CN105785724A - Mask graph optimization method, optimal focal plane position measurement method and system - Google Patents

Abstract

The present invention provides a method and system for optimizing a mask pattern. The objective function adopted is the partial coherent light source illumination, and the difference between the offset of the pattern position corresponding to the spatial image intensity distribution of the lithography under different defocus amounts within the predetermined focal depth range. The slope of the focal amount, the objective function is based on the lithographic imaging theory and combined with the optimization algorithm, and the evaluation function of the measurement sensitivity of the best focal plane position of the projection objective lens system is used to obtain an optimized transmittance that matches the illumination method The mask pattern of phase and phase can effectively improve the measurement sensitivity of the best focal plane position under the illumination condition of partially coherent light source. At the same time, the mask pattern obtained by this optimization method is based on the principle of phase-shift mask measurement. When used for the measurement of the best focal plane position, it does not require special measurement equipment and complex sensors, which can effectively reduce the measurement cost.

Description

Method for optimizing mask pattern, method and system for measuring best focal plane position

technical field

The invention relates to a photolithography system, in particular to a method for acquiring a mask pattern, a method and a system for measuring the best focal plane position.

Background technique

The lithography machine is an important equipment in the manufacture of integrated circuits, and the performance of the lithography machine determines the feature size of the devices in the manufacture of integrated circuits. The projection objective lens system is the core component in the lithography machine, and its main function is to achieve exposure through focusing, so that the mask pattern on the mask plate is imaged on the object to be processed according to a certain ratio.

The depth of focus of the projection objective lens system of the lithography machine is within a certain range, especially as the lithography technology develops to the technology node of 20nm and below, the depth of focus of the lithography machine is below 60nm. The depth of focus determines the size of the image. In general, the actual imaging focal plane will deviate from the position of the best focal plane. By detecting the position of the best focal plane, the position of the focal plane can be detected. and control to improve lithography exposure quality and pattern fidelity.

In the prior art, a grating structure based on a phase shift mask is disclosed, through which the optimal focal plane position of the projection objective lens system is measured, however, this method can only be obtained under the illumination mode with a small partial coherence factor High measurement sensitivity, while the measurement sensitivity is poor under the off-axis illumination method widely used in the industry, and satisfactory measurement results cannot be obtained. In some other methods, it has better sensitivity, but it needs special measuring equipment and complex sensor system to complete, and the detection cost is too high.

Contents of the invention

In view of this, the object of the present invention is to provide a method for optimizing the measurement of the best focal plane, which has high measurement sensitivity and low detection cost.

To achieve the above object, the present invention has the following technical solutions:

A method for optimizing a mask pattern, the mask pattern being used for the measurement of the best focal plane position, comprising:

S01, providing preset transmittance and phase of different regions on the initial mask pattern, where the initial mask pattern corresponds to a phase shift mask;

S02, establish an objective function, obtain the objective function value under the preset transmittance and phase, the objective function value is the current objective function value, wherein the objective function is partial coherent light source illumination, and different defocus amounts within the predetermined focal depth range The slope of the graphic position offset to the defocus amount corresponding to the intensity distribution of the lower lithographic aerial image;

S03, taking the preset transmittance and phase as the starting point, and using the optimization algorithm to obtain the optimized transmittance and phase under the preset conditions of the optimization algorithm;

S04, obtaining an objective function value under the optimized transmittance and phase through an objective function, where the objective function value is an optimized objective function value;

S05, according to the difference between the current objective function value and the optimized objective function value, determine whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern;

If not, reset the preset conditions of the optimization algorithm, use the optimized transmittance and phase as the preset transmittance and phase, and return to step S03.

Optionally, the light source surface of the partially coherent light source is divided into multiple light source points, and the intensity distribution of the lithography aerial image is a superposition of the intensity distribution of the lithography aerial image under each light source point.

Optionally, the method for dividing the light source surface of the partially coherent light source into multiple light source points includes:

Take the circumscribed square of the light source surface of the partially coherent light source, rasterize the circumscribed square into square sub-areas, and use the center point of each square sub-area as a light source point.

Optionally, the optimization algorithm includes a simulated annealing algorithm, a genetic algorithm, an ant colony algorithm, and a gradient algorithm.

Optionally, the optimization algorithm is a simulated annealing algorithm. According to the difference between the current objective function value and the optimized objective function value, it is determined whether the optimized transmittance and phase are optimal mask graphics. The transmittance and phase parameters include:

Judging whether the difference △f between the current objective function value and the optimized objective function value is not less than 0, if so, then determine that the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern;

If △f is less than 0, judge whether e ^(△f/T0) is greater than a random number between 0-1, and if so, determine that the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern parameter, T ₀ is the current temperature of simulated annealing.

Optionally, after judging whether e ^(Δf/T0) is greater than a random number between 0-1, it further includes: if it is smaller than the random number, judging whether a predetermined termination condition is met, and if so, entering the step of terminating optimization.

In addition, the present invention also provides a mask pattern optimization system, the mask pattern is used for the measurement of the best focal plane position, which includes:

The initial mask pattern providing unit is configured to provide preset transmittance and phase of different regions on the initial mask pattern, and the initial mask pattern corresponds to a phase shift mask;

The objective function establishment unit is used to establish an objective function, wherein the objective function is the partial coherent light source illumination, and the difference between the defocus amount and the graphic position offset corresponding to the photolithographic spatial image intensity distribution under different defocus amounts within the predetermined focal depth range slope;

The current objective function value acquisition unit is used to obtain the objective function value under the preset transmittance and phase, and the objective function value is the current objective function value;

The optimization unit is used to use the preset transmittance and phase as the starting point, and use the optimization algorithm to obtain the optimized transmittance and phase under the preset conditions of the optimization algorithm;

An optimized objective function value acquisition unit is used to obtain the optimized objective function value under the transmittance and phase through the objective function, and the objective function value is an optimized objective function value;

The optimal mask pattern judging unit is used to determine whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern according to the difference between the current objective function value and the optimized objective function value;

The default condition reset unit is used to reset the preset conditions of the optimization algorithm when the optimized transmittance and phase are not the transmittance and phase parameters of the optimal mask pattern, and the optimized transmittance and phase as the preset transmittance and phase.

Optionally, a light source point division unit is also included, configured to divide the light source surface of the partially coherent light source into multiple light source points, and the lithography aerial image intensity distribution is a superposition of the lithography aerial image intensity distribution under each light source point.

Optionally, in the light source point division unit, the circumscribed square of the light source surface of the partially coherent light source is taken, and the circumscribed square is divided into square sub-areas by rasterization, and the center point of each square sub-area is used as a light source point.

Optionally, the optimization algorithm includes a simulated annealing algorithm, a genetic algorithm, an ant colony algorithm, and a gradient algorithm.

Optionally, the optimization algorithm is a simulated annealing algorithm. In the optimal mask pattern judging unit, it is judged whether the difference Δf between the current objective function value and the optimized objective function value is not less than 0, and if so, the optimized transmittance is determined and phase are the transmittance and phase of the optimal mask pattern;

If △f is less than 0, judge whether e ^(△f/T0) is greater than a random number between 0-1, and if so, determine that the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern parameter, T ₀ is the current temperature of simulated annealing.

Optionally, a termination judging unit is also included, for judging whether the predetermined termination condition is satisfied after judging that e ^(Δf/T0) is less than a random number between 0-1, and if so, entering termination optimization.

In addition, the present invention also provides a method for measuring the best focal plane position, using the mask pattern corresponding to the transmittance and phase parameters of the optimal mask pattern obtained by any of the above mask pattern optimization methods to perform the best focal plane position measurement method. The measurement of the position.

The method and system for optimizing the mask pattern provided by the embodiment of the present invention adopts the objective function of partially coherent light source illumination, and the pattern position offset corresponding to the photolithography spatial image intensity distribution under different defocus amounts within the predetermined focal depth range. The slope of the defocus amount. The objective function is based on the lithographic imaging theory and combined with the optimization algorithm. The evaluation function of the measurement sensitivity of the best focal plane position of the projection objective lens system is used to obtain an optimized transmission that matches the illumination method. The mask pattern of the ratio and phase can effectively improve the measurement sensitivity of the best focal plane position under the illumination condition of a partially coherent light source. At the same time, the mask pattern obtained by this optimization method is based on the principle of phase-shift mask measurement. When used for the measurement of the best focal plane position, it does not require special measurement equipment and complex sensors, which can effectively reduce the measurement cost.

Furthermore, in the established objective function, the light source surface of the partially coherent light source is divided into multiple light source points, and then the intensity distribution of the lithographic spatial image under each light source point is superimposed as the lithographic spatial image under the illumination of the light source Intensity distribution, thereby effectively improving the measurement sensitivity of the best focal plane position of the projection objective lens system under the lithography vertical axis illumination condition with a partially coherent light source.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are For some embodiments of the present invention, those skilled in the art can also obtain other drawings based on these drawings without creative work.

FIG. 1 shows a flowchart of a method for optimizing a mask pattern according to an embodiment of the present invention;

FIG. 2 shows a schematic cross-sectional structure diagram of an initial mask pattern used in an optimization method according to an embodiment of the present invention;

Fig. 3 shows a schematic diagram of the phase distribution of each region of the initial mask pattern in Fig. 2;

FIG. 4 shows a schematic structural view of the coherent light source used in the optimization method of the embodiment of the present invention after rasterization;

Fig. 5 shows a schematic diagram of intensity distribution of lithographic aerial images corresponding to different defocus amounts in the entire focal depth range of the initial mask pattern in an embodiment;

FIG. 6 shows a schematic diagram of the phase distribution of the mask pattern obtained after the initial mask pattern in FIG. 5 is optimized;

Fig. 7 shows a schematic diagram of intensity distribution of lithographic aerial images corresponding to different defocus amounts in the entire focal depth range of the optimized mask pattern obtained after the initial mask pattern in Fig. 5 is optimized;

FIG. 8 shows a schematic structural diagram of a mask pattern optimization system according to an embodiment of the present invention.

detailed description

In order to make the above objects, features and advantages of the present invention more comprehensible, specific implementations of the present invention will be described in detail below in conjunction with the accompanying drawings.

In the following description, a lot of specific details are set forth in order to fully understand the present invention, but the present invention can also be implemented in other ways different from those described here, and those skilled in the art can do it without departing from the meaning of the present invention. By analogy, the present invention is therefore not limited to the specific examples disclosed below.

In the present invention, an optimization method of a mask pattern is proposed, and the mask pattern is used for the measurement of the best focal plane position, as shown in Fig. 1, the method includes:

S01, providing different areas on the initial mask pattern corresponding to the preset transmittance and phase, the initial mask pattern is a phase shift mask;

S02, establish an objective function, obtain the objective function value under the preset transmittance and phase, the objective function value is the current objective function value, wherein the objective function is partial coherent light source illumination, and different defocus amounts within the predetermined focal depth range The slope of the graphic position offset to the defocus amount corresponding to the intensity distribution of the lower lithographic aerial image;

S03, taking the preset transmittance and phase as the starting point, and using the optimization algorithm to obtain the optimized transmittance and phase under the preset conditions of the optimization algorithm;

S04, obtaining an objective function value under the optimized transmittance and phase through an objective function, where the objective function value is an optimized objective function value;

S05, according to the difference between the current objective function value and the optimized objective function value, determine whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern;

If not, reset the preset conditions of the optimization algorithm, use the optimized transmittance and phase as the preset transmittance and phase, and return to step S03.

This optimization method can be implemented in a simulation algorithm, such as a simulated annealing algorithm in matlab. After optimization, the transmittance and phase parameters of the optimal mask pattern will be obtained, and the optimal mask pattern will be used for the best focus Measurement of plane position.

In the present invention, the objective function adopted is partially coherent light source illumination, and the slope of the defocusing amount corresponding to the graphic position offset amount corresponding to the photolithographic spatial image intensity distribution under different defocusing amounts in the predetermined focal depth range, the objective function is given by Based on the lithographic imaging theory and combined with the optimization algorithm, the evaluation function of the measurement sensitivity of the best focal plane position of the projection objective lens system is used to obtain a mask pattern with optimized transmittance and phase that matches the illumination method, which can effectively Improved sensitivity for measuring the best focal plane position under illumination from partially coherent light sources. At the same time, the mask pattern obtained by this optimization method is based on the principle of phase shift mask measurement. When used for the measurement of the best focal plane position, it does not require special measurement equipment and complex sensors, which can effectively reduce the measurement cost. .

In order to better understand the technical solutions and technical effects of the present invention, specific embodiments will be described in detail below in conjunction with flow charts.

S01, providing preset transmittances and phases of different regions on the initial mask pattern, where the initial mask pattern corresponds to a phase shift mask.

In the present invention, the mask pattern is obtained by an optimization method of simulation. The initial mask pattern can be a non-physical mask pattern, but a related parameter of the mask pattern. In the embodiment of the present invention, the initial mask pattern Corresponding to the dependent mask, there are multiple different regions on it, and each different region is correspondingly set with preset transmittance and phase.

In a specific embodiment, the physical mask pattern corresponding to the initial mask pattern can be two mask patterns. Referring to FIG. 2 and FIG. 3, the physical mask pattern includes a light blocking layer and successively connected transparent For the four different regions of the optical layer, the first phase-shift layer and the second phase-shift layer, the light-blocking layer can be a plurality of non-light-transmitting regions with a certain width, and the light-blocking layer can be realized by a metal material. The metal material is, for example, Metal chromium, the transmittance and phase of the light-blocking layer are both 0; the light-transmitting layer, the first phase-shift layer and the second phase-shift layer can be realized through openings of different depths on the light-transmitting material, such as It can be the mask base of the quartz plate, and the light-transmitting layer can be the surface area not covered with the non-light-transmitting material quartz plate, and its transmittance is 1, and the phase is 0; the first phase shift layer can be a quartz plate with the first The depth of the opening, the depth can be, for example, The transmittance of the first phase shift layer is 1, and the phase is 90°; the second phase shift layer can be an opening with a second depth on the quartz plate, and the depth can be, for example, The transmittance of the second phase shift layer is 1, and the phase is 180°. Wherein, λ is the wavelength of light incident on the test mask in vacuum, n is the refractive index of the light-transmitting layer material, and k is a positive integer. For the mask pattern of this entity, in the simulation algorithm, it can be expressed by the preset transmittance and phase of different regions on the initial mask pattern, and the initial mask pattern can be expressed by the mask function To express, the modulus of the mask function corresponds to the transmittance, The value corresponds to the phase, and the blocking area corresponds to the The value is π/4. It should be noted that the transmittance of the light-blocking area is 0. The phase value here is to ensure that the amplitude term of the mask function, that is, the transmittance is 0. This phase value does not really reflect On the mask pattern, the light-transmitting area corresponds to value of 0, the first phase shift region corresponds to the value of π/2, the second phase shift region corresponds to The value is π.

S02, establish an objective function, obtain the objective function value under the preset transmittance and phase, the objective function value is the current objective function value, wherein the objective function is partial coherent light source illumination, and different defocus amounts within the predetermined focal depth range The slope of the graphic position offset to the defocus amount corresponding to the intensity distribution of the photolithographic aerial image.

In the embodiment of the present invention, it is an optimization method for simulating the lighting conditions of a partially coherent light source. The lighting of a partially coherent light source can be realized by setting the shape of the light source and the coherence factor. The objective function constructed is to pre-focus The slope of the graphic position offset to the defocus amount corresponding to the intensity distribution of the photolithographic aerial image under different defocus amounts in the deep range.

Wherein, the defocus amount d is the difference between the best focal plane position of the projection objective lens system of the lithography machine and the actual aerial image imaging position, and when the defocus amount d=0, it corresponds to the best focal plane position. In the lithography system, due to the existence of factors such as control and environment, the position of the actual imaging surface deviates from the position of the ideal imaging surface, resulting in a defocus amount d, which will make the light beam propagating in the lithography system The phase changes, considering the phase change of the light generated by the defocus amount, the electric field distribution at the actual imaging surface position under the illumination of a partially coherent light source can be obtained, and then the lithography aerial image intensity distribution under the defocus amount can be obtained The corresponding graphic position offset, that is, the position offset of the imaging graphic, and the slope of the graphic position offset relative to the defocus amount reflects the correlation between the graphic position offset and the defocus amount. For different transmittance and phase mask patterns, that is, different mask patterns, correspond to different slope values, that is, the objective function value, and use the slope value as the evaluation function of the measurement sensitivity of the best focal plane position to obtain the optimized mask Graphics, fully considering the lithographic imaging theory, can effectively improve the measurement sensitivity of the best focal plane position of the projection objective lens system under off-axis illumination conditions.

In a more optimal embodiment, as shown in FIG. 4, for a partially coherent light source, its light source surface 110 can be divided into a plurality of light source points 130, and the intensity distribution of the above-mentioned lithography space image is the lithography of each light source point. The superposition of the spatial image intensity distribution is used to effectively improve the measurement sensitivity of the best focal plane position of the projection objective lens system under the off-axis illumination condition of lithography. That is to say, by dividing the light source surface 110 where the light source area 100 of the coherent light source is located, the light source area 100 is converted into light source points 130, and the light source characteristics of the light source area 100 can be expressed by the light source features of each light source 120 points , and for the light source points on the non-light source area part on the light source surface 110 , the expression of the light source characteristic is 0, and the non-light source area is the area on the light source surface 110 outside the light source area 100 .

In order to better understand the objective function constructed in the embodiment of the present invention, the process of constructing the objective function in the simulation implementation will be described in detail below.

First, the initial mask pattern is rasterized into multiple sub-regions, and the transmittance and phase of the initial mask pattern are represented by a mask function M,

Preferably, according to the physical size and pixel size of the initial mask graphic, the initial mask graphic can be rasterized into N*N sub-regions, N is a positive integer, and each sub-region is an element in the simulation calculation matrix, and the grid Gridding into N*N sub-regions is more convenient for simulation calculation.

Next, divide the light source surface of the partially coherent light source into multiple light source points, as shown in FIG. 4 .

Specifically, as shown in FIG. 4 , the light source surface is divided into Ns*Ns subregions 120, each subregion 120 can be a square region, and the center point (x _s , y _s ) of each subregion 120 is regarded as the subregion light source point 130, so that the light source surface 110 is divided into a plurality of light source points 130, each light source point 130 is a sampling point, and the light source feature of each sub-region is based on the center point (x _s , y _s ) of the sub-region The light source intensity and polarization state are expressed as E _i (x _s , y _s ), and E _i (x _s , y _s ) is 0 for the light source point on the non-light source area on the light source surface.

When rasterizing, the following steps can be taken:

Take the circumscribed square of the light source surface 110 of the partially coherent light source.

The circumscribed square is rasterized into square sub-areas 120, and the center point 130 of each square sub-area 120 is used as a light source point.

Each side of the circumscribed square can be equally divided into Ns segments, so that the circumscribed square can be rasterized into Ns*Ns square sub-areas, and the center point of each sub-area can be taken as the light source point of the sub-area. For the light source surface of the partially coherent light source used in the lithography system, there are various shapes, all of which can be rasterized by this method, but in the obtained light source point matrix, the number of different light source point coordinates that are not 0 is different.

Then, the objective function is obtained.

The objective function is the slope of the graphic position offset to the defocus amount corresponding to the intensity distribution of the lithography spatial image under different defocus amounts within the predetermined focal depth range under the illumination of a partially coherent light source, that is, under a partially coherent light source, The sensitivity of the pattern position offset to the defocus amount is an objective function, and the pattern position offset can be obtained through the intensity distribution of the lithographic aerial image, which is related to the defocus amount and the characteristics of the light source. The specific formula is derived as follows:

For the defocus amount d, the phase of the light propagating in the lithography system will change, and the phase change δ is as follows:

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$

in, is the wave number, n _w is the refractive index of the image square medium of the projection system, (α', β', γ') is the direction cosine of the outgoing light. δ is an N×N scalar matrix, each element in the matrix represents the phase change of the light wave passing through a certain point on the pupil in the lithography system, and this phase change is caused by defocus.

When the defocus amount d is 0, the wafer is at the position of the ideal imaging surface, and the electric field distribution at the wafer position is shown in the following formula:

Among them, n _w is the refractive index of the image square medium of the projection system, R is the reduction ratio of the projection objective lens system, generally 4, and F ^-1 {} represents the inverse Fourier transform. ⊙ indicates that the corresponding matrix elements are multiplied. The low-pass filter function U is a scalar matrix of N×N, which represents the limited receiving ability of the numerical aperture of the projection system to the diffraction spectrum, that is, the value inside the pupil is 1, and the value outside the pupil is 0, specifically expressed as follows:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \sqrt{{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\end{array}\right.$

Among them, (f, g) are the normalized global coordinates on the entrance pupil. V is an N×N vector matrix, each element is a 3×3 matrix:

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\frac{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}& <span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}& {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ <span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}& \frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}& {\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& {\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}$

When the defocus amount d is not 0, considering the phase change δ of the propagating light in the lithography system caused by the defocus amount d of the non-ideal lithography system, the electric field distribution at the wafer position in the non-ideal lithography system is as follows express:

Since the element values in E _i (x _s ,y _s ) have nothing to do with the mask coordinates, the electric field distribution at the wafer position can also be written as:

${\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; V</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; m</span>}$

in, Indicates convolution, It is an N×N vector matrix, and each matrix element is a 3×1 vector (v _x ', v _y ', v _z ') ^T , where v _x ', v _y ', v _z ' are all α' and β' functions.

Then the three components of E ^wafer (α _s ,β _s ) in the global coordinate system are

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; m</span>}$

in, p = x, y, z. V _p ' is an N×N scalar matrix, which is composed of a single coordinate component of each element of the vector matrix V'.

Then, the expression of intensity distribution of lithographic aerial image under different defocus amounts is as follows:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

in, Represents taking the modulo of a matrix and squaring it. The spatial image intensity distribution of lithography, that is, the intensity distribution of imaging results at the wafer position, that is, the imaging surface, this formula expresses the intensity distribution of imaging results under different light source points under different defocus amounts, and if d=0, it is ideal Distribution of imaging results at imaging locations.

Through this formula, make d=0, respectively calculate the intensity distribution of the imaging result at the ideal imaging position under different light source points (x _s , y _s ), and then, according to the Abbe (Abbe) principle, the imaging under each light source point By superimposing the resulting intensities, the intensity distribution I _bf (x, y, z) of the lithographic aerial image at the ideal imaging position can be obtained.

Through this formula, let d be different values, and calculate the intensity distribution of imaging results at different defocus positions under different light source points (x _s , y _s ), and then, similarly, according to Abbe’s principle, for each light source point By superimposing the intensities of the imaging results below, the intensity distribution I _def (x, y, z) of the lithographic aerial image at different defocus positions can be obtained.

According to Abbe's principle, the expression of intensity distribution of lithography spatial image at different defocus positions after superposition is as follows:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

where N _s is the number of source points of the partially coherent source. Setting the defocus amount d in the above formula to 0, the imaging result intensity distribution I _bf (x, y, z) at the ideal image plane can be obtained.

In a specific calculation, a predetermined focal depth range can be set, and the defocus amount can be changed according to a certain step size. In a specific embodiment, the focal depth range is, for example, -100nm to 100nm, and the step size is 5nm, to obtain different The intensity distribution of the lithography aerial image after superimposing the distribution of imaging results of each light source point under the defocus amount. Different defocus amounts include the ideal case of d=0 and the case of d being other values.

Furthermore, according to the definition of the graphic offset, the graphic offset is the difference between the actual imaging position of the graphic and the ideal position, and the solution satisfies the equation The x-coordinate value of is the graphic position offset corresponding to the intensity distribution of the lithographic aerial image. And by the graphic position offset when d=0 and the graphic position offset when d is not 0, to obtain the graphic offset under different defocus amounts to the slope of the defocus amount, the slope can be passed to the graphic position The numerical differentiation of the offset is obtained.

Through the objective function established above, first, obtain the objective function value under the preset transmittance and phase, that is, obtain the slope value corresponding to the objective function under the mask function M under the preset transmittance and phase, and obtain the initial The sensitivity of the pattern position offset of the mask pattern relative to the defocus amount. For ease of description, this objective function value is recorded as the current objective function value f _cur .

Then, in S03 , using the preset transmittance and phase as the starting point, under the preset conditions of the optimization algorithm, the optimized transmittance and phase are obtained by using the optimization algorithm.

Optimization is carried out through optimization algorithms, such as simulated annealing algorithm, genetic algorithm, ant colony algorithm, or gradient algorithm. Through these optimization algorithms, algorithm conditions can be set to obtain more optimal transmittance and phase.

In a specific embodiment, the optimization algorithm of the simulated annealing algorithm is used for optimization. In the optimization algorithm, the preset conditions of the optimization algorithm are first set, the initial temperature _T0 is set to 20°C, the final temperature is set to 0.00005°C, and the decay The coefficient _Tξ is 0.97, and the length of the Markov chain is 5000.

Next, in step S04, an objective function value under the optimized transmittance and phase is obtained through an objective function, and the objective function value is an optimized objective function value.

Through the objective function established above, the optimized transmittance obtained in the previous step and the objective function value under the phase are obtained, that is, the slope value corresponding to the objective function under the mask function M obtained under the optimized transmittance and phase , to obtain the sensitivity of the pattern position offset of the optimized mask pattern relative to the defocus amount. For the convenience of description, this objective function value is recorded as the optimized objective function value f _ref .

Then, in step S05, according to the difference between the current objective function value and the optimized objective function value, it is determined whether the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern.

According to the difference △f between the current objective function value f _cur and the optimized objective function value _fref , it is determined whether the transmittance and phase obtained by the optimization algorithm are the transmittance and phase of the optimal mask pattern, where △ f=f _ref −f _cur , depending on the optimization algorithm used, the method of determining the optimal mask pattern according to the difference may also be different.

In this embodiment, the optimization algorithm adopts a simulated annealing algorithm, and then according to the difference between the current objective function value and the optimized objective function value, it is determined whether the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern. In the step of phase parameter, it specifically includes:

First, judge whether the difference Δf between the current objective function value and the optimized objective function value is not less than 0, and if so, determine the optimized transmittance and phase as the transmittance and phase of the optimal mask pattern.

If △f is less than 0, then judge whether e ^(△f/T0) is greater than a random number between 0-1, if so, determine the optimized transmittance and phase as the transmittance and phase of the optimal mask pattern Phase parameter, T0 is the current temperature of simulated annealing.

After the optimized transmittance and phase are determined to be the optimal mask pattern, the optimization method is terminated, and then the current mask pattern is set as the optimized mask pattern, and the transmission corresponding to the data mask pattern Rate, phase and optimized objective function value, the optimized mask pattern can be used for the measurement of the best focal plane position.

If the optimized transmittance and phase cannot be determined to be the optimal mask pattern through the above judgments, the preset conditions of the optimization algorithm can be reset. Usually, some conditions in the preset conditions need to be reset, such as in the simulated annealing algorithm. The initial temperature T ₀ and the attenuation coefficient T _ξ can be reset, and steps S03-S05 can be repeated to re-optimize and judge under the new preset conditions to output the optimal mask pattern.

In order to avoid the situation that the optimization cannot converge, that is, it is impossible to obtain a suitable optimal mask pattern, after judging the size of the random number between e ^(△f/T0) and 0-1, if it is smaller than the random number, then Continue to judge whether the predetermined termination condition is satisfied, if so, enter the termination optimization step, stop the optimization method, the predetermined termination condition can be determined according to different optimization algorithms, in the simulated annealing algorithm, the predetermined termination condition can be the current temperature T ₀ <T _f or the number of optimizations is greater than a predetermined value, etc.

The method for optimizing the mask pattern in the embodiment of the present invention has been described in detail above, and the transmittance and phase parameters of the optimal mask pattern obtained by the above optimization method are used to obtain the mask pattern corresponding to the phase parameter, which can be used to optimize the mask pattern in the photolithography system. Measurement of the best focal plane position.

In order to better understand the technical effects of the optimization method of the present invention, the simulation results of a specific example will be described in detail below. In this specific embodiment, as shown in FIG. 2 , the base 301 of the initial mask pattern is a quartz plate, the area covered with the metal chromium layer on the base 301 is the light-blocking area 302, and the light-transmitting area 303 is not covered with the metal chromium. layer and exposes the region of the substrate 301, the first phase shift layer 304 and the second phase shift layer 305 are opening regions with different depths on the substrate 301; the light-transmitting region 303 is connected with the first phase shift layer 304, and their transmitted light The phase difference is 90°; the first phase shift layer 304 is connected to the second phase shift layer 305, and the phase difference of their transmitted light is 180°. The width ratio of the light blocking region 302, the light transmitting region 302, the first phase shift layer 304 and the second phase shift layer 305 is: 4:1:2:1, the width of the second phase shift layer 305 is 41nm, and the width of the first phase shift layer Layer 304 opening depth is The opening depth of the second phase shift layer 305 is λ is the wavelength of incident light in air, n is the refractive index of the transparent substrate, and k is a positive integer.

Referring to FIG. 4 , it is a partially coherent light source used in this embodiment. The partially coherent light source is divided into multiple light source points by dividing the light source surface. Referring to Fig. 5, A in Fig. 5 is the intensity distribution of the lithographic spatial image corresponding to different defocus amounts of the initial mask pattern in the entire focal depth range under the illumination mode of the light source, and B is the lithographic spatial image intensity distribution under a specific threshold The binary distribution of image intensity in the entire focal depth range, that is, the continuous distribution of photolithographic spatial image intensity in A is converted into a binary distribution through a specific threshold. As can be seen from B, the position of the initial mask pattern There is no obvious linear relationship between the offset and the defocus amount, and the initial mask pattern is not suitable for detection of the best focal plane position under the illumination of the partially coherent light source.

After the above initial mask pattern is optimized by the optimization algorithm, the optimized mask pattern is obtained, as shown in Figure 6, which is a schematic diagram of the phase and transmittance distribution of the optimized mask pattern, a same color The region of represents a phase and transmittance. Referring to Figure 7, A in Figure 7 is the intensity distribution of the lithographic aerial image corresponding to different defocus amounts in the entire focal depth range of the optimized mask pattern under the partially coherent light source, and B is the lithographic aerial image under a specific threshold The binary distribution of intensity in the entire focal depth range, as can be seen from Figure B, its graphic offset varies linearly with the defocus amount, and the defocus can be obtained by linearly fitting the graphic offset in the figure The slope of the linear relationship between the amount and the graph offset is about 0.3501. It can be seen that the mask pattern has better detection sensitivity under off-axis lighting conditions, which also proves the correctness and effectiveness of the optimization method involved in the present invention.

The method for optimizing the mask pattern of the embodiment of the present invention has been described in detail above. In addition, the present invention also provides an optimization system for implementing the above method, as shown in FIG. 8 , including:

The initial mask pattern providing unit 200 is configured to provide preset transmittance and phase of different regions on the initial mask pattern, where the initial mask pattern corresponds to a phase shift mask;

The objective function establishing unit 210 is used to establish an objective function, wherein the objective function is partially coherent light source illumination, and the defocus amount of the graphic position offset corresponding to the photolithography spatial image intensity distribution under different defocus amounts within the predetermined focal depth range The slope of;

The current objective function value obtaining unit 220 is used to obtain the objective function value under the preset transmittance and phase, and the objective function value is the current objective function value;

The optimization unit 230 is configured to use the preset transmittance and phase as the starting point, and use the optimization algorithm to obtain the optimized transmittance and phase under the preset conditions of the optimization algorithm;

An optimized objective function value acquisition unit 240, configured to obtain an optimized objective function value under the transmittance and phase through an objective function, where the objective function value is an optimized objective function value;

The optimal mask pattern judging unit 250 is used to determine whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern according to the difference between the current objective function value and the optimized objective function value;

The default condition reset unit 260 is used to reset the preset conditions of the optimization algorithm when the optimized transmittance and phase are not the transmittance and phase parameters of the optimal mask pattern, and set the optimized transmittance Ratio and phase as the preset transmittance and phase.

Further, it also includes a light source point division unit, which is used to divide the light source surface of the partially coherent light source into multiple light source points, and the lithography aerial image intensity distribution is the superposition of the lithography aerial image intensity distribution under each light source point.

Further, in the light source point division unit, the circumscribed square of the light source surface of the partially coherent light source is taken, and the circumscribed square is divided into square sub-areas by rasterization, and the center point of each square sub-area is used as a light source point.

Further, the optimization algorithm includes simulated annealing algorithm, genetic algorithm, ant colony algorithm, and gradient algorithm.

Further, the optimization algorithm is a simulated annealing algorithm. In the optimal mask pattern judging unit 250, it is judged whether the difference Δf between the current objective function value and the optimized objective function value is not less than 0, and if so, the optimized transmittance is determined and phase are the transmittance and phase of the optimal mask pattern;

If △f is less than 0, judge whether e ^(△f/T0) is greater than a random number between 0-1, and if so, determine that the optimized transmittance and phase are the transmittance and phase of the optimal mask pattern Parameters, T0 is the initial temperature of simulated annealing.

Further, it also includes a termination judging unit, which is used to judge whether the predetermined termination condition is met after judging that e ^(Δf/T0) is less than a random number between 0-1, and if so, enter termination optimization.

Each embodiment in this specification is described in a progressive manner, the same and similar parts of each embodiment can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, as for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and for related parts, please refer to part of the description of the method embodiment.

The above descriptions are only preferred implementations of the present invention. Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. Any person familiar with the art, without departing from the scope of the technical solution of the present invention, can use the methods and technical content disclosed above to make many possible changes and modifications to the technical solution of the present invention, or modify it to be equivalent to equivalent changes Example. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention that do not deviate from the technical solution of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (13)

1. A method for optimizing a mask pattern used for measurement of an optimal focal plane position, comprising:

s01, providing preset transmittance and phase of different areas on the initial mask pattern, wherein the initial mask pattern corresponds to the phase shift mask;

s02, establishing an objective function to obtain an objective function value under preset transmittance and phase, wherein the objective function value is the current objective function value, and the objective function is the slope of the graph position offset corresponding to the photoetching spatial image intensity distribution under different defocusing amounts in a preset focal depth range to the defocusing amount under the illumination of a partially coherent light source;

s03, obtaining optimized transmittance and phase by using an optimization algorithm under the preset condition of the optimization algorithm by taking the preset transmittance and phase as starting points;

s04, obtaining an optimized transmittance and an optimized objective function value under the phase through an objective function, wherein the objective function value is an optimized objective function value;

s05, determining whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask graph according to the difference value between the current objective function value and the optimized objective function value;

if not, resetting the preset conditions of the optimization algorithm, taking the optimized transmittance and phase as the preset transmittance and phase, and returning to the step S03.

2. The method of claim 1, wherein a light source facet of the partially coherent light source is divided into a plurality of light source points, and the lithographic aerial image intensity distribution is a superposition of the lithographic aerial image intensity distributions under each light source point.

3. The method of claim 2, wherein the method of dividing the light source surface of the partially coherent light source into the plurality of light source points comprises:

taking a circumscribed square of a light source surface of a partially coherent light source, rasterizing the circumscribed square into square sub-areas, and taking the center point of each square sub-area as a light source point.

4. The method of claim 1, wherein the optimization algorithm comprises simulated annealing algorithm, genetic algorithm, ant colony algorithm, gradient algorithm.

5. The method of claim 1, wherein the optimization algorithm is a simulated annealing algorithm, and determining whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern according to the difference between the current objective function value and the optimized objective function value comprises:

judging whether the difference value delta f between the current objective function value and the optimized objective function value is not less than 0, if so, determining the optimized transmittance and phase as the transmittance and phase of the optimal mask graph;

if Δ f is less than 0, determine e^(Δf/T0)Whether the random number is larger than the random number between 0 and 1, if so, determining the optimized transmittance and phase as the transmittance and phase parameters of the optimal mask graph, T₀To simulate the current temperature of the anneal.

6. The method of claim 5, wherein at decision e^(Δf/T0)Whether the random number is larger than the random number between 0 and 1 further comprises the following steps: if the random number is smaller than the random number, whether a preset termination condition is met is judged, and if the preset termination condition is met, the optimization termination step is carried out.

7. A system for optimizing a mask pattern used for measurement of an optimal focal plane position, comprising:

the initial mask graph providing unit is used for providing preset transmittance and phases of different areas on the initial mask graph, and the initial mask graph corresponds to the phase shift mask;

the target function establishing unit is used for establishing a target function, wherein the target function is the slope of the image position offset corresponding to the photoetching space image intensity distribution under different defocusing amounts in a preset focal depth range and under the illumination of a partially coherent light source;

a current objective function value obtaining unit, configured to obtain an objective function value at a preset transmittance and a preset phase, where the objective function value is the current objective function value;

the optimization unit is used for obtaining the optimized transmittance and phase by using the optimization algorithm under the preset condition of the optimization algorithm by taking the preset transmittance and phase as starting points;

an optimized objective function value obtaining unit, configured to obtain an optimized objective function value at the transmittance and the phase through an objective function, where the objective function value is an optimized objective function value;

the optimal mask graph judging unit is used for determining whether the optimized transmittance and phase are the transmittance and phase parameters of the optimal mask graph or not according to the difference value between the current objective function value and the optimized objective function value;

and the preset condition resetting unit is used for resetting the preset condition of the optimization algorithm when the optimized transmittance and phase are not the transmittance and phase parameters of the optimal mask pattern, and taking the optimized transmittance and phase as the preset transmittance and phase.

8. The system of claim 7, further comprising a source point dividing unit to divide a source plane of the partially coherent light source into a plurality of source points, the lithographic aerial image intensity distribution being a superposition of the lithographic aerial image intensity distributions under each source point.

9. The system according to claim 8, wherein in the light source point division unit, a circumscribed square of the light source face of the partially coherent light source is taken, the circumscribed square is rasterized into square sub-regions, and the center point of each square sub-region is taken as one light source point.

10. The system of claim 7, wherein the optimization algorithm comprises simulated annealing algorithm, genetic algorithm, ant colony algorithm, gradient algorithm.

11. The system according to claim 7, wherein the optimization algorithm is a simulated annealing algorithm, and in the optimal mask pattern determining unit, it is determined whether a difference Δ f between a current objective function value and an optimal objective function value is not less than 0, and if so, the optimized transmittance and phase are determined as the transmittance and phase of the optimal mask pattern;

if Δ f is less than 0, determine e^(Δf/T0)Whether the random number is larger than the random number between 0 and 1, if so, determining that the random number is larger than the random numberThe optimized transmittance and phase are the transmittance and phase parameters of the optimal mask pattern, T₀To simulate the current temperature of the anneal.

12. The system according to claim 11, further comprising a termination judgment unit operable to judge e^(Δf/T0)And after the random number is smaller than the random number between 0 and 1, judging whether a preset termination condition is met, and if so, entering termination optimization.

13. A method for measuring a position of an optimal focal plane, characterized in that the measurement of the position of the optimal focal plane is performed using a mask pattern corresponding to transmittance and phase parameters of the optimal mask pattern obtained by the method for optimizing a mask pattern according to any one of claims 1 to 6.