Sub-resolution auxiliary graph adding method based on adjoint gradient and mask plate

Abstract

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

Description

Technical Field

[0001] The present disclosure relates to the field of semiconductor manufacturing and integrated circuit technology, specifically to the field of photolithography technology, and in particular to a method for adding sub-resolution auxiliary graphics based on accompanying gradients and a mask. Background Art

[0002] In semiconductor manufacturing technology, the traditional projection lithography technology is limited by the diffraction limit, and the lithography resolution limit is about half a wavelength. Reducing the wavelength of the light source greatly increases the difficulty of manufacturing optical materials and devices. Surface plasmon super-resolution lithography technology uses the evanescent waves on the surface of the object to participate in imaging, which can break through the limitation of the diffraction limit and has the advantages of low cost and high efficiency. It is a very promising nanolithography technology.

[0003] In actual photolithography, photolithography process conditions such as exposure dose and focus position vary to a certain extent, which will cause the characteristic size of the photoresist pattern in the imaging result to change. The combination of exposure dose and defocus when the deviation between the characteristic size in the photoresist pattern and the target characteristic size is within the allowable range is called the process window. The larger the process window, the more robust the process is, and the more beneficial it is to improve the yield in mass production. In common photolithography layouts, there are usually sparsely distributed patterns and densely distributed patterns at the same time, and these two types of patterns have significant differences in photolithography imaging. For common mask layouts with opaque backgrounds, since the light intensity distribution of sparse patterns is smaller than that of dense patterns, under the same photoresist model, the line width of the photoresist pattern corresponding to the sparse pattern of the same characteristic size is much smaller than that of the dense pattern, which makes the common process window of isolated patterns and dense patterns very small, which is not conducive to mass production.

[0004] In this case, we can improve the situation by adding sub-resolution assist features (SRAF) to the sparse pattern to improve its light intensity distribution. For projection lithography, there are some methods for adding sub-resolution assist features. However, in super-resolution lithography, since the convolution kernel of the lithography model cannot be obtained, the existing methods for adding sub-resolution assist features for projection lithography cannot be applied to super-resolution lithography. Summary of the invention

[0005] In view of the above problems, the present disclosure provides a method for adding sub-resolution auxiliary patterns based on accompanying gradients and a mask, which are used to at least partially solve the above technical problems.

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

[0007] According to an embodiment of the present disclosure, an adjoint simulation is performed according to the imaging electric field distribution and the imaging light intensity distribution, including: determining a target function and constructing the target function according to the imaging light intensity distribution, wherein the target function is a function of the imaging light intensity distribution; determining an adjoint source according to the imaging electric field distribution and the target function; and performing an adjoint simulation using the adjoint source according to the target function.

[0008] According to an embodiment of the present disclosure, the objective function includes one of the following: the sum of the imaging light intensity distribution corresponding to the graphic area in the design layout; the graphic error between the target graphic in the design layout and the photoresist graphic corresponding to the design layout; the sum of the squares of the imaging light intensity gradient corresponding to the boundary of the graphic area in the design layout.

[0009] According to an embodiment of the present disclosure, determining an associated gradient based on an associated electric field distribution includes: obtaining a first component of the associated 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 perpendicular to each other; calculating an associated gradient based on the first component, the second component, and the third component, wherein the associated gradient includes a one-dimensional data distribution or a two-dimensional data distribution.

[0010] According to an embodiment of the present disclosure, determining the adding position of a sub-resolution auxiliary graphic in a design layout according to an accompanying gradient includes: determining all peak positions in an area greater than zero in the accompanying gradient distribution to obtain at least one peak position; removing the peak position located inside the target graphic and the peak position 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 adding positions of the sub-resolution auxiliary graphic in the design layout, wherein the preset distance is determined based on the characteristic size of the target graphic.

[0011] According to an embodiment of the present disclosure, the size of the sub-resolution auxiliary pattern does not exceed half of the feature size of the target pattern.

[0012] According to an embodiment of the present disclosure, the target graph includes a Manhattan graph.

[0013] According to an embodiment of the present disclosure, finite-difference time-domain, rigorous coupled wave analysis or finite element method is used to perform forward simulation and adjoint simulation.

[0014] According to an embodiment of the present disclosure, a super-resolution lithography model includes: a substrate, a metal reflective layer, a photoresist layer, a metal transmissive layer, an air spacer layer, and a mask layer stacked in sequence; or, a substrate, a photoresist layer, a metal transmissive layer, an air spacer layer, a multi-layer film structure, and a mask layer stacked in sequence; or, a substrate, a photoresist layer, a metal transmissive layer, an air spacer layer, a multi-layer film structure, and a mask layer stacked in sequence; or, a substrate, a metal reflective layer, a photoresist layer, an air spacer layer, a multi-layer film structure, and a mask layer stacked in sequence; or, a substrate, a metal reflective layer, a photoresist layer, a metal transmissive layer, an air spacer layer, a multi-layer film structure, and a mask layer stacked in sequence.

[0015] The second part of the disclosed embodiment provides a mask plate, which is applied to super-resolution lithography. The mask plate pattern corresponding to the mask plate includes a target pattern and a sub-resolution auxiliary pattern, and the sub-resolution auxiliary pattern is added by using the above method.

[0016] The sub-resolution auxiliary graphics adding method based on accompanying gradient provided by the present disclosure has at least the following technical effects:

[0017] After forward simulation of the design layout, the companion simulation is performed according to the result of the forward simulation to obtain the companion gradient. The position of adding the sub-resolution auxiliary pattern is determined according to the distribution of the companion gradient, and the sub-resolution auxiliary pattern is added at the given position, which can obtain various mask layouts suitable for super-resolution lithography technology, and play a role in expanding the process window of super-resolution lithography. It has the advantages of high efficiency and strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above contents and other objects, features and advantages of the present disclosure will become more apparent through the following description of the embodiments of the present disclosure with reference to the accompanying drawings, in which:

[0019] Figure 1 A flowchart of a method for adding sub-resolution auxiliary graphics based on accompanying gradients according to an embodiment of the present disclosure is schematically shown;

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

[0021] Figure 3 The diagram schematically shows a design layout distribution diagram according to an embodiment of the present disclosure.

[0022] Figure 4 The imaging light intensity distribution diagram corresponding to the design layout according to the embodiment of the present disclosure is schematically shown.

[0023] Figure 5 The accompanying gradient distribution and the sub-resolution auxiliary pattern adding position diagram according to the embodiment of the present disclosure are schematically shown.

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

[0025] Figure 7 Schematically illustrates an embodiment of the present disclosure Figure 6 The imaging light intensity distribution diagram corresponding to the mask pattern shown. DETAILED DESCRIPTION

[0026] Hereinafter, embodiments of the present disclosure will 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 present disclosure. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present disclosure. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present disclosure.

[0027] The terms used herein are only for describing specific embodiments and are not intended to limit the present disclosure. The terms "including", "comprising", etc. used herein indicate the presence of the 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 (including technical and scientific terms) used herein have the meanings commonly understood by those skilled in the art unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0028] Figure 1 The flowchart of the method for adding sub-resolution auxiliary graphics based on accompanying gradient according to an embodiment of the present disclosure is schematically shown.

[0029] like Figure 1 As shown, the method for adding a sub-resolution auxiliary pattern based on an accompanying gradient may include operations S110 to S150.

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

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

[0032] In operation S130, a companion gradient is obtained according to the companion electric field distribution.

[0033] In operation S140, an adding position of a sub-resolution auxiliary pattern in a design layout is determined according to the accompanying gradient.

[0034] In operation S150, a sub-resolution auxiliary pattern is added at an adding position in the design layout to obtain a mask layout including a target pattern and the sub-resolution auxiliary pattern.

[0035] According to the embodiments of the present disclosure, the design layout can be imported into the super-resolution lithography pattern, and the imaging electric field distribution can be obtained in the photoresist layer through simulation through the super-resolution lithography model. and imaging light intensity distribution The design layout is the ideal imaging result on the desired photoresist layer. The design layout contains graphic areas and non-graphic areas. The graphic area is an area covered by polygons, and the non-graphic area is not covered by polygons. The graphics on the design layout are the main graphics, that is, the target graphics. Usually, the non-graphic area is an opaque area, and the polygon area is a translucent area.

[0036] After obtaining the forward simulation results, the accompanying simulation is performed based on the forward simulation results to obtain the accompanying electric field distribution at the mask layer. .

[0037] Through the method for adding sub-resolution auxiliary graphics based on accompanying gradients in the embodiment of the present disclosure, the position for adding sub-resolution auxiliary graphics is determined according to the simulation results through forward simulation and accompanying simulation, and the sub-resolution auxiliary graphics are added at the corresponding position in the design layout. This adding method can be applied to various design layouts in super-resolution lithography technology, and has the advantages of high efficiency and wide application range.

[0038] In some embodiments, the target graphic in the imported design layout includes a Manhattan graphic. All lines in the Manhattan graphic are horizontal or vertical, and there is no non-90 degree angle in the graphic.

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

[0040] Determine the objective function and construct the objective function according to the imaging light field distribution. Determine the adjoint source according to the imaging electric field distribution and the objective function. Perform adjoint simulation using the adjoint source and according to the objective function.

[0041] According to an embodiment of the present disclosure, in the companion simulation, it is necessary to disable the incident source in the forward simulation, and then add the companion source, and at the same time set the mask area in the forward simulation to the material used for the air spacer layer, and obtain the companion electric field distribution of the mask layer through the companion simulation.

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

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

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

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

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

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

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

[0049]

[0050] Here, * represents complex conjugation.

[0051] When the objective function is the sum of the light intensity distribution corresponding to the graphic area in the design layout, the accompanying source can be ,in is the binary matrix corresponding to the design layout, Here, 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] Among them, the pattern error is defined as the sum of the squares of the differences between the target pattern and the photoresist pattern, that is, ,in is the target pattern. The photoresist model is needed to obtain the photoresist pattern. The input of the photoresist model is the imaging light intensity distribution, and the output is the photoresist pattern. For the constant threshold photoresist model, the photoresist model can be expressed as ,in is the photoresist factor, Tr is the photoresist threshold, and the output photoresist pattern is .

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

[0055] It should be noted that the specific manifestation of the above-mentioned companion source is only an example, which is for more clearly describing that the companion source is a function of the imaging light intensity distribution, and is not used to limit the present disclosure.

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

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

[0058] A substrate, a metal reflective layer, a photoresist layer, a metal transmission layer, an air spacer layer, and a mask layer stacked in sequence;

[0059] Alternatively, a substrate, a photoresist layer, an air spacer layer, a multilayer film structure, and a mask layer are sequentially stacked;

[0060] Alternatively, a substrate, a photoresist layer, a metal transmission layer, an air spacer layer, a multilayer film structure, and a mask layer are stacked in sequence;

[0061] Or, a substrate, a metal reflective layer, a photoresist layer, an air spacer layer, a multilayer film structure, and a mask layer stacked in sequence;

[0062] Alternatively, a substrate, a metal reflective layer, a photoresist layer, a metal transmission layer, an air spacer layer, a multi-layer film structure, and a mask layer are stacked in sequence.

[0063] That is, this method has good applicability to different types of super-resolution lithography models.

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

[0065] A first component in the first direction, a second component in the second direction, and a third component in the third direction are obtained along with the electric field distribution.

[0066] An adjoint gradient is calculated according to 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 perpendicular to each other. For example, 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 accompanying gradient can be expressed as:

[0068]

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

[0070] In super-resolution lithography, the lithography model can use a single frequency light source as the incident light source, and the gradient expression is It can be set to 1 for ease of calculation.

[0071] It should be noted that the above-mentioned representation of the accompanying gradient is to more clearly illustrate the specific method of determining the accompanying gradient based on the accompanying electric field distribution, and its representation form may also be other forms. For example, the representation method of the accompanying gradient corresponding to different light sources may be different, and it is not used to limit the present disclosure.

[0072] In some embodiments, determining the location of adding a sub-resolution auxiliary pattern in a design layout according to the accompanying gradient includes:

[0073] All peak positions in the region where the adjoint gradient distribution is greater than zero are determined to obtain at least one peak position.

[0074] The peak position located inside the target graphic and the peak position whose distance from the edge of the target graphic is less than a preset distance are removed from at least one peak position, and the remaining peak positions are determined as the positions for adding sub-resolution auxiliary graphics in the design layout, wherein the preset distance is determined based on the characteristic size of the target graphic.

[0075] For example, in the super-resolution lithography model, for the two-dimensional data distribution of the accompanying gradient, all peak positions in the area where the accompanying gradient distribution is greater than 0 are removed from these peaks, and the positions inside the target pattern and the distance from the main pattern boundary is less than a certain distance. The remaining peaks are all positions where sub-resolution auxiliary graphics can be added. In order to avoid the imaging light intensity corresponding to the sub-resolution auxiliary graphics being too large and being imaged by the super-resolution lithography system, the sub-resolution auxiliary graphics can be set to a small-sized rectangle with a length and width not exceeding half of the characteristic size of the target graphics, and there is a certain spacing between these small-sized rectangles, and multiple small-sized rectangles are set to fill the addable area.

[0076] For another example, when the main graphics in the design graphics are all long line graphics, the super-resolution lithography model can be simplified in the simulation, that is, the dimension along the length direction is removed to obtain a two-dimensional super-resolution lithography model, thereby greatly improving the simulation efficiency. At this time, the accompanying gradient is a one-dimensional data distribution. According to the accompanying gradient distribution, all peaks and their corresponding positions in the area greater than 0 in the accompanying gradient distribution are found, and among these peaks, those located inside the main graphics and less than a certain distance from the boundary of the main graphics are removed. The remaining peaks are where the sub-resolution auxiliary graphics can be added. The value of can be determined according to the target pattern feature size. Generally, in order 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 of the feature size of the main pattern.

[0077] In order to more clearly illustrate the sub-resolution auxiliary graphics adding method based on accompanying gradient provided by the embodiment of the present disclosure, a specific example and corresponding experimental data are listed below for illustration in conjunction with the accompanying drawings.

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

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

[0080] Figure 3 The diagram schematically shows a design layout distribution diagram according to an embodiment of the present disclosure.

[0081] like Figure 3 As shown in the figure, the design layout in this example contains a total of 5 lines, and the line width is 50 nm. The interval with a value of 0 in the figure represents an opaque metal material, and the line interval with a value of 1 represents an air slot.

[0082] Figure 4 The imaging light intensity distribution diagram corresponding to the design layout according to the embodiment of the present disclosure is schematically shown.

[0083] like Figure 4 As shown in the figure, the photoresist threshold corresponding to the dense line pattern in this example can be 0.75. Under this threshold, the line widths in the photoresist profile are 44 nm, 38 nm, 52 nm, 38 nm, and 40 nm, respectively. Since the line widths of the photoresist profiles of the 1st, 2nd, 4th, and 5th lines differ from the line widths 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 when no sub-resolution auxiliary pattern is added.

[0084] Figure 5 The accompanying gradient distribution and the sub-resolution auxiliary pattern adding position diagram according to the embodiment of the present disclosure are schematically shown.

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

[0086] like Figure 5 As shown in the figure, the accompanying gradient is a one-dimensional data distribution, and it can be seen that there are many peaks. The main figure and the area within 100 nm from the boundary of the main figure are set to be prohibited from adding sub-resolution auxiliary figures. For the convenience of data processing, the accompanying gradient in this area is set to 0. In the area where sub-resolution auxiliary figures can be added, a total of 10 sub-resolution auxiliary figure addition positions are set, represented by black dots.

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

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

[0089] Figure 7 Schematically illustrates an embodiment of the present disclosure Figure 6 The imaging light intensity distribution diagram corresponding to the mask pattern shown.

[0090] like Figure 7 As shown in the figure, some peaks with smaller intensity 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 widths of the photoresist profiles of all lines and the line widths of the target pattern is within 10%, indicating that the mask layout has a process window under this process condition 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 designed in the above examples and the specific parameter values ​​are intended to more clearly illustrate the present disclosure and are not intended to limit the present disclosure.

[0092] The embodiment of the present disclosure also provides a mask, which 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 by using the above-mentioned sub-resolution auxiliary pattern adding method based on the accompanying gradient. For specific adding details, please refer to the above-mentioned embodiment of the sub-resolution auxiliary pattern adding method based on the accompanying gradient, which will not be repeated here.

[0093] The embodiments of the present disclosure are described above. However, these embodiments are only for illustrative purposes and are not intended to limit the scope of the present disclosure. Although the embodiments are described above separately, this does not mean that the measures in the various embodiments cannot be used in combination to advantage. The scope of the present disclosure is defined by the attached claims and their equivalents. Without departing from the scope of the present disclosure, those skilled in the art may make a variety of substitutions and modifications, which should all fall within the scope of the present disclosure.

Claims

1. A method for adding sub-resolution auxiliary graphics based on accompanying gradient, characterized in that: include: Performing forward simulation on the design layout based on the super-resolution lithography model, and obtaining imaging electric field distribution and imaging light intensity distribution in the photoresist layer of the super-resolution lithography model; Performing a concomitant simulation according to the imaging electric field distribution and the imaging light intensity distribution to obtain a concomitant electric field distribution in the mask layer of the super-resolution lithography model; Obtaining an accompanying gradient according to the accompanying electric field distribution; Determining the adding position of the sub-resolution auxiliary pattern in the design layout according to the accompanying gradient; Sub-resolution auxiliary patterns are added at the adding positions in the design layout to obtain a mask layout containing the target pattern and the sub-resolution auxiliary patterns.

2. The method according to claim 1, characterized in that The performing accompanying simulation according to the imaging electric field distribution and the imaging light intensity distribution comprises: Determine a target function and construct the target function according to the imaging light intensity distribution, wherein the target function is a function of the imaging light intensity distribution; Determining a companion source according to the imaging electric field distribution and the target function; An adjoint simulation is performed using the adjoint source and according to 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; A pattern error between a target pattern in the design layout and a photoresist pattern corresponding to the design layout; The sum of squares of 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 a companion gradient according to the companion electric field distribution comprises: 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 perpendicular to each other; The associated gradient is calculated according to the first component, the second component, and the third component, and the associated gradient includes a one-dimensional data distribution or a two-dimensional data distribution.

5. The method according to claim 1 or 4, characterized in that: The step of determining the adding position of the sub-resolution auxiliary pattern in the design layout according to the accompanying gradient includes: Determine all peak positions in the region greater than zero in the adjoint gradient distribution to obtain at least one peak position; The peak position located inside the target graphic and the peak position whose distance from the edge of the target graphic is less than a preset distance are removed from the at least one peak position, and the remaining peak positions are determined as the positions for adding sub-resolution auxiliary graphics in the design layout, wherein the preset distance is determined based on the characteristic size of the target graphic.

6. The method according to claim 1, characterized in that The size of the sub-resolution auxiliary pattern does not exceed half of the characteristic size of the target pattern.

7. The method according to claim 1, characterized in that The target graph includes a Manhattan graph.

8. The method according to claim 1, characterized in that Perform forward and adjoint simulations using finite-difference time-domain, rigorous coupled-wave analysis, or finite element methods.

9. The method according to claim 1, characterized in that: The super-resolution lithography model includes: A substrate, a metal reflective layer, a photoresist layer, a metal transmission layer, an air spacer layer, and a mask layer stacked in sequence; Alternatively, a substrate, a photoresist layer, an air spacer layer, a multilayer film structure, and a mask layer are sequentially stacked; Alternatively, a substrate, a photoresist layer, a metal transmission layer, an air spacer layer, a multilayer film structure, and a mask layer are stacked in sequence; Or, a substrate, a metal reflective layer, a photoresist layer, an air spacer layer, a multilayer film structure, and a mask layer stacked in sequence; Alternatively, a substrate, a metal reflective layer, a photoresist layer, a metal transmission layer, an air spacer layer, a multi-layer film structure, and a mask layer are stacked in sequence.

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

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