Three-dimensional gray laser direct writing photoetching method and system based on adaptive moment estimation

Abstract

The invention provides a three-dimensional gray laser direct writing photoetching method and system based on adaptive moment estimation. The method comprises the following steps: constructing a forward imaging physical model based on a Gaussian beam model and a photoresist Sigmoid response function; based on the forward imaging physical model, a parameter conversion and constraint minimization method is adopted to construct an exposure optimization problem with the minimum error between the target three-dimensional structure and the predicted morphology as the target; solving the exposure optimization problem by adopting a self-adaptive moment estimation optimization algorithm to obtain optimal exposure distribution; the optimal exposure distribution is converted into a laser scanning control instruction by adopting a path planning and energy mapping technology, and the laser scanning control instruction is sent to a laser and a two-dimensional scanning galvanometer for scanning exposure; according to the method, the adaptive moment estimation optimization algorithm is adopted, and the convergence speed and the manufacturing precision of three-dimensional laser direct writing photoetching are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of micro-nano fabrication technology, and in particular to a three-dimensional grayscale laser direct-write lithography method and system based on adaptive moment estimation. Background Technology

[0002] Laser direct-write lithography, as a flexible and high-resolution maskless lithography method, is widely used in the fabrication of three-dimensional micro- and nano-structures such as microelectromechanical systems (MEMS), photonic crystals, and micro-optical components. However, in actual manufacturing processes, due to the Gaussian distribution characteristics of the laser beam, the nonlinear photoresist response, and the energy accumulation effect, there are significant deviations between the actual exposed pattern and the target pattern, specifically manifested as "proximity effect" and "grayscale distortion".

[0003] Traditional inverse lithography (ILT) technology often employs gradient descent, simulated annealing, or genetic algorithms to optimize exposure dosage. However, these methods generally suffer from the following problems: slow convergence speed, especially when processing 3D grayscale patterns, requiring numerous iterations and consuming significant computational resources; local optima traps, making it difficult to escape local extrema, leading to unsatisfactory optimization results; sensitivity to noise, with unstable gradient estimation, easily affected by model errors and noise interference; and complex parameter tuning: hyperparameters such as learning rate and momentum require repeated manual adjustments and lack adaptability. Summary of the Invention

[0004] To address the problems of slow convergence, susceptibility to local optima, and sensitivity to noise in existing 3D laser direct-write lithography techniques, this invention proposes a 3D grayscale laser direct-write lithography method based on adaptive moment estimation. This method includes: constructing a forward imaging physical model based on a Gaussian beam model and the sigmoid response function of the photoresist; constructing an exposure optimization problem based on the forward imaging physical model using parameter transformation and constraint minimization methods, with the objective of minimizing the error between the target 3D structure and the predicted morphology; solving the exposure optimization problem using an adaptive moment estimation optimization algorithm to obtain the optimal exposure distribution; and converting the optimal exposure distribution into laser scanning control commands using path planning and energy mapping techniques, and sending these commands to the laser and a 2D scanning galvanometer for scanning exposure.

[0005] A three-dimensional grayscale laser direct-write lithography system based on adaptive moment estimation, the system includes: a forward imaging module, an optimization calculation module, a control execution module, an optical system, and a sensing and feedback system;

[0006] The forward imaging module consists of a laser source and a modulator. The laser source uses a laser that matches the photosensitive characteristics of the photoresist to provide the light source. The modulator uses an acousto-optic modulator or an electro-optic modulator as the core execution component. It achieves nanometer-level laser power adjustment based on real-time voltage control signals to complete high-precision grayscale exposure.

[0007] The optimization calculation module includes an optimization algorithm engine, a data processing and path planning sub-module, a graphical user interface and a system calibration and model maintenance sub-module, which respectively realize the functions of outputting the optimal exposure energy distribution map, converting control commands, human-computer interaction operation and system parameter calibration and maintenance.

[0008] The control execution module consists of a high-precision nano-positioning platform and a Z-axis focusing control system, which is used to execute the laser focus scanning trajectory and realize multi-axis linkage to complete the three-dimensional structure manufacturing.

[0009] The optical system consists of a beam spreading and collimating component and an objective lens, ensuring that the laser beam enters the objective lens in an ideal state and is focused to form a tiny spot. The numerical aperture of the objective lens directly determines the theoretical resolution and minimum spot size of the system.

[0010] The sensing and feedback system is used to monitor the platform position and laser power in real time, providing closed-loop control support for the system and ensuring the accuracy of the exposure process.

[0011] To achieve the above objectives, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the above-described three-dimensional grayscale laser direct-write lithography methods based on adaptive moment estimation.

[0012] To achieve the above objectives, the present invention also provides a three-dimensional grayscale laser direct-write lithography apparatus based on adaptive moment estimation, comprising a processor and a memory; the memory is used to store a computer program; the processor is connected to the memory and is used to execute the computer program stored in the memory, so that the three-dimensional grayscale laser direct-write lithography apparatus based on adaptive moment estimation performs any of the above-mentioned three-dimensional grayscale laser direct-write lithography methods based on adaptive moment estimation.

[0013] The beneficial effects of this invention are:

[0014] This invention addresses the pain points of traditional reverse lithography optimization (gradient descent, simulated annealing, etc.) through a comprehensive design encompassing "precise physical modeling - constraint optimization construction - improved algorithm solution - system architecture implementation." It significantly improves convergence speed and avoids local optima by enhancing the Adam algorithm (including adaptive learning rate decay, gradient pruning, and momentum restart). Furthermore, its adaptive characteristics reduce manual hyperparameter tuning and mitigate noise sensitivity. This invention offers high optimization efficiency, significantly reducing the cost of large-scale 3D structure optimization. It can fabricate complex two- / three-dimensional micro / nano structures such as microelectromechanical systems (MEMS), photonic crystals, and micro-optical elements. It also boasts strong compatibility, easy integration into existing laser direct-writing systems, and outstanding engineering practicality and applicability. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the process of the present invention;

[0016] Figure 2 This is the normalized intensity distribution diagram of the Gaussian beam of the present invention;

[0017] Figure 3 This is a Sigmoid function curve of the photoresist effect in this invention;

[0018] Figure 4 This is a diagram of the exposure optimization iteration framework of the present invention;

[0019] Figure 5 This is a system structure diagram of the present invention;

[0020] Figure 6 This is a comparison of the convergence curves of the Adam optimization algorithm of this invention and the traditional method;

[0021] Figure 7 These are comparison images of the two-dimensional and three-dimensional microstructures before and after optimization in this invention. Detailed Implementation

[0022] 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.

[0023] A three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation, the overall process of which is as follows: Figure 1 As shown, its core lies in using a precise physical model to inversely calculate the exposure distribution required for laser scanning from the target's three-dimensional structure, and then employing the Adam optimization algorithm to efficiently and accurately solve this inverse problem. Specific implementation methods include:

[0024] S1. Using the Gaussian beam model and the Sigmoid response function of the photoresist, establish a forward imaging physical model that accurately describes the laser energy distribution and the nonlinear response of the photoresist, and construct a mathematical model (i.e., the "forward model") that can accurately predict how the laser forms a three-dimensional structure in the photoresist. Specifically, this includes the following steps:

[0025] Step 1.1, Laser Beam Modeling:

[0026] like Figure 2 As shown, the energy of the laser beam exhibits a three-dimensional Gaussian distribution near the focal point. To simplify calculations while maintaining accuracy, a two-dimensional Gaussian model is used on the focal plane to describe the intensity distribution of the light spot:

[0027]

[0028] Where G(x,y) is the Gaussian beam profile model, P is the laser power, and w0 is the beam waist radius (in nm), which determines the spot size and the theoretical resolution of the system. This parameter can be obtained through experimental measurement combined with Gaussian fitting.

[0029] Step 1.2, Dose distribution calculation:

[0030] During laser scanning, the total exposure dose J(x,y) received at a point (x,y) on the substrate is not determined solely by the exposure at that point, but rather by the superposition of contributions from all positions along the laser spot's scanning path. This can be obtained by performing a two-dimensional convolution operation between the laser intensity distribution G(x,y) and the designed exposure distribution pattern L(x,y) (i.e., the variable to be optimized, representing the relative exposure intensity at each point).

[0031] J(x,y)=G(x,y) L(x,y)

[0032] This convolution operation mathematically simulates the "proximity effect" in the laser direct writing process, which means that due to the finite size of the light spot, the energy of adjacent exposure points will diffuse and superimpose.

[0033] Step 1.3, Modeling the response characteristics of photoresist:

[0034] The response of photoresist to exposure dose is non-linear. To accurately simulate the transition from dose to final morphology, a sigmoid function is used to map the dose distribution J(x,y) to the final post-development morphology I(x,y) (e.g., normalized residual resist thickness):

[0035]

[0036] Where I(x,y) is the normalized post-development morphology (e.g., 0 indicates complete photoresist removal, 1 indicates complete photoresist retention); a is a parameter characterizing the steepness of the Sigmoid function, reflecting the contrast of the photoresist; t r This is the development threshold dose of the photoresist. The sigmoid model fits well the nonlinear saturation behavior of most photoresists near the threshold dose, such as... Figure 3 As shown.

[0037] S2. Using parametric transformation and constraint minimization methods, an exposure optimization problem is constructed with the objective of minimizing the error between the target 3D structure and the predicted morphology. The goal of this step is to transform the engineering problem of "finding the optimal exposure distribution" into a well-defined mathematical optimization problem. Specifically, this includes:

[0038] Step 2.1: Define the objective function (loss function):

[0039] The goal of optimization is to make the developed morphology I(x,y) simulated by the forward model as close as possible to the user's desired 3D target pattern. Therefore, we construct an optimization problem with the objective function of minimizing the mean squared error (MSE) between the two:

[0040] minimize

[0041] In the discrete implementation, the double integration operation is transformed into the summation of all pixels.

[0042] Step 2.2, Applying physical constraints and parameterization transformation:

[0043] The exposure distribution L(x,y) must have physical meaning, meaning its values ​​should fall within the achievable output range of the laser or modulator, typically normalized to the [0,1] interval. To ensure that this constraint is automatically satisfied at each iteration in the optimization process, the following parameterization transformation is introduced:

[0044]

[0045] in, Let I(x,y) be the unconstrained optimization variable. Since the range of the cosine function is [-1,1], this transformation ensures that I(x,y) is always constrained within the interval [0,1], thus transforming the original constrained optimization problem into an unconstrained optimization problem. Therefore, the optimization problem is formally formulated as finding a set of optimal parameters. This makes in Under the mapping relationship, the objective function F is minimized.

[0046] S3. The improved Adam optimization algorithm is used to solve the optimal exposure distribution. This step is the core of the invention. The improved adaptive moment estimation (Adam) algorithm is used to efficiently solve the above complex non-convex optimization problem.

[0047] like Figure 4 As shown, the adaptive moment estimation optimization algorithm is used to solve the exposure optimization problem, including:

[0048] Step 1: Initialize parameters; set the first-order moment vector. Second-order moment vector Set the initial learning rate as a hyperparameter. First-order moment attenuation factor Second-order moment attenuation factor Stability constant The number of iterations is t=0;

[0049] Step 2: Iterative calculation. Calculate the gradient of the objective function F with respect to the unconstrained optimization variable ω, and update the first-order moment estimate based on the gradient. and second-order moment estimation ;

[0050] Step 4: Perform gradient clipping and calculate the first moment after bias correction. and second moment ;

[0051] Step 5: Perform adaptive learning rate decay, update the unconstrained optimization variables based on the bias-corrected first and second moments, and trigger the momentum restart mechanism;

[0052] Step 6: Determine if the objective function has converged, i.e., when the relative error of the objective function in two adjacent iterations converges. Less than Or the number of iterations reaches the preset maximum number of iterations. When the iteration stops, output the current unconstrained optimization variables. To restore the optimal exposure distribution, parameterization is used to transform the optimal unconstrained variables. Reducing to the physically feasible optimal exposure distribution .

[0053] Specifically, it includes:

[0054] Step 3.1, Standard Adam Algorithm Iteration Process:

[0055] Adam is a stochastic optimization algorithm that combines first-order momentum (mean gradient) and second-order momentum (uncentered variance gradient). Its iterative steps are as follows:

[0056] First, initialize the vector with its first-order moment. Second-order moment vector Set the hyperparameter: learning rate First-order moment decay factor Second-order moment attenuation factor Stability constant Then, perform the t-th iteration: calculate the gradient. Update the first-order moment estimate Update the second-order moment estimate Calculate the first and second moments after bias correction: , Update parameters: Finally, a convergence check is performed: if the relative error change < The iteration stops when the preset maximum number of iterations is reached.

[0057] Step 3.2, the improvement strategy adopted in this invention:

[0058] To further improve the stability and convergence speed of the optimization process and avoid getting trapped in local optima, this invention introduces three key improvement mechanisms based on the standard Adam: The first is adaptive learning rate decay. Where γ = 0.95, decaying once every T = 1000 steps. This mechanism causes the learning rate to gradually decrease with the number of iterations, which is beneficial for rapid convergence in the early stages and for fine-tuning in the later stages. The second term, gradient clipping mechanism, is used to prevent numerical instability and divergence caused by excessively large gradient magnitudes (gradient explosion) during optimization. The gradient calculated in each iteration is clipped. Implement trimming process Among them, the cropping threshold Set to 1.0. This operation limits the absolute values ​​of the gradient components to 1.0. Within this range, gradient explosion is effectively suppressed, improving the robustness and convergence efficiency of the algorithm in complex non-convex optimization scenarios. The third point is the momentum restart mechanism: if the decrease in the loss function is insufficient after k=50 consecutive iterations... If this is the case, then the optimization may be trapped in a local minimum or a saddle point. In this case, reset the first moment. and second moment Setting the value to zero clears the original momentum history, giving the algorithm a new initial momentum, which helps it break out of the current stagnation zone and continue searching for a better solution.

[0059] S4. Using path planning and energy mapping technology, the optimized exposure distribution is converted into laser scanning control commands and sent to the laser and 2D scanning galvanometer to generate control commands and execute direct-write lithography. Specifically, this includes:

[0060] Step 4.1: Output and transform the optimization results:

[0061] After the optimization process meets the convergence condition, the final optimization variables are obtained. Through parameter transformation Obtain the optimal two-dimensional exposure energy distribution map .

[0062] Step 4.2, Path Planning and Instruction Generation:

[0063] The data processing and path planning module will generate a two-dimensional exposure energy distribution map. Combined with a preset scanning strategy (such as raster scanning or vector scanning), it is converted into a series of time-synchronized control command sequences. These commands mainly include: First, a position command sequence: driving the two-dimensional scanning galvanometer or nano-positioning platform to precisely control the scanning path of the laser focus on the photoresist surface. Second, the energy command sequence: the laser power or exposure time corresponding to each location point, the value of which is determined by... This is mapped to the actual control voltage of the laser or modulator. This step achieves "energy mapping".

[0064] Step 4.3: Perform exposure synchronously:

[0065] The control execution module sends these instructions to the laser (or acousto-optic / electro-optic modulator) and the two-dimensional scanning mirror at high speed and synchronously. This ensures that at every moment, the laser power precisely corresponds to the L(x,y) value at that location in the optimized scheme. The laser scans and exposes the photoresist-coated substrate according to the planned path, and after development, a high-fidelity three-dimensional microstructure is obtained.

[0066] S5. System architecture deployment and collaborative operation: The system consists of three core parts: hardware platform, control and processing unit and software algorithm module, which together realize high-precision grayscale lithography.

[0067] The scanning strategy includes at least one of the following: raster scanning strategy, vector scanning strategy, partitioned scanning strategy, and layered focusing scanning strategy;

[0068] The grating scanning strategy is as follows: scan line by line along the first direction according to the preset line spacing, and after each line is scanned, step the line spacing along the second direction, and adjust the laser power in real time according to the energy command sequence during the scanning process;

[0069] The vector scanning strategy is as follows: extract the feature contours in the optimal exposure distribution, generate vector paths based on line segments and / or arcs, and scan them sequentially according to a preset priority order; wherein, the node spacing of the vector path matches the size of the laser focus.

[0070] The partitioned scanning strategy is as follows: the exposure area is divided into multiple sub-regions according to the difference in grayscale gradient, and each sub-region is scanned using a scanning speed and sampling frequency that matches its grayscale characteristics, and a transition zone with overlapping exposure energy is set between adjacent sub-regions.

[0071] The layered focusing scanning strategy is as follows: for the height dimension of the three-dimensional structure, a corresponding two-dimensional exposure distribution is generated by layering according to a preset layer thickness; during the scanning of each layer, the laser focus is positioned to the corresponding height by the Z-axis focusing control system; and a linear transition strategy of exposure energy is used for scanning exposure between adjacent layers.

[0072] A three-dimensional grayscale laser direct-write lithography system based on adaptive moment estimation, such as Figure 5 As shown, the system includes: a forward imaging module, an optimization calculation module, a control execution module, an optical system, and a sensing and feedback system;

[0073] The forward imaging module consists of a laser source and a modulator. The laser source uses a laser that matches the photosensitive characteristics of the photoresist to provide the light source. The modulator uses an acousto-optic modulator or an electro-optic modulator as the core execution component. It achieves nanometer-level laser power adjustment based on real-time voltage control signals to complete high-precision grayscale exposure.

[0074] The optimization calculation module includes an optimization algorithm engine, a data processing and path planning sub-module, a graphical user interface and a system calibration and model maintenance sub-module, which respectively realize the functions of outputting the optimal exposure energy distribution map, converting control commands, human-computer interaction operation and system parameter calibration and maintenance.

[0075] The control execution module consists of a high-precision nano-positioning platform and a Z-axis focusing control system, which is used to execute the laser focus scanning trajectory and realize multi-axis linkage to complete the three-dimensional structure manufacturing.

[0076] The optical system consists of a beam spreading and collimating component and an objective lens, ensuring that the laser beam enters the objective lens in an ideal state and is focused to form a tiny spot. The numerical aperture of the objective lens directly determines the theoretical resolution and minimum spot size of the system.

[0077] The sensing and feedback system is used to monitor the platform position and laser power in real time, providing closed-loop control support for the system and ensuring the accuracy of the exposure process.

[0078] In this embodiment, the specific implementation of the system is the same as that of the method.

[0079] In this embodiment, the hardware platform is the physical entity that performs the photolithography operation, responsible for precisely generating and positioning the laser exposure. It consists of four key subsystems: a laser source and a modulator. The laser provides a light source that matches the photosensitive characteristics of the photoresist, and an acousto-optic modulator or electro-optic modulator serves as the core actuator. The modulator adjusts the laser power of each scanning point at high speed and with precision according to the real-time voltage signal sent by the control system, thereby achieving grayscale exposure.

[0080] The high-precision motion system comprises an X and Y nanometer positioning platform (or a galvanometer scanning system) and a Z-axis focusing control system. This system possesses nanometer-level positioning accuracy and high motion bandwidth, enabling precise execution of the laser focus's scanning trajectory and achieving multi-axis linkage during the fabrication of three-dimensional structures.

[0081] The optical system consists of a beam expander and collimator and an objective lens, ensuring that the laser beam enters the objective lens in an ideal state and is focused to form a tiny spot. The numerical aperture of the objective lens directly determines the theoretical resolution and minimum spot size of the system.

[0082] The sensing and feedback system, as the recommended configuration, integrates components such as position sensors (e.g., capacitive sensors, grating rulers) and energy meters. It can monitor the platform position and laser power in real time, providing closed-loop control capability for the system and ensuring the accuracy of the exposure process.

[0083] The control and processing unit (CLU) serves as the bridge between software algorithms and the hardware platform, responsible for command issuance, data acquisition, and real-time control. The real-time controller typically employs a high-performance industrial control card based on FPGA or DSP, and its core task is to synchronously control the laser modulator and motion system. The controller converts the optimized exposure pattern L(x,y) and scan path into two strictly synchronized signals: one is an analog voltage signal output to the modulator to control the laser power; the other is a digital position command output to the motion system to control the scan position. This precise synchronization mechanism ensures that at each position (x,y), the laser power precisely corresponds to the L(x,y) value in the optimized scheme.

[0084] The data interface is responsible for communicating with the host computer, receiving optimized exposure data, and providing communication interfaces with various hardware components (such as Ethernet, USB, PCIe, etc.) to ensure coordinated operation between the system components.

[0085] The software algorithm module runs on the host computer and is the intelligent core of the system, containing four functional units:

[0086] The optimization algorithm engine is the core implementation part of this invention. After receiving the user-designed desired three-dimensional structural pattern and system parameters, it executes a complete iterative optimization process, including forward imaging calculation, cost function evaluation, Adam optimization unit and exposure map update, and finally outputs the optimized two-dimensional exposure energy distribution map I_optimized(x,y).

[0087] The data processing and path planning module is responsible for converting the energy distribution matrix output by the optimization algorithm into a scan path and power sequence that can be executed by the control unit, while setting key process parameters such as scan speed and sampling interval.

[0088] The user interface provides a graphical operating environment that allows users to import or design target 3D structures, set and adjust lithography process parameters, start and stop optimization and exposure processes, and visualize simulation results, including exposure images before and after optimization, dose distribution and predicted morphology.

[0089] The system calibration and model maintenance module stores and maintains key physical parameters of the system, such as beam profile and photoresist response curves. Through the system calibration function, it ensures the consistency between the mathematical model and the physical system, thereby significantly improving the accuracy of the optimization effect.

[0090] The convergence curves of the Adam optimization algorithm and traditional methods are compared as follows: Figure 6 As shown, the comparison results of the two-dimensional and three-dimensional microstructures before and after optimization are as follows: Figure 7 As shown, this invention has high optimization efficiency, can significantly reduce the cost of large-scale three-dimensional structure optimization, can fabricate complex two / three-dimensional micro / nano structures such as microelectromechanical systems (MEMS), photonic crystals, and micro-optical elements, and has strong compatibility and is easy to integrate into existing laser direct writing systems, with outstanding engineering practicality and applicability.

[0091] In one embodiment of the present invention, the present invention further includes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-described three-dimensional grayscale laser direct-write lithography methods based on adaptive moment estimation.

[0092] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented using computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0093] A three-dimensional grayscale laser direct-write lithography apparatus based on adaptive moment estimation includes a processor and a memory; the memory is used to store a computer program; the processor is connected to the memory and is used to execute the computer program stored in the memory, so that the three-dimensional grayscale laser direct-write lithography apparatus based on adaptive moment estimation performs any of the above-mentioned three-dimensional grayscale laser direct-write lithography methods based on adaptive moment estimation.

[0094] Specifically, the memory includes various media capable of storing program code, such as ROM, RAM, magnetic disk, USB flash drive, memory card, or optical disk.

[0095] Preferably, the processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0096] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation, characterized in that, include: A forward imaging physical model is constructed based on the Gaussian beam model and the Sigmoid response function of the photoresist. Based on the forward imaging physical model, an exposure optimization problem is constructed with the goal of minimizing the error between the target 3D structure and the predicted morphology using parameter transformation and constraint minimization methods. An adaptive moment estimation optimization algorithm is used to solve the exposure optimization problem to obtain the optimal exposure distribution. Path planning and energy mapping techniques are used to convert the optimal exposure distribution into laser scanning control commands, which are then sent to the laser and the 2D scanning galvanometer for scanning exposure.

2. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 1, characterized in that, The construction of the forward imaging physical model includes: obtaining the exposure position distribution of the substrate, performing a two-dimensional convolution operation on the exposure position distribution using a Gaussian beam profile model to obtain the aerial dose distribution on the substrate surface; and using the photoresist Sigmoid response function to perform a nonlinear mapping on the aerial dose distribution on the substrate surface to obtain the forward imaging pattern after development.

3. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 1, characterized in that, The exposure optimization issue is: minimize ; s.t. ; ； Where F is the target loss function, I target Let ω be the preset target three-dimensional structure, and let ω be the unconstrained optimization variable.

4. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 1, characterized in that, The adaptive moment estimation optimization algorithm includes three optimization strategies: adaptive learning rate decay mechanism, gradient pruning control strategy, and intelligent momentum restart mechanism. The adaptive learning rate decay mechanism is as follows: ； Where, η t Let η be the learning rate at step t, η0 be the initial learning rate, γ be the decay coefficient, and T be the step size; The gradient pruning control strategy is as follows: ； in, This is the trimming threshold; The intelligent momentum restart mechanism is as follows: when the decrease in the loss function after k=50 consecutive iterations falls below a preset threshold, the first moment of momentum is automatically reset. and second moment This helps the algorithm escape the trap of local minima and search for the global optimum.

5. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 4, characterized in that, Solving the exposure optimization problem using an adaptive moment estimation optimization algorithm includes: Step 1: Initialize parameters; set the first-order moment vector. Second-order moment vector Set the initial learning rate as a hyperparameter. First-order moment attenuation factor Second-order moment attenuation factor Stability constant The number of iterations is t=0; Step 2: Iterative calculation. Calculate the gradient of the objective function F with respect to the unconstrained optimization variable ω, and update the first-order moment estimate based on the gradient. and second-order moment estimation ; Step 4: Perform gradient clipping and calculate the first moment after bias correction. and second moment ; Step 5: Perform adaptive learning rate decay, update the unconstrained optimization variables based on the bias-corrected first and second moments, and trigger the momentum restart mechanism; Step 6: Determine if the objective function has converged, i.e., when the relative error of the objective function in two adjacent iterations converges. Less than Or the number of iterations reaches the preset maximum number of iterations. When the iteration stops, output the current unconstrained optimization variables. To restore the optimal exposure distribution, parameterization is used to transform the optimal unconstrained variables. Reducing to the physically feasible optimal exposure distribution .

6. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 1, characterized in that, The optimal exposure distribution is transformed into laser scanning control commands using path planning and energy mapping techniques. This includes setting a scanning strategy and using the scanning strategy to transform the optimal exposure distribution into a time-synchronized sequence of position commands and a sequence of energy commands. The position command sequence is used to precisely control the scanning path of the laser focus on the photoresist surface, and the energy command sequence is used to define the laser power or exposure time corresponding to each position point.

7. The three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation according to claim 6, characterized in that, The scanning strategy includes at least one of the following: raster scanning strategy, vector scanning strategy, partitioned scanning strategy, and layered focusing scanning strategy; The grating scanning strategy is as follows: scan line by line along the first direction according to the preset line spacing, and after each line is scanned, step the line spacing along the second direction, and adjust the laser power in real time according to the energy command sequence during the scanning process; The vector scanning strategy is as follows: extract the feature contours in the optimal exposure distribution, generate vector paths based on line segments and / or arcs, and scan them sequentially according to a preset priority order; wherein, the node spacing of the vector path matches the size of the laser focus. The partitioned scanning strategy is as follows: the exposure area is divided into multiple sub-regions according to the difference in grayscale gradient, and each sub-region is scanned using a scanning speed and sampling frequency that matches its grayscale characteristics, and a transition zone with overlapping exposure energy is set between adjacent sub-regions. The layered focusing scanning strategy is as follows: for the height dimension of the three-dimensional structure, a corresponding two-dimensional exposure distribution is generated by layering according to a preset layer thickness; during the scanning of each layer, the laser focus is positioned to the corresponding height by the Z-axis focusing control system; and a linear transition strategy of exposure energy is used for scanning exposure between adjacent layers.

8. A three-dimensional grayscale laser direct-write lithography system based on adaptive moment estimation, the system being used to execute the three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation as described in any one of claims 1 to 7, characterized in that, The system includes: a forward imaging module, an optimization calculation module, a control execution module, an optical system, and a sensing and feedback system; The forward imaging module consists of a laser source and a modulator. The laser source uses a laser that matches the photosensitive characteristics of the photoresist to provide the light source. The modulator uses an acousto-optic modulator or an electro-optic modulator as the core execution component. It achieves nanometer-level laser power adjustment based on real-time voltage control signals to complete high-precision grayscale exposure. The optimization calculation module includes an optimization algorithm engine, a data processing and path planning sub-module, a graphical user interface and a system calibration and model maintenance sub-module, which respectively realize the functions of outputting the optimal exposure energy distribution map, converting control commands, human-computer interaction operation and system parameter calibration and maintenance. The control execution module consists of a high-precision nano-positioning platform and a Z-axis focusing control system, which is used to execute the laser focus scanning trajectory and realize multi-axis linkage to complete the three-dimensional structure manufacturing. The optical system consists of a beam spreading and collimating component and an objective lens, ensuring that the laser beam enters the objective lens in an ideal state and is focused to form a tiny spot. The numerical aperture of the objective lens directly determines the theoretical resolution and minimum spot size of the system. The sensing and feedback system is used to monitor the platform position and laser power in real time, providing closed-loop control support for the system and ensuring the accuracy of the exposure process.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, enables the implementation of the three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation as described in any one of claims 1 to 7.

10. A three-dimensional grayscale laser direct-write lithography apparatus based on adaptive moment estimation, characterized in that, It includes a processor and a memory; the memory is used to store a computer program, and the processor is connected to the memory to execute the computer program stored in the memory to drive the lithography apparatus to perform the three-dimensional grayscale laser direct-write lithography method based on adaptive moment estimation as described in any one of claims 1 to 7.

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