阅读说明：本技术 一种拟合测量薄膜厚度的方法 (Method for fitting and measuring thickness of thin film ) 是由 李相相 魏慎金 李晶 于 2020-07-07 设计创作，主要内容包括：本发明提出的是一种拟合测量薄膜厚度的方法,该方法包括采用了椭圆偏振测量技术和神经网络相结合的方法,通过薄膜的椭圆偏振光参数以及神经网络模型来拟合测量薄膜的厚度；所述神经网络为LSTM循环神经网络。所述拟合测量薄膜厚度的方法适用于对Al<Sub>2</Sub>O<Sub>3</Sub>薄膜的厚度进行拟合测量。本发明的优点：1)能够更加快速、准确地得到结果；2)所需测量参数数量更少,即更加容易测量；3)无需进行反复的数学迭代,因而结果更加稳定；4)本发明十分适用于大规模光学检测领域。(The invention provides a method for fitting and measuring the thickness of a film, which 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 Al 2 O 3 The 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.)

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.

2. The method of claim 1, wherein the step of fitting the thickness of the thin film by the ellipsometric parameters of the thin film and the neural network model comprises the steps of:

(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.

3. The method of claim 2, wherein the step of using the optical parameters to train the LSTM recurrent neural network to generate the model of the LSTM recurrent neural network comprises the steps of:

(1) constructing LSTM recurrent neural network by using Keras deep learning framework and setting parameters of LSTM recurrent neural networkRandomly 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

said parameterRefers to all parameters of all layers of the entire LSTM recurrent neural network model.

4. A method of fitting measurement of film thickness according to any of claims 1-3, wherein said film is any of a crystalline film, a metal oxide film.

5. The method of claim 1, wherein said elliptically polarized parameters include amplitude reflectance ratio and phase difference.

6. A method for fitting measurement of film thickness according to claim 3, wherein each LSTM layer comprises a plurality of cell structures, different cell structures have transverse connections therebetween, and the mapping relationship of each LSTM layer is expressed by the following formula (1):

formula (1)

Wherein:

is composed ofThe weight of (a) is determined,is composed of

the f function is

wherein sigmoid is an activation function, called sigmoid function.

7. The method of claim 6, wherein the first two of the three 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 inputGo out of sequenceTo

8. A method of fitting measurements of film thickness as claimed in claim 3 wherein said fully-connected layer is a matrix, and is expressed in more detail by the following equation (2):

Wherein the content of the first and second substances,

9. Fitting measurement Al₂O₃The method for the thickness of the thin film material is characterized by comprising the following specific steps of:

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 disks using optical film design softwareAl of the same thickness₂O₃Optical 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.

10. A fitted Al according to claim 9₂O₃Method for the thickness of thin film materials, characterized in that Al of different thickness in step 1) is added₂O₃The 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.

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

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 parametersAnd updating parameters of the LSTM recurrent neural network by Adam algorithm

Thus, the training of the LSTM recurrent neural network is realized;

said parameter

Refers to all parameters of all layers of the whole LSTM recurrent neural network model

Including both LSTM layers

、、Also comprising fully-connected layersAnd

parameter ofIs 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):

formula (3)

Wherein r is_pAnd r_sComplex 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 LSTM layer comprises a plurality of cell structures, the different cell structures have transverse connection, and the mapping relation of each LSTM layer is represented by the following formula (1):

formula (1)

Wherein:

；

is a time sequence, or step;

is the state of the current step (or call timing) and thereforeIs the state of the last time sequence;

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;

as an input to the current timing sequence,

the output of the last time sequence;

is composed ofThe weight of (a) is determined,

is composed ofThe weight of (a) is determined,

is composed of

The weight of (a) is determined,、

、shared among all timings;

andare all outputs of the current time sequence;

function is asA function, or hyperbolic tangent function;

in order to input the information into the gate,

in order to forget to leave the door,

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.

The first two LSTM layers of the three LSTM layers return a sequence with the same length as the input length; the returnThe sequence with the same length as the input sequence refers to the output sequenceTo

Number of and input sequenceTo

The number of the output terminals is the same, and the whole is selected and output in actual use

Sequence or only the last sequence output i.eThe 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):

formula (2)

Wherein the content of the first and second substances,the sequence is the input sequence of the fully-connected layer,the sequence is an output sequence; by usingRefers to the entire matrix:

by using

Referring to the entire bias vector:，

is the coefficient of the number of the first and second,

is an offset;

、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.

Fitting Al₂O₃The method for the thickness of the film material comprises the following specific steps:

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, including the filmThe method comprises the following steps of (1) training and generating an LSTM (laser scanning) circulating neural network model by using optical parameters under the conditions of thickness and elliptical polarized light parameters under different angles, wherein the LSTM circulating neural network model takes the elliptical polarized light parameters as input and outputs 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 FilmWizard optical film design software may not be used to generate data 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.