A design method of an extreme ultraviolet band half-wave plate and quarter-wave plate device based on a super-structured surface

Abstract

This invention discloses a design method for extreme ultraviolet (EUV) half-wave and quarter-wave plate devices based on metasurfaces, comprising: designing the structure of the metasurface; calculating the resonant phase response distribution and transmittance distribution of the nanopore units in the metasurface under different polarization free-space input light sources; and setting π and π according to the functional requirements of the half-wave and quarter-wave plates, respectively. The phase difference condition is determined; combining resonant phase response distribution and transmittance distribution data, an algorithm is used to screen and index the length and width geometric parameters of nanopores that meet the phase condition. Structures with high transmittance are then selected and periodically arranged to complete the design of the metasurface waveplate device. This invention solves the problems of phase modulation failure caused by the sudden drop in refractive index of materials in the extreme ultraviolet band, as well as the large volume and limited band of traditional waveplates. It provides a new metasurface structure that achieves polarization modulation of extreme ultraviolet light sources through silicon nitride, molybdenum, and the nanopore structure that runs through them.

Description

A design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces Technical Field

[0001] This invention relates to the fields of optical technology, integrated photonics technology, and extreme ultraviolet (EUV) light modulation, specifically to a design method for EUV half-wave plates and quarter-wave plates based on metasurfaces. Background Technology

[0002] Extreme ultraviolet (EUV, 10-121nm) electromagnetic waves have high energy and can ionize the atoms and molecules of most substances. 13.5nm is the core operating wavelength for EUV lithography (EUVL) and has extremely high value in fields such as semiconductors and quantum optics. As a key component for light field manipulation, waveplates can directly affect indicators such as photoresist exposure uniformity by introducing phase delay to control the polarization state of light. Traditional waveplates rely on dielectric materials or multilayer film stacking. However, the refractive index of dielectric materials decreases significantly in the EUV band, making it difficult to confine the light field within the dielectric nanostructure. This leads to interference between adjacent units, a sharp increase in material absorption, and huge losses, making it difficult to meet the requirements of efficient transmission and phase manipulation. Multilayer film stacking increases thickness and is extremely sensitive to incident angle and process errors, severely restricting miniaturization and integration requirements.

[0003] Metasurfaces enable optical field manipulation through subwavelength nanostructure arrays, and their ultrathin planar structure is suitable for on-chip integration. However, the design of EUV band devices remains limited by the strong absorption characteristics of metallic materials and the low refractive index of dielectric materials, making it difficult to balance phase modulation and transmittance. Overcoming this challenge and realizing EUV waveplate devices based on metasurfaces will improve the polarization control accuracy and optical integration in key areas such as lithography systems, injecting new degrees of freedom into photonic integrated devices and enabling more complex functions. Summary of the Invention

[0004] This invention provides a design method for extreme ultraviolet (EUV) half-wave and quarter-wave plate devices based on metasurfaces. It achieves optical field modulation in the EUV band by employing a composite structure of a silicon nitride (Si3N4) substrate and a molybdenum (Mo) metal layer, along with a vacuum nanorectangular aperture running through it. The optical field is confined within a high-refractive-index vacuum channel, thus avoiding the significant losses caused by the low refractive index of the EUV medium. Specifically, the phase response and transmittance distribution of the nanopore unit under different polarized incident light are calculated using the finite-difference time-domain method. By changing the structural parameters of the rectangular aperture, the phase delay of X / Y linearly polarized light is controlled to meet the phase difference requirements of the half-wave or quarter-wave plate. The device design is completed through periodic arrangement.

[0005] A design method for extreme ultraviolet half-wave plates and quarter-wave plates based on metasurfaces includes the following steps:

[0006] 1) Design the structure of the metasurface;

[0007] 2) The resonant phase response distribution and transmittance distribution of nanoporous units in metasurfaces under different polarization free space input light sources were calculated using the finite-difference time-domain method.

[0008] 3) Determine the phase difference conditions corresponding to the nanopore units according to the phase requirements of the different functions of half-wave plates and quarter-wave plates;

[0009] 4) Based on the resonant phase response distribution and transmittance distribution data obtained in step 2), and the different target difference conditions obtained in step 3), the structural parameters such as the length and width of the nanopores that meet the requirements of the corresponding functional waveplate are screened by the algorithm, and the metasurface units are periodically arranged to complete the waveplate device design.

[0010] Furthermore, a design method for extreme ultraviolet half-wave plates and quarter-wave plates based on metasurfaces includes the following steps:

[0011] 1) Design the structure of the metasurface;

[0012] 2) Calculate the resonant phase response distribution and transmittance distribution of the nanoporous units in the metasurface structure under the target wavelength and different polarization free space input light sources;

[0013] 3) Based on the phase requirements of the different functions of the half-wave plate and the quarter-wave plate, determine the phase difference conditions corresponding to the nanopore units of the half-wave plate and the phase difference conditions corresponding to the nanopore units of the quarter-wave plate respectively.

[0014] 4) Based on the resonant phase response distribution and transmittance distribution data obtained in step 2), and the phase difference conditions corresponding to the nanopore units of the half-wave plate obtained in step 3), the structural parameters of the rectangular holes that meet the conditions required by the half-wave plate are screened using an algorithm, and the nanopore units are arranged periodically to complete the design of the extreme ultraviolet band half-wave plate device.

[0015] Based on the resonant phase response distribution and transmittance distribution data obtained in step 2), and the phase difference conditions corresponding to the nanopore units of the quarter-wave plate obtained in step 3), the structural parameters of the rectangular holes that meet the conditions required for the quarter-wave plate are screened using an algorithm, and the nanopore units are arranged periodically to complete the design of the extreme ultraviolet band quarter-wave plate device.

[0016] In step 1), the metasurface structure includes: a silicon nitride substrate, a molybdenum metal layer disposed on the silicon nitride substrate, and a nano-rectangular hole array penetrating the silicon nitride substrate and the molybdenum metal layer. The nano-rectangular hole array comprises a plurality of rectangular holes with the same depth and aperture size, which are periodically arranged in a plane.

[0017] More preferably, the metasurface includes a silicon nitride (Si3N4) substrate, a molybdenum (Mo) metal layer disposed on the silicon nitride substrate, and a nano-rectangular hole array penetrating the silicon nitride (Si3N4) substrate and the molybdenum (Mo) metal layer. The nano-hole array includes a plurality of rectangular hole structures with the same depth and pore size, and the rectangular holes are periodically arranged in a plane as required.

[0018] In step 2), the nanoporous unit includes a rectangular hole and a silicon nitride substrate and a molybdenum metal layer corresponding to the edge of the rectangular hole. Different polarizations are X-linear polarization and Y-linear polarization. The resonant phase response distribution and transmittance distribution of the nanoporous unit in the metasurface structure under the target wavelength and different polarized free-space input light sources are calculated using the finite-difference time-domain method.

[0019] In step 3), the phase requirements for the different functions of the half-wave plate and the quarter-wave plate are as follows: the half-wave plate requires a phase difference of (2n+1)π (n is an integer) between X-linear polarization and Y-linear polarization, and the quarter-wave plate requires a phase difference of... (m is an integer). That is, the phase difference condition corresponding to the nanopore unit of the half-wave plate is: the phase difference between X linear polarization and Y linear polarization is π or an odd multiple thereof. The phase difference condition corresponding to the nanopore unit of the quarter-wave plate is: the phase difference between X linear polarization and Y linear polarization is... Or an odd multiple thereof.

[0020] In step 4), the structural dimensions of all nanopores on the metasurface are determined based on the resonant phase response distribution and transmittance distribution obtained in step 2) and the required phase difference condition for the waveplate in step 3). Specifically, this includes:

[0021] 4.1) Based on the target wavelength of 13.5 nm and different waveplate functional types, determine the required phase distribution and structural parameter selection range for the nanopore unit. Specifically, this includes: the geometric parameters of the structure's length and width should be between 0-80 nm; for half-wave plates, the phase difference between X-linear polarization and Y-linear polarization should be π or an odd multiple thereof; for quarter-wave plates, the phase difference between X-linear polarization and Y-linear polarization should be... Or an odd multiple thereof;

[0022] 4.2) Based on the phase response distribution and transmittance distribution of the metasurface unit in step 2), select the structural parameters of the metasurface unit so that the unit has a relatively high transmittance in the extreme ultraviolet band while approaching the required phase difference conditions. Arrange the obtained metasurface unit structure periodically to obtain a nanoporous metasurface structure with corresponding waveplate function.

[0023] Further optimization involves using algorithms to screen the structural parameters of rectangular apertures that meet the requirements of a half-wave plate, and then periodically arranging the nanopore units to complete the design of the extreme ultraviolet (EUV) half-wave plate device. Specifically, this includes:

[0024] The structural parameters of rectangular apertures that meet the requirements of a half-wave plate are selected by using an algorithm. This allows the nanopore units to have relatively high transmittance in the extreme ultraviolet band while approaching the required phase difference conditions. The obtained nanopore units are then arranged periodically to obtain the design of an extreme ultraviolet half-wave plate device.

[0025] The algorithm is used to select the structural parameters of rectangular holes that meet the requirements of the corresponding quarter-wave plate, and the nanopore units are arranged periodically to complete the design of the extreme ultraviolet quarter-wave plate device. Specifically, this includes:

[0026] The structural parameters of rectangular holes that meet the requirements of the corresponding quarter-wave plate are selected by using an algorithm. This allows the nanopore units to have relatively high transmittance in the extreme ultraviolet band while approaching the required phase difference conditions. The obtained nanopore units are then arranged periodically to obtain an extreme ultraviolet quarter-wave plate device.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] I. This invention innovatively proposes a novel structure that uses a silicon nitride (Si3N4) substrate support layer and a molybdenum (Mo) metal layer composite structure. Through the synergistic effect of the upper and lower layer materials, it solves the problem of high absorption rate and insufficient refractive index of traditional optical materials in the extreme ultraviolet band (13.5nm).

[0029] Second, this invention optimizes the rectangular hole structure that penetrates the upper molybdenum metal layer and the lower silicon nitride layer, thereby achieving the control of the phase delay of light waves in the extreme ultraviolet band. By adjusting the parameters of the rectangular hole structure, the function of a half-wave plate or a quarter-wave plate can be realized, breaking through the design bottleneck of polarization control devices in this band.

[0030] Third, this invention adopts a metasurface design, which utilizes the high stability of silicon nitride to support the molybdenum metal layer. The waveplate thickness is less than 300nm, avoiding the space occupation problem of traditional discrete devices, and is easy to integrate. It provides core device support for the miniaturization and high-precision polarization control of extreme ultraviolet lithography machines.

[0031] Fourth, the process of this invention is simple and stable, compatible with existing semiconductor manufacturing processes, and can reduce production costs and process complexity. Attached Figure Description

[0032] Figure 1 is a schematic diagram of the metasurface structure provided in an embodiment of the present invention.

[0033] Figure 2 is a schematic diagram of the nanoporous unit structure in the metasurface provided in the embodiment of the present invention.

[0034] Figure 3 shows the phase response distribution (a) extracted under free-space X-ray polarized incidence, the phase response distribution (b) extracted under free-space Y-ray polarized incidence, and the difference distribution (c) between the X-ray polarized and Y-ray polarized phase responses obtained from numerical simulation of the nanopore unit structure parameters at a working wavelength of 13.5 nm from 0 nm to 80 nm in this embodiment of the invention. In Figure 3(c), squares mark the positions of the selected structural parameters of the half-wave plate, and circles mark the positions of the selected structural parameters of the quarter-wave plate.

[0035] Figure 4 shows the transmission intensity distribution (a) of the unit structure of the half-wave plate device in the XY plane at a wavelength of 13.5 nm, and the real distribution (b) and (c) of the electric field X component of the half-wave plate device under X polarization and Y polarization.

[0036] Figure 5 shows the transmission intensity distribution (a) of the unit structure of the quarter-wave plate device in the XY plane at a wavelength of 13.5 nm, and the real distribution (b) and (c) of the electric field X component of the quarter-wave plate device under X polarization and Y polarization. Detailed Implementation

[0037] The implementation method, principle design, and technical effects of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] The design methodology for metasurfaces includes the following steps:

[0039] 1) Design the structure of the metasurface: The metasurface includes a silicon nitride (Si3N4) substrate, a molybdenum (Mo) metal layer disposed on the silicon nitride substrate, and a nano-rectangular hole array penetrating the silicon nitride (Si3N4) substrate and the molybdenum (Mo) metal layer. The nano-hole array is a periodic structure, including several rectangular hole structures with the same depth and pore size.

[0040] 2) Calculate the phase response and transmittance distributions of nanoporous unit structures under different polarized input light sources. Using the finite-difference time-domain method (commercial Lumerical FDTD software), calculate the resonant phase response spectra and transmittance distributions of nanoporous unit structures with different geometric dimensions under free-space incident light sources of different polarizations at the same operating wavelength.

[0041] 3) Determine the phase difference conditions corresponding to the nanopore units according to the phase requirements of the different functions of half-wave plates and quarter-wave plates;

[0042] 4) Determine the geometric parameters of the nanopore units in the metasurface. Based on the resonant phase response distribution and transmittance distribution data of the unit structure obtained in step 2, and the different target difference conditions obtained in step 3, the geometric parameters such as the length and width of the nanopores that meet the phase conditions required for the corresponding functional waveplate are obtained through an algorithm-based index screening. When the structural phase responses are consistent, the structural parameters with the highest transmittance are selected to describe the corresponding metasurface unit. The metasurface units are arranged periodically to determine the design of the waveplate device based on the metasurface.

[0043] Furthermore, the specific steps are as follows:

[0044] In step 1: Select the operating wavelength λ of the device, determine the thickness of the silicon nitride (Si3N4) substrate and the molybdenum (Mo) metal layer based on parameter simulation optimization, select the unit period of the metasurface, and make the geometric dimension change of the metasurface unit structure satisfy a certain phase coverage and transmittance under the free space incident wavelength λ.

[0045] In step 3: A waveplate is capable of introducing a specific optical path difference ΔL (or phase difference) between two mutually perpendicular light vibrations. Optical devices that enable polarization state manipulation. The functional difference between a half-wave plate (HWP) and a quarter-wave plate (QWP) stems from their ability to manipulate the phase difference of the incident light, with specific phase requirements as follows:

[0046] A quarter-wave plate (QWP) requires the introduction of an optical path difference in orthogonal polarization directions. (m is an integer), corresponding to the phase difference It can convert linearly polarized light into circularly polarized light (or vice versa). This condition can be stated as:

[0047]

[0048] In formula (1), λ is the design wavelength, and ΔL = (n x -n y )·d is the birefringence difference (n x and ny The product of the equivalent refractive index of the nanopore along the x-axis and y-axis and the equivalent thickness d of the metasurface, where m is an integer. To achieve equation (1), the anisotropic geometric parameters of the nanopore (such as the geometric difference in length and width along the x-axis and y-axis of a rectangular hole) need to be adjusted so that the phases of the orthogonal polarization components satisfy the following:

[0049]

[0050] In formula (2) and , representing the phase distribution of the nanopores along the x-axis and y-axis, respectively, where m is an integer.

[0051] Half-wave plates (HWPs) require the introduction of optical path difference. (n is an integer), the corresponding phase difference is A half-wave plate can rotate the vibration direction of linearly polarized light to twice the angle between the incident direction and the fast axis. The condition is:

[0052]

[0053] In formula (3), n is an integer. Similar to a quarter-wave plate, to achieve formula (3), the anisotropic geometric parameters of the nanopore need to be adjusted so that the phases of the orthogonal polarization components satisfy the following:

[0054]

[0055] In formula (4), n is an integer. Based on the phase difference conditions required for different waveplates, a series of geometric parameters corresponding to the phase response are obtained through the existing phase response spectra under different polarization free space light inputs. Combined with the transmission spectrum, the geometric parameters with relatively high transmission intensity in the extreme ultraviolet band are selected to complete the design of waveplate devices based on metasurfaces.

[0056] This embodiment describes an extreme ultraviolet (EUV) half-wave plate and quarter-wave plate device based on a metasurface, as shown in Figure 1. Figure 2 is a schematic diagram of the unit structure. The substrate is a 100 nm thick silicon nitride (Si3N4). To ensure sufficient phase coverage, the upper molybdenum (Mo) metal layer is 150 nm thick and has low absorptivity, which can be used for phase modulation. The materials used in the metasurface are crucial because they significantly affect light absorption loss and phase control. The unit structure of the metasurface consists of vacuum rectangular nanopores penetrating the silicon nitride (Si3N4) substrate and the molybdenum (Mo) metal layer. The metasurface unit period is set to P. X =P y=P=80nm. Although the period of the structure exceeds one wavelength (13.5nm), it does not meet the subwavelength condition, thus making it impossible to avoid the existence of higher-order diffraction orders. However, choosing a structural period of 80nm can accumulate sufficient phase, while still obtaining most of the transmitted energy from zero-order diffraction. Numerical simulation of the unit structure shown in Figure 2 was performed using the electromagnetic simulation software Lumercal FDTD solutions. The phase response spectrum distributions of free-space X-linearly polarized and Y-linearly polarized light inputs at the same wavelength of 13.5nm (the wavelength can be extended to other bands of optical communication) are shown in Figures 3(a) and 3(b), respectively. Figure 3(c) is a two-dimensional image of the phase response difference between X-linearly polarized and Y-linearly polarized light. In the image, squares mark the positions of the selected structural parameters of the half-wave plate, and circles mark the positions of the selected structural parameters of the quarter-wave plate. The period P is fixed at 80nm, and the x-axis length xspan and y-axis length yspan of the metasurface unit vary from 0nm to 80nm. Based on the phase requirements of quarter-wave plates and half-wave plates for X-polarization and Y-polarization respectively, the geometric dimensions of the nanopore units were obtained from the phase response spectrum and transmittance response spectrum in Figure 2. In this invention, the geometric parameters of the half-wave plate unit structure are xspan = 16 nm and yspan = 40 nm, with a phase difference of 179.61° for X-polarized and Y-polarized incident light at a wavelength of 13.5 nm; the geometric parameters of the quarter-wave plate unit structure are xspan = 44 nm and yspan = 16 nm, with a phase difference of 88.9° for X-polarized and Y-polarized incident light at a wavelength of 13.5 nm. The metasurface units were periodically arranged to determine the metasurface structure in Figure 1. The XY plane transmission intensity of the designed half-wave plate unit structure under 13.5nm wavelength X-polarized light source incident light is shown in Figure 4(a). Under X-polarized light source incident light, the real distribution of the X component of the electric field is shown in Figure 4(b). Under Y-polarized light source incident light, the real distribution of the Y component of the electric field is shown in Figure 4(c). It can be seen that the half-wave plate has significant differences under different incident light conditions of X-polarization and Y-polarization, and can achieve a phase modulation effect with a phase difference of about 180 degrees between the X and Y polarization directions. Similarly, the XY plane transmission intensity of the quarter-wave plate unit structure of the present invention under 13.5nm wavelength X-polarized light source incident light is shown in Figure 5(a). Under X-polarized light source incident light, the real distribution of the X component of the electric field is shown in Figure 5(b). Under Y-polarized light source incident light, the real distribution of the Y component of the electric field is shown in Figure 5(c). This structure can achieve a phase modulation effect with a phase difference of about 90 degrees between the X and Y polarization directions.

[0057] The present invention proposes a design method for extreme ultraviolet (EUV) half-wave plates and quarter-wave plates based on metasurfaces. The proposed silicon nitride-molybdenum composite meta-nanoporous unit structure overcomes the problems of phase modulation failure caused by the sharp drop in refractive index of EUV materials and the large volume and limited band of traditional wave plates. It realizes the function of half-wave plate and quarter-wave plate devices and is expected to be used in EUV semiconductor lithography, high-resolution imaging and ultrafast spectroscopy.

Claims

1. A design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces, characterized in that, Includes the following steps: 1) Design the structure of the metasurface; The structure of the metasurface includes: a silicon nitride substrate, a molybdenum metal layer disposed on the silicon nitride substrate, and an array of nano-rectangular holes penetrating the silicon nitride substrate and the molybdenum metal layer; The nano-rectangular aperture array comprises several rectangular apertures with the same depth and aperture size, which are periodically arranged in a plane; 2) Calculate the resonant phase response distribution and transmittance distribution of the nano-aperture units in the metasurface structure under the target wavelength and different polarization free space input light sources; 3) Determine the phase difference conditions corresponding to the nano-aperture units of the half-wave plate and the quarter-wave plate respectively according to the phase requirements of the different functions of the half-wave plate and the quarter-wave plate; 4) Based on the resonant phase response distribution and transmittance distribution data obtained in step 2), and the phase difference conditions corresponding to the nano-aperture units of the half-wave plate obtained in step 3), use the algorithm to screen the structural parameters of the rectangular apertures that meet the requirements of the half-wave plate, and arrange the nano-aperture units periodically to complete the design of the extreme ultraviolet band half-wave plate device; Based on the resonant phase response distribution and transmittance distribution data obtained in step 2), and the phase difference conditions corresponding to the nano-aperture units of the quarter-wave plate obtained in step 3), use the algorithm to screen the structural parameters of the rectangular apertures that meet the requirements of the corresponding quarter-wave plate, and arrange the nano-aperture units periodically to complete the design of the extreme ultraviolet band quarter-wave plate device.

2. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 2), the nanopore unit includes: a rectangular pore and a silicon nitride substrate and a molybdenum metal layer corresponding to the edge of the rectangular pore.

3. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 2), the different polarizations are X linear polarization and Y linear polarization.

4. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 2), the resonant phase response distribution and transmittance distribution of the nanoporous units in the metasurface structure under the target wavelength and different polarization free space input light sources are calculated using the finite-difference time-domain method.

5. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 3), the phase difference condition corresponding to the nanopore unit of the half-wave plate is: the phase difference between X linear polarization and Y linear polarization is... Or an odd multiple thereof.

6. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 3), the phase difference condition corresponding to the nanopore unit of the quarter-wave plate is: the phase difference between X linear polarization and Y linear polarization is... Or an odd multiple thereof.

7. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 4), the structural parameters of the rectangular aperture that meet the requirements of the half-wave plate are selected using an algorithm, and the nanopore units are arranged periodically to complete the design of the extreme ultraviolet half-wave plate device. Specifically, the algorithm is used to select the structural parameters of the rectangular aperture that meet the requirements of the half-wave plate, so that the nanopore units have relatively high transmittance in the extreme ultraviolet band while approaching the required phase difference conditions. The obtained nanopore units are arranged periodically to obtain the design of the extreme ultraviolet half-wave plate device.

8. The design method for extreme ultraviolet half-wave and quarter-wave plate devices based on metasurfaces according to claim 1, characterized in that, In step 4), the structural parameters of rectangular holes that meet the requirements of a quarter-wave plate are selected using an algorithm. The nanopore units are then arranged periodically to complete the design of the extreme ultraviolet (EUV) band quarter-wave plate device. Specifically, this includes: selecting the structural parameters of rectangular holes that meet the requirements of a quarter-wave plate using an algorithm, so that the nanopore units have relatively high transmittance in the EUV band while approaching the required phase difference conditions; and arranging the obtained nanopore units periodically to obtain the EUV band quarter-wave plate device.

Images