Calculation method for optimal focusing height and corresponding size of light spot in graphics-free wafer defect detection equipment

Abstract

The invention discloses a method for calculating the optimal focusing height and the corresponding size of a light spot in non-graphic wafer defect detection equipment. The method comprises the following steps of: setting a focusing height range and a circulation step pitch; in a set focusing height range, uniformly changing the focusing height of the laser spot according to the circulation step pitch to circularly detect and scan the wafer to obtain original scanning data and defect position information; each defect image is sampled in the radial direction and the tangential direction of the wafer, and Gaussian fitting is carried out on a sampling signal value sequence to calculate the light spot width; judging whether all defects are detected or not, and estimating and calculating a light spot width statistical value by adopting a kernel density function according to the obtained two groups of light spot width sequences; and calculating the optimal focusing height of the light spot and the corresponding light spot width by adopting quadratic curve fitting according to the light spot width statistical value sequence under different focusing heights. According to the method, the optimal focusing height and the corresponding light spot size are obtained in one calculation process, and the calculation efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of wafer defect detection technology, and in particular to a method for calculating the optimal focusing height and corresponding size of a spot in a patternless wafer defect detection device. Background Technology

[0002] In the inspection of defects on patternless wafers, a laser beam modulated with a specific wavelength, shape, size, and power is used to illuminate the wafer surface from a specific incident angle. A special optical module receives the scattered signals to identify defects. The projection of the laser beam onto the wafer surface is called the laser spot, and its energy distribution generally approximates a Gaussian distribution. To ensure the accuracy of defect location calculation, the geometric parameters of the laser spot need to be precisely measured. Furthermore, to detect as many defects as possible, the height of the wafer plane needs to be adjusted to ensure its surface is at the optimal focusing height.

[0003] Currently, the main method for measuring spot size is to directly illuminate the surface of a CCD / CMOS sensor with a laser beam, and then calculate the spot size by analyzing the resulting image data using image processing methods. However, this method has the following shortcomings:

[0004] (1) Additional hardware is required, such as CCD / CMOS sensors, which is costly;

[0005] (2) The physical properties of CCD / COMS surface are significantly different from those of wafer surface, and the measurement results cannot be used directly.

[0006] (3) The sensor pixel size is large and the light spot imaging resolution is low, which leads to low measurement accuracy.

[0007] Currently, the optimal focusing height of the laser spot is mainly calculated by manually adjusting the wafer height and determining the approximate location of the optimal focusing height based on the number of detected defects. However, this method has the following shortcomings:

[0008] (1) The wafer height needs to be manually adjusted multiple times, which is time-consuming;

[0009] (2) Only a relatively rough focus height can be obtained, and the accuracy is low.

[0010] Furthermore, the optimal focusing height and corresponding spot size currently need to be measured and calculated separately, which is inefficient.

[0011] Therefore, there is an urgent need to provide a new method for calculating the optimal focusing height and corresponding size of the light spot to solve the above problems. Summary of the Invention

[0012] The technical problem to be solved by the present invention is to provide a method for calculating the optimal focusing height and corresponding size of the spot in a patternless wafer defect detection device, which can obtain the optimal focusing height and its corresponding spot size in one calculation process, thereby improving calculation efficiency.

[0013] To solve the above-mentioned technical problems, one technical solution adopted by the present invention is: to provide a method for calculating the optimal focusing height and corresponding size of the light spot in a patternless wafer defect inspection device, comprising the following steps:

[0014] S1: Set the focus height range and cycle step size of a patternless wafer defect inspection device;

[0015] S2: Within the set focus height range, the focus height of the laser spot is uniformly changed according to the cycle step to perform cyclic detection scanning of the wafer, thereby obtaining the original scan data and defect location information;

[0016] S3: For each defect image, samples are taken along the radial and tangential directions of the wafer, and the sampled signal value sequence is Gaussian fitted to calculate the spot width;

[0017] S4: Determine whether all defects have been detected. If yes, obtain two sets of spot width sequences; otherwise, return to step S3.

[0018] S5: Based on the two sets of spot width sequences obtained in step S4, the final spot width is calculated using kernel density function estimation.

[0019] S6: Determine whether all focus height cyclic measurements have been completed. If yes, obtain the statistical values ​​of the spot width under different focus heights. Otherwise, return to step S2.

[0020] S7: Based on the two sets of spot width statistical value sequences obtained in step S6, the optimal focus height of the spot is calculated by quadratic curve fitting.

[0021] S8: Calculate the spot width corresponding to the optimal focus height based on the fitted quadratic curve model.

[0022] In a preferred embodiment of the present invention, step S3 specifically includes:

[0023] S301: The distribution expression of the Gaussian fitting of the sampled signal value sequence of the light spot profile is:

[0024]

[0025] Where I is the signal strength, A is the signal amplitude, μ is the expected value, σ is the standard deviation, and noise is the additive noise;

[0026] The width of the Gaussian spot along both the radial and tangential directions of the wafer is four times the standard deviation of the Gaussian distribution that its respective cross-section conforms to, i.e.:

[0027] W R =4σ R

[0028] W T =4σ T

[0029] S302: For the sampled signal value sequence G = [g1, g2, ... g...] n The minimum value in the sequence is calculated as additive noise, and then each value is subtracted from this minimum value to obtain a new sequence, i.e.:

[0030] Y = G - min(G) + 1

[0031] The simplified curve model corresponding to this sequence is as follows:

[0032]

[0033] Where x is the planar distance corresponding to the sampled signal value in the Gaussian model, in micrometers;

[0034] S303: Taking the logarithm on both sides of the simplified curve model yields the linearized model:

[0035] z = a0 + a1x + a2x 2

[0036]

[0037] S304: Construct the following matrix based on the linearized sequence:

[0038]

[0039] Where B is the coefficient matrix, W is the weight matrix, L is the observation matrix, and p is the parameter matrix, the normal equations are constructed according to the least squares criterion as follows:

[0040] p = (B T WB) -1 (B T WL)

[0041] Solving this equation will give the values ​​of a0, a1, and a2;

[0042] S305: Based on the linearized expression of the model, the parameters of the Gaussian curve are derived as follows:

[0043]

[0044] μ=a1σ 2

[0045]

[0046] In a preferred embodiment of the present invention, in step S5, for the two sets of spot width sequences [w1, w2… w] obtained in step S4 n Its kernel density estimation function is:

[0047]

[0048] Among them, K h Let w be the kernel function, and n be the number of elements in the spot width sequence. By calculating the kernel density estimation curve for different w values ​​in sequence, the w value corresponding to the maximum value is the statistical value of the spot width.

[0049] In a preferred embodiment of the present invention, in step S7, for the two sets of spot width statistical value sequences obtained in step S6, the least squares method is used to perform quadratic curve fitting, and the quadratic curve model is set as follows:

[0050] w = b0 + b1z + b2z 2

[0051] For a given width statistics sequence [w1, w2… w n The matrix is ​​constructed as follows based on the least squares principle:

[0052]

[0053] Where C is the coefficient matrix, L is the observation matrix, and p is the parameter matrix; the normal equations are constructed according to the least squares criterion as follows:

[0054] p=(C T C) -1 (C T L)

[0055] From this, the parameters b0, b1, and b2 of the conic section can be obtained, and then the optimal focusing height can be determined:

[0056]

[0057] Furthermore, in step S8, the spot width corresponding to the optimal focus height is calculated based on the fitted quadratic curve model:

[0058] w best =b0+b1z best +b2z best

[0059] The beneficial effects of this invention are as follows: This invention proposes a new method for calculating the laser spot size and optimal focusing height in a patternless wafer defect detection device. This method has the following advantages:

[0060] (1) The calculation of the optimal focusing height of the light spot and its corresponding light spot size is integrated into a single calculation process, which improves the calculation efficiency;

[0061] (2) The optimal focus height of the spot and its corresponding spot size can be calculated simply by using the normal scanning process in the patternless wafer defect detection equipment, without the need to add new hardware equipment, thus reducing hardware costs.

[0062] (3) By pre-setting the focus height range and cycle step distance, automated multiple measurements were achieved, reducing time costs;

[0063] (4) The size of the light spot is calculated by sampling the defect imaging, which improves the utilization rate of measurement data;

[0064] (5) Calculate a pair of spot widths for each defect, and then use the kernel density function to estimate the final spot width value based on the spot widths corresponding to all defects, which improves the accuracy of spot size calculation.

[0065] (6) Curve fitting was used to calculate the optimal focusing height of the light spot, which improved the calculation accuracy. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the calculation method for the optimal focusing height and corresponding dimensions of the light spot in the patternless wafer defect detection equipment of the present invention.

[0067] Figure 2 This is a schematic diagram of the approximate Gaussian distribution of the sampled signal value sequence of the light spot profile;

[0068] Figure 3 This is a schematic diagram showing the radius distribution of the Gaussian spot along the tangential and radial directions of the wafer;

[0069] Figure 4 This is a schematic diagram of the kernel density estimation curves calculated from different given light spot width sequences;

[0070] Figure 5 This is a curve model diagram of quadratic curve fitting using the least squares method on the statistical value sequence of light spot width. Detailed Implementation

[0071] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0072] Please see Figure 1 The embodiments of the present invention include:

[0073] A method for calculating the optimal focusing height and corresponding dimensions of a spot in a patternless wafer defect inspection device, characterized by comprising the following steps:

[0074] S1: Set the focus height range and cycle step size of a patternless wafer defect inspection device;

[0075] The cycle step distance is the change in focus height between two consecutive measurements.

[0076] S2: Within the set focus height range, the focus height of the laser spot is uniformly changed according to the cycle step to perform cyclic detection scanning of the wafer, thereby obtaining the original scan data and defect location information;

[0077] Patternless wafer defect inspection equipment typically uses point scanning to collect scattered signals from the wafer surface. The sampling trajectory of the laser spot relative to the wafer is an Archimedean spiral, with the equation:

[0078]

[0079] Where r0 is the scan starting radius, θ is the rotation angle, and pitch is the step size. Different step sizes can be used for scanning at different yield rates. During the scanning process, the acquisition device collects the scattered signals from the wafer surface at a certain frequency to generate signal values. By analyzing the outliers in the signal, the type of defect can be identified and the location information of the defect on the wafer can be calculated.

[0080] S3: Based on the defect location information, each defect is imaged and sampled along the radial and tangential directions of the wafer. The sampled signal value sequence is then fitted with Gaussian to calculate the spot width.

[0081] Preferably, the variation range of the cycle step size is generally 10μm-1000μm. To ensure the accuracy of defect coordinate calculation, the size of the laser spot also needs to match the step size, typically twice the step size. Since most defects on the wafer surface are very small, generally less than 1μm, during the scanning process, a defect will be scanned multiple times along both the tangential and radial directions of the wafer. The signal intensity generated each time depends on the relative position of the defect and the laser spot during each scan. Arranging these in the spatial order of the scan yields an image reflecting the energy distribution of the laser spot. Sampling along the radial and tangential directions of the wafer yields two approximately Gaussian one-dimensional sequences, such as... Figure 2 As shown.

[0082] The Gaussian distribution expression that the sequence of light spot profile sampling signal values ​​follows is:

[0083]

[0084] Where I is the signal strength, A is the signal amplitude, μ is the expected value, σ is the standard deviation, and noise is the additive noise.

[0085] like Figure 3 As shown, the radii of the Gaussian spot along both the tangential and radial directions of the wafer decrease from the strongest signal value A+ noise to A / e towards the periphery. 2 From the distance at +noise, it can be deduced that the width of the Gaussian spot along both the radial and tangential directions of the wafer is four times the standard deviation of the Gaussian distribution that its respective cross-section conforms to. That is:

[0086] W R =4σ R

[0087] W T =4σ T

[0088] In summary, the spot size derived from the defect imaging can be obtained simply by performing Gaussian fitting on the sampled signal sequence and calculating its standard deviation parameter.

[0089] The Gaussian fitting method used in this example is the least squares fitting method, and its calculation process is as follows:

[0090] (1) Simplified model. For the sampled signal value sequence G = [g1, g2, ... g...] n The minimum value in the sequence is calculated as additive noise, and then subtracted from each value to obtain a new sequence.

[0091] Y = G - min(G) + 1

[0092] The curve model corresponding to this sequence is as follows:

[0093]

[0094] Where x is the planar distance corresponding to the sampled signal value in the Gaussian model, in micrometers.

[0095] (2) Model linearization. Taking the logarithm of the simplified curve model on both sides yields the linearized model:

[0096] z = a0 + a1x + a2x 2

[0097]

[0098] (3) Construct the normal equations. Based on the linearized sequence, construct the following matrix:

[0099]

[0100] Where B is the coefficient matrix, W is the weight matrix, L is the observation matrix, and p is the parameter matrix. The normal equations are constructed based on the least squares criterion as follows:

[0101] p = (B T WB) -1 (B T WL)

[0102] Solving this equation will give the values ​​of a0, a1, and a2.

[0103] (4) Recover the Gaussian curve parameters. Based on the linearized expression of the model, the parameters of the Gaussian curve can be deduced as follows:

[0104]

[0105] μ=a1σ 2

[0106]

[0107] For each defect, the above method yields a set of spot dimensions along the radial and tangential directions of the wafer. After processing all defect signals in this way, two sets of spot size sequences are obtained. Statistical analysis of these two sequences is required to calculate the final spot size.

[0108] S4: Determine whether all defects have been detected. If yes, obtain two sets of spot width sequences; otherwise, return to step S3.

[0109] S5: Based on the two sets of spot width sequences obtained in step S4, the statistical value of the spot width is calculated by kernel density function estimation.

[0110] Due to the presence of noise signals, the spot size calculated based on some defect signals deviates significantly from the actual spot size. Therefore, it is necessary to minimize the impact of such data on the final spot size calculation. This invention employs a kernel density function estimation method to calculate the final spot size. For a given spot width sequence [w1, w2… w…], n Its kernel density estimation function is:

[0111]

[0112] Among them, K h Here, is the kernel function, and n is the number of elements in the spot width sequence. In this example, a Gaussian kernel function is used. The kernel density estimation curve can be obtained by calculating the kernel density for different values ​​of w using the above formula. The w corresponding to the maximum value is the statistical value of the spot width, such as... Figure 4 As shown.

[0113] S6: Determine whether all focus height cyclic measurements have been completed. If yes, obtain the sequence of spot width statistics under different focus heights. Otherwise, return to step S2.

[0114] S7: Based on the two sets of spot width statistical value sequences obtained in step S6, the optimal focus height of the spot is calculated by quadratic curve fitting.

[0115] For defect detection results under different focus height settings, the above process can yield a set of statistical widths of the spot along the radial and tangential directions of the wafer. Within a certain focus height range, by sequentially modifying the focus height according to a certain cyclic step size and then executing the above process, two sets of statistical value sequences of spot widths can be obtained. Furthermore, based on the spot defocusing characteristics, the variation of the two sets of sequence values ​​with focus height can be approximately described by a quadratic curve model.

[0116] like Figure 5 As shown, the least squares method is used to fit a quadratic curve to the statistical value sequence of the spot width. The quadratic curve model is as follows:

[0117] w = b0 + b1z + b2z 2

[0118] For a given width statistics sequence [w1, w2… w n The matrix is ​​constructed as follows based on the least squares principle:

[0119]

[0120] Where C is the coefficient matrix, L is the observation matrix, and p is the parameter matrix. The normal equations are constructed based on the least squares criterion as follows:

[0121] p=(C T C) -1 (C T L)

[0122] From this, the parameters b0, b1, and b2 of the conic section can be obtained, and then the optimal focusing height can be determined:

[0123]

[0124] S8: The spot width corresponding to the optimal focus height can be calculated based on the fitted quadratic curve model:

[0125] w best =b0+b1z best +b2z best

[0126] Thus, the present invention has obtained the optimal focus height and its corresponding spot width in a single calculation process.

[0127] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for calculating the optimal focusing height and corresponding dimensions of a laser spot in a patternless wafer defect inspection device, characterized in that, Includes the following steps: S1: Set the focus height range and cycle step size of a patternless wafer defect inspection device; S2: Within the set focus height range, the focus height of the laser spot is uniformly changed according to the cycle step to perform cyclic detection scanning of the wafer, thereby obtaining the original scan data and defect location information; S3: Based on the defect location information, each defect is imaged and sampled along the radial and tangential directions of the wafer. The sampled signal value sequence is then fitted with Gaussian to calculate the spot width. S4: Determine whether all defects have been detected. If yes, obtain two sets of spot width sequences; otherwise, return to step S3. S5: Based on the two sets of spot width sequences obtained in step S4, the statistical value of the spot width is calculated by kernel density function estimation. S6: Determine whether all focus height cyclic measurements have been completed. If yes, obtain the sequence of spot width statistics under different focus heights. Otherwise, return to step S2. S7: Based on the two sets of spot width statistical value sequences obtained in step S6, the optimal focus height of the spot is calculated by quadratic curve fitting. S8: Calculate the spot width corresponding to the optimal focus height based on the fitted quadratic curve model.

2. The method for calculating the optimal focusing height and corresponding size of the light spot in the patternless wafer defect inspection equipment according to claim 1, characterized in that, The specific steps of step S3 include: S301: The distribution expression of the Gaussian fitting of the sampled signal value sequence of the light spot profile is: Where I is the signal strength, A is the signal amplitude, μ is the expected value, σ is the standard deviation, and noise is the additive noise; The width of the Gaussian spot along both the radial and tangential directions of the wafer is four times the standard deviation of the Gaussian distribution that its respective cross-section conforms to, i.e.: W R =4σ R W T =4σ T S302: For the sampled signal value sequence G = [g1, g2, ... g...] n The minimum value in the sequence is calculated as additive noise, and then each value is subtracted from this minimum value to obtain a new sequence, i.e.: Y = G - min(G) + 1 The simplified curve model corresponding to this sequence is as follows: Where x is the planar distance corresponding to the sampled signal value in the Gaussian model, in micrometers; S303: Taking the logarithm on both sides of the simplified curve model yields the linearized model: z=a0+a1x+a2x 2 S304: Construct the following matrix based on the linearized sequence: Where B is the coefficient matrix, W is the weight matrix, L is the observation matrix, and p is the parameter matrix, the normal equations are constructed according to the least squares criterion as follows: p=(B T WB) -1 (B T WL) Solving this equation will give the values ​​of a0, a1, and a2; S305: Based on the linearized expression of the model, the parameters of the Gaussian curve are derived as follows: μ=a1σ 2 3. The method for calculating the optimal focusing height and corresponding size of the light spot in the patternless wafer defect inspection equipment according to claim 1, characterized in that, In step S5, for the two sets of spot width sequences [w1, w2… w] obtained in step S4, n Its kernel density estimation function is: Among them, K h Let w be the kernel function, and n be the number of elements in the spot width sequence. By calculating the kernel density estimation curve for different w values ​​in sequence, the w value corresponding to the maximum value is the statistical value of the spot width.

4. The method for calculating the optimal focusing height and corresponding size of the light spot in the patternless wafer defect inspection equipment according to claim 1, characterized in that, In step S7, for the two sets of spot width statistical value sequences obtained in step S6, the least squares method is used to perform quadratic curve fitting. The quadratic curve model is as follows: w=b0+b1z+b2z 2 For a given width statistics sequence [w1, w2… w n The matrix is ​​constructed as follows based on the least squares principle: Where C is the coefficient matrix, L is the observation matrix, and p is the parameter matrix; the normal equations are constructed according to the least squares criterion as follows: p=(C T C) -1 (C T L) From this, the parameters b0, b1, and b2 of the conic section can be obtained, and then the optimal focusing height can be determined:

5. The method for calculating the optimal focusing height and corresponding size of the light spot in the patternless wafer defect inspection equipment according to claim 4, characterized in that, In step S8, the spot width corresponding to the optimal focus height is calculated based on the fitted quadratic curve model: In best =b0+b1z best +b2z best 。

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