A method for phase generation and optical proximity effect optimization in local high-resolution holographic lithography based on sampling decoupling

Abstract

The application discloses a local high-resolution holographic lithography phase generation and optical proximity effect optimization method based on sampling decoupling, relates to the technical field of digital holography and computer lithography, and comprises the following steps: generating a seed phase by adopting a full-field constraint GSW algorithm, constructing a sampling decoupling propagation matrix to realize ROI local high-resolution iteration; completing light field simulation based on a scalar angular spectrum method and a vector Debye-Wolf integral, and realizing phase reverse optimization by using gradient descent; completing data-driven OPC fast correction by using an improved U-Net network; and finally generating a lithography phase mask. Based on the above scheme, the application can realize high-precision and high-efficiency holographic lithography whole-process optimization, and guarantee complete reproduction of the OPC correction structure and fidelity of the lithography pattern.

Description

Technical Field

[0001] This invention relates to the fields of digital holography and computational lithography, and more specifically to a method for local high-resolution holographic lithography phase generation and optical proximity effect optimization based on sampling decoupling. Background Technology

[0002] Maskless projection lithography (digital mask lithography) is divided into surface projection lithography and holographic projection lithography. Surface projection lithography uses amplitude-type spatial light modulators such as DMDs to transfer a predetermined target pattern onto photoresist by switching pixels. Holographic projection lithography uses devices such as phase-type spatial light modulators to change the phase of the light beam by defining the phase distribution of the SLM modulation surface, thereby dynamically controlling the diffraction direction of the light and generating a predetermined light field using the interference effect of light. It has extremely high diffraction efficiency and a high degree of freedom in light field control.

[0003] In a typical digital holographic lithography process, there are generally three steps: pattern design, phase calculation, and lithography fabrication. As lithography strives for finer structures, feature sizes gradually decrease. When feature sizes approach submicron (or subwavelength) levels, optical proximity effects (OPC) occur. In a broad sense, OPC refers to the mutual influence between adjacent small structures in the lithographic pattern due to light interference, diffraction, and photoresist diffusion. This leads to changes in linewidth and rounded corners in the design pattern on the mask after exposure and development. Therefore, to increase the fidelity of digital holographic patterns, OPC correction is necessary.

[0004] For projection lithography, OPC typically operates on a mask pattern. By adding or removing structures at the edges of the pattern, it utilizes optical proximity and diffusion effects to ensure the final lithographic pattern matches the target. Historically, OPC implementations can be broadly categorized into three types: (1) Rule-based OPC utilizes a large amount of experimental data to analyze the optical proximity effect that may exist between structures and pre-modifies the layout using simple rules. This method often works for classic patterns or simple structures, but if the structure becomes complex or the size is subwavelength, the generation rules will become complex and unreliable.

[0005] (2) Model-based OPC models the optical system using optimization algorithms and performs iterative optimization based on physical properties. This method is often highly accurate; however, each iteration requires a complete physical calculation, resulting in low efficiency.

[0006] (3) Neural network-based OPC is based on model-based algorithms. It utilizes the powerful fitting ability of neural networks to realize the mapping from before optimization to after optimization in a large dataset of pre-optimization mask to post-optimization mask, thereby avoiding the complicated calculation process in model-based OPC and greatly improving efficiency.

[0007] In digital holographic lithography, since the GS algorithm itself is not differentiable, the gradient cannot flow from the physical model to the target pattern. Therefore, the optimization target in this technology is usually the phase map.

[0008] The calculation process from the target pattern to the phase map first requires generating phase information that meets the input requirements of the SLM (Sequencing Model). The GS (Gross-Side Graph) algorithm is the most widely used algorithm for phase retrieval. It was initially developed to infer the lost phase information of the light field based on easily detectable intensity information, and later widely used in fields such as holographic displays. The core function of the GS algorithm is to inversely solve for the two-dimensional phase distribution of the SLM surface that can reconstruct the amplitude distribution of the constrained plane by using iterative Fourier transform, given the known amplitude constraints of the light source (SLM surface) and the target image (view plane).

[0009] For lithography applications, to maximize both computational speed and accuracy, the GS algorithm often uses FFT and i-FFT for Fourier transform calculations in the iterative Fourier transform. The FFT algorithm requires consistent input and output resolution, inherently limiting sampling accuracy. This means that generating the lithographic phase pattern requires an input image with the same resolution as the SLM. To accommodate the propagation of optical systems, some researchers have replaced simple FFT calculations with specific physical beam propagation processes, making the calculation process more consistent with the physical diffraction propagation nature. This process often employs Fresnel diffraction based on the angular spectrum method.

[0010] Photolithography systems are essentially low-pass filtering systems. Due to the limited aperture of optical elements, the spatial frequency of the propagating light beam is strictly limited by the system's numerical aperture (NA). First, due to the sampling rate limitation of the FFT, its computational grid is close to or only slightly smaller than the system's physical diffraction limit. This leads to frequency truncation or mixing when processing sub-pixel features, failing to satisfy the Nyquist sampling theorem and causing high-frequency information loss. Second, if more high-frequency information is desired, zero-padding is required. However, the computation speed and memory usage of FFT for high-dimensional matrices increase exponentially, and signal sizes that are not powers of 2 further reduce computation speed. Therefore, expanding the sampling rate through zero-padding is impractical.

[0011] On the other hand, classic GS algorithms often perform global calculations, while lithographic patterns are usually sparsity-based. Global calculations can lead to wasted computing power in the background area, making it easy to get trapped in local optima and causing adverse effects such as speckle noise.

[0012] Therefore, how to achieve oversampling calculation and high-fidelity reconstruction of the region of interest in a lithographic pattern without significantly increasing the computational burden or reducing diffraction efficiency, while combining high-precision physical simulation and efficient data-driven methods to optimize the optical proximity effect and ensure the complete reproduction of the OPC correction structure and the fidelity of the lithographic pattern, is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0013] In view of this, the present invention provides a method for local high-resolution holographic lithography phase generation and optical proximity effect optimization based on sampling decoupling, which solves the problems existing in the background technology.

[0014] To achieve the above objectives, the present invention provides the following technical solution: A method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling includes the following steps: S1. The seed phase is generated by the full-field constrained GSW algorithm, a sampling decoupled physical propagation matrix is ​​constructed, and local high sampling rate iterative correction is performed in the region of interest (ROI) to suppress coherent speckle, thereby obtaining a local high-resolution holographic phase map. S2. Based on the scalar angle spectrum method, vector Debye-Wolf integral and photoresist diffusion model, light field simulation is performed. The photoresist profile error is used as the loss function and the gradient descent algorithm is used for inverse optimization to obtain the optimized phase map. S3. Extract the OPC layout based on the optimized phase map and construct the training dataset. Use the improved U-Net network for block training and perform overlapping block and Gaussian weight inference to output the corrected OPC layout. S4. Generate a phase mask for photolithography from the OPC modified layout according to S1 to achieve complete phase generation and optical proximity effect optimization.

[0015] Optionally, in S1, the full-field constrained GSW algorithm is used to generate the seed phase. Specifically, the target pattern is reduced in dimension by bilinear interpolation and zero-padding is performed to the center of the black background with the same resolution as the spatial light modulator. The SLM plane and the image plane are iterated through FFT and i-FFT. The phase preservation and amplitude one constraint are performed on the SLM plane, and the phase preservation and amplitude replacement with the target pattern constraint are performed on the image plane. The GSW algorithm uses dynamic amplitude weights for iterative constraints, and the weight formula is as follows:

[0016] In the formula: As amplitude weight, a To update the coefficients, I This represents the current intensity distribution. The target intensity distribution.

[0017] Optionally, in S1, the sampling decoupling physical propagation matrix is ​​constructed, specifically by establishing the physical pixel coordinates of the SLM plane and the high-resolution sampling coordinates of the image plane, and generating the sampling decoupling physical propagation matrix. :

[0018] In the formula: For high-resolution sampling coordinates of the image plane, These are the physical pixel coordinates of the SLM plane. The wavelength of the laser. f It is the focal length.

[0019] Optionally, in S1, perform iterative correction of local high sampling rate, specifically by using sampling to decouple the physical propagation matrix. Perform positive propagation, through Calculate the complex amplitude optical field of the ROI region; convert the complex amplitude optical field of the ROI region... Phase preservation and amplitude replacement with target binarized amplitude; through Inverse inversion is performed, forcing the complex amplitude of the SLM surface to a uniform amplitude while retaining only the phase; where, The complex amplitude of the current SLM surface. To Take the conjugate transpose of the matrix.

[0020] Optionally, in S1, suppressing coherent speckle specifically involves: changing the random seed to generate multiple statistically independent phase holograms with consistent target intensity; and during exposure, using a spatial light modulator to rapidly switch at a set frame rate to reduce the speckle contrast to its original value. .

[0021] Optionally, in S2, the calculation process of the scalar angle spectrum method is as follows: For the scalar diffraction component, the wavefront is converted into different spatial frequency components, i.e., the angular spectrum, through Fourier transform; when the beam propagates a distance in free space... z When the transfer function is used, it is expressed as:

[0022] Thus, it spreads in free space. z hour,

[0023] Ideally, the lens can be considered a phase converter, changing only the curvature of the light wavefront without altering the light intensity distribution, by introducing a quadratic phase factor:

[0024] In the formula: The wavelength of the laser. f Focal length , They are respectively x , y Spatial frequency of direction, For wave number, , This represents the complex amplitude of the input optical field before propagation and the complex amplitude of the output optical field after propagation. , This represents the Fourier transform and the inverse Fourier transform. r Indicates the distance from the optical axis. This represents the phase transformation function of the lens. j The imaginary unit; The scalar diffraction process can be summarized into five stages: free space propagation, lens propagation, lens propagation, and free space propagation. The complex amplitude of the light field at the entrance pupil of the objective lens is obtained through the above calculations.

[0025] Optionally, in S2, the calculation process of the vector Debye-Wolf integral is as follows: pass , Mapping Cartesian coordinates to spherical coordinates using numerical aperture limit The integration range; for x Linearly polarized light Its component on the spherical wavefront near the focal region satisfy:

[0026] When the observation plane translates near the focal point At different times Different angles produce different optical path differences, and corresponding phase differences. Represented as:

[0027] If we consider the light field at the observation plane as a Fourier transform of the exit pupil, for a vector field...

[0028] When the spherical coordinates are transformed back to the Cartesian coordinate system based on the Abbe sine condition, the integral of the above equation is numerically equivalent to the 2D Fourier transform of the light field in the entrance pupil plane. In the formula: x , y These are coordinates in the Cartesian coordinate system. It is the polar angle. It's the azimuth. f Focal length;n The refractive index of the medium, k For wave number, C A constant factor, Indicates the integration region. This represents the vector electric field distribution on the entrance pupil. j It is the imaginary unit.

[0029] Optionally, in S2, the execution flow of the reverse optimization algorithm is as follows: The phase map group involved in the calculation and its corresponding target pattern Introducing the inverse optimization algorithm, assuming that the photoresist pattern corresponding to the phase map group in a certain iteration process is... Fitting using the sigmoid function:

[0030] The final photoacid concentration is set at a threshold. Define the outline as the photoresist; Define loss function for:

[0031] According to the chain rule of gradients, the loss function For phase variables The gradient is expressed as:

[0032] Let the sigmoid function be denoted as... In terms of form, the gradient propagation of the developing layer focuses on:

[0033] Gradient of the exposure layer Nonlinear response of photoresist Correlation, gradient is:

[0034] At the edges of the graph, the Adam optimizer is used to perform adaptive gradient updates on the phase map:

[0035] In the formula: The concentration of photoacid after diffusion of the photoresist model. H , W These are the width and height of the image, respectively. For phase diagram group, p for abbreviation, The average light intensity. Refers to sigmoid. and The first t The parameters updated in the next iteration and the updated parameters For learning rate, This is the bias correction value for the second-order moment estimation. To prevent division by a very small positive number, This is the bias correction value for the first-order moment estimation.

[0036] Optionally, S3 specifically includes the following steps: OPC layouts are extracted from the light field profiles corresponding to the optimized phase map as ground truth labels and used to construct paired training datasets with the original lithography layouts. An improved U-Net network is used to train the training dataset in blocks. The improved U-Net network uses multi-scale convolutional kernels to extract features in the encoding layer and fuses shallow detail information through skip connections in the decoding layer. During the inference phase, the lithography pattern to be optimized is input into the trained improved U-Net network. The large-size pattern is divided using an overlapping block strategy. In the fusion output phase, Gaussian weights are used to weight and fuse the inference results of each sub-block. Finally, the lithography pattern corrected by the optical proximity effect is directly output.

[0037] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for local high-resolution holographic lithography phase generation and optical proximity effect optimization based on sampling decoupling, which has the following beneficial effects: (1) Break the rigid coupling limitation between spatial frequency and sampling interval, eliminate the coupling relationship between image sampling interval and object pixel size under FFT algorithm, and realize accurate reconstruction of micro-nano structure edge without increasing hardware cost.

[0038] (2) Achieve a balanced improvement in computational efficiency and accuracy. Compared with the FFT method without zero padding, only a small increase in computation time is required to achieve a sampling accuracy improvement of more than 16 times. Compared with the zero padding method, it greatly reduces computational resources and computation time.

[0039] (3) Effectively improves the robustness of photolithography process. Combined with optical proximity effect correction, it can reconstruct compensation structure that is much smaller than the equivalent pixel size of SLM, significantly improving the contour accuracy and pattern fidelity after photoresist development.

[0040] (4) Construct a closed-loop technology process from local high-resolution phase generation, physical-driven precise optimization to data-driven fast OPC, taking into account both the high precision and high efficiency of lithography optimization, and meeting the needs of industrial-grade digital holographic lithography applications.

[0041] (5) By using phase high degree of freedom to control the physical cutoff frequency of the optical system, the precise definition of any linewidth greater than the diffraction limit can be achieved without breaking the physical diffraction limit, thus solving the problem that traditional algorithms can only generate linewidth structures that are specific integer multiples. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0043] Figure 1 A flowchart of the local high-resolution holographic lithography phase generation and optical proximity effect optimization method based on sampling decoupling provided by the present invention; Figure 2 A schematic diagram of the local high-resolution phase generation algorithm provided by the present invention; Figure 3 A simplified optical path propagation diagram provided by the present invention; Figure 4 A schematic diagram of the optimization algorithm flow for physics-driven algorithms provided by this invention; Figure 5 This is a schematic diagram of the U-Net-OPC neural network provided by the present invention; Figure 6 Calculate the difference map between the FFT-GS algorithm and our algorithm for a target pattern without OPC; Figure 7 The difference map is calculated between the target pattern obtained by the OPC FFT-GS algorithm and this algorithm; Figure 8 A map showing the differences in detail between images at different resolutions; Figure 9 Time difference plots calculated using FFT and matrix DFT for different iterations of the algorithm; Figure 10 The simulated photoresist outline is obtained by optical imaging and photoresist diffusion of the target pattern and phase map. Figure 11 Phase map imaging and photoresist profile map optimized by a physics-driven optimization algorithm; Figure 12 Comparison of photoresist contours for the target pattern, including unoptimized, optimized, and extracted light field contours; Figure 13 This is a partial training set of graphics; Figure 14 The segmentation logic graph for block training; Figure 15 The loss curve for training the neural network; Figure 16 A diagram illustrating the erroneous predictions that occur when the same block-segmentation strategy is used for both prediction and training. Figure 17 The prediction results are shown in the diagram for misaligned block partitioning and Gaussian weighted logic. Figure 18 The images show the results before optimization, physics-driven optimization, and data-driven (neural network) optimization for some images. Figure 19 Comparison chart of MSE, EPE, and SSIM for different optimization groups; Figure 20 The image shows the simulation results for the high NA group. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] To achieve oversampling calculations and high-fidelity reconstruction within the ROI of a photolithographic pattern without significantly increasing computational burden or affecting diffraction efficiency, suppress noise interference outside the signal region, and improve the edge sharpness and uniformity of the photolithographic pattern, this invention discloses a method for local high-resolution holographic lithography phase generation and optical proximity effect optimization based on sampling decoupling. Figure 1 As shown, it includes the following steps: S1. The seed phase is generated by the full-field constrained GSW algorithm, a sampling decoupled physical propagation matrix is ​​constructed, and local high sampling rate iterative correction is performed in the region of interest (ROI) to suppress coherent speckle, thereby obtaining a local high-resolution holographic phase map. S2. Based on the scalar angle spectrum method, vector Debye-Wolf integral and photoresist diffusion model, light field simulation is performed. The photoresist profile error is used as the loss function and the gradient descent algorithm is used for inverse optimization to obtain the optimized phase map. S3. Extract the OPC layout based on the optimized phase map and construct the training dataset. Use the improved U-Net network for block training and perform overlapping block and Gaussian weight inference to output the corrected OPC layout. S4. Generate a phase mask for photolithography from the OPC modified layout according to S1 to achieve complete phase generation and optical proximity effect optimization.

[0046] The OPC process in digital holographic lithography focuses on the structural differences and pattern fidelity between the photoresist contour and the target pattern in the light field simulation. This invention proposes a series of algorithms to achieve high-precision simulation from the phase map to the photoresist contour, and constructs a reverse calculation lithography algorithm for phase map optimization (i.e., a physics-driven digital holographic lithography phase layout optimization algorithm). At the same time, high sampling rate light field contour information is extracted from the phase map optimization process as training data for neural network training, ultimately realizing rapid calculation of OPC layout optimization.

[0047] Next, for Figure 1 The process shown is described in detail to further understand the solution described in this invention.

[0048] I. A Local High-Resolution Holographic Phase Generation Algorithm for Computational Lithography

[0049] The core idea is to constrain the energy within the ROI range through full-field computation, and then apply fine-grained constraints at local high sampling rates within the ROI. By decoupling full-field computation and local sampling, the coupling relationship between the image plane sampling interval and the object plane pixel size in FFT is eliminated.

[0050] In this embodiment, it is assumed that the resolution of the SLM is 1024. 1024, pixel spacing is 7.48um; for 1024 1024 full-size layout, with its center at 64 Set the 64-pixel area as the exposure ROI. A resolution of 1024 is required. A 1024-bit binary target pattern, where 0 represents the background and 1 represents the exposure structure within the ROI, corresponding to a 16-fold increase in sampling rate, hereinafter referred to as the target pattern.

[0051] 1.1 Initialization of Phase Seed Based on Full-Field Constraints

[0052] At the start of the calculation, the baseline of the energy distribution is established within the entire FOV (Field of View). In S1 of this embodiment, the seed phase is generated using the full-field constrained GSW algorithm, specifically by reducing the dimensionality of the target pattern using bilinear interpolation (64). 64) After padding with zeros to the center of a black background with the same resolution as the spatial light modulator, iterate between the SLM plane and the image plane using FFT and i-FFT. Perform phase preservation and amplitude uniformity constraints on the SLM plane, and perform phase preservation and amplitude replacement with target pattern constraints on the image plane. The GSW algorithm uses dynamic amplitude weights for iterative constraints, and the weight formula is as follows:

[0053] In the formula: As amplitude weight, a To update the coefficients, I This represents the current intensity distribution. The target intensity distribution.

[0054] This process requires approximately 50 iterations. The purpose is to accurately guide most of the laser energy to the target ROI region, preventing energy from dissipating into the background region during subsequent high-precision calculations, and providing initial values ​​for subsequent nonlinear optimization. Since holographic phase retrieval is inherently a non-convex problem, iterating directly at high sampling rates can easily lead to poor local optima. Therefore, this step ensures the correct macroscopic shape of the light field and achieves a rough shaping of the spatial spectrum.

[0055] 1.2 Construction of the decoupling operator between spatial frequency and sampling rate

[0056] In S1 of this embodiment, the sampling decoupling physical propagation matrix is ​​constructed as follows: First, an asymmetric coordinate system is defined. The SLM plane uses discrete coordinates defined by the physical pixel spacing of 7.48 μm; the image plane uses sampling coordinates (16 nm) much higher than the physical diffraction limit. The physical pixel coordinates of the SLM plane and the high-resolution sampling coordinates of the image plane are established, generating a sampling decoupled physical propagation matrix. :

[0057] In the formula: For high-resolution sampling coordinates of the image plane, These are the physical pixel coordinates of the SLM plane. The wavelength of the laser. f Focal length It describes the introduced phase difference between arbitrary sampling points on the SLM plane and the image plane.

[0058] 1.3 Local High-Fidelity Correction Iterative Stage within ROI

[0059] After the GSW iteration in step 1.1, a seed phase is obtained that roughly concentrates energy in the ROI region. However, the reconstructed optical field corresponding to this seed phase suffers from blurred edges and loss of detail because high-frequency information is lost during numerical dimensionality reduction, making it impossible to characterize complex micro / nano structures. The core of step 1.3 is the propagation matrix constructed based on step 1.2. The process iterates repeatedly between the high sampling rate image plane space and the SLM plane, correcting the SLM phase in each iteration to match the high-frequency details of the reconstructed light field with the target pattern.

[0060] In S1 of this embodiment, local high sampling rate iterative correction is performed, specifically as follows: 1) Forward Propagation: Decoupling the physical propagation matrix using sampling. Perform positive propagation, through Calculate the complex amplitude optical field in the ROI region. This represents the complex amplitude of the current SLM surface; this step simulates the complex amplitude distribution formed on the image plane by the lens group after coherent light exits from the SLM surface, due to the propagation matrix. It is a high sampling rate, and the calculation at this time It can clearly present the details of the interference fringes caused by phase modulation, some of which would be smoothed out in conventional FFT calculations.

[0061] 2) Image Area High-Resolution Constraint (ROI Constraint): This step is crucial for improving fidelity and corresponds to the process of replacing the frequency domain amplitude in the classic GS algorithm. It involves converting the complex amplitude optical field of the ROI region... The phase is preserved and the amplitude is replaced with the target binary amplitude; at the corners and edges of the target pattern, the algorithm amplifies the error signal by forcibly assigning the target value.

[0062] 3) Backward Mapping: Through... Perform reverse inversion. To The matrix is ​​taken as a conjugate transpose; this step corresponds to the inverse Fourier transform process of the classic GS algorithm, which is used to solve the complex amplitude arrangement that the SLM should have when the image plane is to present the required detail information; the inverse process is solved by using the conjugate transpose matrix to map the physical space sampling rate from 16nm back to 7.48um on the SLM plane.

[0063] 4) Physical constraint of object plane (SLM Constraint): Since SLM is a pure phase device, it cannot control the intensity of light. Therefore, in this embodiment, the complex amplitude returning in reverse is forced to be uniformly distributed, and only the phase value is retained.

[0064] Because Fourier transform has x , y The property of separability in direction, and the processes of forward and backward propagation. A matrix can also be divided into rows and columns, breaking down complex two-dimensional matrix operations into two one-dimensional matrix multiplications, and pre-calculating... The matrix approach effectively reduces the time complexity of computation.

[0065] After a certain number of iterations, the phase information on the SLM is preserved, resulting in the final output phase hologram. The algorithm flow is as follows: Figure 2 As shown.

[0066] 1.4 Time multiplexing suppresses coherent speckle.

[0067] Because lasers are highly coherent, a single phase hologram will inevitably produce random speckle noise. Even though the phase calculated by the GSW algorithm has constrained the speckle noise to some extent, the improvement effect is limited.

[0068] To address this issue, in S1 of this embodiment, suppressing coherent speckle specifically involves: after step 1.3, changing the random seed input in step 1.2, and repeating steps 1.2 and 1.3 to generate multiple statistically independent phase holograms with consistent target intensity; during exposure, a spatial light modulator is used to rapidly switch between frames. According to statistical principles, unrelated speckles cancel each other out during energy superposition, while the target signal linearly accumulates, reducing the speckle contrast to its original value. This significantly improves the surface roughness of the photoresist after development.

[0069] II. A Physically Driven Digital Holographic Lithography Precision Simulation and Inverse Optimization Algorithm Based on Sampling Decoupling Strategy

[0070] The process first performs a precise physical simulation from the phase mask to its reconstructed light field and photoresist profile. Corresponding to the aforementioned phase calculation process, in this embodiment, digital holographic lithography does not require calculation of the entire field of view (FOV), but instead concentrates computational resources on the ROI region.

[0071] The digital holographic lithography optical system includes a beam expander system, a 4f system, an objective lens system, and an auxiliary focusing system. The beam expander system is used to increase the size of the laser spot to uniformly illuminate the SLM photosensitive surface. The 4f system is used to reduce the SLM modulated light to half its original size to match the entrance pupil diameter of the high-NA objective lens. At the same time, a low-pass filter is set at the focal plane of the first 4f lens to filter out the zero-order stray light and retain only the effective diffraction orders required for holographic processing. The objective lens system is used to achieve high-resolution focused imaging of the holographic pattern.

[0072] The simplified core optical path propagation process is as follows: Figure 3 As shown, the 4f system has two sets of lenses with focal lengths of 200mm and 100mm respectively, an objective lens with a focal length of 2mm, and a numerical aperture NA=0.9; the light source is a fiber laser with a wavelength of 517nm, a repetition frequency of 10MHz, and a pulse width of 300fs.

[0073] Within the optical system, the beam originates at the SLM plane and terminates in the observation area behind the objective lens. The overall propagation process can be divided into two parts: the paraxial approximate scalar diffraction part corresponding to the propagation of the front 4f system, and the vector focusing part corresponding to the high NA objective lens. Because the beam convergence angle in high numerical aperture optical systems is extremely large, the paraxial approximation condition is no longer satisfied, and the polarization characteristics of the light field become a key factor limiting image quality.

[0074] 2.1 Scalar angular spectrum method

[0075] For the scalar diffraction portion, this embodiment employs the angular spectrum method for calculation. In physical optics, any complex wavefront can be represented as the superposition of countless plane waves with different propagation angles. Therefore, in S2 of this embodiment, the calculation process of the scalar angular spectrum method is as follows: The wavefront is converted into different spatial frequency components, i.e., the angular spectrum, by Fourier transform; when the beam propagates a distance in free space... z When the transfer function is used, it is expressed as:

[0076] Thus, it spreads in free space. z hour,

[0077] Ideally, the lens is considered a phase converter, which does not change the light intensity distribution but only the curvature of the light wavefront, introducing a quadratic phase factor (where the negative sign indicates phase lag, converting the plane wave into a converging spherical wave (positive lens)):

[0078] In the formula: The wavelength of the laser. f Focal length , They are respectively x , y Spatial frequency of direction, For wave number, , This represents the complex amplitude of the input optical field before propagation and the complex amplitude of the output optical field after propagation. , This represents the Fourier transform and the inverse Fourier transform. r Indicates the distance from the optical axis. This represents the phase transformation function of the lens. j The imaginary unit; In summary, the scalar diffraction process can be summarized into five stages: free space propagation, lens propagation, lens propagation, and free space propagation. The complex amplitude of the light field at the entrance pupil of the objective lens is obtained through the above calculations.

[0079] 2.2 Vector Debye-Wolf Integral

[0080] In S2 of this embodiment, the core theoretical basis for the calculation of the vector part is the Debye-Wolf integral, and its calculation process is as follows: pass , Mapping Cartesian coordinates to spherical coordinates using numerical aperture limit The integration range; for x Linearly polarized light Its component on the spherical wavefront near the focal region satisfy:

[0081] for x Polarized light can be easily analyzed to draw the following conclusions: the vast majority of the energy of the light field is concentrated in... x Direction, there is a slight presence in the 45° direction of the four quadrants. y Quantity, and z The contribution of the component to the focal spot gradually increases with the increase of the numerical aperture NA.

[0082] When the observation plane translates near the focal point At different times Different angles produce different optical path differences, and corresponding phase differences. Represented as:

[0083] If we consider the light field at the observation plane (focal plane or the plane introducing defocus) as a Fourier transform of the exit pupil, then for a vector field,

[0084] When the spherical coordinates are transformed back to the Cartesian coordinate system based on the Abbe sine condition, the integral of the above equation is numerically equivalent to the 2D Fourier transform of the light field in the entrance pupil plane. In the formula: x , y These are coordinates in the Cartesian coordinate system. It is the polar angle. It's the azimuth. f Focal length; n The refractive index of the medium, k For wave number, C A constant factor, Indicates the integration region. This represents the vector electric field distribution on the entrance pupil. j It is the imaginary unit.

[0085] At this point, a partitioning calculation method for specific ROIs needs to be introduced. The most common implementation of the Discrete Fourier Transform is the Fast Fourier Transform (FFT). The core advantages of this algorithm are its high efficiency and fast computation speed, enabling it to perform Fast Fourier Transform operations across the entire domain. However, the characteristics of the FFT algorithm determine that its output grid resolution is fixed and limited, satisfying the relational... In photolithography applications, only the micro- and nano-scale details within the Region of Interest (ROI) need to be considered, eliminating the need for redundant calculations across the entire region. Conventional FFT output mesh sizes are typically on the order of hundreds of nanometers, which cannot meet the tens of nanometers of detail required for photolithography. Therefore, this approach abandons the traditional FFT solution method and derives its calculations based on the fundamental form of the Discrete Fourier Integral.

[0086] As is already known, this embodiment requires the calculation of the light field at the focal plane. With the light field of the entrance pupil There exists a Fourier transform relationship between them:

[0087] It needs to be converted into the form of Discrete Fourier Transform:

[0088] To decouple the sampling rates on both sides, the entrance pupil and exit pupil are first divided into... and If the sampling points are:

[0089] Separate the exponent terms:

[0090] The first item is only related to x , u Related, the second item is only related to y , v Related. At this point, the two-dimensional Fourier transform becomes two one-dimensional Fourier transforms. Constructing the matrix. :

[0091] in, m and p The sampling points corresponding to the exit pupil and focal plane are physically represented as the entrance pupil. p The light emitted from the point reaches the focal plane m The phase delay generated at each sampling point. After calculating all sampling points, we can obtain:

[0092] Observing the dimensions of each matrix reveals that: P Dimensions ,matrix K Dimensions , Dimensions Then we obtain Dimensions This decouples the sampling rates before and after the Fourier transform. During the Fourier transform calculation, all spatial frequency components of the entrance pupil are fully incorporated, and calculations are performed only on the spatial frequency components within the ROI region of the focal plane, thus enabling customized calculation accuracy.

[0093] After obtaining the accurate light field distribution, the photoresist profile is fitted using a photoresist physical model. The process that most significantly affects the final photoresist profile morphology is the diffusion process of photoacid after exposure, which approximately satisfies the diffusion equation:

[0094] in, TPPI The photoacid concentration distribution after exposure is shown. Therefore, through optical calculation models and photoresist models, accurate simulation from phase map (group) to photoresist profile is achieved.

[0095] 2.3 Inverse Optimization Algorithm

[0096] The diffraction model is coded in Python using the PyTorch framework in a fully differentiable manner. Utilizing the framework's automatic differentiation and backpropagation mechanisms, the forward calculation process is transformed into a reverse optimization process, thus forming the reverse optimization algorithm. Its execution flow is as follows: Figure 4 As shown.

[0097] Specifically, in S2 of this embodiment, the execution flow of the reverse optimization algorithm is as follows: The phase map group involved in the calculation and its corresponding target pattern Introducing the inverse optimization algorithm, assuming that the photoresist pattern corresponding to the phase map group in a certain iteration process is... Fitting using the sigmoid function:

[0098] The final photoacid concentration is set at a threshold. Define the outline as the photoresist; k The larger the value, the steeper the gradient of photoresist development from 0 to 1.

[0099] Define loss function for:

[0100] The loss function is actually... and The mean square error is essentially a measure of the geometric distance between the physical field and the simulated field in Euclidean space. In the current physical context, it penalizes the integral of the area and intensity of the erroneously exposed region.

[0101] According to the chain rule of gradients, the loss function For phase variables The gradient is expressed as:

[0102] From beginning to end, this represents the inverse process of fitting the phase map to the photoresist profile. This function is calculated to achieve an exact derivative of the loss function with respect to the optimization variables.

[0103] Let the sigmoid function be denoted as... In terms of form, the gradient propagation of the developing layer focuses on:

[0104] The above operations amplify the gradient during the iteration process. k Numerical dynamic changes: initial optimization k When the value is small, the optimizer focuses on optimizing the internal pattern fidelity of the photoresist; as the iteration progresses, k As the value gradually increases, the gradient reaches the threshold. It is extremely sensitive in the vicinity, and decays rapidly far away from the threshold, ensuring that the optimization focuses on fine-tuning at the edge position in the later stages.

[0105] Gradient of the exposure layer Nonlinear response of photoresist Correlation, gradient is:

[0106] The gradient magnitude is closely related to the local light intensity, meaning the optimizer primarily operates at locations where the light intensity changes abruptly, i.e., the edges of the graph. PyTorch automatically performs the differential of the complex function, allowing the gradient to be transferred from the real number (light intensity) back to the phase domain, ultimately acting on each phase graph involved in the calculation.

[0107] The Adam optimizer was chosen instead of the traditional SGD (Stochastic Gradient Descent) because low-frequency phase changes and high-frequency phase abrupt changes have similar effects on photoresist morphology, but produce significantly different gradients. Using SGD can easily lead to local optima. This embodiment employs the Adam optimizer for adaptive gradient updates to the phase map.

[0108] In the formula: The concentration of photoacid after diffusion of the photoresist model. H , W These are the width and height of the image, respectively. For phase diagram group, p for abbreviation, The average light intensity Refers to sigmoid. and The first t The parameters updated in the next iteration and the updated parameters For learning rate, This is the bias correction value for the second-order moment estimation. To prevent division by a very small positive number, This is the bias correction value for the first-order moment estimation.

[0109] This algorithm can automatically amplify the step size of gradients and low-frequency parameters that have an unequal impact on the loss function, playing an important role in balancing the overall image fidelity and local edge sharpness during hologram optimization.

[0110] III. A Data-Driven, High-Efficiency Digital Holographic Lithography OPC Algorithm

[0111] While the gradient descent phase inversion lithography (GD-ILT) algorithm based on a physical model can generate high-quality phase masks, it suffers from high computational cost and significant time consumption. This is because each iteration requires a complete lithographic simulation and gradient backpropagation calculation.

[0112] To address this, this embodiment proposes a data-driven deep learning framework. Leveraging the powerful nonlinear mapping capabilities of convolutional neural networks, it transforms the time-consuming iterative optimization process into a single forward inference process. The specific steps are as follows: OPC layouts are extracted from the light field profiles corresponding to the optimized phase map as ground truth labels and used to construct paired training datasets with the original lithography layouts. An improved U-Net network is used to train the training dataset in blocks. The improved U-Net network uses multi-scale convolutional kernels to extract features in the encoding layer and fuses shallow detail information through skip connections in the decoding layer. During the inference phase, the lithography pattern to be optimized is input into the trained improved U-Net network. The large-size pattern is divided using an overlapping block strategy. In the fusion output phase, Gaussian weights are used to weight and fuse the inference results of each sub-block. Finally, the lithography pattern corrected by the optical proximity effect is directly output.

[0113] Specifically, each set of training data comes from the complete GD-ILT process. The phase map generated by the GS algorithm can be used to obtain the corresponding light field intensity distribution through an optical simulation system. Then, the light field profile is extracted from this intensity distribution to construct the training dataset.

[0114] The training dataset construction process is as follows: The initial phase map is solved using the GS algorithm, followed by phase optimization using the GD-ILT algorithm. The light field morphology before and after optimization is extracted and paired as training data. The light field morphology before optimization serves as the network input, and the light field morphology after optimization serves as the ground truth label. Thus, the trained neural network constitutes the inverse lithography calculation function.

[0115] In the formula: For the target graphic, This is the corrected mask pattern. These are network parameters.

[0116] This scheme adopts an improved U-Net network structure adapted to lithography optimization tasks, using U-Net as the core solver to establish the target light field. To OPC optimized layout The nonlinear inverse mapping relationship is described. The network as a whole has a U-shaped symmetric topology and consists of four downsampling layers and four upsampling layers.

[0117] The downsampling shrinkage path progressively transforms the input image into a low-resolution, high-dimensional feature vector. Each downsampling module sequentially includes two 3×3 convolution operations, batch normalization, a ReLU activation function, and a 2×2 pooling layer. As the network layers progress, the number of feature channels doubles layer by layer, achieving effective extraction of deep semantic features. The bottleneck layer introduces a Dropout mechanism to effectively suppress overfitting during model training.

[0118] Upsampling is the inverse process of downsampling. It restores the feature size through four levels of deconvolution and gradually reduces the number of feature channels. Skip connections can directly pass the features extracted from each downsampling level to the upsampling stage. Among them, shallow features correspond to high-frequency details, edge and texture information, while deep features cover low-frequency components, global topology and semantic information. Relying on the skip connection structure, the network can simultaneously fuse high-frequency and low-frequency features to achieve multi-scale information collaborative representation.

[0119] Grayscale information plays a significant role in holographic lithography, but simulations typically involve sigmoid operations, which can make it difficult to fit grayscale information. Therefore, phase generation patterns generally use binary graphics. This model uses binary cross-entropy loss (BCE loss) as the loss function during training.

[0120] This loss function is highly sensitive to binary classification problems and can apply strong gradient constraints to results where the predicted pixels are close to 0 or 1, thereby obtaining a high-contrast OPC mask. The neural network architecture and training diagram are shown below. Figure 5 As shown.

[0121] After model training, only the target pattern needs to be input into the neural network, and the network can output an OPC-optimized pattern in a very short time. The input and output patterns maintain the same resolution. Local high-resolution digital holographic phase calculations are performed on the OPC-optimized pattern to obtain a phase mask, which is then used for photolithography. Compared to directly calculating the phase using the original target pattern, this method significantly reduces the deviation between the actual contour of the photoresist and the target pattern.

[0122] IV. Specific Implementation Cases

[0123] This embodiment uses photolithographic patterns before and after optical proximity correction (OPC) as a comparison object. The pattern resolution is 1024×1024, and the physical resolution is 16nm / pixel. The pattern without OPC has sharp corners, smooth edges, and high contrast. The pattern with OPC exhibits typical compensation structures such as hammerheads and serifs, and its edges are smooth at this sampling accuracy, making it suitable for pre-compensation of optical proximity effects. Phase holograms are calculated using both the traditional FFT-GS algorithm and the method described in this invention. Simulations are performed based on a full-vector optical model and a photoresist diffusion model to verify the advantages of this invention in high-frequency detail preservation, contour fidelity, and computational efficiency. The specific implementation process is as follows.

[0124] 4.1 Simulation Comparison of Phase Generation Algorithms

[0125] The traditional FFT-GS algorithm and the method of this invention are used respectively to calculate phase hologram sets for target patterns without OPC and target patterns with OPC, each set containing 30 phase holograms; the incoherent superposition light field of the phase hologram sets is calculated based on the full vector optical model, and the photoresist morphology is predicted by combining the photoresist diffusion model. The mean square error of the light field profile (MSE, proving the algorithm's ability to reconstruct the light field) and the MSE of the photoresist profile and the target pattern (proving the effect of OPC) are used as evaluation indicators.

[0126] Reference Figure 6 (From left to right: target pattern input to the algorithm, simulated light field of the calculated phase map group, comparison of light field morphology with target pattern, comparison of photoresist contour fitted by photoresist model with target pattern). When the two algorithms are used to calculate the target layout without OPC, there is no significant difference between the results obtained by the two algorithms because the structural line width size in the layout is an integer multiple of the SLM equivalent pixel size of 256nm.

[0127] Reference Figure 7(From left to right: target pattern input to the algorithm, simulated light field of the calculated phase map group, comparison of light field morphology with target pattern, comparison of photoresist contour fitted by photoresist model with target pattern). When the target layout of OPC is calculated using two different algorithms, the traditional FFT-GS algorithm loses a large number of high-frequency details of the layout due to discretization sampling error, and the reconstructed structure deviates significantly from the target pattern. However, the method of this invention can completely preserve the small features in the target pattern that are not integer multiples of the equivalent pixels of SLM, and the mean square error of the obtained light field and photoresist contour is significantly reduced. Under the constraint of physical diffraction limit, it can achieve high-fidelity approximation of the details of the target pattern and effectively eliminate the discretization error caused by traditional FFT sampling. Figure 8 It represents 1024 1024 (gray) and 64 The degree of spatial information retention when a 64 (dark gray) pattern represents the same physical space (16.384µm), 1024 A pattern of 1024 can accommodate more details.

[0128] The above examples fully demonstrate that the advantage of this algorithm lies in its ability to arbitrarily define the feature size of the target pattern. Relying on the high degree of freedom of phase modulation, it achieves higher fidelity reconstruction of the target pattern details within the physical diffraction limit under the condition that the number of pixels in the spatial light modulator (SLM) is limited, while eliminating the discretization error caused by traditional FFT sampling.

[0129] To verify the computational advantage of this invention, the algorithm was uniformly set to a computational dimension of 1024×1024, the number of phase maps generated was set to 1, and GPU acceleration using the PyTorch framework was employed. The computation time for both stages of the traditional FFT-GS and this invention was recorded. (Refer to...) Figure 9 The results show that, under normal iteration counts, the computation time of this invention is approximately 240% of that of the traditional FFT-GS algorithm, but the sampling accuracy is improved by more than 16 times. In comparison, under the same sampling accuracy, the traditional FFT method requires increasing the matrix dimension to 16384×16384, resulting in an exponential increase in computational load and memory consumption, making it difficult to implement in practice. Therefore, this invention achieves an optimal balance between computational efficiency and accuracy.

[0130] 4.2 Physics-Driven Reverse Optimization and Data-Driven OPC Algorithm Implementation

[0131] The OPC algorithm needs to be implemented by combining an optical field calculation model and a photoresist model. After calculating the phase map based on the target pattern, the corresponding photoresist contour is obtained through a simulation model. Affected by the optical proximity effect and photoresist diffusion, the pattern is prone to distortions such as linewidth deviation and corner rounding, resulting in a significant difference between the photoresist contour and the design target. Figure 10As shown, the images sequentially depict the target pattern, the light field distribution simulated from the phase map, the photoacid concentration distribution calculated using the photoresist diffusion model, and the final simulated photoresist outline. Figure 10 As can be seen, after the photoresist diffusion process, the photoresist outline differs significantly from the target pattern, with obvious increases in line width and rounding of corners.

[0132] The gradient descent-based physical-driven optimization algorithm takes the target pattern and its corresponding phase map group as input. It first performs forward simulation calculations, and then updates the distribution of each phase map in the phase map group through backward gradient propagation based on the mean square error (MSE) between the photoresist profile and the target pattern. The optimization objective is to minimize the deviation between the photoresist profile and the target pattern.

[0133] The optimized target pattern, the simulated light field corresponding to the optimized phase map, the photoacid concentration obtained from the photoresist diffusion model, and the final simulated photoresist profile are shown below. Figure 11 As shown in the figure, the results demonstrate that this algorithm can accurately constrain the simulated light field profile, significantly reducing the deviation between the photoresist profile after photoresist diffusion and the target pattern. The mean square error is reduced from 0.04 to 0.001, indicating a good optimization effect.

[0134] The contour information is extracted from the light field contour corresponding to the above optimization results, and used as the target pattern to recalculate the phase map, light field distribution, and photoresist contour. The results are as follows: Figure 12 As shown. Among them, Figure 12 (a) is the calculation result directly using the original target pattern. Figure 12 (b) is the result of gradient descent optimization. Figure 12 (c) shows the calculation results based on the extracted light field profile from the optimized phase map group. The MSE values ​​for the three sets of results are 0.04, 0.002, and 0.01, respectively. This indicates that although the calculation results based on the extracted profile do not reach the accuracy level of gradient descent optimization, the error is reduced by more than 60% compared to the unoptimized results. Since the simulation environment is usually ideal and deviates somewhat from actual experiments, the difference between the two sets of optimized results is small in actual processing. Therefore, the high efficiency advantage brought by the profile extraction method can compensate for the slight loss of accuracy.

[0135] Based on the above approach, this embodiment constructs a large number of basic pattern samples, completing the entire data preparation process from target layout, phase map calculation, gradient descent optimization to light field contour extraction. Some training set graphics are shown below. Figure 13 As shown.

[0136] The pattern resolution used for training is 1024. 1024, with a sampling interval of 16nm, covering typical lithographic structures such as straight lines, diagonal lines, arcs, and lines of different linewidths. To reduce computational power consumption, improve training stability, and avoid problems such as slow training of large-size patterns and difficulties in gradient normalization, this embodiment adopts a block training method, dividing a single training data sheet into 16 256-bit blocks proportionally. 256 sub-blocks enable the network to learn the mapping relationships between sub-blocks. The block division logic is as follows: Figure 14 As shown. During training, blocks with excessively small effective regions and completely blank sub-blocks are removed, and data augmentation is used to improve sample diversity, ensuring that block-based training does not cause the loss of effective information.

[0137] Figure 15 The graph shows the decrease in network training loss. As can be seen from the graph, the model basically converges after about 80 iterations.

[0138] Due to model learning 256 The mapping relationship of the 256-page image requires block-based dimensionality reduction, block-based inference, and result fusion during the inference phase. Unlike the training phase, if the same block-based strategy is directly used, the model is prone to noise and prediction distortion at the block boundaries. This is because each sub-block infers independently, failing to achieve cross-block feature association. Typical erroneous results include... Figure 16 As shown.

[0139] exist Figure 16 In the image, the bottom part shows the input pattern, and the top part shows the OPC output pattern. The output pattern exhibits significant asymmetry and distortion. The main reason is that the target structure is located at the edge of a block, preventing the model from performing cross-block expansion processing, resulting in inconsistent OPC correction results for the same structure. To address this issue, a staggered overlapping block strategy is adopted during the inference phase, initially using 16... The grid is divided into 16 sections, and then sampled in blocks at intervals of 128 pixels, as shown below. Figure 17 As shown.

[0140] This embodiment employs two block-based inference steps, each with a block size of 256. 256 pixels, with a step size of 128 pixels. Areas less than 256 pixels are padded before inference. After each region undergoes two independent inferences, Gaussian weights are used for weighted fusion, meaning the closer the pattern is to the block center, the higher the weight. This ensures that the edge region of one block method corresponds to the center region of another block method, thereby eliminating prediction anomalies caused by block division.

[0141] Figure 18The system parameters corresponding to the simulation results shown are as follows: the spatial light modulator (SLM) resolution is 1080×1080, the pixel pitch is 7.48um; the laser wavelength is 517nm; the focal lengths of the 4f system lenses are 200mm and 100mm respectively; the objective magnification is 100×, the numerical aperture NA=0.9, and the equivalent scaling magnification is 50×; the focal plane ROI size is 16.384um×16.384um, the sampling interval is 16nm, and the corresponding layout resolution is 1024×1024; 30 phase maps are calculated for each layout to form a phase map group.

[0142] Each set of results consists of the following: target pattern, simulated light field, simulated photoresist pattern, light field optimized by the physics-driven algorithm, optimized simulated photoresist pattern, OPC layout output by the neural network, and the simulated light field and simulated photoresist pattern corresponding to the OPC layout. The mirroring phenomenon observed in the figures is caused by the propagation characteristics of the light field.

[0143] The following indicators were used for quantitative evaluation: MSE: Mean Squared Error between Images, used to characterize the overall difference; the smaller the value, the smaller the difference. EPE: Edge Position Error, used to characterize the total offset of the edge of a graphic; the smaller the value, the smaller the offset. SSIM: Structural Similarity, used to characterize the degree of correlation between image structures, with a value range of 0–1, and the higher the value, the higher the correlation.

[0144] The test patterns include various structures such as straight lines, diagonal lines, and arcs, and none of them belong to the neural network training set samples.

[0145] Depend on Figure 19 It can be seen that the physics-driven optimization algorithm has higher computational accuracy, while the neural network data-driven algorithm has slightly lower accuracy, but still has a significant optimization effect compared to the unoptimized scheme.

[0146] This algorithm adopts a modular design, with the optical field calculation module and the photoresist model module in the physics-driven optimization algorithm being independent of each other. By modifying the optical system parameters (such as wavelength, objective lens magnification, numerical aperture NA, etc.), the algorithm can be adapted to various lithography optical systems; by adjusting the photoresist model, it can be compatible with various photoresist systems, including positive photoresist, negative photoresist, chemically amplified photoresist, and non-chemically amplified photoresist.

[0147] 4.3 System Scalability Verification

[0148] Combination Figure 20The scalability of the algorithm is explained below. Keeping the SLM parameters unchanged, the objective lens is replaced with a 100× oil immersion objective lens with NA=1.45 to improve the system's diffraction limit. At this point, the optical system's diffraction limit reaches 153.55 nm. With the increase in the system's numerical aperture, the overall resolution is significantly improved, and the light field details calculated by this algorithm are more uniform. This embodiment only demonstrates the optimization effect of the physics-driven optimization algorithm; if it is to be extended to a neural network model, retraining is required.

[0149] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0150] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling, characterized in that, Includes the following steps: S1. The seed phase is generated by the full-field constrained GSW algorithm, a sampling decoupled physical propagation matrix is ​​constructed, and local high sampling rate iterative correction is performed in the region of interest (ROI) to suppress coherent speckle, thereby obtaining a local high-resolution holographic phase map. S2. Based on the scalar angle spectrum method, vector Debye-Wolf integral and photoresist diffusion model, light field simulation is performed. The photoresist profile error is used as the loss function and the gradient descent algorithm is used for inverse optimization to obtain the optimized phase map. S3. Extract the OPC layout based on the optimized phase map and construct the training dataset. Use the improved U-Net network for block training and perform overlapping block and Gaussian weight inference to output the corrected OPC layout. S4. Generate a phase mask for photolithography from the OPC modified layout according to S1 to achieve complete phase generation and optical proximity effect optimization.

2. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S1, the full-field constraint GSW algorithm is used to generate the seed phase. Specifically, the target pattern is reduced in dimensionality by bilinear interpolation and zero-padding is applied to the center of the black background with the same resolution as the spatial light modulator. The SLM plane and the image plane are iterated through FFT and i-FFT. Phase preservation and amplitude one-constraint are performed on the SLM plane, and phase preservation and amplitude replacement with the target pattern constraint are performed on the image plane. The GSW algorithm uses dynamic amplitude weights for iterative constraints, and the weight formula is as follows: In the formula: As amplitude weight, a To update the coefficients, I This represents the current intensity distribution. The target intensity distribution.

3. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S1, the sampling decoupling physical propagation matrix is ​​constructed, specifically by establishing the physical pixel coordinates of the SLM plane and the high-resolution sampling coordinates of the image plane, and generating the sampling decoupling physical propagation matrix. : In the formula: For high-resolution sampling coordinates of the image plane, These are the physical pixel coordinates of the SLM plane. The wavelength of the laser. f It is the focal length.

4. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S1, local high sampling rate iterative correction is performed, specifically by using sampling to decouple the physical propagation matrix. Perform positive propagation, through Calculate the complex amplitude optical field of the ROI region; convert the complex amplitude optical field of the ROI region... Phase preservation and amplitude replacement with target binarized amplitude; through Inverse inversion is performed, forcing the complex amplitude of the SLM surface to a uniform amplitude while retaining only the phase; where, The complex amplitude of the current SLM surface. To Take the conjugate transpose of the matrix.

5. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S1, suppressing coherent speckle specifically involves: changing the random seed to generate multiple statistically independent phase holograms with consistent target intensity; and during exposure, using a spatial light modulator to rapidly switch at a set frame rate to reduce the speckle contrast to its original value. .

6. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S2, the calculation process of the scalar angle spectrum method is as follows: For the scalar diffraction component, the wavefront is converted into different spatial frequency components, i.e., the angular spectrum, through Fourier transform; when the beam propagates a distance in free space... z When the transfer function is used, it is expressed as: Thus, it spreads in free space. z hour, Ideally, the lens can be considered a phase converter, changing only the curvature of the light wavefront without altering the light intensity distribution, by introducing a quadratic phase factor: In the formula: The wavelength of the laser. f Focal length , They are respectively x , y Spatial frequency of direction, For wave number, , This represents the complex amplitude of the input optical field before propagation and the complex amplitude of the output optical field after propagation. , This represents the Fourier transform and the inverse Fourier transform. r Indicates the distance from the optical axis. This represents the phase transformation function of the lens. j The imaginary unit; The scalar diffraction process can be summarized into five stages: free space propagation, lens propagation, lens propagation, and free space propagation. The complex amplitude of the light field at the entrance pupil of the objective lens is obtained through the above calculations.

7. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S2, the calculation process of the vector Debye-Wolf integral is as follows: pass , Mapping Cartesian coordinates to spherical coordinates using numerical aperture limit The integration range; for x Linearly polarized light Its component on the spherical wavefront near the focal region satisfy: When the observation plane translates near the focal point At different times Different angles produce different optical path differences, and corresponding phase differences. Represented as: If we consider the light field at the observation plane as a Fourier transform of the exit pupil, for a vector field... When the spherical coordinates are transformed back to the Cartesian coordinate system based on the Abbe sine condition, the integral of the above equation is numerically equivalent to the 2D Fourier transform of the light field in the entrance pupil plane. In the formula: x , y These are coordinates in the Cartesian coordinate system. It is the polar angle. It's the azimuth. f Focal length; n The refractive index of the medium, k For wave number, C A constant factor, Indicates the integration region. This represents the vector electric field distribution on the entrance pupil. j It is the imaginary unit.

8. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, In S2, the execution flow of the inverse optimization algorithm is as follows: The phase map group involved in the calculation and its corresponding target pattern Introducing the inverse optimization algorithm, assuming that the photoresist pattern corresponding to the phase map group in a certain iteration process is... Fitting using the sigmoid function: The final photoacid concentration is set at a threshold. Define the outline as the photoresist; Define loss function for: According to the chain rule of gradients, the loss function For phase variables The gradient is expressed as: Let the sigmoid function be denoted as... In terms of form, the gradient propagation of the developing layer focuses on: Gradient of the exposure layer Nonlinear response of photoresist Correlation, gradient is: At the edges of the graph, the Adam optimizer is used to perform adaptive gradient updates on the phase map: In the formula: The concentration of photoacid after diffusion of the photoresist model. H , W These are the width and height of the image, respectively. For phase diagram group, p for abbreviation, The average light intensity Refers to sigmoid. and The first t The parameters updated in the next iteration and the updated parameters. For learning rate, This is the bias correction value for the second-order moment estimation. To prevent division by zero of a very small positive number, This is the bias correction value for the first-order moment estimation.

9. The method for local high-resolution holographic phase generation and optical proximity effect optimization based on sampling decoupling according to claim 1, characterized in that, S3 specifically includes the following steps: OPC layouts are extracted from the light field profiles corresponding to the optimized phase map as ground truth labels and used to construct paired training datasets with the original lithography layouts. An improved U-Net network is used to train the training dataset in blocks. The improved U-Net network uses multi-scale convolutional kernels to extract features in the encoding layer and fuses shallow detail information through skip connections in the decoding layer. During the inference phase, the lithography pattern to be optimized is input into the trained improved U-Net network. The large-size pattern is divided using an overlapping block strategy. In the fusion output phase, Gaussian weights are used to weight and fuse the inference results of each sub-block. Finally, the lithography pattern corrected by the optical proximity effect is directly output.

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