Striped pattern phase extraction method based on two-dimensional hanning self-convolution window spectrum leakage suppression weighted

Abstract

This invention discloses a weighted fringe pattern phase extraction method based on spectral leakage suppression using a two-dimensional Hanning self-convolution window, comprising: S1: acquiring misaligned moiré fringes using a CMOS camera; S2: constructing a self-convolution Hanning window function of the same size as the fringe pattern; S3: performing weighted calculations on the fringes using the Hanning self-convolution window; S4: obtaining the wrapped phase of the fringes using Fast Fourier Transform (FFT); S5: obtaining the continuous phase of the fringe pattern using a least-squares unwrapping algorithm; S6: obtaining the phase difference based on the continuous phase; and S7: calculating the misalignment value based on the phase difference. This invention aims to suppress spectral leakage in moiré fringes, effectively reducing the impact of spectral leakage, thereby enabling the extraction of high-precision phase for high-precision photolithography alignment.

Description

Technical Field

[0001] This invention relates to a method for optimizing the accuracy of fringe phase extraction, and more particularly to a weighted fringe pattern phase extraction method based on two-dimensional Hanning self-convolution window spectral leakage suppression, for wafer and mask alignment, belonging to the fields of nanolithography and signal processing. Background Technology

[0002] Wafer and mask alignment is one of the three core technologies in photolithography. Alignment accuracy must be maintained at 1 / 7 to 1 / 10 of the critical dimension; therefore, for next-generation photolithography, it must achieve nanometer-level precision. In wafer and mask alignment, the use of moiré fringes is a common method. The relative displacement between the wafer and mask is measured by demodulating the phase of the moiré fringes formed by the superposition of alignment marks. The moiré fringes phase is unaffected by changes in the illumination wavelength and the gap between the alignment marks, thus exhibiting high accuracy and good stability. However, in practical applications, the moiré fringe processing can lead to spectral leakage. Spectral leakage affects the accuracy of fringe phase extraction, thus impacting alignment measurements. For photolithography requiring nanometer-level alignment, such an impact is highly detrimental.

[0003] Windowing is a feasible method to effectively address spectral leakage. In one-dimensional signal processing, self-convolution windows have been widely used and have yielded satisfactory results. However, to date, a method for suppressing spectral leakage using self-convolution windows has not been invented in two-dimensional signal processing. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a weighted fringe pattern phase extraction method based on spectral leakage suppression using a two-dimensional Hanning self-convolution window. This method aims to effectively suppress spectral leakage in the fringe pattern, thereby extracting high-precision phase for high-precision photolithography alignment. The proposed method features high accuracy and strong real-time performance, overcomes the spectral leakage problem in fringe patterns to a certain extent, and has strong applicability.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The present invention provides a weighted fringe pattern phase extraction method based on spectral leakage suppression using a two-dimensional Hanning self-convolution window, characterized by the following steps:

[0007] S1: Use a CMOS camera to acquire a single sinusoidal fringe image I(x, y), where x and y are the pixel coordinates in the row and column directions of the sinusoidal fringe image, respectively;

[0008] S2: Construct a two-dimensional Hanning autoconvolution window w for the sinusoidal fringe image I(x,y) using equation (1). p (x, y):

[0009] w p (x, y) = w p (x)·w p (y) (1)

[0010] In equation (1), p is the order of the self-convolution, and w p (x) represents a one-dimensional Hanning autoconvolution window in the row direction, w p (y) represents a one-dimensional Hanning self-convolution window in the column direction, and · represents the dot product operation;

[0011] S3: Use equation (2) to weight the sinusoidal fringe image I(x,y) to obtain the windowed fringe pattern.

[0012]

[0013] S4: Using equation (3) to analyze the windowed stripe pattern The process yields a spatial distribution of windowed fringes containing only target phase information.

[0014]

[0015] In equation (3), H +1 This represents a bandpass filter that extracts the positive first-order spectrum. and Let represent the forward and inverse two-dimensional fast Fourier transform operators, respectively, and then use equation (4) to obtain the wrapping phase.

[0016]

[0017] In equation (4), Im[] and Re[] represent the stripe pattern, respectively. The imaginary and real parts;

[0018] S5: Use the weighted least squares phase unwrapping algorithm to unwrap the wrapped phase. The stripe pattern is obtained through processing. continuous phase

[0019] The present invention relates to a weighted fringe pattern phase extraction method based on two-dimensional Hanning self-convolution window spectral leakage suppression, characterized in that it is applied during the alignment process of wafers and masks, and is performed according to the following steps:

[0020] S6: Based on continuous phase The phase difference associated with the fringe displacement is obtained.

[0021] S7: Based on phase difference The misalignment value Δy between the wafer and the mask is calculated and transmitted to the piezoelectric ceramic drive connected to the image processing system via a feedback system to control the alignment of the wafer and the mask.

[0022] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the fringe pattern phase extraction method, and the processor is configured to execute the program stored in the memory.

[0023] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of the stripe pattern phase extraction method.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] 1. Spectral Leakage Suppression: This invention introduces an innovative two-dimensional Hanning self-convolution window technique to address the spectral leakage problem commonly encountered in fringe pattern phase extraction. Compared to traditional phase extraction algorithms based on classical window functions, the significant advantage of this invention lies in its ability to achieve higher-precision phase extraction. This improvement not only enhances the accuracy of phase extraction but also greatly strengthens the reliability of the measurement results.

[0026] 2. Simple structure and high computational efficiency: Another outstanding advantage of this invention is its superior computational efficiency. This method only requires self-convolution processing of the classic Hanning window function to create a special self-convolution window with low peak sidelobe levels, rapid sidelobe attenuation, and narrow main lobe width. Furthermore, the spectral suppression capability of the self-convolution window increases with the convolution order. By directly weighting the fringe pattern, the spectral leakage problem is successfully solved while ensuring computational speed for real-time applications.

[0027] 3. Wide Range of Applications: The method of this invention has broad applicability and can be used in multiple precision measurement fields based on fringe phase extraction, including but not limited to three-dimensional topography measurement, defect detection, visual mechanical vibration monitoring, and displacement and deformation measurement. This multi-field applicability means that the method of this invention can achieve higher measurement accuracy and more reliable results in various application scenarios. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the application of the method of the present invention to wafer and mask alignment;

[0029] Figure 2 Alignment marks and the resulting moiré pattern are shown, where: (a) wafer alignment marks, (b) mask alignment marks, (c) fringe distribution with misalignment in the Y direction, and (d) fringe distribution when perfectly aligned; solid arrows represent the relevant positions of the moiré patterns.

[0030] Figure 3 The graph shows measurement results for an example where the method of this invention was not used.

[0031] Figure 4 The time-domain amplitude and amplitude-frequency response diagrams of the self-convolution window are shown.

[0032] Figure 5 The graph shows the measurement results of an example using the method of the present invention. Detailed Implementation

[0033] In this embodiment, a weighted fringe pattern phase extraction method based on spectral leakage suppression using a two-dimensional Hanning self-convolution window (2D-HSCW) is presented for wafer and mask alignment. This method aims to suppress spectral leakage from moiré fringes to achieve high-precision lithography alignment. By applying 2D-HSCW to moiré fringes, the impact of spectral leakage can be effectively reduced, improving phase extraction accuracy. This research is significant for lithography and other applications of high-precision measurement based on fringe phase. By suppressing spectral leakage, the 2D-HSCW method holds promise for bringing substantial progress to high-precision lithography alignment technology. Specifically, as... Figure 1 As shown, it includes the following steps:

[0034] S1: Wafer and mask alignment marks as shown Figure 2 As shown in parts (a) and (b), both consist of two sets of line gratings with slightly different periods, P1 = 4 μm and P2 = 4.4 μm. These marks have similar structures but are complementary in position. During alignment, any relative displacement between the wafer and the mask will cause the left and right fringes to move in opposite directions. When uniform and collimated illumination light passes through the alignment marks on the wafer and mask, it forms an array like... Figure 2 Parts (c) and (d) in the diagram represent the moiré fringes when ΔY misalignment and perfect alignment occur, respectively. Each fringe pattern consists of two sets of moiré fringes, left and right, with the same period P. m It can be represented as:

[0035] P m =P1P2 / (P2-P1)=P1P2 / ΔP (1)

[0036] As can be seen from equation (1), compared with the original line grating period P1 or P2, the moiré fringe period P formed by superposition is... m The value of P1 / (P2-P) was magnified.i ) or P2 / (P2-P i This is highly advantageous for measuring minute misalignments in high-precision photolithography at the nanoscale. The magnification increases as ΔP decreases and the grating period increases. Furthermore, these two sets of fringes are further magnified and recorded on a CMOS camera via a lens. Since high-frequency fringes cannot be recorded by the camera, a balance needs to be struck between camera resolution and the alignment mark grating period. Assuming Δy and ΔY represent the actual misalignment and moiré fringe displacement, respectively, their numerical relationship is ΔY = [(P2 + P1) / (P2 - P1)] * Δy. Typically, Figure 2 The continuous fringe I(x, y) in part (c) or part (d) can be represented by the discrete fringe intensity captured by CMOS as follows:

[0037] I left (x,y)=a(x,y)+b(x,y)cos[2πy(f1-f2)+2πf1△y] (2)

[0038] I right (x,y)=a(x,y)+b(x,y)cos[2πy(f1-f2)-2πf2△y] (3)

[0039] Where x and y are the pixel coordinates in the row and column directions of the sinusoidal fringe image, respectively. a(x, y) and b(x, y) represent the background light intensity and amplitude modulation at pixel (x, y) in the fringe image, respectively. f1 = 1 / P1 and f2 = 1 / P2 represent the spatial frequencies of the two line gratings, respectively, and their common difference term (f1 - f2) = 1 / P m This means that both sets of fringes can be considered as carrier fringe patterns with a carrier frequency of (f1-f2). The phase difference between the left and right sets of fringes... for:

[0040]

[0041] here, and These are the spatial average phases on the left and right sides of the moiré fringes, respectively. According to equation (4), the actual misalignment Δy can be derived as:

[0042]

[0043] Although a set of alignment marks can only achieve misalignment measurement in the one-dimensional y-axis direction, misalignment measurement in the two-dimensional x and y-axis directions can be achieved by placing a pair of orthogonal alignment marks.

[0044] S2: In the actual fringe pattern data processing, spectral leakage always exists. Windowing is an effective means to reduce spectral leakage. Therefore, the performance of the window function directly affects the extraction accuracy of the fringe phase, and thus affects the measurement accuracy of the misalignment value. The main evaluation indicators of the window function are: main lobe width, side lobe peak level, and side lobe decay rate. The main lobe width is defined as the distance between the two nearest zero points on both sides of the origin of the frequency domain. The main lobe is related to the frequency resolution. The narrower the main lobe, the higher the frequency resolution. The side lobe peak level refers to the level of the largest side lobe closest to the main lobe. The side lobe is related to leakage. The lower the side lobe peak level, the smaller the side lobe, and the less spectral leakage. The side lobe decay rate reflects the degree of decrease in the side lobe level. The higher the side lobe decay rate, the faster the side lobe level decreases, and the stronger the suppression of leakage. The two-dimensional Hanning self-convolution window w of the sinusoidal fringe image I(x,y) is constructed using Equation (6). p (x, y):

[0045] w p (x, y) = w p (x)·w p (y) (6)

[0046] In equation (6), p is the order of self-convolution, and w p (x) represents a one-dimensional Hanning autoconvolution window in the row direction, w p (y) represents a one-dimensional Hanning self-convolution window in the column direction, and · represents the dot product operation. For ease of explanation, the expression for a one-dimensional Hanning self-convolution window is given here. A two-dimensional Hanning self-convolution window can be achieved by multiplying two one-dimensional Hanning self-convolution windows in the row and column directions (i.e., the length or width directions of the two-dimensional window). As a raised cosine window, a discrete-time Hanning window with a window length or width of M is defined as:

[0047]

[0048] Here, m represents the position of the discrete sampling point. Typically, M is set to an integer multiple of the fringe period to reduce spectral leakage caused by non-integer multiple period truncation. w(m) can represent a one-dimensional w(x) or w(y). Note that the length and width of the two-dimensional window can be different, but to better achieve consistent window size after self-convolution, the window length in the row and column directions is set to be consistent, i.e., the fringe truncation is a square.

[0049] The proposed discretized pth-order HSCW is defined as p discrete Hanning windows implemented through p-1 convolution operations, and is defined as follows:

[0050]

[0051] Here, * denotes convolution operation, p is the order of self-convolution, and M is the length of the parent window w(M) participating in the HSCW. According to the temporal convolution theorem, the length of the sequence resulting from the convolution of two window functions of length M, w(M)*w(M), is 2M-1. Zero padding can be applied to the resulting sequence to obtain a second-order HSCW of length 2M. Similarly, the sequence w P The length is pM-1, and a pth-order HSCW of length N=pM can be generated by padding with p-1 zeros.

[0052] The DFT of a Hanning window of length M can be expressed as:

[0053]

[0054] Where ω is the angular frequency, W R (ω)=[sin(ωM / 2) / sin(ω / 2)]exp -jω(M-1) / 2 It is a rectangular window DTFT. The spectrum of the Hanning window is a linear combination of the spectra of the rectangular windows. The three rectangular window spectra are added together, causing the side lobes to cancel each other out, the energy to be concentrated in the main lobe, the side lobes to decrease, and the main lobe width to increase. According to the convolution theorem, time-domain convolution is equal to frequency-domain multiplication. Through the self-convolution of the Hanning window and frequency-domain sampling, ω in equation (9) is replaced by 2kπ / N, where k is the exponent of the discrete spectral line. Therefore, the frequency domain representation of the pth-order HSCW is:

[0055]

[0056] Where k = 0, 1, 2…N-1. The HSCW consists of three components: the first is the main lobe of the window, and the last two are the left and right side lobes of the window, which are symmetrical about the origin in the frequency domain. As shown in formula (10), the frequency response of the pth-order HSCW is a periodic function with a period of 2π and is symmetrical about the origin. Therefore, its MLW is twice the distance between the nearest zero points on both sides of the origin in the frequency domain.

[0057] According to equations (9) and (10), the amplitude function of the frequency response of the pth-order HSCW is:

[0058]

[0059] S3: Use equation (12) to weight the sinusoidal fringe image I(x,y) to obtain the windowed fringe pattern.

[0060]

[0061] S4: Use equation (13) to analyze the windowed stripe pattern. The process begins by performing an FFT on the windowed fringe pattern. A two-dimensional bandpass filter with low sidelobe characteristics is then selected to filter out the zero frequency while minimizing noise near the fundamental frequency and extracting the positive first-order spectrum containing phase information. Finally, an inverse Fourier transform (IFT) is performed on the positive first-order spectrum to obtain the spatial distribution of the windowed fringes containing only the target phase information.

[0062]

[0063] in and H represents the inverse and forward Fourier transform operators, respectively. +1 This indicates a bandpass filter that extracts the positive first-order spectrum, with its center located at the fundamental frequency peak. The spatial distribution of the positive first-order spectrum, which has been filtered out of other interference terms and contains only the target phase information, is given. Then, the wrapped phase is obtained using equation (14).

[0064]

[0065] In equation (14), Im[] and Re[] represent the stripe pattern, respectively. The imaginary and real parts;

[0066] S5: Phase unwrapping algorithms are crucial for real-time processing and high-precision misalignment measurement. Therefore, the Weighted Least Squares (WLS) phase unwrapping algorithm is chosen to obtain the continuous phase of the fringe pattern. It addresses phase discontinuities by introducing weighting coefficients. These weighting coefficients are determined based on factors such as noise level and signal strength, and are used to limit the influence of residual points and noise. WLS constructs an iterative formula based on the Poisson equation to control the propagation of smoothing errors and avoid the propagation of errors from low-quality points. By appropriately setting the weighting coefficients, WLS can optimize the objective function, thereby optimizing the phase unwrapping results. Therefore, WLS is widely used in phase unwrapping and is an effective and robust unwrapping method. The WLS phase unwrapping algorithm is used to unwrap the wrapped phase. The stripe pattern is obtained through processing. continuous phase

[0067] S6: When continuous phase When applied to the alignment process of wafers and masks, based on continuous phase... Using formula (4), the phase difference related to the fringe displacement is obtained.

[0068] S7: Since the grating periods P1 and P2 of the wafer and mask alignment marks are known, the continuous phase values ​​of the fringe pattern obtained from S5 and S6 can be used to calculate the following using formula (4): Figure 2The phase difference between the left and right fringes of the misaligned moiré fringes shown in part (c) can be calculated using formula (5) to determine the actual misalignment value. Based on the phase difference Δφ, the misalignment value Δy between the wafer and the mask is calculated and transmitted via a feedback system to the piezoelectric ceramic driver connected to the image processing system to control the alignment of the wafer and the mask. Specific misalignment values ​​are obtained through algorithm processing and transmitted via a feedback system to the piezoelectric ceramic driver (PZT) connected to the image processing system to achieve precise alignment control. Due to interference from lighting and marking manufacturing conditions, the fringe contrast may decrease. Morphological methods can be used to improve contrast. If the fringes are subject to severe noise interference, spatial filtering techniques can be considered for noise reduction without losing key information of the original image. By using a self-developed program, misalignment can be automatically processed and adjusted to achieve closed-loop control.

[0069] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0070] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0071] In this embodiment, in order to perform simulation verification of the proposed method, when the method proposed in this invention is not used, the alignment accuracy is as follows: Figure 3 As shown, its alignment error is very large, making it unsuitable for high-precision photolithography alignment applications. Therefore, a time-domain amplitude and amplitude-frequency response of the first-order HSCW (also known as the classic Hanning window), second-order HSCW, third-order HSCW, and fourth-order HSCW with a parent window length M = 220 are established as follows: Figure 4 Parts (a) and (b) of the figure are shown. The figure labels the approximate values ​​of the sidelobe peak level and sidelobe attenuation rate of the HSCW. Its sidelobe peak level A... PSLL It has an approximate numerical relationship with the convolution order p: A psll ≈-32p, the sidelobe decay rate has an approximate numerical relationship with the convolution order p: D SLRR ≈18p. Self-convolution of the window function can improve sidelobe performance, and the sidelobe performance further improves with increasing convolution order. By using the 2D-HSCW proposed in this invention, when the fringe period is P... mWhen the period is 44, even with non-integer multiples of the period truncation, the accuracy of misalignment measurement is greatly improved, and it shows a significant improvement with increasing convolution order. Figure 5 As shown.

[0072] In summary, the present invention provides a spectral leakage suppression method for a two-dimensional Hanning self-convolution window weighted fringe pattern for wafer and mask alignment. Simulation analysis shows that the present invention can effectively suppress spectral leakage of the fringe pattern to achieve high-precision phase extraction, and further achieve high-precision photolithography alignment.

Claims

1. A weighted fringe pattern phase extraction method based on spectral leakage suppression using a two-dimensional Hanning self-convolution window, characterized in that, Includes the following steps: S1: Use a CMOS camera to acquire a single sinusoidal fringe image I(x,y), where x and y are the pixel coordinates in the row and column directions of the sinusoidal fringe image, respectively; S2: Construct a two-dimensional Hanning autoconvolution window w for the sinusoidal fringe image I(x,y) using equation (1). p (x,y): w p (x,y)=w p (x)·w p (y) (1) In equation (1), p is the order of the self-convolution, and w p (x) represents a one-dimensional Hanning autoconvolution window in the row direction, w p (y) represents a one-dimensional Hanning self-convolution window in the column direction, and · represents the dot product operation; S3: Use equation (2) to weight the sinusoidal fringe image I(x,y) to obtain the windowed fringe pattern. S4: Using equation (3) to analyze the windowed stripe pattern The process yields a spatial distribution of windowed fringes containing only target phase information. In equation (3), H +1 This represents a bandpass filter that extracts the positive first-order spectrum. and Let represent the forward and inverse two-dimensional fast Fourier transform operators, respectively, and then use equation (4) to obtain the wrapping phase. In equation (4), Im[] and Re[] represent the stripe pattern, respectively. The imaginary and real parts; S5: Use the weighted least squares phase unwrapping algorithm to unwrap the wrapped phase. The stripe pattern is obtained through processing. continuous phase 2. An application of the weighted fringe pattern phase extraction method based on two-dimensional Hanning self-convolution window spectral leakage suppression as described in claim 1, characterized in that, It is applied during the alignment process of wafers and masks, and is performed according to the following steps: S6: Based on continuous phase The phase difference associated with the fringe displacement is obtained. S7: Based on phase difference The misalignment value Δy between the wafer and the mask is calculated and transmitted to the piezoelectric ceramic driver connected to the image processing system via a feedback system to control the alignment of the wafer and the mask.

3. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the stripe pattern phase extraction method of claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the stripe pattern phase extraction method according to claim 1 or 2.

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