Dark field wafer defect extended depth-of-field detection system based on phase coding

Abstract

The invention belongs to the technical field of optical detection, and particularly relates to a dark-field microscope wafer defect extended depth-of-field detection system. According to the system, a 4f system comprising a phase mask is integrated behind a traditional dark field wafer defect detection system, so that a point spread function of an optical system is modified, and the phase mask is designed by limiting the variation trend of gradient variance of an intensity image of the point spread function of the optical system along with defocusing amount; the depth of field of the detection system is expanded. According to the invention, larger out-of-focus tolerance is provided for a dark-field pattern-free wafer defect detection system, so that wrong detection or missing detection caused by out-of-focus of the detection system due to wafer warping or mechanical vibration is avoided, and thus the dependence on a mechanical real-time automatic focusing system which is high in cost, complex in structure and difficult to manufacture is reduced; the method is especially suitable for related applications in optical detection fields such as wafer defect detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical detection, and particularly relates to a dark-field microscope wafer defect extended depth-of-field detection system. Background Art

[0002] Wafer defect detection is a key link in the semiconductor manufacturing process, directly affecting the production cost, quality, and reliability of chips. Currently, the typical non-patterned wafer detection process mainly includes two steps: first, using an optical dark-field microscopic imaging system to locate the specific position of wafer surface defects, and then rechecking with an electron beam defect rechecking device, so as to combine the advantages of high throughput of the former and high resolution of the latter to solve the contradiction between high precision and high efficiency. However, as the critical dimensions of semiconductor manufacturing continue to shrink, the size of "fatal defects" on the wafer surface also decreases accordingly, resulting in a significant attenuation of the scattered light intensity. To improve the detection sensitivity, existing technologies generally use high numerical aperture objectives and deep ultraviolet light sources to enhance the light energy capture efficiency. However, high numerical aperture and short wavelength will cause a sharp drop in the depth of field of the optical system, making the system extremely vulnerable to defocus due to micron-level warping of the wafer surface or mechanical vibration of the scanning mechanism. This will not only cause energy diffusion of the defect scattered light, reducing the positioning accuracy, but also may completely submerge the already weak signal in the system noise, resulting in false detection or missed detection.

[0003] Although the current mainstream mechanical real-time autofocus system can alleviate the defocus problem, its long data processing time, data transmission delay, and limited response speed of mechanical components limit the further improvement of the detection efficiency. Therefore, the industry has tried to enhance the defocus tolerance by extending the depth of field of the optical system. For example, dark-field holographic microscopy can achieve digital refocusing through complex amplitude reconstruction in the Fourier domain, but it relies on post-processing algorithms with high computational costs, and the detection results are easily interfered by speckle noise caused by coherent light sources; wavefront coding technology can extend the depth of field of the optical system by modifying the point spread function of the optical system to make it insensitive to defocus, but the large wavefront introduced will significantly reduce the light energy efficiency of the system; although deep learning technology can process low signal-to-noise ratio images, its "black box" characteristics limit the generalization ability, and hardware-level imaging defects may cause the algorithm to fail. These technical bottlenecks need to be urgently broken through to meet the stringent requirements of the semiconductor industry for high throughput, high precision, and high reliability.

[0004] At present, in the field of microscopic imaging, the focusing accuracy of an optical system is often determined by measuring the edge features or energy concentration degree of an image. Especially in a dark-field microscopic system, the gradient variance of an image can quantitatively describe the energy distribution condition, and thus effectively characterize the focusing state of the system ([1] Trusiak M, Picazo-Bueno J A, Zdankowski P, et al. Dark Focus: numerical autofocusing in digital in-line holographic microscopy using variance of computational dark-field gradient [J]. Optics and Lasers in Engineering, 2020, 134: 106195.). Specifically, when the system is precisely focused, the light energy is concentrated in a small number of pixel regions, showing a localized distribution characteristic; while when the system is defocused, the light energy diffuses to a wider area range and tends to be evenly distributed. Based on this index, by combining point spread function engineering to modify the hardware structure of the microscopic system, it is possible to ensure that the optical system maintains good energy convergence ability within a large axial range, and thus improve the signal-to-noise ratio and sensitivity of detection ([2] Shechtman Y, Weiss L E, Backer A S, et al. Precise three-dimensional scan-free multiple-particle tracking over large axial ranges with tetrapod point spread functions [J]. Nano letters, 2015, 15(6): 4194-4199.). Summary of the Invention

[0005] The purpose of the present invention is to provide a dark-field wafer defect extended depth-of-field detection system based on phase encoding, so as to provide a larger defocus tolerance for a dark-field patternless wafer defect detection system, and avoid misdetection or missed detection caused by defocusing of the detection system due to wafer warping or mechanical vibration.

[0006] The depth-of-field extended dark-field microscope wafer defect detection system based on phase encoding provided by the present invention integrates a 4f system including a phase mask behind a traditional dark-field wafer defect detection system to modify the point spread function of the optical system, and designs the phase mask by restricting the change trend of the gradient variance of the intensity image of the point spread function of the optical system with the defocus amount, so that the system has a larger defocus tolerance; specifically, it includes a laser, a spatial filter, a mirror, a wafer sample to be measured, a diaphragm, a microscope objective lens, a tube lens, an intermediate image plane, a 4f system including a phase mask, and a monochromatic CCD camera arranged in sequence along the optical path; among them, the 4f system including the phase mask is arranged between the intermediate image plane and the monochromatic CCD camera, and is composed of a first lens L1, a phase mask and a second lens L2; the focal lengths of the first lens L1 and the second lens L2 are both f, and the distances from the intermediate image plane to the first lens L1, from the first lens L1 to the phase mask, from the phase mask to the second lens L2, and from the second lens L2 to the imaging plane of the monochromatic CCD camera are equal, all being f, forming a standard 4f imaging structure, and the phase mask is placed on the spectrum plane of the 4f system to expand the depth of field of the system by modulating the wavefront phase of the scattered light;

[0007] The beam emitted by the laser is shaped by the spatial filter and reflected by the mirror, and then irradiates the surface of the wafer sample to be measured at an oblique angle to excite the scattered light in the defect area. The microscope objective lens collects the scattered light and magnifies and images it on the image plane through the tube lens; then, through the 4f system, the point spread function of the optical system is modified, and the phase mask is designed by restricting the change trend of the gradient variance of the intensity image of the point spread function of the optical system with the defocus amount;

[0008] Specifically, for the phase mask design, the phase distribution is designed based on the Zernike standard polynomial. The specific steps are as follows:

[0009] Step 1: Set the initial phase distribution of the phase mask to zero phase;

[0010] Step 2: Based on the angular spectrum theory, simulate and generate the intensity images of the point spread function of the optical system corresponding to different defocus states under the current phase distribution, and construct an image stack accordingly;

[0011] Step 3: Calculate the gradient variance of each image in the stack as an evaluation index, and take the maximization of the mean value and the minimization of the variance of the image gradient variance in the stack as the joint optimization goal, and execute the optimization to re-determine the phase distribution of the phase mask;

[0012] Step 4: Repeat Step 2 and Step 3 until the phase distribution parameters reach the convergence condition, finally obtain the optimal phase distribution design for depth-of-field extension, and convert it into the thickness of the phase mask for processing.

[0013] Compared with the prior art, the present invention has the following remarkable advantages: (1) It reduces the dependence of the wafer detection device on the traditional mechanical real-time autofocus system which is costly, complex in structure and difficult to manufacture, reduces the detection cost and alleviates the limitation of the mechanical real-time autofocus system on the detection efficiency; (2) The present invention has been successfully applied to the detection of patternless wafers in the laboratory, and it has reference significance for the production design of high-throughput, high-sensitivity and high signal-to-noise ratio dark-field wafer detection equipment in industrial applications; (3) The present invention also has many advantages, such as no speckle noise, no requirement for the coherence of the light source, wide applicability to optical systems with different parameters, etc. Experimental results prove that the present invention has a considerably large defocus tolerance compared with the traditional dark-field wafer detection system, and it is a low-cost and effective detection means.

[0014] The following further elaborates the present invention through specific embodiments in conjunction with the accompanying drawings. Description of the Drawings

[0015] Figure 1 It is an optical path diagram of a dark-field wafer defect extended depth of field detection system based on phase encoding.

[0016] Figure 2 It is a flowchart of a phase mask optimization method for extending the depth of field of a dark-field wafer defect detection system.

[0017] Figure 3 It is a schematic diagram for comparative verification of surface defect detection of patternless wafers: By artificially introducing polystyrene microsphere defects with a nominal diameter of 300 nm, the technical differences between the traditional dark-field detection system and the present invention are systematically compared. Figure 3 (a) The left half shows the phase modulation comparison between the traditional system (upper) and the present invention (lower), and the right half shows the point spread function comparison at their respective different defocus amounts; Figure 3 (b) shows the detection results of microsphere defects by the traditional system (upper) and the present invention (lower) at different defocus amounts (-100 μm to +100 μm), intuitively demonstrating the significant improvement of the present solution in terms of defocus tolerance and imaging consistency. For clarity, Figure 3 All images in (b) have been normalized.

[0018] The reference numerals in the figure are: 1 - laser, 2 - spatial filter, 3 - mirror, 4 - wafer sample to be measured, 5 - aperture, 6 - microscope objective, 7 - tube lens, 8 - intermediate image plane, 9 - first lens L1, 10 - phase mask, 11 - second lens L2, 12 - 4f system including the phase mask, 13 - monochromatic CCD camera. Detailed Embodiment

[0019] The dark-field wafer defect extended depth of field detection system based on phase encoding of the present invention has an optical structure asFigure 1 As shown, it consists of two parts. One part is a traditional dark-field wafer defect detection system, and the other part is a 4f system (12) including a phase mask, which is outlined by a dashed box. The traditional dark-field wafer defect detection system can directly use an existing microscopic system or can be constructed by itself, but it is required that the light source used is approximately monochromatic. It mainly includes a laser (1), a spatial filter (2), a mirror (3), a wafer sample to be measured (4), a diaphragm (5), a microscopic objective lens (6), and a tube lens (7); among them, the beam emitted by the laser (1) is shaped by the spatial filter (2) and reflected by the mirror (3), and then irradiates the surface of the wafer sample to be measured (4) at an inclined angle to excite the scattered light in the defect area. Then, its reflected light is blocked by the diaphragm (5), and the microscopic objective lens (6) collects the scattered light and magnifies and images it on the image plane (8) through the tube lens (7).

[0020] The 4f system (12) including the phase mask is arranged between the intermediate image plane (8) and the monochromatic CCD camera (13), and is composed of a first lens L1 (9), a phase mask (10), and a second lens L2 (11). The focal lengths of the first lens L1 (9) and the second lens L2 (11) are both f. The distances from the intermediate image plane (8) to the first lens L1 (9), from the first lens L1 (9) to the phase mask (10), from the phase mask (10) to the second lens L2 (11), and from the second lens L2 (11) to the imaging plane of the monochromatic CCD camera (13) are all f, and the phase mask (10) is placed on the spectral plane of the 4f system.

[0021] The phase mask (10) in the 4f system (12) including the phase mask is the core part of the system, and its phase distribution is designed based on the first M terms of the Zernike standard polynomial. The expression of the modulation function is as follows:

[0022]

[0023] In the formula, k=(k x ,k y ) is the coordinate of the spectral plane of the 4f system, a m is the weighting coefficient, a is a vector composed of M such coefficients, j is the imaginary unit, Z m is the m-th term of the Zernike standard polynomial, is the normalized radius in the frequency domain, satisfying and where NA is the numerical aperture of the image space of the microscopic system, and k0 is the wave number of the scattered light in the air.

[0024] In order to calculate the vector a to determine the shape of the phase mask (10), a phase mask optimization method for expanding the depth of field of the dark-field wafer defect detection system is used. The specific steps are as follows:

[0025] Step 1: Set the initial phase distribution of the phase mask to zero phase, that is, set the vector a to a zero vector;

[0026] Step 2: Based on the angular spectrum theory, simulate and generate the intensity images of the point spread function of the optical system corresponding to different defocus states under the current phase distribution. Its expression is:

[0027]

[0028] In the formula, r = (x, y) is the coordinate of the imaging plane, z is the defocus amount, denotes performing the Fourier transform, and H(k, z) is the optical transfer function introduced by defocus. Its expression is:

[0029]

[0030] Construct a stack of intensity images of the point spread function corresponding to different defocus states based on the calculation results.

[0031] Step 3: Calculate the gradient variance of each image in the stack as an evaluation index. The specific expression is:

[0032]

[0033] In the formula, denotes calculating the variance, and I(u, v, z; a) represents the pixel gray value at the u-th row and v-th column of the intensity image of the point spread function simulated after applying the phase mask with the modulation function G(k; a) at the defocus amount of z. Taking the maximization of the mean value and the minimization of the variance of the image gradient variance in the stack as the joint optimization goal, the evaluation function is defined as:

[0034] E(a) = -a × M(a) + b × V(a), (5)

[0035] In the formula, α and β are adjustable parameters that determine the degree of energy convergence and its smoothness with the change of the defocus amount respectively. M(a) and V(a) represent the mean value and variance of the image gradient variance in the stack respectively. Their expressions are:

[0036]

[0037] In the formula, Δz is the sampling step of the defocus amount during simulation. Perform optimization with the goal of minimizing the evaluation function E(a), update the vector a, and then recalculate the phase distribution of the mask.

[0038] Step 4: Repeat Step 2 and Step 3 until the phase distribution parameters reach the convergence condition. Finally, obtain the optimal phase distribution design for depth of field extension and convert it into the thickness of the phase mask for processing. The thickness of any point on the phase mask is:

[0039]

[0040] In the formula, λ is the wavelength of the scattered light, Δn is the difference between the refractive index of the material used to fabricate the phase mask and the refractive index of air, a m is the m-th element in vector a, and its specific value is determined by the optimization result. d is the substrate thickness of the phase mask.

[0041] Embodiment

[0042] Set up an optical path as shown in Figure 1 to detect the artificially introduced polystyrene microsphere defects with a nominal diameter of 300 nm on the surface of a patternless wafer. In the experiment, a diode laser with an output wavelength of 405 nm was used as the light source, whose coherence length exceeded 1 meter, the output power was adjustable, and the maximum output power was 65 mW. A microscopic imaging system with a magnification of 15× was composed of an objective lens with 0.3 NA and a tube lens with a focal length of 200 mm, and the focal lengths of the first lens L1 and the second lens L2 used subsequently were both 200 mm. According to experience, the first 55 Zernike standard polynomials were selected to construct the phase mask. During the optimization process of the phase mask, α and β were set to 1E5 and 2E12 respectively, and during the simulation, the sampling step Δz of the defocus amount was set to 0.5 μm, and the number of sampling planes (2N + 1) was set to 101. The obtained phase distribution and its corresponding optical system point spread function are as shown in Figure 3 (a).

[0043] For the same 300-nm polystyrene microsphere defect, the traditional dark-field system and the present invention were respectively used for comparative detection. A precision displacement stage was used to perform a covering scan at a step size of 10 μm within the defocus range from -100 μm to +100 μm (a total of 21 equally spaced defocus positions). The results are as shown in Figure 3 (b). The experimental results show that the traditional system can only respond to defects within the defocus range from -40 μm to +40 μm, while the present invention can detect defects within the extended defocus range greater than -100 μm to +100 μm; in the images captured by the traditional system, energy diffusion occurred even under weak defocus, while the detection results of the present invention within the defocus range from -40 μm to +40 μm hardly changed, which proves the ability of the present invention to improve the defocus tolerance of the dark-field wafer defect detection system.

Claims

1. A dark-field wafer defect extended depth-of-field detection system based on phase encoding, characterized in that, It includes a laser (1), a spatial filter (2), a mirror (3), a wafer sample to be measured (4), a diaphragm (5), a microscope objective lens (6), a tube lens (7), an intermediate image plane (8), a 4f system (12) including a phase mask, and a monochrome CCD camera (13) arranged in sequence along the optical path; wherein, the beam emitted by the laser (1) is shaped by the spatial filter (2) and reflected by the mirror (3), and then irradiates the surface of the wafer sample to be measured (4) at an inclined angle to excite the scattered light in the defect area. The microscope objective lens (6) collects the scattered light and magnifies and images it on the intermediate image plane (8) through the tube lens (7); the 4f system (12) including the phase mask is arranged between the intermediate image plane (8) and the monochrome CCD camera (13), and is composed of a first lens L1 (9), a phase mask (10), and a second lens L2 (11); the focal lengths of the first lens L1 (9) and the second lens L2 (11) are both f, and the distances from the intermediate image plane (8) to the first lens L1 (9), from the first lens L1 (9) to the phase mask (10), from the phase mask (10) to the second lens L2 (11), and from the second lens L2 (11) to the imaging plane of the monochrome CCD camera (13) are all f, forming a standard 4f imaging structure. The phase mask (10) is placed on the spectral plane of the 4f system, and the depth of field of the system is extended by modulating the wavefront phase of the scattered light.

2. The dark-field wafer defect extended depth-of-field detection system based on phase encoding according to claim 1, wherein The phase distribution of the phase mask (10) in the 4f system (12) is designed based on the first M-term Zernike standard polynomial; the expression of the modulation function is: where \(k=(k x ,k y )\) are the coordinates of the spectrum plane of the 4f system, \(a m \) is the weighting coefficient, \(a\) is a vector composed of \(M\) such coefficients, \(j\) is the imaginary unit, \(Z m \) is the \(m\)th term of the Zernike standard polynomial, is the normalized radius in the frequency domain, satisfying and where \(NA\) is the numerical aperture of the image space of the microscopy system and \(k_0\) is the wave number of the scattered light in air.

3. The dark-field wafer defect extended depth-of-field detection system based on phase encoding according to claim 2, wherein The depth of field of the system is extended by modulating the wavefront phase of the scattered light. Specifically, the shape of the phase mask (10) is determined through phase mask optimization. The specific steps are as follows: Step 1: Set the initial phase distribution of the phase mask to a zero phase, that is, set the vector a to a zero vector; Step 2: Based on the angular spectrum theory, simulate and generate the intensity images of the point spread functions of the optical system corresponding to different defocus states under the current phase distribution. Its expression is: where \(r=(x,y)\) is the coordinate of the imaging plane and \(z\) is the defocus amount. denotes performing Fourier transform, \(H(k,z)\) is the optical transfer function introduced by defocus, and its expression is: Construct a stack of intensity images of the point spread functions corresponding to different defocus states based on the calculation results; Step 3: Calculate the gradient variance of each image in the stack as an evaluation index. The specific expression is: In the formula, represents the calculation of variance. I(u, v, z; a) represents the pixel gray value of the (u, v)-th row and column on the intensity image of the point spread function obtained by simulation after applying a phase mask with a modulation function G(k; a) at a defocus amount of z. Taking the maximization of the mean value of the image gradient variances in the stack and the minimization of the variances as the joint optimization objectives, the evaluation function is defined as: E(a) = -a × M(a) + b × V(a), (5) In the formula, α and β are adjustable parameters that determine the degree of energy convergence and its smoothness with the change of defocus amount respectively. M(a) and V(a) respectively represent the mean and variance of the gradient variances of the images in the stack. Their expressions are: In the formula, Δz is the sampling step of the defocus amount during simulation; perform optimization with the goal of minimizing the evaluation function E(a), update the vector a, and then recalculate the phase distribution of the mask; Step 4: Repeat Steps 2 and 3 until the phase distribution parameters reach the convergence condition, and finally obtain the optimal phase distribution design for depth of field extension, and convert it into the thickness of the phase mask for processing. The thickness of any point on the phase mask is: Where λ is the wavelength of the scattered light, Δn is the difference between the refractive index of the material used to fabricate the phase mask and the refractive index of air, a m is the m-th element in vector a, and its specific value is determined by the optimization result. d is the substrate thickness of the phase mask.

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