1. Introduction

It is wildly known that the resolution of conventional lens system is diffraction limited [1]. This resolution limit occurs because the evanescent waves that carry the fine features of objects decay exponentially in natural medium and make no contribution to the image plane. However, the diffraction limit could be overcome by a deliberately designed lens capable of amplifying evanescent waves. This concept is firstly proposed by J. B. Pendry, who has theoretically predicted that a slab of negative index material n = −1 [2] could amplify evanescent waves and achieve sub-diffraction-limited resolution. However, it is difficult to simultaneously achieve negative permittivity and permeability at the optical frequencies. In the electrostatic limit, noble metal film with negative permittivity could regenerate evanescent waves and form superlening effect by the excitation of surface plasmons at interfaces between the metal and dielectric [3,4]. In 2005, the superlens lithography with half-pitch resolution of one-sixth of the illumination wavelength [5] has been reported by a 35 nm-thick silver film and 365 nm illuminating wavelength. In 2011, the half-pitch resolution is further improved to 30 nm by thinner and ultra-smooth silver film fabrication [6]. In practice, the resolution of superlens is constrained by the loss of metal slab [7,8], permittivity mismatch between the metal and dielectrics [9–11] and surface roughness and thickness of metal film. However, it is a great challenge to further improve the resolution of superlens on the basis of those proven designs.

In this paper, PSM for superlens lithography is specially designed and optimized for resolution enhancement. In conventional lithography, Levenson et al suggested that phase-shifting mask (PSM) [12,13] could improve the spatial resolution. PSM induces pi-phase shift between neighboring apertures by different dielectric materials filled. But this method does not function well for nanometer-scale mask. It is difficult to achieve π phase retardation by different dielectric filler. Furthermore, for nano-scale slits, the amplitude transmittance of slits heavily depends on filler in slits. Here, we firstly investigate noble metal as one of the material filler. In contrast to dielectrics filler, phase retardation in silver filled slit shows different behavior due to its negative permittivity at ultraviolet frequency. Furthermore, the amplitude transmittance also matches for two 30 nm-wide slits filled by silver and PMMA, respectively. FDTD simulations are carried out and the results illustrate that deep subwavelength objects can be resolved whereas they are undistinguishable without PSM.

2. Principle

For the transmission mask and coherent light illumination, Fig. 1(b) represents that the constructive interference between the diffracted light by the neighboring apertures degrades the resolution of imaging for same phase retardation. If one aperture has been filled by a transparent dielectric layer with a refractive index of n and a thickness of h = λ/2(n-1) (λ is illumination wavelength) and the neighboring aperture is filled by air, they would deliver reversed phase retardation. As shown in Fig. 1(c), the contrast and spatial resolution are greatly improved because of the destructive interference between waves from two neighboring apertures. Following the principle of PSM, we aim to induce a pi-phase shift into two nano-scale slits by different materials filler.

 

Fig. 1 (a) Schematic of superlens with a silver cladding. (b) Imaging process for a transmission mask. (c) Imaging process for a phase-shifting mask.

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Figure 1(a) shows the schematics of superlens lithography. For a TM plane incident light with λ = 365 nm, the superlens can transmit both propagating and evanescent components of the light from the slits and form sub-diffraction image in the photoresist. If the center-to-center distance between the two slits is too close, the images could overlap and be undistinguishable because of the constructive interference between two slits in the photoresist, as depicted in Fig. 1(b). On the other hand, if the phase retardation difference between the two slits is π, they are distinguishable because of the destructive interference between them, as shown in Fig. 1(c).

3. PSM design for superlens

In our PSM design for superlens, the permittivities of silver and photoresist are −2.4012 + 0.2488i [14] and 2.6 [5] at the illumination wavelength λ = 365nm. As illustrated in Fig. 1(a), two slits with width w and center-to-center distance d are perforated on a 50 nm-thick opaque chromium film (ε _Cr = −8.55 + 8.96i). Then a 40 nm-thick object spacer of PMMA (ε _PMMA = 2.3014 + 0.0014i) layer is deposited under the chrome layer. Below the PMMA, there are a 35-nm-thick silver film and a 30-nm-thick photoresist layer. A silver reflection layer is coated beneath the 30 nm photoresist layer in order to improve the superlens performance [15].

Usually, the propagation of light in nano slit can be considered as the eigen mode propagation of surface plasmons and approximate theoretical calculation can be made [16]. However, this method may not be applied for PSM here. First, the contribution of high order modes could not be ignored as the waveguide length (50nm-thick chromium) is not large enough. Second, the phase change of light happened at the entrance and exit of slit cannot be neglected as well due to the complicated coupling process between incident light and multiple waveguide modes. Third, the superlens and silver film beneath photoresist layer would also add complexity to the light transmission and coupling process in the superlens lithography structure, which is hard to theoretically analyze phase shift in slit. So the promising way for evaluating the phase shift and amplitude of transmitted light through nano slits is full wave numerical simulation of electromagnetic wave, like FDTD.

Hereafter, we firstly investigate the dependence of phase shift and transmittance of electric intensity for single chromium slit on different materials filler and slit width. Figure 2(a) and 2(b) show the dependence of transmittance of electric intensity and the phase shift for slit width ranging from 25nm to 60nm, respectively.

 

Fig. 2 (a) Normalized transmittance of electric intensity in a sole slit superlens structure, T corresponds to peak maximum of electric intensity on the image plane, normalized by the electric intensity in free space. (b) The phase shift in slit is defined as the phase difference between the object plane (upper opening chromium film) and image plane. The refractive index of aluminum nitride (AlN) is 2.19 + 0.011i [17] at working wavelength of 365 nm. The image plane is defined at 10 nm beneath silver/photoresist interface.

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Several conclusions can be drawn from simulation results in Fig. 2. First, for a fixed width of slit filled by dielectric, the transmittance of electric intensity heavily depends on the slit filler. It is difficult to achieve π phase shift between two silts filled by small refractive index difference, whereas the transmittance of electric intensity of two slits is approximately matched in this case. It is possible to achieve higher phase shift by increasing the index difference between the filling materials. However, it would result in greatly unmatched transmittance of electric intensity between two slits. Second, we can note the silver filler slit has different behavior from dielectric filler slit. The extraordinary optical transmission can be seen in Fig. 2(a) [18]. As seen in Fig. 2(b), the phase shift in slit induced by silver filled is quite different from that of dielectrics filled. Specifically, when two slits are filled by PMMA and silver, respectively, the pi-phase shift and matched transmittance of electric intensity could be satisfied with slit width w ranging from 25 nm to 35 nm. In Fig. 2(a), the transmittance of electric intensity of two 30-nm-wide silver-filled and PMMA-filled slits is perfectly matched while their phase shift is approximate to π. This suggests that two 30-nm-wide slits separately filled by silver and PMMA could be used for PSM design.

In addition, it is also worth to discuss possible solutions for the fabrication of PSM. For instance, we can drill slits on chromium film and inducing deposition of SiO₂ (ε _PMMA~ε _SiO2) in some slits by FIB, then the unoccupied slits are filled with silver by electron deposition. In the final step, the structure is polished to get a planar form.

4. Simulation and results of PSM imaging

We apply the PSM technique to superlens structure. FDTD simulations are carried out for the object of two 30 nm-wide slits, center-to-center distance d ranging from 35 nm to 90 nm. The red curves showed in Fig. 3(a) –3(c) are the normalized |E|² distribution on the image plane in same phase case with two slit filled by air. The distance of two slits in Fig. 3(a)–3(c) is 40 nm, 60nm and 80 nm, respectively. As shown in Fig. 3(c), the images of two slits with same phase can be clearly resolved when the distance d = 80 nm, which is large enough. Furthermore, in Fig. 3(a) and 3(b), the image of two slits gradually becomes blurry with d decreasing to 60 nm, and they can’t be distinguished when further decreasing to 40 nm.

 

Fig. 3 Normalized |E|² distribution on image plane for center-to-center distance of (a) d = 40 nm, (b) d = 60 nm, (c) d = 80 nm. Fields distribution of (a) to (c) is normalized by the peak maximum. Two virtual sources which are abbreviated as v/s are fixed on the upper openings mask, with |H _y| = 1 but reversed phase. The distributions of simulated electric intensity in (d) to (f), (g) to (i) and (j) to (l) are corresponding to same phase, PSM design based on slits filled materials and virtual sources illumination on the upper opening mask, respectively. The scale bar in (d) to (l) is 100 nm.

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In contrast, the green curves are those in reversed phase case, which means two slits are filled by PMMA and silver, respectively. The images of two slits could be clearly resolved even though d = 40 nm, which is vividly represented by the green curves in Fig. 3(a)–3(c). To further demonstrate the role of PSM, two virtual sources with π phase shift is incident on two air filled slits. The black curves are the |E|² distribution by virtual sources illumination. The black curves are similar to the green curves of reversed phase case. From the corresponding simulation results in Fig. 3(g) to 3(l), it is demonstrated that introducing pi-phase shift greatly improves the resolution of superlens by PSM design or introducing virtual sources illumination.

5. Discussion

5.1 PSM in superlens lithography for general patterns

The above simulations are focused on two slits super lens imaging lithography. Hereafter, we concentrate on multi-slits imaging. As can be seen in Fig. 4(a) and 4(d), the images of four 30 nm-wide slits with variant distance of 50 nm, 60 nm and 70 nm cannot be resolved because of the constructive interference between neighboring slits. When the pi-phase shift is alternatively induced based on different materials filled or virtual sources illumination, the images of four slits can be clearly resolved, as shown in Fig. 4(b) and 4(d) and Fig. 4(c) and 4(f).

 

Fig. 4 Four slits with center-to-center distance d = 50, 60, 70 nm from left to right. (a) to (c) are the normalized |E|² distribution on image plane. The distributions of simulated electric field intensity in (d), (e) and (f) are corresponding to same phase, reversed phase and alternative virtual sources illumination, respectively. The scale bar in (d) to (f) is 100 nm.

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In above simulations, it is demonstrated that the resolution of closely spaced grating-like pattern is enhanced by PSM design. As for a general case of arbitrary pattern, the simple phase shifting manner presented in this paper would not yield great resolution enhancement. Researches of phase shifting technology in conventional lithography would give some helpful guidance for this problem. Generally, complicated design and optimization of phase shifting mask are required for arbitrary pattern in lithography [19,20]. It is believed that those methods would work in superlens lithography as well, but much more complicated work is required as well due to the coupling of electromagnetic wave in the near field of subwavelength structures.

To see the potential adjacent slits influence for PSM effect, Fig. 5 shows the phase shift and transmittance of electric intensity for two adjacent slits with distance d ranging from 35 nm to 90 nm. The approximate pi-phase shift effect holds for variant d and amplitude transmittance of two slits change in similar manner. This gives rise to the PSM and enhancement of resolution for variant slits patterns, as can be seen in Fig. 4. It is also revealed that the behavior of pi-phase shift is greatly localized around the slit region, which can be attributed to the coupling and imaging of evanescent light between the two sides of superlens. It is helpful to understand this by comparing to microwave transmission anti resonance of compound grating, where lights from slits in unit cell are coupled together and form super modes with opposite phase between adjacent slits [21].

 

Fig. 5 Phase shift (P/S) and normalized transmittance of electric intensity versus center-to-center distance d ranging from 35 nm to 90 nm.

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5.2 Limitation of resolution enhancement by superlens and PSM

It is worth to note that the phase shifting method would not work for object which is unknown in prior. The enhancement of resolution arises from the phase engineering of objects, rather than the optimization of superlens design. So this method is particularly applied in lithography, optical storage, light trapping and manipulation, in which the desired patterns at the image plane are always predefined.

In order to gain a deeper understanding, we can investigate the parameter of intensity contrast, defined as V = (|E|² _max-|E|² _min)/(|E|² _max + |E|² _min), which reveals the spatial resolution and image fidelity. The object of two slits are supposed to be resolved when the minimum contrast requirement V = 0.2 is satisfied for common negative photoresist [22]. In Fig. 6(a) , the red circle curve represents that the image intensity contrast decreases with d without PSM design, while it can’t be resolved at d = 60 nm. The black square and green star curves are the reversed phase case and virtual sources illumination. The spatial resolution has been greatly improved because of the destructive interference in the photoresist. Furthermore, the image fidelity has also been significantly enhanced when pi-phase shift are induced, as shown in Fig. 6(b). However, the contrast of images drops quickly for d below 45nm and false images of slits would occur as d decreasing below 35nm. This can be well understood that the finite range of spatial frequency spectrum is transferred by the 35-nm thick silver slab. However, the resolution can be further improved by thinner silver film combining PSM.

 

Fig. 6 Dependence of image intensity contrast on center-to-center distance d at the image plane (10 nm beneath silver/photoresist interface). (b) Dependence of image intensity contrast on depth position inside photoresist with d = 60 nm. The top and bottom inset are the images of four slits with d = 50 nm and d = 30 nm, respectively.

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6. Conclusions

In conclusion, we have developed the PSM method for improving the resolution of superlens. Compared to the transmission mask, the π phase difference between two 30-nm-width slits is induced based on PMMA and Ag filled. The destructive interference between two slits minimizes the electric field intensity on image plane. The resolution of superlens has been greatly improved to center-to-center distance d = 35 nm, compared to 60 nm without the aid of PSM for representative super lens configurations. This method is believed to have greatly applications in nanolithography, biosening and optical storage etc.