Abstract

A two-dimensional photonic crystal with a large full band gap has been designed, fabricated, and characterized. The photonic crystal design was based on a calculation using inverse iteration with multigrid acceleration. The fabrication of the photonic crystal on silicon was realized by the processes of electron-beam lithography and inductively coupled plasma reactive ion etching. It was found that the hexagonal array of circular columns and rods has an optimal full photonic band gap. In addition, we show that a larger extraction of light from our designed photonic crystal can be obtained when compared with the frequently used photonic crystals reported previously. Our designed PC structure therefore should be very useful for creating highly efficient optoelectronic devices.

©2005 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  3. R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
    [Crossref]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).
  5. A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
    [Crossref]
  6. T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
    [Crossref]
  7. T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
    [Crossref]
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    [Crossref]
  9. M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous Emission Extraction and Purcell Enhancement from Thin-Film 2-D Photonic Crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
    [Crossref]
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    [Crossref]
  12. D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
    [Crossref]
  13. F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
    [Crossref]
  14. A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
    [Crossref]

2004 (1)

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

2003 (2)

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

2002 (1)

Vladimir V. Poborchii, Tetsuya Tada, and Toshihiko Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

2001 (1)

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

1999 (3)

1998 (1)

A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
[Crossref]

1997 (2)

D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
[Crossref]

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

1995 (1)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).

1994 (1)

1987 (1)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Arjavalingam, G.

Astratov, V. N.

Barra, A.

A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
[Crossref]

Bertho, D.

D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
[Crossref]

Bhat, R.

Boroditsky, M.

Cassagne, D.

A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
[Crossref]

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
[Crossref]

Chang, Chien C.

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

Chelnokov, A.

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

Chern, R. L.

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

Chung Chang, C.

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

Coccioli, R.

Crozat, P.

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

Culashaw, I. S.

De La Rue, R. M.

De Lustrac, A.

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

Erchak, A. A.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Fan, S. H.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Fan, Shanhui

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Gadot, F.

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

Hwang, R. R.

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

Ippen, E. P.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Jiang, H. X.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

Joannopoulos, J. D.

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).

Joannoupoulos, J. D.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Johnson, Steven G.

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Jouanin, C.

A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
[Crossref]

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
[Crossref]

Kanayama, Toshihiko

Vladimir V. Poborchii, Tetsuya Tada, and Toshihiko Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Kim, K. H.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

Kolodziejski, L. A.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Krauss, T. F.

Lin, J. Y.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

Lin, S.

Lourtioz, J.-M.

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).

Oder, T. N.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

Petrich, G. S.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Poborchii, Vladimir V.

Vladimir V. Poborchii, Tetsuya Tada, and Toshihiko Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Rakich, P.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Ripin, D. J.

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

Shakya, J.

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

Skolnick, M. S.

Stevenson, R. M.

Tada, Tetsuya

Vladimir V. Poborchii, Tetsuya Tada, and Toshihiko Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Villeneuve, Pierre R.

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Vrijen, R.

Whittaker, D. M.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).

Yablonovitch, E.

Appl. Phys. Lett. (6)

A. A. Erchak, D. J. Ripin, S. H. Fan, P. Rakich, J. D. Joannoupoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[Crossref]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, “III-nitride photonic crystals,” Appl. Phys. Lett. 83, 1231–1233 (2003).
[Crossref]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84, 466–468 (2004).
[Crossref]

D. Cassagne, C. Jouanin, and D. Bertho, “Optical properties of two-dimensional photonic crystals with graphite structure,” Appl. Phys. Lett. 70, 289–291 (1997).
[Crossref]

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, “Experimental demonstration of complete photonic band gap in graphite structure,” Appl. Phys. Lett. 71, 1780–1782 (1997).
[Crossref]

A. Barra, D. Cassagne, and C. Jouanin, “Existence of two-dimensional absolute band gaps in the visible,” Appl. Phys. Lett. 72, 627–629 (1998).
[Crossref]

J. Appl. Phys. (1)

Vladimir V. Poborchii, Tetsuya Tada, and Toshihiko Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Phys. Rev. B (1)

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Phys. Rev. E (1)

R. L. Chern, C. Chung Chang, Chien C. Chang, and R. R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration,” Phys. Rev. E 68, 026704 (2003).
[Crossref]

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Other (1)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).

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Figures (8)

Fig. 1.
Fig. 1. Hexagonal array of circular columns and rods [3]
Fig. 2.
Fig. 2. A map of band gaps for hexagonal lattice in Fig. 1 by varying radius r/a of circle columns with fixed d/a = 0.035 [3].
Fig. 3.
Fig. 3. Sample of hexagonal array of circular columns and rods with lattice constant a = 2.5μm, radius r = 0.328μm, width d = 0.114μm, and height~1μm: (a) side view at a tilt angle of 45°, (b) top view.
Fig. 4.
Fig. 4. (a) Reflectance spectra of hexagonal array of photonic crystals with structure shown in Fig. 3. (b) Transmittance spectra of hexagonal array of photonic crystals with structure shown in Fig. 3. The arrows indicate the position of photonic band gap (PBG).
Fig. 5.
Fig. 5. (a) Top view of a triangular lattice with lattice constant a = 2μm, radius r = 0.5μm, and height~1μm. The ratio r/a = 0.25. (b) A map of band gaps for triangular lattice by varying radius r/a [4].
Fig. 6.
Fig. 6. Reflectance and transmittance spectra of a triangular lattice of silicon pillars with lattice constant a = 2μm and radius r = 0.5μm The arrows indicate the position of photonic band gap (PBG).
Fig. 7.
Fig. 7. (a)Top view of a graphite lattice with lattice constant a = 2.5μm, radius r = 0.4μm, and height~1μm. The ratio r/a = 0.16. (b) A map of band gaps for graphite lattice, also called honeycomb lattice, by varying radius r/a [4].
Fig. 8.
Fig. 8. Reflectance and transmittance spectra of a graphite lattice of silicon pillars with lattice constant a = 2.5μm and radius r = 0.4μm. The arrows indicate the position of photonic band gap (PBG).

Tables (1)

Tables Icon

Table 1. Radius (defined as r), and width (defined as d), and their gap-midgap ratios for the hexagonal array of silicon PCs. The lattice constant (defined as a) of the silicon PCs is 2.5 μm. Δω is the FWHM of PBG. aΔω/2πc is a dimensionless value.

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