Sub-resolution assist pattern addition method and mask based on accompanying gradient

Abstract

The present disclosure provides a sub-resolution auxiliary pattern adding method based on a concomitant gradient and a mask, and relates to the technical field of semiconductor manufacturing. The method comprises the following steps: performing forward simulation on a design layout based on a super-resolution lithography model, obtaining an imaging electric field distribution and an imaging light intensity distribution on a photoresist layer of the super-resolution lithography model; performing concomitant simulation according to the imaging electric field distribution and the imaging light intensity distribution, and obtaining a concomitant electric field distribution on a mask layer of the super-resolution lithography model; obtaining a concomitant gradient according to the concomitant electric field distribution; determining an adding position of a sub-resolution auxiliary pattern in the design layout according to the concomitant gradient; and adding the sub-resolution auxiliary pattern at the adding position in the design layout to obtain a mask pattern containing a target pattern and the sub-resolution auxiliary pattern.

Description

Technical Field

[0001] This disclosure relates to the fields of semiconductor manufacturing and integrated circuit technology, specifically to the field of photolithography technology, and particularly to a sub-resolution auxiliary patterning method and mask based on adjoint gradient. Background Technology

[0002] In semiconductor manufacturing technology, traditional projection lithography is limited by the diffraction limit, with a resolution limit of about half a wavelength. Reducing the wavelength of the light source significantly increases the difficulty of manufacturing optical materials and devices. Surface plasmon super-resolution lithography utilizes the evanescent waves of the object's surface for imaging, which can overcome the diffraction limit and has the advantages of low cost and high efficiency, making it a very promising nanolithography technology.

[0003] In actual photolithography, process conditions such as exposure dose and focal position vary, which alters the feature size of the photoresist pattern in the imaging result. The combination of exposure dose and defocus amount, where the deviation between the feature size of the photoresist pattern and the target feature size is within acceptable limits, is called the process window. A larger process window indicates a more robust process, which is more beneficial for improving yield in mass production. In common photolithography patterns, sparse and dense patterns often coexist, and these two types of patterns differ significantly in photolithography imaging. For common opaque mask patterns, because the light intensity distribution of sparse patterns is lower than that of dense patterns, under the same photoresist model, the linewidth of the photoresist pattern corresponding to the same feature size of a sparse pattern is much smaller than that of a dense pattern. This results in a very small shared process window for both isolated and dense patterns, which is detrimental to mass production.

[0004] To address this issue, the intensity distribution of the sparse pattern can be improved by adding sub-resolution assist features (SRAFs). Several methods for adding SRAFs already exist for projection lithography. However, in super-resolution lithography, because the convolution kernel of the lithographic model cannot be obtained, existing SRAF methods for projection lithography cannot be applied. Summary of the Invention

[0005] In view of the above problems, this disclosure provides a sub-resolution auxiliary image addition method and mask based on adjoint gradient, which can at least partially solve the above technical problems.

[0006] According to a first aspect of the present disclosure, a method for adding sub-resolution auxiliary patterns based on adjoint gradients is provided, comprising: performing forward simulation of a design layout based on a super-resolution lithography model to obtain an imaging electric field distribution and an imaging light intensity distribution on the photoresist layer of the super-resolution lithography model; performing adjoint simulation based on the imaging electric field distribution and the imaging light intensity distribution to obtain an adjoint electric field distribution on the mask layer of the super-resolution lithography model; obtaining an adjoint gradient based on the adjoint electric field distribution; determining the addition position of the sub-resolution auxiliary pattern in the design layout based on the adjoint gradient; and adding the sub-resolution auxiliary pattern at the addition position in the design layout to obtain a mask layout containing a target pattern and the sub-resolution auxiliary pattern.

[0007] According to embodiments of this disclosure, adjoint simulation based on imaging electric field distribution and imaging light intensity distribution includes: determining an objective function and constructing an objective function based on imaging light intensity distribution, wherein the objective function is a function of imaging light intensity distribution; determining an adjoint source based on imaging electric field distribution and objective function; and performing adjoint simulation using the adjoint source and based on the objective function.

[0008] According to embodiments of this disclosure, the objective function includes one of the following: the sum of the imaging light intensity distributions corresponding to the graphic regions in the design layout; the graphic error between the target graphic in the design layout and the photoresist graphic corresponding to the design layout; and the sum of the squares of the imaging light intensity gradients corresponding to the boundaries of the graphic regions in the design layout.

[0009] According to embodiments of this disclosure, determining the accompanying gradient based on the accompanying electric field distribution includes: obtaining a first component of the accompanying electric field distribution in a first direction, a second component in a second direction, and a third component in a third direction, wherein the first direction, the second direction, and the third direction are mutually perpendicular; and calculating the accompanying gradient based on the first component, the second component, and the third component, wherein the accompanying gradient includes a one-dimensional data distribution or a two-dimensional data distribution.

[0010] According to embodiments of this disclosure, determining the addition position of sub-resolution auxiliary graphics in a design layout based on the accompanying gradient includes: determining all peak positions in regions greater than zero in the accompanying gradient distribution to obtain at least one peak position; removing peak positions located inside the target graphic and peak positions whose distance from the edge of the target graphic is less than a preset distance from the at least one peak position, and determining the remaining peak positions as the addition positions of sub-resolution auxiliary graphics in the design layout, wherein the preset distance is determined based on the feature size of the target graphic.

[0011] According to embodiments of this disclosure, the size of the sub-resolution auxiliary graphic does not exceed half the size of the target graphic feature.

[0012] According to embodiments of this disclosure, the target graphic includes a Manhattan graphic.

[0013] According to embodiments of this disclosure, forward and adjoint simulations are performed using finite-difference time-domain, rigorous coupled-wave analysis, or finite element methods.

[0014] According to embodiments of this disclosure, the super-resolution lithography model includes: a substrate, a metal reflective layer, a photoresist layer, a metal transmissive layer, an air gap layer, and a mask layer stacked sequentially; or, a substrate, a photoresist layer, an air gap layer, a multilayer film structure, and a mask layer stacked sequentially; or, a substrate, a photoresist layer, a metal transmissive layer, an air gap layer, a multilayer film structure, and a mask layer stacked sequentially; or, a substrate, a metal reflective layer, a photoresist layer, an air gap layer, a multilayer film structure, and a mask layer stacked sequentially; or, a substrate, a metal reflective layer, a photoresist layer, a metal transmissive layer, an air gap layer, a multilayer film structure, and a mask layer stacked sequentially.

[0015] The second part of this disclosure provides a photomask applied to super-resolution lithography. The photomask pattern includes a target pattern and a sub-resolution auxiliary pattern, which are added using the method described above.

[0016] The subresolution auxiliary image addition method based on adjoint gradient disclosed herein has at least the following technical effects:

[0017] After performing forward simulation on the design layout, the adjoint simulation is performed based on the results to obtain the adjoint gradient. The distribution of the adjoint gradient determines the location for adding sub-resolution auxiliary patterns, and these patterns are added at the given locations. This process yields various mask layouts suitable for super-resolution lithography, effectively expanding the process window of super-resolution lithography. Furthermore, it boasts advantages such as high efficiency and strong applicability. Attached Figure Description

[0018] The foregoing contents, as well as other objects, features, and advantages of this disclosure, will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0019] Figure 1 A flowchart illustrating a sub-resolution auxiliary graphics addition method based on an embodiment of the present disclosure is shown schematically.

[0020] Figure 2 A schematic diagram of a two-dimensional super-resolution lithography model structure according to an embodiment of the present disclosure is shown.

[0021] Figure 3 A schematic diagram of the design layout according to an embodiment of the present disclosure is shown.

[0022] Figure 4 An imaging light intensity distribution diagram corresponding to a design layout according to an embodiment of the present disclosure is illustrated schematically.

[0023] Figure 5 The diagram schematically illustrates the accompanying gradient distribution and sub-resolution auxiliary graphic addition location diagram according to an embodiment of the present disclosure.

[0024] Figure 6 A mask layout containing sub-resolution auxiliary graphics and a main graphic is schematically shown according to an embodiment of the present disclosure.

[0025] Figure 7 This illustration schematically depicts an embodiment according to the present disclosure. Figure 6 The image intensity distribution map corresponding to the mask pattern shown. Detailed Implementation

[0026] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein, indicate the presence of said features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components. All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0028] Figure 1 A flowchart illustrating a sub-resolution auxiliary graphics addition method based on an embodiment of the present disclosure is shown schematically.

[0029] like Figure 1 As shown, the sub-resolution auxiliary image addition method based on the adjoint gradient may include operations S110 to S150.

[0030] In operation S110, forward simulation of the design layout is performed based on the super-resolution lithography model, and the imaging electric field distribution and imaging light intensity distribution are obtained on the photoresist layer of the super-resolution lithography model.

[0031] During operation S120, a simulation is performed based on the imaging electric field distribution and the imaging light intensity distribution to obtain the accompanying electric field distribution on the mask layer of the super-resolution lithography model.

[0032] In operation S130, the associated gradient is obtained based on the associated electric field distribution.

[0033] In operation S140, the location for adding sub-resolution auxiliary graphics in the design layout is determined based on the accompanying gradient.

[0034] In operation S150, a sub-resolution auxiliary graphic is added at the addition location in the design layout to obtain a mask layout containing the target graphic and the sub-resolution auxiliary graphic.

[0035] According to embodiments of this disclosure, a design layout can be imported into a super-resolution lithography pattern, and simulation can be performed using a super-resolution lithography model to obtain the imaging electric field distribution on the photoresist layer. and imaging light intensity distribution The design layout represents the desired imaging result on the photoresist layer. The design layout contains graphic and non-graphic areas. Graphic areas are covered by polygons, while non-graphic areas are not covered by polygons. The graphics on the design layout are the primary graphics, i.e., the target graphics. Typically, non-graphic areas are opaque, while polygonal areas are translucent.

[0036] After obtaining the results of the forward simulation, a co-simulation can be performed based on these results to obtain the co-current electric field distribution at the mask layer. .

[0037] The sub-resolution auxiliary pattern addition method based on adjoint gradient of this disclosure determines the addition position of the sub-resolution auxiliary pattern based on the simulation results through forward simulation and adjoint simulation, and adds the sub-resolution auxiliary pattern at the corresponding position in the design layout. This addition method is applicable to various design layouts in super-resolution lithography technology and has the advantages of high efficiency and wide applicability.

[0038] In some embodiments, the target graphic in the imported design layout includes a Manhattan graphic. All lines in a Manhattan graphic are horizontal or vertical, and there are no angles other than 90 degrees.

[0039] In some embodiments, performing adjoint simulation based on the imaging electric field distribution and the imaging light intensity distribution may include:

[0040] Determine the objective function and construct it based on the imaging light field distribution. Identify the adjoint source based on the imaging electric field distribution and the objective function. Perform adjoint simulation using the adjoint source and the objective function.

[0041] According to embodiments of this disclosure, in the accompanying simulation, it is necessary to disable the incident source in the forward simulation, then add the accompanying source, and at the same time set the mask region in the forward simulation to the material used by the air gap layer, so as to obtain the accompanying electric field distribution of the mask layer through the accompanying simulation.

[0042] The objective function can be determined according to actual needs, and it can be a function of the imaging light intensity distribution. Different objective functions require different forms of adjoint sources.

[0043] In some embodiments, the objective function may include one of the following:

[0044] The sum of the imaging light intensity distributions corresponding to the graphic areas in the design layout;

[0045] The graphic error between the target graphic in the design layout and the corresponding photoresist graphic in the design layout;

[0046] The sum of squares of the imaging light intensity gradients corresponding to the boundaries of the graphic regions in the design layout.

[0047] Imaging light intensity distribution It is the light field intensity distribution of the photoresist layer, and the imaging electric field distribution. The sum of squares; the imaging intensity gradient refers to The rate of change in space describes the trend of light intensity changing from one place to another.

[0048] For example, suppose the objective function is expressed as ,in For the imaging light intensity distribution, the form of the accompanying source is:

[0049]

[0050] In this context, * represents complex conjugation.

[0051] When the objective function is the sum of the light intensity distributions corresponding to the graphic regions in the design layout, the adjoint source can be... ,in To design the binarized matrix corresponding to the layout, In the image, 1 represents the graphic area of ​​the mask layout, and 0 represents the non-graphic area of ​​the mask layout.

[0052] When the objective function is the pattern error between the target pattern and the photoresist pattern, the adjoint source can be... .

[0053] The pattern error is defined as the sum of the squares of the differences between the target pattern and the photoresist pattern, i.e. ,in The target image is the photoresist pattern. A photoresist model is needed to obtain the photoresist pattern. The input to the photoresist model is the imaging light intensity distribution, and the output is the photoresist pattern. For a constant threshold photoresist model, the photoresist model can be represented as follows: ,in Here, Tr is the photoresist factor, Tr is the photoresist threshold, and the output photoresist pattern is... .

[0054] When the objective function is the sum of squares of the gradients of the imaging light intensity corresponding to the boundary of the graphic region in the design layout, the method for setting the adjoint source is similar to the two methods above.

[0055] It should be noted that the specific manifestation of the accompanying source described above is merely an example, intended to more clearly describe that the accompanying source is a function of the imaging light intensity distribution, and is not intended to limit this disclosure.

[0056] In some embodiments, forward simulation and adjoint simulation can be performed using finite-difference time-domain, rigorous coupled-wave analysis, or finite element methods.

[0057] In some embodiments, the super-resolution lithography model may include:

[0058] The substrate, metal reflective layer, photoresist layer, metal transmissive layer, air gap layer, and mask layer are stacked in sequence.

[0059] Alternatively, the substrate, photoresist layer, air gap layer, multilayer film structure, and mask layer are stacked sequentially.

[0060] Alternatively, the substrate, photoresist layer, metal transmission layer, air gap layer, multilayer film structure, and mask layer are stacked in sequence.

[0061] Alternatively, the substrate, metal reflective layer, photoresist layer, air gap layer, multilayer film structure, and mask layer are stacked in sequence.

[0062] Alternatively, the layers can be stacked sequentially as follows: substrate, metal reflective layer, photoresist layer, metal transmissive layer, air spacer layer, multilayer film structure, and mask layer.

[0063] In other words, this method has good applicability to different types of super-resolution lithography models.

[0064] In some embodiments, determining the accompanying gradient based on the accompanying electric field distribution may include:

[0065] The first component of the accompanying electric field distribution in the first direction, the second component in the second direction, and the third component in the third direction are obtained.

[0066] The adjoint gradient is calculated based on the first component, the second component, and the third component, wherein the adjoint gradient includes a one-dimensional data distribution or a two-dimensional data distribution.

[0067] The first direction, the second direction, and the third direction are all perpendicular to each other. For example, if the first direction is along the X-axis, the second direction is along the Y-axis, and the third direction is along the Z-axis, then the adjoint gradient can be expressed as:

[0068]

[0069] in (p = x, y, z) represents the associated electric field distribution The three components.

[0070] In super-resolution lithography, the lithographic model can use a single-frequency light source, and the accompanying gradient expression... It can be set to 1 for easier calculation.

[0071] It should be noted that the above representation of the accompanying gradient is intended to more clearly illustrate the specific method of determining the accompanying gradient based on the accompanying electric field distribution. Its representation can also be in other forms. For example, the representation of the accompanying gradient corresponding to different light sources can be different, and it is not intended to limit this disclosure.

[0072] In some embodiments, determining the location for adding sub-resolution auxiliary graphics in the design layout based on the accompanying gradient includes:

[0073] Determine all peak locations in the regions with a gradient greater than zero in the accompanying gradient distribution, thus obtaining at least one peak location.

[0074] Remove at least one peak position that is located inside the target graphic and peak positions that are less than a preset distance from the edge of the target graphic. Determine the remaining peak positions as the positions to add sub-resolution auxiliary graphics in the design layout. The preset distance is determined based on the feature size of the target graphic.

[0075] For example, in a super-resolution lithography model, for a two-dimensional data distribution with a companion gradient, among all peak locations in the region where the companion gradient is greater than 0, those locations inside the target pattern and those less than a certain distance from the boundary of the main pattern are removed. The peak value and the remaining peak values ​​are all positions where sub-resolution auxiliary patterns can be added. In order to avoid the imaging light intensity corresponding to the sub-resolution auxiliary patterns being too large and thus imaged by the super-resolution lithography system, the sub-resolution auxiliary patterns can be set as small rectangles whose length and width do not exceed half of the feature size of the target pattern, and there is a certain spacing between these small rectangles. Multiple small rectangles are set to fill the area that can be added.

[0076] For example, when the main graphics in a design are all long lines, the super-resolution lithography model can be simplified in simulation by removing the dimension along the length direction to obtain a two-dimensional super-resolution lithography model, thus significantly improving simulation efficiency. In this case, the adjoint gradient is a one-dimensional data distribution. Based on the adjoint gradient distribution, all peaks in the regions with a value greater than 0 and their corresponding positions are found. Among these peaks, those located inside the main graphic and those less than a certain distance from the boundary of the main graphic are removed. The peak value, and the remaining peak values ​​are the locations where sub-resolution auxiliary graphics can be added. The value can be determined based on the feature size of the target pattern. Typically, to prevent the sub-resolution auxiliary pattern from being imaged by the super-resolution lithography system, the size of the sub-resolution auxiliary pattern can be set to not exceed half the feature size of the main pattern.

[0077] To more clearly illustrate the sub-resolution auxiliary image addition method based on the adjoint gradient provided in this disclosure, a specific example and corresponding experimental data are given below in conjunction with the accompanying drawings.

[0078] Figure 2 A schematic diagram of a two-dimensional super-resolution lithography model structure according to an embodiment of the present disclosure is shown.

[0079] like Figure 2 As shown, the super-resolution lithography model used in this example includes a substrate (e.g., quartz), a metal reflective layer (e.g., silver), a photoresist layer, a metal transmission layer (e.g., silver), an air gap layer, and a mask layer (e.g., chromium, where the mask substrate can be quartz). The mask layer thickness is set to 40 nm, the air gap layer thickness to 40 nm, the metal transmission layer thickness to 20 nm, the metal reflective layer thickness to 30 nm, and the photoresist layer thickness to 50 nm. Since the design patterns are all long line patterns, the lithography model can be set as a two-dimensional super-resolution lithography model.

[0080] Figure 3 A schematic diagram of the design layout according to an embodiment of the present disclosure is shown.

[0081] like Figure 3 As shown, the design layout in this example contains 5 lines, each with a width of 50 nm. In the diagram, the range with a value of 0 represents opaque metallic material, and the range with a value of 1 represents air gaps.

[0082] Figure 4 An imaging light intensity distribution diagram corresponding to a design layout according to an embodiment of the present disclosure is illustrated schematically.

[0083] like Figure 4 As shown, the photoresist threshold corresponding to the dense line pattern in this example can be 0.75. At this threshold, the line widths in the photoresist outline are 44 nm, 38 nm, 52 nm, 38 nm, and 40 nm, respectively. Since the line widths of the photoresist outlines of the 1st, 2nd, 4th, and 5th lines differ from the line width of the target pattern (i.e., 50 nm) by more than 10%, it indicates that the design layout does not have a process window under this process condition without adding sub-resolution auxiliary patterns.

[0084] Figure 5 The diagram schematically illustrates the accompanying gradient distribution and sub-resolution auxiliary graphic addition location diagram according to an embodiment of the present disclosure.

[0085] In this example, the objective function is set to the sum of the imaging light intensity distribution corresponding to the main pattern region. Since the imaging light intensity of sparse patterns is often less than that of dense patterns, the overlap between the sparse and dense pattern process windows is smaller, resulting in a smaller process window. Adding sub-resolution auxiliary patterns can increase the imaging light intensity of sparse patterns, i.e., increase the overlap between the sparse and dense pattern process windows, thereby expanding the process window of super-resolution lithography.

[0086] like Figure 5 As shown, the accompanying gradient is a one-dimensional data distribution, exhibiting numerous peaks. The region where sub-resolution auxiliary graphics are prohibited from being added is defined as the main graphic and the area within 100 nm of its boundary. For ease of data processing, the accompanying gradient in this region is set to 0. Within the region where sub-resolution auxiliary graphics can be added, a total of 10 locations are defined, indicated by black dots.

[0087] Figure 6 A mask layout containing sub-resolution auxiliary graphics and a main graphic is schematically shown according to an embodiment of the present disclosure.

[0088] like Figure 6 As shown, the size of all sub-resolution auxiliary patterns in this example is set to 12 nm.

[0089] Figure 7 This illustration schematically depicts an embodiment according to the present disclosure. Figure 6 The image intensity distribution map corresponding to the mask pattern shown.

[0090] like Figure 7 As shown, some of the smaller peak intensities correspond to the imaging light field of the sub-resolution auxiliary pattern. After adding SRAF, the line widths in the photoresist are 52 nm, 50 nm, 54 nm, 50 nm, and 46 nm, respectively. The difference between the line width of the photoresist contour and the line width of the target pattern is within 10% for all lines, indicating that the mask pattern has a process window under the process conditions after adding the sub-resolution auxiliary pattern. That is, adding SRAF achieves the effect of expanding the process window.

[0091] It should be noted that the specific types of structures and parameter values ​​designed in the above examples are for the purpose of more clearly illustrating this disclosure and are not intended to limit this disclosure.

[0092] The embodiments of this disclosure also provide a mask that can be applied to super-resolution lithography. The mask pattern corresponding to the mask includes a target pattern and a sub-resolution auxiliary pattern. The sub-resolution auxiliary pattern is added using the aforementioned sub-resolution auxiliary pattern addition method based on the adjoint gradient. For specific details on the addition, please refer to the aforementioned embodiment of the sub-resolution auxiliary pattern addition method based on the adjoint gradient, which will not be repeated here.

[0093] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this disclosure is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A sub-resolution auxiliary image addition method based on adjoint gradient, characterized in that, include: The design layout is simulated based on the super-resolution lithography model, and the imaging electric field distribution and imaging light intensity distribution are obtained in the photoresist layer of the super-resolution lithography model. Based on the imaging electric field distribution and the imaging light intensity distribution, a companion simulation is performed to obtain the companion electric field distribution in the mask layer of the super-resolution lithography model. The associated gradient is obtained based on the associated electric field distribution; Determine all peak positions in the regions of the accompanying gradient distribution that are greater than zero, thereby obtaining at least one peak position; Remove the peak positions located inside the target graphic and the peak positions that are less than a preset distance from the edge of the target graphic from the at least one peak position, and determine the remaining peak positions as the addition positions of the sub-resolution auxiliary graphic in the design layout, wherein the preset distance is determined based on the feature size of the target graphic; Sub-resolution auxiliary graphics are added at the designated locations in the design layout to obtain a mask layout containing the target graphic and the sub-resolution auxiliary graphics.

2. The method according to claim 1, characterized in that, The accompanying simulation based on the imaging electric field distribution and the imaging light intensity distribution includes: Determine the objective function and construct the objective function based on the imaging light intensity distribution; the objective function is a function of the imaging light intensity distribution. The accompanying source is determined based on the imaging electric field distribution and the objective function; The accompanying source is used to perform an accompanying simulation based on the objective function.

3. The method according to claim 2, characterized in that, The objective function includes one of the following: The sum of the imaging light intensity distributions corresponding to the graphic areas in the design layout; The graphic error between the target graphic in the design layout and the corresponding photoresist graphic in the design layout; The sum of squares of the imaging light intensity gradients corresponding to the boundaries of the graphic regions in the design layout.

4. The method according to claim 1, characterized in that, The step of obtaining the adjoint gradient based on the adjoint electric field distribution includes: The accompanying electric field distribution is obtained by the first component in the first direction, the second component in the second direction, and the third component in the third direction, wherein the first direction, the second direction, and the third direction are perpendicular to each other. The accompanying gradient is calculated based on the first component, the second component, and the third component, wherein the accompanying gradient includes a one-dimensional data distribution or a two-dimensional data distribution.

5. The method according to claim 1, characterized in that, The size of the sub-resolution auxiliary graphic does not exceed half the size of the target graphic feature.

6. The method according to claim 1, characterized in that, The target graphic includes the Manhattan graphic.

7. The method according to claim 1, characterized in that, Forward and adjoint simulations are performed using finite-difference time-domain, rigorous coupled-wave analysis, or finite element methods.

8. The method according to claim 1, characterized in that, The super-resolution lithography model includes: The substrate, metal reflective layer, photoresist layer, metal transmissive layer, air gap layer, and mask layer are stacked in sequence. Alternatively, the substrate, photoresist layer, air gap layer, multilayer film structure, and mask layer are stacked sequentially. Alternatively, the substrate, photoresist layer, metal transmission layer, air gap layer, multilayer film structure, and mask layer are stacked in sequence. Alternatively, the substrate, metal reflective layer, photoresist layer, air gap layer, multilayer film structure, and mask layer are stacked in sequence. Alternatively, the layers can be stacked sequentially as follows: substrate, metal reflective layer, photoresist layer, metal transmissive layer, air spacer layer, multilayer film structure, and mask layer.

9. A photomask, characterized in that, The mask is used in super-resolution lithography, and the mask pattern corresponding to the mask includes a target pattern and a sub-resolution auxiliary pattern. The sub-resolution auxiliary pattern is added by the method described in any one of claims 1-8.

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