CN111895923B - Method for fitting and measuring thickness of thin film - Google Patents

Method for fitting and measuring thickness of thin film Download PDF

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CN111895923B
CN111895923B CN202010645136.3A CN202010645136A CN111895923B CN 111895923 B CN111895923 B CN 111895923B CN 202010645136 A CN202010645136 A CN 202010645136A CN 111895923 B CN111895923 B CN 111895923B
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CN111895923A (en
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李相相
魏慎金
李晶
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Shanghai Fuwa Technology Co.,Ltd.
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Shanghai Chenhuiyuan Technology Development Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
    • G01B11/0616—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
    • G01B11/0641—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating with measurement of polarization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/049—Temporal neural networks, e.g. delay elements, oscillating neurons or pulsed inputs
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Abstract

The invention provides a fitting testThe method for measuring the thickness of the film comprises the steps of adopting a method of combining an elliptical polarization measurement technology and a neural network, and fitting and measuring the thickness of the film through elliptical polarized light parameters of the film and a neural network model; the neural network is an LSTM recurrent neural network. The method for measuring the thickness of the film by fitting is suitable for Al2O3The thickness of the film was measured by fitting. The invention has the advantages that: 1) the result can be obtained more quickly and accurately; 2) the number of required measurement parameters is less, namely the measurement is easier; 3) repeated mathematical iteration is not needed, so that the result is more stable; 4) the invention is very suitable for the field of large-scale optical detection.

Description

Method for fitting and measuring thickness of thin film
Technical Field
The invention relates to a method for measuring the thickness of a thin film in a fitting manner, in particular to a method for obtaining the thickness of a thin film material through elliptical polarization measurement and neural network fitting, and belongs to the technical field of elliptical polarization measurement and neural networks.
Background
An elliptical polarization spectrometer is a traditional non-contact optical measurement device, has high surface sensitivity when approaching a pseudo-brewster angle and non-destructive depth analysis capability, is proved to be a very reliable measurement tool, and can be used for accurately measuring the optical properties of a given sample by combining a specific physical model and proper data spectrum analysis; meanwhile, it has been shown that the harmonic oscillator approximation method employed in the fitting of the measurement data is very effective for simulating the dielectric function spectrum of a given substrate, and as a result, not only the geometry including the sample surface and subsurface layers, but also the doping concentration dependence of the dielectric function spectrum can be determined and analyzed; the ellipsometry technology can analyze the property of a thin film with the thickness smaller than the wavelength by analyzing the phase and amplitude change of the reflected polarized light, the thickness of the tested thin film is generally between tens of nanometers and hundreds of nanometers, and the surface information of a monoatomic layer thin film sample and a body sample can be measured; for the information received by the test, the ellipsometry mainly analyzes the complex refractive index or dielectric function tensor of the material to different wavelengths, and other basic physical property parameters are calculated on the basis of the complex refractive index or dielectric function tensor; the physical property parameters are closely related to the properties of the material such as form, crystallization state, chemical component components and the like, on the basis of the property analysis, the thickness of the film layer can be fitted through a fitting method, different physical models are selected for different materials, so that the data measured through experiments are fitted to the parameters of the models, and the fitting value of the thickness of the sample is obtained; generally, the thickness measurement can be accurate to the nanometer level.
The application of artificial neural networks to various scientific problems is rapidly increasing, and particularly the trend of combining with the traditional physical science field is more obvious; their popularity and utility stems from their ability to mathematically mimic biological neural networks, and thus perform tasks that are generally classified as intelligent behavior; neural networks have been applied to many different problems, including classification and pattern recognition; the several scenarios described above all apply the theory of neural networks and the various techniques involved in "training" and using them; in many previous studies, scholars reported many applications of neural networks, mostly curve fitting to simulated experimental data, avoiding the need for lengthy non-linear least squares fitting procedures.
Disclosure of Invention
The invention provides a method for measuring the thickness of a thin film in a fitting manner, and aims to quickly and accurately obtain the thickness result of the thin film.
The technical solution of the invention is as follows: a method for fitting and measuring the thickness of a film comprises the steps of adopting a method of combining an elliptical polarization measurement technology and a neural network, and fitting and measuring the thickness of the film through elliptical polarized light parameters of the film and a neural network model; the neural network is an LSTM recurrent neural network.
The invention has the advantages that:
1) the result can be obtained more quickly and accurately;
2) the number of required measurement parameters is less, namely the measurement is easier;
3) repeated mathematical iteration is not needed, so that the result is more stable;
4) the invention is very suitable for the field of large-scale optical detection.
Drawings
FIG. 1 is a schematic diagram of the mapping process using the LSTM recurrent neural network.
Fig. 2 is a schematic diagram of the structure of the LSTM layer.
Detailed Description
A method for fitting and measuring the thickness of a film comprises the steps of adopting a method of combining an elliptical polarization measurement technology and a neural network, and fitting and measuring the thickness of the film through elliptical polarized light parameters of the film and a neural network model; the neural network is an LSTM (Long Short-Term Memory networks) cyclic neural network.
The method for measuring the thickness of the film through the elliptical polarized light parameters of the film and the neural network model specifically comprises the following steps:
(1) generating optical parameters of films with different thicknesses by using optical film design software, and then training an LSTM cyclic neural network by using the optical parameters to generate an LSTM cyclic neural network model, wherein the optical parameters comprise the thickness of the films and elliptical polarized light parameters under different angles; the LSTM recurrent neural network model takes the elliptical polarized light parameters as input and outputs the corresponding film thickness;
(2) measuring by an elliptical polarization spectrometer to obtain elliptical polarization parameters of the film;
(3) and inputting the elliptical polarization parameters of the film measured by the elliptical polarization spectrometer into the LSTM recurrent neural network model to obtain the thickness of the film.
The method for generating the LSTM recurrent neural network model by training the LSTM recurrent neural network with the optical parameters comprises the following specific steps:
(1) constructing LSTM recurrent neural network by using Keras deep learning framework and setting parameters of LSTM recurrent neural network
Figure 100002_DEST_PATH_IMAGE002
Randomly initializing, wherein the constructed LSTM recurrent neural network comprises four layers, wherein the first three layers are LSTM layers, and the last layer is a full connection layer;
(2) using Psi parameters and Delta parameters of films with different thicknesses between 30nm and 200nm generated by Film Wizard optical Film design software as training sets to train parameters of an LSTM recurrent neural network;
(3) the LSTM recurrent neural network is trained in a way that Psi parameters and Delta parameters of a Film generated by Film Wizard optical Film design software are sent into the LSTM recurrent neural network, a network predicted thickness value h is obtained after network mapping of the LSTM recurrent neural network, and then a loss function L (h, h ') is calculated with the thickness h ' of the Film generated by the Film Wizard optical Film design software, wherein the loss function L is the mean square error loss of h and h ';
(4) iteratively calculating loss function L vs. LSTM recurrent neural network parameters
Figure 223397DEST_PATH_IMAGE002
And updating parameters of the LSTM recurrent neural network by Adam algorithm
Figure 785966DEST_PATH_IMAGE002
Thus, the training of the LSTM recurrent neural network is realized;
said parameter
Figure 100002_DEST_PATH_IMAGE003
Refers to all parameters of all layers of the whole LSTM recurrent neural network model
Figure 393533DEST_PATH_IMAGE002
Including both LSTM layers
Figure 100002_DEST_PATH_IMAGE005
、
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、
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Also comprising fully-connected layers
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And
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parameter of
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Is the set of all learnable parameters in the entire network structure.
The film is any one of a crystal film and a metal oxide film material, and is preferably Al2O3The film material is further preferably Al suitable for preparing a magnetron sputtering coating system2O3A film material.
The elliptical polarized light parameters comprise an amplitude reflectivity ratio and a phase difference; a beam of linearly polarized light with a known polarization state is incident on the surface of the sample to interact with the sample, the polarization state of the reflected light is changed into an elliptical polarization state, and the ratio of the reflectivity of p light and s light is measured, as shown in the following formula (3):
Figure 100002_DEST_PATH_IMAGE014
formula (3)
Wherein r ispAnd rsComplex reflectivities for p-light and s-light; Ψ represents the ratio of the amplitude reflectivities of the p light and the s light, and Δ represents the phase difference between the p light and the s light, and is called an ellipsometric parameter, where Ψ is Psi and Δ is Delta.
The method for measuring the thickness of the film is suitable for Al2O3The thickness of the film is subjected to fitting measurement, specifically, Al is prepared by using a magnetron sputtering coating system2O3Film samples and Al measurement by ellipsometry2O3Elliptical polarized light parameters of the film sample; then using the trained LSTM recurrent neural network model and the prepared Al2O3Fitting and measuring Al by using elliptical polarized light parameters of film sample2O3The thickness of the film.
The elliptic polarization spectrometer is an advanced optical film nondestructive measuring instrument, and the obtained original measurement data must be subjected to spectrum analysis by a classical data fitting method (such as a Lorentz vibrator model, a Cauchy model and the like) to obtain the final optical parameters and thickness of a sample; as an advanced data fitting mode, the invention firstly proposes that an LSTM recurrent neural network model is used for fitting measurement in ellipsometric data fitting to replace a classical data fitting mode, and compared with a conventional fitting method, the method is higher in speed and accuracy.
Each of the LSTM layers comprises a plurality of cellular structures, the different cellular structures have transverse connections therebetween, and the mapping relationship of each LSTM layer is expressed by the following formula (1):
Figure 100002_DEST_PATH_IMAGE016
formula (1)
Wherein:
Figure 100002_DEST_PATH_IMAGE018
；
Figure 100002_DEST_PATH_IMAGE020
is a time sequence, or step;
Figure 100002_DEST_PATH_IMAGE022
is the state of the current step (or call timing) and therefore
Figure 100002_DEST_PATH_IMAGE024
Is the state of the last time sequence;
Figure DEST_PATH_IMAGE025
namely, the weighted summation of the current time sequence input and the last time sequence output can be understood as the information of the current input;
Figure DEST_PATH_IMAGE027
is as followsThe input of the previous time sequence is input,
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the output of the last time sequence;
Figure 100002_DEST_PATH_IMAGE030
is composed of
Figure 100002_DEST_PATH_IMAGE032
The weight of (a) is determined,
Figure DEST_PATH_IMAGE033
is composed of
Figure DEST_PATH_IMAGE035
The weight of (a) is determined,
Figure 100002_DEST_PATH_IMAGE036
is composed of
Figure 100002_DEST_PATH_IMAGE038
The weight of (a) is determined,
Figure 6317DEST_PATH_IMAGE010
、
Figure 790602DEST_PATH_IMAGE009
、
Figure 873964DEST_PATH_IMAGE036
shared among all timings;
Figure 100002_DEST_PATH_IMAGE040
and
Figure 100002_DEST_PATH_IMAGE042
are all outputs of the current time sequence;
Figure 100002_DEST_PATH_IMAGE044
function is as
Figure 100002_DEST_PATH_IMAGE046
A function, or hyperbolic tangent function;
Figure 100002_DEST_PATH_IMAGE048
in order to input the information into the gate,
Figure 100002_DEST_PATH_IMAGE050
in order to forget to leave the door,
Figure 100002_DEST_PATH_IMAGE052
is an output gate;
wherein sigmoid is an activation function, called sigmoid function.
In practical use, the size of the LSTM layer coefficient matrix is selected according to the size of the LSTM input and output of each layer, the input and output are vectors with different dimensions, and a matrix with a proper size needs to be selected to realize mapping from the input vector to the output vector.
In the LSTM layers, the first two LSTM layers return a sequence with the same input length; the returning of a sequence with the same length as the input is referred to as the output sequence
Figure DEST_PATH_IMAGE054
To
Figure DEST_PATH_IMAGE056
Number of and input sequence
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To
Figure DEST_PATH_IMAGE060
The number of the output terminals is the same, and the whole is selected and output in actual use
Figure 100002_DEST_PATH_IMAGE061
Sequence or only the last sequence output i.e
Figure DEST_PATH_IMAGE062
The neural network is a directed acyclic computational graph, each layer being a function that maps an input vector to an output vector.
The full connection layer is a matrix, and specifically represents the following formula (2):
Figure DEST_PATH_IMAGE064
formula (2)
Wherein the content of the first and second substances,
Figure 149176DEST_PATH_IMAGE032
sequence of
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Is the input sequence of the fully-connected layer,
Figure 100002_DEST_PATH_IMAGE068
sequence of
Figure DEST_PATH_IMAGE070
Is the output sequence; by using
Figure 158762DEST_PATH_IMAGE010
Refers to the entire matrix:
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by using
Figure 758239DEST_PATH_IMAGE012
Referring to the entire bias vector:
Figure DEST_PATH_IMAGE074
，
Figure 176451DEST_PATH_IMAGE010
is the coefficient of the number of the first and second,
Figure DEST_PATH_IMAGE075
is an offset;
Figure 13826DEST_PATH_IMAGE005
、
Figure 265816DEST_PATH_IMAGE012
that is, parameters of the neural network, a proper size needs to be selected according to the dimension of the input vector and the dimension of the output vector, so that the input vector is mapped into the output vector.
The whole neural network is a vector mapper, and the input vector is mapped continuously through different layers to obtain the desired output, as shown in fig. 1, it can be seen that the size of the output of each layer is the same as the size of the input of the next layer.
Al is carried out by using method for measuring film thickness through fitting2O3The specific steps of the film material thickness measurement are as follows:
1) firstly, high-purity Al is taken as a target material, a reactive sputtering method is adopted, namely O is introduced during sputtering2Gas as reaction gas for producing Al2O3A film; different samples are prepared by changing the sputtering time through fixing the sputtering power, and then the samples are annealed in the nitrogen atmosphere to obtain Al with different thicknesses2O3A film; then, Al with different thicknesses is measured by using an elliptical polarization spectrometer2O3Elliptical polarization parameters of the film;
2) generation of Al of varying thickness using optical film design software2O3Optical parameters of the film comprise film thickness and elliptical polarized light parameters under different angles, and then the optical parameters are used for training to generate an LSTM circulating neural network model, wherein the LSTM circulating neural network model takes the elliptical polarized light parameters as input and outputs the corresponding film thickness;
3) using Al of different thicknesses measured in step 1)2O3Fitting the elliptical polarized light parameters of the film and the LSTM recurrent neural network model obtained by training in the step 2) to obtain corresponding Al2O3The thickness of the film.
The optical parameters used for training the LSTM recurrent neural network to generate the LSTM recurrent neural network model can use measured data; when the measured data is limited and insufficient, the data generated by Film Wizard optical Film design software can be further used for providing data for training an LSTM recurrent neural network; the generated data of the Film Wizard optical Film design software may not be used when the measured data is sufficient.
The Film Wizard optical Film design software comprises a plurality of physical models, such as Lorentz oscillator models, Cauchy models and the like, wherein one physical model can be understood as a constraint, so that the generated data can meet the constraint, and the data of the elliptical polarized light parameters and the Film thickness generated by the invention can meet the constraint of the Lorentz oscillator models.
Al of different thicknesses in the step 1)2O3The film is preferably 3-4 Al films of different thickness2O3A film.
In the step 3), an LSTM recurrent neural network model is used and an elliptical polarized light parameter is used as an input to fit Al2O3The thickness of the film material.
The method is simple and effective, does not need to select a specific physical model, uses a more universal LSTM (least squares) cyclic neural network model, and is favorable for realizing the aim of carrying out Al alignment through the elliptical polarized light parameters2O3The thickness of the film is fitted quickly, accurately and stably.
Example 1
Fitting measurement Al2O3The method for the thickness of the film material comprises the following specific steps:
Al2O3the film is prepared on a Si (100) substrate by using a Sunicoat 549L magnetron sputtering coating machine, the target material is an Al target with the purity of 99.99 percent, and the aluminum oxide (Al) is prepared by using a reactive sputtering method2O3) The film reactive sputtering is based on direct current magnetron sputtering, high-purity metal aluminum (Al) is taken as a target material, and high-purity oxygen (O) with the purity of 99.99 percent is introduced2) As a reaction gas, the metal aluminum can generate a chemical reaction with oxygen in the sputtering deposition process to generate an alumina film with higher purity;
in the process of sputtering preparation, the sputtering power is set to be 60W, and the work is switched onArgon gas was supplied at a rate of 100sccm, oxygen partial pressure was controlled at about 2%, and working pressure was set at 3mTor (1Torr =1.33 × 10)2Pa), the distance between the Al target and the substrate is 10mm, the rotating speed of the substrate is 15r/s, the temperature in the cavity is kept consistent with the ambient temperature in the preparation process, the sputtering power is fixed during sputtering, and Al with consistent preparation conditions and different thicknesses can be obtained by using different sputtering time2O3The film is prepared under two sputtering times in actual experiments, wherein the sputtering times are respectively 100s and 200 s; one sample at 100s sputtering time was designated as A; three samples were taken at 200s sputtering time and designated B1, B2, and B3, respectively;
after preparing a sample, characterizing the thickness of the sample by using elliptical polarized light parameters and combining a Lorentz oscillator model; measuring Psi (amplitude reflectance ratio) and Delta (phase difference) parameters of the film sample at three different incident angles, namely 65 °, 70 ° and 75 °; the measuring range is 300nm-800nm, sampling points are taken every 10nm, and 51 sampling points are counted;
selecting five different initial thickness values, using Film Wizard optical Film design software, specifically selecting a Lorentz oscillator model, then fitting the thickness iteratively, wherein the five different initial thickness values are respectively 50nm, 75nm, 100nm, 125nm and 150nm, and then averaging the optimized results of the five different initial thickness values to serve as the final fitting result, wherein the fitting result is shown in Table 1; the initial thickness value is selected by estimating the approximate thickness, and then continuously and iteratively correcting and optimizing to make the thickness closer to the real thickness, wherein five initial thickness values are selected to reduce the influence of accidental errors.
The method comprises the steps of constructing an LSTM recurrent neural network by using a Keras deep learning framework, wherein the network has four layers, the dimensionalities of an input tensor are (6, 6) and are Psi (amplitude reflectivity ratio) and Delta (phase difference) values under 3 angles (65 degrees, 70 degrees, 75 degrees) and 6 wavelengths (300nm, 400nm, 500nm, 600nm, 700nm and 800nm), then, the final output is obtained through three LSTM layers and a full connecting layer, each layer uses a rectification linear unit (ReLU) as an activation function, and in the three LSTM layers, the first two layers still return to one and output to the input LSTMEntering a sequence with the same length as the input of the next LSTM layer, returning a single tensor by the last LSTM layer only in the last unit, mapping the tensor by the full-connection layer to obtain the final output thickness, and drawing up to make a model capable of predicting Al within the thickness range of 30nm-200nm2O3And (3) randomly generating a large number of different thickness values in the range of 30-200 nm by using the Film Wizard optical Film design software, generating corresponding Psi and Delta parameter values by using the Film Wizard optical Film design software to construct a data set, and then training the LSTM recurrent neural network by using the constructed data set to obtain a final LSTM recurrent neural network model.
Applying the well-trained LSTM recurrent neural network model to Al2O3Film samples A, B1, B2, and B3 were fitted to their thickness using Psi and Delta parameters, and the results are shown in Table 2.
From the fitting results, it can be seen that the LSTM neural network is used for Al versus the thickness fitted by the Film Wizard optical Film design software in the classical fitting method2O3The fitting of the film thickness is accurate, and the method has the following advantages:
1. the result can be directly output according to the trained model after only one training without repeated iterative optimization process, so that the calculation is simpler and more stable;
2. the required data volume is less, and a more accurate result can be obtained only by using 1/10 of the parameters required by the Lorentz oscillator model, so that the measurement workload is reduced.
TABLE 1 thickness optimization results for different samples at different initial values of thickness
Figure DEST_PATH_IMAGE077
TABLE 2 comparison of the mean thickness values corresponding to each sample obtained using classical fitting methods for different samples with the thickness values obtained by LSTM neural network fitting
Sample (I) A B1 B2 B3
Thickness (nm) by classical fitting method 37.26 72.77 66.33 66.76
Neural network prediction thickness (nm) 39.20 73.55 68.11 66.20
From table 2, it can be seen that the thickness values obtained by fitting the LSTM neural network only need to be fitted once, and the results consistent with the thickness mean obtained by using the classical fitting method can be obtained; if a classical fitting method is adopted, an initial value of the thickness must be defined firstly, and as shown in table 1, the final fitting values of the thickness of the same sample are different by adopting the classical fitting method due to the difference of the initial values, so that in order to reduce accidental errors, more initial values must be defined by adopting the classical fitting method, and then the optimization results obtained by corresponding to each initial value are averaged, so that the fitting and measuring process of the thickness of the whole film is relatively complicated; according to the technical scheme, after the LSTM recurrent neural network is trained, stable thickness values can be obtained by once fitting for different film samples, and the whole fitting test process is rapid and stable; the fitting by the classical fitting method has a problem that the optimization process from defining an initial value to obtaining a final value needs repeated iteration, and the fitting can be completed at one time by adopting an LSTM neural network.
In this embodiment, different groups of Al are studied by an ellipsometric technique in combination with a neural network method2O3The film is subjected to thickness fitting, and the analysis of the principle of the method and the fitting result shows that compared with the classical fitting method and the fitting method of a corresponding physical model, the method has the advantages of rapidness, accuracy, stability and the like, so that the method is very suitable for the field of large-scale optical detection.

Claims (8)

1. A method for fitting and measuring the thickness of a film is characterized in that the method comprises the steps of adopting a method of combining an elliptical polarization measurement technology and a neural network, and fitting and measuring the thickness of the film through elliptical polarized light parameters of the film and a neural network model; the neural network is an LSTM recurrent neural network;
the method for fitting and measuring the thickness of the thin film through the elliptical polarized light parameters of the thin film and the neural network model specifically comprises the following steps:
(1) generating optical parameters of films with different thicknesses by using optical film design software, and then training an LSTM cyclic neural network by using the optical parameters to generate an LSTM cyclic neural network model, wherein the optical parameters comprise the thickness of the films and elliptical polarized light parameters under different angles; the LSTM recurrent neural network model takes the elliptical polarized light parameters as input and outputs the corresponding film thickness;
(2) measuring by an elliptical polarization spectrometer to obtain elliptical polarization parameters of the film;
(3) inputting the elliptical polarization parameters of the film measured by an elliptical polarization spectrometer into an LSTM recurrent neural network model to obtain the thickness of the film;
the method for generating the LSTM recurrent neural network model by training the LSTM recurrent neural network with the optical parameters comprises the following specific steps:
(1) constructing LSTM recurrent neural network by using Keras deep learning framework and setting parameters of LSTM recurrent neural network
Figure DEST_PATH_IMAGE002
Randomly initializing, wherein the constructed LSTM recurrent neural network comprises four layers, wherein the first three layers are LSTM layers, and the last layer is a full connection layer;
(2) using Psi parameters and Delta parameters of films with different thicknesses between 30nm and 200nm generated by Film Wizard optical Film design software as training sets to train parameters of an LSTM recurrent neural network;
(3) the LSTM recurrent neural network is trained in a way that Psi parameters and Delta parameters of a Film generated by Film Wizard optical Film design software are sent into the LSTM recurrent neural network, the predicted thickness value h of the neural network is obtained after network mapping of the LSTM recurrent neural network, and then a loss function L (h, h ') is calculated with the thickness h ' of the Film generated by the Film Wizard optical Film design software, wherein the loss function L is the mean square error loss of h and h ';
(4) iteratively calculating loss function L vs. LSTM recurrent neural network parameters
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And updating parameters of the LSTM recurrent neural network by Adam algorithm
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Thus, the training of the LSTM recurrent neural network is realized;
said parameter
Figure DEST_PATH_IMAGE003
All parameters of all layers of the whole LSTM recurrent neural network model are represented;
the Psi is the amplitude reflectivity ratio of the p light and the s light, and the Delta is the phase difference of the p light and the s light.
2. The method of claim 1, wherein the thin film is any one of a crystalline thin film and a metal oxide thin film.
3. The method of claim 1, wherein said elliptically polarized parameters include amplitude reflectance ratio and phase difference.
4. The method of claim 1, wherein each of the LSTM layers comprises a plurality of cell structures, different cell structures having transverse connections therebetween, and the mapping of each LSTM layer is represented by the following equation (1):
Figure DEST_PATH_IMAGE005
formula (1)
Wherein:
Figure DEST_PATH_IMAGE007
；
Figure DEST_PATH_IMAGE009
is a time sequence;
Figure DEST_PATH_IMAGE011
is the state of the current time sequence, therefore
Figure DEST_PATH_IMAGE013
Is the state of the last time sequence;
Figure DEST_PATH_IMAGE014
that is, the current timing input and the last timeWeighted summation of the sequence outputs, understood as the information of the current input;
Figure DEST_PATH_IMAGE016
as an input to the current timing sequence,
Figure DEST_PATH_IMAGE018
the output of the last time sequence;
Figure DEST_PATH_IMAGE020
is composed of
Figure DEST_PATH_IMAGE022
The weight of (a) is determined,
Figure DEST_PATH_IMAGE024
is composed of
Figure DEST_PATH_IMAGE026
The weight of (a) is determined,
Figure DEST_PATH_IMAGE028
is composed of
Figure DEST_PATH_IMAGE030
The weight of (a) is determined,
Figure DEST_PATH_IMAGE031
、
Figure DEST_PATH_IMAGE032
、
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shared among all timings;
Figure DEST_PATH_IMAGE034
and
Figure DEST_PATH_IMAGE036
are all outputs of the current time sequence;
the f function is
Figure DEST_PATH_IMAGE038
A function, or hyperbolic tangent function;
Figure DEST_PATH_IMAGE040
in order to input the information into the gate,
Figure DEST_PATH_IMAGE042
in order to forget to leave the door,
Figure DEST_PATH_IMAGE044
is an output gate;
wherein sigmoid is an activation function, called sigmoid function.
5. The method of claim 4, wherein the first two of said LSTM layers return a sequence of the same length as the input length; the returning of a sequence with the same length as the input is referred to as the output sequence
Figure DEST_PATH_IMAGE046
To
Figure DEST_PATH_IMAGE048
Number of and input sequence
Figure DEST_PATH_IMAGE050
To
Figure DEST_PATH_IMAGE052
The number of the output terminals is the same, and the whole is selected and output in actual use
Figure DEST_PATH_IMAGE053
Sequence or only the last sequence output i.e
Figure 817098DEST_PATH_IMAGE048
The neural network is a directed acyclic computational graph, each layer being a function that maps an input vector to an output vector.
6. The method of claim 1, wherein the fully-connected layer is a matrix, and is expressed by the following equation (2):
Figure DEST_PATH_IMAGE055
formula (2)
Wherein the content of the first and second substances,
Figure 269070DEST_PATH_IMAGE022
sequence of
Figure DEST_PATH_IMAGE057
Is the input sequence of the fully-connected layer,
Figure DEST_PATH_IMAGE059
sequence of
Figure DEST_PATH_IMAGE061
Is the output sequence; by using
Figure 706565DEST_PATH_IMAGE031
Refers to the entire matrix:
Figure DEST_PATH_IMAGE063
by using
Figure DEST_PATH_IMAGE065
Referring to the entire bias vector:
Figure DEST_PATH_IMAGE067
，
Figure 627510DEST_PATH_IMAGE031
is the coefficient of the number of the first and second,
Figure 323064DEST_PATH_IMAGE065
is an offset;
Figure 754177DEST_PATH_IMAGE020
、
Figure DEST_PATH_IMAGE068
the input vector needs to be mapped to the output vector by selecting a proper size according to the dimension of the input vector and the dimension of the output vector.
7. The method of claim 1, wherein the method is used to perform Al2O3The specific steps of the film material thickness measurement are as follows:
1) firstly, high-purity Al is taken as a target material, a reactive sputtering method is adopted, namely O is introduced during sputtering2Gas as reaction gas for producing Al2O3A film; different samples are prepared by changing the sputtering time through fixing the sputtering power, and then the samples are annealed in the nitrogen atmosphere to obtain Al with different thicknesses2O3A film; then, Al with different thicknesses is measured by using an elliptical polarization spectrometer2O3Elliptical polarization parameters of the film;
2) generation of Al of varying thickness using optical film design software2O3Optical parameters of the film comprise film thickness and elliptical polarized light parameters under different angles, and then the optical parameters are used for training to generate an LSTM circulating neural network model, wherein the LSTM circulating neural network model takes the elliptical polarized light parameters as input and outputs the corresponding film thickness;
3) using Al of different thicknesses measured in step 1)2O3Elliptical polarization parameter of film and step 2) Fitting the LSTM recurrent neural network model obtained by middle training to obtain corresponding Al2O3The thickness of the film.
8. The method of claim 7, wherein the Al thicknesses in step 1) are different2O3The film is 3-4 Al with different thicknesses2O3A film; in the step 3), an LSTM recurrent neural network model is used and an elliptical polarized light parameter is used as an input to fit Al2O3The thickness of the film material.
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