A gradient calculation method and system for lithography mask optimization

Abstract

The application belongs to the field of photolithography mask optimization, and specifically discloses a gradient calculation method and system for photolithography mask optimization. According to the application, the diffraction field of the mask absorption layer is expanded in space by means of the adjoint method, strong interference and fluctuation between electric fields are avoided, and therefore, a two-dimensional slice of the three-dimensional diffraction field can be used to calculate the gradient, at this time, the entire three-dimensional diffraction field does not need to be saved, only a few two-dimensional slices need to be saved, and therefore, the calculation resources are greatly saved. Meanwhile, the application does not have a limited requirement on the algorithm used in each step, and the decoupling of the algorithm is realized.

Description

Technical Field

[0001] The present application belongs to the field of photolithography mask optimization, and more specifically, relates to a gradient calculation method and system for photolithography mask optimization. Background Art

[0002] Mask optimization is a core component of computational lithography, playing a crucial role in improving lithographic imaging resolution and pattern fidelity. With the continuous reduction of integrated circuit feature sizes and the advancement of lithography technology nodes, traditional lithography techniques are no longer able to meet the demands of high-end chip manufacturing. Driven by Moore's Law, computational lithography is essential for precisely optimizing the mask design to achieve finer circuit pattern transfer. Mask optimization adjusts the mask pattern to compensate for various optical effects and process variations during the lithography process, thereby improving lithographic imaging quality, expanding the process window, reducing manufacturing costs, and shortening R&D cycles. Therefore, mask optimization is a key technology for achieving mass production of high-end chips.

[0003] In the mask optimization process, gradient calculation is key to implementing efficient optimization algorithms. Gradient information reflects the sensitivity of the objective function to changes in the optimization variables and is an important guide for the optimization algorithm's search for the optimal solution. In computational lithography, the objective function is often associated with evaluation metrics for lithographic imaging quality, such as pattern error and edge placement error. By accurately calculating gradients, the optimization algorithm can determine the direction and step size for the search in the multidimensional parameter space, effectively narrowing the search range and accelerating convergence to the optimal solution. The accuracy and efficiency of gradient calculation directly impact the quality of the mask optimization results and the consumption of computing resources. Therefore, gradient calculation is not only the foundation for the implementation of mask optimization algorithms, but also a crucial step in improving the performance of computational lithography. Existing gradient calculation methods require a large amount of memory to store the mask's three-dimensional diffraction field. Especially when considering partially coherent illumination, thousands of three-dimensional diffraction fields need to be stored simultaneously, requiring a very large amount of memory. Summary of the Invention

[0004] In view of the defects of the prior art, the purpose of this application is to provide a gradient calculation method and system for photolithography mask optimization, aiming to solve the problem of extremely large memory required by the existing gradient calculation method.

[0005] A first aspect of the present application relates to a gradient calculation method for photolithography mask optimization, the gradient calculation method comprising:

[0006] S1. Calculate the diffraction field of the first diffraction, the reflection of the multilayer film, and the diffraction field of the second diffraction to obtain a forward simulated diffraction field;

[0007] S2. Obtain a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at a first position inside the absorption layer, obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a second position inside the absorption layer, and obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a third position outside the absorption layer, and use them as the mask near field, wherein the two-dimensional slices are two-dimensional complex arrays of the diffraction field along the pattern plane;

[0008] S3. Using the mask near field as input, calculate the optimization target, and inversely obtain the partial derivative of the optimization target with respect to the mask near field, which is used as the incident field for the accompanying simulation;

[0009] S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, where the position of the incident field is the position of the mask near field in the adjoint simulation;

[0010] S5. Acquire a two-dimensional slice of the diffraction field at the second position inside the absorbing layer accompanied by the simulated first diffraction, and acquire a two-dimensional slice of the diffraction field at the first position accompanied by the simulated second diffraction;

[0011] S6. Calculate the mask optimization gradient by integrating the mask diffraction field and the two-dimensional slices of the first position and the second position of the simulated diffraction field.

[0012] In some embodiments, the first location and the second location are the same or different.

[0013] In some embodiments, the mask optimization gradient is calculated as follows:

[0014]

[0015] in, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorption layer, Represents direct multiplication of corresponding elements of an array.

[0016] In some embodiments, the mask optimization gradient is calculated as follows:

[0017]

[0018] Among them, the pattern plane is in the xOy plane, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorption layer, Represents direct multiplication of corresponding elements of an array.

[0019] In some embodiments, the function Defined as:

[0020]

[0021] in, represents the optimization goal, is the dielectric constant of the material, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

[0022] In some embodiments, a modified Bonn series is used to calculate the diffraction field of the mask's absorbing layer.

[0023] In some embodiments, when wafer fidelity is optimized, a vector projection imaging model is used to obtain the electric field distribution on the wafer surface.

[0024] In some embodiments, the chain rule is used to inversely obtain the partial derivatives of the objective function with respect to the mask near field.

[0025] In some embodiments, the diffraction calculation of the absorption layer is specifically performed using a continuous mask, and the reflection portion of the multilayer film is performed using a transmission matrix method.

[0026] The second aspect of the present application relates to a gradient calculation system for photolithography mask optimization, comprising: at least one memory for storing programs; at least one processor for entering the program stored in the memory, and when the program stored in the memory is entered, the processor is used to enter the calculation method of any embodiment of the present application.

[0027] It can be understood that the beneficial effects of the second aspect mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0028] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies:

[0029] This application proposes a gradient calculation method and system for photolithography mask optimization. Using an adjoint method, the diffraction field of the mask's absorbing layer is spatially expanded, avoiding strong interference and fluctuations between electric fields. This allows gradient calculation using a single 2D slice of the 3D diffraction field. This eliminates the need to save the entire 3D diffraction field, only a few 2D slices, significantly conserving computing resources. Furthermore, this application imposes no specific requirements on the specific algorithms used in each step, achieving algorithm decoupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flowchart of a gradient calculation method for photolithography mask optimization provided in an embodiment of the present application.

[0031] Figure 2 The gradient calculation situation and result comparison provided by the embodiment of this application are shown in Figure 1. Among them, (a) is the optimization variable Distribution in the xOy plane; (b) is the target wafer pattern Distribution in the xOy plane; (c) comparison of the reference gradient at the y=0 nm tangent and the gradient calculated by this method; both the x-axis and the y-axis represent the spatial position coordinates. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0033] The term "and / or" in this application describes an association relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " in this application indicates that the associated objects are in an "or" relationship, for example, A / B means A or B.

[0034] In the specification and claims of this application, the terms "first" and "second" are used to distinguish different objects, rather than to describe a specific order of objects. For example, "first response message" and "second response message" are used to distinguish different response messages, rather than to describe a specific order of response messages.

[0035] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0036] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more, for example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0037] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0038] like Figure 1 As shown, the first aspect of the present application relates to a gradient calculation method for photolithography mask optimization, the gradient calculation method comprising:

[0039] S1. Calculate the diffraction field of the first diffraction, the reflection of the multilayer film, and the diffraction field of the second diffraction to obtain a forward simulated diffraction field;

[0040] S2. Obtain a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at a first position inside the absorption layer, obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a second position inside the absorption layer, and obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a third position outside the absorption layer, and use them as the mask near field, wherein the two-dimensional slices are two-dimensional complex arrays of the diffraction field along the pattern plane;

[0041] S3. Using the mask near field as input, calculate the optimization target, and inversely obtain the partial derivative of the optimization target with respect to the mask near field, which is used as the incident field for the accompanying simulation;

[0042] S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, where the position of the incident field is the position of the mask near field in the adjoint simulation;

[0043] S5. Acquire a two-dimensional slice of the diffraction field at the second position inside the absorbing layer accompanied by the simulated first diffraction, and acquire a two-dimensional slice of the diffraction field at the first position accompanied by the simulated second diffraction;

[0044] S6. Calculate the mask optimization gradient by integrating the mask diffraction field and the two-dimensional slices of the first position and the second position of the simulated diffraction field.

[0045] In some embodiments, the first location and the second location are the same or different.

[0046] In some embodiments, the mask optimization gradient is calculated as follows:

[0047]

[0048] in, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorption layer, Represents direct multiplication of corresponding elements of an array.

[0049] In some embodiments, the mask optimization gradient is calculated as follows:

[0050]

[0051] Among them, the pattern plane is in the xOy plane, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorption layer, Represents direct multiplication of corresponding elements of an array.

[0052] In some embodiments, the function Defined as:

[0053]

[0054] in, represents the optimization goal, is the dielectric constant of the material, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

[0055] In some embodiments, a modified Bonn series is used to calculate the diffraction field of the mask's absorbing layer.

[0056] It should be noted that the present application preferably uses the modified Born series to calculate the diffraction field of the mask absorption layer. This method is not only fast, but also uses a smaller three-dimensional array and occupies less memory space.

[0057] In some embodiments, when wafer fidelity is optimized, a vector projection imaging model is used to obtain the electric field distribution on the wafer surface.

[0058] It should be noted that, compared with the scalar projection imaging model, the vector projection imaging model can obtain a more accurate wafer electric field distribution.

[0059] In some embodiments, the chain rule is used to inversely obtain the partial derivatives of the objective function with respect to the mask near field.

[0060] In some embodiments, the diffraction calculation of the absorption layer is specifically performed using a continuous mask, and the reflection portion of the multilayer film is performed using a transmission matrix method.

[0061] The second aspect of the present application relates to a gradient calculation system for photolithography mask optimization, comprising: at least one memory for storing programs; at least one processor for entering the program stored in the memory, and when the program stored in the memory is entered, the processor is used to enter the calculation method of any embodiment of the present application.

[0062] This embodiment is directed to an extreme ultraviolet lithography mask, and the specific calculation steps are described as follows.

[0063] S1: Calculate the mask diffraction field.

[0064] EUV lithography masks have complex three-dimensional structures, including an absorbing layer with a complex two-dimensional pattern and a multilayer reflective film stacked vertically. Mask calculations typically involve three steps: first, calculating the diffraction field of the absorbing layer (first diffraction); second, calculating the reflection of the multilayer film; and finally, calculating the diffraction field of the absorbing layer again (second diffraction). The incident field used in step S1 is typically a plane wave, and the specific plane wave parameters depend on the lithography illumination configuration being simulated and the light source point selected for the simulation.

[0065] Mask optimization is performed on the two-dimensional pattern of the absorption layer, and the diffraction field of the absorption layer region needs to be preserved. There are many methods for calculating the mask diffraction field, and this application does not limit the calculation method used.

[0066] This embodiment uses the modified Bonn series to calculate the diffraction field of the EUV mask absorption layer. The absorption layer is TaN with a refractive index of =0.9385+0.03776i. The thickness of the absorption layer is 50nm. The optimization variables in the mask optimization are ,like Figure 2 As shown in (a) in the figure, the diffraction calculation of the absorption layer specifically uses a continuous mask with a refractive index of Defined as:

[0067]

[0068] in, is the background refractive index, which is 1.0 in vacuum. The multilayer reflective layer of the EUV mask is calculated using the transfer matrix method. The incident electric field is a y-polarized plane wave with a 6° angle of incidence. After calculation, the diffraction fields of the first and second diffraction events of the absorbing layer are obtained.

[0069] S2: Acquire two two-dimensional slices of the mask diffraction field, where the two-dimensional slice is a two-dimensional complex array of the mask diffraction field along the pattern plane inside the absorption layer, representing the electric field.

[0070] The interface between the absorption layer and the multilayer film is defined as z = 0nm, with the positive z-axis pointing toward the absorption layer. The acquisition position is z=25nm, and the slice The acquisition position is z = 40 nm. There is no requirement for the position of the two slices, and the two acquired two-dimensional slices are used for the calculation in step S6.

[0071] In addition, it is also necessary to obtain a two-dimensional slice of the diffraction field of the second diffraction outside the absorption layer as the mask near field. In this embodiment, 0.5 wavelengths away from the absorption layer is selected as the third position.

[0072] S3: Take the mask near field as input, calculate the optimization target, and reversely obtain the partial derivative of the optimization target with respect to the mask near field, which is used as the incident field for the accompanying simulation.

[0073] The optimization objectives for the scenario, including wafer fidelity and edge deviation error, can be subsequently calculated using the mask near-field. The optimization objective is typically a scalar value, and its acquisition method depends on its specific definition and may involve processing using projection imaging models, photoresist models, and other methods. Once the optimization objective is obtained, the partial derivative of the optimization objective with respect to the mask near-field is reversed and used as the incident field in the accompanying simulation.

[0074] This embodiment uses a vector projection imaging model to obtain the electric field distribution on the wafer surface Note that this application can be used for scalar simulation and vector simulation. The electric field distribution in this embodiment has three polarization components: x, y, and z.

[0075] Through the projection system H, the near field of the mask can be Get the electric field distribution on the wafer surface , the subscript indicates the polarization direction. This embodiment uses vector calculation, which has three polarization directions. This application can also be used for scalar calculation.

[0076]

[0077] Then calculate the corresponding wafer aerial image :

[0078]

[0079] The photoresist model uses the Sigmoid function to obtain the wafer pattern .

[0080]

[0081] in, Indicates the steepness, Indicates the threshold.

[0082] The optimization objective function for this implementation is wafer fidelity, which is defined as: ,in, To optimize the variables, is the wafer pattern determined by the optimization variables, is the target wafer pattern, such as Figure 2 As shown in (b), the partial derivative of the objective function with respect to the mask near field is obtained by inversely using the chain rule.

[0083] S4: Execute adjoint simulation to obtain adjoint simulation diffraction field. In the adjoint simulation, the position of the incident field is the position of the mask near field.

[0084] The adjoint simulation is similar to step S1, except that the incident field is different. The incident field in step S1 is usually a plane wave with oblique incidence, while the incident field of the adjoint simulation depends on the definition of the optimization target and subsequent calculations.

[0085] The partial derivative of the objective function with respect to the mask near field is used as the input electric field to calculate the diffraction field again. The calculation method of the accompanying simulation in this embodiment is the same as step S1.

[0086] S5: Acquire two two-dimensional slices of the accompanying simulated diffraction field, with the slice positions being the same as those in step S2.

[0087] The acquisition of the diffraction field slices accompanying the simulation is similar to step S2, and also includes the first diffraction and the second diffraction. , take a slice from the diffraction field of the second diffraction .in, The slice position needs to be consistent with The slice positions are the same, The slice position needs to be consistent with The slice positions are the same.

[0088] S6: Calculate the mask optimization gradient.

[0089] The calculation formula of the mask optimization gradient is as follows:

[0090]

[0091] Among them, the function f is the post-processing function in the gradient calculation based on the adjoint method; the product in this formula is the direct multiplication of the corresponding elements of the array. In this formula, the diffraction field of the mask absorption layer is expanded in space, avoiding strong interference and fluctuation between the electric fields, that is, and 、 and The interference between the two diffraction fields allows the gradient to be calculated using a two-dimensional slice of the three-dimensional diffraction field.

[0092] Calculate according to the formula in step S6 and perform corresponding post-processing. The post-processing function depends on the relationship between the design variables and the refractive index in the electric field simulation. In this embodiment, the function f Defined as:

[0093]

[0094] in, is the dielectric constant of the material, . is the magnetic permeability, which is 1 in this embodiment. represents the refractive index, and F represents the optimization target.

[0095] If the post-processing function f It is linear, and the calculation according to the following formula is equivalent.

[0096]

[0097] like Figure 2 As shown in (c), the gradient results obtained by this method are highly consistent with the reference gradients obtained by the existing methods, which confirms the effectiveness of this method.

[0098] Based on the adjoint method, the present application expands the diffraction field of the mask absorption layer in space, avoiding strong interference and fluctuation between electric fields, so that the gradient can be calculated using a two-dimensional slice of the three-dimensional diffraction field, saving computing resources.

[0099] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0100] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0101] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0102] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0103] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC.

[0104] The above embodiments can be implemented in whole or in part using software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed on a computer, the computer program instructions fully or partially produce the processes or functions described in the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disk, hard disk, tape), optical media (e.g., DVD), or semiconductor media (e.g., solid-state drive (SSD)).

[0105] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0106] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A gradient calculation method for photolithography mask optimization, characterized in that: include: S1. Calculate the diffraction field of the first diffraction, the reflection of the multilayer film, and the diffraction field of the second diffraction to obtain a forward simulated diffraction field; S2. Obtain a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at a first position inside the absorption layer, obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a second position inside the absorption layer, and obtain a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at a third position outside the absorption layer, and use them as the mask near field, wherein the two-dimensional slices are two-dimensional complex arrays of the diffraction field along the pattern plane; S3. Using the mask near field as input, calculate the optimization target, and inversely obtain the partial derivative of the optimization target with respect to the mask near field, which is used as the incident field for the accompanying simulation; S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, where the position of the incident field is the position of the mask near field in the adjoint simulation; S5. Acquire a two-dimensional slice of the diffraction field at the second position inside the absorbing layer accompanied by the simulated first diffraction, and acquire a two-dimensional slice of the diffraction field at the first position accompanied by the simulated second diffraction; S6. Calculate the mask optimization gradient by integrating the mask diffraction field and the two-dimensional slices of the first position and the second position of the simulated diffraction field.

2. The calculation method according to claim 1, wherein: The first position and the second position are the same or different.

3. The calculation method according to claim 1, wherein: The calculation formula of the mask optimization gradient is as follows: in, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

4. The calculation method according to claim 1, wherein: The calculation formula of the mask optimization gradient is as follows: Among them, the pattern plane is in the xOy plane, represents the mask optimization gradient, represents the post-processing function in the gradient calculation based on the adjoint method, represents a two-dimensional slice of the diffraction field of the first diffraction in the forward simulation at the first position inside the absorption layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorption layer, represents the slice of the diffraction field at the second position inside the absorption layer accompanying the simulation of the first diffraction, The diffraction field of the second diffraction is sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

5. The calculation method according to claim 3 or 4, characterized in that: function Defined as: in, represents the partial derivative, represents the optimization goal, is the dielectric constant of the material, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

6. The calculation method according to claim 1, wherein: The diffraction field of the mask's absorbing layer is calculated using the modified Born series.

7. The calculation method according to claim 1, wherein: When wafer fidelity is optimized, the electric field distribution on the wafer surface is obtained using a vector projection imaging model.

8. The calculation method according to claim 1, wherein: The partial derivative of the objective function with respect to the mask near field is obtained inversely using the chain rule.

9. The calculation method according to claim 1, wherein: The diffraction calculation of the absorption layer is specifically done using a continuous mask, and the reflection part of the multilayer film is completed using the transfer matrix method.

10. A gradient calculation system for photolithography mask optimization, characterized in that: include: at least one memory for storing a program; At least one processor is configured to enter the program stored in the memory, and when the program stored in the memory is entered, the processor is configured to enter the computing method according to any one of claims 1 to 9.

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