A Chirp-Z transform-based method for rapid measurement of film thickness

Abstract

The application discloses a kind of Chirp-Z transformation-based film thickness rapid measurement method, comprising the following steps: 1) spectral data acquisition;2) data preprocessing;3) CZT (linear frequency Z transform) parameter configuration and CZT spectrum calculation;4) peak screening;5) according to the thickness of film calculated from peak value and equivalent refractive index.This application carries out data preprocessing after receiving processed spectrometer acquisition data, uses Chirp-Z transformation to carry out spectrum analysis, obtains spectrum peak accurate positioning, calculates film thickness using equivalent refractive index, to realize efficient, high-precision film thickness measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of thin film thickness measurement, and more particularly to a thin film thickness rapid measurement method based on Chirp-Z transform. BACKGROUND

[0002] The optical method for measuring the thickness of a thin film as a non-contact, high-efficiency non-destructive testing method has an irreplaceable position in material science and semiconductor industry. Its core advantage is to avoid sample damage caused by mechanical contact, and at the same time, it can realize rapid measurement with nanometer to micrometer precision, especially suitable for wafer coating, optical thin film, flexible electronic devices and other scenes with strict requirements on surface integrity.

[0003] At present, the reflection spectrum is commonly used as the detection basis, and the conventional measurement method usually relies on an iterative optimization algorithm (such as Levenberg-Marquardt algorithm or conjugate gradient method) to fit the data collected by the actual spectrometer through repeated calculation, so as to inverse the thickness parameter. However, such iterative algorithm has obvious limitations: firstly, its convergence effect is seriously dependent on the selection of initial parameters, if the initial value is set far away from the true solution, it is easy to fall into a local optimal solution, resulting in distorted output results; secondly, the iterative process itself has high calculation load, especially when dealing with complex film system or low signal-to-noise ratio spectrum, it is time-consuming, and even after spending a lot of time, it may still get a wrong solution.

[0004] Another detection method is based on fast Fourier transform (FFT) measurement. The reflection spectrum is affected by the interference between the thin film layers and forms a periodic fluctuation in the form of cosine. The formula of the spectral intensity is related to the thickness, for example, for a single layer of thin film, the reflection spectrum is proportional to the cosine formula of wavelength . Wherein For wavelength, n is the wavelength-dependent refractive index function of the material. FFT can quickly extract the thickness information by analyzing the transform domain of the reflection spectrum. Although this method can overcome the defect of dependence on initial value to some extent, there are still significant technical bottlenecks in measurement efficiency, accuracy and adaptability. First, the FFT method needs to extend and interpolate the spectrum data to an integer power of 2 length, which increases unnecessary redundant processing and calculation; second, FFT needs to calculate the spectrum of the full frequency band, while the thickness measurement of the film only depends on the peak signal in a certain frequency range, and the full frequency band calculation results in waste of computing power, which cannot meet the rapid online measurement demand in industrial scene; third, the frequency resolution of FFT is fixed by the data length, when the film is nanometer level or close to the theoretical resolution, the fixed resolution of FFT cannot accurately capture the peak signal, and FFT can only have better measurement effect on the film with micron level thickness; fourth, in order to prevent spectrum leakage, FFT usually performs windowing processing, which increases the time consumption of pretreatment and also causes the main lobe of spectrum to spread, further reducing the peak positioning accuracy.

[0005] Therefore, it is an urgent problem for those skilled in the art to provide a Chirp-Z transform-based film thickness rapid measurement method. SUMMARY

[0006] Therefore, the present application provides a Chirp-Z transform-based film thickness rapid measurement method to solve the problems of dependence on initial value, low calculation efficiency and insufficient measurement accuracy of thin film in the existing film thickness measurement.

[0007] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0008] A Chirp-Z transform-based film thickness rapid measurement method, comprising the following steps:

[0009] 1) Spectrum data acquisition;

[0010] 2) Data preprocessing: converting the collected spectrum data into uniform wave number-dependent spectrum, and then removing some boundary interference data by truncation;

[0011] 3) CZT parameter configuration and CZT spectrum calculation, wherein CZT is Chirp-Z transform;

[0012] 4) Peak selection: for single-layer film, there is only one peak, which is directly calculated by maximum value method or selected after Gaussian function fitting; for multi-layer film, set amplitude threshold T=0.6*max(F(f)), or use the judgment criterion that the first derivative is zero and the second derivative is negative, or perform multi-peak fitting through Gaussian function fitting; wherein F(f) is the spectrum function of the spectrum;

[0013] 5) Calculate the thickness of the film according to the peak value and the equivalent refractive index: the abscissa point is converted into thickness by using the equivalent refractive index, and the equivalent refractive index is calculated by using the end point simple method or the multi-point linear weighting method or the integral method, and the corresponding abscissa value formula is:

[0014]

[0015] wherein is the equivalent refractive index, is the minimum thickness when the algorithm is configured, is the maximum thickness configured, N is the point index, and m is the sampling point number.

[0016] By adopting the above technical scheme, the present application has the following beneficial effects:

[0017] After receiving the processed spectrometer acquisition data, data preprocessing is performed, frequency spectrum analysis is performed by using Chirp-Z transform (CZT), frequency spectrum peak value accurate positioning is obtained, and film thickness is calculated by using the equivalent refractive index, so that high-efficiency and high-precision film thickness measurement is realized.

[0018] Further, the specific steps of step 1) include obtaining the reflection or transmission spectrum intensity of the film by using the spectrometer, and calculating the reflectivity of the film sample by comparing the theoretical reflectivity of the standard sheet and the actual reflection intensity.

[0019] Further, the spectrometer is a dispersive spectrometer or an interferometric spectrometer, and if the interferometric spectrometer is used, the obtained spectrum data is directly a wave number related spectrum, so that the step of converting the collected spectrum data into a uniform wave number related spectrum in step 2) is omitted.

[0020] Further, step 2) further includes smoothing processing and direct current signal processing on the spectrum data.

[0021] Further, the smoothing processing mode is any one of low-pass filtering, window filtering and mean filtering; and the direct current signal processing mode is using spectrum filtering or subtracting the mean value.

[0022] Further, the specific steps of step 3) include:

[0023] First step: calculate the core scaling factor and spiral parameter according to the input parameters:

[0024] Calculate the frequency scaling factor scale: the formula is ((fu-fl)*m) / (fs*(m-1)), wherein fs is the wave number sampling frequency of the spectrum data, and m is the output point number;

[0025] Compute starting point factor A: complex number exp(2.0*I*PI*fl / fs) corresponding to the starting phase of the target frequency interval, where I is the unit imaginary number, PI is the circular constant, and exp is the natural exponential;

[0026] Compute spiral factor W: complex number exp(-2.0*I*PI / m*scale) for controlling the spiral sampling trajectory on the Z plane;

[0027] Step 2: Pre-compute the quadratic phase factor vector wk2:

[0028] Loop to compute the quadratic phase factor of each element, formula: wk2(i)= exp(-(I * PI * scale * i²) / m), which is used for subsequent phase correction of the signal and construction of the convolution kernel;

[0029] Step 3: Compute the input sequence correction coefficient Awk2:

[0030] Construct ak vector, each element is exp(-2.0*I_*PI_*fl / fs*i),

[0031] Compute Awk2 by multiplying ak with the first n elements of wk2 point by point, n is the length of the input data;

[0032] Step 4: Construct the convolution kernel and pre-compute its FFT:

[0033] Construct the convolution kernel temphn: take the elements of wk2 with index 1 to n-1, and reverse the order to splice the elements of wk2 with index 0 to m-1;

[0034] Take the point-by-point reciprocal of temphn and save it to Fwk2, which is used for subsequent fast convolution calculation by FFT;

[0035] Step 5: Preprocess the input signal:

[0036] Multiply the input signal by Awk2 to preprocess the original signal in phase, and the result is recorded as gn;

[0037] Step 6: Use FFT transform to speed up convolution calculation:

[0038] Compute the Fourier transform of gn, Gn;

[0039] Multiply Gn with the convolution kernel Fwk2 point by point;

[0040] Take the inverse FFT of the product result to get the convolution result y;

[0041] Step 7: Phase correction

[0042] The effective segment in y is extracted by the start index and the target length, the effective part related to the target frequency interval in the convolution result is screened out, and the edge redundant data is excluded;

[0043] The extracted effective result is multiplied with the pre-calculated wk2 point by point to obtain the spectrum of the target range.

[0044] Therefore, the present application provides a Chirp-Z transform-based thin film thickness rapid measurement method, which has the following beneficial effects compared with the prior art:

[0045] The present application realizes the characteristics of focusing on the specific frequency range required for thin film thickness measurement for spectrum calculation, reduces the redundant operation of data preprocessing and the waste of computing power of full-band calculation, shortens the overall time consumption from spectrum data acquisition to thickness output, reduces the influence of the initial value of thickness, reduces the error between the measured value and the true value during rapid measurement, realizes rapid detection of thin films, and meets the rapid online measurement requirements of thin film thickness in the fields of semiconductors, flexible electronics and the like. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0047] Fig. 1 The accompanying drawings are a flowchart of a Chirp-Z transform-based thin film thickness rapid measurement method provided by the present application.

[0048] Fig. 2 The accompanying drawings are a schematic diagram of using the FFT algorithm to measure the thickness of SiO2 with a thickness of 800nm, wherein the upper graph is the spectrum data that should be measured in theory by the spectrometer, the lower graph is the thickness-intensity relationship graph after Fourier transform of the measured data, and the thickness-intensity relationship graph after Fourier transform of the spectrum data calculated by the algorithm (i.e., the measurement result).

[0049] Fig. 3 The accompanying drawings are a schematic diagram of using the CZT algorithm to measure the thickness of SiO2 with a thickness of 800nm, wherein the upper graph is the spectrum data that should be measured in theory by the spectrometer, the lower graph is the thickness-intensity relationship graph after Chirp-Z transform of the measured data, and the thickness-intensity relationship graph after Chirp-Z transform of the spectrum data calculated by the algorithm (i.e., the measurement result). DETAILED DESCRIPTION

[0050] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0051] As shown in Figs. 1-3 The embodiment of the present application discloses a Chirp-Z transform-based thin film thickness rapid measurement method, comprising the following steps:

[0052] Spectrum data acquisition: using a dispersive, interferometric and other spectrometer equipment to obtain the reflection or transmission spectrum intensity of the thin film, and calculating the reflectivity of the thin film sample by comparing the standard sheet reflectivity and the actual reflection intensity, which is referred to as spectrum data hereinafter;

[0053] 2) Data preprocessing: converting the collected spectrum data into uniform wave number related spectrum, if the data obtained by using an interferometric spectrometer is directly wave number related spectrum, this step can be omitted; further, in order to avoid the interference of the change of the material characteristics from the low wave band or the light source intensity of the edge wave band on the spectrum data, some boundary interference data should be removed by using the truncation method;

[0054] In order to further optimize the technical solutions of the present application, low-pass filtering, window filtering, mean filtering and other methods can be used to smooth the data; at the same time, the data can be removed from the direct current signal by using frequency spectrum filtering or subtracting the mean value, so as to exclude the influence of the baseline peak value on the spectrum peak value;

[0055] 3) CZT parameter configuration and CZT spectrum calculation, CZT is a linear frequency modulation Z transform:

[0056] In the CZT parameter configuration, the CZT algorithm supports free selection of analysis points on the unit circle or spiral path in the Z plane, is suitable for high-precision spectrum analysis and non-uniform signal processing, and needs to configure parameters A and W which are complex numbers, and they together define the path of sampling in the Z plane. In the embodiment, sampling is performed in the partial segment arc of the unit circle, but using the spiral line path sampling should also fall within the scope of the present patent.

[0057] In the CZT parameter configuration, the CZT algorithm supports free selection of analysis points on the unit circle or spiral path in the Z plane, is suitable for high-precision spectrum analysis and non-uniform signal processing, and needs to configure parameters A and W which are complex numbers, and they together define the path of sampling in the Z plane. In the embodiment, sampling is performed in the partial segment arc of the unit circle, but using the spiral line path sampling should also fall within the scope of the present patent.

[0058]

[0059] This is the starting point of sampling, and then each point will be multiplied by W-1 control frequency resolution of the fine degree on the basis of the previous point. For easy call, only the thickness range and the number of sampling points are required in this embodiment, and the corresponding parameters A and W are automatically generated by the algorithm. The specific steps are as follows:

[0060] There is a rough guess range for the thickness of the sample film, for example, assuming an 800nm SiO2 film sample, the range is estimated to be between 0-2000nm before measurement (the lower limit is fl, and the upper limit is fu), and the output sampling point number m determines the accuracy of the measurement, that is, the resolution is (fu-fl) / m, and the resolution here cannot be less than the theoretical value of the Nyquist sampling theorem. After inputting the starting point, the end point, and the sampling point number, the algorithm will automatically generate a sampling path in the Z plane and convert it into parameters A and W.

[0061] The Bluestein algorithm is used inside the algorithm to accelerate the calculation of CZT, and the effective frequency spectrum is output. The algorithm complexity is O((N)log(N)), and the calculation complexity is on par with FFT, which is much higher than the standard Discrete Fourier Transform (DFT);

[0062] The specific steps of CZT spectrum calculation include:

[0063] First step: calculate the core scaling factor and spiral parameter according to the input parameters:

[0064] Calculate the frequency scaling factor scale: the formula is ((fu-fl)*m) / (fs*(m-1)), where fs is the wave number sampling frequency of the spectrum data, and m is the output point number;

[0065] Calculate the starting point factor A: a complex number exp(2.0*I*PI*fl / fs), corresponding to the starting phase of the target frequency interval, where I is the unit imaginary number, PI is the circular constant, and exp is the natural exponential;

[0066] Calculate the spiral factor W: a complex number exp(-2.0*I*PI / m*scale), used to control the spiral sampling track on the Z plane;

[0067] Second step: pre-calculate the quadratic phase factor vector wk2:

[0068] Loop to calculate the quadratic phase factor of each element, the formula is wk2(i)= exp(-(I * PI * scale * i²) / m), and this vector is used for subsequent phase correction and convolution kernel construction of the signal;

[0069] Third step: calculate the input sequence correction coefficient Awk2:

[0070] Construct ak vector each element as exp(-2.0*I_*PI_*fl / fs*i),

[0071] Calculate Awk2 multiply ak with the first n elements of wk2 point by point, n is the length of the input data;

[0072] Fourth step: construct the convolution kernel and pre-compute its FFT:

[0073] Construct the convolution kernel temphn: take the elements of wk2 with index 1 to n-1, and reverse order to splice the elements of wk2 with index 0 to m-1;

[0074] Take the point-by-point reciprocal of temphn and save it to Fwk2, which is used for subsequent fast convolution calculation by FFT;

[0075] The above parameter pre-computation process has no direct connection with the input spectral data; for the application scenario of fixed thickness measurement range and fixed data length, the pre-computation process can be placed in front to shorten the calculation time of single measurement;

[0076] Fifth step: pre-process the input signal:

[0077] Multiply the input signal by Awk2 to pre-process the original signal, and the result is recorded as gn;

[0078] Sixth step: use FFT transform to speed up convolution calculation:

[0079] Calculate the Fourier transform Gn of gn;

[0080] Multiply Gn and convolution kernel Fwk2 point by point;

[0081] Take the inverse FFT of the product result to get the convolution result y;

[0082] Seventh step: phase correction

[0083] Extract the effective segment of y by the starting index and target length, filter out the effective part of the convolution result related to the target frequency interval, and exclude the edge redundant data;

[0084] Multiply the extracted effective result with the pre-computed wk2 point by point to get the target range spectrum.

[0085] 4) Peak selection: for single-layer film, there is only one peak, which can be directly calculated by extracting the maximum value method, or selected after Gaussian function fitting; for multi-layer film, set the amplitude threshold T=0.6*max(F(f)), or use the zero first derivative and negative second derivative as the judgment criterion, or use Gaussian function fitting for multi-peak fitting; where F(f) is the spectral function of the spectrum;

[0086] 5) Calculate the thickness of the film according to the peak value and the equivalent refractive index: the abscissa point is converted into thickness by using the equivalent refractive index, and the equivalent refractive index is calculated by using the end point simple method (the method of taking the average of the refractive index of the maximum and minimum wavelength), or the multi-point linear weighting method (taking multiple points at equal intervals for weighted summation), or the integral method (integrating the refractive index in the wavelength range to average), and the corresponding abscissa value formula is:

[0087]

[0088] wherein is the equivalent refractive index, is the minimum thickness (fl) when the algorithm is configured, is the maximum thickness (fu) configured, N is the point index, and m is the output sampling point number.

[0089] After receiving the processed spectrometer acquisition data, the application performs data preprocessing, uses Chirp-Z transform (CZT) for frequency spectrum analysis, obtains accurate positioning of the frequency spectrum peak, and calculates the film thickness by using the equivalent refractive index, so as to realize efficient and high-precision film thickness measurement.

[0090] The application uses an 800nm sio2 on si sheet to test the algorithm:

[0091] In the FFT algorithm, the resolution of the low-frequency signal is insufficient, and the 800nm thin layer cannot be identified; while the CZT focuses on the wave number range corresponding to 0-2000nm, the resolution is ensured, the running speed of the CZT algorithm is comparable to that of the FFT algorithm, and the measurement result is very close to the theoretical value.

[0092] The real value of the current use case is 800nm.

[0093] It is verified that the return value of the FFT algorithm is 214.142798 nm, and the time consumption is 0.0409 seconds (python verification code); the return value of the CZT algorithm is 804.201050 nm, and the time consumption is 0.0384 seconds (python verification code).

[0094] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same and similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the related parts can be referred to the method part.

[0095] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A rapid method for measuring thin film thickness based on Chirp-Z transform, characterized in that, Includes the following steps: 1) Spectral data acquisition; 2) Data preprocessing: The collected spectral data is converted into a uniform wavenumber correlation spectrum, and then some boundary interference is removed by truncation. 3) CZT parameter configuration and CZT spectrum calculation, where CZT is linear frequency modulated Z-transform; The specific steps include: Step 1: Calculate the core scaling factor and spiral parameters based on the input parameters: Calculate the frequency scaling factor: The formula is ((fu-fl)*m) / (fs*(m-1)), where fs is the wavenumber sampling frequency of the spectral data, m is the number of output points, fu is the upper limit of the specified thickness range, and fl is the lower limit of the specified thickness range. Calculate the starting point factor A: a complex number exp(2.0*I*PI*fl / fs), which corresponds to the starting phase of the target frequency range, where I is the imaginary unit, PI is pi, and exp is the natural exponent. Calculate the spiral factor W: a complex number exp(-2.0*I*PI / m*scale), used to control the spiral sampling trajectory on the Z plane; Step 2: Pre-calculate the quadratic phase factor vector wk2: The quadratic phase factor of each element is calculated iteratively, with the formula wk2(i) = exp(-(I * PI * scale * i²) / m). This vector is used for subsequent phase correction of the signal and construction of the convolution kernel; where i is a discrete variable. Step 3: Calculate the input sequence correction coefficient Awk2: Construct the vector ak, where each element is exp(-2.0*I_*PI_*fl / fs*i). To calculate Awk2, multiply ak by the first n elements of wk2 point by point, where n is the length of the input data; Step 4: Construct the convolution kernel and pre-compute its FFT: Construct the convolution kernel temphn: take the elements from index 1 to n-1 in wk2, and concatenate them in reverse order with the elements from index 0 to m-1 in wk2, where n and m are both positive integers; Take the reciprocal of each element in the temphn array and save the calculated reciprocal result to Fwk2 for subsequent fast convolution calculation via FFT; Step 5: Preprocess the input signal: The input signal is multiplied by Awk2 to perform phase preprocessing on the original signal, and the result is denoted as gn; Step 6: Accelerate convolution calculation using FFT transformation: Calculate the Fourier transform Gn of gn; Multiply Gn by the convolution kernel Fwk2 point by point; Perform an inverse FFT on the product to obtain the convolution result y; Step 7: Phase Correction By extracting effective segments from y using the starting index and target length, the effective parts of the convolution result that are related to the target frequency range are selected, and redundant edge data is excluded. The extracted valid results are multiplied point by point with the pre-calculated wk2 to obtain the spectrum of the target range; 4) Peak selection: For monolayer films, there is only one peak, which can be directly calculated by extracting the maximum value, or selected after fitting with a Gaussian function; for multilayer films, set the amplitude threshold T=0.6×max(F(f)), or use the judgment criterion that the first derivative is zero and the second derivative is negative, or perform multi-peak fitting by fitting with a Gaussian function; where F(f) is the spectral function of the spectrum; 5) Calculate the film thickness based on the peak value and equivalent refractive index: Convert the horizontal axis coordinates to thickness using the equivalent refractive index. The equivalent refractive index is calculated using the endpoint simplified method, multi-point linear weighted method, or integral method. The corresponding formula for the horizontal axis value is: ； in It is the equivalent refractive index. It is the minimum thickness when the algorithm is configured. N is the maximum thickness configured, N is the point index, and m is the number of sampling points.

2. The method for rapid measurement of thin film thickness based on Chirp-Z transform according to claim 1, characterized in that, Step 1) The specific steps include using a spectrometer to obtain the reflection or transmission spectral intensity of the thin film, and calculating the reflectance of the thin film sample by comparing the theoretical reflectance and the actual reflection intensity of the standard sheet.

3. The method for rapid measurement of thin film thickness based on Chirp-Z transform according to claim 2, characterized in that, The spectrometer is either a dispersive spectrometer or an interferometric spectrometer. If an interferometric spectrometer is used, the acquired spectral data is directly a wavenumber-correlated spectrum, thus eliminating the need for step 2) to convert the acquired spectral data into a uniform wavenumber-correlated spectrum.

4. The method for rapid measurement of thin film thickness based on Chirp-Z transform according to claim 1, characterized in that, Step 2) also includes smoothing the spectral data and removing DC signals.

5. The method for rapid measurement of thin film thickness based on Chirp-Z transform according to claim 4, characterized in that, The smoothing method is any one of low-pass filtering, windowing filtering, and mean filtering; the DC signal removal method is to use spectral filtering or subtract the mean.

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