CN113419408B - Method and system for calculating dynamic balance of initial structure of optical system - Google Patents
Method and system for calculating dynamic balance of initial structure of optical system Download PDFInfo
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Abstract
The invention relates to the field of extreme ultraviolet lithography objective optics, in particular to a method and a system for calculating the dynamic balance of an initial structure of an optical system, wherein the method comprises the following steps: the method effectively realizes the dynamic balance of the aberration coefficient and the multiple constraint parameters based on the proposed automatic allocation weight factor method, calculates a corresponding evaluation value according to the existing weight each time according to the weight factor automatically allocated by the mathematical model, and evaluates whether the aberration coefficient and the constraint parameters meet constraint conditions; performing iterative calculation according to the existing evaluation value, automatically allocating weight factors for recalculation, evaluating whether the aberration coefficient and the constraint parameter meet constraint conditions or not until the constraint conditions are met, and outputting structural parameters of the extreme ultraviolet lithography objective optical system meeting the constraint conditions; the optical designer can directly obtain the initial structure meeting the constraint condition so as to solve the problem that the conventional initial structure is too dependent on the experience of the optical designer when solving the weights of the aberration coefficient and the constraint parameter.
Description
Technical Field
The invention relates to the field of extreme ultraviolet lithography objective optics, in particular to a method and a system for calculating the dynamic balance of an initial structure of an optical system.
Background
Extreme Ultraviolet Lithography (EUVL) is a projection Lithography technique that uses Extreme Ultraviolet light with a wavelength of 13.5nm as a working wavelength, and has a natural advantage that the exposure wavelength is reduced by one order of magnitude, so that the limitation on the numerical aperture and the process factor of an objective lens can be well released, the objective lens becomes a next-generation Lithography technique, and the EUVL is a preferred technique for realizing the industrialization of a 7nm and below technology node integrated circuit. The extreme ultraviolet lithography objective optical system is the core of the extreme ultraviolet lithography exposure optical system, and the extreme ultraviolet lithography projection objective has extremely high imaging requirements and needs to realize the super-diffraction limit resolution. The design of an optical system with super-diffraction limit and extremely-small aberration is realized, and the aberration balance is very depended on, which brings great challenges to an optical designer. At present, optical design software mainly solves the optimization problem of an optical system, a local optimization algorithm of a damping least square method is adopted to calculate the minimum value of a multi-dimensional variable space error function, the final optimization result is a local optimal solution which is close to an initial structure in most cases, the method has great limitation, the optimization design by utilizing the optical design software is seriously dependent on the selection of the initial structure, and the construction of the initial structure is the key of the optical system design. Especially for an optical system with extremely small aberration, which is more sensitive to aberration balance, the initial structure construction meeting the aberration balance and multi-constraint control is a key problem.
When the optical system is designed, the determination of the structural form of the optical system is very important, and when the structure is too simple, the degree of freedom is limited, so that the requirement on imaging performance is difficult to meet; when the structure is excessively complicated, the manufacturing difficulty is greatly increased, so that the production cost is increased. Before the initial structure is designed, design indexes are required to be clear, and a relatively appropriate structure form is determined according to the design indexes. The method for acquiring the initial structure of the optical system mainly comprises the following three methods:
the first method is to refer to the existing optical system structure form (patent and literature published reports), select the structure form close to the design index, and complete the design by the subsequent aberration correction.
The second method is to determine a relatively suitable structural form according to design indexes, establish a mathematical model for solving system structural parameters based on an aberration theory, and calculate an initial structure by solving the mathematical model.
The third method is to discretize the surface of the optical element, iteratively calculate the points of the surface of the optical system element point by point, and finally fit the discrete points with a polynomial to obtain the surface equation of the initial structure.
At present, common methods for constructing the initial structure of the extreme ultraviolet lithography objective optical system include a paraxial search method, a Y, Y-bar method and a grouping design method. The paraxial search method is provided by M.F.Bal, the method adopts a paraxial model, and exhales first-order aberration of an optical system, so that the quantity of constraint requirements is too small, and the efficiency is greatly influenced.
Scott a. lerner et al apply the Y, Y-bar method to optical system structure solving, which builds initial structures using the highly resolved radii of curvature and mirror spacing of marginal rays and chief rays at the surface of the optical element. The chief ray and marginal ray heights of the optical surfaces of each structure are not readily determinable and are not universally applicable. When the number of the off-axis reflection optical system elements is large, the calculation amount of the method is greatly increased, and the design efficiency is influenced. The grouping design method is applied to off-axis six-antipode ultraviolet lithography objective optical system design by Hudyma, and the optical system is divided into two groups, but a specific design method is not given.
The grouping design method of real light ray tracing is proposed by the Liyanqiu subject group of Beijing university of rational Engineers and applied to off-axis six-reflector and reflection systems with more element numbers. The method introduces real ray tracing to solve the constraint problem in the initial structure solution, does not consider the aberration balance problem, and completely relies on optical design software optimization to correct the aberration. This would result in: 1. the optimization process may generate large disturbance, and the structure is deviated from the initial structure too much, so that the constraint is difficult to control; 2. in the optimization of optical design software, a large residual amount may occur in the low-order aberration and the high-order aberration in the aberration balancing process, so that the design residual error of an optical system is large, and the realization of a system with extremely small aberration is not facilitated.
When the existing initial structure is solved, the weights of the aberration coefficient and the constraint parameter are too dependent on the experience of an optical designer, the conventional method provides the weight factor of the parameter according to the experience of the optical designer, and different initial structures are calculated and screened through different weight factors.
Disclosure of Invention
The embodiment of the invention provides a method and a system for calculating the dynamic balance of an initial structure of an optical system, wherein the method provides an automatic-allocation weight factor method to realize the dynamic balance of aberration coefficients and constraint parameter control, and an optical designer can directly obtain the initial structure meeting constraint conditions so as to solve the problem that the existing initial structure is too dependent on the experience of the optical designer when solving the weights of the aberration coefficients and the constraint parameters.
According to an embodiment of the present invention, there is provided a method for calculating a dynamic balance of an initial structure of an optical system, including the steps of:
initializing the position and the speed of particles in the particle swarm;
distributing weights to aberration coefficients and constraint parameters in the mathematical model;
setting an initial temperature;
evaluating the fitness value of each particle, and calculating an individual extremum and a global optimum value, wherein the individual extremum is the optimum solution found by each particle, and a global value is found from the optimum solutions and is called the global optimum solution;
updating the position and the speed of each particle according to a simulated annealing algorithm and a particle swarm algorithm;
updating individual extreme values and global optimal solutions among the particles according to the fitness value;
cooling until the temperature is reduced to meet the termination condition, otherwise returning to continuously evaluating the fitness value of each particle, and calculating an individual extreme value and a global optimum value; wherein the termination condition is that the error is small enough or the maximum cycle number is reached;
solving the structural parameters and constraint values of the extreme ultraviolet lithography objective optical system according to the results calculated by the annealing algorithm and the particle swarm algorithm;
evaluating whether the aberration coefficient and the constraint parameter meet the constraint condition, if so, outputting the structural parameter of the extreme ultraviolet lithography objective optical system meeting the constraint condition, otherwise, returning to the distribution of the weight to the aberration coefficient and the constraint parameter in the mathematical model, adjusting the weight factor and redistributing the weight factor until the evaluation aberration and the constraint meet the constraint condition; wherein, the constraint condition is satisfied that the constraint control is small enough or the maximum cycle number is reached.
Further, before initializing the position and velocity of the particles in the population of particles, the method further comprises:
and calculating the structural parameters of the optical system of the extreme ultraviolet lithography objective based on the mathematical model.
Further, before calculating the structural parameters of the euv lithography objective optical system, the method further comprises:
based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system is constrained and parameterized in combination with space ray tracing, and a calculation and calculation mathematical model of the objective optical system structural parameters is established.
Further, the mathematical model is expressed as:
wherein D represents a third-order aberration coefficient of the objective optical system, Cons represents constraint parameters, and ω is i Weight, ω, representing aberration coefficient j Representing the weight of each constraint.
Further, all terms of the aberration coefficients are less than 1E-2 when the mathematical model is established.
According to another embodiment of the present invention, there is provided a calculation system for dynamically balancing an initial structure of an optical system, the system including:
the initialization module is used for initializing the position and the speed of the particles in the particle swarm;
the weight distribution module is used for distributing weights to the aberration coefficients and the constraint parameters in the mathematical model;
the temperature setting module is used for setting an initial temperature;
the fitness evaluation module is used for evaluating the fitness value of each particle and calculating an individual extreme value and a global optimal value, wherein the individual extreme value is the optimal solution found by each particle, and a global value is found from the optimal solutions and is called the global optimal solution;
the particle updating module is used for updating the position and the speed of each particle according to the simulated annealing algorithm and the particle swarm algorithm;
the individual extreme value and optimal solution updating module is used for updating the individual extreme value and the global optimal solution among the particles according to the fitness value;
the cooling module is used for cooling until the temperature is reduced to meet the termination condition, otherwise, the fitness value of each particle is returned to be evaluated continuously, and the individual extreme value and the global optimal value are calculated; wherein the termination condition is that the error is small enough or the maximum cycle number is reached;
the parameter solving module is used for solving the structural parameters and the constraint values of the extreme ultraviolet lithography objective optical system according to the results calculated by the annealing algorithm and the particle swarm algorithm;
the parameter output module is used for evaluating whether the aberration coefficient and the constraint parameter meet the constraint condition, if so, outputting the structural parameter of the extreme ultraviolet lithography objective optical system meeting the constraint condition, otherwise, returning to the distribution of the weight to the aberration coefficient and the constraint parameter in the mathematical model, adjusting the weight factor and redistributing the weight factor until the evaluation of the aberration and the constraint meet the constraint condition; wherein, the constraint condition is satisfied that the constraint control is small enough or the maximum cycle number is reached.
Further, the system also comprises a mathematical model which is established, and the structural parameters of the extreme ultraviolet lithography objective optical system are calculated based on the mathematical model.
Further, based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system is constrained and parameterized in combination with space ray tracing, and a mathematical model for calculating the objective lens optical system structural parameters is established.
Further, the mathematical model is expressed as:
wherein D represents a third-order aberration coefficient of the objective optical system, Cons represents constraint parameters, and ω is i Weight, ω, representing aberration coefficient j Representing the weight of each constraint.
Further, all terms of the aberration coefficients are less than 1E-2 when the mathematical model is established.
In the method and system for calculating the dynamic balance of the initial structure of the optical system in the embodiment of the invention, the method provides that: the method effectively realizes the dynamic balance of the aberration coefficient and the multiple constraint parameters based on the proposed automatic allocation weight factor method, calculates a corresponding evaluation value according to the existing weight each time according to the weight factor automatically allocated by the mathematical model, and evaluates whether the aberration coefficient and the constraint parameters meet constraint conditions; performing iterative calculation according to the existing evaluation value, automatically allocating weight factors for recalculation, evaluating whether the aberration coefficient and the constraint parameter meet constraint conditions or not until the constraint conditions are met, and outputting structural parameters of the extreme ultraviolet lithography objective optical system meeting the constraint conditions; by the method and the device, when the initial structure is used for solving the weight of the aberration coefficient and the constraint parameter, an optical designer can directly obtain the initial structure meeting the constraint condition, and the phenomenon that the experience of the optical designer is excessively depended is avoided.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the drawings:
FIG. 1 is a flow chart of a method for calculating the dynamic balance of an initial structure of an optical system according to the present invention;
FIG. 2 is a schematic diagram of a computing system for dynamic balancing of an initial configuration of an optical system according to the present invention;
FIG. 3 is a graph of the convergence of the evaluation function for each weight assignment according to the present invention;
FIG. 4 is a diagram of the distribution of the maximum third-order aberration coefficient for each weight assignment according to the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Example 1
According to an embodiment of the present invention, there is provided a method for calculating a dynamic balance of an initial structure of an optical system, referring to fig. 1 to 4, including the following steps:
s101: initializing the position and the speed of particles in the particle swarm;
s102: distributing weights to aberration coefficients and constraint parameters in the mathematical model;
s103: setting an initial temperature;
s104: evaluating the fitness value of each particle, and calculating an individual extremum and a global optimum value, wherein the individual extremum is the optimum solution found by each particle, and a global value is found from the optimum solutions and is called the global optimum solution;
s105: updating the position and the speed of each particle according to a simulated annealing algorithm and a particle swarm algorithm;
s106: updating individual extreme values and global optimal solutions among the particles according to the fitness value;
s107: cooling until the temperature is reduced to meet the termination condition, otherwise returning to continuously evaluating the fitness value of each particle, and calculating an individual extreme value and a global optimum value; wherein the termination condition is that the error is small enough or the maximum cycle number is reached;
s108: solving the structural parameters and constraint values of the extreme ultraviolet lithography objective optical system according to the results calculated by the annealing algorithm and the particle swarm algorithm;
s109: evaluating whether the aberration coefficient and the constraint parameter meet the constraint condition, if so, outputting the structural parameter of the extreme ultraviolet lithography objective optical system meeting the constraint condition, otherwise, returning to the distribution of the weight to the aberration coefficient and the constraint parameter in the mathematical model, adjusting the weight factor and redistributing the weight factor until the evaluation aberration and the constraint meet the constraint condition; wherein, the constraint condition is satisfied that the constraint control is small enough or the maximum cycle number is reached.
In the method and system for calculating the dynamic balance of the initial structure of the optical system in the embodiment of the invention, the method provides that: the method effectively realizes the dynamic balance of the aberration coefficient and the multiple constraint parameters based on the proposed automatic allocation weight factor method, calculates a corresponding evaluation value according to the existing weight each time according to the weight factor automatically allocated by the mathematical model, and evaluates whether the aberration coefficient and the constraint parameters meet constraint conditions; performing iterative calculation according to the existing evaluation value, automatically allocating weight factors for recalculation, evaluating whether the aberration coefficient and the constraint parameter meet constraint conditions or not until the constraint conditions are met, and outputting structural parameters of the extreme ultraviolet lithography objective optical system meeting the constraint conditions; by the method, when the initial structure is used for solving the weights of the aberration coefficient and the constraint parameter, an optical designer can directly obtain the initial structure meeting the constraint condition, and the condition that the experience of the optical designer is excessively depended is avoided.
In an embodiment, before initializing the position and velocity of the particles in the population of particles further comprises: and calculating the structural parameters of the optical system of the extreme ultraviolet lithography objective based on the mathematical model.
Aiming at the extreme ultraviolet lithography objective, the invention establishes a mathematical model for calculating the structure parameters of the objective optical system so as to calculate the parameters of the extreme ultraviolet lithography objective optical system, and then randomly initializes the positions and the speeds of the particles in the particle population.
In an embodiment, before calculating the structural parameters of the euv lithography objective optical system, the method further includes: based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system is constrained and parameterized in combination with space ray tracing, and a mathematical model for calculating the structural parameters of the objective optical system is established.
The conventional method provides weighting factors of parameters according to experience of an optical designer, and different initial structures are calculated and screened through different weighting factors; the invention aims to solve the problem that the weights of aberration coefficients and constraint parameters in the process of solving the existing initial structure depend too much on the experience of an optical designer.
The invention provides an automatic-allocation weight factor method for realizing dynamic balance of aberration and constraint control.
For the photoetching objective lens with high resolution and relying on aberration balance, the second initial structure construction form is adopted, and aberration balance and multi-constraint control are realized during initial structure construction; based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system constraint parametrization is combined with space ray tracing, and a mathematical model for calculating the optical system structural parameters is established.
In an embodiment, the mathematical model is expressed as:
wherein D represents a third-order aberration coefficient of the objective optical system, Cons represents constraint parameters, and ω is i Weight, ω, representing aberration coefficient j Representing the weight of each constraint.
In an embodiment, all terms of the aberration coefficients are less than 1E-2 when the mathematical model is established.
According to the aberration coefficient and the constraint parameter requirements, refining the constraint parameter requirements; dynamically distributing a weight factor according to the existing value of the structural parameter solved each time, wherein the weight is unchanged when the value meets the constraint condition, and the weight is increased when the value does not meet the condition and is continuously distributed until the final result meets the design requirement; wherein the constraint condition is that the constraint control is small enough or reaches the maximum cycle number.
Aiming at the extreme ultraviolet lithography objective lens, all items of aberration coefficients are required to be small enough and are required to be less than 1E-2 when a mathematical model is calculated. The invention provides an automatic-allocation weight factor method to realize dynamic balance of aberration and constraint control, so that the final design result meets aberration constraint under the condition of meeting constraint conditions.
Further, the method for automatically adjusting the weighting factors effectively realizes the dynamic balance between the aberration coefficients and the multi-constraint parameters, and the convergence curve of the evaluation function is shown in fig. 3. As can be seen from fig. 3, the method for automatically adjusting the weight factors calculates the corresponding evaluation function value according to the existing weight each time, performs iterative calculation according to the existing function value, and automatically adjusts the weight factors to recalculate until the constraint condition is satisfied; by applying the method, the aberration balance and the constraint control during the initial structure solving are realized by iterating for 19 times. For a clearer description of the aberration balance process, as shown in fig. 3, it can be seen that the method continuously allocates the weighting factors to satisfy the aberration balance and constraint control until the design constraint requirement is finally satisfied.
Example 2
Referring to fig. 1 to 4, according to another embodiment of the present invention, there is provided a calculation system for dynamically balancing an initial structure of an optical system, the system including:
an initialization module 100 for initializing positions and velocities of particles in a population of particles;
a weight distribution module 200, configured to distribute weights to the aberration coefficients and the constraint parameters in the mathematical model;
a temperature setting module 300 for setting an initial temperature;
a fitness evaluation module 400, configured to evaluate a fitness value of each particle, and calculate an individual extremum and a global optimal value, where the individual extremum is an optimal solution found by each particle, and a global value is found from the optimal solutions and is called a global optimal solution;
the particle updating module 500 is used for updating the position and the speed of each particle according to a simulated annealing algorithm and a particle swarm algorithm;
an individual extremum and optimal solution updating module 600, configured to update an individual extremum and a global optimal solution among the particles according to the fitness value;
a cooling module 700, configured to cool down until the temperature drops to meet a termination condition, and otherwise, return to continuously evaluating the fitness value of each particle, and calculate an individual extremum and a global optimum value; wherein the termination condition is that the error is small enough or the maximum cycle number is reached;
the parameter solving module 800 is used for solving the structural parameters and the constraint values of the extreme ultraviolet lithography objective optical system according to the results calculated by the annealing algorithm and the particle swarm algorithm;
the parameter output module 900 is configured to evaluate whether the aberration coefficient and the constraint parameter satisfy the constraint condition, output the euv lithography objective optical system structure parameter satisfying the constraint condition if the constraint condition is satisfied, otherwise return to assigning weights to the aberration coefficient and the constraint parameter in the mathematical model, adjust the weight factor and reassign the weight factor until the evaluation aberration and the constraint satisfy the constraint condition; wherein, the constraint condition is satisfied that the constraint control is small enough or the maximum cycle number is reached.
In the method and system for calculating the dynamic balance of the initial structure of the optical system in the embodiment of the invention, the method provides that: the method effectively realizes the dynamic balance of the aberration coefficient and the multiple constraint parameters based on the proposed automatic allocation weight factor method, calculates a corresponding evaluation value according to the existing weight each time according to the weight factor automatically allocated by the mathematical model, and evaluates whether the aberration coefficient and the constraint parameters meet constraint conditions; performing iterative calculation according to the existing evaluation value, automatically allocating weight factors for recalculation, evaluating whether the aberration coefficient and the constraint parameter meet constraint conditions or not until the constraint conditions are met, and outputting structural parameters of the extreme ultraviolet lithography objective optical system meeting the constraint conditions; by the method, when the initial structure is used for solving the weights of the aberration coefficient and the constraint parameter, an optical designer can directly obtain the initial structure meeting the constraint condition, and the condition that the experience of the optical designer is excessively depended is avoided.
In an embodiment, the system further comprises a mathematical model, and the structural parameters of the extreme ultraviolet lithography objective optical system are calculated based on the mathematical model.
Aiming at the extreme ultraviolet lithography objective lens, the invention establishes a mathematical model for calculating the structure parameters of the objective lens optical system so as to calculate the parameters of the extreme ultraviolet lithography objective lens optical system, and then randomly initializes the position and the speed of the particles in the particle population.
In the embodiment, based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system constraint parametrization is combined with space ray tracing, and a mathematical model for calculating the objective lens optical system structural parameters is established.
The conventional method provides weighting factors of parameters according to experience of an optical designer, and different initial structures are calculated and screened through different weighting factors; the invention aims to solve the problem that the weights of aberration coefficients and constraint parameters in the process of solving the existing initial structure depend too much on the experience of an optical designer.
The invention provides an automatic-allocation weight factor method for realizing dynamic balance of aberration and constraint control.
For the photoetching objective lens with high resolution and relying on aberration balance, the second initial structure construction form is adopted, and aberration balance and multi-constraint control are realized during initial structure construction; based on the third-order aberration theory, aberration coefficients and optical system structural parameters are parameterized, the optical system constraint parametrization is combined with space ray tracing, and a mathematical model for calculating the optical system structural parameters is established.
In an embodiment, the mathematical model is expressed as:
wherein D represents a third-order aberration coefficient of the objective optical system, Cons represents constraint parameters, and ω is i Weight, ω, representing aberration coefficient j Representing the weight of each constraint.
In an embodiment, all terms of the aberration coefficients are less than 1E-2 when the mathematical model is established.
According to the aberration coefficient and the constraint parameter requirements, refining the constraint parameter requirements; dynamically distributing a weight factor according to the existing value of the structural parameter solved each time, wherein the weight is unchanged when the value meets the constraint condition, and the weight is increased when the value does not meet the condition and is continuously distributed until the final result meets the design requirement; wherein the constraint condition is that the constraint control is small enough or reaches the maximum cycle number.
The invention aims at the extreme ultraviolet lithography objective lens, and requires that all items of aberration coefficients are small enough and are required to be less than 1E-2 when a mathematical model is calculated. The invention provides an automatic-allocation weight factor method to realize dynamic balance of aberration and constraint control, so that the final design result meets the aberration constraint condition.
Further, the method for automatically adjusting the weighting factors effectively realizes the dynamic balance between the aberration coefficients and the multi-constraint parameters, and the convergence curve of the evaluation function is shown in fig. 3. As can be seen from fig. 3, the method for automatically adjusting the weight factors calculates the corresponding evaluation function value according to the existing weight each time, performs iterative calculation according to the existing function value, and automatically adjusts the weight factors to recalculate until the constraint condition is satisfied; by using the method, aberration balance and constraint control during initial structure solving are realized by iterating for 19 times. For a clearer description of the aberration balancing process, as shown in fig. 3, it can be seen that the method allocates the weighting factors to meet the requirements of aberration balancing and constraint control continuously until the design constraint requirements are finally met.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A computing system for dynamically balancing an initial configuration of an optical system, the system comprising:
the initialization module is used for initializing the position and the speed of the particles in the particle swarm;
the weight distribution module is used for distributing weights to the aberration coefficients and the constraint parameters in the mathematical model;
the temperature setting module is used for setting an initial temperature;
the fitness evaluation module is used for evaluating the fitness value of each particle and calculating an individual extreme value and a global optimal value, wherein the individual extreme value is the optimal solution found by each particle, and a global value is found from the optimal solutions and is called the global optimal solution;
the particle updating module is used for updating the position and the speed of each particle according to the simulated annealing algorithm and the particle swarm algorithm;
the individual extreme value and optimal solution updating module is used for updating the individual extreme value and the global optimal solution among the particles according to the fitness value;
the cooling module is used for cooling until the temperature is reduced to meet the termination condition, otherwise, the fitness value of each particle is returned to be evaluated continuously, and the individual extreme value and the global optimal value are calculated; wherein the termination condition is that the error is small enough or the maximum cycle number is reached;
the parameter solving module is used for solving the structural parameters and the constraint values of the extreme ultraviolet lithography objective optical system according to the results calculated by the annealing algorithm and the particle swarm algorithm;
the parameter output module is used for evaluating whether the aberration coefficient and the constraint parameter meet the constraint condition, if so, outputting the structural parameter of the extreme ultraviolet lithography objective optical system meeting the constraint condition, otherwise, returning to the distribution of the weight to the aberration coefficient and the constraint parameter in the mathematical model, adjusting the weight factor and redistributing the weight factor until the evaluation of the aberration and the constraint meet the constraint condition; wherein, the constraint condition is satisfied that the constraint control is small enough or the maximum cycle number is reached.
2. The system for calculating the initial structural dynamic balance of an optical system according to claim 1, wherein the system further comprises establishing the mathematical model, and calculating the structural parameters of the optical system of the extreme ultraviolet lithography objective based on the mathematical model.
3. The system of claim 2, wherein the mathematical model for calculating the initial structural dynamic balance of the objective lens system is established by parametrizing aberration coefficients and structural parameters of the optical system based on the third-order aberration theory, parametrizing constraints of the optical system in combination with spatial ray tracing.
4. The system for calculating the initial structural dynamic balance of an optical system according to claim 3, wherein the mathematical model is expressed as:
wherein D represents a third-order aberration coefficient of the objective optical system, Cons represents constraint parameters, and ω is i Weight, ω, representing aberration coefficient j Representing the weight of each constraint.
5. The system of claim 4, wherein all terms of the aberration coefficients are less than 1E-2 when the mathematical model is established.
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| CN109164575B (en) * | 2018-10-12 | 2020-08-28 | 中国科学院上海光学精密机械研究所 | Optical system initial structure generation method based on double-threshold algorithm |
| CN110764257A (en) * | 2019-11-14 | 2020-02-07 | 广东省航空航天装备技术研究所 | Optical system initial structure generation method |
| CN111274673B (en) * | 2020-01-07 | 2021-02-23 | 上海索辰信息科技股份有限公司 | Optical product model optimization method and system based on particle swarm optimization |
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