Film thickness prediction method and system based on sequence angle spectrum analysis

Abstract

The invention discloses a thin film thickness prediction method and system based on sequence angle spectrum analysis, and aims to solve the problem of insufficient measurement precision of complex multilayer films in a traditional method. The method comprises the following steps: acquiring optical reflectivity spectrums of a target film at a plurality of incident angles; arranging the spectrums into a sequence according to an angle sequence; inputting the sequence into a pre-trained long short-term memory (LSTM) network model; and the LSTM model updates the understanding of the film layer structure by utilizing internal cell state angle-by-angle accumulation, and finally outputs a film layer thickness prediction value. The system correspondingly comprises a data acquisition module, a sequence construction module and a prediction module. According to the method, the multi-angle optical response is constructed into the time series data, the deep physical correlation between the angles is captured by using the LSTM network, the limitation of a traditional ideal model is overcome, the precision, efficiency and robustness of predicting the thickness of the complex multi-layer thin film are remarkably improved, and an effective scheme is provided for industrial online detection.

Description

TECHNICAL FIELD

[0001] The present application relates to the fields of optical engineering, semiconductor manufacturing technology and measurement technology, in particular to an optical thin film measurement method based on deep learning. More specifically, it relates to a method and system for non-contact, high-precision intelligent prediction of the thickness of complex multi-layer optical thin films using deep learning technology. BACKGROUND

[0002] Thin film materials play a crucial role in cutting-edge technology fields such as semiconductor manufacturing, biomedical engineering, and optical coatings due to their unique optical, electrical, magnetic, thermal, and chemical properties. The thickness of thin films is a key physical parameter that determines the performance and functionality of devices, so accurate measurement is essential for product quality and technological innovation.

[0003] However, current traditional methods for measuring thin film thickness mainly include optical methods such as ellipsometry and reflectance spectroscopy. Although these methods can provide high measurement accuracy under certain conditions, they have limitations. These traditional optical methods are mostly based on ideal models of single-layer, uniform thin films. When faced with complex non-uniform, multi-layer thin films, due to the nonlinear coupling effects of optical responses, it is difficult to establish an accurate analytical model using traditional methods, resulting in inaccurate and unreliable measurement results, and their limitations are increasingly evident in practical applications.

[0004] In recent years, the development of deep learning technology has brought new ideas for the characterization of complex thin films. Among them, the Long Short-Term Memory (LSTM) network, as a special recurrent neural network, has attracted attention due to its excellent ability to handle and predict time-dependent problems in sequence data. However, in existing research on using machine learning for thin film spectral analysis, most methods treat spectral data collected at different incident angles as independent features or perform simple concatenation. This approach ignores the deep physical correlations and temporal evolution rules contained in the optical response (such as the movement and morphological changes of interference fringes) as the incident angle changes continuously, resulting in insufficient utilization of spectral information and ultimately limiting the model's ability to accurately characterize complex multi-layer film structures.

[0005] Therefore, there is an urgent need for a new method that can overcome the limitations of traditional ideal models and achieve fast and accurate thickness prediction to meet the urgent need for high-precision measurement of complex multi-layer film structures in modern industrial production. SUMMARY

[0006] The present application aims to solve the limitations of traditional optical measurement methods in measuring the thickness of complex multi-layer thin films, overcome the lack of precision and poor reliability caused by the reliance on ideal models, and provide a high-precision, high-efficiency intelligent prediction solution.

[0007] To achieve the above object, the present application provides a composite analysis model and method combining multi-angle optical characteristics and long short-term memory network (LSTM). The method first collects optical reflectivity spectrum data of a target multilayer film sample at multiple different incident angles (for example, 0°, 15°, 30°, 45°, 60°) through simulation or actual measurement. The multilayer film sample is preferably a dielectric film system comprising high refractive index layers and low refractive index layers stacked alternately. For example, the multilayer film can be a HLH three-layer structure, wherein the high refractive index layer (H) material can be Ta2O5, and the low refractive index layer (L) material can be SiO2.

[0008] The key is that the present application does not regard the spectrum data at different angles as independent samples, but arranges them in order of increasing (or decreasing) angle to form an angle sequence with inherent physical correlation, forming an ordered feature sequence. On this basis, a long short-term memory network (LSTM) model is constructed. The LSTM model is designed to process and learn the dependencies in such sequence data. The model learns the spectrum data at each angle in turn and uses its internal unique "cell state" to continuously accumulate and update the understanding of the internal structure of the film. The LSTM model accurately controls the retention, update and output of information through its internal gating mechanisms such as forget gate, input gate and output gate. The update of its cell state follows a specific memory rule, which is realized by combining selective forgetting of the previous state with selective memory of the current input information.

[0009] This design enables the model to effectively capture the subtle changes in optical response (such as interference fringes) as the incident angle changes, and these changes contain the structural information of the film. Ultimately, through comprehensive judgment of the entire angle sequence information, the model can directly output the predicted value of the film thickness without relying on complex physical model iterative fitting. As a preferred scheme of the present application, after outputting the predicted thickness value, a physical consistency verification step can also be performed: taking the predicted thickness value as a known parameter, combining the refractive index of the film material, and calculating the theoretical spectrum reflectivity curve through the optical thin film theory model (such as the transfer matrix method), and comparing and analyzing it with the original spectrum reflectivity curve. This step can effectively verify the physical reasonableness of the prediction result and avoid errors such as "numerical accuracy but physical inappropriateness", providing additional reliability guarantee for industrial online detection.

[0010] Correspondingly, the application also provides a system for implementing the above method, which mainly comprises a data acquisition module, a sequence construction module, a prediction module, and an optional physical consistency verification module. The data acquisition module is used to obtain optical reflectivity spectrum data of a target multilayer film sample at at least two different incident angles; the sequence construction module is used to construct the spectrum data obtained by the data acquisition module into an angle sequence with a sequence-dependent relationship in the order of increasing or decreasing of the incident angles; the prediction module internally integrates a long short-term memory (LSTM) model, and is used to receive the angle sequence, process the sequence angle by angle by using the internal cell state, and regress and output a predicted thickness value of at least one film layer in the multilayer film sample; the physical consistency verification module, as an optional module, is used to calculate a theoretical spectrum reflectivity curve according to the thickness value output by the prediction module through an optical thin film theoretical model, and compare the theoretical spectrum reflectivity curve with the original spectrum reflectivity curve to verify the physical consistency of the predicted thickness value. These modules work cooperatively to perform the method steps as described above. When the system is configured with the physical consistency verification module, it constitutes a closed-loop measurement system with self-checking capability.

[0011] Compared with the prior art, the application has the following beneficial effects: High precision and high generalization ability: the application serializes the multi-angle spectrum data, uses the LSTM network to deeply mine the complex nonlinear relationship between angle change and film thickness, and overcomes the limitations of traditional optical measurement methods in processing non-uniform and multilayer structures. Experimental results show that the model has high accuracy in predicting the thickness of the multilayer film. Specifically, in a test of a typical three-layer film stack, the determination coefficient (R²) of the application method for predicting the thickness of the high refractive index layer (H layer) can reach 0.9214, and the determination coefficient (R²) of the application method for predicting the thickness of the low refractive index layer (L layer) can reach 0.9450, showing excellent generalization ability and prediction accuracy.

[0012] High reliability and physical consistency: the application combines data-driven prediction with physical principle verification by introducing a physical consistency verification step, effectively avoiding prediction errors of "numerical accuracy but physical inconsistency", ensuring the correctness of the results in the physical sense, and providing unprecedented reliability guarantee for industrial online detection.

[0013] High efficiency and high speed: compared with the complex physical model fitting and iterative calculation relied on by traditional optical methods, the method proposed by the application has extremely high calculation efficiency in the prediction process after the model training is completed, has the advantages of fast speed and high efficiency, provides a new idea for measuring the thickness of multilayer films with complex structure, and is suitable for industrial online monitoring.

[0014] Overcome model limitations: the present application is a data-driven model, which does not rely on idealized assumptions of thin film structure (such as absolute uniformity, flat interlayer interface, etc.), so it is more robust when dealing with complex, non-uniform multilayer films in the real world. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a schematic diagram of a multilayer optical film sample structure of an embodiment of the present application.

[0016] Figure 2 is a flowchart of a thin film thickness prediction method of an embodiment of the present application.

[0017] Figure 3 is a schematic diagram of a unit of a long short-term memory network (LSTM) in an embodiment of the present application.

[0018] Figure 4 is a training loss function convergence curve diagram of an LSTM model in an embodiment of the present application.

[0019] Figure 5 is a spectral comparison result schematic diagram of physical consistency verification in an embodiment of the present application. DETAILED DESCRIPTION

[0020] The technical solutions in the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Embodiment 1: High-precision thickness prediction method and system for three-layer film stack As Figure 2 shown, the overall process of the above system executing the prediction method of the present application is as follows: S101 data set construction, through simulation or measurement, systematically collect and organize the data set for model training and testing, including optical reflectance spectra at different incident angles (input features) and their corresponding real film layer thicknesses (output targets).

[0021] S102 angle sequence construction, organize the spectral data of the same thin film sample at different angles into an angle sequence in ascending or descending order of angle, as the input of the LSTM model.

[0022] S103 LSTM model processing and training, use the constructed angle sequence and its corresponding real thickness values to train the LSTM network, so that the model learns the complex mapping relationship from the spectral sequence to the thin film thickness.

[0023] S104 prediction of thickness and evaluation, use the trained LSTM model to predict the thickness of a new angle sequence, and analyze the prediction accuracy through evaluation indicators (such as mean square error, accuracy, etc.).

[0024] S105 Physical consistency verification, as a preferred enhancement step, can generate a theoretical spectral reflectance curve according to the predicted thickness value output by S104 through optical thin film theory, and compare it with the original spectrum to verify the physical reliability and rationality of the prediction result.

[0025] The embodiment details the film thickness prediction method of the present application, and also discloses a prediction system for implementing the method. The system is mainly integrated in a computing device through software and / or hardware, and includes the following functional modules: The data acquisition module is used to perform step S101 to obtain the optical reflectance spectrum data of the target multilayer film sample at multiple different incident angles.

[0026] The sequence construction module is used to perform step S102 to construct the spectral data into an angle sequence with sequence dependence according to the increasing or decreasing order of the incident angles.

[0027] The prediction module internally integrates a pre-trained LSTM model, which is used to perform step S104 to receive the angle sequence, process the sequence angle by angle using its internal cell state, and directly regress the predicted thickness value of at least one film layer in the multilayer film sample. Step S103 provides the prediction module with a trained and ready-to-use LSTM model.

[0028] The physical consistency verification module, as an optional functional module, is configured to perform step S105 in the process to verify and ensure the physical consistency of the thickness value output by the prediction module.

[0029] Step S101: Data set construction In order to train and verify the prediction model, a labeled data set containing a large number of samples is first needed. In this embodiment, COMSOL 6.1 simulation software is used to generate spectral reflectance data.

[0030] Reference Figure 1 The specific film structure is set as a multilayer film stack, which includes a first high refractive index layer 10, a low refractive index layer 20, a second high refractive index layer 30, and a substrate 40. In this embodiment, the material combination is set as a high refractive index layer of Ta2O5 (refractive index of 2.16) and a low refractive index layer of SiO2 (refractive index of 1.46).

[0031] During the simulation process, the thickness parameters of the film layers are systematically scanned. The thickness range of the first high refractive index layer 10 and the second high refractive index layer 30 is set to 20-115 nm with a step of 5 nm. The thickness range of the low refractive index layer 20 is set to 50-145 nm with the same step of 5 nm.

[0032] By full factorial design of these thickness parameters, 400 different film thickness combinations are generated. For each film thickness combination, the reflectivity spectrum data at 0°, 15°, 30°, and 45° incident angles are collected respectively. Therefore, a total of 1600 reflectivity spectrum data (400 combinations x 4 angles) are obtained, which constitute the complete data set for model training and testing.

[0033] Step S102: Model architecture and sequence construction The embodiment adopts a long short-term memory network (LSTM) as the core prediction model because it is good at capturing long-term dependencies in sequence data.

[0034] The key step of the present application is data serialization. The reflectivity spectrum data at four angles (0°, 15°, 30°, and 45°) collected for the same film thickness combination in step S101 are arranged in order of increasing angle to form an angle sequence S = {X1(θ1), X2(θ2), X3(θ3), X4(θ4)} with inherent correlation, where θ1= 0°, θ2= 15°, θ3= 30°, and θ4= 45°.

[0035] In this sequence, X t represents the spectrum data at the tth angle. Here, the subscript t (t = 1, 2, 3, 4) is the sequence position index, and there is a fixed mapping relationship between the index and the incident angle value. This sequence is used as the input of the LSTM model. After the model processes the entire sequence (i.e., all spectrum data from 0° to 45°), it outputs the predicted values of the thicknesses of the two film layers (H layer and L layer) of the sample.

[0036] Step S103: LSTM model principle and training The embodiment adopts a long short-term memory network (LSTM) as the core prediction model. Specifically, the constructed LSTM model contains an LSTM layer with 64 neurons, followed by a fully connected layer as the output layer. The training process of the model uses the Adam optimizer, with an initial learning rate of 0.001, a batch size of 16, a maximum training period (Epoch) of 200, and an early stopping strategy to prevent overfitting during training. In this embodiment, the step index t in the sequence is fixed to correspond to the angle sequence, i.e., t = 1, 2, 3, 4 correspond to incident angles of 0°, 15°, 30°, and 45°, respectively. During model processing, t represents the current sequence step being processed.

[0037] Reference Figure 3This diagram illustrates the structure of a single unit in the LSTM process. LSTM uses "gate" structures to control the inflow and outflow of information and "cell states" to store states long-term, thus better capturing dependencies in long sequences.

[0038] The computation process of the LSTM unit when processing each spectral data in sequence S is as follows: Forgotten Gate ( The network determines the hidden state based on the previous angle. Spectral data at the current angle The cell state is determined by a sigmoid function. What information is forgotten?

[0039] in, and These are the weight matrix and bias term of the forget gate, respectively. Use the Sigmoid activation function; Input gate ( ) and candidate value vector ( The network decides which new information to store. First, the input gate selects the value i to be updated using the Sigmoid function. t Then, one Function layer creates candidate value vector .

[0040] in, and These are the weight matrix and bias term of the input gate, respectively; and These are the weight matrix and bias term for the candidate cell state, respectively; Cell state update ( Cellular states are updated by "forgetting" old information and "adding" new information, thus forming new long-term memories. in, This represents the step in the current angle sequence. This represents the cell state from the previous step. For the Gate of Oblivion For input gate, To pass Candidate value vectors created by the function layer; In this way, LSTM networks can analyze the optical response from angle to angle, dynamically “memorizing” and “updating” their understanding of the internal structure of the thin film.

[0041] Output gate ( ) and hidden state (h t Finally, output gate: Decide which information to output from the updated cell state, and process it. Layered filtering generates the hidden state at the current time step. .

[0042] in, and These are the weight matrix and bias term of the output gate, respectively; The constructed dataset is then fed into the LSTM network for training. (Refer to...) Figure 4 This diagram illustrates the convergence curve of the loss function during model training. The horizontal axis represents the number of training epochs, and the vertical axis represents the mean squared error loss value. In the early stages of training, the model's loss value decreases rapidly, then gradually flattens out and stabilizes at a low level. This indicates that the model's parameters have been sufficiently optimized through training, the training process is stable and effective, no obvious overfitting occurs, and good convergence results are achieved.

[0043] Step S104: Prediction and Performance Evaluation After model training, its predictive performance is comprehensively evaluated using a reserved test set. Evaluation metrics include mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). 2 Three indicators. The formula is: in, y i Representing the i The true thickness value of each sample Representing the i The model predicts the thickness value for each sample. n It represents the number of test samples.

[0044] Experimental results show that the Long Short-Term Memory (LSTM) network model established in this embodiment has high accuracy in predicting the film thickness of multilayer film samples. Specifically, for a film thickness of 1 (H layer), its MAE is 5.48 nm, RMSE is 8.71 nm, and R... 2The value is 0.9214. For a film thickness of 2 (L layers), the MAE and RMSE are 3.99 nm and 6.82 nm, respectively. 2 The value is 0.9450. To verify the effectiveness of the "sequence modeling" method of this invention, it was compared with a baseline model that directly concatenates multi-angle spectral data into a long vector and inputs it into a common fully connected network (MLP). The baseline model (MLP) has a MAE of 6.85 nm, an RMSE of 8.92 nm, and an R² of 0.8953 for film thickness 1 (H layer); and a MAE of 5.65 nm, an RMSE of 8.15 nm, and an R² of 0.8920 for film thickness 2 (L layer). Experimental results show that the LSTM sequence model of this invention significantly outperforms the baseline model in prediction accuracy. This demonstrates that constructing multi-angle spectra into sequences and processing them using LSTM can more effectively uncover the continuous evolution of optical interference effects caused by changes in incident angle, thereby more accurately retrieving film thickness. These results indicate that the model has high prediction accuracy and good generalization ability, meeting the needs for accurate measurement of the thickness of complex multilayer films.

[0045] S105: Physical Consistency Verification To verify the reliability and rationality of the model's predictions from a physical principle perspective, this embodiment introduces a physical consistency verification step. The core of this step is to substitute the model's prediction output back into the classical physical model for inversion calculations to verify whether it follows the interference laws of light waves in thin films.

[0046] Specific methods include: The thickness values ​​of each layer predicted by this method (through steps S101-S104) for any thin film sample are used as known fixed parameters. Combined with the known refractive index of each layer, and using rigorous optical thin film transfer matrix theory, specifically, based on the predicted thickness values ​​of each layer... j physical thickness of layer d j Combined with the first j Complex refractive index of layered materials N j = n j - i k j (in n For refractive index, k (where i is the extinction coefficient and i is the imaginary unit) The characteristic matrix of the multilayer film is constructed using the transfer matrix method.

[0047] First, according to Snell's law, the light in the first... j Angle of refraction in the layer θ j Secondly, define the first jOptical admittance of a layer η j Since the optical admittance of a layer is different for s-polarized (TE wave) and p-polarized (TM wave) light, the actual measurement setup needs to be taken into account. If the light is s-polarized: , if it is p-polarized: , and if it is unpolarized, the reflectivity for both polarizations needs to be calculated separately and averaged.

[0048] The phase thickness of a layer j δ j The formula for calculating the phase thickness of a layer is: . For the first layer, the characteristic matrix j j is given by: M For the system matrix of the entire film stack M , the characteristic matrix of the first layer M 1is multiplied by the characteristic matrix of the second layer M N : Finally, the reflectance r of the film stack is calculated from the four elements of the system matrix m 11 ,m 12 ,m 21 ,m 22 , the optical admittance of the incident medium η 0, and the optical admittance of the substrate η sub : The formula for calculating the theoretical spectral reflectance R is simply the square of the modulus of the reflectance: Subsequently, the theoretically calculated spectral reflectance curve is compared with the original spectral reflectance curve of the sample, which was obtained by simulation or actual measurement. To quantify the comparison, the correlation coefficient (R 2 ) between the two spectral curves is calculated, and the mean absolute error (MAE) between the theoretical and original values for all samples at different angles is calculated. The focus of the comparison is to evaluate the consistency of the two curves in terms of overall shape, number and position of interference extrema, and amplitude of the extrema.

[0049] Verification results and effects: ​​Based on the above quantitative indicators, the comparison results show that for the vast majority of samples in the test set, the theoretically calculated curve and the original curve are in high agreement. Figure 5 This figure demonstrates the physical consistency verification results of a randomly selected sample from the test set. The horizontal axis represents wavelength, and the vertical axis represents optical reflectivity. The solid line corresponds to the theoretical spectrum obtained from the thickness inversion calculation based on the model of this invention, and the dashed line corresponds to the original spectrum of the sample. Figure 5 It can be seen that within a wide wavelength range of 200nm to 1250nm, the curves of the theoretical spectrum and the original spectrum show a high degree of consistency. The average correlation coefficient is above 0.98, and the mean absolute error (MAE) of the spectral reflectance values ​​is less than 0.02 (i.e., 2%). Although slight vertical deviations in local amplitudes may occur due to system noise or substrate non-ideality, this high waveform similarity intuitively demonstrates that the prediction results strictly follow the physical principles of thin-film interference, further confirming the physical reliability and robustness of the method of this invention.

[0050] Although the multilayer film model constructed in this embodiment is a three-layer stack, those skilled in the art should understand that the method of the present invention is not limited to this, and future research can achieve stacking with higher numbers of layers and more methods on this basis.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for predicting the thickness of an optical film based on a sequence angle spectroscopic analysis, characterized by, The method comprises: obtaining optical reflectance spectrum data of a target multilayer thin film sample at at least two different incident angles; constructing the optical reflectance spectrum data at the at least two different incident angles into an angle sequence with a sequence-dependent relationship in an order of increasing or decreasing of the incident angles; inputting the angle sequence into a pre-trained long short-term memory (LSTM) model in the order; accumulating and updating the understanding of the structure information of the multilayer thin film sample by the LSTM model through its internal cell state angle by angle; and outputting a predicted thickness value of at least one film layer in the multilayer thin film sample according to the comprehensive information of the angle sequence. The plurality of different incident angles comprises at least two angles in a range of 0° to 60°.

2. The method of claim 1, wherein, The LSTM model comprises a forget gate, an input gate and an output gate for calculating weights by a Sigmoid function to control the retention, discard and output of information in the cell state. The following formula is implemented:

3. The method of claim 1, wherein, The optical reflectance spectrum data is simulated by optical simulation software based on a preset thin film structure model and material parameters. The multilayer thin film sample is a dielectric film system comprising alternating stacks of high refractive index layers and low refractive index layers.

4. The method of claim 3, wherein, The cell state ( The update was passed. The multilayer thin film sample is a HLH three-layer structure, wherein H is a high refractive index layer, L is a low refractive index layer, the high refractive index layer material is Ta2O5, and the low refractive index layer material is SiO2. wherein, denotes the step in the current angle sequence, is the cell state of the previous angle step, is the forget gate, is the input gate, is the through vector of candidate values created by the function layer.

5. The method of claim 1, wherein, After outputting the predicted thickness value, the method further comprises the following steps: Physical consistency verification: taking the predicted thickness value as a known parameter, combining the material refractive index of the thin film, and calculating a theoretical spectrum reflectance curve by an optical thin film theory model; comparing the theoretical spectrum reflectance curve with the original spectrum reflectance curve to verify the physical consistency of the predicted thickness value.

6. The method of claim 1, wherein, The comparison is achieved by calculating the Pearson correlation coefficient between the theoretical spectrum reflectance curve and the original spectrum reflectance curve. The system comprises:

7. The method of claim 6, wherein, One or more processors and a memory storing a computer program that, when executed by the one or more processors, causes the system to perform the method of any one of claims 1 to 9. The system comprises:

8. The method of claim 1, wherein, A data acquisition module for obtaining optical reflectance spectrum data of a target multilayer thin film sample at at least two different incident angles; A sequence construction module for constructing the spectrum data obtained by the data acquisition module into an angle sequence with a sequence-dependent relationship in an order of increasing or decreasing of the incident angles; A prediction module internally integrated with a long short-term memory (LSTM) model, which processes the sequence angle by angle in the order, accumulates and updates the understanding of the thin film structure through its internal cell state, and regresses to output a predicted thickness value of at least one film layer in the multilayer thin film sample.

9. The method of claim 8, wherein, ​ ​ 10. An optical thin film thickness prediction system based on sequence angle spectroscopy analysis, characterized by, ​ ​ 11. The system of claim 10, wherein, ​ ​ ​ ​ A physical consistency verification module is configured to calculate a theoretical spectral reflectance curve based on the predicted thickness value using an optical thin film theory model, and compare the theoretical spectral reflectance curve with the original spectral reflectance curve to verify the physical consistency of the predicted thickness value.

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