CN112363371B - Light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method - Google Patents
Light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
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- G—PHYSICS
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- G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
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Abstract
The invention discloses a light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method, which takes discretized circuit board diagram variables and discretized light source variables as observation matrixes, takes equal discretization matrixes of corresponding imaging matrixes and target patterns as constraint conditions, and constructs a Lagrange equation containing distance regularized level set items and constraint conditions to obtain a time-varying differential equation; then, discrete terms and non-discrete terms are implicitly and explicitly discretized respectively, a tri-diagonal linear equation set is constructed in two directions of horizontal and vertical by using additive operator splitting, and efficient solving is performed by using a Thomas method. The invention can reduce the optimization dimension and improve the optimization convergence efficiency.
Description
Technical Field
The invention relates to the technical field of optical proximity correction in photoetching resolution enhancement technology, in particular to a light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method.
Background
Projection lithography systems are a core device for fabricating micro-scale and nano-scale linewidth VLSI circuits. The projection lithography system mainly comprises an illumination system, a mask, a projection objective, a pupil, a silicon wafer coated with photoresist and the like, light waves emitted by a light source irradiate and penetrate through the mask to generate a mask near field, mask patterns are transferred onto the silicon wafer through projection of the projection objective, low-pass filtering of the pupil and photoresist etching, but the shape on the silicon wafer is distorted due to information loss in the image transmission process, and the shape on the silicon wafer becomes more obvious along with the reduction of wavelength, the increase of numerical aperture and the improvement of complexity of the technological process.
With the increasing intensity of semiconductor integration, lithography nodes enter 22nm nodes, and images printed on silicon wafers using 193nm deep ultraviolet projection lithography systems must be enhanced in resolution and fidelity by resolution enhancement techniques (resolution enhancement techniques, RETs for short) and optical proximity correction (optical proximity correction, OPC for short). SMO technology is a common RETs technology for improving imaging performance of critical areas in an integrated circuit, and is an important component of OPC as a reverse photolithography technology (inverse lithography technology, abbreviated as ILT), and puts higher demands on optimization and image processing technologies, and proposes a new calculation strategy to improve the calculation efficiency of the pixelated OPC technology. The existing pixelized SMO technology regards a light source and a mask as a pixel map, improves the photoetching imaging performance by optimizing the intensity values of all light source pixels and mask pixels and adjusting the incident angle of the light source, but the huge number of optimized variables and the sensitivity of an ILT algorithm to the optimized step size greatly influence the synthesis efficiency of the light source and the mask. Meanwhile, the continuously improved circuit layout integration density, the perception of process manufacturability and the high-precision restoration further increase the calculation cost of the pixelated SMO technology. Therefore, the computational efficiency and convergence efficiency of the existing pixelized SMO technique need to be further improved.
The relevant literature (Optics Express,2017, 25 (18): 21775) proposes a light source mask collaborative optimization algorithm based on level set evolution. The method characterizes the light source and mask pattern contours as zero level sets for the level set function, thereby realizing the collaborative optimization of the light source mask through the evolution of the level set function according to the normal direction speed. In addition, the method uses Ke Lang-Friedrichs-Column (CFL) conditions to constrain iteration step sizes and ensure the stability of level set evolution.
However, this method has the following two disadvantages:
firstly, the method performs optimization updating on all observation points on the light source and the mask layout in the iterative process, and the gradient of the space image and the cost function on the observation points of the light source and the mask is required to be calculated, so that the calculation efficiency is low, and the large-scale collaborative optimization simulation of the light source mask is not facilitated.
Second, the above method uses a simple and widely applied explicit discretization method, because the iteration step is suppressed to produce excessive iterations due to the limitation of Ke Lang-friedrichs-column-dimension Conditions (CFLs), resulting in slow convergence; while the corresponding implicit discretization method can use enough iteration step length to overcome stability constraint, the corresponding implicit discretization method needs to solve a linear equation set with a quite large scale, has high computational complexity, and is difficult to apply to actual OPC technology.
In summary, the existing SMO method needs to be further improved and raised in terms of optimizing mask frames, calculation efficiency, convergence efficiency, and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a light source mask co-optimization (SMO) semi-implicit (SI) discretized narrow-band level-set (NL) computing method which can reduce the optimization dimension and improve the optimization convergence efficiency, so as to respectively carry out implicit and explicit discretization on diffusion items and non-diffusion items in a stable time related model in a frame, thereby overcoming the stability constraint requirement that the iteration step length is restrained in the explicit discretization method based on gradient descent. Furthermore, instead of optimizing all mask pixels to reduce computational complexity, a local optimization is chosen for observation points (Monitoring pixels) in a narrow band where the level set function zero level set is close.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
a light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method comprises the following steps:
s1, initializing a light source to N s ×N s Is to grid the mask pattern and the target into N x N patterns M and I 0 ；
S2, selecting a level set function phi l L=j or M, and consider the contours of the light source and mask pattern as a level set function phi l Zero level set of (2)
In the above formula, r represents a space coordinate (x, y), l int And l ext Is a predefined negative and positive number;
s3, constructing a vector imaging model of wafer imaging:
I＝Γ(J，M)＝sig(I a ).
in the above formula, I is wafer imaging, I a For aerial image imaging, Γ (·) is the wafer imaging model, sig (·) is the S-shaped activation function for approximating the exposure development process, its expression is
S4, constructing a light source mask collaborative optimization problem as the following energy formula:
in the above formula, mu is a constant,for distance regularized level set terms, defined as:
E ext (phi) is an external energy term for minimizing mask pattern distortion, defined as:
in the above-mentioned method, the step of,zone boundary as a function of level set, +.>Is a gradient operator;
s5, constructing a narrow-band area with a level set function zero level set close to the narrow-band area, and obtaining a stable time model:
in the above formula, delta is Laplace operator, t is artificial time, v (r, t) is normal direction speed of level set function evolution, B b For a narrowband region that contains a near zero level set of phi, b is the specified narrowband width;
s6, performing semi-implicit discretization on the partial differential equation in the step S5, and decomposing the solving problem into two linear equation sets in the coordinate axis direction by using Additive Operator Splitting (AOS);
in the above formula, t is discretized into t k =kτ, k=0, 1,2, …, τ is the iteration step,(mask) or->(light source) is to stack phi in dictionary order, i.e., column vectors, into one vector, constructing the non-diffusion term g (r, t) = -v (r, t) - μΔω;
s7, rapidly solving the tri-diagonal linear equation set by using a Thomas method and updating the light source and the mask;
and S8, continuously repeating the steps S5-S7 until the pattern error is smaller than the designated numerical value or the updating frequency reaches the upper limit.
Further, the specific steps of constructing the narrowband region with the level set function zero level set close to the step S5 are as follows:
when S5-1 and k=0, the narrow band is constructedWherein Z is the set of all observation points crossing zero level set,>a narrow-band region with the central width r of the observation point (x, y);
constructing a stable time model:
in the above formula, delta is Laplace operator, t is artificial time, v (r, t) is normal direction speed of level set function evolution, B b For a narrowband region that contains a near zero level set of phi, b is the specified narrowband width;
s5-2, performing steps S6 and S7 to update the mask and the light source;
s5-3, at the kth iteration, calculate Z k+1 Is thatA set of observation points crossing a zero level set;
s5-4, constructing a New narrowband
Further, the specific steps of performing semi-implicit discretization on the partial differential equation in the step S5, and decomposing the solution problem into two linear equation sets in the coordinate axis direction by using additive operator splitting are as follows:
s6-1, useRepresents t k Time grid node r i Element ω (r) i ，t k ) And will spread the term
Implicit discretization and explicit discretization of "balloon force" g (r, t) = -v (r, t) - μΔω, a semi-implicit discretization scheme is defined as
In the above-mentioned method, the step of,a 4 adjacent node for node i, g (i, k) being a discretized value of g (r, t);
s6-2, converting the semi-implicit discretization formula into a matrix vector form:
in the above, A r Interaction matrix representing r direction, element a thereof ijr The definition is as follows:
s6-3, selection in x-axis directionIs a view point of the camera;
s6-4, solving the linear equation set (I-2τA x (ω k ))u k+1 ＝ω k +τg k Obtaining u k+1 ；
S6-5, selection in y-axis directionIs a view point of the camera;
s6-6, solving the linear equation set (I-2τA y (ω k ))v k+1 ＝ω k +τg k Obtaining v k+1 ；
S6-7, average ω k+1 ＝0.5(u k+1 +v k+1 )。
Compared with the prior art, the scheme has the following principle and advantages:
first, the light source mask collaborative optimization framework related in the scheme comprises distance level set regularization of an objective function. Compared with the traditional level set method, the scheme not only ensures the stability of level set evolution and the accuracy of calculation, does not need repeated level set initialization, but also provides diffusion items required in semi-implicit discretization.
And secondly, the light source mask collaborative optimization algorithm related to the scheme only optimizes the observation points in the narrow band with the adjacent level set function zero level set, reduces the optimization dimension and improves the calculation efficiency.
And thirdly, the light source mask collaborative optimization algorithm related to the scheme adopts semi-implicit discretization, so that the stability requirement of step length constraint of explicit discretization numerical calculation is overcome, a large enough iteration step length is possible, and the convergence efficiency is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the services required in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the figures in the following description are only some embodiments of the present invention, and that other figures can be obtained according to these figures without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of a method for computing a narrow-band level set of a light source mask collaborative optimization semi-implicit discretization of the present invention;
FIG. 2 is a schematic illustration of an optimized light source, mask pattern and imaging of the same in a photoresist at nominal exposure using a conventional level set method;
FIG. 3 shows the iterative step size τ of the light source using the SMO method of the present invention s Mask iteration step τ is 0.08 and 0.1, respectively m 1.0, 1.2 and 1.5, respectively;
FIG. 4 is a graph showing the convergence efficiency versus the conventional level set method, the narrow-band level set method, the semi-implicit discretized SMO based method, and the SMO method of the present invention;
FIG. 5 is a graph showing the comparison of computational efficiency using a conventional level set method, a narrowband level set method, a semi-implicit discretized SMO based method, and the SMO method of the present invention;
FIG. 6 shows the iterative step size τ of the light source in the SMO method according to the present invention s Mask iteration step τ is 0.08 and 0.1, respectively m Comparative diagrams of convergence efficiency at 1.0, 1.2 and 1.5, respectively.
Detailed Description
The invention is further illustrated by the following examples:
the principle of the invention is as follows: in order to improve the operation efficiency and the convergence efficiency, the invention constructs a light source mask collaborative optimization problem as an energy formula, namely:
wherein the first term is a distance regularized level set term to ensure the level set function symbol distance characteristicThe second term is an external energy term for minimizing the mask pattern distortion, forcing optimization to a direction in which the pattern error PE decreases, even if the value of the optimized aerial image at the observation point gradually approaches the value of the target circuit board diagram;
in one aspect, the present invention involves employing narrowband computation to optimize only narrowband region B that contains near zero level sets b B is a specified narrow-band width. The invention can effectively improve the calculation efficiency due to the reduction of the optimization dimension;
on the other hand, the SMO method of the AOS-SI technology uses a Level-set semi-implicit discretization method to convert a time model into a semi-implicit equation, and the equation overcomes the stability requirement of the explicit discretization method on iteration step constraint, so that a sufficiently large iteration step is possible, and the convergence efficiency is effectively improved;
as shown in fig. 1, the method for calculating the narrow-band level set by the semi-implicit discretization of the light source mask collaborative optimization according to the embodiment of the invention specifically comprises the following steps:
s1, initializing a light source to N s ×N s Is to grid the mask pattern and the target into N x N patterns M and I 0 ；
S2, selecting a level set function phi l L=j or M, and consider the contours of the light source and mask pattern as a level set function phi l Zero level set of (2)
In the above formula, r represents a space coordinate (x, y), l int And l ext Is a predefined negative and positive number; s3, constructing a vector imaging model of wafer imaging:
I＝Γ(J，M)＝sig(I a )；
in the above formula, I is wafer imaging, I a For aerial image imaging, Γ (·) is the wafer imaging model, sig (·) is the S-shaped activation function for approximating the exposure development process, its expression is
S4, constructing a light source mask collaborative optimization problem as the following energy formula:
in the above formula, mu is a constant,for distance regularized level set terms, defined as:
E ext (phi) is an external energy term for minimizing mask pattern distortion, defined as:
in the above-mentioned method, the step of,zone boundary as a function of level set, +.>Is a gradientAn operator;
s5, constructing a narrow-band area with a level set function zero level set close to the narrow-band area, and obtaining a stable time model:
when S5-1 and k=0, the narrow band is constructedWherein Z is the set of all observation points crossing zero level set,>a narrow-band region with the central width b of the observation point (x, y);
constructing a stable time model:
in the above formula, delta is Laplace operator, t is artificial time, v (r, t) is normal direction speed of level set function evolution, B b For a narrowband region that contains a near zero level set of phi, b is the specified narrowband width;
s5-2, performing steps S6 and S7 to update the mask and the light source;
s5-3, at the kth iteration, calculate Z k+1 Is thatA set of observation points crossing a zero level set;
s5-4, constructing a New narrowband
S6, performing semi-implicit discretization on the partial differential equation in the step S5, and decomposing the solving problem into two linear equation sets in the coordinate axis direction by using Additive Operator Splitting (AOS):
s6-1, useRepresents t k Time grid sectionPoint r i Element ω (r) i ，t k ) And will spread the term
Implicit discretization and explicit discretization of "balloon force" g (r, t) = -v (r, t) - μΔω, a semi-implicit discretization scheme is defined as
In the above-mentioned method, the step of,a 4 adjacent node for node i, g (i, k) being a discretized value of g (r, t);
discretizing t into t k Kτ, k=0, 1,2, …, where τ is the iteration step;
stacking phi in dictionary order, i.e., column vectors, into a vector construct(mask) or->(light source);
constructing a non-diffusion term g (r, t) = -v (r, t) - μΔω;
s6-2, converting the semi-implicit discretization formula into a matrix vector form:
in the above, A r Interaction matrix representing r direction, element a thereof ijr The definition is as follows:
s6-3, selection in x-axis directionIs a view point of the camera;
s6-4, solving the linear equation set (I-2τA x (ω k ))u k+1 ＝ω k +τg k Obtaining u k+1 ；
S6-5, selection in y-axis directionIs a view point of the camera;
s6-6, solving the linear equation set (I-2τA y (ω k ))v k+1 ＝ω k +τg k Obtaining v k+1 ；
S6-7, average ω k+1 ＝0.5(u k+1 +v k+1 )；
S7, rapidly solving the tri-diagonal linear equation set by using a Thomas method and updating the light source and the mask;
and S8, continuously repeating the steps S5-S7 until the Pattern Error (PE) is smaller than the designated numerical value or the updating times reach the upper limit.
To demonstrate the effectiveness and superiority of the embodiments of the present invention, the following simulations were performed:
as shown in fig. 2, an image of an unoptimized light source and mask through a projection lithography system is schematically illustrated. Reference numeral 201 denotes a light source pattern before optimization, 202 denotes a mask pattern and also denotes a target pattern, 203 denotes an imaging diagram in the photoresist at the optimal focal plane under the rated exposure dose, and the pattern error PE is 3372, which is defined as the square of the euler distance between the photoresist imaging and the target pattern. Wherein, black represents a non-light-emitting area, i.e., the light intensity is 0, and white represents a light-emitting area, i.e., the light intensity is 1. 204 is a light source pattern optimized by a level set method, 205 is a mask pattern optimized by a level set method, 206 is an imaging diagram in the photoresist at the optimal focal plane under the optimized rated exposure dose, and the pattern error PE is 371. In the present system the wavelength of the illumination system is 193nm, the angle of incidence of the annular illumination source is between 0.6 and 0.9, the numerical aperture of the system is 1.35, the size of each grid of the image is 4nm, and the steepness and threshold of the photoresist function are 85 and 0.25, respectively.
As shown in fig. 3, an image of a light source and a mask optimized using the SMO algorithm of the present invention is schematically shown through a projection lithography system. τ for mask iteration step m Representing the iteration step of the light source by tau s And (3) representing. The first behavior adopts tau m ＝1.0，τ s Imaging schematic in photoresist at the optimal focal plane with optimized light source, mask pattern and optimized rated exposure dose=0.08, with pattern error PE of 501; the second row adopts tau m ＝1.2，τ s =0.08, its pattern error PE is 424; the third row adopts tau m ＝1.5，τ s =0.08, its pattern error PE is 367; the fourth row adopts tau m ＝1.0，τ s =0.1, the pattern error PE is 498; the fifth row adopts tau m ＝1.2，τ s =0.1, with a pattern error PE of 419; the sixth row adopts tau m ＝1.5，τ s =0.1, the pattern error PE is 367.
As shown in fig. 4, a schematic diagram is shown comparing convergence efficiency of SMO algorithm based on semi-implicit discretization SMO and SMO algorithm according to the present invention by using level set algorithm, narrowband level set algorithm. As can be seen from fig. 4, the level set algorithm converges to the pattern error PE 371 using 50 iterations; the narrow-band level set algorithm uses 40 iterations, converging to pattern error PE 365; 25 iterations based on semi-implicit discretization SMO are used, and step size tau is adopted m ＝1.0，τ s When=0.08, the pattern error PE 536 is converged, and the step τ is used m ＝1.5，τ s When=0.1, the pattern error PE 383 is converged; the SMO algorithm of the invention uses 25 iterations and adopts the step size tau m ＝1.0，τ s When=0.08, the pattern error PE 501 is converged, and the step τ is used m ＝1.5，τ s When=0.1, the pattern error PE 367 is converged.
As shown in fig. 5, a comparison diagram of the calculation efficiency of the SMO algorithm according to the present invention and the SMO algorithm according to the present invention using a level set algorithm, a narrow-band level set algorithm, and a semi-implicit discretization SMO is shown. Wherein level set algorithm, and narrowband level set algorithmThe iteration step length of the method is constrained by CFL conditions, and the iteration step length based on the semi-implicit discretization SMO is the same as that of the SMO algorithm related to the invention. As can be seen from fig. 4, the level set algorithm uses 50 iterations, with a total duration of 200.4 minutes, each iteration having an average time of 4.01 minutes; the narrow-band level set algorithm uses 40 iterations with a total duration of 41.0 minutes and an average time of 1.02 minutes for each iteration; step size tau is adopted based on semi-implicit discretization SMO m ＝1.0，τ s When=0.08, 25 iterations are used, the total duration is 105.5 minutes, the average time per iteration is 4.22 minutes, and the step size τ is adopted m ＝1.5，τ s At=0.1, 25 iterations were used, with a total duration of 107.5 minutes, each iteration having an average time of 4.30 minutes; the SMO algorithm of the invention adopts the step size tau m ＝1.0，τ s When=0.08, 25 iterations are used, the total duration is 49.1 minutes, the average time of each iteration is 1.96 minutes, and the step size τ is adopted m ＝1.5，τ s At=0.1, 25 iterations were used, with a total duration of 49.9 minutes, each iteration averaging 1.99 minutes.
As shown in fig. 6, a schematic diagram of convergence efficiency of SMO algorithm according to the present invention when different iteration steps are used is shown. The SMO algorithm of the invention uses 25 iterations and adopts tau m ＝1.0，τ s When=0.08, the pattern error PE 501 is converged; by τ m ＝1.2，τ s When=0.08, the pattern error PE 424 is converged; by τ m ＝1.5，τ s When=0.08, the pattern error PE 367 is converged; by τ m ＝1.0，τ s When=0.1, the pattern error PE 498 is converged; by τ m ＝1.2，τ s When=0.1, the pattern error PE 419 is converged; by τ m ＝1.5，τ s When=0.1, the pattern error PE 367 is converged.
As can be seen by comparing fig. 2, 3, 4, 5, and 6, compared with the existing SMO algorithm, the SMO algorithm related to the present invention can use a larger iteration step compared with the narrow-band level set algorithm, thereby improving convergence efficiency; compared with the SMO algorithm based on semi-implicit expression, the optimization dimension is reduced, so that the operation efficiency is improved.
The above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, so variations in shape and principles of the present invention should be covered.
Claims (3)
1. A light source mask collaborative optimization semi-implicit discretization narrow-band level set calculation method is characterized by comprising the following steps:
s1, initializing a light source to N S ×N S Is to grid the mask pattern and the target into N x N patterns M and I 0 ；
S2, selecting a level set function phi l L=j or M, and consider the contours of the light source and mask pattern as a level set function phi l Zero level set of (2)
In the above formula, r represents a space coordinate (x, y), l int And l ext Is a predefined negative and positive number;
s3, constructing a vector imaging model of wafer imaging:
I＝Γ(J,M)＝sig(I a )；
in the above formula, I is wafer imaging, I a For aerial image imaging, Γ (·) is the wafer imaging model, sig (·) is the S-shaped activation function for approximating the exposure development process, its expression is
S4, constructing a light source mask collaborative optimization problem as the following energy formula:
in the above formula, mu is a constant,for distance toThe off-regularization level set term is defined as:
E ext (phi) is an external energy term for minimizing mask pattern distortion, defined as:
in the above-mentioned method, the step of,zone boundary as a function of level set, +.>Is a gradient operator;
s5, constructing a narrow-band area with a level set function zero level set close to the narrow-band area, and obtaining a stable time model:
in the above formula, delta is Laplace operator, t is artificial time, v (r, t) is normal direction speed of level set function evolution, B b For a narrowband region that contains a near zero level set of phi, b is the specified narrowband width;
s6, performing semi-implicit discretization on the partial differential equation in the step S5, and decomposing the solving problem into two linear equation sets in the coordinate axis direction by using additive operator splitting;
in the above formula, t is discretized into t k =kτ, k=0, 1,2,..τ is the iteration step,or->The phi is stacked into a vector according to dictionary sequence, namely, column vectors, and a non-diffusion term g (r, t) = -v (r, t) -mu delta omega is constructed;
s7, rapidly solving the tri-diagonal linear equation set I-2τA by using a Thomassie method r (ω k ) And updating the light source and the mask;
and S8, continuously repeating the steps S5-S7 until the pattern error is smaller than the designated numerical value or the updating frequency reaches the upper limit.
2. The method for calculating the narrow-band level set by the light source mask collaborative optimization semi-implicit discretization according to claim 1, wherein the specific step of constructing the narrow-band area with the level set function zero level set close to the step S5 is as follows:
when S5-1 and k=0, the narrow band is constructedWherein Z is the set of all observation points crossing zero level set,>a narrow-band region with the central width b of the observation point (x, y);
constructing a stable time model:
in the above formula, delta is Laplace operator, t is artificial time, v (r, t) is normal direction speed of level set function evolution, B b For a narrowband region that contains a near zero level set of phi, b is the specified narrowband width;
s5-2, performing steps S6 and S7 to update the mask and the light source;
s5-3, at the kth iteration, calculate Z k+1 Is thatA set of observation points crossing a zero level set;
s5-4, constructing a New narrowband
3. The method for calculating the narrow-band level set by the light source mask collaborative optimization semi-implicit discretization according to claim 1, wherein the specific steps of performing the semi-implicit discretization on the partial differential equation in the step S5 and decomposing the solution problem into two linear equation sets in the coordinate axis direction by using the additive operator splitting are as follows:
s6-1, useRepresents t k Time grid node r i Element ω (r) i ，t k ) And diffusion term +.>Implicit discretization and explicit discretization of "balloon force" g (r, t) = -v (r, t) - μΔω, a semi-implicit discretization scheme is defined as
In the above-mentioned method, the step of,a 4 adjacent node for node i, g (i, k) being a discretized value of g (r, t);
s6-2, converting the semi-implicit discretization formula into a matrix vector form:
in the above, A r An interaction matrix representing the r direction;
s6-3, selection in x-axis directionIs a view point of the camera;
s6-4, solving the linear equation set (I-2τA x (ω k ))u k+1 ＝ω k +τg k Obtaining u k+1 ；
S6-5, selection in y-axis directionIs a view point of the camera;
s6-6, solving the linear equation set (I-2τA y (ω k ))v k+1 ＝ω k +τg k Obtaining v k+1 ；
S6-7, average ω k+1 ＝0.5(u k+1 +v k+1 )。
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| US7124394B1 (en) * | 2003-04-06 | 2006-10-17 | Luminescent Technologies, Inc. | Method for time-evolving rectilinear contours representing photo masks |
| CN102692814A (en) * | 2012-06-18 | 2012-09-26 | 北京理工大学 | Light source-mask mixed optimizing method based on Abbe vector imaging model |
| CN109709772A (en) * | 2019-01-21 | 2019-05-03 | 广东工业大学 | A kind of half implicit light source exposure mask cooperative optimization method based on accelerating operators division |
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