Intelligent manufacturing method for positive temperature coefficient characteristic of fast recovery diode

Abstract

The application discloses an intelligent manufacturing method for the positive temperature coefficient characteristic of a fast recovery diode. The method takes a partition physical information agent model as a first fidelity evaluation layer, takes process simulation as a second fidelity evaluation layer, and determines a process design parameter set through layered fidelity constraint Bayesian search; a P+ anode layer is formed through ion implantation and annealing, and an agent model is updated online; a Pareto optimal irradiation parameter is searched through deep Gaussian process multi-target Bayesian optimization, and after proton irradiation and electron beam irradiation, combined annealing is performed to stabilize two types of defects simultaneously under a single heat budget; the agent model is continuously updated in increments through a layered test strategy, process correction suggestions are output through statistical process control, and a self-evolution process knowledge base is constructed. The application significantly reduces the experimental cost of process development, and realizes continuous improvement of batch-to-batch consistency of the positive temperature coefficient characteristic.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor power device manufacturing technology, specifically relating to an intelligent manufacturing method for the positive temperature coefficient (PTC) characteristics of fast recovery diodes (FRDs), and particularly to an intelligent process method that combines physical information proxy models with multi-objective Bayesian optimization. Background Technology

[0002] Fast recovery diodes are core freewheeling devices in power conversion systems, widely used in motor drive inverters, electric vehicle on-board chargers, photovoltaic grid-connected converters, and industrial uninterruptible power supplies. In high-power scenarios where the rated current exceeds the limit of a single chip, multi-chip parallel packaging is the mainstream engineering method to improve current rating, and the balanced current distribution among parallel chips directly determines the reliability and lifespan of the system.

[0003] The temperature coefficient of the forward voltage drop is a core device parameter determining the quality of current sharing in parallel circuits. The forward voltage drop is composed of the superposition of the thermal drop component of the built-in potential and the thermal rise component of the base-region series resistance. At low current densities, the thermal drop component of the built-in potential dominates, resulting in a negative temperature coefficient for the forward voltage drop. This causes the chip that first receives a large current to heat up faster, attracting more current and increasing the risk of thermal runaway. At high current densities, the thermal rise component of the base-region series resistance gives the forward voltage drop a positive temperature coefficient, exhibiting self-current sharing characteristics. However, traditional fast recovery diode processes have very limited methods for quantitatively controlling the positive temperature coefficient characteristic, and the problems of a narrow positive temperature coefficient window and poor batch-to-batch consistency have long remained unresolved systematically.

[0004] The most relevant prior art to this invention is to modulate the minority carrier lifetime of the N-based region as a whole through electron irradiation or heavy metal diffusion to change the forward voltage drop temperature characteristics. This method uniformly introduces recombination centers into the N-based region, which to some extent enhances the weight of the series resistance component of the base region, but it has two core drawbacks: the defects are uniformly distributed throughout the base region, leading to an unnecessary increase in reverse recovery charge and deterioration of switching losses, and it is impossible to independently and accurately control the anode-side injection efficiency; the mapping relationship between process parameters and device performance is highly nonlinear, and existing methods rely on engineering experience to select single-point parameters, lacking systematic multi-objective trade-off analysis tools.

[0005] Therefore, existing technologies face two core technical problems: First, in the multidimensional process parameter space, there is a lack of intelligent methods that can automatically search for process feasible domains that meet the dual constraints of forward conduction pressure drop temperature coefficient and reverse recovery time in a data-efficient manner; Second, there is a lack of a closed-loop manufacturing system that can capture process drift in real time, automatically correct process parameters, and continuously accumulate process-performance mapping knowledge in batch manufacturing, resulting in the inability to continuously improve the consistency of positive temperature coefficient between batches through learning mechanisms. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides an intelligent manufacturing method for the positive temperature coefficient characteristics of fast recovery diodes, thereby solving the problems of low efficiency in automatic search of the process feasible region in the multidimensional process parameter space and difficulty in continuously improving the consistency of positive temperature coefficient characteristics between batches.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A smart manufacturing method for the positive temperature coefficient characteristics of fast recovery diodes includes: acquiring parameters of an N-type silicon substrate; collecting process simulation anchor points for the N-type silicon substrate parameters; embedding a training loss function with the residual of the partitioned physical equations between the anode P+ layer and the N-base region as a constraint term to train a partitioned physical information proxy model; using the partitioned physical information proxy model as the first fidelity evaluation layer and the process simulation as the second fidelity evaluation layer, performing a hierarchical fidelity-constrained Bayesian search in the parameter space composed of anode implantation efficiency and base region minority carrier lifetime to obtain the process feasible region and process design parameter set; using the target anode implantation efficiency in the process design parameter set as the basis, forming a P+ anode layer on the surface of the N-base region through ion implantation and annealing, and verifying the measured anode implantation efficiency against the target efficiency. The conformity of anode injection efficiency is used as the new anchor point to incrementally update the partitioned physical information proxy model. Based on anode layer parameters and target base region minority carrier lifetime, with irradiation parameters and annealing parameters as optimization variables, and with forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, Pareto optimal irradiation parameter combination is searched through deep Gaussian process multi-objective Bayesian optimization. Proton irradiation is then performed to obtain the irradiated wafer. Based on the irradiated wafer, the minority carrier lifetime of the N base region is controlled by electron beam irradiation. Joint annealing is performed to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget. The lifetime uniformity is verified by full-wafer minority carrier lifetime measurement. The measured results are then updated to the deep Gaussian process proxy model to achieve process update.

[0008] Furthermore, the method also includes: predicting the positive temperature coefficient quantification index using the updated partitioned physical information proxy model; triggering a hierarchical testing strategy based on the predicted value to obtain the measured dataset; incrementally updating the partitioned physical information proxy model based on the deviation between the measured dataset and the predicted value; monitoring the batch distribution in real time through statistical process control and predicting the correction amount through the deep Gaussian process proxy model; and outputting process correction suggestions. The partitioned physical information proxy model, the deep Gaussian process proxy model, and the process database together constitute a self-evolving process knowledge base.

[0009] Further, the step of acquiring N-type silicon substrate parameters, collecting process simulation anchor points for the N-type silicon substrate parameters, and embedding a training loss function with the residual of the partitioned physical equations between the anode P+ layer and the N-base region as a constraint term to train a partitioned physical information proxy model includes: acquiring the N-type silicon substrate parameters, collecting a first number of initial process simulation anchor points in the parameter space using Latin hypercube sampling, and adaptively densifying the collection of a second number of supplementary process simulation anchor points in the region near the P+N interface, wherein the first number is greater than the second number; using the residual of the surface recombination rate equation for the anode P+ layer as a first physical constraint term and the residual of the volume Shockley-Reid-Hall recombination equation for the N-base region as a second physical constraint term, weighting the first physical constraint term and the second physical constraint term and summing it with the data fitting term to form a training loss function, wherein the physical constraint weight coefficient in the training loss function takes a first preset value in the early stage of training and gradually increases to a second preset value in the later stage of training, wherein the second preset value is greater than the first preset value; and training with the process simulation anchor points and the training loss function to obtain the partitioned physical information proxy model.

[0010] Furthermore, the step of using the partitioned physical information proxy model as the first fidelity evaluation layer and process simulation as the second fidelity evaluation layer to perform a hierarchical fidelity-constrained Bayesian search in the parameter space composed of anode injection efficiency and base region minority carrier lifetime to obtain the process feasible domain and process design parameter set includes: using the partitioned physical information proxy model as the first fidelity evaluation layer and process simulation as the second fidelity evaluation layer, with the hard constraint set being that the forward conduction voltage drop temperature coefficient is not lower than a preset lower limit, the reverse recovery time does not exceed a preset upper limit, and the positive temperature coefficient quantification index is not lower than a preset threshold, in the parameter space composed of anode injection efficiency and base region minority carrier lifetime, firstly, the partitioned physical information proxy model is used to pre-screen candidate parameter points, and only the candidate parameter points that pass the pre-screening are called to perform accurate verification by the second fidelity evaluation layer. After iteration until convergence, the process feasible domain and process design parameter set that satisfy the hard constraint set are obtained.

[0011] Preferably, the step of forming a P+ anode layer on the surface of the N-based region by ion implantation and annealing based on the target anode implantation efficiency in the process design parameter set, verifying the conformity between the measured anode implantation efficiency and the target anode implantation efficiency, and using the measured results as new anchor points to incrementally update the partitioned physical information proxy model includes: forming a P+ anode precursor layer on the surface of the N-based region by boron ion implantation based on the target anode implantation efficiency in the process design parameter set, with an implantation energy of 60–100 keV and an implantation dose of 8 × 10⁻⁶ keV. 14 ~5×10 15 cm -2 The P+ anode precursor layer is subjected to gradient activation annealing at a temperature of 900–1000℃ for 30–60 min in a nitrogen atmosphere, with the junction depth controlled to be no more than 2 μm. The measured anode injection efficiency is verified to match the target anode injection efficiency. If the deviation between the measured anode injection efficiency and the target anode injection efficiency exceeds a preset uncertainty range, the measured anode injection efficiency and its corresponding process simulation prediction forward conduction voltage drop temperature characteristics are used as new anchor points. A preset proportion of historical anchor points are randomly selected from the historical anchor point dataset and mixed with the new anchor points to form a training batch. Incremental training is performed using the training loss function to obtain the updated partitioned physical information proxy model.

[0012] Furthermore, the process of performing proton irradiation to obtain an irradiated wafer, based on the anode layer parameters and the minority carrier lifetime of the target base region, with irradiation parameters and annealing parameters as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, involves searching for the Pareto optimal combination of irradiation parameters through a deep Gaussian process multi-objective Bayesian optimization. This includes: using the anode layer parameters and the minority carrier lifetime of the target base region as the basis, with proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing time, and equivalent thermal dose characteristics as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objective outputs, wherein the equivalent thermal dose characteristics are determined based on the combined annealing temperature, combined annealing time, and deep Gaussian process multi-objective Bayesian optimization to search for the Pareto optimal combination of irradiation parameters, and performing proton irradiation, the process further includes: using the anode layer parameters and the minority carrier lifetime of the target base region as the basis, with proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing time, and equivalent thermal dose characteristics as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objective outputs, the equivalent thermal dose characteristics being determined based on the combined annealing temperature, combined annealing time, and deep Gaussian process multi-objective Bayesian optimization to search for the Pareto optimal combination of irradiation parameters, and performing proton irradiation, the process further includes: using the anode layer parameters and the minority carrier lifetime of the target base region, with proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing time, and equivalent thermal dose characteristics as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objective outputs, the equivalent thermal dose characteristics being determined based on the combined annealing temperature, combined annealing time, and deep Gaussian process multi The thermal activation energy of the energy level defects is calculated, and a two-layer Gaussian process stacked surrogate model is constructed. The two-layer Gaussian process stacked surrogate model is trained with initial experimental points sampled by Latin hypercube. The cost-aware upper confidence bound acquisition function is used as the exploration strategy, and the backward recovery time does not exceed a preset upper limit is used as the feasible region constraint. Multiple parallel experimental suggested parameter points are generated in each round. Only proton irradiation is performed and the defect concentration after irradiation is recorded as an intermediate verification quantity. The two-layer Gaussian process stacked surrogate model is updated. After iteration until convergence, the Pareto optimal irradiation parameter combination is extracted from the Pareto front using the ε-constraint method. Proton irradiation is performed according to the Pareto optimal irradiation parameter combination to obtain the irradiated wafer.

[0013] Preferably, the equivalent heat dose characteristic is calculated based on the combined annealing temperature, combined annealing duration, and deep-level defect thermal activation energy, including: using the combined annealing temperature, combined annealing duration, and deep-level defect thermal activation energy as inputs, multiplying the product of the combined annealing temperature and combined annealing duration by the Arrhenius factor corresponding to the thermal activation energy to calculate the equivalent heat dose characteristic; the equivalent heat dose characteristic serves as an auxiliary input to the double-layer Gaussian process stacked proxy model to capture the thermal budget superposition effect when proton irradiation annealing and electron beam irradiation annealing are performed together, thereby obtaining the double-layer Gaussian process stacked proxy model containing the equivalent heat dose characteristic.

[0014] Furthermore, the process of using the irradiated wafer as a basis, controlling the minority carrier lifetime in the N-base region through electron beam irradiation, performing joint annealing to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget, verifying lifetime uniformity through full-wafer minority carrier lifetime measurement, and updating the measured results to the deep Gaussian process proxy model to achieve process updates includes: using the irradiated wafer as a basis, introducing uniform Frenkel pair defects in the N-base region through electron beam irradiation, followed by joint annealing, wherein the temperature and duration of the joint annealing are taken from the Pareto optimal irradiation parameter combination corresponding to... The Pareto optimality eliminates shallow-level damage from proton irradiation and retains deep-level defects as positive temperature coefficient recombination centers under a single thermal budget. Simultaneously, it stabilizes the Frenkel pairs and retains stable double vacancies as minority carrier lifetime control recombination centers in the N-base region. The N-base region is mapped and measured using the microwave photoconductivity attenuation method to verify the consistency between the measured minority carrier lifetime after stabilization and the minority carrier lifetime of the target base region. The joint annealing parameters and the measured minority carrier lifetime are then used as new data points to update the deep Gaussian process surrogate model, resulting in the updated deep Gaussian process surrogate model.

[0015] Further, the step of predicting the positive temperature coefficient quantification index using the updated partitioned physical information proxy model and triggering a tiered testing strategy based on the predicted value to obtain the actual test dataset includes: predicting the positive temperature coefficient quantification index of the wafer under test using the updated partitioned physical information proxy model, and triggering tiered testing based on the predicted value range: performing multi-temperature full-temperature testing on batches with predicted positive temperature coefficient quantification indices not lower than a first threshold; performing single-temperature initial screening testing on batches with predicted positive temperature coefficient quantification indices between a second threshold and the first threshold, where the second threshold is less than the first threshold; marking batches with predicted positive temperature coefficient quantification indices lower than the second threshold as requiring process review; and summarizing the test results of the above levels to obtain the actual test dataset.

[0016] Preferably, the incremental update of the partitioned physical information proxy model based on the deviation between the measured dataset and the predicted value includes: using the deviation between the measured positive temperature coefficient quantification index in the measured dataset and the predicted value of the partitioned physical information proxy model as a criterion; if the deviation exceeds a preset tolerance threshold, randomly selecting a preset proportion of historical anchor points from the historical anchor point dataset and mixing them with new anchor points in the measured dataset to form a training batch; performing incremental training with a complete training loss function containing the first physical constraint term and the second physical constraint term to obtain the updated partitioned physical information proxy model, so as to avoid catastrophic forgetting and maintain historical physical consistency.

[0017] Compared with the prior art, the present invention has the following technical effects: First, the efficiency of process simulation is significantly improved. The partitioned physical information proxy model embeds the residuals of the partitioned physical equations into the training loss, maintaining consistent prediction accuracy in key regions of the P+N interface. The simulation time for each process parameter evaluation is reduced from hours to milliseconds, and its extrapolation capability is superior to that of the pure data-driven proxy model.

[0018] Second, the cost of process development experiments is significantly reduced. Hierarchical fidelity-constrained Bayesian search significantly reduces the number of process simulation calls through pre-screening by a partitioned physical information proxy model; deep Gaussian process multi-objective Bayesian optimization reduces the amount of irradiation parameter experiments by about 50% compared to full factorial experiments through cost-aware acquisition functions and parallel batch exploration.

[0019] Third, it achieves dual-objective synergistic optimization of the forward conduction voltage drop temperature coefficient and the reverse recovery time. The deep Gaussian process proxy model outputs a complete Pareto trade-off curve, allowing engineers to make evidence-based quantitative trade-off decisions between the positive temperature coefficient intensity and switching performance, breaking through the limitations of single-point empirical parameter selection in existing technologies.

[0020] Fourth, batch consistency continues to improve. The incremental learning mechanism of the replay buffer enables the partitioned physical information proxy model to continuously adapt to process drift as batches accumulate, and the self-evolving process knowledge base upgrades the batch-to-batch control of positive temperature coefficient characteristics from passive monitoring to predictive proactive correction. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall process of the intelligent manufacturing method for the positive temperature coefficient characteristics of fast recovery diodes provided in an embodiment of the present invention. Detailed Implementation

[0022] Example 1: As Figure 1 As shown, a smart manufacturing method for the positive temperature coefficient characteristics of a fast recovery diode includes: S1: Obtain the parameters of the N-type silicon substrate, acquire the process simulation anchor point for the parameters of the N-type silicon substrate, and embed the training loss function with the residual of the partitioned physical equation between the anode P+ layer and the N base region as the constraint term to train the partitioned physical information proxy model.

[0023] In this embodiment of the invention, the N-type silicon substrate parameters include resistivity, crystal orientation, and initial minority carrier lifetime. These parameters collectively determine the physical basis of the base region carrier transport characteristics and the forward conduction voltage drop temperature coefficient. The process simulation anchor points are obtained through TCAD full-field simulation, covering the parameter space composed of anode injection efficiency and base region minority carrier lifetime. The partitioned physical equation residuals are designed with constraints for the differences in physical mechanisms between the P+ layer and the N base region: the P+ layer uses the surface recombination rate equation residuals, and the N base region uses the volume Shockley-Reid-Hall recombination equation residuals. Both are embedded in the training loss function to ensure that the prediction results of the surrogate model in the key region of the P+N interface meet the physical equation constraints, avoiding systematic biases in this region caused by purely data-driven surrogate models.

[0024] S2: Using the partitioned physical information proxy model as the first fidelity evaluation layer and the process simulation as the second fidelity evaluation layer, a hierarchical fidelity-constrained Bayesian search is performed in the parameter space composed of anode injection efficiency and base region minority carrier lifetime to obtain the process feasible region and process design parameter set.

[0025] Specifically, the hierarchical fidelity-constrained Bayesian search constructs a two-layer evaluation system: the first fidelity layer is the partitioned physical information proxy model, with an evaluation time in milliseconds; the second fidelity layer is the TCAD full-field process simulation, with an evaluation time in hours. By iteratively sampling in the parameter space, the first fidelity layer is first called to quickly pre-screen candidate parameter points, and only the pre-screened candidate points are submitted to the second fidelity layer for precise verification, thereby significantly reducing the number of high-cost simulation calls and achieving efficient data search in the process feasible domain.

[0026] The search domain of the hierarchical fidelity-constrained Bayesian search is a two-dimensional parameter space composed of anode injection efficiency and base region minority carrier lifetime. During the search process, a trust domain constraint mechanism limits the search range of each round of sampling points, preventing the optimization process from jumping out of local high-quality regions and ensuring that the iterative path converges stably in the parameter space. After each iteration, the algorithm dynamically updates the prediction confidence of the partitioned physical information proxy model based on the TCAD verification results of that round. The pre-screening threshold of high-confidence regions can be appropriately tightened to further reduce unnecessary calls to the second fidelity layer. After 20 to 30 iterations, the algorithm outputs the process feasible region and Pareto optimal parameter set that satisfy the hard constraint set, and also outputs the uncertainty range of each parameter, providing a confidence range reference for subsequent process execution.

[0027] S3: Based on the target anode implantation efficiency in the process design parameter set, a P+ anode layer is formed on the surface of the N-based region through ion implantation and annealing. The conformity between the measured anode implantation efficiency and the target anode implantation efficiency is verified. The measured results are used as new anchor points to incrementally update the partitioned physical information proxy model.

[0028] In this embodiment of the invention, the ion implantation employs a boron ion implantation process. After implantation, gradient activation annealing is used to control the junction depth, forming a P+ anode layer with a peak concentration meeting the requirements. The measured anode implantation efficiency is verified online by secondary ion mass spectrometry or extended resistivity analysis, and the measured results are used as new anchor points for incremental training of the surrogate model, enabling continuous calibration of the surrogate model based on actual process data.

[0029] S4: Based on the anode layer parameters and the minority carrier lifetime of the target base region, with irradiation parameters and annealing parameters as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, the Pareto optimal combination of irradiation parameters is searched through deep Gaussian process multi-objective Bayesian optimization, and proton irradiation is performed to obtain the irradiated wafer.

[0030] Specifically, the deep Gaussian process multi-objective Bayesian optimization employs a surrogate model built using a stacked two-layer Gaussian process structure. It targets the Pareto front of the forward conduction pressure drop temperature coefficient and the reverse recovery time, actively searching the irradiation parameter space through a cost-aware acquisition function. Each round executes only the proton irradiation step and records intermediate verification values, gradually approximating the Pareto optimal combination of irradiation parameters. The proton irradiation creates a spatially localized defect distribution in the N-base region, laying the foundation for subsequent joint annealing stabilization.

[0031] In the iterative process of the deep Gaussian process multi-objective Bayesian optimization, proton irradiation is performed only in each round, without annealing. The initial defect concentration measured by the deep-level transient spectrum after irradiation is recorded as an intermediate verification quantity. This intermediate verification quantity reflects the actual level of defect introduction under the current irradiation parameters and can be compared and verified with the surrogate model prediction value, serving as incremental data for updating the deep Gaussian process surrogate model. The annealing step is deliberately postponed to step S5 for unified execution because: if annealing is performed separately in each iteration, the thermal budget superposition effect between proton irradiation annealing and subsequent electron beam irradiation annealing will introduce unmodeled systematic bias; by merging the two into joint annealing, the thermal budget is uniformly modeled using equivalent thermal dose characteristics, eliminating the above bias and ensuring that the Pareto front prediction result of the surrogate model is consistent with the final device performance.

[0032] S5: Based on the irradiated wafer, the minority carrier lifetime of the N-base region is controlled by electron beam irradiation. Joint annealing is performed to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget. The lifetime uniformity is verified by measuring the minority carrier lifetime of the whole wafer. The measured results are updated to the deep Gaussian process proxy model to realize the process update.

[0033] In this embodiment of the invention, the combined annealing integrates proton irradiation post-annealing and electron beam irradiation post-annealing into a single execution, simultaneously stabilizing both types of defects under a single thermal budget, eliminating the systematic bias of unmodeled thermal budget accumulation effects in traditional two-step annealing. Whole-wafer minority carrier lifetime measurement employs the microwave photoconductivity attenuation method, outputting a wafer-level lifetime uniformity spectrum, and appending the measured results to the deep Gaussian process surrogate model to achieve online process updates of the surrogate model.

[0034] It should be noted that the whole-wafer minority carrier lifetime mapping measurement, in addition to verifying process compliance, also serves to trigger feedback on process anomalies. When the wafer-level lifetime uniformity map shows that the relative standard deviation of the lifetime distribution within the wafer exceeds a preset uniformity threshold, the system determines that the lifetime uniformity of this batch is unqualified and feeds back to the deep Gaussian process proxy model to trigger a local resampling suggestion, prompting the next batch to supplement experimental points within a local range of electron beam irradiation energy or dose to improve whole-wafer uniformity. This mechanism connects the whole-wafer measurement results with the active learning mechanism of the proxy model, enabling the batch-to-batch control capability of lifetime uniformity to continuously improve with production accumulation, without relying on manual analysis and experience-based judgment.

[0035] Example 2: Based on Example 1, the method further includes: Step A: Predict the positive temperature coefficient quantification index using the updated partitioned physical information proxy model, trigger a stratified testing strategy based on the predicted value to obtain the measured dataset, incrementally update the partitioned physical information proxy model based on the deviation between the measured dataset and the predicted value, monitor the batch distribution in real time through statistical process control and predict the correction amount through the deep Gaussian process proxy model, and output process correction suggestions. The partitioned physical information proxy model, the deep Gaussian process proxy model, and the process database together constitute a self-evolving process knowledge base.

[0036] In this embodiment of the invention, the tiered testing strategy is driven by the predicted values ​​of the updated partitioned physical information proxy model. It concentrates full-temperature testing resources on high-probability qualified batches, performs single-temperature initial screening on marginal batches, and directly marks unqualified predicted batches for re-inspection, saving approximately 30% of the machine time for full-temperature automated testing equipment. The statistical process control uses a mean-range control chart to monitor the batch distribution of positive temperature coefficient quantification indicators, forward conduction voltage drop, and reverse recovery time in real time. When an alarm is triggered, the parameter correction amount is predicted by a deep Gaussian process proxy model, and process correction suggestions for the next batch are automatically output. The self-evolving process knowledge base is continuously updated with batch accumulation, enabling the batch-to-batch control capability of the positive temperature coefficient characteristics to continuously improve with the increase in production scale, upgrading the manufacturing system from passive quality monitoring to proactive predictive process optimization.

[0037] The self-evolving process knowledge base is a dynamic learning-based intelligent process system composed of three components: a partitioned physical information proxy model, a deep Gaussian process proxy model, and a process database. It is the core mechanism by which this invention upgrades fast recovery diode manufacturing from passive quality control to proactive predictive process optimization. The "self-evolving" characteristic of the self-evolving process knowledge base is reflected in the following: as batches accumulate, the measured data of each batch updates the partitioned physical information proxy model through an incremental learning mechanism in the replay buffer, updates the deep Gaussian process proxy model online, and archives it into the process database. The updated proxy model has higher prediction accuracy for the process parameters of the next batch, more accurate criteria for triggering stratified testing, and more reliable process correction suggestions. Higher-quality process correction suggestions, in turn, affect the actual manufacturing process, improving the batch-to-batch consistency of the positive temperature coefficient characteristics of the next batch, thereby generating higher-quality measured data, updating the proxy model again, and forming a positive feedback loop.

[0038] The tiered testing strategy is an interface mechanism between the self-evolving process knowledge base and the actual manufacturing testing process. Its technical value lies in transforming the allocation of automated testing equipment resources from passive full-batch full-temperature testing to proactive prediction-driven on-demand testing. In traditional manufacturing processes, all wafers in each batch must undergo multi-temperature full-temperature testing to verify the positive temperature coefficient quantification index. Testing machine time consumption is linearly positively correlated with batch size, and test results are only used for passive acceptance or rejection, without feedback to process parameter adjustments. The tiered testing strategy uses an updated partitioned physical information proxy model to predict the positive temperature coefficient quantification index of each batch of wafers. Based on the interval of the predicted value, the batch is divided into three levels: high-confidence qualified batches undergo multi-temperature full-temperature testing to obtain complete performance data; marginal batches undergo single-temperature initial screening to confirm their qualification at a low cost; and low-confidence batches are directly marked for process review to avoid wasting testing resources. In one embodiment, the three thresholds are set as follows: the first threshold is 4 × 10⁻⁶. -4 / 。C (high confidence qualified), the second threshold is 2×10⁻⁴ / 。 C (marginal batches) are marked for further process inspection if they fall below the second threshold. This stratification strategy can save approximately 30% of the time required for fully automated temperature testing equipment in a typical production scenario, while retaining the screening capability for marginal batches through single-temperature initial screening, without compromising the overall quality assurance level.

[0039] The statistical process control module monitors the batch distribution of positive temperature coefficient quantification indicators, forward conduction voltage drop, and reverse recovery time in real time based on the mean-range control chart. When the batch mean or range violates the control rules (e.g., multiple consecutive batches of mean deviation or a single batch of range abnormally widening), the system automatically extracts the historical irradiation and annealing parameter deviation records corresponding to the alarm mode from the process database, predicts the parameter correction amount using a deep Gaussian process proxy model, and outputs a process correction suggestion report for the next batch. The process correction suggestion is given in terms of the quantified parameter adjustment direction and magnitude, rather than just indicating "process abnormality," providing operators with specific and actionable parameter adjustment basis. As batches accumulate, the historical alarm-correction records in the process database are continuously enriched, and the prediction accuracy of the deep Gaussian process proxy model for parameter deviations continues to improve. This allows the accuracy of the process correction suggestion to improve itself as production scale increases, ultimately upgrading the batch-to-batch control of the positive temperature coefficient characteristics of fast recovery diodes from a passive quality management system relying on engineering experience to an active predictive process optimization system driven by a self-evolving process knowledge base.

[0040] Example 3: Based on Example 1, the acquisition of N-type silicon substrate parameters, the acquisition of process simulation anchor points for the N-type silicon substrate parameters, and the embedding of the partitioned physical equation residuals between the anode P+ layer and the N-base region as constraint terms into the training loss function to train the partitioned physical information proxy model, including: S1.1: Obtain the parameters of the N-type silicon substrate, collect a first number of initial process simulation anchor points in the parameter space using Latin hypercube sampling, and adaptively densify the collection of a second number of supplementary process simulation anchor points in the region near the P+N interface, wherein the first number is greater than the second number.

[0041] In this embodiment of the invention, Latin hypercube sampling ensures that the initial anchor points are uniformly distributed throughout the parameter space, avoiding sampling bias; the adaptive densification of supplementary anchor points near the P+N interface is locally densified to address the complex physical mechanisms and dramatic gradient changes in this region, significantly improving the prediction accuracy of the surrogate model in key interface regions with less additional simulation cost.

[0042] S1.2: Using the residual of the surface recombination rate equation for the anode P+ layer as the first physical constraint term and the residual of the volume Shockley-Reid-Hall recombination equation for the N base region as the second physical constraint term, the first physical constraint term and the second physical constraint term are weighted and summed with the data fitting term to form a training loss function. The physical constraint weight coefficients in the training loss function take a first preset value in the early stage of training and gradually increase to a second preset value in the later stage of training. The second preset value is greater than the first preset value.

[0043] It should be noted that the phased adaptive scheduling strategy of physical constraint weight coefficients takes into account both training efficiency and physical consistency: the smaller weight coefficients in the early stage of training enable the proxy model to quickly fit sparse anchor data, and the gradually increasing weight coefficients in the later stage of training gradually strengthen the physical equation constraints, ensuring that the final proxy model still meets the physical constraints in extrapolation scenarios outside the training range, thus solving the problem of systematic deviation in key areas of the interface of pure data-driven proxies.

[0044] Furthermore, the physical basis of the phased adaptive weight coefficient scheduling strategy lies in the following: In the early stage of training, the number of anchor points is small. If the physical constraint weights are too large, the surrogate model will over-rely on the physical equations and fail to fully fit the data patterns contained in the sparse anchor points, especially the local characteristics near the P+N interface. In the later stage of training, the data fitting terms have basically converged. At this time, the physical constraint weights are gradually increased, forcing the model output to satisfy the residual constraints of the partitioned physical equations, effectively suppressing non-physical prediction biases in the extrapolation region outside the training range. This strategy enables the partitioned physical information surrogate model to simultaneously possess the local accuracy of data-driven surrogates and the extrapolation reliability of physical models, achieving millisecond-level full-parameter spatial prediction while maintaining physical consistency with only about 60 TCAD anchor points.

[0045] S1.3: The partitioned physical information proxy model is obtained by training with the process simulation anchor point and the training loss function.

[0046] Among them, the time taken by the trained partitioned physical information proxy model to predict the forward conduction pressure drop temperature characteristics of any process parameter point is reduced from hours to milliseconds, achieving efficient global evaluation in the parameter space.

[0047] The partitioned physical information proxy model is a proxy modeling method that integrates the physical equation constraints of fast recovery diodes with data-driven neural operators. Unlike traditional pure data-driven proxy models (such as Gaussian process regression, random forest, and ordinary neural networks), this model explicitly embeds residual constraint terms of the device's physical equations into the training loss function, forcing the model output to conform to known physical laws while meeting data fitting requirements. The term "partitioning" refers to designing independent physical constraint terms for the essential differences in the physical mechanisms of the P+ anode layer and the N-base region in the fast recovery diode, rather than applying a uniform physical equation to the entire device. This allows for targeted enhancement of prediction accuracy for key interface regions.

[0048] The technical principle behind the partitioned physical information proxy model's ability to solve the proxy modeling problem in the process parameter space lies in the following: The forward voltage drop temperature characteristics of a fast recovery diode are jointly determined by two parameters: the injection efficiency of the P+ anode layer and the minority carrier lifetime of the N-base region. These two parameters are coupled through the minority carrier injection process at the P+N interface. Carrier recombination in the P+ layer is mainly based on surface recombination, controlled by surface state density and surface recombination rate; carrier recombination in the N-base region is mainly based on bulk Shockley-Reid-Hall recombination, controlled by deep-level defect density and defect level position. These two recombination mechanisms are mathematically distinct. If a unified physical constraint term is used, the physical constraints in the two regions will interfere with each other, especially near the P+N interface, where both recombination mechanisms coexist, and a single physical equation cannot accurately describe the physical behavior of this region. The partitioned design, by independently designing corresponding physical equation residual constraint terms for each region, enables the proxy model to maintain predictive behavior consistent with the TCAD full-field simulation results in the P+ layer, interface region, and N-base region.

[0049] The specific implementation process of the partitioned physical information proxy model is as follows. First, a first number of initial process simulation anchor points are collected in the parameter space composed of anode injection efficiency and base region minority carrier lifetime using Latin hypercube sampling. Then, a second number of supplementary process simulation anchor points are adaptively and densely collected in the region near the P+N interface. In one implementation, the first number is 50, and the second number is 10, totaling approximately 60 TCAD full-field simulation anchor points. Subsequently, a partitioned physical information neural operator network is constructed. Its inputs are N-type silicon substrate parameters (resistivity, crystal orientation, initial minority carrier lifetime) and process parameters (anode injection efficiency, base region minority carrier lifetime), and its output is the predicted forward conduction voltage drop value at multiple temperature points. The training loss function consists of three terms: a data fitting term measures the mean square error between the model's predicted values ​​and the TCAD simulation anchor points; a first physical constraint term is the residual of the P+ layer surface recombination rate equation, requiring the model-predicted P+ layer carrier concentration distribution to satisfy the surface recombination rate equation; and a second physical constraint term is the residual of the N-base region bulk Shockley-Reid-Hall recombination equation, requiring the model-predicted N-base region minority carrier concentration distribution to satisfy the bulk recombination equation. The physical constraint weights are adaptively scheduled in stages: in the first 30% of the training steps, the weights are set to a smaller first preset value (0.01 in one implementation) to quickly fit the sparse anchor point data; in the last 70% of the training steps, the weights are gradually increased to a larger second preset value (0.1 in one implementation) to progressively strengthen the physical equation constraints. After training, the surrogate model's prediction time for the forward conduction pressure drop temperature characteristics at any process parameter point is reduced from 2 to 4 hours in full-field TCAD simulation to milliseconds, representing an approximately 10,000-fold increase in simulation speed.

[0050] Through the aforementioned partitioned physical information proxy model, this invention achieves the following technical effects. First, due to the embedding of partitioned physical constraints, the proxy model's prediction accuracy in key regions of the P+N interface is significantly better than that of the pure data-driven proxy model. Even with approximately 60 sparse anchor points, it can still maintain physically consistent prediction behavior near the interface, avoiding the systematic bias that occurs in this region with the pure data-driven proxy. Second, the phased adaptive weight scheduling enables the model to simultaneously consider both local fitting accuracy under sparse data conditions and extrapolation reliability outside the training range, resolving the binary contradiction of high extrapolation accuracy but poor local adaptability in pure physical models and high local accuracy but high extrapolation risk in pure data models. Third, the millisecond-level prediction speed allows the proxy model to serve as the first fidelity evaluation layer in hierarchical fidelity Bayesian search, rapidly pre-screening a large number of candidate parameter points, thereby reducing the number of high-cost TCAD simulation calls from hundreds in traditional traversal search to 20 to 30.

[0051] Let's take a specific application scenario as an example. Assume the target process specifications are a forward voltage drop temperature coefficient of no less than +0.5 mV / ℃ and a reverse recovery time of no more than 150 ns. Without using a partitioned physical information proxy model, engineers need to run TCAD simulations point-by-point on the parameter grid of anode injection efficiency and base region minority carrier lifetime. If the parameter grid is 10×10 (100 points), it would require approximately 200 to 400 hours of simulation time. After introducing the partitioned physical information proxy model, only about 60 TCAD anchor points (approximately 120 to 240 hours) are needed to complete the proxy model training. Subsequently, the evaluation time for any candidate point in the parameter space is reduced to the millisecond level, and the total search time for the entire process feasible domain (including 20 to 30 TCAD verifications for hierarchical fidelity Bayesian search) is reduced to approximately 40 to 60 hours, significantly shortening the process development cycle.

[0052] Example 4: Based on Example 1, using the partitioned physical information proxy model as the first fidelity evaluation layer and process simulation as the second fidelity evaluation layer, a hierarchical fidelity-constrained Bayesian search is performed in the parameter space composed of anode injection efficiency and base region minority carrier lifetime to obtain the process feasible region and process design parameter set, including: S2.1: Using the partitioned physical information proxy model as the first fidelity evaluation layer and the process simulation as the second fidelity evaluation layer, and taking the forward conduction voltage drop temperature coefficient not lower than a preset lower limit, the reverse recovery time not exceeding a preset upper limit, and the positive temperature coefficient quantification index not lower than a preset threshold as the hard constraint set, in the parameter space composed of the anode injection efficiency and the base region minority carrier lifetime, the partitioned physical information proxy model is first used to pre-screen the candidate parameter points, and only the candidate parameter points that pass the pre-screening are called to perform accurate verification by the second fidelity evaluation layer. After iteration until convergence, the process feasible region and process design parameter set that satisfy the hard constraint set are obtained.

[0053] In this embodiment of the invention, the hard constraint set simultaneously constrains the positive temperature coefficient strength and switching performance, ensuring that the search results meet the requirements of industrial manufacturing in both dimensions. The pre-screening mechanism rapidly filters a large number of infeasible candidate points at a millisecond-level first fidelity layer, submitting only a small number of high-probability feasible points that pass the pre-screening to an hour-level second fidelity layer for precise verification. This significantly reduces the number of process simulation calls from hundreds of traditional traversal searches, achieving efficient and automatic data discovery within the process feasible domain.

[0054] The hierarchical fidelity-constrained Bayesian search is an automatic process feasibility domain discovery method that combines a multi-level precision evaluation system with constrained Bayesian optimization. Its core idea is that in the process parameter space, evaluation tools of different precisions have different computational costs. By constructing a hierarchical evaluation system from low-cost to high-cost, the low-cost evaluation layer quickly filters candidate parameter points, while only high-probability feasible candidate points that pass the screening are precisely verified using the high-cost evaluation layer. This significantly reduces the total evaluation cost while ensuring search quality. The "constraint" refers to the explicit introduction of hard constraints on process specifications into the Bayesian optimization sampling strategy, causing the algorithm to actively bias its exploration direction towards feasible regions that satisfy the constraints, rather than exploring uniformly throughout the entire parameter space.

[0055] The hierarchical fidelity-constrained Bayesian search's efficient discovery of the process feasible region lies in the synergistic effect of Bayesian optimization's active learning mechanism and hierarchical evaluation. Bayesian optimization maintains a probabilistic surrogate model for the objective function (i.e., a partitioned physical information surrogate model). Based on existing evaluation results, it infers the distribution of the objective function in each region of the parameter space and selects the next most informative evaluation point guided by the acquisition function, rather than random sampling or grid traversal. In constrained scenarios, the acquisition function considers both the exploration value of the objective function and the probability of constraint satisfaction, allowing the algorithm to naturally converge towards parameter regions that satisfy the hard constraint set. The hierarchical triggering mechanism further divides each iteration into two stages: pre-screening and precise verification. The pre-screening stage calls the millisecond-level partitioned physical information surrogate model to quickly filter the candidate point set suggested by the acquisition function in the current round, retaining only candidate points whose positive temperature coefficient quantization index predicted by the surrogate model is not lower than a preset threshold. The precise verification stage only calls hourly-level TCAD full-field simulations on the small number of candidate points that have passed the pre-screening to verify their actual performance with high precision. The combination of the two stages significantly increases the effective information density of each iteration, accelerating the convergence of Bayesian optimization.

[0056] The specific implementation process of the hierarchical fidelity-constrained Bayesian search is as follows. The algorithm uses a two-dimensional parameter space composed of anode injection efficiency and base region minority carrier lifetime as the search domain, and sets hard constraints as follows: the forward conduction voltage drop temperature coefficient is not lower than a preset lower limit, the reverse recovery time is not higher than a preset upper limit, and the positive temperature coefficient quantization index is not lower than a preset threshold. In the initial stage, the algorithm starts Bayesian optimization with a small number of Latin hypercube sampling points as the initial evaluation set. In each iteration, the algorithm first updates the predicted distribution of the entire parameter space by the partitioned physical information surrogate model, calculates the acquisition function value, and generates a candidate point set; then, based on the condition that the positive temperature coefficient quantization index predicted by the surrogate model is not lower than a preset pre-screening threshold, the candidate point set is pre-screened. The pre-screening threshold is set to 75% to 85% of the hard constraint threshold to retain a certain exploration margin while filtering infeasible points; the candidate points that pass the pre-screening are accurately verified by calling TCAD full-field simulation, and the verification results are added to the evaluation set and the surrogate model is updated; the trust domain constraint mechanism limits the search range of the candidate points in each round to no more than the preset radius of the neighborhood of the current optimal point to prevent the optimization process from diverging too early in the parameter space. After 20 to 30 iterations, the algorithm converges and outputs the process feasible region and Pareto optimal parameter set that satisfy the hard constraint set, as well as the uncertainty range of each parameter as a confidence range reference for subsequent process execution.

[0057] Through the aforementioned hierarchical fidelity-constrained Bayesian search, the number of calls to TCAD full-field simulation is reduced from hundreds of times in the traditional traversal search method to 20 to 30 times. While ensuring the integrity of the process feasible domain coverage, the total simulation time of the process window search stage is shortened from hundreds of hours to 40 to 60 hours. This achieves efficient and automatic discovery of process feasible domain data, breaking through the limitations of existing technologies that rely on engineering experience for single-point parameter selection and lack systematic multi-objective trade-off analysis.

[0058] Example 5: Based on Example 1, using the target anode implantation efficiency as the basis for the process design parameters, a P+ anode layer is formed on the surface of the N-based region through ion implantation and annealing. The conformity between the measured anode implantation efficiency and the target anode implantation efficiency is verified. The measured results are used as new anchor points to incrementally update the partitioned physical information proxy model, including: S3.1: Based on the target anode implantation efficiency in the aforementioned process design parameter set, a P+ anode precursor layer is formed on the surface of the N-based region by boron ion implantation. The implantation energy is 60–100 keV, and the implantation dose is 8 × 10⁻⁶. 14 ~5×10 15 cm -2 .

[0059] Optionally, the specific values ​​of the injected energy and dose are determined by looking up a table using SRIM Monte Carlo simulation of the target anode injection efficiency to ensure that the peak concentration meets the process specifications of the P+ anode layer.

[0060] S3.2: The P+ anode precursor layer is subjected to gradient activation annealing at a temperature of 900–1000℃ for 30–60 min in a nitrogen atmosphere. The junction depth is controlled to be no more than 2 μm. The measured anode implantation efficiency is verified to be consistent with the target anode implantation efficiency.

[0061] In practice, gradient activation annealing fully activates boron atoms by controlling the heating rate, nitrogen atmosphere prevents oxidation of the N-based region surface, and the junction depth is controlled within 2 μm to ensure the shallow junction characteristics of the P+ layer, which is beneficial for precise control of anode implantation efficiency.

[0062] S3.3: If the deviation between the measured anode injection efficiency and the target anode injection efficiency exceeds the preset uncertainty range, the measured anode injection efficiency and its corresponding process simulation prediction forward conduction pressure drop temperature characteristics are used as new anchor points. A preset proportion of historical anchor points are randomly selected from the historical anchor point dataset and mixed with the new anchor points to form a training batch. Incremental training is performed using the training loss function to obtain the updated partitioned physical information proxy model.

[0063] It is worth noting that the hybrid training batch strategy prevents catastrophic forgetting caused by incremental training by introducing historical anchors, enabling the surrogate model to maintain historical physical consistency with the existing parameter space while absorbing new process data.

[0064] It is worth noting that the extraction ratio of historical anchors in the hybrid batch strategy is a key parameter for catastrophic forgetting prevention. If the extraction ratio of historical anchors is too low, incremental training will be mainly dominated by new anchors, leading to a degradation in the surrogate model's predictive ability in the historical parameter space. If the extraction ratio of historical anchors is too high, the calibration effect of new anchors on the surrogate model will be diluted, failing to respond promptly to process drift. In one implementation, the extraction ratio of historical anchors is set to 30%, meaning that each incremental training batch consists of 30% randomly selected historical anchors mixed with all new anchors in that batch, and each batch performs 20 gradient updates. The incremental training is performed using a complete training loss function that includes the residuals of the partitioned physical equations, ensuring that the updated surrogate model still satisfies the residual constraints of the P+ layer surface composite rate equation and the residual constraints of the N base region volume Shockley-Reid-Hall composite equation, maintaining the historical physical consistency of the entire parameter space.

[0065] Example 6: Based on Example 1, using anode layer parameters and target base region minority carrier lifetime as the basis, irradiation parameters and annealing parameters as optimization variables, and forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, a Pareto optimal irradiation parameter combination is searched through a deep Gaussian process multi-objective Bayesian optimization to perform proton irradiation, resulting in an irradiated wafer, including: S4.1: Based on the anode layer parameters and the minority carrier lifetime of the target base region, and using proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing duration, and equivalent heat dose characteristics as optimization variables, and forward conduction pressure drop temperature coefficient and reverse recovery time as dual objective outputs, the equivalent heat dose characteristics are calculated based on the combined annealing temperature, combined annealing duration, and deep level defect thermal activation energy. A two-layer Gaussian process stacked proxy model is constructed, and the two-layer Gaussian process stacked proxy model is trained with the initial experimental points sampled by Latin hypercube.

[0066] In this embodiment of the invention, the first layer of the dual-layer Gaussian process stacked proxy model learns a latent representation of the irradiation-annealing coupling relationship in a five-dimensional input space, and the second layer maps to a dual-objective performance space of forward conduction voltage drop temperature coefficient and reverse recovery time based on the latent representation, thereby capturing the nonlinear hierarchical mapping relationship from irradiation parameters to device performance, which has a stronger nonlinear modeling capability compared to a single-layer Gaussian process proxy.

[0067] S4.2: Using the cost-aware upper confidence bound acquisition function as the exploration strategy, and taking the reverse recovery time not exceeding the preset upper limit as the feasible region constraint, multiple parallel experimental suggested parameter points are generated in each round. Only proton irradiation is performed and the defect concentration after irradiation is recorded as an intermediate verification quantity. The two-layer Gaussian process stacked surrogate model is updated. After iteration until convergence, the Pareto optimal irradiation parameter combination is extracted from the Pareto front using the ε-constraint method.

[0068] The cost-aware upper confidence bound acquisition function incorporates experimental costs into the exploration strategy, prioritizing the exploration of low-cost verification paths; the parallel batch experimental design enables the simultaneous acquisition of experimental data from multiple parameter points in each iteration, accelerating the convergence of the Pareto front.

[0069] In the cost-aware upper confidence bound acquisition function, the ratio of irradiation experiment cost to annealing experiment cost reflects the difference in resource consumption between the two in actual production. Since proton irradiation requires accelerator time, its cost per experiment is approximately five times that of annealing experiments. The cost-aware acquisition function, by dividing the exploration gain by the experiment cost, prioritizes parameter points with lower costs when exploration gains are similar, i.e., it prioritizes exploration near the annealing parameter dimension, thereby reducing the average experimental cost per iteration. Compared to standard multi-objective Bayesian optimization that does not consider cost, the cost-aware strategy can further reduce the number of high-cost irradiation experiments by approximately 20% while obtaining an equal-quality Pareto front. Five parallel experimental parameter suggestions are generated per round, fully utilizing the parallelism of batch experiments to accelerate the convergence speed of the Pareto front. After 5 to 8 iterations, the algorithm extracts the Pareto optimal irradiation parameter combination from the Pareto front predicted by the surrogate model using the ε-constraint method, and simultaneously outputs complete forward conduction pressure drop temperature coefficient and reverse recovery time trade-off curves, providing engineers with evidence-based quantitative trade-off decision support.

[0070] S4.3: Perform proton irradiation according to the Pareto optimal irradiation parameter combination to obtain the irradiated wafer.

[0071] It should be understood that proton irradiation creates a spatially localized defect distribution in the N-base region, and the position of the defect peak is determined by the irradiation energy. By precisely limiting the defect peak to a preset distance range from the P+N junction, the deterioration of reverse recovery charge caused by whole-region irradiation is avoided, thereby achieving synergistic optimization of positive temperature coefficient characteristics and switching performance.

[0072] The described two-layer Gaussian process stacked surrogate model is a specific implementation of a deep Gaussian process. It is a surrogate modeling method that captures complex nonlinear parameter-performance mapping relationships through a hierarchical nonparametric probabilistic model. Compared with traditional single-layer Gaussian process surrogates, the two-layer stacked structure learns an intermediate latent representation of the irradiation-annealing coupling relationship in the original input space through the first layer, and then maps it to the dual-objective performance output in the latent representation space through the second layer, achieving hierarchical decomposition modeling of high-dimensional nonlinear functions. This hierarchical decomposition enables the surrogate model to capture the nonlinear coupling effects of five optimization variables—irradiation energy, dose, annealing temperature, annealing time, and equivalent heat dose characteristics—on the forward conduction pressure drop temperature coefficient and the reverse recovery time. In contrast, single-layer Gaussian processes often require a large amount of training data to achieve acceptable prediction accuracy when modeling such nonlinear mappings in a five-dimensional input space.

[0073] The technical principle behind the multi-objective Bayesian optimization of the deep Gaussian process for efficiently searching Pareto-optimal irradiation parameters is as follows: The forward conduction voltage drop temperature coefficient and the reverse recovery time are a pair of physically inherently trade-off objectives: increasing the minority carrier lifetime in the base region and controlling the defect density enhances the positive temperature coefficient characteristics but simultaneously prolongs the reverse recovery time; decreasing the defect density shortens the reverse recovery time but weakens the positive temperature coefficient characteristics. This trade-off implies that there is no single parameter point that simultaneously optimizes both objectives, but rather a Pareto front, where each point represents a specific trade-off between the two objectives. Multi-objective Bayesian optimization maintains a joint probabilistic surrogate model of the dual-objective outputs, using the acquisition function to guide the exploration direction and gradually approach the Pareto front, outputting a complete dual-objective trade-off curve with fewer experimental points. The cost-aware mechanism further biases experimental resource allocation towards low-cost verification paths, reducing the overall experimental cost without compromising the quality of the Pareto front.

[0074] The two-layer Gaussian process stacked surrogate model is trained starting with 12 sets of initial experimental points sampled by Latin hypercube. The first layer Gaussian process takes proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing time, and equivalent heat dose characteristics as five-dimensional inputs. A kernel function characterizes the correlation between adjacent parameter points in the five-dimensional input space, outputting a low-dimensional latent representation vector. The second layer Gaussian process takes the latent representation of the first layer as input, establishing independent Gaussian process regression models for the forward conduction pressure drop temperature coefficient and the reverse recovery time, respectively, outputting the predicted mean and predicted variance of the two objectives. The predicted variance reflects the uncertainty of the surrogate model at that parameter point. The acquisition function comprehensively utilizes the predicted mean (exploring known high-quality regions) and the predicted variance (exploring uncertain regions), controlling the aggressiveness of the search strategy by adjusting the exploration-utilization balance coefficient β. In each iteration, the algorithm generates five parallel experimental suggested parameter points guided by the cost-aware upper confidence bound acquisition function. It only performs the proton irradiation step and records the initial defect concentration of the deep-level transient spectrum measurement after irradiation. The measurement results are added to the training set and the surrogate model is updated. After 5 to 8 iterations, the Pareto optimal irradiation parameter combination is extracted from the Pareto front predicted by the surrogate model using the ε-constraint method. At the same time, it outputs the complete forward conduction pressure drop temperature coefficient and reverse recovery time trade-off curve.

[0075] Compared to traditional methods that rely solely on single-point parameter selection based on engineering experience and do not employ multi-objective optimization, the deep Gaussian process multi-objective Bayesian optimization offers the following technical advantages. First, it outputs a complete Pareto front rather than a single parameter point. Engineers can select the most suitable operating point based on the trade-off curve, according to specific application scenarios (different emphases on positive temperature coefficient intensity and switching losses), overcoming the limitation of existing single-point empirical parameter selection lacking systematic trade-off analysis. Second, the double-layer GP stacked structure has stronger modeling capabilities for nonlinear mappings in the five-dimensional parameter space, outputting a reliable Pareto front with only 12 to 40 experimental points, reducing the experimental workload by approximately 50% compared to full-factor experiments (approximately 81 points). Third, the cost-aware acquisition function further reduces the total number of high-cost irradiation experiments by approximately 20%, demonstrating significant practical value in resource-constrained production environments.

[0076] Example 7: Based on Example 6, the equivalent heat dose characteristics are calculated according to the combined annealing temperature, combined annealing time, and deep-level defect thermal activation energy, including: S4.1a: Using the combined annealing temperature, combined annealing duration, and deep-level defect thermal activation energy as inputs, the equivalent heat dose characteristic is calculated by multiplying the product of the combined annealing temperature and the combined annealing duration by the Arrhenius factor corresponding to the thermal activation energy. The equivalent heat dose characteristic serves as an auxiliary input to the double-layer Gaussian process stacking proxy model to capture the thermal budget superposition effect when proton irradiation annealing and electron beam irradiation annealing are performed together, thus obtaining the double-layer Gaussian process stacking proxy model containing the equivalent heat dose characteristic.

[0077] Specifically, the equivalent heat dose feature compresses the combined effect of annealing temperature and time into a single scalar feature, enabling the deep Gaussian process surrogate model to accurately capture the nonlinear influence of the thermal budget on the final defect density distribution. Traditional methods model proton irradiation annealing and electron beam irradiation annealing separately, without explicitly modeling the cumulative effect of the thermal budget, leading to a systematic deviation between the surrogate model's predictions and the actual process. By introducing the equivalent heat dose feature, the superposition effect of the thermal budget from the combined annealing is incorporated into the input space of the surrogate model, eliminating the aforementioned systematic deviation.

[0078] The equivalent heat dose characteristic is a physics-guided feature engineering method that compresses the three elements of combined annealing—temperature, time, and activation energy—into a single scalar characteristic. Essentially, it multiplies the exponential factor describing the rate of thermal activation in the Arrhenius equation by the annealing duration to obtain a normalized heat dose quantification index that is physically equivalent to "the time required to achieve the same degree of defect stabilization at a reference temperature." The calculation of the equivalent heat dose characteristic uses the combined annealing temperature, combined annealing duration, and deep-level defect thermal activation energy as inputs. It is obtained by multiplying the product of the combined annealing temperature and combined annealing duration by the Arrhenius factor corresponding to the thermal activation energy, where the thermal activation energy is approximately 1.1 eV for deep-level oxygen-vacancy recombination defects (V₂O).

[0079] The technical principle behind the equivalent thermal dose feature's ability to eliminate the superposition bias of the two-step thermal budget lies in the following: In traditional processes, a first annealing is performed after proton irradiation to stabilize shallow-level damage introduced by proton irradiation, followed by a second annealing after electron beam irradiation to stabilize the Frenkel pairs. The thermal budgets from the two annealing processes are superimposed on the defect evolution dynamics. That is, the first annealing has already partially activated the stabilization process of deep-level V2O defects, and the second annealing continues to advance on this basis. Ultimately, the defect density is jointly determined by the cumulative thermal budgets of the two annealing processes. If the deep Gaussian process surrogate model only uses the temperature and duration of the two annealing processes as independent inputs without introducing auxiliary features describing the superposition effect of thermal budgets, the surrogate model cannot distinguish the equivalent relationship between "one large thermal budget annealing" and "the sum of two small thermal budget annealings" on the defect density, leading to a systematic deviation between the Pareto front predicted by the model and the actual process execution results. By introducing the equivalent heat dose feature, the total heat budget of the combined annealing is encoded as an auxiliary input feature of the surrogate model in a physically consistent manner, enabling the surrogate model to accurately model the nonlinear effects of the heat budget superposition effect on the deep-level V2O / VO defect density and stable double-vacancy V2 density, thus fundamentally eliminating the aforementioned systematic bias.

[0080] In one specific implementation, assuming the equivalent heat dose feature Q1 calculated in step S4.1a and the equivalent heat dose feature Q2 corresponding to the combined annealing after electron beam irradiation in step S5.1, the sum of the two, Q_total = Q1 + Q2, is the equivalent quantized value of the total thermal budget of this batch of processes. The deep Gaussian process surrogate model uses Q_total as an auxiliary input and learns the nonlinear mapping relationship between Q_total and the final deep level defect density during training, thereby accurately predicting the stable defect density distribution and the corresponding forward conduction pressure drop temperature coefficient and reverse recovery time given the combined annealing parameters. Through this mechanism, the thermal budget superposition effect that is not modeled in the traditional two-step annealing scheme is transformed into an explicit input feature that the surrogate model can perceive and learn, achieving a high degree of consistency between the surrogate model's prediction results and the actual process execution results, and ensuring the effectiveness of the Pareto optimal parameter combination output by the multi-objective Bayesian optimization of the deep Gaussian process in actual execution.

[0081] Example 8: Based on Example 1, using the irradiated wafer as a basis, the minority carrier lifetime of the N-base region is controlled by electron beam irradiation. Combined annealing is performed to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget. Lifetime uniformity is verified by full-wafer minority carrier lifetime measurement. The measured results are then updated to the deep Gaussian process proxy model to achieve process updates. This includes: S5.1: Based on the irradiated wafer, uniform Frenkel pair defects are introduced into the N-base region by electron beam irradiation, followed by joint annealing. The temperature and duration of the joint annealing are taken from the Pareto optimal point corresponding to the Pareto optimal irradiation parameter combination. Under a single thermal budget, the shallow energy level damage caused by proton irradiation is eliminated while the deep energy level defects are retained as positive temperature coefficient recombination centers. At the same time, the Frenkel pairs are stabilized and stable double vacancies are retained as minority carrier lifetime control recombination centers in the N-base region.

[0082] In this embodiment of the invention, the combined annealing integrates the traditional two-step annealing process into a single operation. The retained deep-level defects possess temperature-sensitive trapping cross-section characteristics, which, combined with the series resistance effect in the base region, drive stable positive temperature coefficient characteristics over a wide temperature range. The retained stable double vacancies serve as control recombination centers for the minority carrier lifetime in the base region, regulating the reverse recovery characteristics. The two types of defects are synergistically stabilized under a single thermal budget, ensuring the repeatability of device performance.

[0083] In this embodiment of the invention, the mechanism by which the combined annealing eliminates the superposition bias of the two-step thermal budget is as follows. In traditional processes, proton irradiation is followed by separate annealing to stabilize shallow-level damage, and electron beam irradiation is followed by separate annealing again to stabilize Frenkel pairs. The thermal budgets of the two annealings are superimposed in time, and the cumulative effect of the thermal budgets between the two is not explicitly modeled in the surrogate model, resulting in a systematic deviation between the actual defect density distribution and the prediction results of the surrogate model. This invention combines the two annealings into a single combined annealing, uses the equivalent heat dose feature defined in step S4.1a to uniformly describe the combined total thermal budget, and uses it as an auxiliary input feature of the deep Gaussian process surrogate model, thereby enabling the surrogate model to accurately model the nonlinear influence of the thermal budget superposition effect on the final density of the two types of defects. The temperature and duration of the combined annealing are derived from the Pareto optimality of the multi-objective Bayesian optimization output of the deep Gaussian process. In a single heat treatment, the following are simultaneously achieved: eliminating shallow-level damage (E-type defects) caused by proton irradiation while preserving deep-level V₂O / VO recombination centers (physical carriers of positive temperature coefficient characteristics); stabilizing Frenkel pairs generated by electron beam irradiation while preserving stable double-vacancy V₂ sites (control recombination centers controlling minority carrier lifetime in the N-based region). Both types of defects are synergistically stabilized under the same thermal budget, eliminating the process repeatability bias introduced by inconsistent thermal budgets in stepwise annealing.

[0084] S5.2: The minority carrier lifetime of the N-base region is mapped and measured using the microwave photoconductivity attenuation method. The consistency between the measured minority carrier lifetime after stabilization and the minority carrier lifetime of the target base region is verified. The joint annealing parameters and the measured minority carrier lifetime are used as new data points to update the deep Gaussian process proxy model, and the updated deep Gaussian process proxy model is obtained.

[0085] Preferably, the microwave photoconductivity attenuation method measures the wafer-level lifetime uniformity spectrum. If the wafer-level lifetime uniformity exceeds a preset threshold, it triggers a local resampling suggestion from the deep Gaussian process proxy model, providing a basis for adjusting the process parameters for the next batch.

[0086] Example 9: Based on Example 2, the step of predicting the positive temperature coefficient quantification index using the updated partitioned physical information proxy model, and triggering a tiered testing strategy based on the predicted value to obtain the measured dataset, includes: Step A.1: Using the updated partitioned physical information proxy model, predict the positive temperature coefficient quantization index of the wafer under test, and trigger tiered testing based on the predicted value range: batches with predicted positive temperature coefficient quantization indices not lower than the first threshold undergo multi-temperature full-temperature testing; batches with predicted positive temperature coefficient quantization indices between the second threshold and the first threshold undergo single-temperature initial screening testing, where the second threshold is less than the first threshold; batches with predicted positive temperature coefficient quantization indices lower than the second threshold are marked as requiring process review; summarize the test results of the above categories to obtain the measured dataset.

[0087] In this embodiment of the invention, the tiered testing strategy concentrates the full-temperature testing resources of the automated testing equipment on high-probability qualified batches. Single-temperature initial screening retains the ability to screen edge batches, while batches predicted to fail do not occupy testing resources but are directly marked for process re-inspection, saving approximately 30% of the full-temperature automated testing equipment's time. The positive temperature coefficient quantification index is defined as the normalized slope of the forward conduction voltage drop as a function of temperature within a preset temperature range, used to quantitatively characterize the device's self-current equalization capability.

[0088] Example 10: Based on Example 2, the incremental update of the partitioned physical information proxy model according to the deviation between the measured dataset and the predicted value includes: Step A.2: Using the deviation between the measured positive temperature coefficient quantization index in the measured dataset and the predicted value of the partitioned physical information proxy model as a criterion, if the deviation exceeds a preset tolerance threshold, a preset proportion of historical anchor points are randomly selected from the historical anchor point dataset and mixed with the new anchor points in the measured dataset to form a training batch. Incremental training is performed using a complete training loss function that includes the first physical constraint term and the second physical constraint term to obtain the updated partitioned physical information proxy model, so as to avoid catastrophic forgetting and maintain historical physical consistency.

[0089] In specific implementation, the preset tolerance threshold is a sensitivity control parameter for triggering incremental updates. A threshold that is too small will lead to frequent triggering of invalid updates, while a threshold that is too large will result in process drift not being captured in time. The actual value is set according to process stability requirements. The complete training loss function includes residual constraint terms for the partitioned physical equations, ensuring that the surrogate model after incremental training still satisfies the physical equation constraints, maintaining historical physical consistency, and avoiding forgetting the historical parameter space due to training only with new anchor points. As batches accumulate, the self-evolving process knowledge base, composed of the partitioned physical information surrogate model, the deep Gaussian process surrogate model, and the process database, is continuously optimized, achieving self-improvement of the consistency of the positive temperature coefficient characteristics across batches.

[0090] The replay buffer incremental learning strategy is a catastrophic forgetting prevention method originating from the field of continuous learning, and in this invention, it is applied to the online incremental update scenario of the partitioned physical information proxy model. "Catastrophic forgetting" refers to the phenomenon where, when a neural network model is incrementally trained using only new data, the model parameters are dominated by the gradient direction of the new data, leading to a sharp decline in its ability to fit the distribution of existing historical data. In the manufacturing scenario of this invention, if the partitioned physical information proxy model is trained only with the new measured process data each time it is received, the proxy model will gradually forget the process-performance mapping knowledge accumulated in the historical parameter space, resulting in a continuous degradation in the prediction accuracy of historical process parameter regions, ultimately causing the first fidelity pre-screening of the hierarchical fidelity-constrained Bayesian search to fail. The replay buffer strategy, by mixing in historical samples randomly drawn from the historical anchor dataset during each incremental training, makes the training gradient constrained by both new and historical data, thereby maintaining the predictive ability of the historical parameter space while incorporating new process information.

[0091] The replay buffer incremental learning strategy prevents catastrophic forgetting through the following technical principle. During the training of a deep neural network, the parameter update direction is determined by the weighted average of the gradients of all samples in the training batch. When the training batch contains only new anchors, the gradient direction is entirely determined by the distribution of the new data. If there is a difference between the new data distribution and the historical data distribution (i.e., a process drift scenario), the gradient update will cause the model parameters to move towards adapting to the new distribution, while deviating from the historical distribution, resulting in catastrophic forgetting. The replay buffer strategy mixes 30% of the historical anchors into each training batch, making the gradient direction constrained by both the historical distribution (approximately 30% weight) and the new distribution (approximately 70% weight). The gradient contribution from the historical distribution prevents the model parameters from deviating excessively from their historical adaptation state, while the gradient contribution from the new distribution updates the model parameters towards adapting to the new process conditions, achieving a dynamic balance between preserving historical knowledge and absorbing new knowledge. Furthermore, incremental training is performed using a complete training loss function that includes the residuals of the partitioned physical equations. The physical constraint term acts as an additional regularization force, further constraining the model parameters from non-physical drift in the historical parameter space. This dual mechanism jointly ensures the maintenance of historical physical consistency.

[0092] The trigger condition for incremental learning in the replay buffer in this invention is: the deviation between the measured positive temperature coefficient quantization index and the predicted value of the partitioned physical information proxy model exceeds a preset tolerance threshold. In one embodiment, the preset tolerance threshold is set to 0.5 × 10⁻⁶. -4 / 。C. When the measured deviation exceeds the threshold, the system determines that the current surrogate model's prediction of the latest process state has significantly deviated, triggering an incremental update: 30% of the historical anchor points are randomly selected from the historical anchor point dataset and mixed with all new anchor points in the current batch (from the multi-parameter measured dataset), forming a mixed training batch of approximately 50 to 80 samples. A 20-step gradient update is performed using the full training loss function. After the update, it is verified whether the surrogate model's prediction error on the historical anchor points exceeds the preset degradation threshold. If it does, the proportion of historical anchor points extracted is increased, and retraining is performed until the historical prediction accuracy meets the requirements. Through this adaptive mechanism, the partitioned physical information surrogate model can continuously track process drift, capture the gradual changes in process parameters between batches, and maintain the predictive ability for the entire historical parameter space, providing a continuous and reliable prediction basis for the pre-screening of hierarchical fidelity-constrained Bayesian search and the triggering criteria of the hierarchical testing strategy.

Claims

1. A smart manufacturing method for the positive temperature coefficient characteristics of a fast recovery diode, characterized in that, include: Obtain N-type silicon substrate parameters, acquire process simulation anchor points for the N-type silicon substrate parameters, embed training loss function with the partitioned physical equation residuals of the anode P+ layer and N base region as constraint terms, and train partitioned physical information proxy model. Using the partitioned physical information proxy model as the first fidelity evaluation layer and the process simulation as the second fidelity evaluation layer, a hierarchical fidelity-constrained Bayesian search is performed in the parameter space composed of anode injection efficiency and base region minority carrier lifetime to obtain the process feasible region and process design parameter set. Based on the target anode implantation efficiency in the process design parameter set, a P+ anode layer is formed on the surface of the N-based region through ion implantation and annealing. The conformity between the measured anode implantation efficiency and the target anode implantation efficiency is verified. The measured results are used as new anchor points to incrementally update the partitioned physical information proxy model. Based on the anode layer parameters and the minority carrier lifetime of the target base region, with irradiation parameters and annealing parameters as optimization variables, and with the forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, Pareto optimal irradiation parameter combination is searched through deep Gaussian process multi-objective Bayesian optimization, and proton irradiation is performed to obtain the irradiated wafer. Based on the irradiated wafer, the minority carrier lifetime of the N-base region is controlled by electron beam irradiation. Joint annealing is performed to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget. The lifetime uniformity is verified by measuring the minority carrier lifetime of the whole wafer. The measured results are then updated to the deep Gaussian process proxy model to achieve process updates.

2. The method according to claim 1, characterized in that, The method further includes: The updated partitioned physical information proxy model is used to predict the positive temperature coefficient quantification index. Based on the predicted value, a hierarchical testing strategy is triggered to obtain the actual test dataset. The partitioned physical information proxy model is incrementally updated according to the deviation between the actual test dataset and the predicted value. The batch distribution is monitored in real time through statistical process control and the correction amount is predicted by the deep Gaussian process proxy model. Process correction suggestions are output. The partitioned physical information proxy model, the deep Gaussian process proxy model and the process database together constitute a self-evolving process knowledge base.

3. The method according to claim 1, characterized in that, The acquisition of N-type silicon substrate parameters, using the process simulation anchor point for acquiring these parameters, embeds the residual of the partitioned physical equations between the anode P+ layer and the N-base region as a constraint term into a training loss function to train a partitioned physical information proxy model, including: The parameters of the N-type silicon substrate are obtained, and a first number of initial process simulation anchor points are collected in the parameter space using Latin hypercube sampling. A second number of supplementary process simulation anchor points are collected in the region near the P+N interface with adaptive densification. The first number is greater than the second number. The first physical constraint term is the residual of the surface recombination rate equation for the anode P+ layer, and the second physical constraint term is the residual of the volume Shockley-Reid-Hall recombination equation for the N base region. The first physical constraint term and the second physical constraint term are weighted and then summed with the data fitting term to form a training loss function. The physical constraint weight coefficients in the training loss function take a first preset value in the early stage of training and gradually increase to a second preset value in the later stage of training. The second preset value is greater than the first preset value. The partitioned physical information proxy model is obtained by training with the process simulation anchor points and the training loss function.

4. The method according to claim 1, characterized in that, The process uses the partitioned physical information proxy model as the first fidelity evaluation layer and process simulation as the second fidelity evaluation layer. A hierarchical fidelity-constrained Bayesian search is performed in the parameter space composed of anode injection efficiency and base region minority carrier lifetime to obtain the process feasible region and process design parameter set, including: Using the partitioned physical information proxy model as the first fidelity evaluation layer and process simulation as the second fidelity evaluation layer, and with the forward conduction voltage drop temperature coefficient not lower than a preset lower limit, the reverse recovery time not exceeding a preset upper limit, and the positive temperature coefficient quantification index not lower than a preset threshold as the hard constraint set, in the parameter space composed of the anode injection efficiency and the base region minority carrier lifetime, the partitioned physical information proxy model is first used to pre-screen candidate parameter points, and only the candidate parameter points that pass the pre-screening are called to perform accurate verification by the second fidelity evaluation layer. After iteration until convergence, the process feasible region and process design parameter set that satisfy the hard constraint set are obtained.

5. The method according to claim 1, characterized in that, The process design parameters are used as a basis to determine the target anode implantation efficiency. A P+ anode layer is formed on the surface of the N-based region through ion implantation and annealing. The consistency between the measured anode implantation efficiency and the target anode implantation efficiency is verified. The measured results are used as new anchor points to incrementally update the partitioned physical information proxy model, including: Based on the target anode implantation efficiency in the aforementioned process design parameter set, a P+ anode precursor layer is formed on the surface of the N-based region by boron ion implantation. The implantation energy is 60–100 keV, and the implantation dose is 8 × 10⁻⁶. 14 ~5×10 15 cm -2 ; The P+ anode precursor layer was subjected to gradient activation annealing at a temperature of 900–1000℃ for 30–60 min in a nitrogen atmosphere, with the junction depth controlled to be no more than 2 μm. The measured anode implantation efficiency was verified to be consistent with the target anode implantation efficiency. If the deviation between the measured anode injection efficiency and the target anode injection efficiency exceeds a preset uncertainty range, the measured anode injection efficiency and its corresponding process simulation prediction forward conduction pressure drop temperature characteristics are used as new anchor points. A preset proportion of historical anchor points are randomly selected from the historical anchor point dataset and mixed with the new anchor points to form a training batch. Incremental training is performed using the training loss function to obtain the updated partitioned physical information proxy model.

6. The method according to claim 1, characterized in that, The process, based on anode layer parameters and target base region minority carrier lifetime, with irradiation parameters and annealing parameters as optimization variables, and forward conduction voltage drop temperature coefficient and reverse recovery time as dual objectives, uses a deep Gaussian process multi-objective Bayesian optimization to search for the Pareto optimal combination of irradiation parameters, performs proton irradiation, and obtains an irradiated wafer, including: Based on the anode layer parameters and the minority carrier lifetime of the target base region, and with proton irradiation energy, irradiation dose, combined annealing temperature, combined annealing duration and equivalent heat dose characteristics as optimization variables, and with forward conduction pressure drop temperature coefficient and reverse recovery time as dual-objective outputs, the equivalent heat dose characteristics are calculated based on the combined annealing temperature, combined annealing duration and deep level defect thermal activation energy. A two-layer Gaussian process stacked proxy model is constructed, and the two-layer Gaussian process stacked proxy model is trained with the initial experimental points sampled by Latin hypercube. Using a cost-aware upper confidence bound acquisition function as the exploration strategy, and taking the reverse recovery time not exceeding a preset upper limit as the feasible region constraint, multiple parallel experimental suggested parameter points are generated in each round. Only proton irradiation is performed and the defect concentration after irradiation is recorded as an intermediate verification quantity. The two-layer Gaussian process stacked surrogate model is updated. After iteration to convergence, the Pareto optimal irradiation parameter combination is extracted from the Pareto front using the ε-constraint method. Proton irradiation is performed according to the Pareto optimal irradiation parameter combination to obtain the irradiated wafer.

7. The method according to claim 6, characterized in that, The equivalent heat dose characteristics are calculated based on the combined annealing temperature, combined annealing time, and deep-level defect thermal activation energy, including: Using the combined annealing temperature, combined annealing duration, and deep-level defect thermal activation energy as inputs, the equivalent heat dose characteristic is calculated by multiplying the product of the combined annealing temperature and combined annealing duration by the Arrhenius factor corresponding to the thermal activation energy. The equivalent heat dose characteristic serves as an auxiliary input to the double-layer Gaussian process stacking proxy model to capture the thermal budget superposition effect when proton irradiation annealing and electron beam irradiation annealing are performed together, thus obtaining the double-layer Gaussian process stacking proxy model that includes the equivalent heat dose characteristic.

8. The method according to claim 1, characterized in that, Based on the irradiated wafer, the minority carrier lifetime of the N-base region is controlled by electron beam irradiation. Combined annealing is performed to simultaneously stabilize proton irradiation defects and electron beam irradiation defects under a single thermal budget. Lifetime uniformity is verified by full-wafer minority carrier lifetime measurement. The measured results are then updated to the deep Gaussian process proxy model to achieve process updates, including: Based on the irradiated wafer, uniform Frenkel pair defects are introduced into the N-base region by electron beam irradiation, followed by joint annealing. The temperature and duration of the joint annealing are taken from the Pareto optimal point corresponding to the Pareto optimal irradiation parameter combination. Under a single thermal budget, the shallow energy level damage caused by proton irradiation is eliminated while the deep energy level defects are retained as positive temperature coefficient recombination centers. At the same time, the Frenkel pairs are stabilized and stable double vacancies are retained as minority carrier lifetime control recombination centers in the N-base region. The minority carrier lifetime of the N-base region was mapped and measured across the entire wafer using the microwave photoconductivity attenuation method. The consistency between the measured minority carrier lifetime after stabilization and the minority carrier lifetime of the target base region was verified. The joint annealing parameters and the measured minority carrier lifetime were used as new data points to update the deep Gaussian process proxy model, resulting in the updated deep Gaussian process proxy model.

9. The method according to claim 2, characterized in that, The step of predicting the positive temperature coefficient quantification index using the updated partitioned physical information proxy model and triggering a tiered testing strategy based on the predicted value to obtain the actual test dataset includes: The updated partitioned physical information proxy model is used to predict the positive temperature coefficient quantification index of the wafer under test. Based on the predicted value range, stratified testing is triggered: batches with predicted positive temperature coefficient quantification index not lower than the first threshold are subjected to multi-temperature full-temperature testing; batches with predicted positive temperature coefficient quantification index between the second threshold and the first threshold are subjected to single-temperature preliminary screening testing, where the second threshold is less than the first threshold; batches with predicted positive temperature coefficient quantification index lower than the second threshold are marked as requiring process review. The test results from the above tests are combined to obtain the actual test dataset.

10. The method according to claim 2, characterized in that, The incremental update of the partitioned physical information proxy model based on the deviation between the measured dataset and the predicted value includes: Using the deviation between the measured positive temperature coefficient quantification index in the measured dataset and the predicted value of the partitioned physical information proxy model as a criterion, if the deviation exceeds a preset tolerance threshold, a preset proportion of historical anchor points are randomly selected from the historical anchor point dataset and mixed with new anchor points in the measured dataset to form a training batch. Incremental training is performed using a complete training loss function that includes the first physical constraint term and the second physical constraint term to obtain the updated partitioned physical information proxy model, so as to avoid catastrophic forgetting and maintain historical physical consistency.

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