Fast simulation method of scattered near field of extreme ultraviolet lithography mask containing defect multilayer film

Abstract

This invention belongs to the field of extreme ultraviolet (EUV) lithography masks, specifically relating to a rapid simulation method for the near-field scattering of defective multilayer films in EUV lithography masks. The EUV lithography mask is constructed along the incident light direction, comprising a defective multilayer film and a substrate. The substrate contains Gaussian defects. The defective multilayer film is modeled using a mesh generation method and a transfer matrix method, including the following steps: S1: Divide the defective multilayer film into multiple multilayer film sub-regions along the horizontal direction; S2: Discretize each multilayer film sub-region into a set of square element meshes in the x and y directions; S3: Calculate the analytical reflection coefficient and transmission coefficient of all element meshes in each multilayer film sub-region using the transfer matrix method to obtain the local reflection field and transmission field of the multilayer film sub-region; S4: Add the reflection fields of each multilayer film sub-region to obtain the total reflection field of the defective multilayer film. This invention improves the simulation speed and calculation accuracy of the near-field scattering of defective multilayer films.

Description

Technical Field

[0001] This invention belongs to the field of extreme ultraviolet lithography masks, and more specifically, relates to a rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks. Background Technology

[0002] Photolithography is a core technology in integrated circuit manufacturing, and extreme ultraviolet (EUV) lithography is considered the most promising next-generation lithography technology. Mask defects are one of the main challenges hindering the development of EUV lithography technology. Defects in EUV masks are mainly divided into two types: amplitude defects and phase defects.

[0003] Amplitude-type defects are mostly found in the absorption layer pattern, primarily affecting the amplitude of the near-field scattering of the mask. Phase-type defects are mostly found at the bottom of multilayer films. Due to the short exposure wavelength of extreme ultraviolet lithography, phase-type defects, with sizes only on the nanometer scale, can cause significant amplitude and phase changes in the near-field scattering of the mask. Compared to amplitude-type defects, the impact of phase-type defects on the near-field scattering of the mask is more complex and more difficult to repair. Therefore, some compensation is needed for phase-type defects. Fast near-field simulation of masks containing phase-type defects can obtain the light field distribution after mask reflection and diffraction, and use this to study the impact of defects on mask imaging. This is the main basis for compensating for phase-type defects and the requirement for large-scale mask simulation. Fast simulation of masks containing phase-type defects can be divided into two parts: the absorption layer region and the multilayer film region. Fast simulation of the near-field scattering of the multilayer film containing defects is an important component of this process.

[0004] Currently, the fast simulation methods for near-field scattering of defective multilayer films typically employ single-plane approximation (see Prior Art 1, Gullikson EM, Cerjan C, Stearns DG, et al. Practical approach for modeling extreme ultraviolet lithography mask defects[J]. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, 2002, 20(1):81-86.) and ray tracing (see Prior Art 2, Lam, MC, et al., “Modeling methodologies and defect printability maps for buried defects in EUV mask blanks,” Proc.SPIE 6151, (2007)).

[0005] The existing related technologies have the following problems: Prior technology 1 uses the phase abrupt change on the surface of the multilayer film to approximate the phase change caused by defects. When the defects in the multilayer film are large, the phase abrupt change approximation alone cannot guarantee the accuracy of the simulation, and the influence of defects on the reflectivity amplitude of the multilayer film needs to be considered. Prior technology 2 uses Fresnel formula to calculate the reflection and transmission coefficients of each pair of Mo / Si bilayer films. During the incident process of light, the light rays tilt accordingly with the tilt of the film layers caused by the defects in the multilayer film. During the outgoing process of light, the multilayer film is approximated as a defect-free ideal multilayer film. When the defects in the multilayer film are large, the defects will cause severe deformation of the multilayer film structure, and the approximation error is large at this time. Summary of the Invention

[0006] To accurately simulate the effect of phase defects on the near-field scattering of multilayer films and to improve the simulation speed of the near-field scattering of defective multilayer films, this invention provides a rapid simulation method for the near-field scattering of defective multilayer films using extreme ultraviolet lithography masks.

[0007] The present invention provides a rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks, employing the following technical solution: A rapid simulation method for the near-field scattering of a defective multilayer film in an extreme ultraviolet (EUV) lithography mask is provided. The EUV lithography mask is composed of a defective multilayer film and a substrate, arranged sequentially along the incident light direction. The substrate contains Gaussian defects. The defective multilayer film is modeled using a mesh generation method and a transfer matrix method. The method includes the following steps: S1: Divide the defective multilayer film into multiple multilayer film sub-regions along the horizontal direction; S2: Discretize each multilayer membrane sub-region into a set of square unit grids in the x and y directions respectively. In each grid of multilayer membranes, the membrane layers are distributed in parallel. After dividing the grid, non-uniform sampling is performed on the grid. S3: The propagation of the light field in the multilayer subregion is performed in the spatial domain, while the propagation of the light field in the vacuum region is calculated in the frequency domain. Given the incident angle and polarization conditions, the analytical reflection coefficients of all element grids in each multilayer subregion are calculated using the transfer matrix method. With transmission coefficient Thus, the local reflection and transmission fields of the multilayer membrane sub-regions are obtained; S4: Add the reflection fields from each sub-region of the multilayer film to obtain the total reflection field of the defective multilayer film.

[0008] As a further preferred embodiment, in S1, a vacuum region is provided between two adjacent multilayer film sub-regions, and the sum of the thicknesses of the vacuum regions is equal to the height of the multilayer film.

[0009] As a further preferred embodiment, in S2, the non-uniform sampling method is as follows: the multilayer film region unaffected by defects is sampled only once to avoid repeated calculation of the reflection coefficient of the perfect multilayer film. For the same incident angle, the reflection coefficient of the multilayer film region unaffected by defects is the same.

[0010] As a further preferred embodiment, in S3, before calculating the local analytical reflection and transmission of each unit grid, the determined incident angle and polarization state are adjusted according to the surface normal vector of each multilayer film sub-region. The equivalent incident angle in the multilayer film region disturbed by the defect is calculated and the change in the polarization state of the incident light is taken into account. Then, the analytical reflection and transmission of all unit grids are calculated using the transfer matrix method.

[0011] As a further preferred embodiment, the reflected or transmitted field after being acted upon by the multilayer membrane sub-region is subjected to a Fourier transform before entering the vacuum region. When it propagates a certain distance in the frequency domain to reach the interface of the next multilayer membrane sub-region, an inverse Fourier transform is performed, and then the propagation in the multilayer membrane sub-region is calculated.

[0012] As a further preferred embodiment, the Fourier transform is a two-dimensional discrete Fourier transform; The following formula defines the discrete Fourier transform Y of an m×n matrix X:

[0013] in, and It is a complex unit root:

[0014]

[0015] It is the imaginary unit, p and j are indices in the range of values ​​from 0 to m-1, and q and k are indices in the range of values ​​from 0 to n-1.

[0016] As a further preferred embodiment, the transmission matrix method involves calculating the reflection and transmission coefficients of the multilayer film by obtaining the characteristic matrix of the multilayer film. The characteristic matrix of a single layer period in a multilayer film is as follows:

[0017] in,

[0018]

[0019] , The refractive index and thickness of the film, The angle of refraction in the film layer, The wavelength of extreme ultraviolet light; If a multilayer film consists of N periods, then the overall characteristic matrix of the multilayer film is:

[0020] For s-polarized light, the reflection coefficient and transmission coefficient of the multilayer film are:

[0021] If it is p-polarized light, the formula above needs to be adjusted. Replace with / .

[0022] As a further preferred embodiment, in step S4, the phase is adjusted to incorporate the optical path difference effect caused by the surface defect profile into the total reflection field, thereby obtaining the near field after reflection from the defective multilayer film as follows:

[0023] in, The reflection field comes from the j-th multilayer membrane sub-region. Let x be the height of the surface defect protrusion of the defective multilayer film at the x and y coordinates. For multilayer film defects The complex refractive index of the trap, The equivalent incident angle at the x and y coordinates, adjusted for the defective multilayer film surface. The imaginary unit, The wavelength of extreme ultraviolet light; This is the simulated near-field of a defective multilayer film.

[0024] In summary, the present invention has at least the following beneficial technical effects: 1. The present invention provides a rapid simulation method for the near-field scattering of defective multilayer films in extreme ultraviolet lithography masks, which improves the simulation speed of the near-field scattering of defective multilayer films, thereby enabling rapid simulation of large-size defective masks; 2. Even when the defect size of a multilayer film is large, the accuracy of near-field calculation for scattering of defective multilayer films can still be guaranteed. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the basic structure of the defective multilayer film of the extreme ultraviolet lithography mask of the present invention; Figure 2 This is a schematic diagram illustrating the basic principles and structure of the rapid simulation model of this invention; Figure 3 This is a schematic diagram of the multilayer membrane subregion mesh division and optical field calculation in this invention.

[0026] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1. Defective multilayer film; 2. Substrate; 3. Gaussian defects. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0028] In the description of this invention, it should be understood that the terms "center," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0029] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0030] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0031] The following is in conjunction with the appendix Figure 1-3 The present invention will be described in further detail below.

[0032] This invention discloses a rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks.

[0033] Reference Figure 1A rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet (EUV) lithography masks includes the following: the EUV lithography mask is composed of a defective multilayer film 1 and a substrate 2 along the incident light direction. The substrate 2 contains Gaussian defects 3. The defective multilayer film 1 is modeled using a mesh generation method and a transfer matrix method. The height of the Gaussian defect 3 is 40 nm, the full width at half maximum (FWHM) is 40 nm, the height of the surface defect is 3 nm, the FWHM is 65 nm, and the size of the defective multilayer film 1 is 400 nm × 400 nm. It is composed of 40 pairs of molybdenum / silicon (Mo / Si) bilayer films. The thickness of the Mo layer is 2.78 nm, the thickness of the Si layer is 4.16 nm, and the total height H is 277.6 nm. The method includes the following steps: S1: The defective multilayer film 1 is decomposed into computational regions. The entire defective multilayer film 1 is uniformly divided into four multilayer film sub-regions 11, 12, 13, and 14 along the horizontal direction. The height of each multilayer film sub-region is H / 4, and a vacuum region with a height of H / 3 is inserted between every two multilayer film sub-regions. The sum of the thicknesses of all vacuum regions is equal to the height H of the defect-free perfect multilayer film composed of 40 pairs of Mo / Si bilayer films.

[0034] S2: The defective multilayer film 1 is decomposed into each multilayer film sub-region and discretized into a set of square unit grids in the x and y directions. The size of each unit grid is 1nm×1nm. In each grid, the multilayer film is distributed in parallel and there is no interaction between the unit grids. After the grid is divided, non-uniform sampling is performed on the grid. Specifically, the non-uniform sampling method is as follows: the multilayer film region that is not disturbed by defects is sampled only once to avoid repeated calculation of the reflection coefficient of the perfect multilayer film. For the same incident angle, the reflection coefficient of the multilayer film region that is not disturbed by defects is the same.

[0035] S3: The propagation of the light field in the multilayer film sub-region is performed in the spatial domain, while the propagation of the light field in the vacuum region is calculated in the frequency domain. The incident light is a monochromatic plane wave with s-polarization at a wavelength of 13.5 nm and an incident angle of 6°. Given the incident angle and polarization conditions, the analytical reflection coefficients of all element grids in each multilayer film sub-region, such as sub-region 13, are calculated using the transfer matrix method. With transmission coefficient Thus, the local reflection field of the multilayer membrane sub-region is obtained. and transmission field , refer to Figure 3 ,

[0036]

[0037] A0 is the complex amplitude of the incident light, and (x, y) are the coordinates of the element grid. In the spatial domain, the coordinates are spatial length, and in the frequency domain, the coordinates are spatial frequency. A Fourier transform is required to convert from the spatial domain to the frequency domain. This is the reflection and transmission from a periodic layered medium. The multilayer size is the same as the cell column of the multilayer below the cell grid in the subregion, and the thickness of each layer is determined by the thickness of each film layer at the center of the multilayer film in the grid.

[0038] Since surface protrusions in multilayer films affected by defects can influence incident conditions, before calculating the local analytical reflection and transmission of each cell grid, the determined incident angle and polarization state are adjusted based on the surface normal vector of each multilayer film sub-region. The equivalent incident angle in the multilayer film region affected by defects is calculated, taking into account the change in the polarization state of the incident light. Then, the analytical reflection and transmission of all cell grids are calculated using the transfer matrix method.

[0039] Before entering the vacuum region, the reflected or transmitted field after passing through the multilayer membrane sub-region undergoes a Fourier transform. When it reaches the interface of the next multilayer membrane sub-region after propagating a distance of H / 3 in the frequency domain, an inverse Fourier transform is performed, and the propagation within the multilayer membrane sub-region is then calculated. The Fourier transform uses a two-dimensional discrete Fourier transform, and the discrete Fourier transform Y of an m×n matrix X is defined by the following formula:

[0040] in, and It is a complex unit root:

[0041]

[0042] It is the imaginary unit, p and j are indices in the range of values ​​from 0 to m-1, and q and k are indices in the range of values ​​from 0 to n-1.

[0043] The transmission matrix method calculates the reflection and transmission coefficients of multilayer films by obtaining the characteristic matrix of the multilayer film. The characteristic matrix of a single layer period in a multilayer film is as follows:

[0044] in,

[0045]

[0046] , The refractive index and thickness of the film, The angle of refraction in the film layer, The wavelength of extreme ultraviolet light; If a multilayer film consists of N periods, then the overall characteristic matrix of the multilayer film is:

[0047] In this embodiment, the multilayer film includes 40 cycles, and the overall characteristic matrix of the multilayer film is:

[0048] For s-polarized light, the reflection coefficient and transmission coefficient of the multilayer film are:

[0049] If it is p-polarized light, the formula above needs to be adjusted. Replace with / .

[0050] S4: The reflection fields from sub-regions 11, 12, 13, and 14 of the multilayer film are added together to obtain the total reflection field of the defective multilayer film 1; the phase is adjusted to incorporate the optical path difference effect caused by the surface defect profile into the total reflection field, thus obtaining the near field of the defective multilayer film 1 after reflection:

[0051] in, The reflection field comes from the j-th multilayer membrane sub-region. The x and y coordinates represent the surface defect protrusion height of the defective multilayer film 1. The complex refractive index of the defects in the multilayer film. The equivalent incident angle at x and y coordinates is the adjusted angle of incidence on the surface of the defective multilayer film 1. The imaginary unit, The wavelength of extreme ultraviolet light; This is the near field of the simulated defective multilayer film.

[0052] In this embodiment, under the same simulation parameters, the fast simulation method for the near-field scattering of defective multilayer films using extreme ultraviolet lithography masks is 95 times faster than the existing rigorous FDTD simulation (see T. Pistor, Y. Deng, and A. Neureuther, “Extreme ultraviolet mask defect simulation: low-profile defects”, J. Vac. Sci. Technol. B18, 2926-2929 (2000)) while maintaining accuracy.

[0053] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A fast simulation method of extreme ultraviolet lithography mask defect-containing multilayer film scattering near field, characterized in that, The extreme ultraviolet lithography mask is composed of a defective multilayer film (1) and a substrate (2) along the incident light direction. The substrate (2) contains Gaussian defects (3). The defective multilayer film (1) is modeled using the mesh generation method and the transfer matrix method, including the following steps: S1: Divide the defective multilayer film (1) into multiple multilayer film sub-regions along the horizontal direction; S2: Discretize each multilayer membrane sub-region into a set of square unit grids in the x and y directions respectively. In each grid of multilayer membranes, the membrane layers are distributed in parallel. After dividing the grid, non-uniform sampling is performed on the grid. S3: The propagation of the light field in the multilayer subregion is performed in the spatial domain, while the propagation of the light field in the vacuum region is calculated in the frequency domain. Given the incident angle and polarization conditions, the analytical reflection coefficients of all element grids in each multilayer subregion are calculated using the transfer matrix method. With transmission coefficient Thus, the local reflection and transmission fields of the multilayer membrane sub-regions are obtained; S4: Add the reflection fields from each multilayer film sub-region to obtain the total reflection field of the defective multilayer film (1); In S1, a vacuum region is provided between two adjacent multilayer film sub-regions, and the sum of the thicknesses of the vacuum regions is equal to the height of the multilayer film. In S2, the non-uniform sampling method is as follows: the multilayer film region that is not disturbed by defects is sampled only once to avoid repeated calculation of the reflection coefficient of the perfect multilayer film. For the same incident angle, the reflection coefficient of the multilayer film region that is not disturbed by defects is the same. In S3, before calculating the local analytical reflection and transmission of each unit grid, the determined incident angle and polarization state are adjusted according to the surface normal vector of each multilayer film sub-region. The equivalent incident angle in the multilayer film region disturbed by the defect is calculated and the change in the polarization state of the incident light is taken into account. Then, the analytical reflection and transmission of all unit grids are calculated using the transfer matrix method. In step S4, the phase is adjusted to incorporate the optical path difference effect caused by the surface defect profile into the total reflection field. The resulting near-field after reflection from the defective multilayer film (1) is: in, The reflection field comes from the j-th multilayer membrane sub-region. The height of the surface defect protrusion of the defective multilayer film (1) at the x and y coordinates is given. The complex refractive index of the defects in the multilayer film. The equivalent incident angle after surface adjustment for the defective multilayer film (1) at the x and y coordinates. The imaginary unit, The wavelength of extreme ultraviolet light; That is, the near field of the simulated defective multilayer film (1).

2. The rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks according to claim 1, characterized in that, Before entering the vacuum region, the reflected or transmitted field after being acted upon by the multilayer membrane sub-region undergoes a Fourier transform. When it propagates a certain distance in the frequency domain to the interface of the next multilayer membrane sub-region, an inverse Fourier transform is performed, and then the propagation in the multilayer membrane sub-region is calculated.

3. The rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks according to claim 2, characterized in that, The Fourier transform is a two-dimensional discrete Fourier transform; The following formula defines the discrete Fourier transform Y of an m×n matrix X: in, and It is a complex unit root: It is the imaginary unit, p and j are indices in the range of values ​​from 0 to m-1, and q and k are indices in the range of values ​​from 0 to n-1.

4. The rapid simulation method for near-field scattering of defective multilayer films in extreme ultraviolet lithography masks according to claim 1, characterized in that, The transmission matrix method calculates the reflection and transmission coefficients of multilayer films by obtaining the characteristic matrix of the multilayer film. The characteristic matrix of a single layer period in a multilayer film is as follows: in, , The refractive index and thickness of the film, The angle of refraction in the film layer, The wavelength of extreme ultraviolet light; If a multilayer film consists of N periods, then the overall characteristic matrix of the multilayer film is: For s-polarized light, the reflection coefficient and transmission coefficient of the multilayer film are: If it is p-polarized light, the formula above needs to be adjusted. Replace with / .

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