Gradient calculation method and system for photoetching mask optimization

Abstract

The invention belongs to the field of photoetching mask optimization, and particularly discloses a gradient calculation method and system for photoetching mask optimization. According to the invention, the diffraction field of the mask absorption layer is expanded in space by means of an accompanying method, strong interference and fluctuation between electric fields are avoided, so that the gradient can be calculated by using one two-dimensional slice of the three-dimensional diffraction field, the whole three-dimensional diffraction field does not need to be stored at the moment, only several two-dimensional slices need to be stored, and therefore, calculation resources are greatly saved. Meanwhile, the method has no limitation requirement on the algorithm specifically 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, to a gradient calculation method and system for photolithography mask optimization. Background Art

[0002] Mask optimization is the core link in computational lithography technology, and plays a vital role in improving the resolution and fidelity of lithography imaging. With the continuous reduction of integrated circuit feature size and the continuous advancement of lithography technology nodes, traditional lithography technology has been unable to meet the needs of high-end chip manufacturing. Driven by Moore's Law, in order to achieve more sophisticated circuit pattern transfer, computational lithography technology must be used to accurately optimize the design of the mask. Mask optimization adjusts the graphics on the mask to compensate for various optical effects and process deviations in the lithography process, thereby improving the quality of lithography imaging, expanding the process window, reducing manufacturing costs, and shortening the R&D cycle. Therefore, mask optimization technology is one of the key technologies to achieve mass production of high-end chips.

[0003] In the mask optimization process, gradient calculation is the key to realizing efficient optimization algorithms. Gradient information reflects the sensitivity of the objective function to the change of the optimization variable, and is an important basis for guiding the optimization algorithm to search for the optimal solution. In computational lithography, the objective function is usually related to the evaluation index of lithography imaging quality, such as graphic error, edge placement error, etc. By accurately calculating the gradient, the optimization algorithm can determine the direction and step size of the search in the multidimensional parameter space, thereby effectively narrowing the search range and accelerating the convergence to the optimal solution. The accuracy and efficiency of gradient calculation directly affect the quality of the mask optimization results and the consumption of computing resources. Therefore, gradient calculation is not only the basis for the implementation of mask optimization algorithms, but also an important link in improving the performance of computational lithography technology. Existing gradient calculation methods require a large amount of memory to store the three-dimensional diffraction field of the mask. Especially when considering partially coherent illumination, thousands of three-dimensional diffraction fields need to be stored at the same time, and the required memory is extremely large. Summary of the invention

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

[0005] A first aspect of the present application relates to a gradient calculation method for photolithography mask optimization, the gradient calculation method comprising: 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, 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 slice is a two-dimensional complex array of the diffraction field along the pattern plane; S3. Taking the mask near field as input, calculate the optimization target, reversely obtain the partial derivative of the optimization target with respect to the mask near field, and use it as the incident field of the accompanying simulation; S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, wherein the position of the incident field is the position of the mask near field in the adjoint simulation; S5. Obtaining a two-dimensional slice of the diffraction field at the second position inside the absorption layer accompanied by the simulation of the first diffraction, and obtaining a two-dimensional slice of the diffraction field at the first position accompanied by the simulation of the 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.

[0006] In some embodiments, the first position and the second position are the same or different.

[0007] In some embodiments, the calculation formula of the mask optimization gradient is as follows:

[0008] 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

[0009] In some embodiments, the calculation formula of the mask optimization gradient is as follows:

[0010] 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

[0011] In some embodiments, the function Defined as:

[0012] in, represents the optimization goal, is the material dielectric constant, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

[0013] In some embodiments, the diffraction field of the mask's absorbing layer is calculated using a modified Bonn series.

[0014] 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.

[0015] In some embodiments, the chain rule is used to inversely obtain the partial derivative of the objective function with respect to the mask near field.

[0016] 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 completed using a transmission matrix method.

[0017] 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.

[0018] 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.

[0019] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art: This application proposes a gradient calculation method and system for photolithography mask optimization. With the help of the adjoint method, the diffraction field of the mask absorption layer is spatially expanded to avoid strong interference and fluctuations between electric fields, so that a two-dimensional slice of the three-dimensional diffraction field can be used to calculate the gradient. At this time, it is not necessary to save the entire three-dimensional diffraction field, only a few two-dimensional slices need to be saved, thus greatly saving computing resources. At the same time, this application has no specific requirements for the specific algorithm used in each step, realizing algorithm decoupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flow chart of a gradient calculation method for photolithography mask optimization provided in an embodiment of the present application.

[0021] Figure 2 The following is a comparison of the gradient calculation scenarios and results provided in the embodiments of the present application. Distribution in the xOy plane; (b) is the target wafer pattern Distribution in the xOy plane; (c) comparison of the reference gradient at the tangent line of y=0 nm and the gradient calculated by this method; both the x-axis and the y-axis represent the spatial position coordinates. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0023] The term "and / or" in this application is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and 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.

[0024] The terms "first" and "second" in the specification and claims of this application are used to distinguish different objects rather than to describe a specific order of objects. For example, a first response message and a second response message are used to distinguish different response messages rather than to describe a specific order of response messages.

[0025] In the embodiments of the present 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 the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0026] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more than two. For example, multiple processing units refer to two or more processing units, etc.; multiple elements refer to two or more elements, etc.

[0027] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0028] 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: 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, 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 slice is a two-dimensional complex array of the diffraction field along the pattern plane; S3. Taking the mask near field as input, calculate the optimization target, reversely obtain the partial derivative of the optimization target with respect to the mask near field, and use it as the incident field of the accompanying simulation; S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, wherein the position of the incident field is the position of the mask near field in the adjoint simulation; S5. Obtaining a two-dimensional slice of the diffraction field at the second position inside the absorption layer accompanied by the simulation of the first diffraction, and obtaining a two-dimensional slice of the diffraction field at the first position accompanied by the simulation of the 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.

[0029] In some embodiments, the first position and the second position are the same or different.

[0030] In some embodiments, the calculation formula of the mask optimization gradient is as follows:

[0031] 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

[0032] In some embodiments, the calculation formula of the mask optimization gradient is as follows:

[0033] 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction sliced ​​at the first position inside the absorbing layer, Represents direct multiplication of corresponding elements of an array.

[0034] In some embodiments, the function Defined as:

[0035] in, represents the optimization goal, is the material dielectric constant, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

[0036] In some embodiments, the diffraction field of the mask's absorbing layer is calculated using a modified Bonn series.

[0037] 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.

[0038] 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.

[0039] It should be noted that, compared with the scalar projection imaging model, the use of the vector projection imaging model can obtain a more accurate wafer electric field distribution.

[0040] In some embodiments, the chain rule is used to inversely obtain the partial derivative of the objective function with respect to the mask near field.

[0041] 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 completed using a transmission matrix method.

[0042] 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.

[0043] This embodiment is directed to an extreme ultraviolet lithography mask, and the specific calculation steps are described as follows.

[0044] S1: Calculate the mask diffraction field.

[0045] EUV lithography masks have complex three-dimensional structures, including an absorption layer with a complex two-dimensional pattern and a multilayer reflective film stacked in the vertical direction. Usually, the calculation of the mask is divided into three steps: first, the diffraction field of the absorption layer is calculated (first diffraction); second, the reflection of the multilayer film is calculated; finally, the diffraction field of the absorption layer is calculated again (second diffraction). The incident field used in step S1 is usually a plane wave, and the specific plane wave parameters depend on the lithography illumination configuration to be simulated and the light source point selected for this simulation.

[0046] The mask optimization is to optimize the two-dimensional pattern of the absorption layer, and the diffraction field of the absorption layer region needs to be saved. There are many methods for calculating the mask diffraction field, and this application has no limitation on the calculation method used.

[0047] This embodiment uses the modified Bonn series to calculate the diffraction field of the absorption layer of the extreme ultraviolet mask. 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 The diffraction calculation of the absorption layer specifically uses a continuous mask with a refractive index of Defined as:

[0048] in, is the background refractive index, which is the vacuum refractive index of 1.0. The multilayer film reflection part of the EUV mask is completed using the transfer matrix method. The incident electric field is a 6° inclined incident plane wave with y polarization. After the calculation is completed, the diffraction field of the first diffraction of the absorption layer and the diffraction field of the second diffraction can be obtained.

[0049] S2: Acquire two two-dimensional slices of the mask diffraction field, where the two-dimensional slices are a two-dimensional complex array of the mask diffraction field along the pattern plane inside the absorption layer, representing the electric field.

[0050] The interface between the absorption layer and the multilayer film is defined as z = 0nm, and the positive z-axis is 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.

[0051] 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 wavelength away from the absorption layer is selected as the third position.

[0052] S3: Taking 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 of the accompanying simulation.

[0053] The optimization targets of the scene include wafer fidelity, edge deviation error, etc., which can be obtained by subsequent calculation using the mask near field. The optimization target is usually a scalar value, and the way to obtain it depends on its specific definition, which may involve processing using projection imaging models, photoresist models, etc. After obtaining the optimization target, the partial derivative of the optimization target with respect to the mask near field is obtained inversely and used as the incident field of the accompanying simulation.

[0054] This embodiment uses a vector projection imaging model to obtain the electric field distribution on the wafer surface. Note that the present 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.

[0055] 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, and this embodiment uses vector calculation, which has three polarization directions. This application can also be used for scalar calculation.

[0056]

[0057] Then calculate the corresponding wafer aerial image :

[0058] The photoresist model uses the Sigmoid function to obtain the wafer pattern .

[0059]

[0060] in, Indicates the steepness, Indicates the threshold value.

[0061] 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.

[0062] S4: Execute adjoint simulation to obtain an adjoint simulation diffraction field. In the adjoint simulation, the position of the incident field is the position of the mask near field.

[0063] 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.

[0064] 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.

[0065] S5: Obtain two two-dimensional slices of the accompanying simulated diffraction field, and the slice positions are the same as those in step S2.

[0066] The acquisition of the diffraction field slice 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.

[0067] S6: Calculate the mask optimization gradient.

[0068] The calculation formula of the mask optimization gradient is as follows:

[0069] 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 allows the gradient to be calculated using a 2D slice of the 3D diffraction field.

[0070] Calculate according to the formula of step S6 and perform corresponding post-processing. The post-processing function depends on the relationship between the design variable and the refractive index in the electric field simulation. In this embodiment, the function f Defined as:

[0071] in, is the material dielectric constant, . is the magnetic permeability, which is 1 in this embodiment, represents the refractive index, and F represents the optimization target.

[0072] If the post-processing function f It is linear, and the calculation according to the following formula is also equivalent.

[0073]

[0074] like Figure 2 As shown in (c), the gradient result obtained by this method is highly consistent with the reference gradient obtained by the existing method, which confirms the effectiveness of this method.

[0075] 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 a two-dimensional slice of the three-dimensional diffraction field can be used to calculate the gradient, saving computing resources.

[0076] 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, which will not be repeated here.

[0077] 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.

[0078] 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.

[0079] It is understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or 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.

[0080] 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, and the software modules 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 a component of the processor. The processor and the storage medium can be located in an ASIC.

[0081] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by 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 may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0082] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0083] It will be easily understood by those skilled in the art that the above description 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 shall 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, 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 slice is a two-dimensional complex array of the diffraction field along the pattern plane; S3. Taking the mask near field as input, calculate the optimization target, reversely obtain the partial derivative of the optimization target with respect to the mask near field, and use it as the incident field of the accompanying simulation; S4. Execute adjoint simulation to obtain adjoint simulated diffraction field, wherein the position of the incident field is the position of the mask near field in the adjoint simulation; S5. Obtaining a two-dimensional slice of the diffraction field at the second position inside the absorption layer accompanied by the simulation of the first diffraction, and obtaining a two-dimensional slice of the diffraction field at the first position accompanied by the simulation of the 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, characterized in that: The first position and the second position may be the same or different.

3. The calculation method according to claim 1, characterized in that: 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction 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, characterized in that: 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 absorbing layer, represents a two-dimensional slice of the diffraction field of the second diffraction in the forward simulation at the second position inside the absorbing layer, represents the slice of the diffraction field at the second position inside the absorbing layer accompanying the simulation of the first diffraction, represents the diffraction field of the second diffraction 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 partial derivative, represents the optimization goal, is the material dielectric constant, , is the magnetic permeability, represents the refractive index, θ Represents the optimization variable in mask optimization.

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

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

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

9. The calculation method according to claim 1, characterized in that: 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 used to enter the program stored in the memory, and when the program stored in the memory is entered, the processor is used to enter the computing method as described in any one of claims 1 to 9.

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