Deep subwavelength interference lithography with tunable pattern period based on bulk plasmon polaritons

Hongchao Liu; Weijie Kong; Kaipeng Liu; Chengwei Zhao; Wenjuan Du; Changtao Wang; Ling Liu; Ping Gao; Mingbo Pu; Xiangang Luo

doi:10.1364/OE.25.020511

1. Introduction

Laser interference lithography enables fabrication of the large area periodic tunable features with two or more dimensions that can find potential applications in gratings [1], nanodot arrays based sensors [2,3] and photonic crystals [4,5]. However, the theoretic resolution of laser interference lithography is about λ/4, which suffers from the diffraction limit. In order to obtain smaller features, deep ultraviolet (DUV) [6] and extreme ultraviolet (EUV) lithography [7,8] by using much shorter wavelengths has been developed, while the expensive laser setups and complex processing hinders theirs applications.

Recently, plasmonic lithography, which based on surface plasmon polariton (SPP) exited at the interface between the metal and dielectric films, has been demonstrated to break the diffraction limit [9–15]. The main reason is the wavelength of SPP is much smaller than that of the excitation light [16,17]. Meanwhile, the most studied subwavelength imaging system is based on Ag film, which has been approved to greatly enhance the near-field intensity compared to the ordinary material [18]. In 2004, silver grating with 300 nm period was used to form interference lines with 100 nm period through SPP excitation at a wavelength of 436 nm [19]. Further, SPP interference lithography in metal-dielectric-metal structures is extended to 193 nm DUV illumination light and demonstrated to push sub-diffraction resolution beyond 22 nm in simulations [20]. Yet, these SPP interference lithography approaches suffer from the low aspect ratio owing to the shallow penetrating depth of SPP waves. In order to solve this issue, recently, periodic patterns (122 nm) with high aspect ratios (2:1) were proposed by a special mask and photoresist system to select a single high spatial frequency mode, and incorporating with a waveguide configuration [21]. But, the critical feature size of SPP excitation structures of above SPP interference lithography are usually in the same nanodimention as that of the interference patterns, which diminish the advantages of the low cost and high resolution for SPP interference lithography. Lately, the multilayer structure has been proved to transform the scatter light with evanescent character into a far field light with propagating character far beyond the diffraction limit, which promotes the application in super resolution lithography [22–24]. Since the hyperbolic metamaterials (HMM), composed of alternate metal-dielectric films, support bulk plasmon polaritons (BPPs) modes with high transmitted wave vector [24,25], the BPPs interference lithography with 45 nm half-pitch, about 1/8 of the excitation grating, were experimental achieved by using 5 pairs of SiO₂/Al multifilms [26]. However, due to the fixed surface wave mode excited by given structure, almost all the experimental efforts were unable to form patterns with flexible tunable period. The interference of evanescent waves excited by the pyramid-shaped prism provide interesting way in obtain 1D and 2D subwavelength imaging [27].

In this paper, the BPPs interference lithography is proposed to generate one-dimensional (1D) and two-dimensional (2D) sub-diffraction-limit patterns with tunable pattern period. And the imaging contrast is larger than the sensitivity threshold (0.4) of positive photoresist (PR). Therefore, the generated patterns could be recorded in the PR layer. According to the diffraction equation, the transmitted wave vector of the symmetrical BPP modes, employed to form periodic interference patterns, can be continuously changed by adjusting the incident light angle. As a result, at the symmetric illumination of 436 nm wavelength, the pitch of the patterns can be continuously tuned from 45 nm (~λ/10) to 115 nm (~λ/4). Furthermore, the general method and crucial influence factors when designing such an interference lithography system were also investigated. In contrast to the aforementioned SPP interference methods, this technique has the ability of continuously adjusting the period of patterns by simple altering the incident light angle. It is one promising technique in lithography and can promote the applications of BPPs interference lithography.

2. Principle and design of BPPs interference structure

Figure 1 presents the pattern period tunable interference lithography system based on BPPs using HMM. A couple of symmetrical plane wave with 436 nm wavelength in transverse magnetic (TM) polarization with electric field perpendicular to the grating line impinges on the Al grating from the fused silica substrate side at the same incident angles, between the incident light and the normal plane. A thin dielectric spacer composed of TiO₂ underneath the grating can enhance the coupling between the diffraction grating and the HMM [3], and thus improve the intensity of BPPs modes. Beneath the spacer is the HMM composed of alternately stacked 5 pairs Ag (30 nm)/SiO₂ (35 nm) films, followed by 30 nm photoresist (PR) layer and 70 nm Al film, which acts as reflector for improving the imaging contrast [28]. At this wavelength of 436 nm, the dielectric constants of Al, Ag, TiO₂ and SiO₂ are −18.5868 + 6.4345i, −6.0598 + 0.1970i, 7.9, 2.16, respectively [29]. The measured dielectric constant of PR is 2.74.

Fig. 1 Schematic of pattern period tunable BPPs interference lithography.

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According to the effective medium theory (EMT) [30], the HMM system can regarded as anisotropic dielectric, followed by

ε_{∥} = f * ε_{m} + (1 - f) * ε_{d},

ε_{⊥} = ε_{m} ε_{d} / [(1 - f) * ε_{m} + f * ε_{d}],

where, f is the fill factor of metal, ε_m and ε_d are permittivity of metal and dielectric, respectively. ε_‖ and ε_⊥ represent the components of effective dielectric permittivity parallel and perpendicular to the x axis, respectively. Consequently, the tensors of effective dielectric permittivity calculated by EMT are ε_‖ = −7.41 + 2.97i and ε_⊥ = 4.41 + 1.15i for multifilms described in Fig. 1. The dispersion relation for TM and TE polarization light inside the multifilms can be written as

(k_{x}^{2} + k_{y}^{2}) / ε_{z} + k_{z}^{2} / ε_{x} = k_{0}^{2}

and

k_{x}^{2} + k_{y}^{2} + k_{z}^{2} = ε_{x} k_{0}^{2}

, respectively. For TM polarization, ε_x and ε_z have opposite sign, the equi-frequency contour (EFC) surface shows a cylindrical hyperbolic profile in k_x-k_y or k_x-k_z planes as depicted in Fig. 2(a), which means only the light with large transverse vector can propagate through it. The TE polarization light will be restrained by the mutifilms owing to the negative sign of ε_x. Figure 2(b) exhibits the optical transmission function (OTF) of the HMM, having the pass-band characteristic for the light wave, and calculated by rigorous coupled wave analysis (RCWA) [31].

Fig. 2 (a) 3D plot of EFC surface (b) and OTF respectively calculated by EMT and RCWA for HMM system defined in Fig. 1. OTF plots in logarithm scale as function of (c) unit thickness h-pair, (d) the metal film thickness h-metal, (e) fill factor of metal f (f) and the dielectric film thickness h-die for 5 pairs Ag/SiO₂ films.

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Under the illumination of TM polarization light, different orders of diffraction waves are excited according to the diffraction equation given by

k_{x} = n k_{0} \sin θ + 2 π m / Λ, (m = 0, \pm 1, \pm 2......) .

Here, n is the refractive index of incident dielectric, θ represents the incident angle, Λ is the period of excited grating, m is the diffraction order. k_x and k₀ are the transmitted transverse and incident wave vectors, respectively. As illustrated in Fig. 2(b), the ± 1st orders of diffraction light approximately locate at the low cut-off wave vector (|k_L|) of OTF pass-band by adopting suitable grating period under normal incidence. The peaks in the dash circle indicate the existence of surface modes. With the increment of incident angle, the absolute value of the wave vector of −1st order of diffraction wave would increase, as a result, it could be transmitted through HMM and the + 1st diffraction order of wave is inhibited at the same time. On the contrary, when considering the + 1st diffraction order wave as the transmitted wave, the direction of incident light should be switched to mirror symmetric direction relative to normal surface. Under this condition, the + 1st diffraction light is coupled effectively to the exit surface through HMM, while the −1st diffraction order wave is screened out. It should be noted that the incident angle should be confined from 0 degree to |arcsin((|k_H|-2π/Λ)/n/k₀)| degree and both ± 1st diffraction orders will be inhibited beyond this range due to the limited pass-band of OTF. When a couple of symmetrical plane light illuminate this structure, the ± 1st diffraction orders waves, selected by the HMM system, will form interference patterns in the PR layer.

On the other hand, the initial position of ± 1st diffraction orders can lay at the high cut-off wave vector (|k_H|) of OTF passband by employing corresponding grating period under normal incidence condition. Here, the ± 1st orders diffraction light could penetrate into the HMM as the result of the decrease of absolute value of transmitted transverse wave vectors, by increasing the incident angle. Combined with both situations, the wave vector of ± 1st diffraction orders light can be tuned from |k_L| to |k_H|. The B_w (B_w = |k_H|-|k_L|) should be confined to (|k _{± 2}|-|k _{± 1}|)/2 in order to avoid the interference of ± 2nd and 0th diffraction orders, which may enter the passband window with the increment of incident angle.

Variant films thicknesses were considered in order to analyze the position and pass-band of the OTF window. Figure 2(c) shows the cut-off wave vector k_H of the OTF window can be greatly extended by lessening the SiO₂/Ag unit thickness, while the transverse wave vector k_L keeping small shift at given metal fill factor as f = 0.65. On the contrary, the change of fill factor of metal can apparently shift the lower boundary k_L and the OTF window can transform to low-pass band (white dashed line) from band-pass (white solid line) band as illustrated in Fig. 2(d). Furthermore, the pass-band range will greatly extend as the thickness of metal decrease in Fig. 2(e). Additionally, Fig. 2(f) depicts that the transmitted wave vector of the BPPs modes would increase by decreasing the thickness of dielectric layer. Meanwhile, the bandwidth of passband almost keeps fixed for different dielectric thickness marked by the white and black arrowed line. Since the wave vector of the BPPs modes launching by the HMM system lie in the passband of the OTF windows, that feature provides the flexibility in designing them, which is crucial for obtaining continually altered wave vector in the achievement of deep subwavelength interference lithography with tunable pattern period.

The modulation action of unit numbers on the pass band and the nonuniformity of the interference patterns should also be considered. Figure 3(a) presents the OTF in logarithm scale for different pair numbers, in which the black solid line shows the isolines of OTF. Although, the pass band is wider for layer pairs less than 3, waves with small wave vector like 0th diffraction orders light will introduced to damage the uniformity of the interference pattern, which could be approved in Fig. 3(b). With the increment of layer pairs, the intensity of interference pattern will be reduced owing to the decreasing amplitude of OTF. Meanwhile, the pass band of OTF is almost holding unchanged and will hardly alter the range of pitch regulation. Furthermore, the nonuniformity (defined in section 3) of interference patterns at 5 or more unit pairs are far below 0.2. Herein, considering the good inhabitation of low wave vectors, sufficient amplitude and width of OTF pass band, 5 pairs Ag/SiO₂ multifilms were chosen.

Fig. 3 (a) OTF plots in logarithm scale as function of number of SiO₂/Ag (15nm/30nm) pairs. (b) Nonuniformity of the interference patterns for variant incident angles with 3, 5 and 7 units.

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3. BPPs interference lithography with tunable pattern period

The calculated OTFs for 5 pairs SiO₂/Ag films with different dielectric film thickness of 35 nm and 15 nm, and the same Ag film (30 nm) are defined as OTF1 and OTF2 in Fig. 4(a), respectively. And the passband of the OTFs range about from 1.9k₀ to 3.4k₀ and from 3.4k₀ to 4.8k₀. From the Fig. 4(b) and 4(c) obtained from Bloch model [24,32], one can conclude that the OTF takes the form of filtering window, in which the BPP modes supported by the HMM have nearly zero imaginary part of k_z, indicating that BPP propagate without significant loss. And light modes beyond the ranges would be greatly inhibited. It is worthy to note that the BPPs modes show propagation behavior in the bulk space of multiple films system and decay exponentially outside, which formed by the mutual coupling of plasmonic polaritons field between adjacent metal-dielectric film interfaces [33,34]. One can see that the upper boundaries of the OTF window coincide with that of the Bloch modes, but the lower boundaries do not agree with the k_x limit of Bloch modes. That can be explained by the surface modes excited at the two interfaces between the dielectric medium and the HMM.

Fig. 4 (a) OTF for 5 pairs Ag/SiO₂ films with variant SiO₂ thickness calculated by RCWA. (b) and (c) are real and imaginary part of k_z as a function of k_x calculated in Bloch theorem. (d) Amplitude transmission of different diffraction orders for variant incident angle with grating period of 190 nm (f) and of 130 nm in logarithm scale. (e) The amplitude transmission ratio of + 1st (g) and −1st diffraction order vary with incident angle corresponding to above situation.

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Figure 4(d) describes the amplitude transmission of different diffraction orders with grating period of 190 nm. The amplitude of + 1st diffraction order can be transmitted through the HMM, while the rest orders are restrained with the incident angle ranging from 0°-52°. Beyond this range, the amplitude transmission of −2nd diffraction order would exceed other orders, as the transverse wave vector -k_x larger than the -k_H with the increment of incident angle. The transmission window could also be defined by the ratio of amplitude transmission of required diffraction order larger than 0.5 as shown in Fig. 4(e).

Similarly, the initial ± 1st diffraction orders are close to the upper boundary ( ± |k_H|) of the OTF1 window by setting diffraction grating period with 130 nm and the corresponding amplitude transmission of diffraction orders is given in Fig. 4(f). Here, it presents all-pass property for −1st diffraction order varies with the incident angle as shown in Fig. 4(g). The amplitude transmission ratio of + 1st in Fig. 4(e) and −1st in Fig. 4(g) orders are defined as $A_{+ 1} / (A_{0}_{t h} + A_{\pm}_{1 s t} + A_{\pm 2 t h})$ and $A_{- 1} / (A_{0}_{t h} + A_{\pm}_{1 s t} + A_{\pm 2 t h})$ , respectively. Here, A_0th, A_1st and A_2nd represent the amplitude of 0th, ± 1st and ± 2nd orders of diffraction light.

Numerical methods of the RCWA for structure with 1D grating and the finite-difference time-domain method (FDTD) for configuration with 2D grating are performed to demonstrate the deep sub-wavelength BPPs interference lithography with tunable pattern period. Herein, the key physical quantities for lithography are defined as follows. The value of |E|²/|E₀|² is defined as the normalized optical intensity, where E₀ is the incident electric field intensity. The imaging contrast is defined as $({| E_{\max} |}^{2} - {| E_{\min} |}^{2}) / ({| E_{\max} |}^{2} + {| E_{\min} |}^{2})$ . The nonuniformity factor of interference pattern is defined as $Δ I_{p e a k} / {\bar{I}}_{p e a k}$ , where $Δ I_{p e a k}$ is the max difference among the light intensity peaks of the interference patterns, ${\bar{I}}_{p e a k}$ is the mean value of those peaks.

Firstly, we demonstrate BPPs interference lithography with 1D periodic tunable pattern. The period of 1D grating, with 60% duty cycle, is 130 nm for OTF1. Here, the wave vector of BPP modes adopted in this structure can be continuous altered by changing the incident angle. Consequently, the period of interference patterns exhibit as the function of incident angle. The theoretical pitch value is given by

P_{u} = (λ / (2 * (m λ / p - n \sin θ))),

P_{l} = (λ / (2 * (m λ / p + n \sin θ))),

where m is the diffraction order, p presents the period of grating, λ and θ are the wavelength and angle of incident light, respectively. The two equations are applied for the instances that the required diffraction orders located at the upper and lower boundary of the OTF, respectively. Figure 5(a) and 5(e) depict the electric field intensity normalized by that under the normal incidence. The pitch resolution of the interference patterns can be tuned from 45 nm to 115 nm as shown in Fig. 5(b) and 5(f), which is in good agreement with the theoretical values denoted by the red dashed line. Almost all the image contrasts are larger than the minimum contrast (0.4) required for the positive photoresist in experiments as shown in Fig. 0.5(b) and 5(f). The uniformity of the interference patterns is mainly determined by the purity of ± 1st diffraction orders that penetrate through the HMM. Clearly, the appearance of unwanted −1st and 0th diffraction orders slightly damage the uniformity of those patterns around 0° and 85° as shown by blue solid line in Fig. 5(c) and 5(g). But all the nonuniformity factors are smaller than 0.2, which means the patterns in PR layer have little distortion. Moreover, the nonuniformity factor varies with the incident angle at an oscillation way, which is mainly related to the amplitude transmission fluctuation of diffraction light with HMM as shown in Fig. 5(c) and 5(g). The intensity of interference fringes depicted by red line in Fig. 5(c) and 5(g) have similar trend with the amplitude transmission of OTF in Fig. 2(a). Figure 5(d) and 5(h) shows the image contrast in the different depth of PR layer for variant incident angle. The parameters for 5 pairs Ag (30 nm)/SiO₂ (15 nm) films are similar to that of the 5 pairs Ag (30 nm)/SiO₂ (35 nm) films as depicted in Fig. 5(e)-5(h). Here, the grating period is set to 90 nm (60% duty cycle).

Fig. 5 RCWA simulations for OTF1 with 5 pairs Ag (30 nm)/SiO₂ (35 nm) films as follows: (a) electric field intensity normalized by that of the perpendicular incident light along the horizontal lines at the middle of PR layer for variant incident angles. (b) The image contrast, numerical and theoretical pitch (c) and intensity, nonuniformity for interference fringes as function of incident angle. (d) Imaging contrast distribution in the different depth of Pr layer for different incident angles. Similarly, (e)-(f) are corresponding to OTF2 with 5 pairs Ag (30 nm)/SiO₂ (15 nm) films.

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The transmission difference between the |E_z| the |E_x| plays the key role in BPPs interference lithography for high pattern contrast. In order to improve the contrast of interference pattern, Al reflector was introduced. It clearly shows the magnitude ratio |E_z|/|E_x| of the patterns for the interference lithography with Al reflector is greatly improved in contrast to that without Al reflector in Fig. 6(a). The PR layer sandwiched between the top Ag film and the bottom Al reflector forms a cavity. Due to the resonance coupling of the BPPs between the cavity walls, the field component |E_z| is greatly enhanced and longitudinal extended as depicted in Fig. 6(c). On the contrary, the electric component |E_z| decay dramatically in the PR layer for BPPs interference with bare SiO₂ substrate as depicted in Fig. 6(d). Benefiting from the inhibition of |E_x| component, the pattern contrasts were remarkably enhanced and shows similar trend with the magnitude ratio |E_z|/|E_x| as shown in Fig. 6(b).

Fig. 6 (a) The amplitude ratio between |E_z| and |Ex| in logarithm scale for BPPs interference lithography with and without Al reflector as function of incident angles. (b) The pattern contrast corresponding to above mentioned BPPs interference lithography. (c) Electric intensity distribution of |E_x|², |E_z|² and |E_x|² + |E_z|² without Al reflector and (d) with Al reflector.

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Combing the multiple symmetrical illumination and 2D grating, we can easily generate 2D periodic tunable pattern. The sketch of 2D structure with HMM and grating is shown in Fig. 7(a). The principle for 2D periodic tunable lithography is similar to that of the 1D case. The period of 2D dots array grating in square grids is 130 nm and 90 nm for two structures above mentioned. Here, the ± 1st diffraction orders are approximately locate at the positions of (0, 3.4k0), (0, -3.4k0), (3.4k0, 0) and (-3.4k0, 0), which are the max absolute values of cut-off wave vector of kx and ky while ky = 0 and kx = 0, respectively, as described in Fig. 7(c). By adjusting the incident angle, these four diffraction orders excited by two couples of TM light can be transmitted. The angles between TM incident light with the x, y axis are defined as α and β, respectively.

Fig. 7 Schematic for periodic tunable BPPs interference lithography with 2D grating. (b) Square grating for BPPs excitation. (c) The position of diffraction light orders and optical transmission amplitude band for 5 pairs Ag (30nm) /SiO₂ (35 nm) films.

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Normalized electric field intensity distributions (3 × 3 periods at 0°, 40° and 85°) in the x-y plane at the middle of the PR layer for given incident angles are exhibited in Fig. 8(a)-8(c) and Fig. 8(e)-8(g) for configurations of 5 pairs Ag (30 nm)/SiO₂ films with different dielectric film thickness of 30 nm and 15 nm, respectively. It can be seen that the 2D interference array dots with pitch resolution ranging from 65 nm to 115 nm and from 45 nm to 65 nm are produced for BPPs interference lithography with above structures. The contrast increases until the peak value around 50° and slightly decreases with the increase of incident angle, as shown in Fig. 8(d), while the contrast in Fig. 8(h) increases among the entire incident angle range from 0°-85°. The simulated period of the interference array dots increase and agree well with the theoretical values described by red dashed line from 0°-85° in both Fig. 8(d) and 8(h).

Fig. 8 Structure with 5 pairs Ag (30 nm)/SiO₂ (35 nm) films. (a) Normalized electric field intensity distributions (3 × 3 periods) in the xy plane at 0°, (b) 40° (c) and 85°. (d) The image contrast, numerical and theoretical pitch resolution of the interference array dots for variant incident angle. The same in (e)–(h) for structure with 5 pairs Ag (30 nm)/SiO₂ (15 nm).

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Additionally, 2D interference array dots with different period along x, y direction are also generated. The periods of the 2D array dots are P_x in the x direction and P_y in the y direction. Since the wave vector |k_x| and |k_y| is no more equal induced by the different incident angle for two couples of TM light, the period in x and y direction can be altered independently. Now, the incident light angle α is not equal to β, there exists the intensity difference according to the amplitude distribution of the OTF, which can be solved by adjusting the exposure time in experiment. Here, the field intensities under two couples of TM polarization light should be normalized first before the overlay of them. Then, the normalized electric field intensity distributions corresponding to over mentioned cases (3 × 3 periods) added together as shown in Fig. 9. For configuration with 5 pairs Ag (30 nm)/SiO₂ (35 nm) films, the period along x, y direction can be flexibly adjusted from 65 nm to 115 nm, by simply changing the incident angle from 0° to 85°. Here, only three cases with 65 × 65 nm, 95 × 65 nm and 115 × 65 nm are exhibited in Fig. 9.

Fig. 9 Normalized electric field intensity distributions (3 × 3 periods) in the middle of the PR layer on the x-y plane for 2D array dots with period of (a) 65 × 65 nm, (b) 90 × 65 nm (c) and 115 × 65 nm in x and y direction, while under the incident light angle in x direction of 0°, 40°, and 85°, respectively.

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4. Conclusion

In conclusion, we designed and proved deep subwavelength interference lithography with tunable pattern period based on BPPs. And the BPPs is engineered to hold suitable range of transmitted transverse wave vector by optimizing the geometrical parameters of Ag/SiO₂ films, enabling the period adjustment of interference pattern based on the continuous spatial frequency selection of BPPs mode. This proposed approach overcomes the major drawback where the period of interference pattern cannot be flexibly altered for given structure in previous plasmonic lithography. The periodic patterns with pitch resolution ranging from 45 nm to 115 nm have been numerically demonstrated under 436 nm illumination. Moreover, the pitch resolution with different periods of square array dots along x, y direction has also been presented. Our findings open up an avenue for period tunable plasmonic lithography and broaden its application in the flexible fabrication of nano-scale patterns.

Funding

973 Program of China (2013CBA01700); National Natural Science Foundation of China (NSFC) (61575202, 61175204).

References and links

1. N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu, and C. H. Lin, “Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique,” Opt. Express 13(23), 9605–9611 (2005). [CrossRef] [PubMed]

2. X. Zhang, X. Ma, F. Dou, P. Zhao, and H. Liu, “A Biosensor Based on Metallic Photonic Crystals for the Detection of Specific Bioreactions,” Adv. Funct. Mater. 21(22), 4219–4227 (2011). [CrossRef]

3. K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016). [CrossRef] [PubMed]

4. M. Miyake, Y. Chen, P. V. Braun, and P. Wiltzius, “Fabrication of Three ‐ Dimensional Photonic Crystals Using Multibeam Interference Lithography and Electrodeposition,” Adv. Mater. 21(29), 3012–3015 (2009). [CrossRef]

5. I. B. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, “Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography,” Appl. Phys. Lett. 82(11), 1667–1669 (2003). [CrossRef]

6. J. A. Hoffnagle, W. D. Hinsberg, M. I. Sanchez, and F. A. Houle, “Liquid immersion deep-ultraviolet interferometric lithography,” J. Vac. Sci. Technol. B 17(6), 3306–3309 (1999). [CrossRef]

7. C. Wagner and N. Harned, “EUV lithography: Lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010). [CrossRef]

8. K. Kemp and S. Wurm, “EUV lithography,” C. R. Phys. 7(8), 875–886 (2006). [CrossRef]

9. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]

10. C. H. Chang, Y. Zhao, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 50 nm period gratings with multilevel interference lithography,” Opt. Lett. 33(14), 1572–1574 (2008). [CrossRef] [PubMed]

11. X. Guo, J. Du, Y. Guo, and J. Yao, “Large-area surface-plasmon polariton interference lithography,” Opt. Lett. 31(17), 2613–2615 (2006). [CrossRef] [PubMed]

12. F. Yang, X. Chen, E. Cho, C. S. Lee, P. Jin, and L. J. Guo, “Period reduction lithography in normal UV range with surface plasmon polaritons interference and hyperbolic metamaterial multilayer structure,” Appl. Phys. Express 8(6), 062004 (2015). [CrossRef]

13. K. V. Sreekanth and V. M. Murukeshan, “Large-area maskless surface plasmon interference for one- and two-dimensional periodic nanoscale feature patterning,” J. Opt. Soc. Am. A 27(1), 95–99 (2010). [CrossRef] [PubMed]

14. P. Mehrotra, C. A. Mack, and R. J. Blaikie, “A detailed study of resonance-assisted evanescent interference lithography to create high aspect ratio, super-resolved structures,” Opt. Express 21(11), 13710–13725 (2013). [CrossRef] [PubMed]

15. P. Gao, N. Yao, C. Wang, Z. Zhao, Y. Luo, Y. Wang, G. Gao, K. Liu, C. Zhao, and X. Luo, “Enhancing aspect profile of half-pitch 32 nm and 22 nm lithography with plasmonic cavity lens,” Appl. Phys. Lett. 106(9), 093110 (2015). [CrossRef]

16. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005). [CrossRef] [PubMed]

17. X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58(9), 594201 (2015). [CrossRef]

18. W. Liu, C. Y. Wen, K. Chen, W. C. Lin, and D. P. Tsai, “Near-field images of the AgOx-type super-resolution near-field structure,” Appl. Phys. Lett. 78(6), 685–687 (2001). [CrossRef]

19. J. Dong, J. Liu, P. Liu, J. Liu, X. Zhao, G. Kang, J. Xie, and Y. Wang, “Surface plasmon interference lithography with a surface relief metal grating,” Opt. Commun. 288, 122–126 (2013). [CrossRef]

20. J. Dong, J. Liu, G. Kang, J. Xie, and Y. Wang, “Pushing the resolution of photolithography down to 15nm by surface plasmon interference,” Sci. Rep. 4(1), 5618 (2015). [CrossRef] [PubMed]

21. X. Chen, F. Yang, C. Zhang, J. Zhou, and L. J. Guo, “Large-Area High Aspect Ratio Plasmonic Interference Lithography Utilizing a Single High-k Mode,” ACS Nano 10(4), 4039–4045 (2016). [CrossRef] [PubMed]

22. T. Fukaya, D. Buchel, S. Shinbori, J. Tominaga, N. Atoda, D. P. Tsai, and W. C. Lin, “Micro-optical nonlinearity of a silver oxide layer,” J. Appl. Phys. 89(11), 6139–6144 (2001). [CrossRef]

23. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

24. B. Wood, J. B. Pendry, and D. Tsai, “Directed sub-wavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]

25. I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly Confined Optical Modes in Nanoscale Metal-Dielectric Multilayers,” Phys. Rev. B 75(24), 241402 (2007). [CrossRef]

26. G. Liang, C. Wang, Z. Zhao, Y. Wang, N. Yao, P. Gao, Y. Luo, G. Gao, Q. Zhao, and X. Luo, “Squeezing Bulk Plasmon Polaritons through Hyperbolic Metamaterials for Large Area Deep Subwavelength Interference Lithography,” Adv. Optical Mater. 3(9), 1248–1256 (2015). [CrossRef]

27. C.-S. Lin, C.-F. Yu, H.-W. Liu, N. H. Lu, H.-P. Chiang, and D. P. Tsai, “Near-field imaging of the interactions of evanescent fields,” Scanning 26(5), I47–I51 (2004). [PubMed]

28. C. Wang, P. Gao, Z. Zhao, N. Yao, Y. Wang, L. Liu, K. Liu, and X. Luo, “Deep sub-wavelength imaging lithography by a reflective plasmonic slab,” Opt. Express 21(18), 20683–20691 (2013). [CrossRef] [PubMed]

29. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

30. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

31. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981). [CrossRef]

32. J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006). [CrossRef] [PubMed]

33. K. V. Sreekanth, A. De Luca, and G. Strangi, “Experimental demonstration of surface and bulk plasmon polaritons in hypergratings,” Sci. Rep. 3(1), 3291 (2013). [CrossRef] [PubMed]

34. Y. Xiong, Z. Liu, and X. Zhang, “Projecting Deep-Subwavelength Patterns from Diffraction-Limited Masks Using Metal-Dielectric Multilayers,” Appl. Phys. Lett. 93(11), 111116 (2008). [CrossRef]

Deep subwavelength interference lithography with tunable pattern period based on bulk plasmon polaritons

Abstract

1. Introduction

2. Principle and design of BPPs interference structure

3. BPPs interference lithography with tunable pattern period

4. Conclusion

Funding

References and links

Cited By

Figures (9)

Equations (5)

Optics Express