Fast Simulation Method for Diffraction Spectrum of Extreme Ultraviolet Lithography Mask

Abstract

A fast simulation method for the diffraction spectrum of an extreme ultraviolet lithography mask regards the entire mask as a multilayer film structure, which is divided into an area covered by an absorption layer and an area not covered by an absorption layer. In the case of oblique incidence, the complex reflection coefficients of the film layers in the two regions are calculated based on the equivalent film layer method, and the Kirchhoff approximation is used to calculate the diffraction spectrum of the mask. The method of the present invention can quickly simulate the diffraction spectrum of the extreme ultraviolet lithography mask and improve the simulation accuracy of the diffraction spectrum in the case of oblique incidence.

Description

Technical Field

[0001] The present invention relates to an extreme ultraviolet lithography mask, in particular to a fast simulation method for the diffraction spectrum of an extreme ultraviolet lithography mask based on the Fresnel formula. Background Art

[0002] Lithography technology is one of the key technologies in integrated circuit manufacturing. Extreme ultraviolet lithography technology (EUVL) is the most advanced lithography technology at present, which is the development of deep ultraviolet lithography towards a shorter wavelength. Lithography simulation technology is an important means to study extreme ultraviolet lithography technology. Through lithography simulation, the cost can be greatly saved and the development cycle can be shortened, which is of great significance. Mask diffraction spectrum simulation is an important part of lithography simulation.

[0003] The simulation methods of mask diffraction spectra can be divided into rigorous simulation methods and fast simulation methods. Rigorous simulation methods, such as the finite-difference time-domain method (FDTD) (see Prior Art 1, Vial A, Erdman A, Schmoeller T, et al. Modification of boundaries conditions in the FDTD algorithm for EUV mask modeling[J]. Proceedings of SPIE, 2002, 4574:890-899.), the waveguide method (WG) (see Prior Art 2, Zhu Z R, Lucas K, Cobb J L, et al. Rigorous EUV mask simulator using 2D and 3D waveguide methods[J]. Proceedings of SPIE, 2003, 5037:494-503.), and the rigorous coupled-wave analysis (RCWA) (see Prior Art 3, Sinaali R, Besacier M, Schiavone P. Three-dimensional rigorous simulation of EUV defective masks using modal method by Fourier expansion[J]. Proceedings of SPIE, 2006, 6151:615124.). Although rigorous simulation has high accuracy, it requires a large amount of resources and time for large-area mask simulation, and is suitable for small-area simulation and verification. Although the fast simulation method sacrifices a certain simulation accuracy, its simulation speed is usually much higher than that of the rigorous simulation method and is widely used in large-area simulation calculations. For example, in the pre-computation of defect simulation, the fast simulation method is first used to roughly calculate and locate the local pattern areas where defects may occur, and then a method with higher simulation accuracy is used to accurately simulate the defect conditions in the corresponding areas, which can greatly improve the speed of defect simulation prediction and is a feasible solution. In similar applications, the speed of the simulation method is the primary consideration factor. However, when the speeds are similar, improving the accuracy of the simulation method will enhance the implementation effect of the solution.Common fast simulation models include the DDM model based on domain decomposition (see Prior Art 4, Adam K, Neureuther A R. Methodology for accurate and rapid simulation of large arbitrary 2D layouts of advanced photomasks[J]. Proceedings of SPIE, 2002, 4562: 1051 - 1067.) and the M3D+ model (see Prior Art 5, Liu P, Xie X B, Liu W, et al. Fast 3D thickmask model for full-chip EUVL simulations[J]. Proceedings of SPIE, 2013, 8679: 86790W.). The M3D+ model requires a large amount of data to be calculated and stored in advance, which is not conducive to fast simulation. Among all fast simulation methods, the Kirchhoff approximation method is the fastest simulation method, but it sacrifices the most in terms of simulation accuracy. To improve the simulation accuracy of the Kirchhoff approximation method, Yuting Cao et al. proposed a mask model based on Kirchhoff boundary condition correction and mask structure decomposition (see Prior Art 6, Cao Y T, Wang X Z, Erdman A, et al. Analytical model for EUV mask diffraction field calculation[J]. Proceedings of SPIE, 2011, 8171: 81710N.). Liu Xiaolei et al. proposed a fast simulation method for the mask diffraction field based on the equivalent film layer method (see Prior Art 7, Liu Xiaolei, Li Sikun, Wang Xiangchao. Simulation model of multilayer films of EUV lithography masks with defects based on the equivalent film layer method[J]. Acta Optica Sinica, 2015, 35(06): 271 - 279.). However, both Prior Art 6 and 7 split the mask into absorption layer multilayer films for separate modeling. Completing the simulation of 1 diffraction spectrum requires 3 steps: absorption layer diffraction, multilayer film reflection, and absorption layer secondary diffraction, which is equivalent to performing 3 fast simulations, undoubtedly greatly reducing the speed of the Kirchhoff approximation method. The existing Kirchhoff approximation method equivalentizes the mask to an infinitely thin layer with transmittances of 0 and 1, calculates the mask diffraction spectrum using Fourier transform under the condition of normal incidence or direct incidence, and simply equivalentizes the diffraction spectrum under the condition of oblique incidence illumination as the frequency shift of the former, making a large number of approximations for the simulation of the diffraction spectrum under the condition of oblique incidence illumination, resulting in a reduction in the simulation accuracy of the model. Summary of the Invention

[0004] The object of the present invention is to provide a method for rapidly simulating the diffraction spectrum of an extreme ultraviolet lithography mask. The present invention can rapidly simulate the diffraction spectrum of an extreme ultraviolet lithography mask and improve the simulation accuracy at the same time.

[0005] The technical solution of the present invention is as follows:

[0006] A method for rapidly simulating the diffraction spectrum of an extreme ultraviolet lithography mask, which divides the mask into an area covered by a non-absorbing layer composed of an air layer, a multilayer film and a substrate, and an area covered by an absorbing layer composed of an absorbing layer, a multilayer film and a substrate. The multilayer film is composed of a first single-layer film, a second single-layer film,..., a Kth single-layer film from bottom to top; characterized in that the method includes:

[0007] (1) Simulate the complex reflection coefficients of the first, second,..., (k-1)th single-layer films in sequence. The simulation steps are as follows:

[0008]

[0009] where r (i+1)i is the complex reflection coefficient of light incident from the (i+1)th single-layer film to the ith single-layer film, r (i-1) is the complex reflection coefficient of the (i-1)th single-layer film (layer(i-1)), s i is the phase difference of light traveling back and forth once in the ith single-layer film, and n i is the refractive index of the ith single-layer film, d i is the thickness of the ith single-layer film;

[0010] (2) Simulate the complex reflection coefficients of the top layer of the multilayer film and the top layer of the mask. The simulation steps are as follows:

[0011] When the top layer of the mask is an air layer:

[0012] ① Simulate the complex reflection coefficient of the top layer of the multilayer film. The simulation steps are as follows:

[0013]

[0014] where r air(t_air) is the complex reflection coefficient of light incident from the air layer to the top layer of the multilayer film, r (k-1) is the complex reflection coefficient of the (k-1)th single-layer film (layer(k-1)), s t_air is the phase difference of light traveling back and forth once in the top layer of the multilayer film, and n t_air is the refractive index of the top layer of the multilayer film, d t_air is the thickness of the top layer of the multilayer film;

[0015] ②Simulate the complex reflection coefficient r of the mask area without the absorption layer covering air , and the formula is as follows:

[0016]

[0017] Among them, r 0air is the complex reflection coefficient of light incident from vacuum to the air layer, and r t_air is the complex reflection coefficient of the top layer of the multi-layer film. s air is the phase difference of light traveling back and forth once in the air layer, and n air is the refractive index of the air layer, and d air is the thickness of the air layer;

[0018] When the top layer of the mask is the absorption layer:

[0019] ①Simulate the complex reflection coefficient of the top layer of the multi-layer film. The simulation steps are as follows:

[0020]

[0021] Among them, r abs(t_abs) is the complex reflection coefficient of light incident from the absorption layer to the top layer of the multi-layer film, and r (k-1) is the complex reflection coefficient of the (k - 1)-th single-layer film. s t_abs is the phase difference of light traveling back and forth once in the top layer of the multi-layer film, and n t_abs is the refractive index of the top layer of the multi-layer film, and d t_abs is the thickness of the top layer of the multi-layer film;

[0022] ②Simulate the complex reflection coefficient r of the mask area with the absorption layer covering abs , and the formula is as follows:

[0023]

[0024] Among them, r 0abs is the complex reflection coefficient of light incident from vacuum to the absorption layer, and r t_abs is the complex reflection coefficient of the top layer of the multi-layer film, abs is the phase difference of light traveling back and forth once in the absorption layer, and n abs is the refractive index of the absorption layer, and d abs is the thickness of the absorption layer;

[0025] (2) Simulation of the mask diffraction spectrum

[0026] Use the complex reflection coefficient r of the mask area without the absorption layer covering obtained from the above simulation calculation air and the complex reflection coefficient r of the mask area with the absorption layer covering abs, substitute it into the effective transmittance function of the mask, and then through Fourier transform, the expression of the mask diffraction spectrum can be obtained.

[0027] (2) Simulation of the mask diffraction spectrum

[0028] Effective complex reflectivity function of mask approximation:

[0029]

[0030] Among them, w is the pattern period, p is the pattern size, A and are the amplitude and phase of the boundary point impulse function.

[0031] Perform Fourier transform on the effective complex reflection function to obtain the mask diffraction spectrum F(m) under normal incidence. The formula is as follows:

[0032]

[0033] m is the diffraction order after diffraction through the absorption layer. The Hopkins frequency shift can be expressed as

[0034]

[0035] Among them, m shift is the diffraction order after Hopkins frequency shift, and α is the cosine of the incident light direction

[0036]

[0037] is the incident angle of the incident light, and θ is the azimuth angle of the incident light.

[0038] The mask diffraction spectrum F(m ′ ) under oblique incidence after Hopkins frequency shift. The formula is as follows:

[0039]

[0040] Among them, m′ = m + m shift is the diffraction order.

[0041] The diffraction spectrum of the mask under oblique incidence can be obtained by Hopkins frequency shift without recalculating the model parameters. The traditional Kirchhoff approximation model uses an infinitely thin layer with a transmittance of 0 or 1, which simplifies the calculation of the mask diffraction field. However, the EUV mask thickness is much larger than the incident light wavelength. Under oblique incidence, the diffraction effect of the thick mask will affect the lithography imaging quality. The diffraction spectrum under oblique incidence can be obtained to a certain extent by Hopkins frequency shift. There is an error between the phase of the diffraction spectrum and the strict simulation, mainly caused by the absorption layer thickness. This error can be reduced by propagating the phase of the diffraction spectrum over a certain distance. Compared with the diffraction spectra obtained by the simplified model and the strict simulation, the root mean square (RMS) errors of the amplitude and phase of the diffraction spectrum obtained by this method are smaller.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] The present invention regards the whole mask as a multilayer film structure, which is divided into an area covered by an absorption layer and an area not covered by an absorption layer. Under oblique incidence illumination conditions, the complex reflection coefficients of the two regions are calculated respectively using the Fresnel formula, and then the Kirchhoff approximation method is used to calculate the mask diffraction spectrum, which improves the simulation accuracy of the diffraction spectrum under oblique incidence and avoids the process of calibrating the complex reflection coefficient of the model using strict simulation. It is applicable to the fast simulation of the mask diffraction field under different mask thicknesses, mask materials, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic diagram of the basic structure of the extreme ultraviolet lithography mask used in the present invention

[0045] Figure 2 is a schematic diagram of the basic principle and structure of the mask model covered with an absorption layer

[0046] Figure 3 is a schematic diagram of the basic principle and structure of the mask model not covered with an absorption layer DETAILED DESCRIPTION OF THE INVENTION

[0047] The present invention will be further described below in conjunction with the embodiments and the drawings, but the protection scope of the present invention should not be limited by these embodiments.

[0048] Refer to Figure 1 , the schematic diagram of the basic structure of the extreme ultraviolet lithography mask used in the present invention mainly includes a mask absorption layer 1, an air layer 2, a multilayer film 3 and a substrate 4. The material of the absorption layer 1 is TaN with a thickness of 70 nm. The multilayer film 3 is an alternating stack structure of Mo / Si, with a total of 80 layers (40 pairs). The thickness of the Mo layer is 2.17 nm, and the thickness of the Si layer is 4.78 nm. The material of the substrate 4 is SiO2 with a thickness of 6.35 mm. The obtained mask model without an absorption layer covering is as shown in Figure 2 , and the mask model with an absorption layer covering is as shown in Figure 3As shown. The mask pattern uses 500 nm horizontal lines, the pattern period is 1000 nm, TE light illumination is adopted, and the incident light direction is normal incidence. The wavelength is 13.5 nm. The numerical aperture of the projection objective is 0.35, and the reduction ratio is 4.

[0049] (1) Simulation of the mask complex reflection coefficient

[0050] 1) Mask complex reflection coefficient in the area without the absorption layer The simulation steps are as follows:

[0051] ① The complex reflection coefficient of the first single-layer film is simulated as:

[0052]

[0053] Among them, r MoSi is the complex reflection coefficient of light incident from the Mo layer to the Si layer, is the complex reflection coefficient of light incident from the Si layer to the substrate SiO2, and θ Mo is the incident angle of light on the Mo layer, that is, the refraction angle of the Si layer. s Si is the phase difference of light traveling back and forth once in the Si layer, and n Si is the refractive index of the Si layer, and d Si is the thickness of the Si layer.

[0054] ② The complex reflection coefficient of the kth single-layer film is simulated as:

[0055] Calculate the complex reflection coefficients of the second layer, the third layer,..., the kth single-layer film in sequence, then the complex reflection coefficient of the kth layer is

[0056]

[0057] Among them, r airMo is the complex reflection coefficient of light incident from the air layer to the Mo layer, is the complex reflection coefficient of light incident from the Mo layer to the Si layer, and θ air is the incident angle of light on the air layer, that is, the refraction angle of the Mo layer. s Mo is the phase difference of light traveling back and forth once in the Mo layer, and n Mo is the refractive index of the Mo layer, and d Si is the thickness of the Mo layer.

[0058] ③ The complex reflection coefficient of the air layer is simulated as:

[0059]

[0060] Among them, r 0airis the complex reflection coefficient of light incident from vacuum into the air layer. is the complex reflection coefficient of light incident from the air layer into the Mo film, and θ0 is the incident angle of light into the air layer. s air is the phase difference of light traveling back and forth once in the air layer, and n air is the refractive index of the air layer, d air is the thickness of the air layer.

[0061] Thus, the complex reflection coefficient of the mask in the area covered without the absorption layer is

[0062] 2) The simulation steps of the complex reflection coefficient of the mask in the area covered with the absorption layer are as follows:

[0063] ① The complex reflection coefficient of the first single-layer film in the simulation is:

[0064]

[0065] where r MoSi is the complex reflection coefficient of light incident from the Mo layer into the Si layer, is the complex reflection coefficient of light incident from the Si layer into the substrate SiO2, θ Mo is the incident angle of light into the Mo layer, that is, the refraction angle of the Si layer. s Si is the phase difference of light traveling back and forth once in the Si layer, and n Si is the refractive index of the Si layer, d Si is the thickness of the Si layer.

[0066] ② The complex reflection coefficient of the k-th single-layer film in the simulation is:

[0067] Calculate the complex reflection coefficients of the second layer, the third layer,..., the k-th single-layer film in turn, then the complex reflection coefficient of the k-th layer is

[0068]

[0069] where r airMo is the complex reflection coefficient of light incident from the air layer into the Mo layer, is the complex reflection coefficient of light incident from the Mo layer into the Si layer, θ air is the incident angle of light into the air layer, that is, the refraction angle of the Mo layer. s Mo is the phase difference of light traveling back and forth once in the Mo layer, and n Mo is the refractive index of the Mo layer, d Si is the thickness of the Mo layer.

[0070] ③ The complex reflection coefficient of the simulated absorption layer is as follows:

[0071]

[0072] Among them, r 0abs is the complex reflection coefficient of light incident from vacuum to the absorption layer, is the complex reflection coefficient of light incident from the absorption layer to the Mo layer, and θ0 is the incident angle of light on the absorption layer. s abs is the phase difference of light traveling back and forth once in the absorption layer, and n abs is the refractive index of the absorption layer, and d abs is the thickness of the absorption layer.

[0073] Therefore, the complex reflection coefficient of the mask in the area covered by the absorption layer can be obtained as

[0074] (2) Simulation of the mask diffraction spectrum

[0075] The effective complex reflectivity function of the mask approximation:

[0076]

[0077] Among them, w is the pattern period, p is the pattern size, A and are the amplitude and phase of the boundary point pulse function.

[0078] The Fourier transform of the effective complex reflection function gives the mask diffraction spectrum F(m) under normal incidence, and the formula is as follows:

[0079]

[0080] m is the diffraction order after diffraction by the absorption layer. The Hopkins frequency shift can be expressed as

[0081]

[0082] where m shift is the diffraction order after the Hopkins frequency shift, and α is the cosine of the incident light direction

[0083]

[0084] is the incident angle of the incident light, and θ is the azimuth angle of the incident light.

[0085] The mask diffraction spectrum F(m ′ ) under oblique incidence after the Hopkins frequency shift is as follows:

[0086]

[0087] where m′ = m + m shift is the diffraction order.

Claims

1. A fast simulation method for the diffraction spectrum of an extreme ultraviolet lithography mask, including an absorption layer (1), an air layer (2), a multilayer film (3) and a substrate (4), wherein the multilayer film (3) is composed of a first single-layer film layer1, a second single-layer film layer2, ……, a Kth single-layer film layerk from bottom to top; characterized in that, The method includes: (1) Simulating the complex reflection coefficients of the single-layer films of the first layer, the second layer, …, the (k−1)-th layer in sequence. The simulation steps are as follows: where r (i+1)i is the complex reflection coefficient of light incident from the (i + 1)-th single-layer film layer(i + 1) to the i-th single-layer film layeri, r (i-1) is the complex reflection coefficient of the (i - 1)-th single-layer film layer(i - 1), s i is the phase difference of light traveling back and forth once in the i-th single-layer film layeri, and n i is the refractive index of the i-th single-layer film layeri, d i is the thickness of the i-th single-layer film layeri; (2) Simulating the complex reflection coefficients of the top layer of the multi-layer film (3) and the top layer of the mask. The simulation steps are as follows: When the top layer of the mask is an air layer (2): ① Simulating the complex reflection coefficient of the top layer of the multi-layer film (3). The simulation steps are as follows: where r air(t_air) is the complex reflection coefficient of light incident from the air layer (2) onto the top layer layert_air of the multilayer film, and r (k-1) is the complex reflection coefficient of the (k - 1)-th single-layer film layer(k - 1), s t_air is the phase difference of light traveling back and forth once in the top layer layert_air of the multilayer film, and n t_air is the refractive index of the top layer layert_air of the multilayer film, and d t_air is the thickness of the top layer layert_air of the multilayer film; ② The complex reflection coefficient r of the simulation for the mask region without the absorption layer coverage air , and the formula is as follows: where r 0air is the complex reflection coefficient of light incident from vacuum to the air layer (2), and r t_air is the complex reflection coefficient of the top layer layert_air of the multilayer film, s air is the phase difference of light traveling back and forth once in the air layer (2), and n air is the refractive index of the air layer (2), and d air is the thickness of the air layer (2); When the top layer of the mask is an absorption layer (1): ① Simulating the complex reflection coefficient of the top layer of the multi-layer film (3). The simulation steps are as follows: where r abs(t_abs) is the complex reflection coefficient of light incident from the absorption layer (1) onto the top layer layert_abs of the multilayer film, and r (k-1) is the complex reflection coefficient of the (k - 1)-th single-layer film layer(k - 1), s t_abs is the phase difference of light traveling back and forth once in the top layer layert_abs of the multilayer film, and n t_abs is the refractive index of the top layer layert_abs of the multilayer film, and d t_abs is the thickness of the top layer layert_abs of the multilayer film; ②Simulate the complex reflection coefficient r of the mask region covered by the absorption layer abs , and the formula is as follows: where r 0abs is the complex reflection coefficient of light incident from vacuum to the absorption layer (1), and r t_abs is the complex reflection coefficient of the top layer layert_abs of the multilayer film, s abs is the phase difference of light traveling back and forth once in the absorption layer (1), and n abs is the refractive index of the absorption layer (1), and d abs is the thickness of the absorption layer (1); (2) Simulation of the diffraction spectrum of the mask Bring the complex reflection coefficient r of the mask region without the absorption layer coverage obtained from the above simulation calculation air and the complex reflection coefficient r of the mask region with the absorption layer coverage abs , into the effective complex reflectivity function of the mask, and then through Fourier transform, the mask diffraction spectrum expression can be obtained.

2. The method for rapid simulation of the diffraction spectrum of an extreme ultraviolet lithography mask according to claim 1, wherein The specific steps of the simulation of the diffraction spectrum of the mask are as follows: The effective complex reflectivity function of the mask approximation: Among them, w is the graphic period, p is the graphic size, A and are the amplitude and phase of the boundary point pulse function; Performing a Fourier transform on the effective complex reflection function to obtain the diffraction spectrum F(m) of the mask under normal incidence. The formula is as follows: m is the diffraction order after diffraction by the absorption layer; The Hopkins frequency shift can be expressed as where m shift is the diffraction order after Hopkins frequency shift, and α is the direction cosine of the incident light is the incident angle of the incident light, and θ is the azimuth angle of the incident light; The mask diffraction spectrum F(m ′ ) under the oblique incidence condition after Hopkins frequency shift is as follows: where m ′ = m + m shift is the diffraction order.

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