## Abstract

Plasmonic lens imaging with some resolution enhancement methods are investigated in this paper, mainly by physical modeling and numerical simulations. The imaging model is based on the refined optical transfer function with extra reflection in imaging space and measured in variant magnetic and electric field components. The influences of structured light illumination and mask patterns^{'} modifications are considered as well. As experimental demonstrations, L-shaped slits pattern with a half-pitch of 60 nm is successfully imaged with 50 nm air distance, by using plasmonic cavity lens lithography and off-axis illumination with 365 nm wavelength light. This study is believed to provide the model and methods for the design of high resolution plasmonic lens employed in nano lithography and optical storage etc.

© 2016 Optical Society of America

## 1. Introduction

Diffraction limit of resolution in conventional imaging optics hampers observing subwavelength details of specimens and fabricating nano patterns in optical lithography [1,2]. It is reasoned that evanescent waves carrying subwavelength informations of objects decay exponentially and make no contribution to imaging. Recently, perfect lens concept is proposed to achieve super resolution imaging [3], in which all of objects’ spectrum components could be homogeneously restored by a negative refactive index slab with evanescent wave amplification ability [4, 5]. In near field quasistatic case, a metal film with negative permmitivity could enable subwavelength imaging as well by exciting surface plasmon (SP) modes [6–15]. Using exposure recording scheme, a silver superlens is experimentally demonstrated to succeed in resolving dense lines with a half-pitch (hp) of 60 nm (~1/6 wavelength) [16]. The superlens imaging resolution and fidelity are practically influenced by many factors, such as light loss [17–21], surface roughness [22] and mismatch of permmitivty of metal film and media surrounding it [23–26]. To explore practical performance (resolution or image contrast) of SPs imaging, the inherent influences of the silver film (optical loss, surface roughness and film thickness etc) are investigated [27, 28]. Experimental studies of resolution and profile depth enhancement on basis of plasmonic lens fabrication and optimization are also demonstrated by utilizing ultra-smooth superlens [29–33], loss-reduction superlens [34, 35], plasmonic cavity lens etc [36–39]. These exciting achievements show remarkable advantages of high resolution, high throughput and cost effectiveness in realizing superresolution imaging nanolithography. Until now, feature size of plasmonic lithography is even extended up to hp 22 nm [40].

In spite of plasmonic lens optimization and fabrication, the issue of plasmonic lens contacting with mask patterns still remain a great concern for practical lithography application. The near field diffraction limit, which indicates that near field resolution is constrained by the near field air distance and ligth wavelength, greatly hampers the separation between plasmonic lens and nano mask patterns [41, 42]. Some methods to address the issue of poor plasmonic imaging quality in the case of separated manner would be desirable [41]. On the other hand, the present design and analysis of plasmonic lens are performed dominantly by some numerical calculation methods, like finite difference time domian (FDTD) [43, 44] and finite element method (FEM) [45, 46]. As for a given plasmonic lens, an interesting question arises as to how the plasmonic imaging process are theoretically described and how the imaging performance are further improved. In analogy to Fourier optics, the optical transfer function (*OTF*) of Fourier spatial components ${k}_{x}$ and point-spread function (PSF) have been used to theoretically evaluate superresolution imaging performance [47]. The reported studies mainly quantified resolution enhancement with the band width of *OTF*. In fact, the actual imaging quality is influenced by many other factors, including light illumination, mask pattern and contributions from variant electric field components, which are not fully considered in present investigations.

In this paper, a plasmonic imaging model is built and used to analyze imaging beyond the near field diffraction limit in multiple ways, like plasmonic cavity lens, off-axis illumination, phase shifting mask, etc. To evaluate the imaging performance, the transmitted electric field components of transverse (*E*_{x}) and longitudinal (*E*_{z}) are calculated in plasmonic cavity lens, which shows the *E*_{x} is enhanced and *E*_{z} is depressed after introducing a reflective Ag layer to traditional superlens. This leads to the result of the imaging resolution enhancement in plasmonic lens lithography. Additionally, the resolution enhancement in plasmonic lens lithography is further analyzed and demontrated both in theory and in experiment. It shows that surface plasmon wave engineering of wavevectors, phases, and amplitudes of variant electric field components helps to improve plasmonic lens imaging even beyond the near field diffraction limit. This study is believed to pave the way to theoretically analysis and design of plasmonic lens in nano lithography, optical storage, holograms, etc.

## 2. Methods

#### 2.1 Numerical simulations

Rigorous coupled wave analysis (RCWA) was applied to calculate the optical transfer functions shown in Fig. 2, the electric field intensity distributions shown in Figs. 3 and 4, and imaging intensity contrast shown in Fig. 6. The RCWA code was written based on the Eq. given in [48], Moharam et al . The electric field intensity distributions shown in Figs. 5(a) and 5(b) were simulated using a commercially available CST software.

#### 2.2 Fabrication, Exposure and Development procedures

Fabrication procedures for the plasmonic cavity lens and mask can be found in [37], Zhao et al. The substrate with Ag-Pr-Ag plasmonic cavity lens was physically contacted with the Cr mask with a spacer around pattern regions to generate fixed air gap and avoid abrasion in the lithography process. The high-NA illumination light (NA = 1.5) was excited by plane wave vertically impinging the upside-down isosceles trapeze sapphire prism under a 365 nm mercury lamp illuminating system. The exposure with uniform flux of 1.0 mW/cm^{2} and exposure time ranging from 10 s to 50 s were applied in the experiment. Before the developing process, the physical method was used to peel off the top Ag layer. After that, the substrate with photoresist was developed by the diluted AR 300-35 (ALLRESIST GMBH, Strausberg) with de-ionized water with a ratio of 1:1 for 40 s at temperature 0 °C. Scanning electron microscopy (SEM S-8010 HITACHI cool field emission) was used to characterize the topography of the lithography patterns. The samples were sputtered with several nanometers-thick Pt layer prior to imaging to reduce the charging effects.

## 3. Results and discussion

#### 3.1 Super resolution imaging model

Figure 1 shows the schematic diagram of plasmonic lens system with surface plasmon wavefront engineering. The lens system is composed of mask pattern, air spacer, top silver film, photo resist layer and bottom silver film. The air spacer ridge helps to avoid mask degradation in imaging lithography and requires super resolution beyond the diffraction limit. The mask patterns are illuminated by 365nm light wavelength at which the permittivity of silver and photo resist matches well, and could be projected into the cavity surrounded by the two silver layer.

A superresolution imaging model is proposed to analytically describe the plasmonic imaging process. It is assumed that the coupling interaction between plasmonic lens and mask is neglected to simplify the discussion, while this assumption may give rise to imperfect analyses, particularly when mask-lens interactions are strong [49]. According to the vectorial angular spectrum theory, the electric fields of images are then generally given as

In Eq. (1), the ${\tilde{E}}_{obj}({k}_{x},{k}_{y})$ = $\left[{\tilde{E}}_{x,obj},{\tilde{E}}_{y,obj},\frac{{k}_{x}{\tilde{E}}_{x,obj}+{k}_{y}{\tilde{E}}_{y,obj}}{-{k}_{z}}\right]$ are the E-field spectrums components of light transmitted through nano patterns, while $\text{G}({k}_{x},{k}_{y})$ and $\text{OTF}({k}_{x},{k}_{y})$ are the illumination function and optical transfer function of the plasmonic lens for different Fourier components, respectively. In this model, the OTF of plasmonic lens and contributions of wavefront engineering, including plasmonic reflection lens, plasmonic structured illumination and phase-shifting mask, are considered as well. In the next section, the effect of wavefront engineering would be detailedly discussed with plasmonic imaging enhancement demonstration.

#### 3.2 Plasmonic cavity lens

Figure 2(a) shows cross section structure of plasmonic cavity lens, which is composed of Ag-Pr-Ag films. To simplify the analysis and discussion, the nano patterns are assumed to be a one dimensional case with nano transparent slits on opaque film and illuminated by transversal magnetic polarization. In this case, the components in transversal electric polarization are not considered here as surface plasmons would not be excited, so the transverse magnetic fields dominate imaging. For TM polarized UV light illumination, the black curve in Fig. 2(a) schematically illustrates amplitude profile of *H _{y}* transmitted through the Ag superlens. In analogy to evanescent wave amplification in superlens, the objects’ featured spectrums could be further amplified due to the plasmonic reflection lens. In this case, the amplitude distribution of

*H*in plasmonic cavity lens imaging space includes the transmitted field (black curve) and multiple reflected field (red curve) as shown in Fig. 2(a). For incident plane wave with variant

_{y}*k*, the multi-reflection approximation

_{x}*OTF*of plasmonic cavity lens for different electromagnetic field components inside the photoresist is given by

In Eqs. (2)-(4), $t({k}_{x})$ is the *OTF* of top Ag superlens for ${H}_{y}$, while $t({k}_{x})\frac{{k}_{z,\mathrm{Pr}}{\epsilon}_{{\mathrm{SiO}}_{2}}}{{\epsilon}_{\mathrm{Pr}}{k}_{z,{\mathrm{SiO}}_{2}}}$ and $t({k}_{x})\frac{{\epsilon}_{{\mathrm{SiO}}_{2}}}{{\epsilon}_{\mathrm{Pr}}}$ are the *OTF* for ${E}_{x}$ and ${E}_{z}$, respectively. The second term in the brackets of Eqs. (2)-(4) should be eliminated during the *OTF* calculation of superlens despite of reflection amplification. However, the multi-reflection coefficients of ${r}_{x(z)}({k}_{x})=\frac{{r}_{\text{Ag}}({k}_{x}){e}^{i{k}_{z,\mathrm{Pr}}{d}_{\mathrm{Pr}}}({e}^{-i{k}_{z,\mathrm{Pr}}{d}_{\mathrm{Pr},1}}\mp {r}_{\text{SL}}({k}_{x}){e}^{i{k}_{z,\mathrm{Pr}}{d}_{\mathrm{Pr},1}})}{1-{r}_{\text{Ag}}({k}_{x}){r}_{\text{SL}}({k}_{x}){e}^{2i{k}_{z,\mathrm{Pr}}{d}_{\mathrm{Pr}}}}$ contribute to *OTF* modification of plasmonic cavity lens due to the Ag reflection lens. ${r}_{\text{Ag}}({k}_{x})=\frac{{\epsilon}_{\text{Ag}}{k}_{z,\mathrm{Pr}}-{\epsilon}_{\text{Pr}}{k}_{z,\text{Ag}}}{{\epsilon}_{\text{Ag}}{k}_{z,\mathrm{Pr}}+{\epsilon}_{\text{Pr}}{k}_{z,\text{Ag}}}$ and ${r}_{\text{SL}}({k}_{x})$ are the reflection coefficients of the Pr-Ag reflection lens interface and the Pr-Ag supelens-Air scheme, respectively. ${\epsilon}_{\text{Ag}}$ and ${\epsilon}_{\text{Pr}}$ are the permittivities of the Ag and photoresist layers, respectively. ${k}_{z,\text{Ag}}=\sqrt{{\epsilon}_{\text{Ag}}{k}_{0}^{2}-{k}_{x}^{2}}$ and ${k}_{z,\mathrm{Pr}}=\sqrt{{\epsilon}_{\mathrm{Pr}}{k}_{0}^{2}-{k}_{x}^{2}}$ are the longitudinal wave vector in the Ag and Pr layers, respectively. ${d}_{\mathrm{Pr}}$ is the photoresist thickness and ${d}_{\mathrm{Pr},1}$ is the selected depth position of observation line in photoresist. In the analytical expression of ${r}_{x(z)}({k}_{x})$, the subtraction and plus signs in the bracket of numerator term correspond to the *OTF* for ${E}_{x}$ and ${E}_{z}$, respectively.

Numerical calculation is performed to investigate the *OTF* of superlens and plasmonic cavity lens by rigorous coupled wave analysis (RCWA) and multi-reflection approximation (Eqs. (2)-(4). The thickness of air, Ag superlens and photoresist layers are ${d}_{\text{Air}}=20nm$, ${d}_{\text{Ag}}=20nm$ and ${d}_{\mathrm{Pr}}=40nm$, respectively. The permittivities of Ag and Pr are $\text{-2}\text{.168+0}\text{.358i}$ and 2.59 at 365 nm wavelength, respectively. Figures 2(b)-2(d) give the calculated *OTF* of superlens and plasmonic cavity lens in depth direction of the photoresist ${d}_{\mathrm{Pr},1}=20nm$. For superlens, the black curve in Fig. 2(b) illustrates the *OTF* for ${H}_{y}$ ($\left|t({k}_{x})\right|$). The black curves in Figs. 2(c) and 2(d) are the *OTF* for ${E}_{x}$ ($\left|t({k}_{x})\frac{{k}_{z,\mathrm{Pr}}{\epsilon}_{{\mathrm{SiO}}_{2}}}{{\epsilon}_{\mathrm{Pr}}{k}_{z,{\mathrm{SiO}}_{2}}}\right|$) and ${E}_{z}$ ($\left|t({k}_{x})\frac{{\epsilon}_{{\mathrm{SiO}}_{2}}}{{\epsilon}_{\mathrm{Pr}}}\right|$), respectively. The amplitude magnifying for ${k}_{x}>{k}_{0}$ in Figs. 2(b)-2(d) represents subdiffraction spectrums transmission of the superlens, while the two peaks of black curves represent the resonant surface modes. As for the 70 nm thick Ag reflection lens scheme (thick enough as reflection mirror), the red dashed curves in Figs. 2(b)-2(d) illustrate the *OTF* of plasmonic cavity lens for ${H}_{y}$, ${E}_{x}$ and ${E}_{z}$ with Eqs. (2)-(4). The red dashed curves perfectly agree with the blue dotted curves through RCWA and the multi-reflection approximation is validated. Unlike transmission amplitude of superlens *OTF* for ${E}_{x}$ and ${E}_{z}$, the plasmonic cavity lens *OTF* of ${E}_{x}$ is enhanced and that of ${E}_{z}$ is depressed when ${k}_{x}<4{k}_{0}$. This phenomena could explain the reason of imaging enhancement with plasmonic reflection lens in Fig. 3.

For simplification, we just concentrate on the analytical plasmonic imaging discussion of two dimensional objects (infinite in *y*-direction). As discussed above in Eq. (1), the imaging field of the subwavelength objects are then represented by

*x*-direction and

*z*-direction electric field components of the objects, respectively. Numerical imaging comparisons are performed to testify the superresolution imaging model. The thickness and permittivity of Cr mask are 50 nm and $\text{-8}\text{.55+8}\text{.96i}$, while others geometry parameters and permittivities are maintained as the above mentioned

*OTF*calculation.

Figure 3 is the calculated E-field imaging intensity distribution of half-pitch 60 nm line-pair and dense lines with normal illumination superlens and plasmonic cavity lens. The normal illumination means plane wave incidence in the normal direction and $G({k}_{x})=1$, while the slits pattern object function for Ex is ${E}_{x}(x,0)={\displaystyle \sum _{n=-\infty}^{\infty}rect(\frac{x-2nw}{w})}$ and ${E}_{z}(x,0)={\displaystyle \sum _{n=-\infty}^{\infty}\widehat{F}\left\{\frac{-{k}_{x}w}{{k}_{z,{\mathrm{SiO}}_{2}}}\text{sinc}({k}_{x}w){\text{e}}^{-i{k}_{x}2nw}\right\}}$. $\widehat{F}$ is the Fourier transformation of Ex. $w=60nm$ is the slit width and n depicts the slit number. In Figs. 3(b) and 3(d), the superresolution imaging model well describes imaging results of half-pitch 60 nm line-pair and dense lines according to E-field intensity agreement with FEM simulations (red dashed and blue curves). As for plasmonic cavity lens imaging, the Ag cavity lens contributes to the imaging field tailoring of ${E}_{x}(x,z)$ and ${E}_{z}(x,z)$ in Eqs. (5) and (6). Compared to superlens imaging, the imaging contrast of the same patterns is significantly improved as shown in Figs. 3(f) and 3(h). In addition, the plasmonic cavity lens bring images with better position fidelity in comparison with the super lens, as could be seen in Figs. 3(b) and 3(f).

In superlens imaging of subwavelength objects, the transmitted field amplitude of $\left|{\tilde{E}}_{z}({k}_{x})\right|\propto \left|t({k}_{x}){k}_{x}\right|$ is comparable to that of $\left|{\tilde{E}}_{x}({k}_{x})\right|\propto \left|-t({k}_{x}){k}_{z,\mathrm{Pr}}\right|$ due to $\left|{k}_{x}\right|~\left|{k}_{z,\mathrm{Pr}}\right|$ for high evanescent waves, while ${\tilde{E}}_{z}({k}_{x})$ field shares $\pi /2$ phase difference from ${\tilde{E}}_{x}({k}_{x})$ field for ${k}_{x}>{k}_{0}$. In this case, the image quality could be blurred by the negative imaging contribution of ${E}_{z}$ intensity. For plasmonic cavity lens with sufficiently thin photoresist (${d}_{\mathrm{Pr}}=40nm$), the surface plasmons field coupling between two Ag-Pr interfaces with approximate mirror symmetry surface charges distributeion generates an anti-symmetric electromagnetic mode. This results in transmission field amplitude of $\left|{\tilde{E}}_{x}({k}_{x})\right|\propto \left|-t({k}_{x})(1-{r}_{x}({k}_{x}){e}^{i{k}_{z,\mathrm{Pr}}({d}_{\mathrm{Pr}}-{d}_{\mathrm{Pr},1})}){k}_{z,\mathrm{Pr}}\right|$ larger than $\left|{\tilde{E}}_{z}({k}_{x})\right|\propto \left|t({k}_{x})(1+{r}_{z}({k}_{x}){e}^{i{k}_{z,\mathrm{Pr}}({d}_{\mathrm{Pr}}-{d}_{\mathrm{Pr},1})}){k}_{x}\right|$, as can be justified from the OTF curves in Figs. 2(c) and 2(d). Thus, the negative imaging contribution of ${E}_{z}$ intensity is inhibited and feature information of ${E}_{x}$ intensity is relatively enhanced. This field tailoring effect by plasmonic cavity lens helps to improve image contrast and fidelity.

#### 3.3 Phase-shifting mask

In general, imaging contrast depends on the ratio of peak and valley intensity of two overlapping spots. As for normal light illumination, the constructive light interference and superposition between the neighboring slits with same phase difference may degrade the imaging contrast. This phenomena could be clearly seen from the blue curves in Fig. 4. With a phase-shifting mask design, the *π* phase shift between neighbouring slits is induced in the object fields of ${E}_{x}(x,0)$ in Eq. (5) and ${E}_{z}(x,0)$ in Eq. (6). For phase-shifting mask with *π* phase difference, the destructive interference between neighboring slits cancels the valley light intensity of two neighboring slits and contributes to the imaging contrast improvement. The red dashed curves in Fig. 4 show that the imaging resluts of different patterns are fully resolved and imaging contrast under phase-shifting mask is significantly improved. In addition, the improvement could be obtained significantly even for neighbouring slits with variant width 45 nm, 60 nm, 75 nm and 90 nm, as could be seen in Fig. 4(c).

#### 3.4 Plasmonic lens with structured light illumination

As discussed above, the plasmonic lens imaging usually requires the air distance between mask and plasmonic slab lens should be extremely small, such that the feature spectrums of subwavelength objects could be restored before damped vanishing. Provided that the object distance could be extended to tens of nanometers air distance, the issues of the scratch and abrasion of mask and challenge of air distance control are readily solved by non-contacted plasmonic lithography by introducing off axis illumination with high transversal wavevectors or numerical aperture (NA).

As demonstrative examples, plasmonic structured illumination $NA=1.5$ is utilized to replace the normal illumination $NA=0$, so the illumination function is $G({k}_{x})=\mathrm{exp}(i1.5{k}_{0}x)$. The previous feature spectrums ($0,\pm 3{k}_{0}$) of hp 60 nm objects under normal illumination are shifted to $\pm 1.5{k}_{0}$ and $4.5{k}_{0}$. Due to interference imaging of amplitude enhanced $-1.5{k}_{0}$ and $1.5{k}_{0}$ spectrums ($4.5{k}_{0}$could be ignored with much smaller magnitude), the numerical imaging result in Fig. 5(b) under *NA* = 1.5 quadrupole off axis illuminations is also clearly resolved and intensity contrast along the dashed line is 0.7 even at 50 nm air distance. In addition, the plasmonic structured illumination is also feasible for others half-pitch object with extended air distance. However, the control imaging result in Fig. 5(a) under normal illumination is nearly undistinguishable and intensity contrast is decreased to 0.35. Experimental demonstration of air distance extension is performed by plasmonic imaging of half-pitch 60 nm *L*-shaped dense lines under different illumination schemes. Figures 5(c) and 5(d) are the SEM pictures of 2D resist patterns with *NA* = 0 and 1.5 plasmonic structured illumination. The comparison of photoresist patterns in Figs. 5(c) and 5(d) demonstrates the effect of plasmonic structured illumination in enhancing plasmonic imaging performance.

To further investigate contrast and resolution enhancement of wavefront engineering in plasmonic imaging process, Fig. 6(a) illustrates superresolution imaging model calculated image contrast of different half-pitch objects ranging from 16 nm to 130 nm under NA = 0, 0.84 and 1.5 illumination plasmonic cavity lens. As for air distance ${d}_{\text{Air}}=20nm$, the resolution limit for NA = 0 (black curve) is about 55 nm by selecting image contrast criterion of 0.4, while the resolution limit is further improved to 40 nm for NA = 1.5 (red dashed curve). A higher resolution could be obtained by utilizing evanescent waves illumination with a larger NA. Moreover, the intensity contrast saturates at half-pitch beyond 90 nm regardless of NA. The reason for this fact is that the intensity contrast of such half-pitch patterns is large enough under normal illumination.

The imaging contrasts for grating lines pattern with 45 nm, 60 nm and 75 nm half pitch and off-axis light illumination with NA ranging from 0 to 2.5 are presented in Fig. 6(b). Clearly, optimum NA exists for fixed half pitch with relation NA~0.5*l /*d*, where *d* is period of grating pattern. For instance, for the feature size of 60 nm dense lines (green line), the imaging contrast grows steadily as NA increases from 0, and reaches the highest value for structured illumination with NA = 1.5, and drops in the nearly the same velocity after that. The reason for this feature is mainly related to the fact that two evanescent wave components with same absolute value of transverse wavevector and opposite signs are excited in the imaging space for this configuration, which helps to generate light interference with high contrast.

The black curve in Fig. 7 represents the dilemma between resolution and air distance in superlens imaging. That is, a higher resolution requires a smaller working distance. This brings the issues of engineering control and mask damage in operation. By adopting plasmonic cavity lens, the air distance depicted by blue dotted curve in Fig. 7 is slightly extended for half-pitch larger than 60 nm. As for half-pitch below it, the imaging contrast improvement could not compensate for the contrast decreased with air distance elongation due to the rapid decay of the featured spectrums. However, the red dashed curve in Fig. 7 illustrates that the air distance is significantly extended by plasmonic structured illumination with $NA={k}_{g}/2{k}_{0}$, while ${k}_{0}=2\pi /\lambda $ and ${k}_{g}=2\pi /\Lambda $ are the wave vectors of illumination light and objects. For example, both of the maximum air distance of superlens or plasmonic cavity lens under *NA* = 0 illumination are below 10 nm for 32 nm half pitch imaging, while the working distance with optimized $NA=2.85$ illumination exceeds 40 nm [38,39]. The illumination source with $NA=2.85$ could be implemented by exciting coupled bulk plasmon polaritons with Al-SiO_{2} hyperbolic metamaterial.

## 4. Conclusion

In conclusion, we have established a superresolution imaging model to describe the wavefront engineering in plasmonic lens imaging. It has been demonstrated that the imaging resolution and quality of a given plasmonic lens structure could be further improved by the surface plasmon wave front engineering, including wavevectors, phases, and amplitudes of variant electric field components, as demonstrated by numerical and experimental results. The plasmonic imaging enhancement with wavefront engineering technique is attributed to imaging field tailoring effect of plasmonic reflection lens or phase-shifting mask and wave vector shifting effect of plasmonic structured illumination. It is also demonstrated that the resolution and near-field object distance of plasmonic cavity lens are enhenced. This study makes plasmonic lens combined with wavefront engineering to be a cost-effective and promising method for nanolithography of hp 32 nm, 22 nm, and beyond.

## Funding

973 Program of China (No.2013CBA01700) and National Natural Science Funds (61138002, 61177013, 61575204).

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