Global scattering matrix calculation method and device

Abstract

The invention provides a global scattering matrix calculation method and a global scattering matrix calculation device. The global scattering matrix calculation method comprises the following steps: acquiring a target imaging structure comprising a plurality of target film layers in plasma photoetching imaging; and determining the same second target film layers among the plurality of target film layers and the plurality of initial film layers of the initial imaging structure. The initial scattering matrix of the initial film layer is stored in a database, and the second scattering matrix of the second target film layer can be directly determined according to the initial scattering matrix. And independently calculating a first scattering matrix of a first target film layer different from the initial film layer in the target imaging structure, and calculating according to the first scattering matrix and the second scattering matrix to obtain a global scattering matrix. The second scattering matrix of the second target film layer can be directly obtained by directly utilizing the initial scattering matrix, the scattering matrix of the second target film layer does not need to be independently calculated, the calculation efficiency of the global scattering matrix is improved, the global scattering matrix is obtained by calculating the first target film layer only by utilizing fewer calculation resources, and the calculation time is shortened.

Description

Technical Field

[0001] The present invention relates to the field of computers, and in particular to a global scattering matrix calculation method and device. Background Art

[0002] With the development of semiconductor-related technologies, lithography, one of the important technologies for manufacturing semiconductor devices, is also developing rapidly. As a supplement to mainstream lithography, plasma lithography is very different from traditional optical lithography, such as deep ultraviolet lithography (DUVL) and extreme ultraviolet lithography (EUVL).

[0003] Plasma lithography technology can break through the diffraction limit in traditional lithography by utilizing evanescent near-field imaging containing high-frequency information. Experiments have shown that even with a light source with a wavelength of 365 nanometers (nm), the resolution can reach about 20nm under single exposure conditions, which is about 1 / 17 of the wavelength of light, and it is possible to further improve. This method provides a reliable technical approach for studying low-cost, large-area, and efficient lithography technology, and has therefore attracted widespread attention.

[0004] In order to improve the imaging effect of plasma lithography, it is necessary to use algorithms to calculate the electromagnetic field distribution of the imaging structure of plasma lithography. However, the current calculation of electromagnetic field distribution requires the calculation of the global scattering matrix of the imaging structure. The global scattering matrix is ​​affected by the film structure and film material of the imaging structure, and the calculation is relatively complex, resulting in more computing resources and longer computing time each time the electromagnetic field distribution of different imaging structures is calculated. Summary of the invention

[0005] In view of this, the purpose of the present application is to provide a global scattering matrix calculation method and device, which can calculate the global scattering matrix with less computing resources, reduce the calculation time, and improve the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures.

[0006] To achieve the above purpose, this application has the following technical solutions:

[0007] The present application provides a global scattering matrix calculation method, comprising:

[0008] Acquire a target imaging structure for plasma lithography imaging, wherein the target imaging structure includes a plurality of target film layers;

[0009] Determine a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, wherein the initial imaging structure includes multiple initial film layers, and initial scattering matrices of the initial film layers are stored in a database;

[0010] Calculate a first scattering matrix of a first target film layer in the target imaging structure that is different from the initial film layer;

[0011] Directly determining a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to the initial scattering matrix of the initial film layer;

[0012] A global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix.

[0013] Optionally, the method further comprises:

[0014] A spacer layer with a predefined thickness of 0 wraps the target film layer;

[0015] Predefine an operation symbol for calculating the global scattering matrix;

[0016] The global scattering matrix is ​​calculated by sequentially connecting the scattering matrices of each target film layer using the operation symbol.

[0017] Optionally, calculating a global scattering matrix according to the first scattering matrix and the second scattering matrix comprises:

[0018] The global scattering matrix is ​​calculated by sequentially connecting the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the operation symbol.

[0019] Optionally, the method further comprises:

[0020] Precalculating an initial scattering matrix of each of the initial film layers in the initial imaging structure;

[0021] An initial scattering matrix of the initial film layer is stored in the database.

[0022] Optionally, the precalculating an initial scattering matrix of each initial film layer in the initial imaging structure comprises:

[0023] The initial scattering matrix of each initial film layer in the initial imaging structure is calculated according to the rigorous coupled wave analysis (RCWA) algorithm.

[0024] Optionally, the method further comprises:

[0025] Calculating the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field according to the global scattering matrix and the spatial frequency distribution of the incident electric field;

[0026] Fourier transform is performed on the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field respectively to obtain the spatial domain electric field distribution of the reflected electric field and the spatial domain electric field distribution of the transmitted electric field.

[0027] Optionally, the target imaging structure and the initial imaging structure have the same arrangement and material of at least some film layers.

[0028] The present application provides a global scattering matrix calculation device, comprising:

[0029] An acquisition unit, used for acquiring a target imaging structure of plasma lithography imaging, wherein the target imaging structure includes a plurality of target film layers;

[0030] A first determining unit is used to determine a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, wherein the initial imaging structure includes multiple initial film layers, and the initial scattering matrix of the initial film layer is stored in a database;

[0031] A first calculation unit, used for calculating a first scattering matrix of a first target film layer different from the initial film layer in the target imaging structure;

[0032] A second determining unit, configured to directly determine a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to an initial scattering matrix of the initial film layer;

[0033] The second calculation unit is configured to calculate a global scattering matrix according to the first scattering matrix and the second scattering matrix.

[0034] Optionally, the device further includes a third computing unit, configured to:

[0035] A spacer layer with a predefined thickness of 0 wraps the target film layer;

[0036] Predefine an operation symbol for calculating the global scattering matrix;

[0037] The global scattering matrix is ​​calculated by sequentially connecting the scattering matrices of each target film layer using the operation symbol.

[0038] Optionally, the device further comprises a storage unit, wherein the storage unit is configured to:

[0039] Precalculating an initial scattering matrix of each of the initial film layers in the initial imaging structure;

[0040] An initial scattering matrix of the initial film layer is stored in the database.

[0041] The present application provides a method for calculating a global scattering matrix, including: obtaining a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target film layers. Determining the second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, the initial imaging structure including multiple initial film layers, that is, comparing the target imaging structure with the initial imaging structure to obtain the second target film layer that is the same as the initial film layer and the different first target film layer. The initial scattering matrix of the initial film layer is stored in a database, so that the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure can be directly determined based on the initial scattering matrix of the initial film layer. Then, the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure is calculated separately, and finally the global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix. In this way, by directly using the initial scattering matrix of the initial film layer, the second scattering matrix of the second target film layer that is the same as the initial film layer can be directly obtained. There is no need to separately calculate the scattering matrix of the second target film layer in the target imaging structure, which greatly improves the calculation efficiency of the global scattering matrix. In addition, only fewer computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, which reduces the calculation time and ultimately improves the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 A schematic structural diagram of an imaging structure for plasma lithography imaging is shown;

[0044] Figure 2 A schematic diagram of a process for calculating a global scattering matrix provided in an embodiment of the present application is shown;

[0045] Figure 3 A schematic diagram of a scattering matrix of the i-th layer provided in an embodiment of the present application is shown;

[0046] Figure 4 A schematic diagram of a global scattering matrix provided in an embodiment of the present application is shown;

[0047] Figure 5A schematic structural diagram of an imaging structure for plasma lithography imaging provided in an embodiment of the present application is shown;

[0048] Figure 6 A schematic diagram of a mask pattern provided in an embodiment of the present application is shown;

[0049] Figure 7 A schematic diagram of imaging light field distribution provided by an embodiment of the present application is shown;

[0050] Figure 8 A schematic diagram of the structure of a global scattering matrix calculation device provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0051] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below with reference to the accompanying drawings.

[0052] In the following description, many specific details are set forth to facilitate a full understanding of the present application, but the present application may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0053] This application is described in detail with reference to schematic diagrams. When describing the embodiments of this application in detail, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of this application. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0054] With the development of semiconductor-related technologies, lithography, one of the important technologies for manufacturing semiconductor devices, is also developing rapidly. As a supplement to mainstream lithography, plasma lithography is very different from traditional optical lithography, such as deep ultraviolet lithography (DUVL) and extreme ultraviolet lithography (EUVL).

[0055] Plasma lithography technology can break through the diffraction limit in traditional lithography by utilizing evanescent near-field imaging containing high-frequency information. Experiments have shown that even with a light source with a wavelength of 365 nanometers (nm), the resolution can reach about 20nm under single exposure conditions, which is about 1 / 17 of the wavelength of light, and it is possible to further improve. This method provides a reliable technical approach for studying low-cost, large-area, and efficient lithography technology, and has therefore attracted widespread attention.

[0056] Compared with traditional ultraviolet projection lithography, plasma lithography has different principles. For example, the imaging range is localized in the near field, the evanescent wave containing the high-frequency information of the object (mask) can be resonantly amplified and participate in the imaging, and the imaging lens is no longer an ordinary optical lens but a single-layer metal film with a thickness of nanometers or a multi-layer film with alternating metal / medium arrangements.

[0057] Plasma lithography mainly includes plasma imaging lithography, interference lithography and direct writing lithography. Direct writing lithography usually has no imaging structure, while imaging lithography and interference lithography have imaging structures including mask patterns. Figure 1 shown. Figure 1 The imaging structure shown is a hyperbolic metamaterial (HMM) structure with metal / dielectric alternating arrangements, including a quartz substrate (Glass), a mask pattern, polymethyl methacrylate (PMMA), a metal / dielectric stacked alternating film, a photoresist (PR) and a reflective layer stacked in sequence, wherein the mask pattern is, for example, a chromium (Cr) mask, the metal / dielectric stacked alternating film is, for example, an aluminum (Al) / silicon oxide (SiO2) stacked alternating film, and the reflective layer is, for example, aluminum.

[0058] The plasma lithography imaging process including the imaging structure is roughly as follows: the light source is incident on the mask pattern and diffracted, generating various diffraction orders, including low-frequency transmission waves and high-frequency evanescent waves. These diffracted light waves will continue to propagate through the single-layer metal film or the multi-layer film with metal / medium alternating arrangement behind the mask pattern until the photoresist layer, and transfer the information of the mask pattern to the photoresist. In the process of the diffraction order being transferred to the photoresist, if the wave vector of the high-frequency evanescent diffraction order matches the wave vector of the surface plasmon polariton (SPP) at the metal / medium interface, the SPP can be excited at the metal / medium interface, so that the high-frequency evanescent wave is resonantly amplified and transferred to the photoresist layer, thereby achieving an improvement in the lithography resolution. In addition, a reflective layer is often placed behind the photoresist layer to further improve the imaging effect of the photoresist layer through the reflection resonance effect.

[0059] In order to solve the electromagnetic field distribution of different imaging structures in plasma lithography, the rigorous coupled wave analysis (RCWA) algorithm can be used. The RCWA algorithm, also known as the Fourier modal method (FMM), is a semi-analytical and semi-numerical method suitable for the simulation of a plane wave source incident on a multilayer structure with a non-uniform and periodic pattern in the lateral direction. The typical structure is Figure 1The plasma lithography imaging structure shown. The RCWA algorithm expresses the electromagnetic field distribution and the material parameters of the imaging structure to be solved as an infinite series of Fourier expansions, but it often requires a certain truncation order as an approximate solution. Therefore, the speed and accuracy of the RCWA algorithm depend on the number of truncation orders. For the multilayer films in the imaging structure, in order to connect these layers, the boundary conditions are achieved by making the tangential components of the field on both sides of the interface equal. In this way, the propagation through the entire imaging device can be strictly described. In order to effectively solve the boundary condition problem, the scattering matrix method can be used. The scattering matrix method solves the boundary condition problems of one layer at a time instead of solving the boundary condition problems of all layers at the same time. In this way, the RCWA algorithm takes into account the advantages of both numerical and analytical methods, ensuring both high calculation accuracy and fast running speed.

[0060] Since the RCMA algorithm was proposed by MG Moharam and TK Gaylord in the 1980s, the RCWA algorithm has been continuously developed and optimized and has become a very mature algorithm. Its calculation speed and numerical stability have been continuously improved, and its application scenarios have become more and more. In addition, commercial software based on this RCMA algorithm has also emerged, such as Ansys Lumerical-RCWA and MC Grating. However, there are not many modeling studies specifically for plasma lithography based on this RCMA algorithm, especially the establishment of three-dimensional models and how to improve the calculation speed of three-dimensional models. With the development of plasma lithography technology, computational lithography technologies for plasma lithography, such as light source optimization (SO), mask optimization (MO), light source mask joint optimization (SMO), optical proximity correction (OPC), etc., will also be launched. These technologies will further improve the imaging level of plasma lithography and improve the resolution of plasma lithography, and are important tools to promote the industrial application of plasma lithography. However, plasma lithography technology requires repeated calls to the model of the imaging structure, so it places high demands on the rapid calculation of the model of the imaging structure. Therefore, it is very necessary to establish a fast and accurate optical imaging model for plasma lithography. The RCWA algorithm, as a method for solving multilayer structures with periodic patterns, is a very suitable candidate algorithm for establishing a fast and accurate imaging structure model for plasma lithography.

[0061] In other words, in order to improve the imaging effect of plasma lithography, it is necessary to use an algorithm to calculate the electromagnetic field distribution of the imaging structure of plasma lithography. However, the current calculation of the electromagnetic field distribution requires the calculation of the global scattering matrix of the imaging structure. The global scattering matrix is ​​affected by the film structure and film material of the imaging structure, and the calculation is relatively complicated. In addition, it is necessary to calculate the scattering matrix of each film layer before calculating the global scattering matrix. When the imaging structure is slightly changed, the calculated global scattering matrix is ​​also different, resulting in more computing resources and longer computing time each time the electromagnetic field distribution of different imaging structures is calculated.

[0062] Based on this, the present application provides a method for calculating a global scattering matrix, including: obtaining a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target film layers. Determine the second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, the initial imaging structure including multiple initial film layers, that is, compare the target imaging structure with the initial imaging structure to obtain the second target film layer that is the same as the initial film layer and the different first target film layer. The initial scattering matrix of the initial film layer is stored in a database, so that the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure can be directly determined according to the initial scattering matrix of the initial film layer. Then, the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure is calculated separately, and finally the global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix. In this way, by directly using the initial scattering matrix of the initial film layer, the second scattering matrix of the second target film layer that is the same as the initial film layer can be directly obtained. There is no need to separately calculate the scattering matrix of the second target film layer in the target imaging structure, which greatly improves the calculation efficiency of the global scattering matrix. In addition, only fewer computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, which reduces the calculation time and ultimately improves the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures.

[0063] In order to better understand the technical solution and technical effects of the present application, specific embodiments will be described in detail below with reference to the accompanying drawings.

[0064] refer to Figure 2 FIG. 1 is a flow chart of a method for calculating a global scattering matrix provided in an embodiment of the present application, the method comprising the following steps:

[0065] S101, acquiring a target imaging structure for plasma lithography imaging.

[0066] In the embodiments of the present application, there are multiple imaging structures for plasma lithography imaging, and a target imaging structure can be obtained, wherein the target imaging structure includes multiple target film layers.

[0067] As an example, refer to Figure 1 As shown, the target imaging structure can be a hyperbolic multilayer film structure with metal / dielectric alternating arrangement, including a quartz substrate, organic glass, a mask pattern (MASK), a metal / dielectric alternating film, a photoresist and a reflective layer stacked in sequence, wherein the parameter information of the target imaging structure is: the mask pattern is a Cr mask, the adjacent Cr masks are transparent titanium oxide (TiO2), the metal / dielectric alternating film is a TiO2 / Al multilayer film, and the reflective layer is Al. The illumination condition used in plasma lithography imaging is a normally incident 365nm wavelength TM polarized light.

[0068] An initial imaging structure may also be obtained at the same time, the initial imaging structure comprising a plurality of initial film layers, wherein the initial scattering matrix of the initial film layer is stored in the database, that is, the initial imaging structure is an imaging structure for which the scattering matrix has been calculated.

[0069] In an embodiment of the present application, an initial scattering matrix of each initial film layer in the initial imaging structure may be pre-calculated, and the initial scattering matrix of the initial film layer may be stored in a database.

[0070] The RCMA algorithm can be used to calculate the scattering matrix of any film layer and the global scattering matrix of the entire imaging structure. For example, the rigorous coupled wave analysis (RCWA) algorithm can be used to calculate the initial scattering matrix of each initial film layer in the initial imaging structure.

[0071] As a possible implementation, refer to Figure 3 As shown, the scattering matrix S of the i-th layer of the initial imaging structure (i) It can be defined as:

[0072]

[0073] Among them, the column vector and contains the modal coefficients of the field outside the ith layer in the forward and reverse directions. The subscript indicates which side of the layer is being described, while the sign in the superscript indicates the direction of propagation. and Represents the scattering matrix S of the i-th layer (i) There are 4 parts in it. The parameter quantifies how much of a wave applied to port 1 is reflected from port 1. quantifies how much of the same applied wave is transmitted through the device to port 2, quantify how much of a wave applied to port 2 will be transmitted through port 1, and finally, Quantifies how much of the second applied wave is reflected from port 2. This can usually be understood as Represents reflection, Represents transmission.

[0074] You can predefine the spacer layer with a thickness of 0, including the initial film layer, and predefine the operator for calculating the global scattering matrix. The global scattering matrix is ​​calculated by connecting the initial scattering matrices of each initial film layer in sequence using operation symbols.

[0075] As an example, refer to Figure 4 The initial imaging structure shown, the global scattering matrix S (global) Can be:

[0076]

[0077] Among them, the superscripts of the scattering matrix represent a certain film layer area, ref and trn represent the incident substrate area and the exit substrate area respectively, and mask is the mask pattern area.

[0078] In other words, the global scattering matrix needs to calculate the scattering matrix of each film layer. The above calculation method reduces the influence between the scattering matrices of different film layers to 0, that is, the scattering matrices of each film layer do not affect each other. In this way, when the geometric information or material information of one or more film layers is changed, there is no need to repeatedly calculate the scattering matrices of other film layers. The historical calculation results of the scattering matrices of other film layers can be directly called, which can greatly reduce the calculation time.

[0079] In practical applications, the target imaging structure and the initial imaging structure have the same arrangement and material of at least part of the film layers, that is, the target imaging structure and the initial imaging structure have the same part, and the same part includes geometric information and material information. This makes it convenient to subsequently obtain the scattering matrix of part of the film layer of the target imaging structure based on the scattering matrix of the film layer of a similar part of the initial imaging structure.

[0080] S102, determining a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure.

[0081] In an embodiment of the present application, after obtaining the target imaging structure and the initial imaging structure, the target imaging structure and the initial imaging structure can be compared to determine a different first target film layer and a same second target film layer between multiple target film layers of the target imaging structure and multiple initial film layers of the initial imaging structure, that is, the first target film layer is a target film layer among the multiple target film layers that is different from the initial film layer, and the second target film layer is a target film layer among the multiple target film layers that is the same as the initial film layer.

[0082] For example, the number of the first target film layers may be 0, and the number of the second target film layers may be the number of the initial film layers, that is, the target imaging structure and the initial imaging structure are completely the same.

[0083] S103, calculating a first scattering matrix of a first target film layer different from the initial film layer in the target imaging structure.

[0084] In an embodiment of the present application, after determining a second target film layer having a target imaging structure identical to the initial film layer and a first target film layer different from the initial film layer, a first scattering matrix of the first target film layer may be calculated.

[0085] Specifically, the RCWA algorithm may be used to calculate the first scattering matrix of the first target film layer.

[0086] As an example, if the first target film layer of the target imaging structure is a mask pattern compared to the initial film layer, that is, the mask patterns of the initial imaging structure and the target imaging structure are different. Then the first scattering matrix of the first target film layer calculated by the RCWA algorithm is S (mask) .

[0087] S104, directly determining a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to the initial scattering matrix of the initial film layer.

[0088] In an embodiment of the present application, according to the pre-defined scattering matrices between different film layers of the present application, they do not affect each other. Therefore, the second target film layer that is the same as the initial film layer can directly call the initial scattering matrix of the initial film layer in the database, that is, the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure is directly determined according to the initial scattering matrix of the initial film layer. In this way, by directly using the initial scattering matrix of the initial film layer, the second scattering matrix of the second target film layer that is the same as the initial film layer can be directly obtained, and there is no need to separately calculate the scattering matrix of the second target film layer in the target imaging structure, which greatly improves the calculation efficiency of the scattering matrix.

[0089] As an example, the initial imaging structure reference Figure 1 As shown in FIG. 1 , if the target imaging structure only modifies the mask pattern compared to the initial film layer, the first target film layer is the mask pattern. The change of the mask pattern will cause the scattering matrix of the film layer to change, while the other film layers as imaging systems have not changed, so the scattering matrix of the other film layers will not change either, so the second target scattering matrix of the second target film layer is the initial scattering matrix of the unchanged initial film layer.

[0090] The initial scattering matrix of the unchanged initial film layer is S (ref) , S (PMMA) , S (Al) , S (PR) and S (trn) , then the second target scattering matrix of the second target film layer is S (ref) , S(PMMA) , S (Al) , S (PR) and S (trn) .

[0091] S105, obtaining a global scattering matrix by calculation according to the first scattering matrix and the second scattering matrix.

[0092] In an embodiment of the present application, after the first scattering matrix is ​​calculated and the second scattering matrix is ​​acquired, a global scattering matrix can be calculated based on the first scattering matrix and the second scattering matrix.

[0093] As can be seen from the above, the global scattering matrix in the present application is calculated by connecting the scattering matrices of each target film layer in sequence using an operator. Then, the global scattering matrix of the target imaging structure can be calculated by connecting the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer in sequence using an operator.

[0094] As an example, the initial imaging structure reference Figure 1 As shown in FIG. 1 , if the target imaging structure only modifies the mask pattern compared to the initial film layer, the first target film layer is the mask pattern. The first scattering matrix of the first target film layer calculated by the RCWA algorithm is S (mask) , directly obtain the second scattering matrix of the second film structure of the target imaging structure from the database and are S (ref) , S (PMMA) , S (Al) , S (PR) and S (trn) The global scattering matrix S of the target imaging structure (global) (MASK) can be:

[0095]

[0096] in, After integration, it is regarded as a whole scattering matrix, and the several scattering matrices it contains are the initial scattering matrices of the initial film layer and S is calculated in this way. (TR+) After storage, it can be called later. (ref) The initial scattering matrix of the initial film layer is also stored for subsequent retrieval.

[0097] That is, when performing mask optimization (MO), the mask pattern will change, and the corresponding S (mask) will change accordingly, but S (global) (MASK) The main computing energy is spent on S (mask) The remaining S (ref) and S (TR+)It only needs to be called without recalculation, which will greatly reduce the calculation time, especially the more structural layers there are after the mask graphic, the more time will be saved.

[0098] It can be seen that for the multi-layer film layers of the imaging structure, when only the geometric information and material information of a certain film layer are changed, such as the mask optimization problem in plasma lithography, that is, only the mask pattern is changed, and other film layers are not changed, since the scattering matrix of each film layer has a specific writing method, the scattering matrix changes when the structure of this layer changes, and does not change when the structure of this layer remains unchanged. Therefore, there is no need to repeat the calculation, and only needs to be stored for the first calculation for future use, thereby saving time. In this way, only the scattering matrix of the film layer of the mask pattern can be calculated, and the scattering matrices of other film layers can directly call the historical calculation results, thereby greatly reducing the calculation time of the global scattering matrix and improving the calculation efficiency.

[0099] In an embodiment of the present application, the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field can be calculated based on the global scattering matrix and the spatial frequency distribution of the incident electric field, and then the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field are respectively Fourier transformed to obtain the spatial domain electric field distribution of the reflected electric field and the spatial domain electric field distribution of the transmitted electric field.

[0100] Specifically, the global scattering matrix S (global) It can also be expressed as:

[0101]

[0102] Among them, inc represents the incident field, c inc represents the incidence coefficient, c ref represents the reflection coefficient, c ％rn represents the transmission coefficient.

[0103] According to the scattering matrix S (global) And the spatial frequency distribution of the incident electric field The Fourier space frequency distribution of the tangential component of the reflected electric field is calculated and the Fourier space frequency distribution of the tangential component of the transmitted electric field

[0104]

[0105]

[0106] Among them, W ref represents the eigenvector of the incident substrate, W ％rn represents the eigenvector of the exiting substrate.

[0107] Then according to the electric field divergence equation, one of Maxwell's equations The longitudinal z components of the reflected electric field and the transmitted electric field can be solved separately and

[0108]

[0109]

[0110] in, represents the inversion of the z-component matrix of the incident substrate region wave vector, represents the inversion of the z-component matrix of the incident substrate region wave vector, represents the wave vector x component matrix, Represents the wave vector y component matrix.

[0111] In this way, the Fourier space frequency distribution of the reflected electric field and the Fourier space frequency distribution of the transmitted electric field are obtained respectively.

[0112] As an example, the global scattering matrix calculation method provided in the present application can improve the calculation speed of the calculated electric field distribution in the spatial domain.

[0113] Initial imaging structure reference Figure 5 As shown, Figure 5 The imaging structure shown is a single-layer metal film superlens structure, including a quartz substrate (Glass), a mask pattern, organic glass (PMMA), a metal film, a photoresist (PR) and a reflective layer stacked in sequence, wherein the mask pattern is, for example, a chromium (Cr) mask, the metal film is, for example, silver (Ag), and the reflective layer is, for example, silver. If the target imaging structure only modifies the mask pattern compared to the initial film layer, the first target film layer is the mask pattern, and the mask pattern of the target imaging structure is set to a T-shaped pattern, referring to Figure 6 As shown, the T-shaped area is light-transmissive, and the other areas are light-impermeable. The period of the mask pattern is set to 800nm, and the light-transmitting area is a rectangular hole of 600nm×200nm and forms a T-shaped pattern. The illumination condition is normal incident x-polarized light, and the imaging plane is the middle plane of the photoresist layer ( Figure 6 The sampling point precision is 1nm×1nm square grid, and the expansion order is kx=ky=[-20,-19,…,0,…,19,20].

[0114] The time taken to calculate the scattering matrix in sequence to obtain the global scattering matrix and then solve the electromagnetic field distribution, that is, the light field distribution, is 222 seconds. The time taken to calculate the scattering matrix of different film layers and call the scattering matrix of the same film layer to obtain the global scattering matrix and then solve the light field distribution is 83 seconds. In other words, the calculation speed is increased by about 1.7 times by the method provided in the embodiment of the present application. Figure 7 The calculated light field distribution is the same in both methods.

[0115] The present application provides a method for calculating a global scattering matrix, including: obtaining a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target film layers. Determining the second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, the initial imaging structure including multiple initial film layers, that is, comparing the target imaging structure with the initial imaging structure to obtain the second target film layer that is the same as the initial film layer and the different first target film layer. The initial scattering matrix of the initial film layer is stored in a database, so that the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure can be directly determined based on the initial scattering matrix of the initial film layer. Then, the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure is calculated separately, and finally the global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix. In this way, by directly using the initial scattering matrix of the initial film layer, the second scattering matrix of the second target film layer that is the same as the initial film layer can be directly obtained. There is no need to separately calculate the scattering matrix of the second target film layer in the target imaging structure, which greatly improves the calculation efficiency of the global scattering matrix. In addition, only fewer computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, which reduces the calculation time and ultimately improves the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures.

[0116] Based on the global scattering matrix calculation method provided in the above embodiment, the present application embodiment also provides a global scattering matrix calculation device, referring to Figure 8 , which is a schematic diagram of the structure of a global scattering matrix calculation device provided in an embodiment of the present application. The global scattering matrix calculation device 200 provided in an embodiment of the present application includes:

[0117] An acquisition unit 210 is used to acquire a target imaging structure of plasma lithography imaging, wherein the target imaging structure includes a plurality of target film layers;

[0118] A first determining unit 220, configured to determine a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, wherein the initial imaging structure includes multiple initial film layers, and the initial scattering matrix of the initial film layers is stored in a database;

[0119] A first calculation unit 230, configured to calculate a first scattering matrix of a first target film layer in the target imaging structure that is different from the initial film layer;

[0120] A second determining unit 240 is used to directly determine a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to the initial scattering matrix of the initial film layer;

[0121] The second calculation unit 250 is configured to calculate a global scattering matrix according to the first scattering matrix and the second scattering matrix.

[0122] Optionally, the device further includes a third computing unit, configured to:

[0123] A spacer layer with a predefined thickness of 0 wraps the target film layer;

[0124] Predefine an operation symbol for calculating the global scattering matrix;

[0125] The global scattering matrix is ​​calculated by sequentially connecting the scattering matrices of each target film layer using the operation symbol.

[0126] Optionally, the device further comprises a storage unit, wherein the storage unit is configured to:

[0127] Precalculating an initial scattering matrix of each of the initial film layers in the initial imaging structure;

[0128] An initial scattering matrix of the initial film layer is stored in the database.

[0129] Optionally, the second calculating unit 250 is configured to:

[0130] The global scattering matrix is ​​calculated by sequentially connecting the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the operation symbol.

[0131] Optionally, the storage unit is used to:

[0132] The initial scattering matrix of each initial film layer in the initial imaging structure is calculated according to the rigorous coupled wave analysis (RCWA) algorithm.

[0133] Optionally, the device further includes a fourth computing unit, wherein the fourth computing unit is configured to:

[0134] Calculating the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field according to the global scattering matrix and the spatial frequency distribution of the incident electric field;

[0135] Fourier transform is performed on the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field respectively to obtain the spatial domain electric field distribution of the reflected electric field and the spatial domain electric field distribution of the transmitted electric field.

[0136] Optionally, the target imaging structure and the initial imaging structure have the same arrangement and material of at least some film layers.

[0137] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0138] The above is only a preferred implementation of the present application. Although the present application has been disclosed as a preferred embodiment, it is not intended to limit the present application. Any technician familiar with the art can use the above disclosed methods and technical contents to make many possible changes and modifications to the technical solution of the present application without departing from the scope of the technical solution of the present application, or modify it into an equivalent embodiment of equivalent changes. Therefore, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present application without departing from the content of the technical solution of the present application still falls within the scope of protection of the technical solution of the present application.

Claims

1. A global scattering matrix calculation method, characterized in that: include: Acquire a target imaging structure for plasma lithography imaging, wherein the target imaging structure includes a plurality of target film layers; Determine a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, wherein the initial imaging structure includes multiple initial film layers, and initial scattering matrices of the initial film layers are stored in a database; Calculate a first scattering matrix of a first target film layer in the target imaging structure that is different from the initial film layer; Directly determining a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to the initial scattering matrix of the initial film layer; A global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix.

2. The method according to claim 1, characterized in that The method further comprises: A spacer layer with a predefined thickness of 0 wraps the target film layer; Predefine an operation symbol for calculating the global scattering matrix; The global scattering matrix is ​​calculated by sequentially connecting the scattering matrices of each target film layer using the operation symbol.

3. The method according to claim 2, characterized in that The calculating a global scattering matrix according to the first scattering matrix and the second scattering matrix comprises: The global scattering matrix is ​​calculated by sequentially connecting the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the operation symbol.

4. The method according to claim 1, characterized in that The method further comprises: Precalculating an initial scattering matrix of each of the initial film layers in the initial imaging structure; An initial scattering matrix of the initial film layer is stored in the database.

5. The method according to claim 4, characterized in that The precalculating the initial scattering matrix of each initial film layer in the initial imaging structure comprises: The initial scattering matrix of each initial film layer in the initial imaging structure is calculated according to the rigorous coupled wave analysis (RCWA) algorithm.

6. The method according to any one of claims 1 to 5, characterized in that: The method further comprises: Calculating the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field according to the global scattering matrix and the spatial frequency distribution of the incident electric field; Fourier transform is performed on the Fourier spatial frequency distribution of the reflected electric field and the Fourier spatial frequency distribution of the transmitted electric field respectively to obtain the spatial domain electric field distribution of the reflected electric field and the spatial domain electric field distribution of the transmitted electric field.

7. The method according to any one of claims 1 to 5, characterized in that: The target imaging structure and the initial imaging structure have at least a portion of film layers with the same order and material.

8. A global scattering matrix calculation device, characterized in that: include: An acquisition unit, used for acquiring a target imaging structure of plasma lithography imaging, wherein the target imaging structure includes a plurality of target film layers; A first determining unit is used to determine a second target film layer that is the same between the multiple target film layers of the target imaging structure and the multiple initial film layers of the initial imaging structure, wherein the initial imaging structure includes multiple initial film layers, and the initial scattering matrix of the initial film layer is stored in a database; A first calculation unit, used for calculating a first scattering matrix of a first target film layer different from the initial film layer in the target imaging structure; A second determining unit, configured to directly determine a second scattering matrix of a second target film layer in the target imaging structure that is the same as the initial film layer according to an initial scattering matrix of the initial film layer; The second calculation unit is configured to calculate a global scattering matrix according to the first scattering matrix and the second scattering matrix.

9. The device according to claim 8, characterized in that The device further comprises a third computing unit, configured to: A spacer layer with a predefined thickness of 0 wraps the target film layer; Predefine an operation symbol for calculating the global scattering matrix; The global scattering matrix is ​​calculated by sequentially connecting the scattering matrices of each target film layer using the operation symbol.

10. The device according to claim 8, characterized in that The device further comprises a storage unit, wherein the storage unit is configured to: Precalculating an initial scattering matrix of each of the initial film layers in the initial imaging structure; An initial scattering matrix of the initial film layer is stored in the database.

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