Mask construction method based on digital holographic computational lithography

Abstract

The invention belongs to the technical field of holographic lithography, and provides a mask construction method based on digital holographic calculation lithography, which comprises the following steps: 1, reversely constructing complex plane distribution of mask emergent waves based on a target lithography image; 2, modeling is carried out according to a light field regulation and control method, and an illumination wavefront initial value and a mask initial value are calculated through numerical values; 3, alternately optimizing the mask Um and the illumination wavefront U1 through variational inference; and 4, repeating the step 3 until the constructed mask Um meets a process processing constraint condition. According to the method, the technical problem that a mask construction method is lacked in digital holographic calculation photoetching is effectively solved, and a reliable solution is provided for construction of a next-generation high-precision holographic calculation photoetching mask.

Description

Technical Field

[0001] This invention relates to the field of holographic lithography, and more specifically, to a mask construction method based on digital holographic computational lithography. Background Technology

[0002] Photolithography is a core component of integrated circuit manufacturing. Its precision directly determines the feature size and process node of chips, making it a key indicator of semiconductor manufacturing capabilities and technological self-reliance. Over the past four decades, the continuous iteration of photolithography technology has powerfully driven the continuation of Moore's Law, becoming a core driving force for the development of the global semiconductor industry. By continuously shortening the wavelength of the light source, the critical dimensions of devices have evolved from the micrometer level to the nanometer level, achieving a leapfrog improvement in process capabilities.

[0003] However, since the commercial application of Extreme Ultraviolet (EUV) lithography, the rate of improvement in lithography resolution has slowed significantly, and Moore's Law is approaching its physical limits. Although the EUV exposure wavelength has been reduced to 13.5 nm, the technology still faces multiple engineering bottlenecks, including insufficient light source power, high optical system complexity, and difficulty in mask manufacturing. The traditional projection lithography technology route, which relies on "wavelength reduction + numerical aperture improvement," can no longer sustainably support the evolution of future advanced processes. Digital holographic computational lithography, based on the principle of lensless holographic imaging, does not require a complex projection optical system and can fully utilize the wavefront control capability of the light source. While significantly reducing system complexity, it is expected to achieve higher resolution and exposure throughput.

[0004] Despite the immense technological potential of digital holographic computational lithography, a core challenge to its engineering applications lies in the lack of a well-established method for constructing holographic masks. Unlike traditional projection lithography, which directly replicates mask patterns, holographic masks require precise encoding of the complex amplitude holographic information of the target pattern. The design process involves complex backpropagation calculations and phase optimization. Currently, research on holographic mask construction methods is still in its early stages, lacking systematic reverse design techniques from target images to mask structures, and particularly lacking robust mask reconstruction algorithms to address practical engineering problems such as manufacturing errors and light source instability. This technological gap severely restricts the transformation of digital holographic computational lithography from proof-of-concept to engineering applications. Summary of the Invention

[0005] To address the above-mentioned needs of existing technologies, this invention provides a mask construction method based on digital holographic computational lithography. By establishing a precise mapping relationship between the target pattern and the mask structure, it aims to achieve high-precision and robust mask design, thereby providing reliable technical support for the engineering application of digital holographic computational lithography.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The mask construction method based on digital holographic computational lithography of this invention includes the following steps: Step 1: Acquire the target lithography image I GT Let the distance between the mask and the photolithography wafer be Z; the wavelength of the illumination source be... ; Step 2: Based on the target lithography image I GT Reconstructing the mask's emitted wave under light source illumination ; Step 2.1: Define the current iteration number as k, and initialize k=0; define the mask outgoing wave in the k-th iteration as... and initialize ; Step 2.2: Based on the angular spectrum propagation model, calculate the intermediate variables in the k-th iteration using equation (1). Thus, the intermediate variables under the (k+1)th iteration can be calculated using equation (2). Then, the mask-out wave under the (k+1)th iteration is calculated using equation (3). ; (1) (2) (3) In equations (1)-(3), H represents the propagation operator based on the angular spectrum transfer model. and These represent the forward and inverse Fourier transform operators, respectively. Step 2.3, Assign to Then, return to step 2.2 and execute sequentially until the convergence condition is met, at which point the iteration stops, and the mask-out wave under the last iteration is denoted as... ; Step 3, according to Inference Mask With illumination wavefront ; Step 3.1: Define the index of the wavefront modulation method for the lighting source as j, initialize j=1, and construct the physical constraint R; Step 3.2: Initialize k=0; initialize the j-th illumination wavefront for the j-th wavefront modulation method. ; Based on the mask light field transmission model, calculate Corresponding mask initial value ; Step 3.3: Based on the physical constraint R and the mask light field transmission model, use the variational inference model to iterate alternately. and The mask corresponding to the j-th illumination wavefront under the k-th iteration is obtained accordingly. and the j-th illumination wavefront in the (k+1)-th iteration ; Step 3.4: After assigning k+1 to k, return to step 3.3 and execute sequentially until the convergence condition is met. The mask corresponding to the j-th illumination wavefront in the last iteration is then obtained, denoted as [Mask Name]. And the j-th illumination wavefront in the last iteration is denoted as ; Step 3.5: After assigning j+1 to j, return to step 3.2 and execute sequentially until j=J, at which point the iteration stops, thus obtaining the masks corresponding to the J illumination wavefronts. and J types of illumination wavefront J represents the total number of wavefront modulation methods; Step 4, from as well as The best pair of masks and illumination wavefronts for processing and photolithography results were selected for photolithography.

[0007] The mask construction method based on digital holographic computational lithography described in this invention is also characterized in that step 2.2 uses equation (4) to construct an angular spectrum propagation model: (4) In formula (4), i represents an imaginary number, f x and f y These represent the frequency domain coordinates of H in the x and y directions, respectively.

[0008] Furthermore, in step 3.3, the mask light field propagation model is constructed using equation (5): (5) In equation (5), Г represents the Maxwell electromagnetic wave vector propagation operator. This represents the wavefront that actually illuminates the mask. Indicates the actual mask, This represents the emitted wave from the mask after actual illumination.

[0009] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in performing the method described therein, and the processor is configured to execute the program stored in the memory.

[0010] The present invention provides a computer-readable storage medium on which a computer program is stored, characterized in that the computer program is executed by a processor to perform the steps of the method described thereon.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Filling a technological gap: This invention addresses the technological bottleneck of the lack of mask construction methods in digital holographic computational lithography by proposing a systematic mask reconstruction scheme, providing key technical support for the transformation of holographic lithography from theoretical research to engineering applications.

[0012] 2. Achieving Robust Decomposition and Optimization: This invention introduces a Bayesian variational inference framework to recover the mask-embedded wave. Based on this, the illumination wavefront U1 and mask U1 were implemented. m The separation and joint optimization effectively balances the contradiction between the manufacturability of the mask process and the feasibility of illumination.

[0013] 3. Ensuring process feasibility: This invention ensures that the reconstructed mask meets the actual processing requirements by using a process-constrained projection operator, which significantly improves the engineering feasibility of the solution.

[0014] 4. Improved reconstruction accuracy: This invention achieves high-precision and robust mask and illumination wavefront reconstruction by using an alternating iterative optimization strategy, while satisfying physical constraints and considering noise effects and prior constraints. This provides a reliable mask design method for high-resolution digital holographic lithography. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a mask construction method for digital holographic computational lithography provided by the present invention; Figure 2 Parts 201 and 202 in the example target lithography pattern I are respectively GT and the reconstructed mask output wave ; Figure 3 Parts 301, 302, and 303 in the figure represent the three initial values ​​of the illumination wavefront calculated after numerical modeling of the three light field manipulation methods. Parts 304, 305, and 306 are based on the initial values ​​of the illumination wavefront, respectively. Waves emitted from the mask Three corresponding initial mask values ​​were separated. ; Figure 4 Parts 401, 402, and 403 represent three optimization results after variational inference of the illumination wavefront U1; parts 404, 405, and 406 represent optimization results after variational inference of the mask U1.m Three optimization results after variational inference. Detailed Implementation

[0016] Please see Figure 1 In this embodiment, a mask construction method for digital holographic computational lithography involves reverse-engineering the mask's outgoing wave from the target lithographic image. The complex plane distribution of the mask is determined, and the mask Um and illumination wavefront U1 are iteratively applied according to a variational inference model. This solves the technical problem of the lack of mask construction methods in digital holographic computational lithography and provides a reliable solution for the construction of next-generation high-precision holographic computational lithography masks. Specifically, the mask construction method of this digital holographic computational lithography mainly includes the following steps: Step 101, define the target lithography image as (like Figure 2 As shown in section 201), the distance between the mask and the photolithography wafer is Z; the distance between the mask and the photolithography wafer is Z, and in a specific embodiment, Z=3mm. Z is not limited to a specific shape or number.

[0017] Step 102, based on the target lithography image I GT Reconstructing the mask emitted wave First, the light field propagation model needs to be numerically modeled using the angular spectrum propagation model, as shown in equation (1): (1) In equation (1), Z represents the distance from the mask emission plane to the wafer, λ represents the illumination wavelength, i represents the imaginary number, and f x and f y These represent the frequency domain coordinates of H in the x and y directions, respectively.

[0018] Subsequently, the target lithography pattern I was used. GT Multiple iterations to reconstruct the complex plane of the emitted wave from the mask As shown in equations (2) to (4): (2) (3) (4) in, As an intermediate variable, This represents the updated emitted wave from the mask, where k is the number of iterations. and These represent the Fourier transform and inverse Fourier transform operators, respectively.

[0019] Repeat the above steps until the convergence condition is met, then stop the iteration. The convergence condition is shown in equation (5): (5) In equation (5), This represents the set sample residual threshold. When the residual of the mask emitted from the (k+1)th iteration and the residual from the kth iteration are less than the threshold, the iteration result is considered convergent. Figure 2 As shown in section 202.

[0020] Step 103, output the result based on step 102. Inference Mask With illumination wavefront The mask light field transmission model is numerically modeled using equation (6): (6) In equation (6), Г represents the propagation operator of Maxwell's electromagnetic wave vector. This represents the wavefront that actually illuminates the mask. Indicates the actual mask, This represents the emitted wave from the mask after actual illumination.

[0021] Step 104: Select multiple wavefront modulation methods and initialize the corresponding illumination wavefronts for each wavefront modulation method, inputting the physical constraint R; in this embodiment, three light field modulation methods are selected: orbital angular momentum, off-axis illumination, and structured light illumination, and the j-th illumination wavefront of the j-th wavefront modulation method is initialized. , ,like Figure 3 As shown in sections 301, 302, and 303; subsequently, the corresponding initial mask values ​​are calculated based on the mask transport model. , ,like Figure 3 As shown in sections 304, 305, and 306; Step 105: Alternately optimize mask U through variational inference. m With the illumination wavefront U1, iterate repeatedly until the mask U is obtained. m Processing constraints.

[0022] The mask initialized at k=0 and the initial value of the illumination wavefront are used. , As the starting point for optimization, the physical constraint R is determined by the process requirements of the required mask (e.g., the mask amplitude is a binary amplitude, and the phase is nπ). Based on this, a variational inference method is used for alternating iterations. and In this embodiment, Bayesian variational inference is used for iteration; The Bayesian posterior probability distribution model is shown in equations (7) and (8): (7) (8) The likelihood function is shown in equation (9): (9) The mask and illumination wavefront, after physical constraints, are a priori as shown in equations (10) and (11): (10) (11) in, Indicates the variance of environmental noise. , R represents the regularization weighting coefficients for the mask and illumination wavefront. m This is a function for penalizing process constraints, constructed based on the actual constraints.

[0023] Based on this, the energy formula is constructed as shown in equation (12): (12) According to the energy formula, for the mask With illumination wavefront By taking the derivatives separately, we can obtain the result. and Perform alternating iterative updates.

[0024] (13) (14) The iteration stops when the convergence criteria of equations (13) and (14) are met. , Each condition represents a convergence criterion, and the iteration results are output. , like Figure 4 As shown in sections 401-406.

[0025] Based on the actual processing conditions and environmental factors in photolithography, the best pair of illumination wavefronts and masks are selected for photolithography.

[0026] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0027] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0028] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A mask construction method based on digital holographic computer lithography, characterized in that, The method comprises the following steps: Step 1, obtaining a target lithography image I GT , let the distance between the mask and the lithography wafer be Z; the wavelength of the illumination light source be ; Step 2, reconstructing the target lithography image I from the mask exit wave GT reconstructing the mask exit wave from the source illumination under source illumination ; Step 3, according to inferred mask with an illumination wavefront ; Step 4, from and The best pair of mask and illumination wavefront is selected for lithography from the set of process and lithography results.

2. The mask construction method based on digital holographic computer lithography according to claim 1, characterized in that, The step 2 comprises: Step 2.1, define the current iteration number as k, initialize k = 0; define the mask exit wave under the kth iteration as ; and initialize ; Step 2.

2. Calculate the intermediate variable at the kth iteration using equation (1) based on the angular spectrum propagation model Step 2.

3. Calculate the intermediate variable at the k+1th iteration using equation (2) based on the angular spectrum propagation model Step 2.

4. Calculate the mask exit wave at the k+1th iteration using equation (3) based on the angular spectrum propagation model ​ (1) (2) (3) In equations (1)-(3), H represents the propagation operator based on the angular spectrum transfer model. and These represent the forward and inverse Fourier transform operators, respectively. Step 2.3, set to After that, return to step 2.2 and sequentially execute until the iteration is stopped after the convergence condition is met, thereby recording the mask exit wave under the last iteration as .

3. The mask construction method based on digital holographic computer lithography according to claim 2, characterized in that, The step 2.2 is to construct an angular spectrum propagation model by using formula (4): (4) In formula (4), i represents an imaginary number, f x and f y respectively represent frequency domain coordinates of H in the x direction and the y direction.

4. The mask construction method based on digital holographic computer lithography according to claim 1, wherein, The step 3 comprises: Step 3.1, defining the index of the wavefront regulation method for the illumination light source as j, initializing j=1, and constructing a physical constraint R; Step 3.2, initialize k = 0; initialize the jth illumination wavefront of the jth wavefront modulation method ; According to the mask light field transmission model, the calculation corresponding mask initial value ; Step 3.3, according to the physical constraint R and the mask light field transmission model, using the variational inference model to alternately iterate With , the corresponding mask under the jth illumination wave front under the kth iteration is obtained And the jth illumination wave front under the k+1th iteration ; Step 3.4, after k+1 is assigned to k, return to step 3.3 to sequentially execute until the convergence condition is met, and the mask corresponding to the jth illumination wave front under the last iteration is obtained , and the jth illumination wave front under the last iteration is ; Step 3.5, after j+1 is assigned to j, return to step 3.2 for sequential execution until j=J, stop iteration, thereby obtaining the corresponding mask under J kinds of illumination wavefronts and J kinds of illumination wavefronts ; J represents the total number of wavefront control methods.

5. The mask formation method based on digital holographic computer lithography according to claim 4, characterized in that, In the step 3.3, a mask light field propagation model is constructed by using formula (5): (5) In formula (5), Г represents a transmission operator of a Maxwell electromagnetic wave vector, represents a wave front actually irradiated to a mask, represents an actual mask, represents an exit wave of the mask after irradiation in an actual situation.

6. An electronic device comprising a memory and a processor, characterized in that The memory is used to store a program supporting the processor to execute the method in any one of claims 1-5, and the processor is configured to execute the program stored in the memory.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to perform the steps of the method in any one of claims 1-5.

Images