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Abstract
Plasmonic lithography, which exploits a bowtie nanoaperture (BNA) for the purpose of subwavelength near-field focusing, has the capability of high-resolution patterning. However, the ultra-small feature size is achieved at the price of sharply decay of the surface plasmon waves (SPWs) in the photoresist (PR) layer, which directly leads to some unfavorable patterning issues, such as non-uniformity and shallow pattern depth even over small exposure areas. In this work, a special hybrid plasmonic waveguide (HPW) patterning system, which is composed of the plasmonic BNA-PR layer-silver reflector, is designed to facilitate high spatial frequency selection and amplify the evanescent field in the PR layer. Theoretical calculations indicate that the antisymmetric coupled SPWs and plasmonic waveguide modes excited by the HPW structure can remove the exponential decay and ensure uniform exposure over the entire depth of the PR layer. Importantly, the hyperbolic decaying characteristic of the SPWs in the PR layer plays a noticeable role in the improvement of achievable resolution, depth-of-field, and line array pattern profile. It is worth to note that the uniform periodic patterns in sub-20 nm feature can be achieved with high aspect ratio. Additionally, further numerical simulation results are presented to demonstrate the achievement of spatial frequency selection of high-k mode in HPW structure by controlling the PR thickness and gap size. Our findings may provide a new perspective on the manufacture of surface nanostructures and broaden the potential promising applications of plasmonic lithography in nanoscale patterning.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Lithography technology lays the foundation for the nanostructure fabrication with low cost, ultrahigh resolution, and high aspect ratio [1–3]. Thus far, various lithography techniques have been extensively investigated to achieve ultra-small feature size, such as electron beam lithography (EBL), He ion beam lithography (HIBL), extreme ultraviolet (EUV) lithography, and nanoimprint lithography. However, these techniques are costly and further improvements are needed in defect control, accuracy, and yield [4–7]. Photolithography as the essential technology of micro and nano manufacturing, has been the driving force for the development of the semiconductor industry and is also the important reason why integrated circuits developed following the Moore’s law. Unfortunately, the further advance of photolithography resolution is limited by the diffraction of light waves. This is because the diffraction limit of photolithography comes from the fact that the high frequency information is only carried by the evanescent waves, which only existing in the near-field region and are lost before reaching the image plane [8,9]. Accordingly, one way to enhance the pattern resolution of photolithography far below the diffraction limit is manipulating the evanescent waves.
Surface plasmon waves (SPWs) are known as evanescent waves, which bounded at metal-dielectric interface and have larger transversal wave vector than that in free space [10–12]. Based on the characteristics of local field enhancement and subwavelength confinement of SPWs and subdiffractional resolution imaging capabilities, a series of nanolithography technologies have been reported, such as plasmonic lithography, sphere-lens-array lithography, and near-field lithography [13–15]. Plasmonic lithography, which is maskless, low cost, and can achieve ultra-high resolution, have been extensively investigated [16–27]. Both theoretical and experimental results showed that resolution of plasmonic lithography can be reduced to sub-20 nm-feature. However, almost all of the plasmonic lithography technologies were only able to show very shallow patterns, due to the exponential decaying characteristic of SPWs in the patterning depth direction. A bowtie nanoaperture (BNA) combined with metal-insulator-metal (MIM) structure has been proposed to improve the pattern depth, however, due to the geometrical asymmetry of the BNA, the obtained beam spot in photoresist (PR) appear elliptic morphology [28]. To solve the problem, a double bowtie aperture with MIM structure (DBMIM) has been designed to high-aspect circle-symmetric beam spots, but the spot size is still limited by the rapid divergence of evanescent field generated by the BNA [29]. As a result, increasing the aspect ratio and achieving high pattern uniformity are critical to plasmonic lithography for practical applications.
In this paper, a hybrid plasmonic waveguide (HPW) structure is proposed to overcome shallow pattern depth issue of plasmonic lithography. By exciting the antisymmetric coupled SPWs in the sandwiched PR layer by a plasmonic BNA and a metal reflector film, uniform deep-subwavelength patterns can be generated in the PR layer. Due to the dispersion relation can be engineered by the geometric structure of HPW [30,31], high-k modes can be selected to contribute the high confinement of SPWs in the PR, and sub-20 nm resolution with high aspect ratio can be formed. Moreover, a theoretical model is introduced to analyze the hyperbolic decaying characteristic and achievable pattern depth of the HPW structure. We find that the decaying feature of the SPWs in the PR layer plays a noticeable role in the aspect profile and pattern quality. The dominance of high-k mode is further numerically investigated by controlling the PR thickness and gap size. These analyses show that the spatial frequency filtering characteristic of HPW structure may provide a new method to realize uniform deep-subwavelength patterns with high aspect ratios.
2. Modeling
2.1 Characteristics analysis of the HPW structure in plasmonic lithography
In plasmonic nanofocusing studies, the goal is to focus the illuminated electromagnetic beam into a deep subwavelength hot spot. Although nanoridge apertures can be used as a plasmonic nanofocusing structure due to their high local field enhancement, the generated SPWs around the aperture rapidly decays instead of propagates, seriously limiting the exposure depth. As a consequence, almost all of the theoretical and experimental results were only able to show shallow exposure depth far below the requirement for nano-photolithography due to the evanescent nature of the SPWs [17,18]. To understand the issue of shallow pattern depth reported in previous literature, we consider a well-known maskless plasmonic lithography scheme, as displayed in Fig. 1(a). In this scheme, a scanning plasmonic BNA serves as the focusing element to record the target pattern into the PR. The plasmonic BNA is embedded into the thin aluminum (Al) by using ion-beam milling method. When an x-polarized UV light is incident on the plasmonic BNA, which would induce the redistribution of the free electrons at the exit of BNA and excite local surface plasmon polaritons (SPPs) at the interface between BNA and PR. In light of this, the plasmonic BNA structure can be regarded as a basic metal-insulator-metal (MIM) plasmonic waveguide structure (Al/air/Al). During the exposure process, the plasmonic BNA is in conformal contact with the PR layer on the substrate to ensure the SPWs coupling. Unlike the typical plasmonic lithography, a schematic of the nanopatterning process with HPW structure is illustrated in Fig. 1(b). The PR layer is sandwiched between the plasmonic BNA and a plasmonic back reflector, hence, a HPW mode composed of a horizontal MIM plasmonic waveguide (i.e., the planar Al/air/Al) and a vertical MIM plasmonic waveguide (i.e., the input plasmonic BNA/PR/reflector) is constituted. Notably, the horizontal MIM plasmonic waveguide and the vertical MIM plasmonic waveguide can further stimulate the excitation of SPPs at the top and bottom of PR layer respectively, thereby inducing an extraordinarily complicated surface-wave coupling mode in the PR layer. The high efficient coupling between the plasmonic waveguide modes and SPP waves of the HPW structure can achieve a strong and consistent photoenergy distribution in the PR layer.
Fig. 1. (a) Schematic configuration of a typical plasmonic lithography including a scanning plasmonic BNA, PR, and Si substrate. (b) Schematic configuration of HPW in plasmonic lithography system including a scanning plasmonic BNA, PR, metal-reflector layer, and Si substrate. (c) Single PR layer, red dash line implies the location of plasmonic BNA exit, red circle marks the SPPs resonance peak, and the nanopatterning occurs in yellow shaded region. (d) HPW structure, Red and blue dash lines imply the interfaces of plasmonic BNA/PR and PR/metal reflector respectively, two red circles mark the generated SPPs resonance peaks, and nanopatterning occurs in purple shaded region. (e) Geometry of a plasmonic BNA. The outline dimension is ${O_x} = {O_y} = 150\; nm$ with various ridge-gap size (g) from 5 to 40 nm.
In order to study the field confinement ability in PR layer, a finite differential time domain (FDTD, ansys lumerical v2021) calculation is performed to obtain the electronic field distribution in the two plasmonic lithography systems. The geometries and dimensions of the two plasmonic lithography systems are the same with those given in Fig. 1. A transverse magnetic (TM) polarized plane wave is illuminated on the plasmonic BNA, and the wavelength is 365 nm. At this illumination wavelength, the permittivities of Al, Ag, and PR are ${\varepsilon _{Al}} ={-} 19.4 + 3.6i$, ${\varepsilon _{Ag}} ={-} 2.4 + 0.25i$, and ${\varepsilon _{PR}} = 2.9$[26–28], respectively. The outline dimension of BNA in an Al film is assumed to be 150 nm x 150 nm, and the ridge-gap size is set as 20 nm. The Fabry-Pérot (F-P) like resonance of the plasmonic BNA plays an essential role in enhancing optical transmission, thus, the thickness of Al film is set as 150 nm to match the F-P like resonance condition [17,28]. For the conventional plasmonic lithography system, the PR recording structure is a 40-nm single PR layer on the silicon substrate. In contrast, the PR recording structure in the HPW structure is composed of 150 nm plasmonic BNA, 20 nm PR layer, and 20 nm Ag reflector film. The minimum mesh size of $x \times y \times z$ is $1\textrm{nm} \times 1\textrm{nm} \times 1\textrm{nm}$, The longitudinal coordinate in Fig. 1(c) and (d) represent the intensity distribution of the electric field, while the abscissa represents the position variation in each film layer, which was previously illustrated as the z-axis in Fig. 1(a) and (b), respectively. The red dash line is the interface between the plasmonic BNA and the PR layer, where SPPs are excited. Additionally, the blue dash line is the interface between the PR layer and the metal reflector film, where SPPs are excited again. The PR layer is the nanopatterning region, which is the main observation section of the photoenergy distribution. Figure 1(c) shows the intensity distribution when there is a single PR layer. It can be observed that the field intensity of SPWs excited by the interface of the plasmonic BNA/PR layer decreases exponentially as the vertical distance increases.
When the photoenergy approaches the SPPs excitation level, it can reach the threshold dose of the PR. Then the exposure dose continues to decay rapidly in the PR layer, which is very harmful to the pattern width and depth. Figure 1(d) indicates that the SPPs reflected by the Ag reflector film is reasonably coupled with the SPPs excited by the plasmonic BNA/PR interface, which greatly compensates the intensity attenuation in PR layer and thus leads to a better photoenergy distribution in the PR layer. This is mainly due to the asymmetry electromagnetic mode excitation in the HPW structure [32–36], which can enhance the resonance coupling between the generated SPWs at the top and bottom of PR layer and the plasmonic waveguide. Significantly, the uniform distribution of the field intensity of SPWs in the PR layer improves the pattern depth, and ensures high resolution and uniformity of patterns. Therefore, the findings demonstrate that the HPW structure is useful for improving the aspect ratio of plasmonic lithography.
2.2 Spatial frequency selection for higher pattern quality
Based on the principle of HPW mode, the metal reflector could be regarded as a plasmonic mirror which amplifies the SPWs and modulates the distribution of the electric field intensity in the PR layer. However, the permittivity of the metal reflector significantly effects the propagation characteristics of SPWs in the PR layer. For this reason, the material selection of the metal reflector is the key factor to determine the high field enhancement in the PR layer. In order to facilitate the theoretical analyses, Maxwell’s equations are carried out to evaluate the tangential reflected and transmitted electric field in the PR layer [22,37,38]. The total local spatial field $\textrm{E}({{k_x},z} )$ in the PR layer can be defined as
2.3 Theoretical analysis of the exposure depth in plasmonic lithography
In a maskless plasmonic lithography system, while the plasmonic BNA provides deep sub-wavelength confinement on the PR surface, the evanescent field decays rapidly in the normal direction, rapidly loosing the component of high spatial frequency, seriously limiting the generated pattern depth in PR layer. In order to intuitively analyze the effect of the decay characteristics of evanescent field on the intensity distribution in the PR layer, a linear function $\beta (z )= a + bz$ was proposed to estimate the decay length in PR layer, where a is the decay constant at z = 0, and b is a dimensionless parameter [17,43]. Then, the point-spread function (PSF) in the PR layer can be solved as $I(z )= {I_i}{\left( {1 + \frac{b}{a}z} \right)^{ - 1/b}}$, and Ii is the intensity at z = 0. The constants a and b depend on the spatial distribution of evanescent field and can be obtained by fitting the peak intensity decay of the evanescent field distribution obtained by the FDTD calculation. The plot of the PSFs versus the pattern depth is shown in Fig. 2(a). It shows that the proposed PSF formula agrees well with the simulation result. The parameters (a, b) of the decay length β were fitted as (8.661 nm, 0.029) from the PSF curve.
Fig. 2. Estimation of the decay characteristics of SPWs in the PR layer. (a) PSFs in the PR layer generated by a plasmonic BNA, simulation results (red circles) and fitting data (black solid line) are shown. (b) PSFs in the PR layer generated by HPW structure, simulation results (red triangles) and fitting data (black solid line) are shown.
Unlike the conventional plasmonic nanopatterning, the HPW structure exploits the strong coupling effect of SPWs and plasmonic waveguide modes, leading to uniform distribution of near-field intensity in the PR layer. Thereby, the HPW mode can be formulated as coming from the sum of SPWs modes on the top and bottom of PR layer. In the PR layer, the field has a hyperbolic cosine dependence from the sum of two exponential decaying SPWs modes on the top and bottom of PR layer. The decay characteristic of near-field in PR layer is no longer the exponential form, the decay length increases first and then reduces with the increasing pattern depth due to the evanescent wave amplification of metal reflector. To express the decay characteristics in HPW mode accurately, we assume β(z) is approximated by a hyperbola curve:
then, Eq. (1) can be further approximated for PSF in HPW mode, ${I_{HPW}}(z )$ asFigure 2(b) indicates that the calculated PSF obtained from Eq. (5) is in good agreement with the simulated PSF. The constants (a, b) of the decay length β were fitted as (3.947, 5.87451 nm2), and the reflection coefficient γ was fitted as 1.815 from the PSF curve.
The dose distribution in PR layer is described by $D(z )= I(z ){t_i}$, where ${t_i}$ is the exposure time, and ${D_i} = {I_i}{t_i}$ is the exposure dose on the PR surface at z = 0. In general, the generated pattern profile is mainly determined by the exposure dose distribution in the PR layer. In previous work, it was proved that dose modulation function (DMF) needs to be larger than or equal to the critical modulation transfer function (CMTF) to meet the patterning condition in plasmonic lithography [17,44]. DMF is defined as $\textrm{DMF} = ({{\textrm{D}_{\textrm{max}}} - {\textrm{D}_{\textrm{min}}}} )/({{\textrm{D}_{\textrm{max}}} + {\textrm{D}_{\textrm{min}}}} )$, where Dmax and Dmin represent the maximum and minimum intensity, respectively. The CMTF is defined using the PR contrast γ as $\textrm{CMTF} = ({{\textrm{e}^{1/\mathrm{\gamma }}} - 1} )/({{\textrm{e}^{1/\mathrm{\gamma }}} + 1} )$, where $\mathrm{\gamma } = \textrm{ln}{({{\textrm{E}_\textrm{c}}/{\textrm{E}_{\textrm{th}}}} )^{ - 1}}$. By comparing the DMF to the CMTF for the evanescent field distribution, we can theoretically calculate the maximum depth at variant half pitch. For a conventional plasmonic lithography system the exposure depth can be derived as $\textrm{z} \cong \frac{\textrm{a}}{\textrm{b}}\left\{ {{{\left( {\frac{{1 + \textrm{DMF}}}{{1 - \textrm{DMF}}}} \right)}^\textrm{b}} - 1} \right\}$. Then, the pattern depth generated by the HPW structure can be extracted from the follow formula,
3. Results and discussion
3.1 Achievable resolution in plasmonic lithography
Typically, the spot size of the near-field distribution generated by a plasmonic BNA is the most important feature of plasmonic lithography, because it indicates the capability of high density nanopatterning. In plasmonic lithography with a scanning plasmonic BNA, resolution down to approximately 14 nm has been theoretically demonstrated [45]. However, because the image contrast of the high-resolution pattern is below 0.1, which can’t satisfy the minimum requirement for PR, and this resolution is hard to be further improved [18]. To further demonstrate the property of the HPW mode, we will estimate the achievable resolution of plasmonic lithography.
In general, the achievable resolution of plasmonic lithography is decided by two factors: the transmitted field distribution and the image contrast. A sufficient image contrast $\ge 0.1$ is required for PR to generate patterns with high quality, and it can be defined as $\textrm{M}({z,r} )= {I_{max}}(z )- I({z,r} )/{I_{max}}(z )+ I({z,r} )$, where z is the distance from the exit of plasmonic BNA, r is the radial coordinate, ${I_{max}}(z )$ is the maximum intensity in the plane, and I(z, r) is the appropriate intensity where the image contrast needs to be calculated. By calculating the resolution values at a different exposure depth where the image contrast equals 0.1, we can obtain the achievable resolution at different exposure depth in the PR layer for the two patterning systems, as illustrated in Fig. 3(a). Considering the asymmetrical field distribution determined by the plasmonic BNA, we evaluated the achievable resolution along the x- and y-directions with a gap size of 14 nm, respectively. Obviously, the plasmonic lithography with HPW structure can achieve a higher resolution than that with a single PR layer, which indicate the light transmitted from the plasmonic BNA propagates perpendicular to the xy-plane with low divergence angle benefit from the HPW mode, and also imply that achievable resolution of the plasmonic lithography with HPW structure can go beyond 10 nm. More importantly, for a conventional plasmonic lithography patterning system, the electric field distribution is strongly affected by the SPWs confined within the BNA along the x-direction, leading to the achievable resolution in the x-direction is higher than that in the y-direction. On the contrary, the plasmonic lithography with HPW structure has a higher achievable resolution in the y-direction, in addition, unlike the achievable resolution of a single PR patterning system varies greatly with changes in the exposure depth, the achievable resolution of HPW patterning system becomes stable after a propagation distance, mainly because of the HPW structure can induce a strong coupling effect between the SPWs and plasmonic waveguide, and thereby change the effect of the asymmetrical field decay characteristic on the exposure dose distribution in the PR layer.
Fig. 3. The achievable resolution of the plasmonic lithography with two patterning systems. (a) Achievable resolution as a function of exposure depth along the horizontal (solid squares) and vertical directions (dotted squares), the single PR patterning system (black lines) and the HPW structure (red lines). (b) Transmission as a function of incident wavelength at the top and bottom surface of the PR layer.
To verify this further, we investigate the transmission spectral resonance of HPW structure. As shown in the Fig. 3(b), the transmission spectrum of the HPW is dominated by the Fabry-Pérot (F-P) like resonance and plasmonic waveguide resonance [24,46]. As the exposure depth increases, the transmission efficiency of the plasmonic waveguide mode is drastically reduced, while the transmission efficiency of the F-P like resonance remains is less sensitive. This is due to the fact that the HPW structure can incorporate the PR layer into a plasmonic waveguide mode to couple to the SPWs at the two interfaces of the PR layer, allowing a single high-k mode in the PR layer and producing a uniform field distribution over the entire depth of the PR layer, which is crucial to the elongation of the aspect profile for plasmonic lithography. However, it is notable that because of the strong confinement of the SPWs in the HPW structure, the generated pattern uniformity is still sensitive to the PR thickness.
3.2 Improvement of depth-of-field in plasmonic lithography
Since the high confinement of SPWs and the exponential decaying of the featured evanescent component in the PR layer, the photoenergy is mainly located at the interfaces of the PR layer, resulting in that the uniform patterns were only acquired for PR layers with a small thickness. As a result, increasing the depth-of-field is critical to plasmonic lithography. For validating the possibility of high depth-of-field in HPW, the electric field distributions in PR layer of two plasmonic lithography system are quantitatively analyzed in Fig. 4(a) and (b), respectively. It can be seen from the figure that, the field distribution of conventional structure is longitudinally asymmetric, but the field distribution with HPW structure (Fig. 4(b)) becomes more symmetry which can improve the pattern quality. We define local contrast $\gamma (z )\equiv {I_1}(z )/{I_0}(z )$ along the z-direction of the PR layer, and global contrast $\Gamma = \min ({{I_1}} )/\max ({{I_0}} )$ over the whole patterning domain $0 \le \textrm{z} \le \textrm{pattern\; depth}.$ An alternative measure of contrast is visibility $V = {{({\Gamma - 1} )} / {({\Gamma + 1} )}},$ and the depth-of-field D is given by the distance over which $V > 0$ [37], as shown in Fig. 4(c). For the conventional plasmonic lithography, its intrinsic property of evanescent decay results in competition between the global contrast and depth-of-field. However, the HPW structure is a very effective way to improve the trade-off between these two important metrics, as shown in Fig. 4(d). Unlike a single PR layer, in which the decaying feature of evanescent waves inevitably cause the pattern with a shallow profile, the sandwiched PR layer of HPW can significantly enhance the aspect profile of plasmonic lithography. The reason is because of the appropriate interference between the forward and reflected SPWs in PR layer, which can effectively compensate the evanescent field decaying features. Thereby, the electric field distribution in PR layer is magnified and further modulated, and then significantly enhance the depth-of-focus.
Fig. 4. Cross-section of the electric field intensity distribution in the PR layer with no Ag reflect layer (a) and with Ag reflect layer (b). The medial longitudinal profiles and as marked in (a) and (b) are shown in (c) and (d), respectively. The limited depth-of-field D is indicated in (c).
3.3 Comparison of the generated pattern quality in the two plasmonic lithography patterning systems
Although SPWs can be used in plasmonic lithography directly, generated pattern with high uniformity and high aspect ratio is difficult to be realized. Therefore, we design a HPW structure to excite strong coupling between SPWs and waveguide modes. The physical understanding of pattern quality improvement could be indicated by analyzing the field distribution inside the PR layer. We then investigated the performance of the HPW in plasmonic lithography by evaluating the pattern quality of line array patterns. The electric field intensity distribution in the PR layer for a line array pattern is depicted in Fig. 5(a). The field distribution shows that the SPWs are excited at the top and bottom surfaces of PR layer. The forward- and backward-propagating SPWs in the PR layer interfere with each other, and consequently pattern profiles with high uniformity and high contrast are clearly observed in the PR. Figure 5(b) presents the electric field intensity distribution in PR layer of conventional plasmonic lithography system. It can be seen that the intensity of the interference image along the z-direction degrades, and the uniformity is also decreased. This is because the SPWs cannot be excited at the bottom surface of PR layer without the Ag reflect film, the electric field intensity carrying fine features information cannot be reflectively amplified in the longitudinal direction throughout the PR layer. Figure 5(c) and (d) show the field intensity distribution at the top, middle, and bottom lines in the PR layer corresponding to the plasmonic lithography with HPW structure and a single PR layer, respectively. It is worth to note that the half-pitch (HP) resolutions of these 3 curves in HPW structure are almost identical, which are 20.5 nm, 21.5 nm, and 20.5 nm, respectively. In addition, the image contrasts defined by $({{I_{max}} - {I_{min}}} )/({I_{max}} + {I_{min}})$ of these 3 lines are 0.98, 0.93, and 0.96, respectively. Interestingly, the maximum field intensity in the PR layer becomes higher than the incident light, which further confirms the field enhancement effects by the strong coupling strategy between SPWs and plasmonic waveguide modes. The high field intensity and image contrast in the PR layer ensure the exposure stability in the patterning process. On the contrary, in the conventional structure, not only the resolution and intensity are both decreased but also the image becomes blurred. As a result, it is not suitable for the application that requires features with high aspect ratios.
Fig. 5. Electric field distribution in the PR layer corresponding to (a) the HPW structure and (b) the conventional structure, respectively. Electric field intensities at 3 positions of z=0 nm, z=10 nm and z=20 nm in the PR layer corresponding to (c) the HPW structure and (d) the conventional structure, respectively.
The electric field intensity distribution in the PR layer can be assumed to be the exposure dose distribution, because the exposure time is maintained uniformly during the whole patterning process. In plasmonic lithography, PR is sensitive to the total field intensity which scales with the square of the near-field. Therefore, sufficient DMF is required to the expose areas for recording patterns with good quality. The calculated DMF curves for the plasmonic lithography system with two PR recording structures are depicted in Fig. 6(a). The higher DMF can be obtained with the HPW mode, and the DMF decreases gradually as the half pitch decreases from 30 nm to 7 nm. The high DMF of plasmonic lithography with HPW structure can ensure the stable performance in the patterning process and the generated pattern with good fidelity. To further demonstrate the advantages of the HPW structure, we also plot the aspect ratio for various half pitches in Fig. 6 to compare the theoretical model of maximum pattern depth with the simulation. The blue dotted line and blue diamonds in Fig. 6(b) show the obtainable aspect ratio of the conventional plasmonic lithography. Since the decaying character of the featured spectra, the aspect ratio is decreasing with feature size reducing. The black solid line and red squares theoretically indicate plasmonic lithography with HPW structure could improve the aspect ratio in contrast to single PR structure as shown in Fig. 6(d). According to the agreement between the calculated aspect ratio and simulation results, the aspect profile enhancement with HPW structure in plasmonic lithography is rigorously validated both analytically and numerically.
Fig. 6. (a) DMF curves as a function of half pitch of the line array pattern. Simulation results (red circles) and fitting data (black solid line) are plotted by the HPW structure, and simulation results (blue triangles) and fitting data (blue dotted line) are plotted by the conventional structure. (b) Aspect ratio curves as a function of half pitch of the line array pattern. Simulation results (red squares) and fitting data (black solid line) are plotted by the HPW structure, and simulation results (blue diamonds) and fitting data (blue dotted line) are plotted by the conventional structure.
3.4 Achievement of the high spatial frequency selection in HPW patterning system
In order to deeply study the property of pattern depth enhancement and the spatial frequency selection in plasmonic lithography with HPW structure, we quantitatively analyze the normalized intensity distribution in the PR layer and the dispersion relation in the HPW structure. For a comparison, the normalized intensity map in the PR layer of the single PR layer patterning system with a 20 nm thick PR is shown in the Fig. 7(a), and the normalized intensity maps in the PR layer of the HPW patterning system are given in Fig. 7(b) for PR with a 20 nm thickness and in Fig. 7(c) for PR with a 40 nm thickness. The normalized intensity at the center of the plasmonic BNA along the z-direction in the PR layer corresponding to the Fig. 7(a), b, and c are plotted in Fig. 7(d). Clearly the electric field intensity in the HPW structure can be significantly enhanced, and it is sensitive to the PR thickness. As mentioned above, to achieve high aspect ratio feature, the effective index ${n_{eff}}$ of the HPW can be adjusted to satisfy the phase matching condition, by optimizing the thickness of PR. The effective index ${n_{eff}}$ of the HPW mode as a function of the PR thickness is given in Fig. 7(e). The effective index of the HPW mode decreases as the PR thickness varies from 10 to 50 nm, and comes close to the effective index of the single PR structure. The SPW wavevector ${k_{spp}}$ of the single PR structure is ${k_{spp}} = {k_0}\sqrt {{\varepsilon _m}{\varepsilon _d}/{\varepsilon _m} + {\varepsilon _d}} $ [47], $\textrm{Re}({{\textrm{k}_{\textrm{spp}}}} )$ equals to 3.73k0. These results verify the spatial frequency selection characteristic of the HPW structure, and indicate that such a HPW mode design in plasmonic lithography can be used to expose a PR of different thickness, and thereby generating patterns in PR with the desired aspect ratio features, which is useful for practical applications.
Fig. 7. (a) Normalized intensity map in the PR layer of the conventional plasmonic lithography for a 20 nm thick PR. Normalized intensity map in the PR layer of the plasmonic lithography with HPW structure corresponding to the PR thickness (b) ${d_1} = 20\; nm$ and (c)${d_1} = 40\; nm$. (d) The intensity distribution as a function of exposure depth. (e) Dispersion relation in the HPW mode, the effective index of the two patterning systems dependent on the PR thickness. The gap size of the plasmonic BNA in the two patterning systems is $\textrm{g} = 30\; nm$.
To gain a better insight of the nature of the spatial frequency filtering characteristics of the HPW structure, the distribution of the electric field components in the PR layer is analyzed with gap sizes varying from 5 to 40 nm [48]. The total intensity distribution on the xz-plane is ${I_{total}} = {|{{E_x} + {E_z}} |^2},$ where Ex and Ez are the x and z components of the electric field, respectively. Due to the natural phase shift between the ${|{{E_x}} |^2}$ and ${|{{E_z}} |^2}$ for high-k evanescent waves, if the ratio between them goes to 1, blurred pattern will be recorded in the PR layer [49]. Therefore, a high ratio between ${|{{E_x}} |^2}$ and ${|{{E_z}} |^2}$ is desired to generate an aerial image with good contrast [23,27,50,51]. Because the dominance and distribution of ${|{{E_x}} |^2}$ and ${|{{E_z}} |^2}$ components are different in the two patterning systems, the component ${|{{E_x}} |^2}$ dominates the imaging area for the single PR patterning layer, while the component ${|{{E_z}} |^2}$ is dominant in the PR layer for the HPW structure [27,29]. Thus, as shown in Fig. 8(c), we calculate the ratio of ${|{{E_x}} |^2}/{|{{E_z}} |^2}$ and ${|{{E_z}} |^2}/{|{{E_x}} |^2}$ for the two patterning systems with various gap sizes, respectively. For a single PR patterning system, a larger ratio of the ${|{{E_x}} |^2}/{|{{E_z}} |^2}$ can be obtained with decreasing the gap size, which is mainly determined by the gap-size-dependent field-coupling effect in the conventional plasmonic lithography. However, for the HPW structure, the ratio of ${|{{E_z}} |^2}/{|{{E_x}} |^2}$ can be greatly improved with decreasing the gap size, thus yielding the enhancement of the patterning resolution and aspect ratio. The physical understanding of this phenomenon can be explained as follows. For the HPW structure, at the interface between the PR layer and the Ag reflector film, the ${|{{E_x}} |^2}$ component of the reflected SPWs has a π phase shift, whereas the ${|{{E_z}} |^2}$ component of the reflected SPWs has no phase shift. Therefore, the interference between the forward SPWs and the reflected SPWs in the PR layer is nearly destructive for the ${|{{E_x}} |^2}$ component and constructive for the ${|{{E_z}} |^2}$ component. As a result, ultrahigh resolution patterns can be generated in the PR layer by the HPW structure with a relatively high image contrast.
Fig. 8. Normalized intensity maps in the PR layer of the plasmonic lithography with HPW structure corresponding to the gap size (a) g=20 nm and (b) g=10 nm. (c) Calculated ratio of ${|{{E_x}} |^2}/{|{{E_z}} |^2}$ as a function of the gap size of plasmonic BNA in a single PR patterning system, and the calculated ratio of ${|{{E_z}} |^2}/{|{{E_x}} |^2}$ as a function of the gap size of plasmonic BNA in HPW patterning system. The inset shows the geometry of the plasmonic BNA.
4. Conclusions
In summary, we have numerically demonstrated that the half-pitch resolution of the generated patterns by plasmonic lithography can achieve sub-20 nm with high aspect ratio. This is achieved by employing a HPW structure through antisymmetric coupled SPWs and plasmonic waveguide modes in the PR layer. The HPW structure is based on the spatial frequency filtering characteristics of evanescent waves, so that high-k mode can be selected, which results in the generated pattern with high quality. An image PSF, which is mainly determined by the evanescent mode of SPWs, is employed to quantitatively analyze the effect of the decaying feature of SPWs on the exposure depth. Significantly, the hyperbolic decaying characteristic of SPWs is numerically proved to contribute greatly to the patterning process in plasmonic lithography, with considerably improve the achievable resolution, depth-of-field, line array pattern profile, DMF, and aspect ratio in comparison with a single PR patterning structure. Furthermore, simulation results show that the wavevector of SPWs is changed with the PR thickness and the ratio of ${|{{E_z}} |^2}/{|{{E_x}} |^2}$ is improved with decreasing the gap size, thereby, these two effects deliver the aspect ratio enhancement in the plasmonic lithography patterning system. We expect that the configuration of HPW structure will be helpful in solving the low imaging contrast and poor pattern profile problems encountered in the plasmonic nanofocusing, near-field lithography etc.
Funding
University of Chinese Academy of Sciences (118900M032).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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