Abstract

We present a dual beam multiple exposure technique that can generate complex 2-D quasi-crystal template structures. The optical system is based on the interference of two laser beams producing a family of high intensity planes. Controlled reorientation of a photosensitive sample between exposures results in an exposure dose, when developed, returns a quasi-crystal pattern. Results are shown in which quasi-crystal patterns with 8, 10, and 12-fold rotation symmetry are produced in photoresist. The results of several test runs are shown in which the quasi-crystal patterns developed in photoresist are subsequently etched into silicon. Based on an extended application of the dual beam multiple exposure optical system, a potential technique for producing 3-D quasi-crystal patterns is presented.

© 2004 Optical Society of America

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References

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Adv. Mater.

X. Wang, C.Y. Ng, W. Y. Tam, C. T. Chan and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. 15, 1526-1528 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, M. Deubel and M. Wegener, "Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Chem. Mater.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. Chaikin and W. B. Russel, "Creating periodic three-dimensional structures by multibeam interference of visible laser," Chem. Mater. 14, 2831-2833 (2002).
[CrossRef]

J. Mod. Opt.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue and P. Millar, "The design of two-dimensional photonic quasicrystals by means of a Fourier transform method," J. Mod. Opt. 48, 9-14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes," J. Mod. Opt. 47, 1771- 1778 (2000).

J. Opt. A: Pure Appl. Opt.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang and J. Li, "Photonic bandgaps in two-dimensional short-range periodic structures," J. Opt. A: Pure Appl. Opt. 4, 23-28 (2002).
[CrossRef]

J. Opt. Laser Technol.

See for instance; M. Loncar, T. Doll, J. Vuckovic and A. Scherer, "Design and fabrication of photonic crystal optical waveguides," J. Opt. Laser Technol. 18, 1402-1411 (2000).

J. Opt. Soc. Am. A

Nature

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg and M. C. Netti, "Complete photonic bandgaps in 12-fold symmetric quasicrystals," Nature 404, 740-743 (2000).
[CrossRef] [PubMed]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef] [PubMed]

Phys. Rev. A

S. John and T. Quang, "Spontaneous emission near the edge of a photonic band gap," Phys. Rev. A 50, 1764-1769 (1994).
[CrossRef] [PubMed]

Phys. Rev. B

S. S. M. Cheng, L. M. Li, C. T. Chan and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4098 (1999).
[CrossRef]

Phys. Rev. B.

X. Zhang, Z. Q. Zhang and C. T. Chang, "Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Y. S. Chan, C. T. Chang and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
[CrossRef]

Other

See for instance; K. Sakoda, Optical properties of photonic crystals, (Springer-Verlag Berlin 2001)

J. D. Joannopoulus, R. D. Meade and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).

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Figures (11)

Fig. 1.
Fig. 1.

Experimental dual beam multiple exposure optical system. The blue line of the Argon Ion laser is linearly polarized and divided into two equal intensity beams. These beams are recombined producing an interference pattern in a photosensitive material. The three rotation and translation stages allow the accurate orientation and positioning of the interference pattern relative to previous exposure steps.

Fig. 2.
Fig. 2.

Interface planes used in the production of an 8-fold quasi-crystal pattern. (A) Extend view of the intersecting planes indicating zones where the 4 planes overlap. (B) Enlarged view of the central region of (A) and (C) is a 3-D view of the interference planes extending through the thickness of the exposed material.

Fig. 3.
Fig. 3.

Simulation of the exposed pattern in the photosensitive material when a threshold level of 8 out of a maximum of 16 selected. All exposure levels below 8 are in black and levels above 8 are in white. The 8-fold symmetry about the central point and other plane coincidence locations is clearly visible in the figure.

Fig. 4.
Fig. 4.

Image of the 8-fold symmetry pattern produced using 4 exposures of the dual beam multiple exposure experimental system. The intersected projection of the two arrows indicates the center of the pattern. About the center 8-fold rotational symmetry is observed. Dimension bar shown inclined to correspond to orientation of the quasi-crystal pattern.

Fig. 5.
Fig. 5.

Image of the 10-fold rotational symmetry pattern produced through 5 equal time exposures. (A) Extended view of the 10-fold pattern, experimental. (B) Orientation of the family of exposure planes taken about the center. (C) Computed exposure pattern about the center (exposure threshold of 10 out of a maximum of 20).

Fig. 6.
Fig. 6.

12-fold rotational symmetry pattern produced using 6 equal time exposures. (A) Extended view of the 12-fold pattern, experimental. (B) Orientation of the family of exposure planes taken about the center. (C) Computed exposure pattern about the center (exposure threshold of 12 out of a maximum of 24). (D) Expanded view of the central region of the experimentally obtained 12-fold pattern of (A).

Fig. 7.
Fig. 7.

Eight-fold (left) and 12-fold (right) quasi-crystal patterns produced and etched into a silicon wafer. Etch is 1 µm deep.

Fig. 8.
Fig. 8.

Quasi-crystal patterns produced using a lower threshold of 6 out of 16 for the 8-fold symmetry (A) theory, (B) experimental. A highly interconnected pattern results. Quasi-crystal patterns produced using a lower threshold of 10 out of 16 for the 8-fold symmetry (C) theory, (D) experimental. A disconnected pattern results.

Fig. 9.
Fig. 9.

Experimentally obtained diffraction patterns for the (A) 8-fold, (B) 10-fold and (C) 12-fold quasi-crystal patterns experimentally produced and displayed in Fig. 4, 5, and 6 respectively. The diffraction patterns display the rotational symmetry associated with the corresponding quasi-crystal pattern.

Fig. 10.
Fig. 10.

View of the interference planes required producing the three axes 8-fold symmetric 3-D quasi-crystal pattern. There are 4 sets of intersection planes oriented at angles of 0, 45, 90 and 135 degrees about each of the three mutually perpendicular axes.

Fig. 11.
Fig. 11.

3-D view and (x, y) plane slices of the 8-fold 3 axis quasi-crystal pattern produced using the interference planes of Fig. 10. Slices are in 0.1-micron increments along the z-axis starting at A1 (z=0 microns) to C3 (z=1.0 microns). Increment sequence is A1, A2, A3, A4, B1, B2, B3, B4, C1, C2 and C3. The center of the pattern in A1 corresponds to the coordinate origin.

Equations (5)

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I j = E j 1 2 + E j 2 2 + 2 F j 1 E j 2 cos ( θ j 12 ) cos ( [ k j 1 k j 2 ] r + φ o j 1 + φ o j 2 )
A j x + B j y + C j z + D j = 0
D j = ( φ o j 1 φ o j 2 ) + w j λ ( 1 2 ) 2 + ( m 1 m 2 ) 2 + ( n 1 n 2 ) 2
N = R 2 , θ = 360 R , t = 2 * t total R
( Step ) ( Euler angels ) ( 1 2 3 4 5 6 7 8 9 ) = ( 0 0 0 45 0 0 90 0 0 135 0 0 90 45 0 90 90 0 90 135 0 90 45 90 90 135 90 )

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