1. Introduction

As an important part of advanced manufacturing, micro-nano processing technology is one of the criteria to evaluate the national high-end manufacturing level, and improving the resolution is an important means to increase the integration and miniaturization of devices. Current commercial extreme ultraviolet (EUV) lithography, which is an extension of traditional optical projection lithography, sets an exposure wavelength of 13.5 nm and a numerical aperture of 0.33, achieving a single-exposure resolution of 13 nm. In the development and mass production of integrated circuits at the 5 nm or even 3 nm technology nodes, EUV lithography machines play an indispensable role [1–3]. However, the extremely high manufacturing and operating costs of EUV lithography machines limit their potential for large-scale production.

In recent years, several new techniques on the basis of reduced period lithography principle have been proposed, including interference lithography [3] and Talbot lithography [4]. In theory, utilizing EUV as interference source can produce interference patterns with periods of about 10 nm. In 2011, B. Päivänranta et al. obtained interference patterns with a half-pitch resolution of less than 10 nm using EUV interference lithography [3]. In 2014, K. Hyun-su et al. used the fractional Talbot effect and EUV to obtain a subwavelength pattern with a half-pitch resolution of 1/5 of the grating period [4], where the fractional Talbot effect demonstrates that there is an image with a 1/2 period that of the grating at 1/2 Talbot distance, an image with a 1/4 period that of the grating at 1/4 Talbot distance, and et al. Both approaches, however, are constrained by the high cost and high absorption of the EUV, which precludes them from being widely employed.

SPIL is an interference lithography technique based on SPP, where two counter-propagating SPPs interfere with one another and then produce a sub-wavelength periodic interference pattern. SPP with the characteristic of local field enhancement and subwavelength constraint is a promising tool to break the diffraction limit of lithography [5–7]. SPIL overcomes the restrictions of space charge and serial writing and is not constrained by the far-field optical diffraction limit of Abbe's law, which allows the fabrication of large-area periodic structures [5–7]. Typically, a metallic grating is always used in SPIL as a mask to excite the SPP. When the diffraction wave of the grating is coupled with SPP, the homogeneous interference patterns with large area and high contrast can be produced [8–13].

Early, the period of the interference pattern obtained by SPIL is consistent with the period of the grating [14]. X. Luo et al. proposed that SPIL can be performed using high-order diffraction [15], but as a pioneering work, the resolution, uniformity and dependence on PR thickness of interference patterns need to be improved. In 2016, X. Luo et al. realized large area and deep sub-wavelength interference patterns with a half-pitch resolution of 45 nm experimentally by using the odd mode in the metal/insulator/metal structure with a higher transverse wave vector and inhibition of tangential electric field components [11]. In recent years, by designing the dielectric constant and thickness of the material in hyperbolic metamaterials (HMMs) [16] to obtain high-k modes that can be transmitted in the PR, the resolution of nanolithographic systems has been further improved [6,17,18]. In 2017, Y. Fan et al. designed a metamaterial structure of Ag-Al₂O₃ multilayer film with tangential dielectric constant close to zero, which improved the transmittance of SPP and finally obtained an interference pattern with a half-pitch resolution of 58.3 nm [6]. In 2019, Y. Qian et al. used the hyperbolic dispersion characteristics of hyperbolic multilayer graphene (HMG) and the symmetric mode of the waveguide formed by the HMG on the upper and lower sides of the PR layer to obtain uniform and high-contrast interference patterns in the PR [8]. However, further improvement of the pattern resolution only by reducing the grating period will make the grating processing more difficult and costly. Moreover, the direct contact between the PR layer and the mask makes the reuse of the mask difficult.

In this paper, a plasmonic interference lithography based on the second-order diffracted wave of grating and hyperbolic multilayer graphene is proposed. By using the grating's second-order diffracted waves to match the SPP, an interference pattern with a half-pitch resolution of 1/8 of the grating period and 1/6.7 of incident wavelength can be produced. When the PR thickness is 25, 45, 65, 85 nm, the corresponding contrast at the bottom of the PR is 0.79, 0.97, 0.73, and 0.70, respectively. The grating structure used to excite SPP could be easily fabricated using conventional lithography. In addition, due to the introduction of air gaps between the grating and the lithography films, the grating is expected to be reusable.

2. Results and discussion

The designed SPIL structure based on hyperbolic multilayer graphene (HMG) [8] is shown in Fig. 1(a). An aluminum grating with SiO₂ grooves is used as the mask, the upper SiO₂ layer is the substrate, and an air gap with a thickness of d_a = 5 nm is present between the grating structure and the lithography films. The depth, groove width, and period of grating are d₁ = 50 nm, w = 111 nm, and P_x = 222 nm, respectively. The thicknesses of the bottom SiO₂, the hyperbolic multilayer graphene films, and the PR layer are d_m = 25 nm, d₂ = 35 nm, and d₃ = 25 nm, respectively. The incident UV light is TM-polarized (electric field component oscillates along the x-axis), and the wavelength is 193 nm. It is assumed that all the materials were non-magnetic materials with a permeability of µ = 1, and the dielectric constants of Al, SiO₂, PR, and Si at 193 nm are -4.84 + 0.5i, 2.44, 2.89, and -6.94 + 4.91i [12], respectively. At the wavelength of 193 nm, the dielectric constant of HMG can be expressed as: ε_x = ε_y = -0.53 + 0.94i, ε_z= 2.44 [8].

 

Fig. 1. (a) Schematic of SPP interference structure. (HMG: hyperbolic multilayer graphene, PR: photoresist.) (b) Electric field intensity distribution in the lithography structure. (c) The normalized electric field intensity at three positions of the PR layer in this work and the middle part of the PR layer of the structure in the Ref. [8].

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The SPP mode can be excited by the mth order diffracted waves of the grating according to the following condition:

Full-wave electromagnetic simulation software is used to simulate the performance of the proposed structure. The electric field intensity distribution is depicted in Fig. 1(b), where z = 0 is located at the interface between the PR layer and bottom HMG. The SPP interference wave, the multi-order diffracted waves, and the incident wave are all superimposed inside the SiO₂ grooves, with the electric field intensity being the highest. HMG can be regarded as a kind of HMMs with the function of transmitting and shaping electromagnetic waves. Moreover, due to the narrow-band nature of its transmission spectrum, only modes with wave number around 1.74k₀ are supported [8], so incident waves and other-order diffracted waves are filtered out, and only the SPP excited by the second-order diffracted wave can pass through. The transmitted electromagnetic wave changes from evanescent wave to transfer wave after leaving HMG, and the propagation ability in z direction is enhanced [16].

As shown in Fig. 1(b), in the PR layer (z = 0∼25 nm), the field intensity can be observed to change periodically along the x-axis, which is the 29 nm half-pitch interference pattern obtained by the SPP interference induced by the second-order diffraction wave of the grating. Figure 1(c) shows the normalized electric field intensity distribution at the top (z = 0 nm), middle (z = 12.5 nm), and bottom (z = 25 nm) in the PR layer in this work. The normalized electric field intensity is defined as |E|²/|E₀|², where E₀ is the electric field intensity of the incident electric field. It can be seen that the resolutions of these 3 curves are almost identical. The contrast of the interference pattern is defined as (|E_max|²-|E_min|²) / (E_max|² +|E_min|²), where E_max and E_min represent the maximum and minimum of the electric field along the x direction, respectively. The contrast ratios at the three positions are 0.7, 0.67, and 0.79, respectively, all larger than the minimum contrast ratio required for positive PR (0.4), and the minimum contrast ratio required for negative PR (0.2) [19]. Therefore, the proposed structure is able to efficiently record the generated periodical patterns in the PR layer. Figure 1(c) also shows the field intensity distribution in the middle of the PR layer (z = 12.5 nm) of the structure presented in the structure in Ref. [8]. It can be seen that even when the second-order diffracted wave is utilized, the normalized electric field intensity of the interference pattern is still higher than that obtained from the first order diffraction wave excitation.

The influence of the grating groove width w and the bottom SiO₂ thickness d_m on the interference pattern is discussed below. Firstly, the groove width of the metal grating w has a great influence on the interference pattern's normalized electric field intensity in the PR. When w = n λ_sp (n is an integer, and λ_sp is the SPP wavelength), a diffracted wave of wavelength λ_sp can generate a Fabry-Perot resonance in the transverse cavity consisting of two walls of the groove. The Fabry-Perot resonance enhances the transmission of the diffraction wave, and thus the electric field intensity of the excited SPP at the interface between the grating and the medium is enhanced [13]. Figure 2(a) demonstrates the normalized electric field intensities in the middle of the PR when w = 15 nm and w = 111 nm without the bottom SiO₂. It is shown that although the intensity of the interference pattern corresponding to w = 111 nm is higher, the contrast and uniformity of the interference pattern are significantly reduced. This phenomenon is caused by two main factors: the poor coupling from free space to the grating and the severe loss of the metal itself (which is more noticeable at short wavelengths) [20–22].

 

Fig. 2. (a) The normalized electric field intensities (without bottom SiO₂) in the PR layer (z = 12.5 nm) corresponding to w = 15 nm and w = 111 nm, respectively. (b) The normalized electric field intensities (with bottom SiO₂) in the PR layer (z = 12.5 nm) corresponding to w = 15 nm, w = 65 nm and w = 111 nm, respectively.

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Buried metal grating is a grating in which the metal grating is buried in dielectric. In this structure, incident light energy can be more easily coupled into the dielectric groove, thus facilitating electromagnetic wave transmission and significantly enhancing electromagnetic wave transmission capability [20]. Additionally, the in-plane directed scattering of SPP waves on the buried metal grating is decreased and the propagation length is increased compared to the conventional grating [22]. In this paper, the embedded metal grating is used, in which the Al metal is completely wrapped in SiO₂. In order to determine the appropriate thickness of the bottom SiO₂, the structures under different thicknesses d_m were analyzed, and the results were shown in Fig. 3. It can be seen that when d_m increases from 10 nm to 30 nm, the normalized electric field intensity in PR directly below the groove gradually decreases, while the normalized electric field intensity in PR directly below the metal gradually increases, and the contrast of the interference fringe is improved. When the thickness increases to 40 nm, the electric field strength and contrast of the interference fringes begin to deteriorate. Based on the simulation results, 25 nm was selected as the thickness of the bottom SiO₂.

 

Fig. 3. The normalized electric field intensities in the PR layer (z = 12.5 nm) with different SiO₂ thickness d_m.

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Furthermore, the influence of grating groove width w on the interference pattern's normalized electric field intensity, while leaving the bottom SiO₂ in place, is also discussed. Figure 2(b) shows the normalized electric field intensities (with bottom SiO₂) in the PR layer (z = 12.5 nm) when w = 15 nm, w = 65 nm and w = 111 nm. When w = 15 nm and w = 65 nm, the interference pattern period in PR is 222 nm. The reason for the above appearance is that the size of the grating groove width w determines the light intensity through it, and the distribution of SPP interference patterns in PR is affected.

In addition to the grating structure, the introduction of an air gap also has an impact on the quality of the interference pattern in the PR layer. Figure 4 shows the normalized electric field intensity in the middle of the PR layer under different air gap thicknesses. It can be seen that the intensity and contrast of the interference pattern decrease with the increase of the air gap thickness. The thickness of the PR layer must be reduced in order to generate large-contrast pattern under the condition of a greater air gap thickness [9], which is unfavorable to the subsequent pattern transfer process. After comprehensive consideration, 5 nm is chosen as the thickness of the air gap.

 

Fig. 4. The normalized electric field intensities in the PR layer (z = 12.5 nm) with different air gap thicknesses d_a.

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It is also worth mentioning that, in contrast to the antisymmetric mode and the higher mode, the symmetric SPP mode excited in lithography films is insensitive to the thickness of the PR layer [8]. In order to study the interference pattern dependent on the PR thickness, the field intensities at z = 0 when d₃ = 45 nm, 65 nm, and 85 nm are plotted in Fig. 5. The half-pitch resolutions of the bottom line in the PR are all close to 29 nm, and the corresponding contrasts are 0.97, 0.73, and 0.7, respectively. Consequently, in the designed period-reduction lithography, the characteristic of insensitive to the PR thickness remains.

 

Fig. 5. The normalized electric field intensities at the bottom of PR with different PR thicknesses d₃.

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3. Conclusion

Plasmonic interference lithography based on the second-order diffracted wave of grating and hyperbolic multilayer graphene is proposed in this work, and a 29 nm half-pitch interference pattern is obtained using a grating with a period of 222 nm and an incident wave of 193 nm. By utilizing a grating with a groove width that is an integer multiple of the SPP wavelength and adding a SiO₂ dielectric layer at the bottom of the grating, the electric field intensity and contrast of the interference pattern are effectively improved, with an average contrast of about 0.7. The introduction of an air gap between the grating and the lithography films is beneficial to the etch transfer process from PR to substrate after lithography, and makes the grating reusable. Moreover, the method is insensitive to PR thickness and can maintain a good contrast when PR thickness is increased to 85 nm. Finally, because the half-pitch resolution of the interference pattern is 1/8 of the grating period, the method is expected to reduce the difficulty of manufacturing, and provides a promising way for period-reduction lithography to achieve a higher resolution.