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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 24 — Nov. 23, 2009
  • pp: 21560–21565
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Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer

Xuefeng Yang, Beibei Zeng, Changtao Wang, and Xiangang Luo  »View Author Affiliations


Optics Express, Vol. 17, Issue 24, pp. 21560-21565 (2009)
http://dx.doi.org/10.1364/OE.17.021560


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Abstract

We have developed the plasmonic interference lithography technique to achieve the feature sizes theoretically down to sub-22 nm even to 16.5 nm by using dielectric-metal multilayer (DMM) with diffraction-limited masks at the wavelength of 193 nm with p-polarization. An 8 pairs of GaN (10 nm) / Al (12 nm) multilayer is designed as a filter allowing only a part of high wavevector k (evanescent waves) to pass through for interference lithography. The analysis of the influence by the number of DMM layers is presented. 4 pairs of the proposed multilayer can be competent for pattern the minimal feature size down to 21.5 nm at the visibility about 0.4 to satisfy the minimum visibility required with positive resist. Finite-difference time-domain analysis method is used to demonstrate the validity of the theory.

© 2009 OSA

1. Introduction

2. Principle

For a periodic chromium mask with period Λ, the waves generating from the mask can be decomposed a series of diffracted plane waves. We define x as the grating direction of the mask and z as the wavevector direction of the illumination light [see Fig. 1
Fig. 1 Schematic of the plasmonic interference lithography with dielectric-metal multilayer.
]. The diffraction wavevector follows the grating function,
kx=k0sinθ+2πmΛ,
(1)
where k x is the transmitted transverse wavevector, k 0 and θ are the incident wavevector and angle, respectively; and m is an integer diffraction order. In this letter, we only consider the case of perpendicular illumination, Eq. (1) can be reduced as k x = 2πm /Λ, that is the diffraction wavevector only depending on the diffracted order and the period of the mask.

In our interference lithography approach in this letter, we need a special device that only allows a part range of evanescent waves transmitted through it. However, the special device does not exist in the real world. It can be realized by an artificial metamaterial for its extraordinary properties that are not observed in the nature [10

10. Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett. 7(11), 3360–3365 ( 2007). [CrossRef] [PubMed]

,12

12. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 ( 2006). [CrossRef] [PubMed]

14

14. I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 ( 2007). [CrossRef]

]. The dielectric-metal multilayer, which has been proposed for various applications as a special metamaterial [10

10. Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett. 7(11), 3360–3365 ( 2007). [CrossRef] [PubMed]

,15

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

], can be designed to meet the need we expected in this letter. In addition, the choosing of the metal is also a key to design the metamaterial for different wavelength range. Generally, Au is not appropriate for plasmonic lithography purposes because its plasmonic frequency ωsp locates at visible range. Ag and Al are good material candidates for plasmonic lithography for their plasmonic frequency locates at UV range. In this letter, Al is chosen as an example in this letter because of its relatively lower energy loss at 193 nm.

The DMM structure designed in this paper is an 8 pairs of GaN(10 nm) and aluminum(12 nm) multilayer. We used rigorous-coupled wave analysis method [16

16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 ( 1995). [CrossRef]

] to calculate the transmission as a function of transverse k [see Fig. 2
Fig. 2 The transmitted amplitude VS the transverse wavenumber for an 8 pairs of 10 nm GaN and 12 nm Al multilayer at a wavelength of 193 nm with p-polarization.
] for the proposed DMM at a wavelength of 193 nm with p-polarization. The Drude model, εr(ω) = ε - ωp 2 [ω (ω + iVc)]−1, was used to describe the permittivity of Al, where the parameters, ε = 1.0, ωp = 2.4 × 1016 rad/s, Vc = 3.8 × 1015 rad/s, are obtained by fitting the model to the experimental data taken from the literature [17

17. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 ( 1972). [CrossRef]

]. The permittivity of GaN is 1.295 [18

18. M. J. Weber, Handbook of Optical Materials, (CRC Press, 2003).

]. The permittivity of the photoresist below the multilayer is 2.89. From this transfer function of the dielectric-metal multilayer, only a part of high wavevector k (evanescent waves) can pass through for interference lithography we expected.

3. Numerical Simulation and Discussion

Here we discuss the first order diffracted waves pass through the filter. From the Fig. 2, a period of mask is about 86 nm corresponds to a high transmission. The finite-difference time-domain method is then performed for numerical analysis. The x directional boundary condition is perfect electrical conductor (PEC) and the z directional one is perfect matched layer (PML). The two dimensions with a grid size of 0.2 nm and the input light intensity is set as 1. The mask is 43 nm half-pitch and 40 nm thickness Cr grating, only the ± 1 order pass through the proposed DMM structure for interference, the simulated total electric field intensity (E2 = Ex 2 + Ez 2) distribution in the photoresist zone is shown in Fig. 3(a)
Fig. 3 The distribution of simulated electric-field intensities for the mask with periods of (a) 86 nm, and (c) 66 nm. The zero value along the vertical axis corresponds to the multilayer/ photoresist interface. The corresponding electric-field intensities at the planes 0 (red), 10 nm (blue), and 20 nm (black) are shown in (b) and (d), respectively.
. Clearly the feature size of the formed pattern is down to 21.5 nm. For photolithography purpose, the normalized total electric field intensity distribution at planes 0(red), 10(blue), and 20(black) nm below the DMM/photoresist interface is also shown in Fig. 3(b). The intensity visibility (or contrast) V = (I max-I min)/(I max + I min) ≈0.4, which satisfy the minimum contrast (~0.4) for positive photoresist in modern lithographic fabrication processes.

Because there exists a π phase shift between the interference fringes of Ex and Ez components for p-polarized wave, the ratio of Ez/ Ex must be high (or low) enough to provide sufficient intensity contrast. The ratio of Ez/Ex=kx/kz. For larger values of the transverse wave vector (evanescent waves),kz=ikx2εPRk02. Then V can be deduced as,
V=|Ez2Ex2Ez2+Ex2|=εPRk022kx2εPRk02,
(2)
where ε PR is the permittivity of the photoresist. Thus, to satisfy the minimum contrast required for common negative photoresist [11

11. M. J. Madou, Fundamentals of Microfabrication, (CRC, Boca Raton, 2002).

], the critical period of the mask is 66 nm for the first order with the proposed structure and materials in this letter. We then simulate the 33 nm half pitch and 40 nm thickness chrome grating with the proposed DMM structure and photoresist. The simulated total electric field intensity distribution in the photoresist zone is shown in Fig. 3(c), and the normalized total electric field intensity distribution at planes 0(red), 10(blue), and 20(black) nm below the DMM/photoresist interface is also shown in Fig. 3(d). As what we forecasted, the 16.5 nm half pitch fringes are formed and the simulation contrast (~0.2007) is well agreement with the theoretical result (~0.2033) from Eq. (2). With the periodic of the mask getting less and less, the interference fringes contrast would be too worse to meet the photolithography need. For the evanescent waves decay exponentially with the distance away from the propagating path, the absolute intensity of the fringes formed in the photoresist decay sharply with the distance away from the DMM/photoresist interface, and it is validated from the simulation results shown in Fig. 3(b) and (d).

From Fig. 2 and Eq. (2), we can conclude that within the range of the periodic of the mask from 110 nm to 66 nm, corresponding to the first diffracted order transverse k band from 1.755 k 0 to 2.9242 k 0, feature sizes using the proposed DMM structure could be formed from 27.5nm to 16.5 nm. Figure 4
Fig. 4 The feature sizes VS the visibility and the normalized electric field intensity, respectively, with the proposed dielectric-metal multilayer. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity 5 nm below the interface of multilayer/photoresist.
shows the feature sizes versus the visibility and the normalized electric field intensity, respectively, with the proposed dielectric-metal multilayer. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity at the plane of 5 nm below the interface of multilayer/photoresist. From Fig. 4, the simulation visibilities agree with the theoretical ones from Eq. (2). And the normalized electric field intensity can be explained by the transmission from Fig. 2.

Combined with the number of proposed DMM structure and its corresponding transmitted amplitude distribution, we can forecast that with increased number layer of the DMM structure, the zeroth order diffracted wave will be further filtered, the simulation visibility will approach to the theoretical results, and the normalized electric intensity will be strongly decreased for additional metallic absorption. In order to validity it, we here demonstrate two examples with two other different number of the DMM layers. One is 4 pairs and the other is 12 pairs of the GaN(10 nm)/Al(12 nm) multilayer. In Fig. 5
Fig. 5 The feature sizes VS the visibility and the normalized electric field intensity with (a) 4 pairs and (b) 12 pairs of the GaN(10 nm)/Al(12 nm) DMM layers, respectively. The black square and the red solid circle represent visibility with theoretical and simulation results, respectively. The blue triangle represents the average normalized intensity 5 nm below the interface of multilayer/photoresist. The transmitted amplitude of the two structures at the wavelength of 193 nm is also presented (see inset).
, the feature sizes versus the visibility and the normalized electric field intensity (at the plane of 5 nm below the interface of multilayer/photoresist) are shown for (a) 4 pairs and (b) 12 pairs of the DMM layers, respectively. The two structures transmitted amplitude distribution is also presented (see inset). For 4 pairs DMM layers, the simulation visibility has some divergence to theoretical results due to the impact of the zeroth order which cannot be filtered completely. For 12 pairs one, the zeroth order diffracted wave was well filtered, the simulation visibilities agree well with theoretical results for the mask whose period less than 84 nm, but for bigger period of mask, the more divergence between them, this can be well explained by the transmitted amplitude of the structure. The distinct difference between the Fig. 4 and Fig. 5 is that with more normalized electric field intensity endowed the fewer number of DMM layers and this can also be easily understood through the transmitted amplitude of the DMM layers. Considering today’s fabrication facilities in modern lithographic fabrication processes with positive photoresist, 4 pairs of the proposed multilayer can be competent for pattern the minimal feature size with 21.5 nm at the visibility about 0.4 (see Fig. 5(a)). This would drastically reduce the difficulty of the multilayer fabrication and the corresponding experimental errors. Lower than 4 pairs DMM layers, the zeroth order wave transmitted through it can strongly impact the contrast of the pattern.

4. Conclusion

In conclusion, we have developed and numerically illustrated the plasmonic interference lithography technique to obtain the feature sizes down to sub-22 nm for today’s fabrication facilities with positive photoresist with a 4 pairs of proposed dielectric-metal multilayer at the wavelength 193 nm with p-polarized. If common negative photoresist can be possibly used, the feature size would down to 16.5 nm through increasing the number of the DMM layer to 8 pairs. The dielectric-metal multilayer was designed as a filter which makes only a narrow evanescent waves band pass through for interference lithography. The influence by the number of the DMM layer was also analyzed in detail. Finite-difference time-domain method is used for confirming the validity of this technique. For the 22 nm half pitch mask can be mass fabricated, we believe that this technique has an exciting potential to print pattern with half pitch 16 nm and below.

Acknowledgement

The authors thank Ting Xu, Liang Fang, Ling Liu, and Hui Zhang for their helpful suggestion and contribution to this work. This work was partially supported by 973 Program of China (No.2006-CB302900) and the Chinese Nature Science Grant (No.60778018 and No. 60736037).

References and links

1.

A. K. Bates, M. Rothschild, T. M. Bloomstein, T. H. Fedynyshyn, R. R. Kunz, V. Liberman, and M. Switkes, “Review of technology for 157-nm lithography,” IBM J. Res. Develop. 45, 605–614 ( 2001). [CrossRef]

2.

J. P. Silverman, “Challenges and progress in x-ray lithography,” J. Vac. Sci. Technol. B 16(6), 3137–3141 ( 1998). [CrossRef]

3.

T. M. Bloomstein, M. F. Marchant, S. Deneault, D. E. Hardy, and M. Rothschild, “22-nm immersion interference lithography,” Opt. Express 14(14), 6434–6443 ( 2006). [CrossRef] [PubMed]

4.

H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer, Heidelberg, 1988).

5.

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

6.

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

7.

T. Xu, Y. Zhao, C. Wang, J. Cui, C. Du, and X. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 ( 2008). [CrossRef] [PubMed]

8.

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]

9.

V. M. Murukeshan and K. V. Sreekanth, “Excitation of gap modes in a metal particle-surface system for sub-30 nm plasmonic lithography,” Opt. Lett. 34(6), 845–847 ( 2009). [CrossRef] [PubMed]

10.

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett. 7(11), 3360–3365 ( 2007). [CrossRef] [PubMed]

11.

M. J. Madou, Fundamentals of Microfabrication, (CRC, Boca Raton, 2002).

12.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 ( 2006). [CrossRef] [PubMed]

13.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 ( 2008). [CrossRef] [PubMed]

14.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 ( 2007). [CrossRef]

15.

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

16.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 ( 1995). [CrossRef]

17.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 ( 1972). [CrossRef]

18.

M. J. Weber, Handbook of Optical Materials, (CRC Press, 2003).

19.

L. Kong, Q. Pan, B. Cui, M. Li, and S. Y. Chou, “Magnetotransport and domain structures in nanoscale NiFe/Cu/Co spin valve,” J. Appl. Phys. 85(8), 5492–5494 ( 1999). [CrossRef]

20.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 ( 2006). [CrossRef] [PubMed]

OCIS Codes
(220.3740) Optical design and fabrication : Lithography
(240.6680) Optics at surfaces : Surface plasmons
(260.3160) Physical optics : Interference
(160.3918) Materials : Metamaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 8, 2009
Revised Manuscript: July 30, 2009
Manuscript Accepted: October 1, 2009
Published: November 11, 2009

Citation
Xuefeng Yang, Beibei Zeng, Changtao Wang, and Xiangang Luo, "Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer," Opt. Express 17, 21560-21565 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21560


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References

  1. A. K. Bates, M. Rothschild, T. M. Bloomstein, T. H. Fedynyshyn, R. R. Kunz, V. Liberman, and M. Switkes, “Review of technology for 157-nm lithography,” IBM J. Res. Develop. 45, 605–614 (2001). [CrossRef]
  2. J. P. Silverman, “Challenges and progress in x-ray lithography,” J. Vac. Sci. Technol. B 16(6), 3137–3141 (1998). [CrossRef]
  3. T. M. Bloomstein, M. F. Marchant, S. Deneault, D. E. Hardy, and M. Rothschild, “22-nm immersion interference lithography,” Opt. Express 14(14), 6434–6443 (2006). [CrossRef] [PubMed]
  4. H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer, Heidelberg, 1988).
  5. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]
  6. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005). [CrossRef] [PubMed]
  7. T. Xu, Y. Zhao, C. Wang, J. Cui, C. Du, and X. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 (2008). [CrossRef] [PubMed]
  8. 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]
  9. V. M. Murukeshan and K. V. Sreekanth, “Excitation of gap modes in a metal particle-surface system for sub-30 nm plasmonic lithography,” Opt. Lett. 34(6), 845–847 (2009). [CrossRef] [PubMed]
  10. Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett. 7(11), 3360–3365 (2007). [CrossRef] [PubMed]
  11. M. J. Madou, Fundamentals of Microfabrication, (CRC, Boca Raton, 2002).
  12. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]
  13. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008). [CrossRef] [PubMed]
  14. I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007). [CrossRef]
  15. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavlength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]
  16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995). [CrossRef]
  17. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  18. M. J. Weber, Handbook of Optical Materials, (CRC Press, 2003).
  19. L. Kong, Q. Pan, B. Cui, M. Li, and S. Y. Chou, “Magnetotransport and domain structures in nanoscale NiFe/Cu/Co spin valve,” J. Appl. Phys. 85(8), 5492–5494 (1999). [CrossRef]
  20. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

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