A global scattering matrix calculation method and apparatus

Abstract

This application provides a method and apparatus for calculating a global scattering matrix, comprising: acquiring a target imaging structure including multiple target films in plasma lithography imaging; identifying a second target film that is identical to multiple initial films in the initial imaging structure; storing the initial scattering matrix of the initial films in a database, and directly determining the second scattering matrix of the second target films based on the initial scattering matrix; calculating the first scattering matrix of the first target films in the target imaging structure that are different from the initial films separately; and calculating the global scattering matrix based on the first and second scattering matrices. By directly utilizing the initial scattering matrix, the second scattering matrix of the second target films can be obtained directly, eliminating the need to calculate the scattering matrix of the second target films separately, thus improving the computational efficiency of the global scattering matrix. Only a small amount of computational resources are needed to calculate the first target films to obtain the global scattering matrix, reducing computation time.

Description

Technical Field

[0001] This invention relates to the field of computers, and in particular to a method and apparatus for calculating a global scattering matrix. Background Technology

[0002] With the development of semiconductor-related technologies, photolithography, one of the key technologies in the manufacture of semiconductor devices, is also developing rapidly. Plasma lithography, as a supplement to mainstream photolithography, differs significantly from traditional optical lithography techniques such as deep ultraviolet lithography (DUVL) and extreme ultraviolet lithography (EUVL).

[0003] Plasma lithography, by utilizing evanescent near-field imaging that incorporates high-frequency information, can overcome the diffraction limit in traditional lithography. Experiments have shown that even using a 365-nanometer (nm) light source, a resolution of approximately 20 nm can be achieved in a single exposure, about 1 / 17th of the light wavelength, with the potential for further improvement. This method provides a reliable technical pathway for researching low-cost, large-area, and efficient lithography techniques, and has therefore attracted widespread attention.

[0004] To improve the imaging effect of plasma lithography, it is necessary to use algorithms to calculate the electromagnetic field distribution of the imaging structure. However, current calculations of the electromagnetic field distribution require calculating 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, making the calculation quite complex. This results in a significant amount of computational resources and a long computation time being spent on calculating the electromagnetic field distribution of different imaging structures each time. Summary of the Invention

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

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] This application provides a method for calculating a global scattering matrix, including:

[0008] To obtain a target imaging structure for plasma lithography imaging, wherein the target imaging structure comprises multiple target film layers;

[0009] A second target film layer is identified that is identical between multiple target films of the target imaging structure and multiple initial films of the initial imaging structure, wherein the initial imaging structure includes multiple initial films and the initial scattering matrix of the initial films is stored in a database;

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

[0011] 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 based on the initial scattering matrix of the initial film layer.

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

[0013] Optionally, the method further includes:

[0014] The target film is wrapped with a predefined spacer layer of zero thickness;

[0015] Predefine the operators for calculating the global scattering matrix;

[0016] The global scattering matrix is ​​calculated by sequentially concatenating the scattering matrices of each target film layer using the aforementioned operators.

[0017] Optionally, the step of calculating the global scattering matrix based on the first scattering matrix and the second scattering matrix includes:

[0018] The global scattering matrix is ​​calculated by sequentially concatenating the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the aforementioned operators.

[0019] Optionally, the method further includes:

[0020] The initial scattering matrix of each of the initial films in the initial imaging structure is calculated in advance;

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

[0022] Optionally, the pre-calculation of the initial scattering matrix for each of the initial films in the initial imaging structure includes:

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

[0024] Optionally, the method further includes:

[0025] The Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field are calculated based on the global scattering matrix and the incident electric field spatial frequency distribution.

[0026] Fourier transforms are performed on the Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field to obtain the spatial domain electric field distributions of the reflected electric field and the transmitted electric field, respectively.

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

[0028] This application provides a global scattering matrix calculation device, including:

[0029] An acquisition unit is used to acquire the target imaging structure of plasma lithography imaging, wherein the target imaging structure includes multiple target film layers;

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

[0031] The first computing unit is used to calculate the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure;

[0032] The second determining unit is used to directly determine the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure, based on the initial scattering matrix of the initial film layer;

[0033] The second calculation unit is used to calculate the global scattering matrix based on the first scattering matrix and the second scattering matrix.

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

[0035] The target film is wrapped with a predefined spacer layer of zero thickness;

[0036] Predefine the operators for calculating the global scattering matrix;

[0037] The global scattering matrix is ​​calculated by sequentially concatenating the scattering matrices of each target film layer using the aforementioned operators.

[0038] Optionally, the device further includes a storage unit, the storage unit being used for:

[0039] The initial scattering matrix of each of the initial films in the initial imaging structure is calculated in advance;

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

[0041] This application provides a method for calculating a global scattering matrix, comprising: acquiring a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target films; determining a second target film that is identical between the multiple target films of the target imaging structure and the multiple initial films of an initial imaging structure, the initial imaging structure including multiple initial films, i.e., comparing the target imaging structure and the initial imaging structure to obtain the second target film that is identical to the first target film and the different first target films. The initial scattering matrix of the initial films is stored in a database, so the second scattering matrix of the second target film that is identical to the initial films in the target imaging structure can be directly determined based on the initial scattering matrix of the initial films. Then, the first scattering matrix of the first target film that is different from the initial films 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, which is the same as that of the initial film layer, can be obtained directly. There is no need to calculate the scattering matrix of the second target film layer in the target imaging structure separately, which greatly improves the calculation efficiency of the global scattering matrix. Furthermore, only a small amount of computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, reducing the calculation time and ultimately improving the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

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

[0044] Figure 2 A flowchart illustrating a global scattering matrix calculation method provided in an embodiment of this application is shown.

[0045] Figure 3 This illustration shows a schematic diagram of a scattering matrix of the i-th layer provided in an embodiment of this application;

[0046] Figure 4 This illustration shows a schematic diagram of a global scattering matrix provided in an embodiment of this application;

[0047] Figure 5A schematic diagram of an imaging structure for plasma lithography imaging provided in an embodiment of this application is shown.

[0048] Figure 6 This illustration shows a schematic diagram of a mask pattern provided in an embodiment of this application;

[0049] Figure 7 This illustration shows a schematic diagram of an imaging light field distribution provided in an embodiment of this application;

[0050] Figure 8 A schematic diagram of a global scattering matrix calculation device provided in an embodiment of this application is shown. Detailed Implementation

[0051] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0052] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0053] This application is described in detail with reference to the schematic diagrams. When detailing the embodiments of this application, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of this application. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0054] With the development of semiconductor-related technologies, photolithography, one of the key technologies in the manufacture of semiconductor devices, is also developing rapidly. Plasma lithography, as a supplement to mainstream photolithography, differs significantly from traditional optical lithography techniques such as deep ultraviolet lithography (DUVL) and extreme ultraviolet lithography (EUVL).

[0055] Plasma lithography, by utilizing evanescent near-field imaging that incorporates high-frequency information, can overcome the diffraction limit in traditional lithography. Experiments have shown that even using a 365-nanometer (nm) light source, a resolution of approximately 20 nm can be achieved in a single exposure, about 1 / 17th of the light wavelength, with the potential for further improvement. This method provides a reliable technical pathway for researching low-cost, large-area, and efficient lithography techniques, and has therefore attracted widespread attention.

[0056] Compared to traditional ultraviolet projection lithography, plasma lithography has a different principle. For example, the imaging range is localized in the near field, evanescent waves containing high-frequency information of the object (mask) can be resonantly amplified and participate in imaging, and the imaging lens is no longer an ordinary optical lens but a single-layer metal thin film with a thickness at the nanometer level or a multilayer film with alternating metal / dielectric materials.

[0057] Plasma lithography mainly includes plasma imaging lithography, interference lithography, and direct-write lithography. Direct-write lithography typically lacks an imaging structure, while imaging lithography and interference lithography have imaging structures including mask patterns. (See reference...) Figure 1 As shown. Figure 1 The imaging structure shown is a hyperbolic metamaterial (HMM) structure with alternating metal and dielectric layers, including a quartz substrate (Glass), a mask pattern, polymethyl methacrylate (PMMA), alternating metal / dielectric thin films, photoresist (PR), and a reflective layer stacked sequentially. The mask pattern is, for example, a chromium (Cr) mask, the alternating metal / dielectric thin films are, for example, alternating aluminum (Al) / silicon oxide (SiO2) thin films, and the reflective layer is, for example, aluminum.

[0058] The plasma lithography imaging process, including the imaging structure, is roughly as follows: A light source is incident on a mask pattern, causing diffraction and generating various diffraction orders, including low-frequency propagating waves and high-frequency evanescent waves. These diffracted light waves continue to propagate through a single-layer metal film or a multilayer film with alternating metal / dielectric structures behind the mask pattern until they reach the photoresist layer, transferring the information from the mask pattern to the photoresist. During the transmission of diffraction orders 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 / dielectric interface, the SPP can be excited at the metal / dielectric interface. This causes the high-frequency evanescent wave to be resonantly amplified and transmitted to the photoresist layer, thereby improving the lithographic resolution. Furthermore, a reflective layer is often placed behind the photoresist layer to further enhance the imaging effect of the photoresist layer through reflection resonance.

[0059] To solve for 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 Mode Method (FMM), is a semi-analytical, semi-numerical method suitable for simulating multilayer structures with transversely non-uniform and periodic patterns caused by a plane wave source. A typical structure is... Figure 1The plasma lithography imaging structure is shown. The RCWA algorithm represents both the solved electromagnetic field distribution and the material parameters of the imaging structure as infinite-series Fourier expansions. However, it often requires a defined 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, the boundary conditions are achieved by ensuring that the tangential components of the field on both sides of the interface are equal in order to connect these layers. In this way, the propagation through the entire imaging device can be rigorously described. To effectively solve the boundary condition problem, the scattering matrix method can be used, which solves the boundary condition problem of one layer at a time instead of solving all layers simultaneously. In this way, the RCWA algorithm combines the advantages of numerical and analytical methods, ensuring both high computational accuracy and fast running speed.

[0060] Since the RCMA algorithm was proposed by MGMomoharam and TKGaylord in the 1980s, the RCWA algorithm has undergone continuous development and optimization, becoming a very mature algorithm with constantly improving computational speed and numerical stability, and its application scenarios are expanding. Furthermore, commercial software based on this RCMA algorithm has emerged, such as Ansys Lumerical-RCWA and MC Grating. However, there is relatively little research specifically on plasma lithography modeling based on this RCMA algorithm, especially on the establishment of 3D models and how to improve the computational speed of 3D models. With the development of plasma lithography technology, computational lithography techniques for plasma lithography, such as source optimization (SO), mask optimization (MO), source-mask joint optimization (SMO), and optical proximity correction (OPC), will also be developed. These techniques will further improve the imaging level and resolution of plasma lithography, and are important tools for promoting the industrial application of plasma lithography technology. Plasma lithography technology requires repeated calls to the model of the imaging structure, thus placing high demands on the rapid computation of the imaging structure model. Therefore, establishing a fast and accurate optical imaging model for plasma lithography is essential. The RCWA algorithm, as a method for solving multilayer structures of periodic patterns, is a very suitable alternative algorithm for establishing a fast and accurate imaging structure model of plasma lithography.

[0061] In other words, to improve the imaging effect of plasma lithography, it is necessary to use algorithms to calculate the electromagnetic field distribution of the imaging structure. However, current methods for calculating the electromagnetic field distribution require calculating the global scattering matrix of the imaging structure. The global scattering matrix is ​​affected by the film structure and material of the imaging structure, making the calculation quite complex. Furthermore, 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 will also be different, resulting in a significant amount of computational resources and a long computation time required to calculate the electromagnetic field distribution of different imaging structures each time.

[0062] Based on this, this application provides a method for calculating a global scattering matrix, comprising: acquiring a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target films; determining a second target film that is identical between the multiple target films of the target imaging structure and the multiple initial films of an initial imaging structure, the initial imaging structure including multiple initial films, i.e., comparing the target imaging structure and the initial imaging structure to obtain the second target film that is identical between them and the first target film that is different. The initial scattering matrix of the initial film is stored in a database, so that the second scattering matrix of the second target film that is identical to the initial film in the target imaging structure can be directly determined based on the initial scattering matrix of the initial film. Then, the first scattering matrix of the first target film that is different from the initial film 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, which is the same as that of the initial film layer, can be obtained directly. There is no need to calculate the scattering matrix of the second target film layer in the target imaging structure separately, which greatly improves the calculation efficiency of the global scattering matrix. Furthermore, only a small amount of computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, reducing the calculation time and ultimately improving the calculation efficiency of obtaining the electromagnetic field distribution when calculating different imaging structures.

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

[0064] refer to Figure 2 The diagram shown is a flowchart illustrating a global scattering matrix calculation method provided in an embodiment of this application. The method includes the following steps:

[0065] S101, acquire the target imaging structure for plasma lithography imaging.

[0066] In the embodiments of this application, the imaging structure of plasma lithography imaging has a variety of characteristics, and a target imaging structure can be obtained, wherein the target imaging structure includes multiple target film layers.

[0067] As an example, see reference Figure 1 As shown, the target imaging structure can be a hyperbolic multilayer film structure with alternating metal / dielectric layers, including a quartz substrate, plexiglass, a mask pattern, alternating metal / dielectric thin films, photoresist, and a reflective layer stacked sequentially. The parameters of the target imaging structure are as follows: the mask pattern is a Cr mask, with transparent titanium oxide (TiO2) between adjacent Cr masks; the alternating metal / dielectric thin films are TiO2 / Al multilayer films; and the reflective layer is Al. The illumination conditions used for plasma lithography imaging are normally incident 365nm wavelength TM-polarized light.

[0068] It can also acquire the initial imaging structure simultaneously, which includes multiple initial film layers. The initial scattering matrix of the initial film layers is stored in the database, meaning that the initial imaging structure is the imaging structure whose scattering matrix has already been calculated.

[0069] In the embodiments of this application, the initial scattering matrix of each initial film layer in the initial imaging structure can be pre-calculated and 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 strict 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 one 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, column vectors and It contains the modal coefficients of the field outside the i-th layer in the forward and reverse directions. The subscript indicates which side of the layer is being described, while the superscript sign indicates the direction of propagation. and S represents the scattering matrix of the i-th layer. (i) It consists of four parts. The parameters quantify how much of the wave applied to port 1 is reflected from port 1. The amount of the same applied wave transmitted through the device to port 2 is quantized. The amount of wave applied to port 2 that will be transmitted through port 1 is quantified, and finally, Quantize the amount of the second applied wave reflected from port 2. This can generally be understood as... Represents reflection. Represents transmission.

[0074] A spacer layer with a thickness of 0 can be predefined, including the initial film layer, and predefined operators for calculating the global scattering matrix can be used. The global scattering matrix is ​​calculated by sequentially concatenating the initial scattering matrices of each initial film layer using operators.

[0075] As an example, see reference Figure 4 The initial imaging structure shown has a global scattering matrix S. (global) It can be:

[0076]

[0077] In this context, the superscript of the scattering matrix represents a certain film layer region, ref and trn represent the incident substrate region and the exit substrate region, respectively, and mask is the mask pattern region.

[0078] In other words, the global scattering matrix requires the calculation of 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 or material information of one or more film layers is changed, there is no need to recalculate 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 at least some of the same film layers in terms of order and material. That is, the target imaging structure and the initial imaging structure have the same part, including geometric information and material information. This makes it convenient to obtain the scattering matrix of some film layers of the target imaging structure based on the scattering matrix of the similar part of the film layers of the initial imaging structure.

[0080] S102, 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.

[0081] In the embodiments of this 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 the first target film layer that is different from the multiple target film layers of the target imaging structure and the second target film layer that is the same as the multiple initial film layers of the initial imaging structure. That is, the first target film layer is the target film layer that is different from the initial film layer among the multiple target film layers, and the second target film layer is the target film layer that is the same as the initial film layer among the multiple target film layers.

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

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

[0084] In the embodiments of this application, after determining a second target film layer that is the same as the initial film layer and a first target film layer that is different from the initial film layer, the first scattering matrix of the first target film layer can be calculated.

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

[0086] As an example, if the first target film of the target imaging structure is a mask pattern compared to the initial film layer, meaning 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 using the RCWA algorithm is S. (mask) .

[0087] S104, directly determine the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure based on the initial scattering matrix of the initial film layer.

[0088] In the embodiments of this application, since the scattering matrices of different films do not affect each other according to the predefined rules of this application, the second target film that is the same as the initial film can directly call the initial scattering matrix of the initial film from the database. That is, the second scattering matrix of the second target film that is the same as the initial film in the target imaging structure can be directly determined based on the initial scattering matrix of the initial film. In this way, by directly using the initial scattering matrix of the initial film, the second scattering matrix of the second target film that is the same as the initial film can be directly obtained without having to calculate the scattering matrix of the second target film in the target imaging structure separately, which greatly improves the calculation efficiency of the scattering matrix.

[0089] As an example, the initial imaging structure reference Figure 1 As shown, if the target imaging structure only modifies the mask pattern compared to the initial film layer, then the first target film layer is the mask pattern. Changing the mask pattern will cause a change in the scattering matrix of that film layer, while the other film layers, as part of the imaging system, remain unchanged. Therefore, the scattering matrices of the other film layers will also remain unchanged. Thus, the second target scattering matrix of the second target film layer is the same as 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 is S. (ref) S(PMMA) S (Al) , S (PR) and S (trn) .

[0091] S105, the global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix.

[0092] In the embodiments of this application, after calculating the first scattering matrix and obtaining the second scattering matrix, the 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 this application is calculated by sequentially connecting the scattering matrices of each target film layer using operators. Therefore, the global scattering matrix of the target imaging structure can be 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 operators.

[0094] As an example, the initial imaging structure reference Figure 1 As shown, if the target imaging structure has only modified the mask pattern compared to the initial film layer, then the first target film layer is the mask pattern. The first scattering matrix of the first target film layer is calculated using the RCWA algorithm as S. (mask) The second scattering matrix of the second film layer structure of the target imaging structure is obtained directly from the database, namely 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 becomes a single scattering matrix, which contains several scattering matrices that are the initial scattering matrices of the initial film layer. S is then calculated in this manner. (TR+) Stored later for later retrieval. Similarly, S (ref) It also stores the initial scattering matrix of the initial film layer for later use.

[0097] In other words, when performing mask optimization (MO), the mask pattern changes, and the corresponding S... (mask) It will change accordingly, but S (global) (MASK) The main computational effort is spent on S (mask) In the calculation, the remaining S (ref) and S (TR+)It only requires calling the function without recalculating, which greatly reduces computation time, especially the more structural layers there are after the mask pattern, the more time is saved.

[0098] Therefore, when dealing with multilayer imaging structures where only the geometric and material information of a single layer is changed, such as in mask optimization problems in plasma lithography (i.e., only the mask pattern is altered without affecting other layers), the scattering matrix of each layer has a specific notation. Since the scattering matrix changes when the structure of a single layer changes, and remains unchanged when the structure remains the same, repeated calculations are unnecessary. Only the initial calculation needs to be stored for later retrieval, thus saving time. This allows for the calculation of only the scattering matrix of the layer within the mask pattern; the scattering matrices of other layers can be directly retrieved from historical calculations, significantly reducing the computation time for the global scattering matrix and improving computational efficiency.

[0099] In the embodiments of this 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. Then, Fourier transforms are performed on the Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field 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, respectively.

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

[0101]

[0102] Where inc represents the incident field, c inc Represents the incident coefficient, c ref Represents the reflection coefficient, c ％rn This represents the transmission coefficient.

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

[0104]

[0105]

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

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

[0108]

[0109]

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

[0111] This yields the Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field, respectively.

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

[0113] Initial Imaging Structure Reference Figure 5 As shown, Figure 5 The imaging structure shown is a single-layer metal thin-film superlens structure, comprising a quartz substrate (Glass), a mask pattern, polymethyl methacrylate (PMMA), a metal thin film, photoresist (PR), and a reflective layer stacked sequentially. The mask pattern is, for example, a chromium (Cr) mask, the metal thin film is, for example, silver (Ag), and the reflective layer is, for example, silver. If, compared to the initial film layers, the target imaging structure only modifies the mask pattern, then the first target film layer is the mask pattern, and the mask pattern of the target imaging structure is set as a T-shaped pattern, as shown in the reference diagram. Figure 6 As shown, the T-shaped region is transparent, while other regions are opaque. The period of the mask pattern is set to 800nm, and the transparent region consists of rectangular holes of 600nm × 200nm forming a T-shaped pattern. The illumination condition is normally incident x-polarized light, and the imaging plane is the middle plane of the photoresist layer. Figure 6 (The area within the black dashed line). The sampling point precision is a 1nm×1nm square, and the expansion order is kx=ky=[-20,-19,…,0,…,19,20].

[0114] The process of calculating the scattering matrix sequentially to obtain the global scattering matrix and then solving for the electromagnetic field distribution (i.e., the light field distribution) took 222 seconds. Using the method provided in this application embodiment—that is, calculating the scattering matrices of different film layers and using the scattering matrix of the same film layer to obtain the global scattering matrix and then solving for the light field distribution—took 83 seconds. In other words, the calculation speed is improved by approximately 1.7 times using the method provided in this application embodiment. Figure 7 The calculated light field distribution yields the same result from both methods.

[0115] This application provides a method for calculating a global scattering matrix, comprising: acquiring a target imaging structure for plasma lithography imaging, the target imaging structure including multiple target films; determining a second target film that is identical between the multiple target films of the target imaging structure and the multiple initial films of an initial imaging structure, the initial imaging structure including multiple initial films, i.e., comparing the target imaging structure and the initial imaging structure to obtain the second target film that is identical to the first target film and the different first target films. The initial scattering matrix of the initial films is stored in a database, so the second scattering matrix of the second target film that is identical to the initial films in the target imaging structure can be directly determined based on the initial scattering matrix of the initial films. Then, the first scattering matrix of the first target film that is different from the initial films 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, which is the same as that of the initial film layer, can be obtained directly. There is no need to calculate the scattering matrix of the second target film layer in the target imaging structure separately, which greatly improves the calculation efficiency of the global scattering matrix. Furthermore, only a small amount of computing resources are needed to calculate the first target film layer and then obtain the global scattering matrix, reducing the calculation time and ultimately improving 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 embodiments, this application also provides a global scattering matrix calculation device, see reference. Figure 8 The diagram shown is a structural schematic of a global scattering matrix calculation device provided in an embodiment of this application. The global scattering matrix calculation device 200 provided in this embodiment includes:

[0117] Acquisition unit 210 is used to acquire the target imaging structure of plasma lithography imaging, wherein the target imaging structure includes multiple target film layers;

[0118] The first determining unit 220 is used to determine a second target film layer that is the same between the multiple target films of the target imaging structure and the multiple initial films of the initial imaging structure. The initial imaging structure includes multiple initial films, and the initial scattering matrix of the initial films is stored in a database.

[0119] The first computing unit 230 is used to calculate the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure;

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

[0121] The second calculation unit 250 is used to calculate the global scattering matrix based on the first scattering matrix and the second scattering matrix.

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

[0123] The target film is wrapped with a predefined spacer layer of zero thickness;

[0124] Predefine the operators for calculating the global scattering matrix;

[0125] The global scattering matrix is ​​calculated by sequentially concatenating the scattering matrices of each target film layer using the aforementioned operators.

[0126] Optionally, the device further includes a storage unit, the storage unit being used for:

[0127] The initial scattering matrix of each of the initial films in the initial imaging structure is calculated in advance;

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

[0129] Optionally, the second computing unit 250 is used for:

[0130] The global scattering matrix is ​​calculated by sequentially concatenating the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the aforementioned operators.

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

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

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

[0134] The Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field are calculated based on the global scattering matrix and the incident electric field spatial frequency distribution.

[0135] Fourier transforms are performed on the Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field to obtain the spatial domain electric field distributions of the reflected electric field and the transmitted electric field, respectively.

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

[0137] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the apparatus embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0138] The above description is merely a preferred embodiment of this application. Although this application has disclosed preferred embodiments above, it is not intended to limit this application. Any person skilled in the art can make many possible variations and modifications to the technical solutions of this application using the methods and techniques disclosed above, or modify them into equivalent embodiments with equivalent changes, without departing from the scope of the technical solutions of this application. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of this application without departing from the content of the technical solutions of this application shall still fall within the protection scope of the technical solutions of this application.

Claims

1. A method for calculating a global scattering matrix, characterized in that, include: To obtain a target imaging structure for plasma lithography imaging, wherein the target imaging structure comprises multiple target film layers; A second target film layer is identified that is identical between multiple target films of the target imaging structure and multiple initial films of the initial imaging structure, wherein the initial imaging structure includes multiple initial films and the initial scattering matrix of the initial films is stored in a database; Calculate the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure; 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 based on the initial scattering matrix of the initial film layer. The global scattering matrix is ​​calculated based on the first scattering matrix and the second scattering matrix; The method further includes: The target film is wrapped with a predefined spacer layer of zero thickness; Predefine the operators for calculating the global scattering matrix; The global scattering matrix is ​​calculated by sequentially concatenating the scattering matrices of each target film layer using the aforementioned operators.

2. The method according to claim 1, characterized in that, The calculation of the global scattering matrix based on the first scattering matrix and the second scattering matrix includes: The global scattering matrix is ​​calculated by sequentially concatenating the first scattering matrix of each first target film layer and the second scattering matrix of each second target film layer using the aforementioned operators.

3. The method according to claim 1, characterized in that, The method further includes: The initial scattering matrix of each of the initial films in the initial imaging structure is calculated in advance; The initial scattering matrix of the initial film layer is stored in the database.

4. The method according to claim 3, characterized in that, The pre-calculation of the initial scattering matrix for each initial film layer in the initial imaging structure includes: The initial scattering matrix of each initial film layer in the initial imaging structure is calculated using the rigorous coupled-wave analysis (RCWA) algorithm.

5. The method according to any one of claims 1-4, characterized in that, The method further includes: The Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field are calculated based on the global scattering matrix and the incident electric field spatial frequency distribution. Fourier transforms are performed on the Fourier spatial frequency distributions of the reflected electric field and the transmitted electric field to obtain the spatial domain electric field distributions of the reflected electric field and the transmitted electric field, respectively.

6. The method according to any one of claims 1-4, characterized in that, The target imaging structure and the initial imaging structure have at least some of the same film layers in terms of arrangement and material.

7. A global scattering matrix calculation device, characterized in that, include: An acquisition unit is used to acquire the target imaging structure of plasma lithography imaging, wherein the target imaging structure includes multiple target film layers; A first determining unit is configured to determine a second target film layer that is the same between multiple target films of the target imaging structure and multiple initial films of the initial imaging structure, wherein the initial imaging structure includes multiple initial films and the initial scattering matrix of the initial films is stored in a database. The first computing unit is used to calculate the first scattering matrix of the first target film layer that is different from the initial film layer in the target imaging structure; The second determining unit is used to directly determine the second scattering matrix of the second target film layer that is the same as the initial film layer in the target imaging structure, based on the initial scattering matrix of the initial film layer; The second calculation unit is used to calculate the global scattering matrix based on the first scattering matrix and the second scattering matrix; The device further includes a third computing unit for: The target film is wrapped with a predefined spacer layer of zero thickness; Predefine the operators for calculating the global scattering matrix; The global scattering matrix is ​​calculated by sequentially concatenating the scattering matrices of each target film layer using the aforementioned operators.

8. The apparatus according to claim 7, characterized in that, The device further includes a storage unit, the storage unit being used for: The initial scattering matrix of each of the initial films in the initial imaging structure is calculated in advance; The initial scattering matrix of the initial film layer is stored in the database.

Images