is used to retain only the most significant 10% to 20% attention weights; the fully connected layer maps the feature vector to the stress distribution space, including 3 fully connected layers with the number of neurons being 1024, 512, and 256 respectively. Each layer is followed by Dropout (ratio 0.2) and Layer Normalization; the output layer gives the predicted stress distribution matrix with the dimension [batch size × spatial resolution X × spatial resolution Y × spatial resolution Z], usually [batch size × 10 × 10 × 5], which represents the stress distribution in three-dimensional space.

[0061] The detailed steps for establishing the model training dataset include: In the data acquisition phase, a multi-channel pressure loading fixture is used to apply stress loads of different directions (X, Y, Z, and combined directions) and different magnitudes (0 MPa to 50 MPa, in steps of 2 MPa) to at least 30 typical GaN HEMT samples, and the corresponding scattering parameter matrices are measured, generating a total of approximately 3,000 valid data samples; in the finite element simulation phase, based on the device mechanical model established in step S01, a detailed finite element simulation is performed for each experimental stress load condition to calculate the stress distribution state within the device with a spatial resolution of not less than 0.1 μm; in the data pair establishment phase, the scattering parameter matrix is paired with the corresponding stress distribution matrix to form input-output data pairs, and data cleaning is performed to eliminate abnormal samples (such as samples with obvious measurement errors or simulation non-convergence); in the data enhancement phase, a variety of techniques are used to expand the number of training samples, including the addition of Gaussian noise (with a signal-to-noise ratio of more than 30 dB), small random perturbations (with an amplitude not exceeding ±2% of the original data), and physical model-based interpolation generation, ultimately expanding the dataset to approximately 10

[0062] The mathematical model or calculation process involved in the present invention is described in detail below.

[0063] Constructing the device mechanical foundation matrix in step S01 involves finite element analysis and stress calculation, wherein the mathematical expression of the device mechanical foundation matrix is as follows:

[0064]

[0065] Wherein, C is the stiffness matrix with the unit of GPa; C ij (i, j = 1, 2, 3, 4, 5, 6) are the stiffness coefficients, which describe the relationship between stress and strain. For isotropic materials, the stiffness matrix can be simplified as:

[0066]

[0067] Wherein, λ and μ are the Lame constants, which can be calculated from the elastic modulus E and Poisson's ratio ν:

[0068]

[0069] Among them, for gallium nitride materials, E is about 330 GPa and v is about 0.23; for packaging materials, E is about 15 - 25 GPa and v is about 0.35 - 0.45.

[0070] The generalized Hooke's law expresses the relationship between stress and strain:

[0071]

[0072] Wherein, σ xx 、σ yy 、σ zz are the normal stress components with the unit of MPa; τ xy 、τ yz 、τ zx are the shear stress components with the unit of MPa; ε xx 、ε yy 、ε zz are the normal strain components, dimensionless; γ xy 、γ yz 、γ zx are the shear strain components, dimensionless.

[0073] In finite element analysis, the following equilibrium equation needs to be solved:

[0074]

[0075] Wherein, σ is the stress tensor; f is the body force with the unit of N / m 3 ; ρ is the material density with the unit of kg / m 3 ; u is the displacement vector with the unit of m; t is the time with the unit of s. In static analysis, the right - hand side inertial term is zero.

[0076] The determination of the stress - sensitive region is based on the von Mises stress calculation, and its expression is:

[0077]

[0078] Wherein, σ vmis the von Mises stress, with the unit of MPa. When the gradient of σ vm is greater than 10 MPa / μm, this area is determined as the stress-sensitive area.

[0079] In step S02, it involves measuring the scattering parameter matrix by a microwave network analyzer, and its mathematical expression is:

[0080]

[0081] In the formula, S is the scattering parameter matrix; S 11 is the input reflection coefficient; S 22 is the output reflection coefficient; S 21 is the forward transmission coefficient; S 12 is the reverse transmission coefficient. Each scattering parameter is a complex number and can be expressed as:

[0082]

[0083] In the formula, |S ij | is the amplitude, with the unit of dB, usually in the range of -60 to 0 dB; φ ij is the phase, with the unit of degree, in the range of -180° to 180°; i, j ∈ {1, 2}.

[0084] During the measurement process, to improve the accuracy, multiple measurements are taken for each frequency point and the average value is calculated:

[0085]

[0086] In the formula, is the average value of the scattering parameter S ij at the frequency f; S ij，k (f) is the value of the k-th measurement; N is the number of repeated measurements, not less than 10 times.

[0087] The formula for the standard deviation is:

[0088]

[0089] In the formula, is the standard deviation of the scattering parameter S ij at the frequency f, which should be controlled within ±0.05 dB.

[0090] In step S04, the change of the scattering parameter under different stress load conditions is measured, and the formula for calculating the change amount of the scattering parameter is:

[0091] Δ|S ij |(f, σ) = |S ij (f, σ)| - |S ij (f, 0)|;

[0092] Δφ ij (f, σ) = φ ij (f, σ) - φ ij (f, 0);

[0093] In the formula, Δ|S ij |(f, σ) is the change in the magnitude of the scattering parameter S at frequency f under the stress load σ ij , with the unit of dB; Δφ ij (f, σ) is the phase change, with the unit of degree; |S ij (f, σ)| and φ ij (f, σ) are respectively the magnitude and phase of the scattering parameter under the stress load σ; |S ij (f, 0)| and φ ij (f, 0) are respectively the magnitude and phase of the scattering parameter in the stress-free state.

[0094] The stress load vector σ is expressed as:

[0095] σ = [σ x , σ y , σ z , τ xy , τ yz , τ zx T ;

[0096] In the formula, σ x , σ y , σ z are respectively the normal stresses in the x, y, and z directions, with the unit of MPa and the range of 0 - 50 MPa; τ xy , τ yz , τ zx are the shear stress components, with the unit of MPa.

[0097] In step S05, to establish the frequency-sensitive stress amplification matrix, first perform data preprocessing. The 3σ criterion for eliminating outliers is expressed as:

[0098] The data point is an outlier;

[0099] In the formula, is the standard deviation of the scattering parameter S at frequency f under the stress load σ ij .

[0100] The mathematical expression of the Savitzky-Golay filtering algorithm is:

[0101]

[0102] In the formula, is the smoothed value of the scattering parameter; c k ​are the Savitzky-Golay filter coefficients, which are solved by the least squares method; m is the half-width of the window, the window width is 2m + 1, and m = 2 is taken; Δf is the frequency step, and 0.1 GHz is taken.

[0103] A preliminary mapping relationship between the change in scattering parameters and the stress load is established by the multiple linear regression method:

[0104]

[0105] In the formula, α ij，0 (f) and β ij，0 (f) are the intercept terms; α ij，l (f) and β ij，l (f) are the regression coefficients, indicating the sensitivity of the scattering parameter to the stress component σ l ; and are the residual terms; σ l is the l-th component of the stress load vector σ. The regression coefficients are solved by the least squares method:

[0106]

[0107] In the formula, α ij (f)=[α ij，0 (f), α ij，1 (f),..., α ij，6 (f)] T ; β ij (f)=[β ij，0 (f), β ij，1 (f),..., β ij，6 (f)]T; X is the design matrix, including the constant term 1 and the stress load data; and are the amplitude change vector and the phase change vector of the scattering parameter S ij at the frequency f, respectively.

[0108] The calculation formula of the stress sensitivity coefficient K s is:

[0109]

[0110] In the formula, is the sensitivity coefficient of the amplitude of the scattering parameter S ij to the stress component σ l , with the unit of dB / MPa; is the sensitivity coefficient of the phase to the stress component σ l , with the unit of degree / MPa.

[0111] The frequency-sensitive stress amplification matrix M ampThe elements of are defined as:

[0112]

[0113] Where G(i, j, f, l) is the gain factor, which is used to improve the detection sensitivity of small stress changes. Its value is determined by experimental calibration and usually ranges from 1 to 10.

[0114] Considering the nonlinear effect, a multivariate polynomial regression model with second-order correction is introduced:

[0115]

[0116] Where, α ij，lm (f) and β ij，lm (f) is the second-order cross-term coefficient.

[0117] The goodness of fit of the model R 2 The calculation formula is:

[0118]

[0119] In the formula, is the residual sum of squares; is the total sum of squares; y n is the actual observed value; is the model prediction value; is the mean of the observed values; N is the number of data points. 2 Should be greater than 0.95.

[0120] In step S06, the characteristic frequency points are selected by calculating the Pearson correlation coefficient. The mathematical expression of the Pearson correlation coefficient is:

[0121]

[0122] Where r f，s，l is the scattering parameter component s and stress component σ at frequency f l The Pearson correlation coefficient between the two is in the range of [-1, 1]; ΔS s (f, n) is the change in the scattering parameter component s of the nth sample at frequency f; is the average value of the variation of the scattering parameter component s of all samples at frequency f; σ l (n) is the stress component σ of the nth sample l ; is the stress component σ l The average value of ; N is the number of samples. The scattering parameter components s include |S 11 |、φ 11 、|S 12 |、φ 12 、|S 21|, φ 21 |, S 22 |, φ 22 There are a total of 8 components.

[0123] The screening conditions for the characteristic frequency points are as follows:

[0124] |r f，s，l | > r threshold The frequency point f is a candidate characteristic frequency point;

[0125] In the formula, r threshold is the correlation coefficient threshold, usually taken as 0.8.

[0126] The K-means clustering algorithm is used to group the candidate characteristic frequency points, and its objective function is:

[0127]

[0128] In the formula, J is the objective function; K is the number of clusters, usually 5 - 10; C i is the i-th cluster; f is the frequency value; μ i is the center of the i-th cluster. The clustering algorithm iteratively minimizes the objective function J.

[0129] The frequency stress sparse matrix M sparse is constructed as follows:

[0130]

[0131] In the formula, M sparse (s, f, l) is an element of the frequency stress sparse matrix, representing the correlation between the scattering parameter component s at frequency f and the stress component σ l The number of characteristic frequency points is usually 10 - 20.

[0132] In step S07, a stress distribution matrix is established based on the stress response curve of the characteristic frequency points, and the expression of the fitting polynomial is:

[0133]

[0134] In the formula, ΔS s (f, σ l ) is the response of the scattering parameter component s at frequency f to the stress component σ l ; a s，f，l，p is the polynomial coefficient; P is the polynomial order, usually 2 - 3. The coefficients are determined by the least squares method, and the goodness of fit R 2 should not be less than 0.98.

[0135] The establishment of the inverse function relationship, that is, the inverse deduction of the stress distribution from the change of scattering parameters, involves solving an inverse problem. Considering the ill-posedness of the inverse problem, the Tikhonov regularization method is introduced:

[0136]

[0137] where σ est is the estimated stress distribution; A is the coefficient matrix, representing the sensitivity of the scattering parameters to the stress; b is the vector of the measured change in scattering parameters; λ is the regularization parameter, usually selected in the range of 10 -3 to 10 -5 ; Γ is the regularization matrix, usually selected as the identity matrix or the gradient operator.

[0138] The stress distribution matrix σ dist is expressed as:

[0139]

[0140]

[0141] where σ i，j，k represents the stress value at the spatial coordinates (i, j, k), with the unit of MPa; N x , N y , N z are the number of discrete points in the x, y, and z directions respectively, usually N x =N y =10, N z =5.

[0142] The Levenberg-Marquardt algorithm is used for the inverse calculation of the stress distribution, and the iterative formula is:

[0143]

[0144] where σ (n) and σ (n+1) are the stress estimates at the nth and (n + 1)th steps respectively; J n is the Jacobian matrix, and its elements are μ n is the damping factor; I is the identity matrix. The iteration termination condition is:

[0145] ||σ (n+1) -σ (n) || ∞ <0.1 MPa;

[0146] or the number of iterations reaches 100 times.

[0147] The above formulas and calculation processes constitute the mathematical basis of the stress detection method for GaN HEMT packaging, and the specific principle is described as follows.

[0148] 1. The generalized Hooke's law is the basic law describing the elastic deformation of materials. The linear relationship is applicable to the case where the material is within the elastic deformation range. In the packaging of GaN HEMT devices, the stress level is usually controlled within the elastic range of the material, so the linear relationship is applicable.

[0149] 2. The von Mises stress formula takes into account the comprehensive effect under the three-dimensional stress state and is suitable for evaluating the possible damage caused by the complex stress field to the material, and is used to determine the stress-sensitive area.

[0150] 3. The scattering parameter matrix is the standard method for describing the characteristics of microwave devices. Using the complex form can express both the amplitude and phase information of the signal simultaneously, providing comprehensive electrical parameter change data for stress detection.

[0151] 4. The Savitzky-Golay filtering algorithm can effectively filter out noise while maintaining the characteristics of the original data (such as peaks and valleys), and is especially suitable for processing high-frequency noise in scattering parameter measurements.

[0152] 5. The multiple linear regression model initially establishes the relationship between the scattering parameters and stress, while the polynomial regression introducing the second-order term can capture the non-linear effect and improve the accuracy of the model. The piezoelectric effect of GaN materials shows non-linear characteristics under high stress, so the second-order term needs to be introduced.

[0153] 6. The Pearson correlation coefficient is used to quantify the linear correlation between the scattering parameters and stress, and is suitable for screening the characteristic frequency points that are most sensitive to stress changes. The K-means clustering algorithm ensures the uniform distribution of the characteristic frequency points in the frequency domain and avoids information redundancy.

[0154] 7. The Tikhonov regularization method deals with the ill-posedness in the inverse problem. While ensuring the uniqueness and stability of the solution, it effectively suppresses the influence of measurement noise. The selection of the regularization parameter λ is based on the L-curve method to balance the fitting error and the complexity of the solution.

[0155] 8. The Levenberg-Marquardt algorithm combines the advantages of the gradient descent method and the Gauss-Newton method and has good convergence performance in non-linear least squares problems, and is suitable for solving the stress distribution inversion problem.

[0156] The comprehensive application of these equations and calculation methods realizes the accurate mapping from the change of electrical parameters to the stress distribution, providing an effective means for the stress detection of GaN HEMT devices. Compared with the traditional stress detection methods, the advantages of this solution are as follows:

[0157] 1. Non-contact measurement: Stress information is indirectly obtained by measuring scattering parameters, without the need to directly contact the stress-sensitive area and without introducing additional stress interference.

[0158] 2. High sensitivity: The frequency-sensitive stress amplification matrix improves the detection sensitivity of small stress changes and can theoretically detect stress changes as low as 0.1MPa.

[0159] 3. High resolution: The screening and sparse representation of characteristic frequency points reduce the impact of measurement noise and improve the spatial resolution of stress distribution reconstruction.

[0160] 4. Comprehensive information: Acquiring both amplitude and phase information simultaneously provides a more comprehensive stress response characteristic, helping to distinguish different types of stress effects.

[0161] 5. Real-time monitoring: Based on the trained prediction model, the stress state of the device packaging process can be monitored in real time, facilitating the timely detection of potential problems.

[0162] Specifically, the present invention is based on the unique piezoelectric and strain effects of gallium nitride (GaN) HEMTs under high-frequency operation. When operating at high frequencies ranging from several to tens of GHz, the stress distribution within the device affects its high-frequency electrical properties through various physical mechanisms. These include stress-induced changes in the band structure, modulation of the piezoelectric polarization field intensity, changes in the two-dimensional electron gas concentration and mobility, and variations in the interface state density. These changes are ultimately reflected in the device's high-frequency scattering parameters.

[0163] First, the present invention constructs a device mechanical matrix through finite element analysis, precisely identifying the most stress-sensitive regions within the GaN HEMT, particularly the gate metal-semiconductor interface and the two-dimensional electron gas channel layer. Under high-frequency electric fields, stress-induced microstructural changes in these regions significantly affect electron transport properties, thereby altering the amplitude and phase of scattering parameters. Unlike traditional static stress analysis, this invention specifically focuses on the stress-electrical coupling effect under high-frequency conditions, which provides the theoretical basis for accurate high-frequency stress detection.

[0164] Secondly, the core innovation of this invention lies in establishing a frequency-sensitive stress augmentation matrix and a frequency-stress sparse matrix. At high frequencies in the GHz range, the scattering parameters of some frequency points show significant sensitivity to stress changes, and this sensitivity exhibits nonlinear characteristics with frequency. By calculating the Pearson correlation coefficient, this method can accurately screen the characteristic frequencies that are most sensitive to stress within a wide frequency band from 1 GHz to 40 GHz. The sparse matrix composed of these characteristic frequencies significantly improves computational efficiency while retaining the most discernible stress information.

[0165] Another key technology is to construct a stress prediction model using a multi-head attention neural network. This network architecture is particularly suitable for processing high-dimensional, non-linear data with complex correlations between frequency domains such as high-frequency scattering parameters. The multi-head attention mechanism can simultaneously focus on feature changes at different frequencies. The self-attention layer captures the internal correlations between frequency points, while the sparse attention mechanism strengthens the weight assignment to feature frequency points. This deep learning model can effectively learn the complex mapping relationship between scattering parameters and stress distribution under high-frequency conditions, overcoming the limitations of traditional linear analysis methods.

[0166] In addition, the multi-channel pressure loading fixture designed in the present invention solves the technical problem of accurately controlling the stress load during high-frequency measurement, ensuring the experimental conditions required for establishing an accurate electrical-force mapping relationship. The entire technical solution forms a complete system from theoretical analysis, experimental measurement to data processing, realizing non-invasive stress detection of GaN HEMT under high-frequency working conditions.

[0167] A specific embodiment 1 of the present invention is provided below, and the specific implementation manners of each step in this embodiment 1 are described in detail as follows.

[0168] The specific implementation manner of step S01 is to construct a device mechanics basic matrix, establish a geometric model and material parameters of the GaN HEMT package structure through finite element analysis, and determine the stress-sensitive region. In this step, a three-dimensional geometric model of the GaN HEMT device is first constructed using computer-aided design software, including the substrate layer, epitaxial layer, active region, gate, source, drain structures, and packaging materials, with a model accuracy of not less than 1 μm. Then, the material parameters are set, including the elastic modulus (about 330 GPa), Poisson's ratio (about 0.23), and anisotropic thermal expansion coefficient of the GaN material; the elastic modulus (about 15 - 25 GPa), Poisson's ratio (about 0.35 - 0.45), and thermal expansion coefficient of the packaging material. Next, a mesh model is established, and the mesh size is refined to less than 0.1 μm in key regions such as the two-dimensional electron gas channel region and the gate-semiconductor interface, and can be appropriately relaxed to 0.5 - 5 μm in other regions. The mathematical expression for constructing the device mechanics basic matrix is as follows:

[0169]

[0170] In the formula, C is the stiffness matrix, with the unit of GPa; C ij (i, j = 1, 2, 3, 4, 5, 6) are stiffness coefficients, describing the relationship between stress and strain. For isotropic materials, the stiffness matrix can be simplified as:

[0171]

[0172] In the formula, λ and μ are Lame constants, which can be calculated from the elastic modulus E and Poisson's ratio v:

[0173]

[0174] The stress distribution under predefined stress load conditions is calculated using a partial differential equation solver, such as a uniaxial pressure ranging from 0 MPa to 100 MPa, a temperature ranging from 25 °C to 200 °C, etc. The generalized Hooke's law expresses the relationship between stress and strain:

[0175]

[0176] where σ xx 、σ yy 、σ zz are the normal stress components, with the unit of MPa; τ xy 、τ yz 、τ zx are the shear stress components, with the unit of MPa; ε xx 、ε yy 、ε zz are the normal strain components, dimensionless; γ xy 、γ yz 、γ ax are the shear strain components, dimensionless. In finite element analysis, the following equilibrium equation needs to be solved:

[0177]

[0178] where σ is the stress tensor; f is the body force, with the unit of N / m 3 ; ρ is the material density, with the unit of kg / m 3 ; u is the displacement vector, with the unit of m; t is the time, with the unit of s. In static analysis, the right-side inertial term is zero. By analyzing the stress distribution contour map, the stress-sensitive regions are determined. Typical stress-sensitive regions include the gate metal-semiconductor interface, the two-dimensional electron gas channel layer, the transition interface between the epitaxial layer and the substrate, and the connection between the package solder joints and the chip. The determination of the stress-sensitive regions is based on the von Mises stress calculation, and its expression is:

[0179]

[0180] where σ vm is the von Mises stress, with the unit of MPa. When the gradient of σ vm is greater than 10 MPa / μm, this region is determined as a stress-sensitive region. The purpose of this step is to establish a mechanical model of the GaN HEMT device, provide a theoretical basis and guidance for subsequent experimental measurements, and determine the key measurement regions.

[0181] The specific implementation of step S02 is to use a microwave network analyzer to measure the scattering parameter matrix of a gallium nitride HEMT in the frequency range from 1 GHz to 40 GHz under a stress-free state. This step first prepares the test environment, including a shielded room with the temperature controlled at 25 ± 1 °C and the humidity controlled at 45% ± 5% to eliminate the interference of environmental factors on high-frequency measurements. Then, a standard calibration component is connected to the vector network analyzer for full two-port calibration, including open-circuit, short-circuit, load, and through calibration (SOLT calibration method), ensuring that the measurement error is less than ±0.1 dB and ±1°. Next, the gallium nitride HEMT device to be tested is fixed on the test fixture to ensure that the device is in a state without external force and thermal stress, and it is monitored by an infrared thermal imager to confirm that the device temperature is uniform and maintained at 25 ± 0.5 °C. The mathematical expression of the scattering parameter matrix is:

[0182]

[0183] where S is the scattering parameter matrix; S 11 is the input reflection coefficient; S 22 is the output reflection coefficient; S 21 is the forward transmission coefficient; S 12 is the reverse transmission coefficient. Each scattering parameter is a complex number and can be expressed as:

[0184]

[0185] where |S ij | is the amplitude, with the unit of dB, usually in the range of -60 to 0 dB; φ ij is the phase, with the unit of degree, in the range of -180° to 180°; i, j ∈ {1, 2}. Set the scanning parameters of the vector network analyzer, with the frequency range from 1 GHz to 40 GHz, the frequency step of 0.1 GHz, the intermediate frequency bandwidth set to 1 kHz to improve the signal-to-noise ratio, and the input power controlled below -20 dBm to avoid the non-linear effect of the device. During the measurement process, to improve the accuracy, multiple measurements are taken at each frequency point and averaged:

[0186]

[0187] where is the average value of the scattering parameter S ij at frequency f; S ij，k (f) is the value of the k-th measurement; N is the number of repeated measurements, not less than 10 times. The standard deviation calculation formula is:

[0188]

[0189] where is the scattering parameter S ijThe standard deviation should be controlled within ±0.05 dB. The measured reference scattering parameter matrix data is stored as a reference standard for subsequent comparison with the measurement results under the stressed state. The purpose of this step is to obtain the high-frequency electrical characteristic data of the device in the stress-free reference state and establish a reference benchmark for stress monitoring.

[0190] The specific implementation of step S03 is to design and fabricate a multi-channel pressure loading fixture to subject the gallium nitride HEMT to precisely controlled uniaxial or multiaxial mechanical stress. This step first designs the multi-channel pressure loading fixture based on the finite element analysis results. The fixture material is selected as invar alloy with a low coefficient of thermal expansion (≤5×10 -6 / °C) to minimize the influence of thermal stress caused by temperature changes. The fixture includes at least four independently controlled pressure channels, which can apply precise mechanical stress to the device in the three main axis directions (X, Y, Z) and the torsion direction respectively. Each pressure channel is equipped with a precision piezoelectric ceramic actuator with a displacement resolution better than 0.01 μm and a maximum stroke of not less than 100 μm; at the same time, a high-precision force sensor is integrated, with a measurement accuracy better than 0.1 N and a range of 0 - 50 N. The microwave test interface is integrated in the fixture design, using low-loss coaxial connectors, with a working frequency covering DC to 40 GHz and an insertion loss less than 0.5 dB. Each component of the fixture is machined and manufactured, with the surface roughness controlled below Ra0.4 μm and the tolerance of each key dimension controlled within ±0.01 mm. The fixture system is assembled and connected to the computer control system, and the control software is developed to achieve precise control of stress loading, with a stress control accuracy better than ±0.1 MPa and the stress loading rate adjustable in the range of 0.01 - 10 MPa / s. The fixture is calibrated, and a standard strain gauge is used to verify the linearity and repeatability of stress loading in each direction, ensuring that the linear error is less than 1% and the repeatability error is less than 0.5%. The purpose of this step is to construct an experimental platform that can apply precisely controllable mechanical stress to the gallium nitride HEMT device and provide the necessary conditions for studying the influence of stress on the high-frequency characteristics of the device.

[0191] The specific implementation of step S04 is to measure the high-frequency scattering parameter matrix of the gallium nitride HEMT under different stress load conditions and record the change values of electrical parameters. This step first installs the gallium nitride HEMT device in the multi-channel pressure loading fixture to ensure that the main axis direction of the device is precisely aligned with the fixture loading direction, with the deviation angle controlled within ±0.5°. Then, a stress loading scheme is set, including uniaxial stress tests (from 0 MPa to 50 MPa in the X, Y, Z directions respectively, with a step of 5 MPa) and combined stress tests (including at least 5 typical stress combination modes). The stress load vector σ is expressed as:

[0192] σ = [σ x ,σ y ,σ z ,τ xy, τ yz , τ zx T ;

[0193] wherein, σ x , σ y , σ z are the normal stresses in the x, y, and z directions respectively, with the unit of MPa and the range of 0 to 50 MPa; τ xy , τ yz , τ zx are shear stress components, with the unit of MPa. For each stress load condition, a control system is used to stably apply a set stress, and the stabilization time is not less than 30 seconds, and the stress fluctuation is controlled within ±0.5% of the set value. After each stress load condition is stabilized, a microwave network analyzer is used to measure the scattering parameter matrix of the device in the frequency range of 1 GHz to 40 GHz, with the same measurement settings and accuracy requirements as in step S02. Measure the changes in the scattering parameters under different stress load conditions, and the formula for calculating the change in the scattering parameters is:

[0194] Δ|S ij |(f, σ) = |S ij (f, σ)| - |S ij [[ID=3]](f, 0);

[0195] Δφ ij (f, σ) = φ ij (f, σ) - φ ij (f, 0);

[0196] wherein, Δ|S ij |(f, σ) is the change in the amplitude of the scattering parameter S ij at frequency f under the stress load σ, with the unit of dB; Δφ ij (f, σ) is the phase change amount, with the unit of degree; |S ij (f, σ)| and φ ij (f, σ) are respectively the amplitude and phase of the scattering parameter under the stress load σ; |S ij (f, 0)| and φ ij (f, 0) are respectively the amplitude and phase of the scattering parameter in the stress-free state. To eliminate random errors, each stress load condition is measured at least 5 times repeatedly, and the average value is taken as the effective measurement result under this condition. Establish a corresponding database of stress load and scattering parameter changes, including high-frequency scattering parameter change data under at least 100 different stress load conditions. The purpose of this step is to obtain the high-frequency electrical property change data of the gallium nitride HEMT device under different stress load conditions, and provide an experimental basis for establishing the corresponding relationship between stress and electrical properties in the follow-up.

[0197] ​The specific implementation of step S05 is to establish a frequency-sensitive stress amplification matrix, and establish a mathematical correspondence between the scattering parameter matrix and the stress load. This step first preprocesses the experimental data obtained in step S04, including outlier detection and removal, and data smoothing. The 3σ criterion for removing outliers is expressed as:

[0198] The data point is an outlier;

[0199] In the formula, is the standard deviation of the scattering parameter S at frequency f under stress load σ ij . The Savitzky-Golay filtering algorithm is used for data smoothing, and its mathematical expression is:

[0200]

[0201] In the formula, is the smoothed scattering parameter value; c k is the Savitzky-Golay filter coefficient, which is solved by the least squares method; m is the window half-width, the window width is 2m + 1, and m = 2 is taken; Δf is the frequency step, and 0.1 GHz is taken. Then, for each frequency point (from 1 GHz to 40 GHz, at an interval of 0.1 GHz), the relationship between the change in the scattering parameter (amplitude and phase) and the stress load is calculated respectively, and a preliminary mapping relationship is established using the multiple linear regression method:

[0202]

[0203] In the formula, α ij，0 (f) and β ij，0 (f) are the intercept terms; α ij，l (f) and β ij，l (f) are the regression coefficients, indicating the sensitivity of the scattering parameter to the stress component σ l ; and are the residual terms; σ l is the l-th component of the stress load vector σ. The regression coefficients are solved by the least squares method:

[0204]

[0205] In the formula, α ij (f) = [α ij，0 (f), α ij，1 (f),..., α ij，6 (f)] T ; β ij (f) = [β ij，0 (f), β ij，1 (f),..., β ij，6(f)] T ; x is the design matrix, including the constant term 1 and stress load data; and are the amplitude change amount and phase change amount vectors of the scattering parameter S ij at frequency f, respectively. Sensitivity analysis is performed on each component of the scattering parameter at each frequency point to calculate the stress sensitivity coefficient K s , which is defined as the ratio of the change amount of the scattering parameter to the change amount of the stress:

[0206]

[0207] In the formula, is the sensitivity coefficient of the amplitude of the scattering parameter S ij at frequency f to the stress component σ l , with the unit of dB / MPa; is the sensitivity coefficient of the phase to the stress component σ l , with the unit of degree / MPa. Based on the sensitivity analysis results, a frequency-sensitive stress amplification matrix M amp is constructed, and its elements are defined as:

[0208]

[0209] In the formula, G(i, j, f, l) is the gain factor, which is used to improve the detection sensitivity of small stress changes, and its value is determined by experimental calibration, usually in the range of 1 to 10. Considering the nonlinear effect of the scattering parameter, a second-order term correction is introduced, and a multiple polynomial regression model is used to improve the mapping relationship:

[0210]

[0211] In the formula, α ij，lm (f) and β ij，lm (f) are the second-order cross-term coefficients. The goodness of fit R 2 of the model is calculated as:

[0212]

[0213] In the formula, is the sum of squared residuals; is the total sum of squares; y n is the actual observed value; is the model predicted value; is the average value of the observed values; N is the number of data points. R 2It should be greater than 0.95. The cross-validation method (K-fold cross-validation, K = 5) is used to evaluate the generalization ability of the model, ensuring that the model still has good prediction accuracy under unseen stress load conditions, and the prediction error is controlled within ±5%. The purpose of this step is to establish a quantitative correspondence between the change of scattering parameters and stress loads, laying a mathematical foundation for subsequent stress prediction.

[0214] The specific implementation of step S06 is to calculate and construct a frequency-stress sparse matrix using the Pearson correlation coefficient, and screen out the characteristic frequency points that are most sensitive to stress loads. This step first conducts statistical analysis on the frequency-sensitive stress augmented matrix data obtained in step S05, and calculates the Pearson correlation coefficient between the change of scattering parameters and the change of stress loads at each frequency point. The mathematical expression of the Pearson correlation coefficient is:

[0215]

[0216] In the formula, r f，s，l is the Pearson correlation coefficient between the scattering parameter component s and the stress component σ l at frequency f, and its value range is [-1, 1]; ΔS s (f, n) is the change amount of the scattering parameter component s at frequency f for the nth sample; is the average value of the change amounts of the scattering parameter component s at frequency f for all samples; σ l (n) is the stress component σ l of the nth sample; is the average value of the stress component σ l ; N is the number of samples. The scattering parameter component s includes |S 11 |, φ 11 , |S 12 |, φ 12 , |S 21 |, φ 21 , |S 22 , φ 22 a total of 8 components. The screening conditions for characteristic frequency points are:

[0217] |r f，s，l | > r threshold The frequency point f is a candidate characteristic frequency point;

[0218] In the formula, r threshold is the correlation coefficient threshold, usually taken as 0.8. According to the absolute value of the correlation coefficient, all frequency points are sorted from high to low in terms of sensitivity, and the frequency points with the absolute value of the correlation coefficient greater than the threshold (usually taken as 0.8) are screened as candidate characteristic frequency points. Considering the distribution characteristics of the frequency points, the K-means clustering algorithm is applied to group the candidate characteristic frequency points, and its objective function is:

[0219]

[0220] In the formula, J is the objective function; K is the number of clusters, usually 5 to 10; C i is the i-th cluster; f is the frequency value; μ i is the center of the i-th cluster. The clustering algorithm iteratively minimizes the objective function J. The frequency point with the largest absolute value of the correlation coefficient is selected from each group as the final characteristic frequency point to ensure the dispersion of the characteristic frequency points in the frequency domain. Construct the frequency stress sparse matrix M sparse , and only the elements corresponding to the characteristic frequency points are retained in this matrix, and the remaining elements are set to zero:

[0221]

[0222] In the formula, M sparse (s, f, l) is an element of the frequency stress sparse matrix, representing the correlation between the scattering parameter component s and the stress component σ l at frequency f. The effectiveness of the frequency stress sparse matrix is verified through reconstruction experiments to ensure that the stress prediction accuracy using the sparse matrix is not less than 95% of the accuracy using the complete matrix. The number of finally selected characteristic frequency points is usually 10 to 20, and these characteristic frequency points should be distributed throughout the frequency range from 1 GHz to 40 GHz. The purpose of this step is to reduce the data dimension, extract the most informative characteristic frequency points, reduce redundant information, and improve the efficiency and robustness of stress prediction.

[0223] The specific implementation of step S07 is to establish a stress distribution matrix based on the stress response curve of the characteristic frequency points for back-inferring the unknown stress distribution. This step first plots the stress response curve for each characteristic frequency point, that is, the curve of the change in the scattering parameter as a function of the stress load. The stress response curve is mathematically expressed using the polynomial fitting method, and the expression of the fitting polynomial is:

[0224]

[0225] In the formula, ΔS s (f, σ l ) is the response of the scattering parameter component s to the stress component σ l at frequency f; a s，f，l，p is the polynomial coefficient; P is the polynomial order, usually 2 to 3. The coefficients are determined by the least squares method, and the goodness of fit R 2 should not be less than 0.98. Then, an inverse function relationship between the change in the scattering parameter and the stress distribution is established, and the inverse mapping method is used to map the change in the scattering parameter to the stress distribution space. Considering the ill-posedness of the inverse problem (i.e., multiple stress distributions may lead to similar changes in the scattering parameter), the Tikhonov regularization method is introduced for solution stabilization:

[0226]

[0227] where σ est is the estimated stress distribution; A is the coefficient matrix representing the sensitivity of the scattering parameter to stress; b is the vector of measured changes in the scattering parameter; λ is the regularization parameter, usually chosen in the range of 10 -3 to 10 -5 ; Γ is the regularization matrix, usually chosen as the identity matrix or the gradient operator. The stress distribution matrix σ dist is constructed, which represents the stress values at key points inside the GaN HEMT device and is expressed as:

[0228]

[0229] where σ i，j，k represents the stress value at the spatial coordinates (i, j, k) with the unit of MPa; N x , N y , N z are the number of discrete points in the x, y, and z directions respectively, usually N x = N y = 10, N z = 5. The Levenberg - Marquardt algorithm is applied for stress distribution inversion calculation, and the iterative formula is:

[0230]

[0231] where σ (n) and σ (n+1) are the stress estimates at the nth and (n + 1)th steps respectively; J n is the Jacobian matrix, and its elements are μ n is the damping factor; I is the identity matrix. The convergence condition is set as the change in stress distribution between adjacent iterative steps is less than 0.1 MPa or the number of iterations reaches 100 times:

[0232] ||σ (n+1) - σ (n) || ∞ < 0.1 MPa.

[0233] The rationality of the inversion result is verified by finite element to ensure that the consistency error between the inverted stress distribution and the finite element simulation result is less than 10%. The purpose of this step is to establish an inversion method from electrical parameter changes to stress distribution to achieve indirect measurement and evaluation of the internal stress state of the device.

[0234] The specific implementation of step S08 is to use a pre-trained stress prediction model for prediction. The input is the scattering parameter matrix, and the output is the stress distribution matrix of the key area of the gallium nitride HEMT. This step first loads a pre-trained multi-head attention neural network model, which includes an input layer, multiple self-attention layers, a sparse attention mechanism layer, a fully connected layer, and an output layer. The measured scattering parameter matrix data is preprocessed, including normalization (using the Z-score normalization method to make the data mean 0 and the standard deviation 1) and dimension transformation (reorganized into a data format suitable for network input). According to the normalization method, the calculation formula for the normalized scattering parameter is:

[0235]

[0236] In the formula, S ij，norm (f) is the normalized scattering parameter; S ij (f) is the original scattering parameter; is the mean of this scattering parameter in the training dataset; is the standard deviation of this scattering parameter in the training dataset. The preprocessed scattering parameter matrix data is input into the neural network model. In the forward propagation process of the neural network, the multi-head self-attention layer is first used to capture the correlation between scattering parameters of different frequencies. The number of attention heads is usually set to 8, and the hidden layer dimension is 256. The mathematical expression of the multi-head self-attention mechanism is:

[0237] MultiHead(Q, K, V) = Concat(head1, head2,..., head h )W O ;

[0238] head i = Attention(QW i Q , KW i K , VW i V );

[0239]

[0240] In the formula, Q, K, and V are the query, key, and value matrices respectively; W i Q , W i K , W i V and W O are weight matrices; d kis the dimension of the key vector; h is the number of attention heads, usually 8. Then, through the sparse attention mechanism layer, this layer sparsifies the attention weights according to the characteristic frequency point information determined in step S06, and the sparsity is usually controlled above 90%, that is, most of the attention weights are approximately zero. The mathematical expression of the sparse attention mechanism is:

[0241]

[0242] In the formula, M is the mask matrix, the elements corresponding to the characteristic frequency points are 1, and the rest are 0; ⊙ represents element-wise multiplication. Then, the feature vector is mapped to the stress distribution space through a fully connected layer. The number of neurons in the fully connected layer usually decreases layer by layer as 1024, 512, 256. The mathematical expression of the fully connected layer is:

[0243] y = σ(Wx + b);

[0244] In the formula, y is the output vector; x is the input vector; W is the weight matrix; b is the bias vector; σ is the activation function, usually the ReLU function: σ(x) = max(0, x). Finally, the predicted stress distribution matrix is given through the output layer, and this matrix represents the stress distribution state of the key regions of the device (such as the gate metal-semiconductor interface, two-dimensional electron gas channel layer, etc.):

[0245]

[0246] In the formula, is the predicted stress distribution matrix; f NN is the function representation of the entire neural network model; S norm is the normalized scattering parameter matrix. Evaluate the reliability of the prediction results, including prediction error analysis (compared with finite element simulation) and uncertainty quantification (estimating the confidence interval of the prediction results using the Monte Carlo method). The prediction error is defined as:

[0247]

[0248] In the formula, is the predicted stress distribution matrix; σ true is the true stress distribution matrix (obtained through finite element simulation or experimental measurement); ||·||2 represents the 2-norm of the matrix. The prediction error should be controlled within 10%. The purpose of this step is to use the deep learning model to achieve fast and accurate prediction of the internal stress distribution of the gallium nitride HEMT device, providing an important basis for device reliability evaluation and failure analysis.

[0249] The stress prediction model adopts a multi-head attention neural network structure based on deep learning. This model is used to predict the internal stress distribution of GaN HEMT from the high-frequency scattering parameter matrix. The model structure includes the following key components: The input layer receives the normalized scattering parameter matrix data with a dimension of [batch size × number of frequency points × 4], where 4 represents the amplitudes and phases of S 11 、S 12 、S 21 、S 22 in total 8 features, which are processed for dimensionality reduction into 4 complex parameters; The encoding layer uses a 1D convolutional neural network for feature extraction, including 3 convolutional layers with kernel sizes of 5, 3, 3 respectively, and the number of channels are 64, 128, 256 respectively. After each layer, batch normalization and ReLU activation function are connected; The multi-layer self-attention layer captures the correlation between different frequency scattering parameters, including 4 attention layers, each layer has 8 attention heads, the embedding dimension is 256, and the dimension of the feed-forward network is 1024; The sparse attention mechanism layer assigns weights according to the frequency stress sensitivity index, and the weight coefficients corresponding to important frequency points increase significantly. The Top-K sparsification method is adopted to retain only the most significant 10% - 20% of the attention weights; The fully connected layer maps the feature vector to the stress distribution space, including 3 fully connected layers with the number of neurons being 1024, 512, 256 respectively. After each layer, Dropout (ratio 0.2) and Layer Normalization are connected; The output layer gives the predicted stress distribution matrix with a dimension of [batch size × spatial resolution X × spatial resolution Y × spatial resolution Z], usually [batch size × 10 × 10 × 5], representing the stress distribution in three-dimensional space.

[0250] The detailed steps for establishing the model training data set include: in the data acquisition phase, a multi-channel pressure loading fixture is used to apply stress loads of different directions (X, Y, Z and combined directions) and different sizes (0MPa to 50MPa, with a step of 2MPa) to at least 30 typical GaN HEMT samples, and the corresponding scattering parameter matrix is measured, generating a total of about 3000 valid data samples; in the finite element simulation phase, based on the device mechanical model established in step S01, a detailed finite element simulation is performed for each experimental stress load condition to calculate the stress distribution state inside the device with a spatial resolution of not less than 0.1μm; in the data pair establishment phase, the scattering parameter matrix is compared with the The corresponding stress distribution matrices are paired to form input-output data pairs, and data cleaning is performed to eliminate abnormal samples (such as samples with obvious measurement errors or non-convergence of simulation); in the data enhancement stage, a variety of techniques are used to expand the number of training samples, including adding Gaussian noise (the signal-to-noise ratio is controlled above 30dB), small random perturbations (the amplitude does not exceed ±2% of the original data), and interpolation generation based on physical models, ultimately expanding the data set to approximately 10,000 samples; in the data set division stage, a stratified sampling method is used to divide the data set into a training set (70%), a validation set (15%), and a test set (15%) to ensure the balance of stress load distribution in each subset.

[0251] The specific training process of the stress prediction model is as follows: First, initialize the weight parameters of the multi-head attention neural network using the He initialization method, that is, the initial value of the weight obeys the mean of 0 and the standard deviation of Normal distribution, where n in is the number of input units; the training data is input batch by batch using the mini-batch stochastic gradient descent optimization algorithm, the batch size is 64, and the learning rate is initially set to 0.001; the mean square error loss function between the predicted stress distribution matrix and the true stress distribution matrix is calculated:

[0252]

[0253] Where, is the mean square error loss; N is the batch size; is the predicted stress distribution matrix of the i-th sample; σ i，true is the true stress distribution matrix of the i-th sample. The network weights are updated using the back-propagation algorithm, and the Adam optimizer is used with parameters set to β1 = 0.9, β2 = 0.999, ∈ = 10 -8 ; Dynamically adjust the learning rate, using the cosine annealing strategy, and the learning rate changes with the training rounds:

[0254]

[0255] Where η t is the learning rate of the tth round; η minand η max are the minimum and maximum learning rates, usually set to η min = 10 -5 , η max = 10 -3 ; T is the total number of training rounds, usually set to 100 rounds. To avoid overfitting, L2 regularization and early stopping strategies are adopted. The L2 regularization coefficient is set to 10 -4 , and the early stopping patience value is set to 20 rounds, that is, if the loss on the validation set has not improved for 20 consecutive rounds, the training is stopped; the model performance is evaluated on the validation set, and the metrics include mean squared error (MSE), mean absolute error (MAE), and relative error percentage; the sparse attention mechanism weight coefficient is adjusted for the feature frequency points with high frequency sensitivity, and the attention distribution function is used:

[0256]

[0257] In the formula, A(f) is the attention degree of frequency point f; S(f) is the sensitivity index of frequency point f, which is determined by the Pearson correlation coefficient; α is the temperature parameter, which controls the concentration degree of the attention distribution, usually set to 5 - 10; the optimal model parameters are saved for actual stress prediction, and the judgment criterion for the optimal model is the minimum average relative error on the validation set.

[0258] To better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: In a study on the encapsulation stress detection of gallium nitride HEMT, researchers conducted an encapsulation stress detection and analysis on high-power gallium nitride HEMT devices used in 5G communication base stations. The studied gallium nitride HEMT devices adopt a GaN / AlGaN heterostructure, with a gate length of 0.25 μm, a gate width of 8 × 200 μm, a working frequency range of 1 - 40 GHz, a maximum working power of 12 W, and a working temperature range of -40 - 125°C. The device uses a metal-ceramic package, and the chip is bonded to the package substrate with AuSn solder. The size after encapsulation is 10 mm × 8 mm × 2 mm.

[0259] First, the researchers constructed a three-dimensional geometric model and a mechanical basis matrix of the gallium nitride HEMT device according to step S01. A fine model including the substrate, buffer layer, active layer, gate, source, drain, and packaging material was established through finite element software. In the model, the mesh size of key regions such as the two-dimensional electron gas channel and near the gate was set to 0.08 μm, and the mesh size of other regions was 0.5 - 3 μm. The total number of meshes was approximately 2.36 million. The material parameters used are shown in Table 1:

[0260] Table 1 Material Parameter Table of Gallium Nitride HEMT Devices

[0261] Material Elastic Modulus (GPa) Poisson's Ratio <![CDATA[Coefficient of thermal expansion (10 -6 / K)]]> GaN 330 0.23 3.17 AlGaN 315 0.25 4.03 SiC Substrate 450 0.21 4.6 Gate Metal (Au) 78 0.42 14.2 Source / Drain Metal (Al) 70 0.35 23.1 AuSn Solder 68 0.40 16.3 Packaging Ceramic 340 0.26 6.8

[0262] Through finite element analysis, the main stress-sensitive regions of the device were determined to include: the gate metal-semiconductor interface, the two-dimensional electron gas channel region, the chip-substrate transition interface, and the connection between the chip and the package solder joint. The von Mises stress gradients in these regions all exceeded 12 MPa / μm, indicating that these regions are particularly sensitive to external mechanical stress.

[0263] According to step S02, the researchers used a Keysight N5247A vector network analyzer to measure the scattering parameter matrix of the device in a stress-free state. The measurement was carried out in a shielded room at a temperature of 25 ± 0.3 °C and a humidity of 40 ± 3%, calibrated using the SOLT method, scanned at intervals of 0.1 GHz in the frequency range of 1 - 40 GHz, and measured 12 times at each frequency point and averaged to obtain the reference scattering parameter matrix data. The scattering parameter values at some characteristic frequency points in the stress-free state are shown in Table 2:

[0264] Table 2 Scattering parameter values at characteristic frequency points in the stress-free state

[0265] Frequency (GHz) <![CDATA[||S 11 ||(dB)]]> <![CDATA[φ 11 (degree)]]> <![CDATA[||S 21 ||(dB)]]> <![CDATA[φ 21 (degree)]]> 2.5 -18.35 -45.63 8.92 70.21 5.8 -16.42 -74.85 7.86 42.37 9.3 -14.75 -113.24 6.54 11.82 15.7 -13.28 -157.46 5.03 -35.64 22.4 -10.53 176.82 3.85 -82.46 28.9 -8.76 132.35 2.47 -134.53 35.2 -7.42 85.67 1.28 -173.28

[0266] Next, the researchers designed and fabricated a multi-channel pressure loading fixture according to step S03. The fixture is made of invar alloy material with a thermal expansion coefficient of 1.3×10 -6 / K, equipped with 4 precision piezoelectric actuators with a displacement accuracy of 0.005 μm and a maximum stroke of 120 μm. The fixture integrates a high-precision force sensor (accuracy ±0.05 N) and a microwave test interface (insertion loss <0.3 dB), and can apply precisely controlled mechanical stress in the X, Y, Z three directions and the torsion direction.

[0267] Specifically, as Figure 2 shown, in this embodiment, the specific implementation of the multi-channel pressure loading fixture uses a high-rigidity titanium alloy base platform to ensure the overall structural stiffness during the measurement process. Micro-vibration isolation support feet are set around the base to effectively suppress the interference of external vibration on the measurement accuracy. The precision positioning system consists of a three-axis micro-motion platform with an X-Y plane displacement accuracy of 0.5 μm for the initial positioning of the device; the Z-axis uses a piezoelectric ceramic actuator with closed-loop control and a displacement resolution of 10 nm to ensure the accuracy of the vertical direction pressure application. As Figure 3As shown in the figure, the multi-axis pressure application mechanism includes four independent pressure channels, namely two orthogonal horizontal directions (X, Y axes), the vertical direction (Z axis), and a rotary channel for applying torsional moment. The force measurement ranges of the X, Y, and Z directions are from 0.1 N to 50 N, with an accuracy better than 0.05 N. The torque measurement range of the rotary channel is from 0.01 N·m to 2 N·m, with an accuracy better than 0.005 N·m. All pressure channels achieve precise control of force and displacement through a stiffness compensation algorithm, eliminating the errors caused by the elastic deformation of the mechanism itself. As Figure 4 shown, the high-frequency test interface adopts a G-S-G (Ground-Signal-Ground) probe structure, supporting S-parameter measurements in the frequency range of 1 GHz to 40 GHz. The probes are installed on independent high-precision three-dimensional micro-motion brackets, independent of the pressure loading system to avoid mutual interference. A specially designed probe pressure self-compensation mechanism ensures that when the device is deformed by external stress, the probe contact pressure and the contact point position remain stable. The entire fixture system realizes automated operation through a customized multi-channel control software. The software integrates functions such as pressure loading, high-frequency measurement, data acquisition and processing, and can preset various complex stress loading modes, such as stepped loading, sinusoidal dynamic loading, etc. At the same time, it records the data of the force sensor and the microwave network analyzer in real time, establishing the corresponding relationship between stress and the S-parameter matrix. The test area is designed with a constant temperature, and the temperature fluctuation is controlled within the range of ±0.5 °C to eliminate the influence of temperature changes on the measurement results.

[0268] According to step S04, the researchers measured the changes in the high-frequency scattering parameters of the device under different stress load conditions. Systematic measurements were carried out under the stress in the X direction from 0 MPa to 45 MPa (step 5 MPa), in the Y direction from 0 MPa to 30 MPa (step 5 MPa), in the Z direction from 0 MPa to 20 MPa (step 5 MPa), and under 6 combined stresses. Each stress condition was measured 6 times repeatedly, and a database containing 135 different stress load conditions was established.

[0269] According to step S05, the researchers processed and analyzed the measurement data and constructed a frequency-sensitive stress amplification matrix. The Savitzky-Golay filtering algorithm (window width 5, polynomial order 2) was used to smooth the scattering parameter data, and then a multivariate polynomial regression model was applied to establish the mapping relationship between the changes in scattering parameters and stress loads.

[0270] Table 3 shows the stress sensitivity coefficients at some frequency points:

[0271] Table 3 Stress Sensitivity Coefficients at Some Frequency Points

[0272]

[0273]

[0274] In step S06, the researchers used the Pearson correlation coefficient to calculate and screen out the characteristic frequency points that are most sensitive to stress. By setting the correlation coefficient threshold to 0.82, 43 candidate characteristic frequency points were initially screened out, and then the K-means clustering algorithm (K = 8) was applied for grouping. Finally, 16 characteristic frequency points were selected, which are evenly distributed in the range of 1 - 40 GHz.

[0275] According to step S07, the researchers established a stress distribution matrix based on the stress response curves of the characteristic frequency points. The stress response curves of each characteristic frequency point were fitted with a third-order polynomial, and the goodness of fit R 2 reached an average of 0.987. The Tikhonov regularization method (regularization parameter λ = 5×10 -4 ) was used to establish the inverse function relationship between the change in scattering parameters and the stress distribution. The Levenberg-Marquardt algorithm was used for iterative calculation, with an average convergence speed of 32 iterations. The spatial resolution of the finally reconstructed stress distribution matrix is 10×10×5.

[0276] Finally, according to step S08, the researchers used the trained multi-head attention neural network model for stress prediction. The model includes 4 layers of attention mechanisms (8 attention heads, embedding dimension 256), 1 layer of sparse attention mechanism (sparsity 92%), and 3 layers of fully connected layers (the number of neurons is 1024, 512, and 256 respectively). After 100 rounds of training (batch size 64, initial learning rate 0.001), the average relative error of the model on the test set is 7.3%. By inputting the scattering parameters under the unknown stress state into the model, the stress distribution state inside the device can be quickly predicted, and the entire prediction process only takes 0.8 seconds. The comparison and verification of the prediction results with finite element simulation show that the stress prediction accuracy in the key area reaches 91.2%.

[0277] Compared with traditional stress detection methods, the technology implemented in the present invention has significant advantages. Traditional methods mainly rely on direct measurement techniques (such as optical interferometry, X-ray diffraction, Raman spectroscopy, etc.) or finite element simulations. These methods have problems such as limited measurement range, low spatial resolution, the need for complex equipment, inability to monitor in real time, or large computational requirements. The present invention indirectly obtains stress information by measuring the high-frequency scattering parameters of the device, realizing non-contact detection of internal stress. The spatial resolution has been increased by more than 3 times, the detection sensitivity has been increased by about 5 times (able to detect stress changes as low as 1 MPa), and the detection speed has been increased by about 20 times. Especially in combination with deep learning technology, it has realized the rapid and accurate prediction of stress distribution in complex packaging structures, providing a more efficient tool for the reliability evaluation and failure analysis of gallium nitride HEMT devices. This method has been successfully applied to the design optimization of a certain type of 5G base station power amplifier module, effectively reducing the failure rate caused by stress of the device from 3.7% in the early stage to 0.8%, and greatly extending the service life of the device.

[0278] It should be noted that the detailed explanations of the variables involved in the present invention are shown in Tables 4 and 5 below.

[0279] Table 4 Variable Explanation Table (First Part)

[0280]

[0281]

[0282] Table 5 Variable Explanation Table (Second Part)

[0283]

[0284]

[0285] Table 6 Variable Explanation Table (Third Part)

[0286]

[0287] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A method for detecting the stress of a gallium nitride HEMT package, characterized in that, include: Construct the basic mechanical matrix of the device and determine the stress-sensitive area; Measure the scattering parameter matrix of GaN HEMT in the unstressed state from 1 GHz to 40 GHz; Design and manufacture a multi-channel pressure loading fixture to subject the GaN HEMT to precisely controlled mechanical stress; measure the high-frequency scattering parameter matrix of the GaN HEMT under different stress loading conditions and record the changes in electrical parameters; Establish a frequency-sensitive stress augmentation matrix and establish a mathematical correspondence between the scattering parameter matrix and the stress load; The Pearson correlation coefficient is used to calculate and construct a frequency stress sparse matrix to screen out the characteristic frequency points that are most sensitive to stress loads; Based on the characteristic frequency stress response curve, a stress distribution matrix is established to infer the unknown stress distribution; The stress prediction model is used for prediction, with the input being the scattering parameter matrix and the output being the stress distribution matrix of the key area of the GaN HEMT.

2. The method for detecting the stress of the gallium nitride HEMT package according to claim 1, wherein The mechanical basic matrix of the device is constructed by establishing a geometric model of the GaN HEMT packaging structure and material parameters through finite element analysis to determine the stress sensitive area.

3. The method for detecting the stress of the gallium nitride HEMT package according to claim 2, characterized in that The device mechanical basic matrix refers to a mathematical expression established through finite element analysis to describe the stress distribution of gallium nitride HEMT under different stress load conditions, including the material elastic modulus, Poisson's ratio and geometric dimensions as key parameters.

4. The method for detecting the stress of the gallium nitride HEMT package according to claim 3, wherein The scattering parameter matrix refers to a complex matrix that describes the relationship between the input and output signals of a microwave network, and is usually expressed as S parameters, including the S11 reflection coefficient and the S21 transmission coefficient.

5. The method for detecting the stress of a gallium nitride HEMT package according to claim 4, wherein The frequency-sensitive stress augmentation matrix refers to an amplification relationship matrix established between the electrical parameter changes and mechanical stress changes of the gallium nitride HEMT at the characteristic frequency point, which is used to improve the detection sensitivity of small stress changes.

6. The gallium nitride HEMT package stress detection method according to claim 5, wherein The frequency stress sparse matrix refers to a matrix composed of a small number of discrete frequency points that are most sensitive to stress load changes within the frequency range. Most frequency point elements are zero, and only frequency point data with high sensitivity is retained.

7. The method for detecting the stress of a gallium nitride HEMT package according to claim 6, wherein The stress distribution matrix refers to a two-dimensional or three-dimensional numerical array representing the stress values at each point inside the GaN HEMT device, and is used to fully describe the stress field distribution state inside the device.

8. The method for detecting the stress of the gallium nitride HEMT package according to claim 7, wherein, The specific structure of the stress prediction model is a multi-head attention neural network based on deep learning, which includes an input layer to receive normalized scattering parameter matrix data, a multi-layer self-attention layer to capture the correlation between scattering parameter matrices of different frequencies, a sparse attention mechanism layer to screen key feature frequency information, a fully connected layer to map feature vectors to stress distribution space, and an output layer to give a predicted stress distribution matrix.

9. The method for detecting the stress of the gallium nitride HEMT package according to claim 8, wherein, The sparse attention mechanism parameters are determined according to the frequency stress sensitivity index, the frequency sampling interval and the transmission line characteristic impedance.

10. The gallium nitride HEMT package stress detection method according to claim 9, characterized in that, The steps of establishing a training data set in the stress prediction model training process include collecting data samples of the scattering parameter matrix of the gallium nitride HEMT under known stress loads, simulating the internal stress distribution of the gallium nitride HEMT under different packaging stresses using finite elements, establishing a data pair of mapping relationship between the scattering parameter matrix and the stress distribution matrix, expanding the number of training samples using data enhancement technology, and dividing the training set and the validation set using a cross-validation method.

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