CN107504910A - White light reflection dynamic measurement film thickness method based on threshold value wavelet transformation - Google Patents

Abstract

The invention discloses a kind of white light reflection dynamic measurement film thickness method based on threshold value wavelet transformation.White light reflectance spectrum signal is carried out three layers of wavelet decomposition by this method, then extract and carry out denoising with default threshold after each layer approximation coefficient and detail coefficients, finally by the characteristic value for asking for white light reflectance spectrum, i.e. the minimum value of reflectivity quickly judge so as to obtain film thickness.Invention enhances the degree of accuracy to film thickness measuring to be measured and speed.

Description

Thin Film Thickness Measuring Method Based on Threshold Wavelet Transform

technical field

The invention belongs to the field of optical precision measurement and signal processing, and in particular relates to a method for judging film thickness by processing white light reflectance spectrum signals by using threshold wavelet transform.

Background technique

With the rapid development of manufacturing technology, thin films have become an important component to meet some equipment performance indicators. Thin films are widely used in many fields, such as optics, informatics, biology, and aerospace. Therefore, it is very important to accurately measure the thickness of the film to judge whether the film is working properly.

The present invention proposes to use white light reflectance spectroscopy (WLRS) to measure the film thickness. This method has the advantages of fast response, high precision and high accuracy of measurement results. The specific principle of WLRS measurement of film thickness is as follows: As shown in Figure 1, white light enters the film to be tested vertically from point A, and after several times of refraction and reflection on the surfaces of S1 and S2, its phase changes, and thus its WLRS can be obtained . Moreover, there is a one-to-one correspondence between the WLRS and the thickness of the film to be measured. Thus, the film thickness on the surface of the base layer can be measured in a non-contact manner according to the above principle. Since the precision can reach the nanometer level during the dynamic measurement of film thickness, a lot of noise will inevitably be introduced. These noises directly affect the accuracy of film thickness measurement. Therefore, how to quickly deal with the noise introduced by various reasons in the measurement process has become an important issue.

Traditional denoising methods, such as Fourier signal analysis, analyze the overall signal, but cannot deal with the subtle parts of the signal well. Wavelet transform (wavelet transform, WT) can achieve the purpose of effectively extracting information through local transformation of time and frequency. It does not need Fourier transform and is more convenient to use. WT processes the details of the signal, and can adapt to the time domain and frequency domain signals, so it can achieve fine processing of the signal.

Usually, a segment of noisy signal is decomposed in the frequency domain, the low frequency is the useful signal, and the high frequency is the noise signal. Therefore, the ideal state in denoising is to remove the high frequency part of the signal while retaining its low frequency part. The wavelet transform is a time-frequency analysis of the signal, which has the advantage of high resolution, and can easily distinguish the high and low frequency parts of the signal to achieve the purpose of removing noise.

The basic principle of wavelet denoising is: first select the number of layers to be decomposed on the signal, and then decompose the signal containing noise by wavelet (the noise is usually in the high frequency part). Then the threshold is calculated, and the details of each layer that have been decomposed from the signal are processed to remove noise. Finally, it is reconstructed according to the number of decomposition layers and corresponding details to restore the real signal.

Contents of the invention

The invention proposes a method for quickly denoising the WLRS signal by using wavelet transform so as to measure the thickness of the film.

The present invention has following steps:

1) Make the light source of white light incident on the film to be tested nearly vertically to obtain the original signal of WLRS;

2) carrying out wavelet decomposition to the WLRS original signal gained in step 1;

3) extract approximate coefficient and detail coefficient to the signal of wavelet decomposition in step 2;

4) Threshold processing is carried out to each layer coefficient in step 3;

5) Reconstruct the WLRS signal;

6) Extract eigenvalues from the denoised WLRS signal obtained in step 5, and obtain the film thickness of the film to be measured through the eigenvalues.

The beneficial effect of the present invention is that the denoising effect is good, the processing speed is fast, the useful signal and the noise can be better distinguished, and the accuracy rate of judging the thickness of the film by using the characteristic value is better improved.

Description of drawings

Figure 1 schematic diagram;

Figure 2 overall block diagram;

Figure 3 WLRS dynamic measurement results of different film thicknesses before denoising (300-345nm);

Fig. 4 Distribution diagram of characteristic parameters before denoising (300-350nm);

Figure 5 wavelet denoising decomposition three-layer approximation diagram (film thickness: 300nm);

Figure 6 Wavelet denoising decomposes a layer of details (film thickness: 300nm);

Figure 7 Wavelet denoising decomposition of the second layer details (film thickness: 300nm);

Figure 8 Wavelet denoising decomposes three-layer details (film thickness: 300nm);

Figure 9 WLRS dynamic measurement results of different film thickness after denoising (300-345nm);

Fig. 10 Distribution diagram of characteristic parameters after denoising (300-350nm).

detailed description

The present invention will be further described in conjunction with accompanying drawing 2 below.

1) Make the light source of white light incident on the film to be tested nearly vertically to obtain the original signal of WLRS;

Specifically: the specific principle is shown in Figure 1. White light enters the film to be tested from point A near vertical (the maximum angle does not exceed ±5°). After several times of refraction and reflection _on the surfaces _of S1 and S2, its phase Variety. By collecting B ₁ , B ₂ , . . . , B _n , the original WLRS signal can be obtained. Let the model of the original signal be:

S(x)＝f(x)+n ₁ (x)×n ₂ (x) (1)

Among them, S(x) is a noisy signal, f(x) is a real signal, n ₁ (x) is additive noise, and n ₂ (x) is multiplicative noise. In this embodiment, the signal model can be simplified as:

S(x)=f(x)+n(x) (2)

Among them, S(x) is the noisy signal, f(x) is the real signal, and n(x) is the noise.

2) carrying out wavelet decomposition to the WLRS original signal gained in step 1;

Specifically: After WLRS is decomposed by wavelet, its low frequency is a useful signal, while its high frequency is a noise signal. Therefore, WLRS can be decomposed into a certain number of layers, and then processed with different thresholds on each layer to achieve the purpose of denoising. The more the number of decomposition layers, the more the high-frequency part is removed, but too many layers will remove some useful signals together, that is, the decomposition is excessive. Therefore, the wavelet with 3 layers is selected to decompose the WLRS original signal f(x) by wavelet.

3) extract approximate coefficient and detail coefficient to the signal of wavelet decomposition in step 2;

Specifically: extract the three-layer approximation c _k of the signal from the three-layer decomposition obtained in step 2 and its details d _j,k of layers 1, 2, and 3, where j represents the number of decomposition layers, and k represents the kth data.

4) Threshold processing is carried out to the wavelet coefficient in step 3;

Specifically: use the calculated threshold δ _j to process the detail part d _{j, k} of the jth layer with formula (3). The processing formula is as follows:

That is, when |d _j,k |＞δ _j , set d _j,k =d _j,k ; when |d _j,k |≤δ _j , set d _j,k =0. In this way, d _{j, k} are screened.

In general, the threshold is selected by the signal-to-noise ratio of the original signal. This embodiment adopts a fixed threshold. The threshold δ _j is determined by the following formula:

Where n is the length of the signal.

5) Reconstruct the WLRS signal;

Specifically: the 3-layer approximation and the 1-3 layer details d _j,k are reconstructed using an algorithm to obtain the real signal.

6) Extract eigenvalues from the denoised WLRS signal obtained in step 4, and obtain the film thickness of the film to be measured through the eigenvalues.

Specifically, the minimum value of the reflectivity of the denoised WLRS signal is calculated as the eigenvalue, and there is a certain linear relationship between the eigenvalue and the film thickness, and the film thickness to be measured can be obtained through this linear relationship.

Further description will be given below through examples. In the range of film thickness 300nm-350nm, a dynamic measurement is performed every 1nm, and a total of 50 WLRSs are obtained. Select 4 WLRSs of 300nm, 315nm, 330nm and 345nm from the 50 WLRSs, as shown in Figure 3. During the high-precision dynamic measurement process, some noise will be introduced, which will cause some deviations when using the eigenvalues to calculate the actual film thickness. As shown in Figure 4, it is not difficult to see that there is a certain correlation between the eigenvalues and the film thickness. In other words, as the film thickness increases, its eigenvalues generally decrease. However, if we want to calculate the film thickness more accurately from the eigenvalues, we need to do some processing. Therefore, wavelet transform is used to denoise it. Taking the WLRS wavelet transform with a film thickness of 300nm as an example, firstly, a model of the original signal is established according to the formula (2) to decompose the WLRS original signal by three-layer wavelet, and then the three-layer approximation of the signal and its 1, 2, 3-layer details, the three-layer signal approximation is shown in Figure 5, the 1-layer details are shown in Figure 6, the 2-layer details are shown in Figure 7, and the 3-layer details are shown in Figure 8. The total threshold value calculated by the formula (4) is 0.0277, and the 1-3 layer details are processed by the formula (3) (when |d _j,k |>δ _j , let d _j,k =d _j,k ; When |d _j,k |≤δ _j , set d _j,k =0). Finally, the WLRS signal is reconstructed to obtain the real WLRS curve. The above-mentioned processing is performed on the 300-350nm signal, and the result is shown in Fig. 9 . Find the minimum value of the reflectance of the denoised WLRS, and draw the characteristic value-film thickness curve, which is shown in Figure 10. It can be seen that the eigenvalues are basically linearly correlated with the film thickness. At this time, the film thickness can be calculated according to the characteristic value, so as to achieve the purpose of dynamic measurement.

Claims (7)

1. The white light reflection dynamic measurement film thickness method based on threshold wavelet transform, is characterized in that, comprises the steps: 1) Make the light source of white light incident on the film to be tested nearly vertically to obtain the original signal of white light reflectance spectrum; 2) performing wavelet decomposition on the original signal of the white light reflectance spectrum obtained in step 1); 3) extract approximate coefficient and detail coefficient to the signal of wavelet decomposition in step 2); 4) carry out threshold value processing to each layer coefficient in step 3); 5) Reconstruct the white light reflectance spectrum signal; 6) Extract eigenvalues from the denoised white light reflectance spectrum signal obtained in step 5), and obtain the film thickness of the film to be measured through the eigenvalues. 2. The white light reflection dynamic method for measuring film thickness based on threshold wavelet transform according to claim 1, characterized in that, said step 1 is specifically: white light enters the film to be measured from point A nearly vertically, at S ₁ and S ₂ After several times of refraction and reflection on the surface, its phase changes; the original signal of WLRS is obtained by collecting the light rays B ₁ , B ₂ , ..., B _n after repeated refraction and reflection; the model of the original signal is set as: S(x)=f(x)+n1(x)×n2(x) Among them, S(x) is a noisy signal, f(x) is a real signal, n1(x) is an additive noise, and n2(x) is a multiplicative noise; then the signal model can be simplified as: S(x)=f(x)+n(x) Among them, S(x) is the noisy signal, f(x) is the real signal, and n(x) is the noise. 3. according to the white light reflection dynamic measurement film thickness method based on threshold value wavelet transform according to claim 1, it is characterized in that, described step 2 is specially: choose the wavelet that number of layers is 3 to carry out wavelet to WLRS original signal f (x) break down. 4. according to claim 3 based on the white light reflection dynamic measurement film thickness method of threshold value wavelet transform, it is characterized in that, described step 3 is specifically: extract the three-layer approximation of signal in the 3-layer decomposition that step 2 obtains c _k and its level 1, 2, and 3 details d _j,k , where j represents the number of decomposition layers, and k represents the kth data. 5. The method for dynamically measuring film thickness based on threshold wavelet transform according to claim 4, wherein the step 4 is specifically: taking out the details d _j,k of the jth layer, and according to the selected threshold δ _j processing; the formula is as follows: The threshold δ _j is determined by the following formula: <mrow><msub><mi>&amp;delta;</mi><mi>j</mi></msub><mo>=</mo><msqrt><mrow><mn>2</mn><mi>l</mi><mi>o</mi><mi>g</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msqrt></mrow> Where n is the length of the signal. 6. according to claim 5, based on the white light reflection dynamic measurement film thickness method of threshold value wavelet transform, it is characterized in that, described step 5 is specifically: three-layer approximation c _k and 1-3 layer details d _{j, k} are carried out Refactor to get the real signal. 7. according to claim 6 based on the white light reflection dynamic measurement film thickness method of threshold value wavelet transform, it is characterized in that, described step 6 is specifically: seek the minimum value of the reflectivity of the white light reflectance spectrum signal after denoising There is a certain linear relationship between the eigenvalue and the film thickness, and the film thickness to be measured is obtained through this linear relationship.