A production machine amplitude death prediction method applied to semiconductor manufacturing

Abstract

The application relates to a production machine amplitude death prediction method applied to semiconductor manufacturing, which comprises the following steps: S1, historical production machine data is acquired, data normalization processing is carried out, a training set and a test set are constructed; S2, an LSTM neural network model is established, and the LSTM neural network model is optimized based on a whale optimization algorithm; S3, training settings are defined, the optimized LSTM neural network is subjected to network training and testing by using the training set and the test set, and an amplitude death prediction model is obtained; and S4, actual data of a current production machine is acquired, input into the amplitude death prediction model, and corresponding amplitude death prediction results are output. Compared with the prior art, the application has the advantages of high accuracy, high application generalization, simple operation steps and the like, can quickly and accurately obtain amplitude death prediction results, is favorable for timely corresponding maintenance of the production machine, and thus improves a wafer production yield.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of criticality prediction of complex manufacturing systems, and in particular to a production machine amplitude death prediction method applied to semiconductor manufacturing. BACKGROUND

[0002] In daily life, there are many complex systems, which are non-trivial systems formed by a large number of individuals interacting with each other, and they often exhibit complex phenomena that are difficult for people to understand. In fact, complex phenomena often occur near critical states, i.e. states where significant changes in the system occur, and such state mutations can trigger innovation changes or functional collapse.

[0003] With the digitalization and intelligentization transformation of industry and the proposal of the "zero defect manufacturing" goal, various manufacturing industries have begun to pay attention to the improvement of product quality and quality control capability, rather than just the upgrading of production equipment. Among them, the semiconductor industry has always been a key industry for the development of high-tech, and the production machine in semiconductor production can be regarded as a complex system, and the process of producing wafers often exhibits complex phenomena.

[0004] In semiconductor manufacturing, product quality is the first priority of the production line, and only good quality can make high productivity meaningful. Low yield indicates the loss of production capacity and the waste of capital, so improving product yield is a key factor for high-tech industries to make a profit. In order to achieve this goal, all semi-finished and finished products must be fully inspected during production. However, if you want to achieve full inspection of products, you must set up a large number of measurement machines and spend a lot of production time.

[0005] In order to save costs, the industry currently adopts a sampling detection method for quality monitoring, but this method cannot achieve comprehensive quality control. In order to achieve the goal of comprehensive detection economically and practically, the application of virtual measurement technology is a feasible method. Virtual measurement technology can estimate the quality of products that have not been or cannot be actually measured using production machine parameters, and can change the offline and delayed quality sampling inspection to online and real-time quality full inspection. In this way, this technology can improve quality detection problems, improve product yield, and can also maintain process stability.

[0006] "Amplitude death" refers to a dynamic phenomenon in which "oscillatory systems" stop their own vibration behavior due to interaction with each other, so that the state quantity of the system no longer changes, and the vibration amplitude is zero. Amplitude death and strong vibration can cause serious harm to industrial and agricultural production, scientific research and daily life. Therefore, if a parameter of a semiconductor production machine exhibits "amplitude death" phenomenon, it may symbolize that the quality of the wafer being produced will have quality problems, i.e. defective products.

[0007] Therefore, predicting the critical state transition has important practical significance for engineering and manufacturing industry, and the current research mainly focuses on the evolution of system dynamic variables based on model-free prediction, such as model-free machine learning-based "reservoir algorithm", which can integrate parameter input channels by developing reservoir computing, and accurately predict the transition point by training in the normal operation state of the system chaotic attractor (i.e. before the critical transition), and has good network memory ability, approximation ability and simple training method, but still has limitations such as too complex optimization of hyperparameters, too long training process, too complicated operation, lack of prediction timeliness, etc., which leads to inaccurate and fast prediction results. SUMMARY

[0008] The purpose of the present application is to provide a method for predicting whether the production machine in semiconductor production will occur amplitude death for virtual metrology technology, which can quickly and accurately obtain the amplitude death prediction result, so as to timely repair the production machine and improve the yield of wafer production.

[0009] The purpose of the present application can be achieved by the following technical solutions:

[0010] A production machine amplitude death prediction method applied to semiconductor manufacturing, comprising the following steps:

[0011] S1, obtaining historical production machine data and performing data normalization processing to construct a training set and a test set;

[0012] S2, establishing an LSTM (Long short-term memory) neural network model, and optimizing the LSTM neural network model based on a whale optimization algorithm;

[0013] S3, defining training settings, and using the training set and the test set to train and test the optimized LSTM neural network to obtain an amplitude death prediction model;

[0014] S4, obtaining actual data of the current production machine, inputting the amplitude death prediction model, and outputting the corresponding amplitude death prediction result.

[0015] Further, the historical production machine data in step S1 includes positive sample data and negative sample data, and the positive sample data and the negative sample data each include device parameters, product parameters and key process parameters of multiple production machines.

[0016] Further, the specific operation of the data normalization processing in step S1 is to subtract the mean value and then divide by the standard value.

[0017] Further, the step S1 is specifically to divide the historical production machine data into a training set and a test set according to a set ratio.

[0018] Further, in the step S2, the whale optimization algorithm first sets the maximum number of iterations and the number of search agents, randomly selects the initial position of the search agent within the value range, sets the parameter related to iteration by evaluating the distance of each individual from the target value, and sets the nearest distance as the best search agent.

[0019] Further, the specific process of the whale optimization algorithm in the step S2 is as follows:

[0020] After each iteration, the position of each individual is updated to find the optimal solution, and the formula is as follows:

[0021]

[0022] wherein, and is a coefficient vector, is the position vector of the current best agent, is the position vector of the current individual;

[0023] When a new best agent appears in each iteration, the and

[0024]

[0025] wherein, decreases linearly from 2 to 0 during iteration, is a random vector between [0, 1];

[0026] The spiral motion path is represented as:

[0027]

[0028] wherein, represents the distance between the ith individual and the current best search agent, b is a constant, and l is a random number between [-1, 1], and a parameter p is selected to combine the simultaneous spiral rising behavior and search behavior:

[0029]

[0030] Further, the step S3 is specifically to combine the key process parameters in the training set and use a time series with a length of t=800 to train the optimized LSTM neural network.

[0031] Further, the step S3 specifically uses TrainNetWork to train the optimized LSTM neural network.

[0032] Further, in the step S3, the test set is used to predict the state at the next time point by using the PredictAndUpdateState function in MATLAB.

[0033] Further, in the step S3, the output result of the amplitude death prediction model is the change curve of the key process parameters, and when the numerical value change of the key process parameters increases to the preset corresponding critical point, it indicates that a sudden transition from chaotic oscillation to amplitude death will occur, i.e. amplitude death.

[0034] Compared with the prior art, the present application has the following beneficial effects:

[0035] 1. The present application proposes an amplitude death prediction method applied to a production machine in semiconductor manufacturing, which can train an amplitude death prediction model by establishing an LSTM neural network, optimizing the LSTM neural network by using a whale optimization algorithm, and combining a training set and a test set constructed from historical production machine data. By using the amplitude death prediction model, the predicted change curve of the corresponding key process parameters can be quickly and accurately obtained by inputting the equipment parameters and product parameters of the actual production machine, so as to obtain the amplitude death prediction result of the production machine.

[0036] 2. In the present application, the whale optimization algorithm is used to optimize the LSTM neural network when establishing the amplitude death prediction model, which can effectively increase the generalization ability and robustness of the LSTM neural network model, has the advantages of strong prediction timeliness and high accuracy compared with the traditional machine learning-based method, and thus ensures the reliability of the trained amplitude death prediction model.

[0037] 3. The whale optimization algorithm used in the present application starts from a group of random solutions, can effectively update the best solution obtained in each iteration, and will randomly move according to the positions of each other when preying on the group, which is equivalent to a kind of global search behavior, can prevent the algorithm from falling into a local optimal solution to a certain extent, has wide universality, has no limitation and requirement on the nature and size of the problem in practical application, and has simple structure, few parameters, strong search ability and easy realization, solves the drawbacks of the existing traditional amplitude death prediction, and is an important step for criticality prediction of complex systems. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 The present application is a method flowchart;

[0039] Figure 2 The present application is a schematic diagram of the application process of the embodiment;

[0040] Figure 3 This is a simulation diagram of the amplitude death of the coupled Lorentz-Cours system in the embodiment;

[0041] Figure 4 This is a flowchart of the training set generated in the example;

[0042] Figure 5(a) is a schematic diagram of the actual and predicted chaotic time series when ε = 0.34 in the embodiment;

[0043] Figure 5(b) is a schematic diagram of the actual and predicted chaotic time series when ε = 0.36 in the embodiment;

[0044] Figure 5(c) is a schematic diagram of the actual and predicted chaotic time series when ε = 0.5 in the embodiment;

[0045] Figure 6(a) is a schematic diagram of the training progress of using an LSTM neural network to predict the amplitude death of a coupled Lorentz system in the embodiment.

[0046] Figure 6(b) is a schematic diagram of the time series prediction of the coupled system in the embodiment;

[0047] Figure 7(a) is a schematic diagram of the training progress of the algorithm optimized by the whale optimization algorithm in the embodiment for predicting the amplitude death of the coupled system;

[0048] Figure 7(b) is a schematic diagram of the optimized time series prediction of the coupled system in the embodiment. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0050] like Figure 1 As shown, a method for predicting the amplitude death of production machines in semiconductor manufacturing includes the following steps:

[0051] S1. Obtain historical production machine data and perform data normalization processing to construct training set and test set. The historical production machine data includes positive sample data and negative sample data. Both positive sample data and negative sample data include equipment parameters, product parameters and key process parameters of multiple production machines.

[0052] S2. Establish an LSTM neural network model and optimize the LSTM neural network model based on the whale optimization algorithm;

[0053] S3. Define the training settings, and use the training set and test set to train and test the optimized LSTM neural network to obtain the amplitude death prediction model.

[0054] S4, acquiring actual data of the current production machine, i.e., equipment data and product data, inputting the amplitude death prediction model, and outputting corresponding amplitude death prediction results, i.e., predicting a key process parameter change curve of the current production machine, when the value of the key process parameter changes and increases to a preset corresponding critical point, it indicates that a sudden transition from chaotic oscillation to amplitude death will occur, i.e., it is predicted that amplitude death will occur.

[0055] To verify the effectiveness of the technical solution, the embodiment adopts a theoretical verification method, and experiments are performed by building a coupled RL system and combining the above technical solution, as shown in FIG. 1, the main contents include: Figure 2

[0056] I. Building a coupled RL system and obtaining simulation image data through the system;

[0057] II. Preprocessing the simulation image data and dividing it into a training set and a test set;

[0058] III. Establishing an LSTM neural network model and optimizing the model based on a whale optimization algorithm;

[0059] IV. Defining training settings, and using the training set and the test set to train and test the optimized LSTM neural network;

[0060] V. Amplitude death prediction of the coupled RL system based on the optimized LSTM neural network.

[0061] In step I, specifically:

[0062] First, the RL system before and after coupling is simulated by using MATLAB / simulink, and system bifurcation diagrams and attractor models are obtained;

[0063] Then, the coupled RL system is used as a loop parameter, and the image of the state of the coupled system changing with the coupling parameter is obtained through the MATLAB platform.

[0064] In step II, the simulation image data is used as a data set, and the data therein is normalized (subtracting the mean value and dividing by the standard value), and is divided into a training set and a test set according to a certain proportion. In this embodiment, for each selected coupling parameter in the simulation image data, a time series with a length of t=800 is used to train the network, and a training set.mat file required for training is generated.

[0065] ​In step three, the whale optimization algorithm first sets the maximum number of iterations and the number of search agents, randomly selects the initial position of the search agent in the value range, evaluates the size of the distance to the target value of each individual, sets the nearest distance as the best search agent, sets the iteration-related parameters, such as; update the position of each individual after each iteration, find the optimal solution, the formula is as follows:

[0066]

[0067] Wherein, and is the coefficient vector, is the position vector of the best agent at the current time, is the position vector of the current individual;

[0068] Each time a new best agent appears, update and

[0069]

[0070] Wherein, Linearly decreases from 2 to 0 during iteration, is a random vector between [0, 1];

[0071] The spiral motion path is represented as:

[0072]

[0073] Wherein, represents the distance between the ith individual and the current best search agent, b is a constant, l is a random number between [-1, 1], and a parameter p is selected to combine the two behaviors (i.e. spiral rise and search behavior) that occur simultaneously:

[0074]

[0075] In step four, the MATLAB code is generated in the deep network designer to obtain the real-time exchange file, and the layer group code is created to define the training settings.

[0076] The TrainNetWork is used to train the LSTM neural network.

[0077] In addition, the test set uses the PredictAndUpdateState function in MATLAB to predict the state at the next time point, and when the coupling parameter of the predicted output increases to the critical point, it indicates that a sudden transition from chaotic oscillation to amplitude death will occur, i.e. amplitude death.

[0078] Figure 3Figures shown are amplitude death simulation diagrams in the example of coupling R-L system, wherein the coupling system is described by the following six-dimensional system:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] wherein parameters a = b = 0.1, c = 18, μ = 10, r = 28, ε is the coupling strength, and initial conditions are randomly selected in the phase space region {(-10, 10), (-10, 10), (0, 1), (-20, 20), (-20, 20), (0, 50)}. Through MATLAB, simulation time t = 10 5 , integral time step dt = 0.01, taking the coupling strength as the cycle parameter, selecting the maximum value of a time sequence under different coupling parameters as the result of each cycle, and observing the change of the maximum value of the time sequence x1 with the change of ε, the following results are obtained Figure 3 It can be seen that when ε increases to a critical point ε c ≈0.426, a sudden transition from chaotic oscillation to amplitude death occurs. The transition appears quite abrupt because the system enters the basin of the amplitude death attractor as ε changes.

[0086] Figure 4 Figures shown are flowcharts for generating a training set, and then using the echo state network algorithm to predict amplitude death of the coupling system, including the following steps:

[0087] A1: Select three coupling parameters ε = 0.32, 0.33, 0.34 in the chaotic oscillation region to train the machine, randomly select initial conditions in the phase space region {(-10, 10), (-10, 10), (0, 1), (-20, 20), (-20, 20), (0, 50)}, and use a time sequence with a length of t = 800, which is equivalent to about 700 Lyapunov time, to train the machine to generate the data set required for training;

[0088] A2: Before predicting amplitude death at the coupling parameter to be predicted, generate a prediction set, and the program flow is consistent with that of generating the training set;

[0089] A3: Optimizing the hyperparameters required for training using the Bayesian optimization method <k>, s, p, a, b, p b , k p , and generate a random reservoir matrix W out , train and predict using the training set and the prediction set, and generate a random reservoir matrix according to the following formula and model:

[0090] v(t) = [v(t); (p-p b )k p ]

[0091]

[0092]

[0093] where p b and k p are two hyperparameters, W in is an input matrix, the elements of which are randomly selected from a uniform distribution in the interval [-s, s], W r is a weighted matrix, a e (0, 1] is the leakage rate, a hyperparameter used to control the speed of weight update of each node in the reservoir; r is the state of each reservoir node at time t; is the same as the odd row elements of r, and the even row elements are the square values of the corresponding even row elements of r; v(t) is the input data vector.

[0094] A4: Take e = 0.50 as an example to predict the amplitude death of the coupled system, and the prediction result is shown in Fig. 5(c). It is found that the amplitude of the coupled system no longer changes after a period of chaotic oscillation, i.e. the amplitude death phenomenon occurs. From the simulation diagram of the coupling coefficient, it can be seen that when e = 0.50, the system is in the amplitude death stage, so the correctness and quality of the training can be verified. Figure 3

[0095] As shown in Figs. 6(a) and 6(b), the amplitude death prediction is performed using LSTM neurons, including the following steps:

[0096] B1: The data points in the amplitude death simulation diagram of the coupled LOR system are generated into a.txt file as a data set, i.e. the data is imported. Figure 3 B2: Divide the data set, the first 70% part is the training set, and the last 30% part is the prediction set. In order to prevent data divergence and overfitting, data normalization is performed, i.e. subtract the mean and divide by the standard deviation.

[0097]

[0098] ​​B3: define the LSTM network architecture, train the LSTM network with TrainNetwork, and use the PredictAndUpdateState function, which takes the prediction result as the input of the next time function after each prediction of the network state, and thus obtains the prediction of the last 30% sequence as shown in Fig. 6(b).

[0099] Through the training progress, it is found that after 500 iterations, the maximum loss does not decrease to close to zero but maintains at about 0.4, and due to the dense and random oscillation of the time series in the chaotic oscillation state of the coupled system, the learning rate of the training process is also low.

[0100] As shown in Fig. 7(a) and Fig. 7(b), the amplitude death prediction result of the LSTM neuron after adopting the whale optimization algorithm, in recent years, the swarm intelligence optimization algorithm abstracted by imitating some hunting or other behaviors of animal groups has been greatly researched and applied, because the swarm intelligence optimization algorithm has wide universality, no limitation and requirement on the nature and size of the problem, and simple structure, few parameters, strong search ability and easy implementation, so the present application selects a whale optimization algorithm (WOA) which is a meta-heuristic algorithm inspired by nature and solves optimization problems by imitating biological or physical phenomena to optimize. The WOA algorithm starts from a set of random solutions, and in each iteration, it can effectively update the best solution obtained, and when hunting in the group, it will randomly move according to the positions of each other, at this time, it is equivalent to a kind of global search behavior, which can prevent the algorithm from falling into a local optimal solution to a certain extent.

[0101] The implementation process of the optimization algorithm can be briefly described as follows: first, set the maximum number of iterations and the number of search agents; second, randomly select the initial position of the search agent, but ensure that the value is within the range; then evaluate the distance of each individual to the target value, and set the nearest distance as the best search agent; next, set the parameters related to iteration, such as; finally, update the position of each individual after each iteration, find the optimal solution, the formula is as follows:

[0102]

[0103] wherein, and is a coefficient vector, is the position vector of the best agent at the current time, is the position vector of the current individual;

[0104] Each time a new best agent appears, the best agent is updated and

[0105]

[0106] where, In the iterative process, from 2 linearly to 0, is a random vector between [0, 1];

[0107] The spiral motion path is expressed as:

[0108]

[0109] where, The distance between the ith individual and the current best search agent, b is a constant, l is a random number between [-1, 1], and a parameter p is selected to combine the two behaviors:

[0110]

[0111] In the optimization of the LSTM time series prediction problem, the optimization process is also the process of finding the optimal prediction value.

[0112] C1: the horizontal and vertical coordinates of the coupling Rössler-Lorenz system amplitude death occurrence graph are derived as input and output data respectively, and then the input and output data are normalized;

[0113] C2: Next, relevant parameters are defined (evolution times are set to 20, and population size is set to 5);

[0114] C3: the establishment, training and prediction of the LSTM network are consistent with the above, and the mean absolute error of the prediction is calculated. The training progress chart and the prediction of the amplitude death of the coupling Rössler-Lorenz system are shown in Figures 7(a) and 7(b).

[0115] According to the training progress chart of the LSTM network, it can be seen that the loss decreases to close to zero. It is found that the prediction results of the previous chaotic oscillation region are more consistent with the actual situation, and the prediction of the amplitude death occurrence region is better. The sudden occurrence of the amplitude death is better predicted. Since the focus of the application is the amplitude death prediction of the coupling Rössler-Lorenz system, the prediction of the chaotic oscillation region is not strictly required.

[0116] From the above experimental results of the algorithm before and after optimization for the coupled Routh-Lorenz system, it can be seen that the LSTM network optimized by the whale optimization algorithm can make up for the shortcomings of the LSTM network before optimization that cannot prove the prediction ability, and effectively improve the training learning rate, reduce the loss in the training process and the final mean absolute error, and accurately predict the change of the coupled system state with the coupling parameter; compared with the reserve pool algorithm, the prediction idea is different, effectively simplifies the operation steps, and the predicted time and amplitude size of amplitude death occurrence are closer to the actual. Therefore, it can be effectively applied to various processes of semiconductor manufacturing (chemical mechanical polishing, etching) as a prediction algorithm of virtual metrology technology, using the equipment and product parameters (polishing head speed, wafer rotation speed, wafer edge pressure, slurry flow rate, etc.) of various production machines to predict the trend of key process parameters (different according to different processes), if amplitude death occurs, further detection needs to be arranged for the wafers produced by the machine to prevent the production of defective products.

[0117] The preferred embodiments of the present application are described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and changes without creative work based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the prior art according to the concept of the present application shall be within the protection scope defined by the claims.< / k>

Claims

1. A method for predicting amplitude death of a production tool applied to semiconductor manufacturing, characterized by, The method comprises the following steps: S1, obtaining historical production machine data and performing data normalization processing to construct a training set and a test set; the historical production machine data comprises positive sample data and negative sample data, and the positive sample data and the negative sample data each comprise device parameters, product parameters and key process parameters of multiple production machines; S2, establishing an LSTM neural network model and optimizing the LSTM neural network model based on a whale optimization algorithm; S3, defining training settings, and performing network training and testing on the optimized LSTM neural network using the training set and the test set to obtain an amplitude death prediction model; S4, obtaining actual data of a current production machine, inputting the actual data into the amplitude death prediction model, and outputting corresponding amplitude death prediction results; In step S2, the whale optimization algorithm first sets a maximum number of iterations and a number of search agents, randomly selects initial positions of the search agents within a value range, sets a best search agent by evaluating distances of each individual from a target value, and sets parameters related to iterations; The specific process of the whale optimization algorithm in step S2 is as follows: After each iteration, the position of each individual is updated to find an optimal solution, and the formula is as follows: wherein, and is a coefficient vector, is a position vector of the best agent at the current time, is a position vector in which the current individual is located; The best agent is updated each time a new best agent appears , and : wherein, decreases from 2 to 0 in an iterative process, for a random vector between 0 and 1. The spiral motion path is represented as follows: wherein, denotes the distance between the i th individual and the current best search agent, b is a constant, l is a random number between the interval and a parameter p combines the simultaneous spiraling-up behavior and search behavior: 。 2. The method for predicting the amplitude death of a production machine in semiconductor manufacturing according to claim 1, characterized in that, The specific operation of the data normalization processing in step S1 is to subtract a mean value and divide by a standard value.

3. The method of claim 1, wherein the method is applied to a semiconductor manufacturing tool amplitude death prediction.

3. The method of claim 1, wherein the method is applied to a semiconductor manufacturing tool amplitude death prediction. Step S1 specifically divides the historical production machine data into the training set and the test set according to a set proportion.

4. The method for predicting the amplitude death of a production machine in semiconductor manufacturing according to claim 1, characterized in that, The step S3 is specifically to train the optimized LSTM neural network using the time series of length of the key process parameters in the training set.

5. The method for predicting the amplitude death of a production machine in semiconductor manufacturing according to claim 4, characterized in that, Step S3 specifically uses TrainNetWork to train the optimized LSTM neural network.

6. The method of claim 5, wherein the method is applied to a semiconductor manufacturing process. 5 In step S3, the test set uses a PredictAndUpdateState function in MATLAB to predict a state at a next time point.

7. The method of claim 4, wherein the method is applied to a semiconductor manufacturing process.

7. The method of claim 4, wherein the method is applied to a semiconductor manufacturing process. The output result of the amplitude death prediction model in step S3 is a change curve of the key process parameters, and when a value change of the key process parameters increases to a preset corresponding critical point, it is indicated that a sudden transition from chaotic oscillation to amplitude death will occur, that is, amplitude death.

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