A method and system for producing a lightly boron-doped high-resistance epitaxial wafer

Abstract

The application discloses a production method and system of a lightly boron-doped substrate high-resistance wafer, and belongs to the technical field of production control. The method comprises the following steps: calculating a waste gas residual index based on ion concentration of waste gas; if abnormality occurs in a plurality of waste gas residual indexes in succession, updating model parameters of a layered state observer; otherwise, inputting online monitoring data into the layered state observer to obtain real-time distribution and uncertainty distribution of resistivity in a wafer growth process; setting an expected state evolution track, wherein the expected state evolution track comprises an ideal distribution matrix of resistivity at each preset time, calculating error distribution based on the real-time distribution and the ideal distribution matrix; obtaining an adjustment instruction based on fuzzy reasoning model processing of the error distribution and the uncertainty distribution, adjusting production process parameters based on the adjustment instruction; and generating an expected state evolution track of the next batch based on average quality error. The application can guarantee the stability of production quality.

Description

Technical Field

[0001] This invention belongs to the field of production control technology, specifically relating to a method and system for producing high-resistivity epitaxial wafers on lightly boron-doped substrates. Background Technology

[0002] In the semiconductor field, epitaxial wafers are a collective term for substrate wafers and epitaxial layers. The epitaxial layer refers to a single-crystal silicon thin film grown according to the crystal structure of the substrate. Lightly boron-doped substrate high-resistivity epitaxial wafers can effectively isolate signal interference between different components within a chip, and are therefore widely used in radio frequency chips and high-frequency analog chips.

[0003] The existing production process for epitaxial wafers involves melting polycrystalline silicon into liquid silicon, adding trace amounts of boron, and obtaining a high-resistivity substrate polished wafer through shape processing during the solidification process of the liquid silicon. The chemically cleaned high-resistivity substrate polished wafer is then placed in an epitaxial reaction chamber, which is either evacuated or purged with a protective gas. The reaction chamber is then heated to a high temperature, and a gas containing a silicon source is introduced into the reaction chamber. Silicon atoms adhere to the surface of the high-resistivity substrate polished wafer, ultimately forming a single-crystal silicon thin film.

[0004] The production of high-resistivity epitaxial wafers on lightly boron-doped substrates currently relies mainly on fixed process formulations set offline. However, the inner wall of the reaction chamber will adsorb waste gas ions, such as boron, due to the previous heavy doping process, thus producing a memory effect. These ions are slowly released during subsequent light doping production, thereby contaminating the high-resistivity epitaxial layer and damaging its resistivity. This gradual environmental change makes it difficult for fixed process formulations to guarantee the stability of product quality in the long term. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method and system for producing high-resistivity epitaxial wafers on lightly boron-doped substrates, thereby resolving the issues present in the background art.

[0006] To achieve the aforementioned objective, this invention proposes a method for producing a high-resistivity epitaxial wafer on a lightly boron-doped substrate, comprising:

[0007] A stratified state observer is constructed based on historical process data. The concentration of exhaust gas ions at the exhaust gas outlet is collected at preset intervals, and the exhaust gas residue index is calculated based on the exhaust gas ion concentration.

[0008] If multiple consecutive exhaust gas residue indices show abnormalities, the model parameters of the layered state observer are updated; otherwise, online monitoring data is input into the layered state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth.

[0009] A desired state evolution trajectory is set, which includes the ideal distribution matrix of resistivity at each preset time, and the error distribution is calculated based on the real-time distribution and the ideal distribution matrix;

[0010] The error distribution and the uncertainty distribution are processed based on a fuzzy inference model to obtain adjustment instructions, and the production process parameters are adjusted based on the adjustment instructions.

[0011] After the current production batch ends, the average quality error of the product is obtained, a baseline control trajectory is generated based on the average quality error, and the expected state evolution trajectory of the next batch is generated based on the baseline control trajectory.

[0012] The next batch of wafers is produced based on the reference control trajectory, and the production process parameters are adjusted based on the corresponding generated desired state evolution trajectory.

[0013] Furthermore, obtaining the real-time resistivity distribution and corresponding uncertainty distribution during wafer growth includes the following steps:

[0014] The wafer is divided into multiple grid points. The hierarchical state observer includes a first model and a second model. The first model includes multiple low-dimensional Gaussian regression models. The first model groups the online monitoring data to obtain multiple sets of independent data. The independent data is input into the corresponding low-dimensional Gaussian regression model to obtain first data. The first data includes the first predicted value and first confidence level of the resistivity of various grid points by the first model. The second model includes a nonlinear model. The second model outputs second data based on the first data. The second data includes the second predicted value and second confidence level of the resistivity of the grid points. The real-time distribution and the uncertainty distribution are obtained by combining the second data of all grid points.

[0015] Furthermore, processing the error distribution and the uncertainty distribution based on the fuzzy inference model to obtain the adjustment instruction includes the following steps:

[0016] Based on the error distribution and the uncertainty distribution, the statistical characteristics of the parameters are calculated. A fuzzy set is set for each parameter statistical characteristic. The fuzzy set includes multiple state rules. Each state rule corresponds to a Gaussian membership function. The width parameter in the Gaussian membership function is dynamically adjusted based on the corresponding parameter statistical characteristics. The membership degree between the input feature and each state rule is calculated based on the Gaussian membership function.

[0017] The control rules for setting production parameters are as follows: each control rule corresponds to at least one state rule and a membership degree; each control rule has an adjustment weight, which is associated with the membership degree of the state rule; the control rule to be triggered is determined based on the state rule and the membership degree; the adjustment amount of the control rule is weighted and summed based on the adjustment weight to obtain the final adjustment amount; and the adjustment instruction is obtained by combining the final adjustment amounts of each production parameter.

[0018] Furthermore, calculating the statistical characteristics of the parameters based on the error distribution and the uncertainty distribution includes the following steps:

[0019] The epitaxial wafer is divided into a central region and an edge region. Based on the error distribution, the average error and standard deviation of all grid points are calculated, as well as the deviation of the average error of the central region and the edge region.

[0020] The uncertainty distribution includes the variance of each grid point. Based on the uncertainty distribution, the cumulative value of the sum of the mean variances of the central region and the edge region is calculated. The cumulative value represents the total uncertainty of the hierarchical state observer's prediction of the central region and the edge region. The average error, standard deviation, deviation value, and cumulative value of the error distribution are used as the parameter statistical features.

[0021] Furthermore, updating the model parameters of the hierarchical state observer includes the following steps:

[0022] A model memory is established, which includes various model parameters, corresponding Fisher information matrices, and embedding vectors. The embedding vectors are obtained by dimensionality reduction of historical process data used to train the model parameters.

[0023] The online monitoring data after the first abnormality of the exhaust gas residue index is obtained is acquired, the online monitoring data is dimensionality reduced to obtain a real-time vector, the similarity between the real-time vector and each embedded vector in the model memory is calculated, and the regularization coefficient is determined based on the similarity distribution.

[0024] Select the embedding vector with the highest similarity to the real-time vector, obtain the model parameters and Fisher information matrix corresponding to the embedding vector, construct a composite loss function based on the model parameters, Fisher information matrix and regularization coefficients, and use the composite loss function to supervise the model parameter update of the hierarchical state observer.

[0025] Furthermore, calculating the exhaust gas residue index based on online monitoring data includes the following steps:

[0026] The concentration of exhaust gas ions in the reaction chamber is obtained by online mass spectrometry. After normalizing the concentration of exhaust gas ions, the exhaust gas ion signal intensity is obtained. The exhaust gas residual index at the previous moment is corrected based on the exhaust gas ion signal intensity to obtain the exhaust gas residual index at the current moment.

[0027] Furthermore, generating a baseline control trajectory based on the average quality error includes the following steps:

[0028] A sensitivity model is established, which includes the influence relationship between production process parameters and resistivity. After the current batch of production is completed, the online monitoring data of the current batch is input into the stratified state observer to obtain the predicted distribution of the final resistivity quality. The prediction error between the predicted distribution and the actual resistivity distribution is calculated. If the prediction error is greater than a first threshold, the model parameters of the stratified state observer are adjusted. Otherwise, the average quality error is analyzed based on the sensitivity model to generate the baseline control trajectory.

[0029] The present invention also provides a production system for high-resistivity epitaxial wafers on lightly boron-doped substrates, the system being used to implement the above-described method, the system comprising:

[0030] The detection module constructs a layered state observer based on historical process data, collects the ion concentration of exhaust gas at the exhaust gas outlet at preset intervals, and calculates the exhaust gas residue index based on the ion concentration.

[0031] If multiple consecutive exhaust gas residue indices show abnormalities, the prediction module updates the model parameters of the layered state observer; otherwise, it inputs online monitoring data into the layered state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth.

[0032] The control module sets a desired state evolution trajectory, which includes the ideal distribution matrix of resistivity at each preset time. Based on the real-time distribution and the ideal distribution matrix, it calculates the error distribution. Based on the fuzzy inference model, it processes the error distribution and the uncertainty distribution to obtain adjustment instructions. Based on the adjustment instructions, it adjusts the production process parameters.

[0033] The optimization module obtains the average quality error of the product after the current production batch ends, generates a baseline control trajectory based on the average quality error, generates the desired state evolution trajectory for the next batch based on the baseline control trajectory, controls the production of the next batch of wafers based on the baseline control trajectory, and adjusts the production process parameters based on the corresponding generated desired state evolution trajectory.

[0034] The beneficial effects of this invention are as follows:

[0035] This invention first determines whether to update the observer model parameters based on the anomaly judgment of the exhaust gas residual index, ensuring the prediction accuracy of the observer model. By setting the desired state evolution trajectory and comparing it with the real-time distribution to calculate the error distribution, the degree of deviation and spatial distribution characteristics between the current production state and the ideal target can be quantified. Using a fuzzy inference model combined with the error distribution and the uncertainty distribution of the prediction, an adjustment command is generated that can respond to deviations while avoiding over-adjustment when the model prediction is inaccurate, realizing real-time dynamic adjustment of production process parameters. After the current batch ends, the baseline control trajectory and desired state evolution trajectory for the next batch are generated based on the average quality error of the final product. This enables the entire production process to not only perform real-time correction within the batch but also achieve continuous improvement across batches, solving the problem in the prior art where fixed process formulas cannot guarantee the long-term stability of product quality. Attached Figure Description

[0036] Figure 1 This is a flowchart of the steps in a method for producing a high-resistivity epitaxial wafer on a lightly boron-doped substrate according to the present invention.

[0037] Figure 2 This is a schematic diagram illustrating the principle of the layered state observer outputting wafer resistivity in this invention.

[0038] Figure 3 This is a comparison chart of the output performance of the hierarchical state observer of this invention and existing models;

[0039] Figure 4 A schematic diagram of the structure of a production system for a lightly boron-doped substrate high-resistivity epitaxial wafer according to the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] It is understood that the terms "first," "second," etc., used in this application may be used herein to describe various elements, but unless otherwise specified, these elements are not limited by these terms. These terms are used only to distinguish one element from another. For example, without departing from the scope of this application, a first script may be referred to as a second script, and similarly, a second script may be referred to as a first script.

[0042] like Figure 1 As shown, a method for producing a high-resistivity epitaxial wafer on a lightly boron-doped substrate includes:

[0043] S1: Construct a stratified state observer based on historical process data, collect the exhaust gas ion concentration at the exhaust gas outlet at preset intervals, and calculate the exhaust gas residue index based on the exhaust gas ion concentration.

[0044] Historical process data comprises data generated during extensive historical production processes. Each historical process data entry includes input and output data. Input data records all process parameters changing over time, such as the complete data from 0 to 3600 seconds, the silane flow rate increasing from 0 to 100 sccm and then decreasing back to 0, the switching times and flow rates of the doping gas flow, etc. The wafer surface is divided into multiple grid points, and the output data includes the specific resistivity value of each grid point.

[0045] Online monitoring data is data collected in real time by sensors installed on the equipment during the production process. It includes real-time temperature values ​​measured by a multi-point optical pyrometer at different radius positions of the wafer, real-time epitaxial layer growth thickness values ​​measured by a multi-point laser interferometer at a fixed point, real-time intensity signals of specific gas components measured by a quadrupole mass spectrometer in the exhaust gas pipeline, and exhaust gas ion concentrations obtained by an online mass spectrometer installed at the exhaust gas outlet.

[0046] S2: If multiple consecutive exhaust gas residual indices show abnormalities, update the model parameters of the layered state observer; otherwise, input the online monitoring data into the layered state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth.

[0047] In this embodiment, before inputting online monitoring data into the stratified state observer, a residual gas index is calculated based on the exhaust gas ion concentration in the online monitoring data. The residual gas index measures the contamination level within the reaction chamber. During epitaxial wafer production, the input reaction gas includes diborane, in which boron ions are adsorbed onto the inner wall surface of the reaction chamber. Ideally, when the injection of diborane stops, the boron signal in the exhaust gas should quickly drop to zero. However, due to the memory effect, boron is slowly released from the chamber wall, graphite disk, etc., resulting in a persistent boron signal in the exhaust gas. Therefore, the residual gas index is initially very low. With each batch of doped products produced, more and more boron is adsorbed onto the chamber wall, affecting the boron concentration participating in the reaction. As production continues, the residual gas index slowly increases. When the residual gas index rises to a certain level, or when it suddenly rises, it indicates a change in the production environment, requiring adjustment of the stratified state observer's model parameters to improve the model's prediction accuracy.

[0048] In this embodiment, the residual exhaust gas index ranges from 0 to 1, where 0 represents a clean reaction chamber and 1 represents a dirty reaction chamber. When the residual exhaust gas index increases from 0 to 0.4 and remains above 0.4, or increases from 0.4 to over 0.8, it indicates that the dirtiness of the reaction chamber exceeds a critical value. Alternatively, if the rate of increase in the residual exhaust gas index continuously exceeds a preset rate of increase, it indicates that the equipment may be malfunctioning. When the above situations occur, the residual exhaust gas index is determined to be abnormal. In this case, the parameters of the stratified state observer model are adjusted; the specific adjustment method will be described later.

[0049] If the residual exhaust gas index is normal, the currently collected online monitoring data is directly input into the stratified state observer. If the residual exhaust gas index is abnormal, the model parameters are updated first, and then the currently collected online monitoring data is input into the updated stratified state observer. This ensures the accuracy of the model prediction and, consequently, the accuracy of subsequent process parameter adjustments.

[0050] Real-time wafer resistivity distribution can be obtained by inputting online monitoring data into a layered state observer. Since the resistivity distribution of a wafer cannot be measured in real time during production, a layered state observer is needed for indirect observation. A layered state observer can be, for example, a Gaussian process regression, a neural network model, or an SVM model. The layered state observer outputs the prediction results at any given time. For example, at 1800 seconds, the layered state observer outputs the predicted resistivity values ​​for each grid point of the virtual wafer at that time, including the resistivity of each grid point. These resistivities constitute the resistivity distribution matrix of the entire wafer surface. Additionally, the Gaussian process regression also outputs the wafer resistivity distribution probability, specifically the variance. For example, if the predicted resistivity is 995 Ω·cm, the model output variance is 25 Ω·cm. 2 That is, the standard deviation is 5Ω·cm. By looking up the probability distribution table, it is determined that the true value of this point has a 95% probability of falling within the interval [985, 1005].

[0051] S3: Set the desired state evolution trajectory, which includes the ideal distribution matrix of resistivity at each preset time. Calculate the error distribution based on the real-time distribution and the ideal distribution matrix.

[0052] S4: Based on the fuzzy inference model, process the error distribution and uncertainty distribution to obtain adjustment instructions, and adjust the production process parameters based on the adjustment instructions.

[0053] First, an initial production control process is preset. The expected state evolution trajectory generated based on this production control process is only used in the production process of the first batch of epitaxial wafers. In subsequent production processes, the expected state evolution trajectory of the second batch of epitaxial wafers will be generated based on the production process data of the first batch of epitaxial wafers. This will be explained in detail later.

[0054] The desired state evolution trajectory includes the resistivity values ​​of each grid point at each preset time under the initial production control process. If 10 preset time points are set during production, the layered state observer predicts the resistivity of each grid point in the wafer based on the acquired online monitoring data at each preset time. For the desired state evolution trajectory of the first batch, simulated data can be generated using finite element method simulation software. Then, a basic state observer can be built by training the simulated data. Finally, the initial process recipe parameters are input into the state observer to obtain the desired state evolution trajectory. Alternatively, the resistivity that each grid point should reach at each preset time point can be determined by deriving formulas from the standard process recipe parameters to obtain the desired evolution trajectory. The optimal method is to actually conduct test production and remove the wafer and measure its resistivity when the preset time is reached to obtain a high-precision desired evolution trajectory.

[0055] By comparing the real-time resistivity distribution with the ideal distribution matrix, the actual resistivity at each grid point can be determined to be significantly different from the ideal resistivity. Based on this deviation, the error distribution of the entire wafer is generated. Then, the error distribution and uncertainty distribution are input into the fuzzy inference model to obtain the parameter adjustment amounts for each production device. How the fuzzy inference model outputs the parameter adjustment amounts will be introduced later.

[0056] S5: After the current production batch ends, obtain the average quality error of the product, generate a baseline control trajectory based on the average quality error, and generate the expected state evolution trajectory for the next batch based on the baseline control trajectory.

[0057] S6: Control the production of the next batch of wafers based on the baseline control trajectory, and adjust the production process parameters based on the corresponding generated desired state evolution trajectory.

[0058] After the current production batch is completed, quality inspection is performed on the epitaxial wafer to obtain the actual resistivity of each grid point. An ideal resistivity is set for each grid point, and the actual resistivity is subtracted from the ideal resistivity to obtain the quality error. The baseline control trajectory for the current batch production process is obtained and defined as the first trajectory matrix. The first trajectory matrix includes the set values ​​and changes of all controlled process parameters throughout the entire process duration. Then, a parameter adjustment matrix is ​​generated using the first trajectory matrix and the quality error. The parameter adjustment matrix includes the adjustment amount for each parameter in the first trajectory matrix. Finally, the parameter adjustment matrix is ​​added to the first trajectory matrix to obtain the baseline control trajectory for the next batch, which determines how the process parameters should be adjusted at each preset time. This is defined as the second trajectory matrix.

[0059] The parameter adjustment matrix can be obtained in the following way: by systematically analyzing historical production data to obtain the causal relationship between process parameters and quality changes, i.e., constructing a sensitivity model. For example, by using the sensitivity model, it can be found that if the process parameter u is increased by one unit at time t, the resistivity of each measurement point on the wafer will increase by p accordingly. Then, based on the previously calculated average quality error, it can be determined how many parameters need to be adjusted to correct this error, thereby obtaining the parameter adjustment matrix.

[0060] Then, based on the second trajectory, the desired state trajectory for the next batch of production is obtained. The desired state trajectory includes the resistivity distribution matrix at each preset time, which represents an idealized resistivity change process. Subsequently, the production of the next batch of epitaxial wafers is controlled based on the second trajectory. During production, real-time distribution is obtained by acquiring online monitoring data and combining it with a layered state observer. In actual production, due to the influence of external disturbances, such as ambient temperature and equipment aging, deviations may occur between the actual wafer production and the ideal process. Therefore, it is necessary to dynamically adjust the production process parameters during epitaxial wafer production by comparing the real-time distribution with the desired state trajectory.

[0061] In this embodiment, obtaining the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth includes the following steps:

[0062] The wafer is divided into multiple grid points. The hierarchical state observer includes a first model and a second model. The first model includes multiple low-dimensional Gaussian regression models. The first model groups the online monitoring data to obtain multiple sets of independent data. The independent data is input into the corresponding low-dimensional Gaussian regression model to obtain the first data. The first data includes the first predicted value and first confidence level of the first model for various resistivities of the grid points. The second model includes a nonlinear model. The second model outputs second data based on the first data. The second data includes the second predicted value and second confidence level of the resistivity of the grid points. The real-time distribution and uncertainty distribution are obtained by combining the second data of all grid points.

[0063] To increase the interpretability and prediction speed of the model, the hierarchical state observer in this embodiment includes multiple low-dimensional models. The first data output by each low-dimensional Gaussian regression model includes the resistivity of each grid point and the corresponding first confidence level. For example, the low-dimensional Gaussian regression model includes a thermodynamic model, a chemical model and a doping model. The input data of the thermodynamic model includes the temperature of each heating zone in the reaction chamber and the pressure value in the reaction chamber. The data input into the thermodynamic model can be real-time monitoring data or time series data between the start time point and the current time point.

[0064] The input data for the chemical model includes the mass of gases such as dichlorosilane, hydrogen, and hydrogen chloride fed into the reaction chamber. The input data for the doping model includes the doping mass of diborane or trimethylborane. Finally, the thermodynamic, chemical, and doping models all output a first predicted value and a first confidence level for the resistivity at each grid point. Subsequently, each low-dimensional Gaussian regression model inputs its own first data into a second model. The second model integrates the first data to obtain a second predicted value and a second confidence level for the resistivity at each grid point. Figure 2 As shown, the second model will output the predicted resistivity values ​​for each grid point, which can then be used as a reference by production personnel. Figure 3 As shown, the prediction accuracy of this invention is better than that of using a single linear regression model.

[0065] To facilitate explanation and understanding, the statistical characteristics of the parameters will be introduced first.

[0066] Calculating the statistical characteristics of parameters based on error distribution and uncertainty distribution includes the following steps:

[0067] The epitaxial wafer is divided into a central region and an edge region. The average error and standard deviation of all grid points are calculated based on the error distribution, as well as the deviation of the average error of the central region and the edge region.

[0068] The uncertainty distribution includes the variance of each grid point. Based on the uncertainty distribution, the cumulative value of the sum of the mean variances of the central and peripheral regions is calculated. The cumulative value represents the total uncertainty of the stratified state observer's prediction of the central and peripheral regions. The mean error, standard deviation, deviation value, and cumulative value of the error distribution are used as parametric statistical features.

[0069] Here, the distance between a grid point and the center point of the wafer is defined as the first distance. The total radius of the wafer is obtained, and 1 / 3 of the total radius is set as the first value, and 9 / 10 of the total radius is set as the second value. If the first distance of a grid point is less than the first value, the area where the grid point is located is defined as the central region; if the first distance of a grid point is greater than the second value, the area where the grid point is located is defined as the edge region. The remaining grid points are defined as being located within the central region. The mean and standard deviation of the errors corresponding to all grid points are calculated. The mean error represents the overall resistivity, and the standard deviation represents the dispersion of the resistivity distribution. Then, the first average error of each grid point in the central region and the second average error of each grid point in the edge region are calculated, and the difference between the first and second average errors, i.e., the deviation value, is calculated. If the deviation value is greater than 0, it represents a first pattern of resistivity distribution with high resistivity in the center and low resistivity at the edges; if the deviation value is less than 0, it represents a second pattern of resistivity distribution with low resistivity in the center and high resistivity at the edges. In other embodiments, the wafer region can be further subdivided.

[0070] The variance of all grid points is obtained based on the uncertainty distribution. The average variance of the central region is calculated and defined as the third average. Similarly, the fourth average is calculated, which is the average variance of all grid points in the edge region. The third and fourth averages are directly added together to obtain the cumulative value. The larger the cumulative value, the less reliable the prediction of the current distribution pattern. Theoretically, the process of directly adding the third and fourth averages to obtain the confidence of the overall distribution pattern is a simplified calculation process, but it will lose some accuracy. In practice, it is also necessary to introduce the covariance of the error distribution in the central and edge regions. However, introducing the covariance will greatly increase the computational complexity and time, making it less feasible in real-time engineering control. In addition, many perturbations on the wafer are global. For example, a small fluctuation in the main carrier gas flow will affect both the center and the edge of the wafer simultaneously, which will cause the third and fourth averages to be too high or too low. Therefore, the simpler algorithm in this embodiment can achieve better practical engineering results.

[0071] When the cumulative value is low, the confidence level of the resistivity being in the current predicted distribution pattern is considered high, and the fuzzy controller is more likely to adjust the parameters subsequently. When the cumulative value is high, the confidence level of the resistivity being in the current predicted distribution pattern is considered low, and the fuzzy controller may not adjust the parameters subsequently.

[0072] This embodiment, based on a fuzzy inference model, processes error distribution and uncertainty distribution to obtain adjustment instructions, including the following steps:

[0073] The statistical characteristics of the parameters are calculated based on the error distribution and uncertainty distribution. A fuzzy set is set for each parameter statistical characteristic. The fuzzy set includes multiple state rules. Each state rule corresponds to a Gaussian membership function. The width parameter in the Gaussian membership function is dynamically adjusted based on the corresponding parameter statistical characteristics. The membership degree between the input feature and each state rule is calculated based on the Gaussian membership function.

[0074] As previously described, the parametric statistical characteristics represent the predicted wafer resistivity distribution characteristics. According to the manufacturing process manual, a fuzzy set is pre-defined for each parametric statistical characteristic; that is, one fuzzy set corresponds to one parametric statistical characteristic. For example, a corresponding fuzzy set 1 is defined for the average error. Fuzzy set 1 includes five state rules: average error much less than 0, average error less than 0, average error equal to 0, average error greater than 0, and average error much greater than 0. Each state rule corresponds to a Gaussian membership function. For the state rule that average error equals 0, it is defined as state rule 3, and its Gaussian membership function is, for example, [missing information]. ,in, The statistical characteristics of the input parameters and the membership scores of state rule 3 are used. Statistical characteristics of the input parameters. Given the width parameter, according to the formula, when the width parameter is large, even if the average error deviates far from 0, the calculated membership score will be close to 1.

[0075] The width parameter is dynamically adjusted based on statistical characteristics. In this embodiment, the value of the width parameter is determined by the following formula: ,in, The base variance is the preset value. Sensitivity coefficient The average variance is the sum of the variances of all grid points. State rule 3 corresponds to zero deviation, meaning that production will proceed according to the current process, and the final product quality will be close to the ideal product quality. Therefore, the corresponding control rule should be conservative, meaning that the current process parameters should not be adjusted as much as possible. Thus, the greater the membership degree between the average error and state rule 3, the more conservative the subsequent control will be.

[0076] Under the above logic, the variance mean In cases where the uncertainty is large, the overall uncertainty of the hierarchical state observer's prediction results is higher. This increases the width parameter, making it easier for the membership score of the subsequent average error to approach 1, thus making the control strategy more conservative. With a large sensitivity coefficient, the membership score is more likely to approach 1, meaning the control behavior is more likely to become conservative. The advantage of this approach is that when the uncertainty of the hierarchical state observer's prediction results is high, the fuzzy controller will suppress its own control input, avoiding over-control.

[0077] Set control rules for production parameters. Each control rule corresponds to at least one state rule and membership degree. The control rules have adjustment weights, which are related to the membership degree of the state rule. The triggering control rule is determined based on the state rule and membership degree. The adjustment amount of the control rule is weighted and summed based on the adjustment weight to obtain the final adjustment amount. The adjustment instruction is obtained by combining the final adjustment amounts of each production parameter.

[0078] Control rules define how the system should be controlled under the conditions specified in the state rules. For example, if the average error is much greater than 0, it indicates that the overall resistivity is significantly high, and the adjustment amount of the diborane gas flow rate needs to be greatly reduced. The adjustment weight for each control rule can be calculated using the following formula: ,in, To control the adjustment weights corresponding to the rules, As the preset base weights, This is the weight decay coefficient, a preset value that represents the rate at which the adjusted weights decay as uncertainty increases. To control the magnitude of the uncertainty of the state rule upon which the control rule depends, for the state rule with a mean error of 0, its uncertainty depends on the mean variance. Therefore, This represents the average variance. For other state rules, such as the one where resistivity is high at the center and low at the edges, the uncertainty depends on the deviation value. Therefore, in the formula... This is the deviation value.

[0079] Finally, to filter control rules, a trigger threshold is first set. Only when the membership degree between the parameter statistical characteristics and the state rule is greater than the trigger threshold will the corresponding control rule be triggered. When multiple control rules adjusting the same process parameter are triggered simultaneously, the control quantities of the control rules are weighted and summed based on the adjustment weights, and the sum is used as the final adjustment amount of the parameter.

[0080] This embodiment updates the model parameters of the hierarchical state observer by including the following steps:

[0081] A model memory is established, which includes various model parameters, the corresponding Fisher information matrix, and embedding vectors. The embedding vectors are obtained by dimensionality reduction of the historical process data used to train the model parameters.

[0082] The online monitoring data after the first abnormality of the exhaust gas residual index is obtained is acquired. The online monitoring data is dimensionality reduced to obtain a real-time vector. The similarity between the real-time vector and each embedded vector in the model memory is calculated. The regularization coefficient is determined based on the similarity distribution.

[0083] Select the embedding vector with the highest similarity to the real-time vector, obtain the model parameters and Fisher information matrix corresponding to the embedding vector, construct a composite loss function based on the model parameters, Fisher information matrix and regularization coefficients, and use the composite loss function to supervise the model parameter update of the hierarchical state observer.

[0084] In this embodiment, since the first model is a low-dimensional Gaussian model that incorporates physical mechanisms, its model parameters do not need to be updated. The second model is a feedforward neural network. When the exhaust gas residue index becomes abnormal, the model parameters in the second model need to be updated. The model parameters include the connection weights between neurons. For example, after updating, the connection weights between the input neurons of the doping model and the neurons in the subsequent hidden layers will be increased.

[0085] For a set of pre-trained optimal model parameters, the Fisher information matrix is ​​obtained by calculating the expected value of the square of the second or first derivative of the loss function with respect to each parameter. The elements with larger values ​​in the Fisher information matrix correspond to the parameters that have the greatest impact on the model's prediction results. When updating model parameters, introducing the Fisher information matrix can avoid drastic modifications to important model parameters, ensuring the stability of the prediction model. The embedding vector is obtained by first acquiring training data for training the second model. The training data includes the output data of the first model and the actually collected resistivity distribution data. An autoencoder is used to process the training data into a low-dimensional vector.

[0086] When the exhaust gas residue index is abnormal, the system acquires online monitoring data after the anomaly occurs. Since model parameter updates are only triggered when anomalies occur continuously, a certain amount of data has already accumulated by the time the model parameters are updated. The collected online monitoring data is used to generate a real-time embedding vector through an autoencoder. The similarity between the real-time embedding vector and each historical embedding vector stored in the model memory is calculated. This embodiment uses cosine similarity, and then obtains the top N similarity values, calculates their average value. The larger the average value, the higher the regularization coefficient. A comparison table between the average similarity value and the regularization coefficient can be established, thereby determining the specific value of the regularization coefficient based on the calculated average similarity value.

[0087] Next, the embedding vector with the highest similarity to the real-time vector is obtained, and its corresponding model parameters are defined as the optimal model parameters. A composite function is then constructed, and the constructed composite loss function is... ,in, It is a loss function used to measure the prediction error of the current model parameters on the currently acquired online monitoring data. It is the regularization coefficient. The elastic weight consolidation penalty term is calculated using the following formula. in, This is the vector of model parameters that is currently being updated. This corresponds to the optimal model parameter vector. This is the Fisher information matrix corresponding to the optimal model parameters.

[0088] When training the model, the optimal model parameters are used as the initial parameters for the second model. To minimize the composite loss function, the loss function within the composite loss function needs to be optimized. and They are all relatively small, and the loss function among them... During model training, gradient descent is used to minimize it. In the middle, the elastic weighting consolidates the penalty term. Determined by the difference between the Fisher information matrix and the model parameters, and due to the addition of a regularization coefficient, a larger regularization coefficient represents a penalty term for consolidating the elastic weights. The restrictions are stricter, meaning the updates to model parameters are more stringent, making the model more conservative when updating parameters. In other words, if a historical embedding vector with high similarity is found, it means that the current production situation has occurred in the historical production process, so its corresponding model parameters should be used as much as possible. If no historical embedding vector with high similarity is found, it means that the current production situation has not occurred in the historical production process, so the restrictions on model parameters should be relaxed during training.

[0089] After multiple rounds of iterative optimization, the parameters of the second model were updated to a new state. This new state not only adapts to data changes caused by the intensified boron memory effect or equipment malfunctions, but also retains the core knowledge learned in the past to the greatest extent possible. Moreover, the updated model can be put into use immediately.

[0090] In this embodiment, calculating the exhaust gas residue index based on online monitoring data includes the following steps:

[0091] The concentration of exhaust gas ions in the reaction chamber is obtained by online mass spectrometry. After normalizing the concentration of exhaust gas ions, the exhaust gas ion signal intensity is obtained. The exhaust gas residual index at the previous moment is corrected based on the exhaust gas ion signal intensity to obtain the exhaust gas residual index at the current moment.

[0092] An online mass spectrometer is installed at the exhaust outlet of the reaction chamber. The boron ion concentration peak during the intrinsic growth stage is obtained using this online mass spectrometer. In reality, multiple boron-related ion peaks may be detected; the highest and most stable boron-related ion peak is selected as the exhaust gas ion concentration. Since the flow rate of diborane doped during the intrinsic growth stage is 0, the boron ion concentration detected at this time is the residual concentration. The exhaust gas residual index is calculated using the following formula: ,in, for The residual exhaust gas index at any given time for The residual exhaust gas index at any given time A preset smoothing factor is used. The larger the preset smoothing factor, the slower the contamination of the reaction chamber. The value of the preset smoothing factor can be determined experimentally. In this embodiment, it is set to 0.99. for The normalized concentration of exhaust gas ions at any given time, i.e., the exhaust gas ion signal intensity.

[0093] In this embodiment, generating a baseline control trajectory based on the average quality error includes the following steps:

[0094] A sensitivity model is established, which includes the influence relationship between production process parameters and resistivity. After the current batch of production is completed, the online monitoring data of the current batch is input into the stratified state observer to obtain the predicted distribution of the final resistivity quality. The prediction error between the predicted distribution and the actual resistivity distribution is calculated. If the prediction error is greater than the first threshold, the model parameters of the stratified state observer are adjusted. Otherwise, the average quality error is analyzed based on the sensitivity model to generate a baseline control trajectory.

[0095] Assuming this is the second batch, the baseline control trajectory needs to be updated after production. Before updating the baseline control trajectory, the accuracy of the layered state observer needs to be verified. Specifically, after the current batch is produced, the online monitoring data acquired for this batch is input into the layered state observer to obtain the predicted resistivity of the epitaxial wafers after production. This predicted result is compared with the actual result to obtain the prediction error, which can be the average of the errors of all epitaxial wafers. If the prediction error is large, it means that the layered state observer itself is inaccurate, that is, the final production error is caused by the layered state observer. In this case, the baseline control trajectory is not updated. It is updated only after the accuracy of the layered state observer reaches the standard. Theoretically, the prediction results of the layered state observer are generally accurate after data verification before being put into use.

[0096] If the prediction error is less than the first threshold, it means that the hierarchical state observer itself is accurate. At this time, the actual control trajectory of each production in the batch of production process data is obtained, and multiple actual control trajectories that are highly similar to the reference control trajectory are obtained. In other words, production data that strictly follows the reference control trajectory is found, and the actual distribution of resistivity in the batch of production data is obtained. The average error between the actual distribution and the ideal distribution is calculated, and the initially determined production process is adjusted in combination with the sensitivity model. After the correction is completed, the reference control trajectory is obtained.

[0097] like Figure 4 As shown, the present invention also provides a production system for high-resistivity epitaxial wafers on lightly boron-doped substrates. This system is used to implement the above-described method and includes:

[0098] The detection module constructs a layered state observer based on historical process data, collects the ion concentration of exhaust gas at the exhaust gas outlet at preset intervals, and calculates the exhaust gas residue index based on the ion concentration.

[0099] If multiple consecutive exhaust gas residue indices show abnormalities, the prediction module updates the model parameters of the stratified state observer; otherwise, it inputs online monitoring data into the stratified state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth.

[0100] The control module sets the desired state evolution trajectory, which includes the ideal distribution matrix of resistivity at each preset time. It calculates the error distribution based on the real-time distribution and the ideal distribution matrix, processes the error distribution and uncertainty distribution based on the fuzzy inference model to obtain adjustment instructions, and adjusts the production process parameters based on the adjustment instructions.

[0101] The optimization module obtains the average quality error of the product after the current production batch ends, generates a baseline control trajectory based on the average quality error, generates the expected state evolution trajectory for the next batch based on the baseline control trajectory, controls the production of the next batch of wafers based on the baseline control trajectory, and adjusts the production process parameters based on the corresponding generated expected state evolution trajectory.

[0102] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0103] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

[0104] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for producing a high-resistivity epitaxial wafer on a lightly boron-doped substrate, characterized in that, include: A stratified state observer is constructed based on historical process data. The concentration of exhaust gas ions at the exhaust gas outlet is collected at preset intervals, and the exhaust gas residue index is calculated based on the exhaust gas ion concentration. If multiple consecutive exhaust gas residue indices show abnormalities, the model parameters of the layered state observer are updated; otherwise, online monitoring data is input into the layered state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth. This includes: dividing the wafer into multiple grid points; the layered state observer includes a first model and a second model; the first model includes multiple low-dimensional Gaussian regression models; the first model groups the online monitoring data to obtain multiple sets of independent data; the independent data is input into the corresponding low-dimensional Gaussian regression model to obtain first data; the first data includes the first predicted value and first confidence level of the first model for various resistivities of the grid points; the second model includes a nonlinear model; the second model outputs second data based on the first data; the second data includes the second predicted value and second confidence level of the resistivity of the grid points; and the real-time distribution and the uncertainty distribution are obtained by combining the second data of all the grid points. A desired state evolution trajectory is set, which includes the ideal distribution matrix of resistivity at each preset time, and the error distribution is calculated based on the real-time distribution and the ideal distribution matrix; The method for processing the error distribution and the uncertainty distribution based on the fuzzy inference model to obtain adjustment instructions includes: calculating parameter statistical features based on the error distribution and the uncertainty distribution; setting a fuzzy set for each parameter statistical feature; the fuzzy set includes multiple state rules; each state rule corresponds to a Gaussian membership function; the width parameter in the Gaussian membership function is dynamically adjusted based on the corresponding parameter statistical features; and calculating the membership degree between the input feature and each state rule based on the Gaussian membership function. The control rules for setting production parameters are as follows: each control rule corresponds to at least one state rule and a membership degree; each control rule has an adjustment weight, which is associated with the membership degree of the state rule; the control rule to be triggered is determined based on the state rule and the membership degree; the adjustment amount of the control rule is weighted and summed based on the adjustment weight to obtain the final adjustment amount; and the adjustment instruction is obtained by combining the final adjustment amounts of each production parameter. Adjust the production process parameters based on the adjustment instructions; After the current production batch ends, the average quality error of the product is obtained, a baseline control trajectory is generated based on the average quality error, and the expected state evolution trajectory of the next batch is generated based on the baseline control trajectory. The next batch of wafers is produced based on the reference control trajectory, and the production process parameters are adjusted based on the corresponding generated desired state evolution trajectory.

2. The method according to claim 1, characterized in that, Calculating the statistical characteristics of parameters based on the error distribution and the uncertainty distribution includes the following steps: The epitaxial wafer is divided into a central region and an edge region. Based on the error distribution, the average error and standard deviation of all grid points are calculated, as well as the deviation of the average error of the central region and the edge region. The uncertainty distribution includes the variance of each grid point. Based on the uncertainty distribution, the cumulative value of the sum of the mean variances of the central region and the edge region is calculated. The cumulative value represents the total uncertainty of the hierarchical state observer's prediction of the central region and the edge region. The average error, standard deviation, deviation value, and cumulative value of the error distribution are used as the parameter statistical features.

3. The method according to claim 1, characterized in that, Updating the model parameters of the hierarchical state observer includes the following steps: A model memory is established, which includes various model parameters, corresponding Fisher information matrices, and embedding vectors. The embedding vectors are obtained by dimensionality reduction of historical process data used to train the model parameters. The online monitoring data after the first abnormality of the exhaust gas residue index is obtained is acquired, the online monitoring data is dimensionality reduced to obtain a real-time vector, the similarity between the real-time vector and each embedded vector in the model memory is calculated, and the regularization coefficient is determined based on the similarity distribution. Select the embedding vector with the highest similarity to the real-time vector, obtain the model parameters and Fisher information matrix corresponding to the embedding vector, construct a composite loss function based on the model parameters, Fisher information matrix and regularization coefficients, and use the composite loss function to supervise the model parameter update of the hierarchical state observer.

4. The method according to claim 1, characterized in that, Calculating the residual index of exhaust gas based on online monitoring data includes the following steps: The concentration of exhaust gas ions in the reaction chamber is obtained by online mass spectrometry. After normalizing the concentration of exhaust gas ions, the exhaust gas ion signal intensity is obtained. The exhaust gas residual index at the previous moment is corrected based on the exhaust gas ion signal intensity to obtain the exhaust gas residual index at the current moment.

5. The method according to claim 1, characterized in that, Generating a baseline control trajectory based on the average quality error includes the following steps: A sensitivity model is established, which includes the influence relationship between production process parameters and resistivity. After the current batch of production is completed, the online monitoring data of the current batch is input into the stratified state observer to obtain the predicted distribution of the final resistivity quality. The prediction error between the predicted distribution and the actual resistivity distribution is calculated. If the prediction error is greater than a first threshold, the model parameters of the stratified state observer are adjusted. Otherwise, the average quality error is analyzed based on the sensitivity model to generate the baseline control trajectory.

6. A production system for high-resistivity epitaxial wafers on lightly boron-doped substrates, used to implement the method as described in any one of claims 1-5, characterized in that, The system includes: The detection module constructs a layered state observer based on historical process data, collects the ion concentration of exhaust gas at the exhaust gas outlet at preset intervals, and calculates the exhaust gas residue index based on the ion concentration. The prediction module updates the model parameters of the layered state observer if multiple consecutive exhaust gas residue indices show abnormalities; otherwise, it inputs online monitoring data into the layered state observer to obtain the real-time distribution of resistivity and the corresponding uncertainty distribution during wafer growth. This includes: dividing the wafer into multiple grid points; the layered state observer includes a first model and a second model; the first model includes multiple low-dimensional Gaussian regression models; the first model groups the online monitoring data to obtain multiple sets of independent data; the independent data is input into the corresponding low-dimensional Gaussian regression model to obtain first data; the first data includes the first predicted value and first confidence level of the first model for various resistivities at the grid points; the second model includes a nonlinear model; the second model outputs second data based on the first data; the second data includes the second predicted value and second confidence level of the resistivity at the grid points; and the real-time distribution and uncertainty distribution are obtained by combining the second data from all the grid points. The control module sets a desired state evolution trajectory, which includes the ideal distribution matrix of resistivity at each preset time. It calculates an error distribution based on the real-time distribution and the ideal distribution matrix, and processes the error distribution and the uncertainty distribution using a fuzzy inference model to obtain adjustment instructions. This includes: calculating parameter statistical features based on the error distribution and the uncertainty distribution; setting a fuzzy set for each parameter statistical feature; the fuzzy set including multiple state rules, each state rule corresponding to a Gaussian membership function; dynamically adjusting the width parameter in the Gaussian membership function based on the corresponding parameter statistical features; and calculating the membership degree between the input feature and each state rule based on the Gaussian membership function. The control rules for setting production parameters are as follows: each control rule corresponds to at least one state rule and a membership degree; each control rule has an adjustment weight, which is associated with the membership degree of the state rule; the control rule to be triggered is determined based on the state rule and the membership degree; the adjustment amount of the control rule is weighted and summed based on the adjustment weight to obtain the final adjustment amount; and the adjustment instruction is obtained by combining the final adjustment amounts of each production parameter. Adjust the production process parameters based on the adjustment instructions; The optimization module obtains the average quality error of the product after the current production batch ends, generates a baseline control trajectory based on the average quality error, generates the desired state evolution trajectory for the next batch based on the baseline control trajectory, controls the production of the next batch of wafers based on the baseline control trajectory, and adjusts the production process parameters based on the corresponding generated desired state evolution trajectory.

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