CN111368434B - Prediction method of Czochralski method monocrystalline silicon solid-liquid interface based on ANN - Google Patents
Prediction method of Czochralski method monocrystalline silicon solid-liquid interface based on ANN Download PDFInfo
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- C—CHEMISTRY; METALLURGY
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- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B15/00—Single-crystal growth by pulling from a melt, e.g. Czochralski method
- C30B15/20—Controlling or regulating
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- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B29/00—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
- C30B29/02—Elements
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Abstract
The invention discloses a prediction method of a Czochralski method monocrystalline silicon solid-liquid interface based on ANN. Firstly, establishing a two-dimensional global heat transfer numerical model of a Czochralski single crystal silicon growth furnace by adopting a finite volume method; numerical simulation under each technological parameter is carried out, simulation data of monocrystalline silicon growth are collected and are arranged into a data set. Dividing the data set into a training set and a testing set, carrying out normalization processing, determining a machine learning algorithm, establishing a prediction model of the quality of the Czochralski monocrystalline silicon, and evaluating the reliability of the model. Then, the growth quality of the single crystal silicon is calculated by using the prediction model, and the prediction result is evaluated on the test set. And finally, predicting the optimal growth condition. The invention can rapidly find out the key factors influencing the quality of the single crystal silicon by the pulling method, and accurately predict the quality of the crystal under the key factors, thereby obtaining proper growth conditions, improving the research and development efficiency, saving the cost and growing large-size and high-quality single crystal silicon.
Description
Technical Field
The invention relates to a method for detecting the quality of a silicon single crystal product, in particular to a method for predicting a solid-liquid interface of a single crystal silicon by a Czochralski method based on ANN.
Background
Silicon single crystal is an indispensable basic material in industries such as integrated circuits and solar photovoltaic power generation, and the demand of the silicon single crystal is increasing with the rising of emerging technologies such as 5G, artificial intelligence and the like and the popularization of solar photovoltaic power generation. Large diameter, high quality, low cost are the trend of silicon single crystal in the future.
Czochralski (CZ) single crystal silicon growth technique is the dominant method for producing silicon single crystals. However, as the crystal size increases, the latent heat of crystallization released at the solid-liquid interface increases drastically, making it difficult to control the shape of the solid-liquid interface. In the growth process of the Czochralski method monocrystalline silicon, the macroscopic shape of the solid-liquid interface is closely related to the segregation of solute in the crystal, the formation of defects, the distribution of stress and the like. The current method for controlling the solid-liquid interface in the single crystal silicon by the pulling method is mainly divided into structural optimization and process optimization. Compared with process optimization, the structure optimization needs to modify the existing furnace body structure, and the cost is high. The method for researching the influence of the growth technological parameters of the Czochralski method on the quality of the silicon single crystal product mainly comprises an experimental method and numerical simulation. The experimental method relies on specific growth equipment, requires professional technicians and a large amount of experimental expenses, and has long experimental period. Numerical simulation is an important technology for reducing the cost of crystal growth experiments and shortening the period, and the macroscopic numerical simulation of heat transfer in the existing monocrystalline silicon growth process is relatively mature and derives a series of special commercial software such as: ansys Fluent, CGSim, FEMAG, CFX, etc. The conventional method for controlling the solid-liquid interface by adjusting the crystal rotation speed, the crucible rotation speed and the pulling speed according to a specific interval in a certain range in the current numerical simulation cannot ensure that the obtained process parameters are optimal, and the calculation is complex and the time consumption is long due to the nonlinear strong coupling characteristic of a monocrystalline silicon growth system. In addition, the CZ method monocrystalline silicon growth system has a plurality of growth process parameters, the growth process parameters and the crystal quality do not have an explicit relation, and the relation between the plurality of growth parameters and the crystal quality is difficult to obtain quickly by means of a traditional numerical simulation method.
Disclosure of Invention
Aiming at the defects existing in the existing Czochralski single crystal silicon growth technology, the invention aims to provide a prediction method of a Czochralski single crystal silicon solid-liquid interface based on an ANN (artificial neural network) by combining a single crystal silicon heat transfer model and a crystal growth experiment, a prediction system between a Czochralski single crystal silicon growth process parameter and the quality of a silicon single crystal product is built through the ANN, key factors influencing the Czochralski single crystal silicon quality can be rapidly found out, the crystal quality under the process parameter can be accurately predicted, thus obtaining proper growth conditions, reducing exploratory experiment times, improving research and development efficiency, saving research and development costs, and growing the Czochralski single crystal silicon with large size and high quality.
A prediction method of a Czochralski method monocrystalline silicon solid-liquid interface based on ANN comprises the following steps:
s1, solving mass, momentum and energy equations in a growth furnace by adopting a finite volume method, simulating a phase change process by adopting an interface tracking method, establishing a two-dimensional global axisymmetric heat transfer numerical model, carrying out numerical simulation under each technological parameter based on the heat transfer model, carrying out heat transfer numerical simulation, collecting simulation data of single crystal silicon growth, carrying out correlation analysis by adopting a regression analysis method, determining influence factors, and finishing into a data set;
s2, dividing the data set into a training set and a testing set, and respectively carrying out normalization processing on the training set and the testing set by adopting a mapmin max function;
s3, determining a machine learning algorithm, establishing a prediction model of the quality of Czochralski monocrystalline silicon on the whole training set, and evaluating the reliability of the prediction model on the training set;
s4, calculating the growth quality of the monocrystalline silicon on the test set by using a prediction model, and evaluating a prediction result;
s5, predicting the optimal growth condition.
Preferably, the influencing factor in step S1 is the crystal speed, crucible speed or pulling speed.
Preferably, the partitioning method of the data set in step S2 is a random partitioning or a 10-fold Cross Validation method (Cross Validation).
Preferably, the machine learning algorithm in step S3 is an artificial neural network, a support vector machine, a genetic algorithm, a simulated annealing algorithm or a decision tree.
Preferably, in the step S4, the growth quality of the monocrystalline silicon is solid-liquid interface, V/G, or oxygen impurity concentration; the evaluation index of the reliability of the prediction method is a correlation coefficient R or a mean square error MSE.
Further preferably, the calculation formula of the correlation coefficient R is as follows:
the mean square error MSE is calculated as follows:
wherein n is the number of samples, y i And (3) with
For the analog value and the predicted value of the ith sample,/->
For the average value of all sample analog values in the corresponding dataset, +.>
Is the average of all sample predictions in the corresponding dataset.
The beneficial effects are that:
compared with the prior art, the prediction method of the Czochralski method monocrystalline silicon solid-liquid interface based on ANN has the advantages that:
the ANN is adopted to replace time-consuming and labor-consuming heat transfer calculation or experimental process, and under the condition of given technological parameters such as crystal rotation speed, crucible rotation speed, lifting speed and the like, the solid-liquid interface shape can be rapidly and accurately predicted, and compared with the traditional heat transfer calculation, the prediction method shortens the calculation time by nearly three orders of magnitude while ensuring that the crystal quality prediction accuracy is up to more than 96%. The solid-liquid interface roughness was also reduced by about 30% in the examples. By adopting the method, the optimization direction can be rapidly determined, the research and development efficiency is improved, the research and development cost is saved, and the crystal quality is improved.
Drawings
FIG. 1 is a flow chart of a method for predicting a solid-liquid interface of a single crystal silicon by the Czochralski method based on ANN according to the present invention;
FIG. 2 is a graph showing the comparison of solid-liquid interface shape simulation values and experimental values obtained by a single crystal silicon heat transfer numerical model;
FIG. 3 is a graph showing simulated solid-liquid interface values and predicted solid-liquid interface values for a test set according to an embodiment of the present invention;
FIG. 4 is a diagram showing the solid-liquid interface shape of the single crystal silicon before and after optimization by the rapid lift-off method in the implementation of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
According to the flow chart of fig. 1, the method comprises the following steps:
step one: establishing a data set by Czochralski method monocrystalline silicon heat transfer numerical simulation
The global calculation grid of the single crystal silicon by adopting Gambit software is mainly composed of areas such as a quartz crucible, a graphite baffle, crystals, a melt, a guide cylinder, protective gas and the like. And solving mass, momentum and energy equations in the growth furnace by adopting a finite volume method, simulating a phase change process by adopting an interface tracking method, and establishing a global two-dimensional axisymmetric heat transfer numerical model. Wherein the diameter of the crystal ranges from 150 mm to 400mm, the diameter of the corresponding quartz crucible ranges from 350 mm to 1000mm, the height of the crystal ranges from 0mm to 4000mm, the pressure of the furnace chamber is 2000Pa, and the flow rate of argon is 30slpm. The crystal is set against rotation with the crucible. After convergence by iterative calculation (residual is 1×10) -6 ) And comparing the simulation value of the solid-liquid interface under the corresponding crystal height (50% of the grown crystal) with the experimental value, and verifying the accuracy of the heat transfer numerical model.
As shown in FIG. 2, the simulation value and the experimental value are well matched, which proves that the established Czochralski method monocrystalline silicon heat transfer model is effective. Then, a regression analysis method is adopted to carry out correlation analysis on the growth technological parameters and the crystal quality, and the technological parameters affecting the shape of the solid-liquid interface in the example are determined to be the crystal rotating speed and the crucible rotating speed. Setting the crystal rotation speed range to be 0-40rpm in the calculation model, setting the crucible rotation speed range to be 0-20rpm, and reversely rotating the crystal and the crucible, wherein other calculation conditions are kept unchanged. And obtaining solid-liquid interface shapes under various process conditions through carrying out simulation calculation on the heat transfer value of the single crystal silicon by a pulling method, and recording. And taking 50 groups of simulation values of crystal rotating speed, crucible rotating speed and the corresponding solid-liquid interface shape, and establishing a data set.
Step two: data processing
And carrying out normalization processing on the maximum value and the minimum value in the data set by adopting a mapmin max function so that all data are in a (0, 1) range, and dividing the whole data set into a training set and a testing set by using a random division method or a 10-fold cross validation method. In this example, the training set is 90% of the total data set and the test set is 10% of the total data set.
Step three: determining a machine learning algorithm, and establishing a prediction model based on ANN
The method comprises the steps of establishing a prediction model of the production quality of the single crystal silicon by the pulling method on a training set by using an ANN algorithm, and using a correlation coefficient R and a mean square error MSE as indexes for judging the prediction precision of the model. And based on the hidden layer number and the number of neurons in each layer of the neural network are determined by adopting 10-fold cross validation. Wherein the calculation formula of the correlation coefficient R is as follows:
the mean square error MSE is calculated as follows:
wherein n is the number of samples, y i And (3) with
For the analog value and the predicted value of the ith sample,/->
For the average value of all sample analog values in the corresponding dataset, +.>
Is the average of all sample predictions in the corresponding dataset.
The network structure of the ANN is 2-5-1, namely the input layer is two technological parameters of crystal rotating speed and crucible rotating speed. The number of hidden layers was determined to be 1 layer, with the number of neurons being 5. The output layer is a solid-liquid interface variable. Solid-liquid interface predicted on training set under network structureThe correlation coefficient between the deformation and the analog value is as high as 0.96, and the mean square error is 4.1×10 -4 It is illustrated that the model is feasible on a training set.
Step four: crystal quality prediction
In this example, the growth quality of the monocrystalline silicon is the deformation of the shape of the solid-liquid interface, the macroscopic shape of the solid-liquid interface can be measured by adopting the interface unevenness delta H, and the calculation formula is as follows:
ΔH＝H tri -H center
wherein H is tri Is three-phase point height, H center Is the interface center height.
The relative error delta can be used for measuring the quality of the predicted result, and the calculation formula is as follows:
wherein y is i And (3) with
The analog value and the predicted value of the i-th sample.
The prediction model is applied to the test set, and fig. 3 is a distribution diagram of the simulation value of the solid-liquid interface unevenness of the test set and the prediction value thereof in the specific embodiment of the invention, and the prediction value and the simulation value are better matched, the specific prediction precision is shown in table 1, the relative error of the interface unevenness is controlled within 4%, namely, the prediction accuracy is as high as 96%, which is enough to indicate that the model can well predict the solid-liquid interface shape of the single crystal by the pulling method, and can be used for predicting the crystal quality. Meanwhile, compared with the traditional heat transfer calculation, the method shortens the calculation time by nearly three orders of magnitude.
Table 1 prediction error obtained by applying a prediction model to a test set in the example
Step five: verification experiment
And screening out the preferred crystal rotating speed and the crucible rotating speed, wherein the preferred crystal rotating speed ranges from 12 rpm to 16rpm, and the crucible rotating speed ranges from 9 rpm to 13rpm, and preparing the monocrystalline silicon by using the parameters. The interface shape of the high-quality single crystal silicon obtained is shown in fig. 4 (b). The solid-liquid interface roughness was reduced by about 30% after optimization relative to the single crystal silicon interface shape at the original process parameters as shown in fig. 4 (a).
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (6)
1. The prediction method of the solid-liquid interface of the Czochralski method monocrystalline silicon based on the ANN is characterized by comprising the following steps of:
s1, for a pulling method monocrystalline silicon growth furnace, generating a pulling method monocrystalline silicon global calculation grid by adopting Gambit software, solving mass, momentum and energy equations in the growth furnace by adopting a finite volume method, simulating a phase change process by adopting an interface tracking method, and establishing a global two-dimensional axisymmetric heat transfer numerical model; based on the heat transfer model, carrying out numerical simulation under each technological parameter, collecting simulation data of monocrystalline silicon growth, carrying out correlation analysis by adopting a regression analysis method, determining influence factors, and finishing into a data set;
s2, dividing the data set into a training set and a testing set, and respectively carrying out normalization processing on the training set and the testing set by adopting a mapmin max function;
s3, determining a machine learning algorithm, establishing a prediction model of the quality of Czochralski monocrystalline silicon on the whole training set, and evaluating the reliability of the prediction model on the training set;
s4, calculating the growth quality of the monocrystalline silicon on the test set by using a prediction model, and evaluating a prediction result;
s5, predicting the optimal growth condition.
2. The method for predicting a solid-liquid interface of monocrystalline silicon by an ANN-based pulling method of claim 1, wherein the partitioning method of the dataset in step S2 is a random partitioning or 10-fold cross-validation method.
3. The method for predicting a solid-liquid interface of silicon single crystal by an ANN-based pulling method according to claim 1, wherein the influencing factor in step S1 is a crystal rotation speed, a crucible rotation speed or a pulling speed.
4. The method for predicting a solid-liquid interface of monocrystalline silicon by an ANN-based pulling method of claim 1, wherein the machine learning algorithm in step S3 is an artificial neural network, a support vector machine, a genetic algorithm, a simulated annealing algorithm or a decision tree.
5. The method for predicting a solid-liquid interface of monocrystalline silicon by an ANN-based pulling method of claim 1, wherein in step S4, the growth quality of the monocrystalline silicon is a solid-liquid interface, V/G, or oxygen impurity concentration; the index evaluating the predicted result is a correlation coefficient R or a mean square error MSE.
6. The method for predicting a solid-liquid interface of monocrystalline silicon by an ANN-based pulling method of claim 5, wherein the correlation coefficient R is calculated according to the following formula:
the mean square error MSE is calculated as follows:
wherein n is the number of samples, y i And (3) with
For the analog value and the predicted value of the ith sample,/->
For the average value of all sample analog values in the corresponding dataset, +.>
Is the average of the predicted values. />
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