Wafer three-dimensional shape detection method based on sparse sampling

Abstract

The invention provides a wafer three-dimensional shape detection method based on sparse sampling, and the method comprises the steps: 1, carrying out the longitudinal scanning of each pixel point of a to-be-detected wafer based on a white light interference measurement method, and obtaining an interference signal # imgabs0 # in a longitudinal scanning range at a certain sampling step length; 2, during longitudinal scanning, a sparse sampling mode of equal-phase interval sampling is adopted, the sampling interval used by scanning sampling is n more than the full sampling interval, and sparse sampling interference signals are obtained; and 3, processing a sparse sampling interference signal obtained from the surface of the wafer to be measured by using an improved gravity center method, and reconstructing the three-dimensional shape of the wafer.

Description

Technical Field

[0001] The present invention relates to the field of wafer three-dimensional morphology detection, and in particular to a wafer three-dimensional morphology detection method based on sparse sampling. Background Art

[0002] In semiconductor manufacturing, overlay accuracy is one of the core performance indicators of the lithography system. As the chip feature size decreases, the overlay accuracy requirements become more and more stringent. Changes in wafer surface morphology and errors in the wafer stage will significantly affect the overlay accuracy. Especially in large field of view exposure systems, subtle morphological changes may lead to the accumulation of overlay errors, that is, the positional misalignment between different lithography layers, which in turn affects the performance and reliability of the chip. The key factors affecting the wafer surface morphology include the flatness of the wafer stage, changes in wafer thickness, and changes in wafer surface shape caused by particle contamination. In order to effectively control the surface morphology of the wafer and improve the overlay accuracy, the wafer stage, wafer thickness and surface morphology must be accurately measured. Interferometry is an optical technology that measures the surface profile, thickness and texture of an object with extremely high precision, and can achieve nanometer or even sub-nanometer resolution. Its core principle is to use the interference of two coherent light beams to generate fringes, and calculate the height difference at different positions on the surface by analyzing the phase information of the interference fringes, and then reconstruct the three-dimensional morphology of the object. For wafer topography measurement, high-precision topography data can effectively help control the alignment and exposure of each layer, thereby reducing overlay errors.

[0003] Short coherence interferometry (LCSI) has shown some unique advantages in the field of interferometry. LCSI uses the short coherence length of broadband light sources to localize the interference signal in time, thus avoiding the 2π ambiguity problem in traditional phase-shift interferometry. However, since LCSI relies on a scanning mechanism to adjust the optical path difference between the reference arm and the measurement arm, multiple scans and image acquisitions will significantly increase the measurement time. Especially when using narrow-band light sources (such as SLD), the temporal coherence length is about 10 , hundreds of images need to be collected to ensure measurement accuracy. This makes the data processing process complicated and time-consuming, which is particularly prominent compared to traditional white light. Since the interference signal is essentially an approximation of a continuous signal, this method requires a smaller sampling interval to obtain high-precision measurement results. However, this also brings a large amount of sampling data and high computational costs.

[0004] In order to shorten the data acquisition time, how to expand the sampling interval of the signal while maintaining the measurement accuracy has become the focus of current research. In order to improve the sampling efficiency, domestic and foreign research first proposed the spatial frequency domain method (FDA). This method extracts the phase information of the high-frequency region through Fourier transform and fits it to obtain the surface height difference. Experiments show that FDA is less sensitive to the sampling interval, and can effectively process even if the signal frequency is lower than the Nyquist sampling frequency, thereby achieving a larger sampling interval. However, the sampling interval extension range of FDA is still limited. With the development of deep learning technology, it has also been applied to sparse sampling interferometry. By calculating the envelope of the sub-Nyquist sampling signal, a sampling interval of 300 nanometers was used in a white light interferometry system to achieve results better than FDA, providing a new idea for improving the efficiency of interferometry. However, this method mainly relies on simulation data for training, and may face the problem of insufficient generalization ability in actual scenarios. Summary of the invention

[0005] In order to overcome the limitations of the above-mentioned current technologies, the present invention will provide a wafer three-dimensional morphology detection method based on sparse sampling, whose sampling interval can span multiple cycles, and the core adopts an improved center of gravity method to achieve accurate and rapid wafer three-dimensional morphology detection. The short coherence interference wafer three-dimensional morphology detection method based on sparse sampling proposed in the present invention adopts a sparse sampling method across cycles, which reduces the number of sampling points, thereby reducing the computational burden of data collection and processing. Compared with full sampling, sparse sampling requires less data to be processed, but by improving the correction of the center of gravity method, efficiency can be improved while maintaining detection accuracy.

[0006] Based on this, the present invention provides a wafer three-dimensional shape detection method based on sparse sampling, the method comprising:

[0007] Step 1: Based on the white light interferometry method, each pixel point of the wafer to be measured is scanned longitudinally, and the interference signal is obtained at a certain sampling step length within the longitudinal scanning range. ;

[0008] Step 2: During longitudinal scanning, a sparse sampling method with equal phase interval sampling is adopted, and the sampling interval used in the scanning sampling is n cycles more than the full sampling interval, so as to obtain a sparse sampling interference signal;

[0009] Step 3: The sparsely sampled interference signal obtained from the surface of the wafer to be tested is processed using an improved center of gravity method to reconstruct the three-dimensional morphology of the wafer.

[0010] The present invention has the following beneficial effects:

[0011] The general interferometric scanning method is based on the Nyquist sampling theorem to obtain the interference signal on the surface of the object to be measured, and then restore the information of the complete interference signal through the reconstruction algorithm. The sampling theorem can ensure that high-density data points are obtained on each interference fringe to capture all the details of the interference signal. However, under practical conditions, this method has certain challenges in the storage, processing and display of data volume, especially the long-stroke low-coherence measurement method, which leads to limited detection efficiency. In order to break through the limitations of the Nyquist sampling theorem, the three-dimensional shape detection method based on sparse sampling is gradually used in three-dimensional shape measurement. Its sparse sampling method significantly speeds up the measurement speed. However, when the sampling frequency is lower than the Nyquist frequency, the signal components higher than the Nyquist frequency cannot be correctly sampled and reconstructed, but will be aliased to a lower frequency position, that is, noise aliasing. This phenomenon will cause the reconstructed signal to be different from the original signal, resulting in errors and a significant reduction in the signal-to-noise ratio. Because the original data is missing in the undersampled signal, this reduction in the signal-to-noise ratio is usually unreasonable. When the sampling interval is much larger than the full sampling interval, the traditional reconstruction algorithm is obviously not enough to solve the problem of missing data, and it also clearly shows the disadvantage of being sensitive to larger sampling intervals.

[0012] According to Nyquist sampling theory, the sampling frequency should be greater than twice the signal frequency to reconstruct the signal. If the period of I(z) is , then the maximum sampling step size is . For example, if the central wavelength of the light source is 800 nm, the maximum step length is 200 nm. In fact, since the interference light goes back and forth in the optical path, its maximum sampling step length should be , that is, 100 nm. Therefore, when the scanning distance is 100 μm, the number of image superpositions reaches 1000, and as the scanning distance increases, the number of image superpositions increases further. If the scanning step length is increased to 1.7 μm, only 36 images need to be obtained, which can significantly speed up the scanning and the acquisition of interference signals.

[0013] The sparse sampling theory is to use a sampling interval larger than the full sampling interval to significantly reduce the number of image stacks. The sparse sampling method of equal-phase interval sampling is:

[0014] ,

[0015] ,

[0016] in, is the interference fringe period: , represents the number of cycles of the complete interference fringe spanned; Refers to the full sampling interval, It represents the sampling density within the interference fringe period, which follows the Nyquist sampling theorem. During interferometric measurement, the light beam converges on the surface of the object to be measured and reflects on the surface, doubling the effective optical path, which results in doubling the actual interference period. Therefore, in interferometric measurement, m is equal to 4. This sampling strategy allows the sampling interval to span multiple periods, which can greatly increase the scanning speed, improve the shape detection rate, and fully retain the signal phase information. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of a wafer three-dimensional shape detection method based on sparse sampling according to the present invention;

[0018] Figure 2 This is a diagram of an experimental device for a wafer three-dimensional topography detection method based on sparse sampling according to the present invention;

[0019] Figure 3 It is a height simulation diagram of each pixel point when the sparse sampling interval and the full sampling interval span n cycles of the present invention;

[0020] Figure 4 It is the RMS diagram of the restored height under different n values ​​when the sparse sampling interval and the full sampling interval span n cycles;

[0021] Figure 5 It is a schematic diagram of the influence of interference microscopes with different numerical apertures on the highly restored structure when the sampling interval spans four periods of the present invention;

[0022] Figure 6 This is the RMS diagram of height restored by sparse sampling at different numerical apertures when the sampling interval spans four cycles.

[0023] Among them, 201 is a CCD camera, 202 is a tube lens, 203 is a spectroscope, 204 is a micro-interference objective lens, 205 is a wafer to be measured, 206 is an illumination light source, 207 is a collimating lens, 208 is a reference mirror, and 209 is a reference surface. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above-mentioned purpose, the present invention adopts the following technical scheme.

[0025] Figure 1 FIG. 1 is a flow chart of a wafer three-dimensional morphology detection method based on sparse sampling provided by an embodiment of the present disclosure. Figure 1As shown, the wafer three-dimensional morphology detection method based on sparse sampling includes:

[0026] Step 1: Based on the white light interferometry method, each pixel point of the wafer to be measured is vertically scanned, and the interference signal is obtained with a certain scanning step length within the vertical scanning range. ;

[0027] Step 2: Use sparse sampling with equal phase interval sampling. The full sampling interval of the interference signal is determined by the Nyquist sampling theory, and its interval is ; The sampling interval used by sparse sampling is n cycles more than the full sampling interval, which is , and obtain the sparsely sampled interference signal;

[0028] Step 3: The sparsely sampled interference signal obtained from the surface of the wafer to be tested is processed using the improved center of gravity method to reconstruct the three-dimensional morphology of the wafer to verify the effectiveness of the equiphase interval sampling method.

[0029] Figure 2 A diagram showing an experimental setup of a wafer three-dimensional topography detection method based on sparse sampling provided in an embodiment of the present disclosure.

[0030] like Figure 2 As shown, the present invention includes: a CCD camera 201, a tube lens 202, a beam splitter 203, a microscopic interference objective lens 204, a wafer to be measured 205, an illumination light source 206, a collimator 207, a reference mirror 208, and a reference surface 209. Among them, the CCD camera 201 is located at the focal plane of the tube lens 202, and is used to collect interference images. The microscopic interference objective lens 204 is used to image the surface of the wafer to be measured 205, the beam splitter 203 is used to separate the light beam, the illumination light source 206 is used to provide a light source for the measurement system, and the wafer to be measured 205 is located at the focal plane of the interference objective lens 204. The specific interference principle is as follows: a beam of light from a multi-wavelength broadband light source with a wavelength of 700nm to 1100nm passes through the collimator 207 to form parallel light, which improves the illumination of the measurement system. Then, it is reflected by the beam splitter 203, and the light emitted from the objective lens passes through the uncoated area of ​​the reference surface 209 and enters the surface of the reference mirror 208. Since the reference mirror 208 is coated with a semi-transparent and semi-reflective film, after the beam splitting effect of the beam splitter, part of the incident light is reflected back to the reference mirror surface, and is reflected by the high-reflective film at the center of the reference surface 209, and returns to the optical path along the original path as the reference light; the other part of the incident light passes through the reference mirror 208 and converges to the surface of the wafer 205 to be measured, and returns to the optical path after being reflected by the sample surface as the test light. The reference light and the test light meet in the optical path and interfere, generating interference fringes. The scanning mechanism is used to move the entire tube mirror with high precision at a fixed vertical step length to generate interference images at different scanning positions. The intensity of the light beam changes with the change of the height of the measurement surface, which is called an interference pattern.

[0031] Figure 3 The figure shows a simulation comparison of the height of each pixel point and the full sampling height when the sparse sampling interval and the full sampling interval span n cycles: (a) is the height value obtained when spanning one cycle, (b) is the height value obtained when the sampling interval spans two cycles, (c) is the height value obtained when the sampling interval spans three cycles, and (d) is the height value obtained when the sampling interval spans four cycles.

[0032] like Figure 3 As shown, when the sparse sampling interval and the full sampling interval span a cycle, the calculated height value is consistent with the height value calculated under full sampling. The specific implementation method is:

[0033] ,

[0034] In the formula, is the central wave number, is the central wavelength, is the angle between the light ray and the optical axis ( ), full width at half maximum , is the spectrum width, , is the scanning center position, are discrete positions in the scan range.

[0035] In this specific example, the central wavelength is 800nm, the spectrum width is 0.02μm, the numerical aperture NA of the 10x interference objective is 0.15, the longitudinal scanning range is 60μm, and the object to be measured is a three-dimensional step surface structure with a theoretical height of 2μm. The scanning step length of sparse sampling is:

[0036] ,

[0037] ,

[0038] in, is the interference fringe period, , is the full sampling interval.

[0039] Figure 3 Different n values ​​have different specific sampling intervals and sampling points, as shown in Table 1:

[0040] Table 1

[0041]

[0042] It can be seen from Table 1 that as the value of n increases, the sampling points of the interference signal are significantly reduced. The sampling interval across four cycles is 17 times the full sampling interval, which effectively improves the sampling efficiency.

[0043] Furthermore, in order to simulate the error in actual measurement, the interference signal Random Gaussian white noise is used:

[0044] ,

[0045] in, The mean is 0 and the variance is After adding random noise, the robustness of the invention can be verified, that is, the stability after random interference.

[0046] Based on the short coherence interference model, a series of interference signals I= , and take its first-order difference:

[0047] ,

[0048] The trend of signal changes with scanning position can be captured.

[0049] Furthermore, the obtained difference Square it:

[0050] ,

[0051] The square of the difference is used as a weight to calculate the centroid position:

[0052] ,

[0053] Squaring the difference enhances the peak value of the signal and reduces the interference of noise.

[0054] Compute the normalized centroid position using a weighted average of the squared differences:

[0055] ,

[0056] in, is the weighted sum, is the total weight, is the normalized center of gravity position.

[0057] The normalized center of gravity position calculated by Get the height value of each pixel of the wafer:

[0058] ,

[0059] in, is the sampling step size for sparse sampling.

[0060] By comparing the simulated height values ​​of full sampling and sparse sampling, it can be seen that the method of the present invention can accurately detect the height of the sparse sampling intervals across four cycles. At the same time, as the sampling interval increases, the fluctuation on the step plane gradually increases, which proves the feasibility of the equal-phase interval sampling method.

[0061] Figure 4 The figure shows the change of the root mean square of the step surface height as the value of n changes when the sparse sampling interval and the full sampling interval provided by the example of the present disclosure span n cycles.

[0062] like Figure 4 As shown, through sparse sampling across multiple cycles and multiple simulations, the root mean square RMS measured by the method of the present invention is within 1.1nm, which shows that the present invention can accurately restore the surface morphology of the object to be measured under cross-cycle sampling conditions, and also shows that the present invention has high measurement repeatability and high stability.

[0063] Figure 5 , Figure 6 The figure shows the influence of the interference microscope with numerical apertures of 0.1, 0.2, 0.3 and 0.4 on the height measurement when the sampling interval spans four periods provided by the embodiment of the present disclosure. Figure 5 In the figure, (a) is the height value obtained when the NA is 0.1, (b) is the height value obtained when the NA is 0.2, (c) is the height value obtained when the NA is 0.3, and (d) is the height value obtained when the NA is 0.4.

[0064] like Figure 5 and Figure 6 As shown in the figure, by comparing the heights measured at different numerical apertures, it is found that as the numerical aperture increases to 0.4, the height restoration fluctuation of the step plane is large, but the root mean square of the height difference is still 3nm, which shows that the equiphase-interval sparse sampling method has good adaptability and can accurately restore the surface morphology of the object to be measured under different optical settings.

[0065] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A wafer three-dimensional morphology detection method based on sparse sampling, characterized in that: The method comprises the following steps: Step 1: Based on the white light interferometry method, each pixel point of the wafer to be measured is scanned longitudinally, and the interference signal is obtained at a certain sampling step length within the longitudinal scanning range. ; Step 2: During longitudinal scanning, a sparse sampling method with equal phase interval sampling is adopted, and the sampling interval used in the scanning sampling is n cycles more than the full sampling interval, so as to obtain a sparse sampling interference signal; Step 3: The sparsely sampled interference signal obtained from the surface of the wafer to be tested is processed using an improved center of gravity method to reconstruct the three-dimensional morphology of the wafer.

2. The wafer three-dimensional shape detection method according to claim 1, characterized in that: In the step 1, the white light interferometry method is specifically as follows: the wavelength range used is 700nm to 1100nm, the longitudinal scanning is within the range of 700μm, and the upper and lower surface morphologies of the wafer are scanned to measure the upper and lower surfaces of the wafer; The short coherence interference model of each pixel point on the upper and lower surfaces of the wafer is expressed as: ， In the formula, is the central wave number, is the central wavelength, is the angle between the light ray and the optical axis, , full width at half maximum , is the spectrum width, , is the scanning center position, are discrete positions in the scan range.

3. The wafer three-dimensional shape detection method according to claim 2, characterized in that: In step 2, if the z-direction scanning range is , then the scanning step size based on sparse sampling with equal phase intervals is for: ， ， in, is the interference fringe period, ; is the full sampling interval based on Nyquist sampling theory, represents the sampling density within the interference fringe period, that is, represents the sampling step length within one interference fringe period, Represents the number of complete interference fringe cycles spanned.

4. The wafer three-dimensional shape detection method according to claim 3, characterized in that: A series of interference signals are obtained within the longitudinal scanning range = , for the interference signal Use random white Gaussian noise: ， in, The mean is 0 and the variance is Gaussian noise; The three-dimensional morphology reconstruction method based on the improved centroid method is as follows: firstly, the interference signal after noise processing is first-order differentiated and squared: ， From this, the changing trend of the signal with the scanning position is captured; The square of the difference is used as a weight to calculate the centroid position: ， For the peak part of the enhanced signal after square difference, the normalized centroid position is calculated using the weighted average of square difference: ， in, is the weighted sum, is the total weight, To normalize the center of gravity position, the normalized center of gravity position obtained is Get the height value of each pixel of the wafer: ， in, is the sampling step size of the longitudinal scan.

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