A method for predicting initial values of thin film optical constants and thickness using artificial intelligence

Abstract

A method for predicting the initial values ​​of optical constants and thickness of thin films using artificial intelligence includes: establishing a dataset containing multiple data points, each data point including the transmittance spectrum of a substrate and the transmittance spectrum of a thin film passing through it; extracting feature value sets for each data point; dividing the data into training and testing subsets, and training and testing with multiple machine learning models; selecting the model with the highest accuracy based on a comparison of the predicted initial values ​​and target values; inputting the spectral features of the sample to be predicted into the prediction model to output the initial values ​​of optical constants and thickness; using these initial values ​​as input to the fitting program to help accelerate convergence and improve optimization efficiency.

Claims

1. A method for predicting initial values ​​of optical constants and thickness of thin films using artificial intelligence, comprising the following steps: establishing a dataset including a plurality of data points, each of the plurality of data points including a substrate transmittance spectrum of a substrate and a thin film transmittance spectrum through the substrate; selecting a set of feature values ​​for each of the plurality of data points, the set of feature values ​​including features selected from the thin film transmittance spectrum, features selected from the relationship between the thin film transmittance spectrum and the substrate transmittance spectrum, features selected from the first derivative of the thin film transmittance spectrum with respect to wavelength, and features selected from the second derivative of the thin film transmittance spectrum with respect to wavelength; dividing the dataset into a training subset and a test subset; inputting the set of feature values ​​of each of the training subset into each of a plurality of machine learning models to train the plurality of machine learning models respectively, thereby training a set of weight parameters for each of the plurality of machine learning models respectively; The feature value set of each of the test subsets is input into each of the plurality of machine learning models using the weight parameter set for testing, so that each of the plurality of machine learning models outputs a plurality of initial test values ​​corresponding to the test subset; the accuracy of one of the plurality of initial test values ​​output by each of the plurality of machine learning models is evaluated, and the prediction model with the highest accuracy is selected from the plurality of machine learning models; and the feature value set of the measured substrate transmittance spectrum of one of the substrates to be predicted and the thin film transmittance spectrum of the measured substrate to be predicted is input into the prediction model, so that the prediction model outputs an initial value, wherein the initial value is used to provide a fitting program for optimization to converge the initial value.

2. The method as described in claim 1, wherein the features selected from the transmittance spectrum of the thin film include a standard deviation of the transmittance spectrum of the thin film, a number of peaks in the transmittance spectrum of the thin film, a number of valleys, a positional difference between a first peak and a wavelength of 188 nm, a positional difference between a first valley and a wavelength of 188 nm, and an oscillation amplitude between the first peak and the first valley; wherein the features selected from the relationship between the transmittance spectrum of the thin film and the transmittance spectrum of the substrate include an average value of the difference between the peak transmittance of the thin film and the transmittance of the substrate, wherein the average value of the difference between the peak transmittance of the thin film and the transmittance of the substrate is obtained by summing up the difference between each peak in the transmittance spectrum of the thin film and the corresponding wavelength position of the transmittance spectrum of the substrate and then dividing by the number of peaks.

3. The method as claimed in claim 1, wherein the features selected from the first derivative of the thin film transmittance spectrum with respect to wavelength include a number of peaks, a number of valleys, a positional difference between a first peak and a wavelength of 188 nm, a positional difference between a first valley and a wavelength of 188 nm, an oscillation amplitude between the first peak and the first valley, and a standard deviation.

4. The method as claimed in claim 1, wherein the features selected from the second derivative of the thin film transmittance spectrum with respect to wavelength include a number of peaks, a number of valleys, a positional difference between a first peak and a wavelength of 188 nm, a positional difference between a first valley and a wavelength of 188 nm, an oscillation amplitude of the first peak and the first valley, and a standard deviation.

5. The method as described in any one of claims 1 to 4, wherein the accuracy is evaluated by calculating a root mean square error and a coefficient of determination based on the plurality of initial test values ​​obtained from the test subset input to the prediction model and the corresponding plurality of data values.

6. The method as described in any one of claims 1 to 4, wherein the plurality of machine learning models includes a multiple linear regression model, a multinomial regression model, a robust regression model, a decision tree model, a random forest model, and a limiting gradient boosting model.

7. The method as described in claim 6, wherein the prediction model is the limiting gradient boosting model.

8. The method as described in any one of claims 1 to 4, wherein the measured thin film transmittance spectrum is the transmittance spectrum of a thin film to be tested, the initial values ​​including a thickness of the thin film to be predicted, the refractive index constant of the thin film material, and the thin film material constants kamp and exp, and a thin film edge wavelength of the absorption band of the thin film material.

9. The method as described in claim 8, wherein the thin film to be tested is composed of aluminum oxide.

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