Abstract

For the experiments of surface plasmon polaritons (SPPs) interference lithography based on attenuated total reflection-coupling mode to be done conveniently, we introduce a backside-exposure technique in this paper. The physical mechanisms of SPPs interference with the backside -exposure method are studied and the interference fringes with feature size below 65nm are experimentally obtained. The technique can be used to fabricate nanostructures conveniently with large area, and avoids the difficulties for seeking high refractive prism and matching fluid.

©2010 Optical Society of America

1. Introduction

Developing a convenient method to fabricate nanostructures in large-area with low cost has become a goal of the researchers in the area of micro-fabrication. At the beginning of this century, the contact evanescent wave interference lithography (EIL) [110] was proposed for the first time and then the nanostructures in large-area could be achieved. However, EIL has some limitations such as short transmission distance, shallow exposure depth and low contrast etc. all of which lead to a low efficiency in exposure and a difficulty in controlling the technique. Enhancement of local SPPs [11,12] provides a possibility to solve these problems and also improves the quality of the lithography patterns. In order to excite SPPs a method with metal masks [1319] is adopted. However, the metal masks have to be fabricated by other precise lithography techniques such as E-Beam writing [20] and focused ion beam writing [21,22] etc. which are time consuming and waste money. The maskless surface plasmon polaritons interference lithography (SPPIL) is proposed with attenuated total reflection (ATR) coupling mode that reduces the cost for fabricating nanostructures in large-area [23]. For this method, the silver film is plated on the surface of the prism and resist is coated on the quartz substrate. In the process of experiments, the resist and silver film should be contacted closely by vacsorb pump or matching fluid. So the surfaces of the silver and resist film used to be damaged or polluted and the thickness of the matching fluid is difficult to control. Moreover, the silver film is easy to be oxygenated due to it is exposed in air. In this paper, we present a method of backside-exposure maskless SPPIL, so that these problems can be avoided and SPPIL will be used more easily and conveniently. We analyze the process of backside-exposure SPPIL and obtain the interference fringes with feature size below 65nm experimentally. The research results will put the maskless SPPs interference lithography technique into practical application.

2. Theory and scheme design of backside-exposure SPPIL

Figure 1(a) is the schematic of the former reported maskless SPPIL [23] which contains two parts. One is the isosceles triangle or hemispherical prism with high refractive index coated with a thin silver film on its bottom surface and the other part is the resist coated on the substrate. These two separate parts are contacted closely during exposing, which will cause the damage and pollution to the silver and the resist.

 figure: Fig. 1

Fig. 1 Schematic of the maskless SPPIL with ATR structure. (a) Structure of prism-silver-resist-substrate. (b) Backside-exposure SPPIL structure: ε0, ε1, ε2 and ε3are the permittivity of the prism, silver, resist and air respectively; the thickness of the silver layer is d1 and that of resist is d2.

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The structure of the backside-exposure SPPIL is shown in Fig. 1(b) which composes a prism, matching fluid layer and glass substrate with dielectric constants of ε0, silver film withε1=ε1+jε1, resist layer with ε2 and air layer with ε3. When the thickness of the silver film and resist are finite, the dispersive relationship in the silver layer is different from that when the silver film is infinite. According to Maxwell equations and boundary conditions, the wave vectorksppcan be obtained which determines the resolution of SPPIL (Λ=2π/2kspp) and the enhancement factor Tspp which determines the exposure intensity and depth in the condition of surface plasmon resonance.Theksppcan be expressed as [24]:

kspp=kxhalfspace+kxphotoresist+kxmetal
Where, kxhalfspacedescribes the well known dispersion relationship of SPPs at the boundary of the silver halfspace and air halfspace, the second term (kxphotoresist) gives the influence of the resist to SPPs and it is considered in the third term (kxmetal) that the thickness of the silver film is finite. They can be written as follows:
kxhalfspace=(ω/c)[ε1ε3/(ε1+ε3)]1/2
kxphotoresist=(ω/c)[(ε2ε3)/ε2][ε1ε3/(ε1+ε3)]2[(ε2ε1)/(ε3ε1)](ε1ε3)1/2(2πd2/λ)+(ω/c)r01[2/(ε3ε1)][ε1ε3/(ε1+ε3)]3/2exp{2(2πd1/λ)[(ε1)/((ε1ε3)1/2)]}
Let kxpC=(ω/c)[(ε2ε3)/ε2](ε1ε3/(ε1+ε3)]2[(ε2ε1)/(ε3ε1)](ε1ε3)1/2(2πd2/λ)
And kxpR=(ω/c)r01[2/(ε3ε1)][ε1ε3/(ε1+ε3)]3/2exp{2(2πd1/λ)[ε1/(ε1ε3)1/2]}
Then,
kxmetal=kxpC{[kxpC/2/Re(kxhalfspace)][2(2ε32ε22)/ε3/(ε3ε2)+(ε1+ε3)/(ε3)]iε1/2/ε1}+kxpR{[kxpR/2/Re(kx(halfspace)][(2ε1+ε3)/(ε3)]jε1/(ε1ε3)}+kxpCkxpR/[Re(kxhalfspace)][ε1/ε3+2ε3/(ε3ε2)+ε2/2ε3]
Suppose the electric amplitude of the incident waves isE0 and that at the interface of the resist and air is|Et|=(Ex2+Ez2)1/2, thus the enhancement factor of excite SPPs can be defined as: Tspp=|Et/E0|

=ε0/ε3[(ε0/k0z+ε1/k1z)/(2ε0/k0z)][(A+Br01ejk1zd1)/(r23ejk2zd2+ejk1zd1)]
Here, A=[(ε1/k1z+ε2/k2z)/2ε1/k1z][(1+r12r23e2jk2zd2)/ejk1zd1],
B=Aejk1zd1+r23e2jk2zd2ejk1zd11;
rij=(kjz/εjkiz/εi)/(kjz/εj+kiz/εi), (i,j = 0,1,2,3); kiz=[εi(ω/c)2kx2]1/2.

To analyze how the thickness of the silver film and resist affect the surface plasmon resonant condition and the enhancement factor, we will discuss the process of backside-exposure SPPIL with Eqs. (1) and 2.

3. Simulation and analysis of backside-exposure SPPIL

The resonant condition of surface plasmon and resolution of interference patterns are varied with different thickness of the resist layer. For calculations, we select silver film with thickness 40nm and permittivityε1 = −8.92 + 0.233i at incident wavelength 441.6nm [23]. The refractive index of the prism made of dense flint is n = 1.89 (ε0=3.57) and K9 glass is n = 1.527(ε0=2.33). The resist is AR-P3170 with n = 1.53 (ε2=2.34) and the outside layer is air (ε31).

Figure 2(a) shows the relation betweenTspp, incident angle and the thickness of the resist layer (d2). Figure 2(a)(i) corresponds to the prism with high refractive index (n = 1.89) and (ii) corresponds to the low refractive index (n = 1.527). It shows that Tsppdecreases and the resonant angle increases with d2 increasing. In Fig. 2(a) (i), when d2 is larger than 100nm Tspp is very small and the resonant angle is almost the same and the resist layer can be regarded infinite. Figure 2 (a)(ii) shows a similar variation as (i), but the corresponding resonant angle is larger than that corresponding to (i) and the resist layer is not thicker than 60nm, otherwise, the resonant angle will be beyond 90°. Figure 2(a)(ii) also means that to the resist with finite thickness, prism with low refractive index can be used to excite SPPs for interference lithography, but the thickness of the resist layer and the incident angle should satisfy the resonant condition. Being different from the former SPPs interference lithography [23] which requires a high refractive prism to be used, a low refractive prism could also be used to excite SPPs by the backside-exposure SPPIL device.

 figure: Fig. 2

Fig. 2 (a) Tspp varies with d2 and incident angle: (i) n = 1.89 and(ii) n = 1.53. (b) Resolution of patterns varies with d2.

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The resolution is important to the lithography ant it can be written asΛ=2π/2ksppto the backside-exposure SPPIL structure, ksppis determined by Eq. (1). We draw the curves of resolution varying with the thickness of the resist layer as shown in Fig. 2(b). Curve i) corresponds to the prism with n = 1.89. With the thickness of the resist layer (d2) varies from 30nm to 100nm, the resolution decreases from 88nm to 64nm. And when d2 reaches a certain thickness the resolution does not change anymore, which is equivalent to the situation when the thickness of the resist layer is infinite. Curved ii)corresponds to the prism with n = 1.527. When d2 varies from 30nm to 70nm, the resolution decreases from 89nm to 69nm and when d2>70nm the enhancement of SPPs disappears.

From Fig. 2 it can be known that if a high refractive prism and a thicker resist layer used, the high resolution patterns can be achieved. But due to the limited transmission distance of SPPs it can pass through a resist layer only when it is thinner than 100nm. In this condition, the resolution of the patterns gotten by the backside-exposure SPPIL can reach 65nm. Based on the analysis above, we know that when a prism with high refractive index is used, the scheme of former exposure method [23] also can be used to achieve patterns with high resolution. However, the damage and pollution caused by this method cannot be avoided and due to the transmission distance of SPPs the lithography patterns are only formed at the surface of the resist layer which leads the resist difficult to be etched through. When a prism with low refractive index is used, the patterns with super resolution can be achieved with the maskless SPPIL method by adjusting the thickness of the resist layer. It should be noticed that when the resist is too thick, the prism with low refractive index cannot be used to satisfy the surface plasmon resonant condition. Thus, the thickness of the resist layer should be thinner than 60nm in the condition corresponding to Fig. 2(b). Due to the resist layer is very thin SPPs can pass through it easily which makes sure the whole resist layer to be exposed through. Thus, the backside-exposure method is proper for the maskless SPPs lithography.

We simulate and analysis the electric field interference with the thickness of the resist layer 50nm and the refractive index of prism 1.89 and 1.527 respectively. When the refractive index of prism is 1.89, the optimal incident angle is 52.3°. The amplitude distribution of the electric field in the resist is shown in Fig. 3(a) from which we can see that the transmission depth (T-D) of the SPPs is approximate 120nm [11]. The patterns in the resist are uniform and the period of the fringes is about 148nm (resolution is 72nm) which agrees with the calculation by Eq. (1).

 figure: Fig. 3

Fig. 3 Simulation result by FDTD, with incident wavelength 441.6nm, thickness of silver film 40nm, refractive index of resist 1.53 and thickness 50nm. (a) Electric field distribution when refractive index of the prism is 1.89. (b) Normalized amplitude of the electric field at the interface of the metal film and resist when the refractive index of the prism is 1.89 and 1.527 respectively.

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Prism with low refractive index(n = 1.527)can also be used to excite SPPs. Figure 3(b) shows the normalized amplitude of the electric field at the interface of the metal film and resist when the refraction of the prism is 1.89 and 1.527 respectively. To the prism with high refractive index the optimal matching angle is 52.2° and to the prism with low refractive index the optimal matching angle is 77°. In each condition the period of the interference fringes is 148nm. When using the prism with low refractive index, the amplitude and definition of the interference fringes are much the same as those gotten by using a prism with n = 1.89.

4. Experiment of backside-exposure SPPIL

Relevant experiment was developed based on the simulated results. The dense flint was used as the material of the prime and substrate, and thickness of the substrate was 2mm. The substrate was cleaned with ultrasonic washer for 20 minutes in alcohol and soaked in boiled concentrated sulfuric acid for 5 minutes to clean up the impurity on the surface, then it was dried at 80°C for 90 minutes in vacuum. After that, a 40 nm silver film was deposited on the substrate through electron beam evaporation. A 50nm layer of diluted resist (AR-P3170) was coated on the silver film. The refractive index of the matching fluid between the prism and substrate was n = 1.53. The resist was exposed with a laser of wavelength 441.6nm at the resonant angle. Then the periodical structure was obtained after development. Figure 4(a) is the SEM image of the patterns gotten by the backside-exposure SPPIL method. The period of the patterns is about 150 nm, which agrees with the theoretical value 148nm. Figure 4(b) shows the SPPIL experimental result when the material of the prime and substrate was k9 glass. The period is as same as that gotten by using a prism with high refractive prism.

 figure: Fig. 4

Fig. 4 The SEM imaging with period 150nm. (a) Prism with high refractive index, backside-exposure. (b) Prism with low refractive index, backside-exposure. (Time for exposure and development are 18s and 35s, respectively).

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When the backside-exposure method is used for SPPs interference lithography, fringes with high quality are easy to be obtained and the repeated experiments are also easy to do. In theory, prism with high refractive index can be used to achieve patterns with high resolution. But in experiment, matching fluid with high refractive index is hardly to find. Figure 4(a) shows that the scattering of light in the matching fluid layer lead to a low contrast of the lithography patterns, as the matching fluid with low refractive index does not match the high refractive prism and high refractive substrate well in backside-exposure SPPIL experiment. When a low refractive index prism and substrate is used, prism can match well with the matching fluid, so the better quality lithography patterns can be obtained easily, as shown in Fig. 4(b). It indicates that using prism and substrate with low refractive index for backside-exposure SPPIL is more practical and feasible.

5. Conclusions

The resolution of the nano-patterns fabricated with backside-exposure-maskless SPPIL can be adjusted by varying the thickness of the resist layer and the prism with low refractive index can be used to excite SPPs. This new SPPs interference structure not only avoids the difficulty of finding high refractive matching fluid but also prevents the damage and pollution caused by compactness. With this method it is feasible to produce large-area nanostructures at low cost which could promote the development of nanoscale machining farther more.

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No 60878031, the National Basic Research Program of China under Grant No 2006CD302902.

References and links

1. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999). [CrossRef]  

2. T. D. Milster, J. S. Jo, and K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38(23), 5046–5057 (1999). [CrossRef]  

3. B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994). [CrossRef]  

4. R. J. Blaikie and S. J. McNab, “Evanescent interferometric lithography,” Appl. Opt. 40(10), 1692–1698 (2001). [CrossRef]  

5. Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005). [CrossRef]  

6. J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A, Pure Appl. Opt. 8(4), 213–218 (2006). [CrossRef]  

7. J. K. Chua, V. M. Murukeshan, S. K. Tan, and Q. Y. Lin, “Four beams evanescent waves interference lithography for patterning of two dimensional features,” Opt. Express 15(6), 3437–3451 (2007). [CrossRef]   [PubMed]  

8. B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

9. Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007). [CrossRef]  

10. V. M. Murukeshan, J. K. Chua, S. K. Tan, and Q. Y. Lin, “Nano-scale three dimensional surface relief features using single exposure counterpropagating multiple evanescent waves interference phenomenon,” Opt. Express 16(18), 13857–13870 (2008). [CrossRef]   [PubMed]  

11. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

12. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]   [PubMed]  

13. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]  

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

15. D. B. Shao and S. C. Chen, “Numerical simulation of surface-plasmon-assisted nanolithography,” Opt. Express 13(18), 6964–6973 (2005). [CrossRef]   [PubMed]  

16. W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005). [CrossRef]  

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

18. D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005). [CrossRef]  

19. D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006). [CrossRef]   [PubMed]  

20. M. A. McCord, “Electron beam lithography for 0.13 µm manufacturing,” J. Vac. Sci. Technol. B 15(6), 2125–2129 (1997). [CrossRef]  

21. F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007). [CrossRef]  

22. J. Melngailis, “Focused ion beam lithography,” Nucl. Instrum. Methods Phys. Res. B 80, 1271–1280 (1993). [CrossRef]  

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

24. I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72(3), 577–588 (1978). [CrossRef]  

References

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  1. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
    [Crossref]
  2. T. D. Milster, J. S. Jo, and K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38(23), 5046–5057 (1999).
    [Crossref]
  3. B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
    [Crossref]
  4. R. J. Blaikie and S. J. McNab, “Evanescent interferometric lithography,” Appl. Opt. 40(10), 1692–1698 (2001).
    [Crossref]
  5. Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
    [Crossref]
  6. J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A, Pure Appl. Opt. 8(4), 213–218 (2006).
    [Crossref]
  7. J. K. Chua, V. M. Murukeshan, S. K. Tan, and Q. Y. Lin, “Four beams evanescent waves interference lithography for patterning of two dimensional features,” Opt. Express 15(6), 3437–3451 (2007).
    [Crossref] [PubMed]
  8. B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).
  9. Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
    [Crossref]
  10. V. M. Murukeshan, J. K. Chua, S. K. Tan, and Q. Y. Lin, “Nano-scale three dimensional surface relief features using single exposure counterpropagating multiple evanescent waves interference phenomenon,” Opt. Express 16(18), 13857–13870 (2008).
    [Crossref] [PubMed]
  11. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  12. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  13. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
    [Crossref]
  14. X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
    [Crossref]
  15. D. B. Shao and S. C. Chen, “Numerical simulation of surface-plasmon-assisted nanolithography,” Opt. Express 13(18), 6964–6973 (2005).
    [Crossref] [PubMed]
  16. W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
    [Crossref]
  17. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
    [Crossref] [PubMed]
  18. D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005).
    [Crossref]
  19. D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006).
    [Crossref] [PubMed]
  20. M. A. McCord, “Electron beam lithography for 0.13 µm manufacturing,” J. Vac. Sci. Technol. B 15(6), 2125–2129 (1997).
    [Crossref]
  21. F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
    [Crossref]
  22. J. Melngailis, “Focused ion beam lithography,” Nucl. Instrum. Methods Phys. Res. B 80, 1271–1280 (1993).
    [Crossref]
  23. X. W. Guo, J. L. Du, Y. K. Guo, and J. Yao, “Large-area surface-plasmon polariton interference lithography,” Opt. Lett. 31(17), 2613–2615 (2006).
    [Crossref] [PubMed]
  24. I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72(3), 577–588 (1978).
    [Crossref]

2008 (1)

2007 (3)

J. K. Chua, V. M. Murukeshan, S. K. Tan, and Q. Y. Lin, “Four beams evanescent waves interference lithography for patterning of two dimensional features,” Opt. Express 15(6), 3437–3451 (2007).
[Crossref] [PubMed]

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

2006 (4)

D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006).
[Crossref] [PubMed]

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

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A, Pure Appl. Opt. 8(4), 213–218 (2006).
[Crossref]

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

2005 (5)

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

D. B. Shao and S. C. Chen, “Numerical simulation of surface-plasmon-assisted nanolithography,” Opt. Express 13(18), 6964–6973 (2005).
[Crossref] [PubMed]

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

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

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005).
[Crossref]

2004 (2)

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

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

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

2001 (1)

1999 (2)

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

T. D. Milster, J. S. Jo, and K. Hirota, “Roles of propagating and evanescent waves in solid immersion lens systems,” Appl. Opt. 38(23), 5046–5057 (1999).
[Crossref]

1997 (1)

M. A. McCord, “Electron beam lithography for 0.13 µm manufacturing,” J. Vac. Sci. Technol. B 15(6), 2125–2129 (1997).
[Crossref]

1994 (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

1993 (1)

J. Melngailis, “Focused ion beam lithography,” Nucl. Instrum. Methods Phys. Res. B 80, 1271–1280 (1993).
[Crossref]

1978 (1)

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72(3), 577–588 (1978).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bettiol, A. A.

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

Blaikie, R. J.

Breese, M. B. H.

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

Chen, S. C.

D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006).
[Crossref] [PubMed]

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005).
[Crossref]

D. B. Shao and S. C. Chen, “Numerical simulation of surface-plasmon-assisted nanolithography,” Opt. Express 13(18), 6964–6973 (2005).
[Crossref] [PubMed]

Chua, J. K.

Crozier, K. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Du, J. L.

Durant, S.

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Elings, V. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Estroff, A.

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Fan, Y.

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Fuh, J. Y. H.

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Ghislain, L. P.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Guo, X. W.

Guo, Y. K.

Hirota, K.

Hong, M. H.

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Hoshiyama, S.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Ishihara, T.

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

Jo, J. S.

Kaneko, F.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Kato, K.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Kawakami, T.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Kino, G. S.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

Lafferty, N.

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Lee, H.

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

Lin, Q. Y.

Liu, Z. W.

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

Lu, L.

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Lukiyanchuk, B. S.

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Luo, X. G.

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

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

Manalis, S. R.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Martinez-Anton, J. C.

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A, Pure Appl. Opt. 8(4), 213–218 (2006).
[Crossref]

McCord, M. A.

M. A. McCord, “Electron beam lithography for 0.13 µm manufacturing,” J. Vac. Sci. Technol. B 15(6), 2125–2129 (1997).
[Crossref]

McNab, S. J.

Melngailis, J.

J. Melngailis, “Focused ion beam lithography,” Nucl. Instrum. Methods Phys. Res. B 80, 1271–1280 (1993).
[Crossref]

Milster, T. D.

Minne, S. C.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Murukeshan, V. M.

Ohdaira, Y.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Pockrand, I.

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72(3), 577–588 (1978).
[Crossref]

Quate, C. F.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

Shao, D. B.

D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006).
[Crossref] [PubMed]

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005).
[Crossref]

D. B. Shao and S. C. Chen, “Numerical simulation of surface-plasmon-assisted nanolithography,” Opt. Express 13(18), 6964–6973 (2005).
[Crossref] [PubMed]

Shinbo, K.

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

Smith, B. W.

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Srituravanich, W.

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

Sun, C.

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Tan, S. K.

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

van Kan, J. A.

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

Watt, F.

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

Wei, Q. H.

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

Wilder, K.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Yao, J.

Zhang, X.

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

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Zhou, J.

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Zhou, Y.

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (5)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388 (1994).
[Crossref]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999).
[Crossref]

Y. Ohdaira, S. Hoshiyama, T. Kawakami, K. Shinbo, K. Kato, and F. Kaneko, “Fabrication of surface relief gratings on azo dye thin films utilizing an interference of evanescent waves,” Appl. Phys. Lett. 86(5), 051102 (2005).
[Crossref]

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

D. B. Shao and S. C. Chen, “Surface-plasmon-assisted nanoscale photolithography by polarized light,” Appl. Phys. Lett. 86(25), 253107 (2005).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

J. C. Martinez-Anton, “Surface relief subwavelength gratings by means of total internal reflection evanescent wave interference lithography,” J. Opt. A, Pure Appl. Opt. 8(4), 213–218 (2006).
[Crossref]

J. Vac. Sci. Technol. B (2)

W. Srituravanich, S. Durant, H. Lee, C. Sun, and X. Zhang, “Deep subwavelength nanolithography using localized surface plasmons on planar silver mask,” J. Vac. Sci. Technol. B 23(6), 2636–2639 (2005).
[Crossref]

M. A. McCord, “Electron beam lithography for 0.13 µm manufacturing,” J. Vac. Sci. Technol. B 15(6), 2125–2129 (1997).
[Crossref]

Mater. Today (1)

F. Watt, M. B. H. Breese, A. A. Bettiol, and J. A. van Kan, “Proton beam writing,” Mater. Today 10(6), 20–29 (2007).
[Crossref]

Nano Lett. (3)

D. B. Shao and S. C. Chen, “Direct patterning of three-dimensional periodic nanostructures by surface-plasmon-assisted nanolithography,” Nano Lett. 6(10), 2279–2283 (2006).
[Crossref] [PubMed]

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

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic Nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Nucl. Instrum. Methods Phys. Res. B (1)

J. Melngailis, “Focused ion beam lithography,” Nucl. Instrum. Methods Phys. Res. B 80, 1271–1280 (1993).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Scr. (1)

Y. Zhou, M. H. Hong, J. Y. H. Fuh, L. Lu, and B. S. Lukiyanchuk, “Evanescent wave interference lithography for surface nano-structuring,” Phys. Scr. T 129, 35–37 (2007).
[Crossref]

Proc. SPIE (1)

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, and A. Estroff, “Evanescent wave imaging in optical lithography,” Proc. SPIE 6154, 100–108 (2006).

Surf. Sci. (1)

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72(3), 577–588 (1978).
[Crossref]

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

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Figures (4)

Fig. 1
Fig. 1 Schematic of the maskless SPPIL with ATR structure. (a) Structure of prism-silver-resist-substrate. (b) Backside-exposure SPPIL structure: ε 0 , ε 1 , ε 2 and ε 3 are the permittivity of the prism, silver, resist and air respectively; the thickness of the silver layer is d1 and that of resist is d2.
Fig. 2
Fig. 2 (a) T s p p varies with d2 and incident angle: (i) n = 1.89 and(ii) n = 1.53. (b) Resolution of patterns varies with d2.
Fig. 3
Fig. 3 Simulation result by FDTD, with incident wavelength 441.6nm, thickness of silver film 40nm, refractive index of resist 1.53 and thickness 50nm. (a) Electric field distribution when refractive index of the prism is 1.89. (b) Normalized amplitude of the electric field at the interface of the metal film and resist when the refractive index of the prism is 1.89 and 1.527 respectively.
Fig. 4
Fig. 4 The SEM imaging with period 150nm. (a) Prism with high refractive index, backside-exposure. (b) Prism with low refractive index, backside-exposure. (Time for exposure and development are 18s and 35s, respectively).

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

k s p p = k x h a l f s p a c e + k x p h o t o r e s i s t + k x m e t a l
k x h a l f s p a c e = ( ω / c ) [ ε 1 ε 3 / ( ε 1 + ε 3 ) ] 1 / 2
k x p h o t o r e s i s t = ( ω / c ) [ ( ε 2 ε 3 ) / ε 2 ] [ ε 1 ε 3 /( ε 1 + ε 3 ) ] 2 [ ( ε 2 ε 1 ) / ( ε 3 ε 1 ) ] ( ε 1 ε 3 ) 1/2 ( 2 π d 2 / λ ) + ( ω / c ) r 01 [ 2 / ( ε 3 ε 1 ) ] [ ε 1 ε 3 /( ε 1 + ε 3 ) ] 3/2 exp { 2 ( 2 π d 1 / λ ) [ ( ε 1 ) / ( ( ε 1 ε 3 ) 1/2 ) ] }
k x p C = ( ω / c ) [ ( ε 2 ε 3 ) / ε 2 ] ( ε 1 ε 3 / ( ε 1 + ε 3 ) ] 2 [ ( ε 2 ε 1 ) / ( ε 3 ε 1 ) ] ( ε 1 ε 3 ) 1 / 2 ( 2 π d 2 / λ )
k x p R = ( ω / c ) r 01 [ 2 / ( ε 3 ε 1 ) ] [ ε 1 ε 3 / ( ε 1 + ε 3 ) ] 3 / 2 exp { 2 ( 2 π d 1 / λ ) [ ε 1 / ( ε 1 ε 3 ) 1 / 2 ] }
k x m e t a l = k x p C { [ k x p C / 2 / Re ( k x h a l f s p a c e ) ] [ 2 ( 2 ε 3 2 ε 2 2 ) / ε 3 / ( ε 3 ε 2 ) + ( ε 1 + ε 3 ) / ( ε 3 ) ] i ε 1 / 2 / ε 1 } + k x p R { [ k x p R / 2 / Re ( k x ( h a l f s p a c e ) ] [ ( 2 ε 1 + ε 3 ) / ( ε 3 ) ] j ε 1 / ( ε 1 ε 3 ) } + k x p C k x p R / [ Re ( k x h a l f s p a c e ) ] [ ε 1 / ε 3 + 2 ε 3 / ( ε 3 ε 2 ) + ε 2 / 2 ε 3 ]
= ε 0 / ε 3 [ ( ε 0 / k 0 z + ε 1 / k 1 z ) / ( 2 ε 0 / k 0 z ) ] [ ( A + B r 01 e j k 1 z d 1 ) / ( r 23 e j k 2 z d 2 + e j k 1 z d 1 ) ]
A = [ ( ε 1 / k 1 z + ε 2 / k 2 z ) / 2 ε 1 / k 1 z ] [ ( 1 + r 12 r 23 e 2 j k 2 z d 2 ) / e j k 1 z d 1 ] ,
B = A e j k 1 z d 1 + r 23 e 2 j k 2 z d 2 e j k 1 z d 1 1 ;
r i j = ( k j z / ε j k i z / ε i ) / ( k j z / ε j + k i z / ε i ) ,
k i z = [ ε i ( ω / c ) 2 k x 2 ] 1 / 2 .

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