Abstract

In this paper, a nano-pillar array integrated near quantum dots (QDs), which serves as a Purcell cavity as well as a column antenna, is studied in order to enhance the spontaneous emission (SE) rate of low emission efficiency QDs. A systematic analysis for treating the isolated nano-pillar and loose ordered pillar is demonstrated by solving the electromagnetic field equations. As an illustrative example of potential applications, we proposed a new structure that Germanium (Ge) QDs are located in close proximity to the isolated Indium Tin Oxide (ITO) nano-pillar to raise its efficiency. From the results of numerical calculation, it is predicted that ITO pillars with slim (e.g., the radius is 25 nm and the height is 500 nm) and flat morphology (e.g., the radius is 40 nm and the height is 60 nm) exhibit superior enhancement over 20 folds. Finite difference time domain (FDTD) simulation is utilized for demonstrating the distinctive enhancement when QDs radiate at surface plasmonic resonance frequency of ITO nano-pillar. It can be found that the QDs emission enhancement profile accords with our results obtained from numerical analysis.

© 2016 Optical Society of America

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References

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  1. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
    [Crossref] [PubMed]
  2. F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
    [Crossref]
  3. A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
    [Crossref]
  4. C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
    [Crossref]
  5. G. Sun, J. B. Khurgin, and R. A. Soref, “Plasmonic light-emission enhancement with isolated metal nanoparticles and their coupled arrays,” J. Opt. Soc. Am. B 25(10), 1748–1755 (2008).
    [Crossref]
  6. R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
    [Crossref]
  7. J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys J. Chem. Phys. 75(3), 1139–1152 (1981).
  8. A. C. Pineda and D. Ronis, “Fluorescence quenching in molecules near rough metal surfaces,” J. Chem. Phys. 83(10), 5330–5337 (1985).
    [Crossref]
  9. D. J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 1995).
  10. E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
    [Crossref]
  11. E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
    [Crossref]
  12. K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
    [Crossref]
  13. S. A. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).
  14. H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17(23) 20878–20884 (2009).
    [Crossref] [PubMed]
  15. R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982).
    [Crossref]
  16. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2007).
  17. F. Michelotti, L. Dominici, E. Descrovi, N. Danz, and F. Menchini, “Thickness dependence of surface plasmon polariton dispersion in transparent conducting oxide films at 1.55 m,” Opt. Lett. 34(6), 839–841 (2009).
    [Crossref] [PubMed]
  18. J. B. Khurgin and G. Sun, “Enhancement of optical properties of nanoscaled objects by metal nanoparticles,” J. Opt. Soc. Am. B 26(12), 83–95 (2009).
    [Crossref]
  19. G. Ritchie, E. Burstein, and R. B. Stephens, “Optical phenomena at a silver surface with siibmicroscopic bumps,” J. Opt. Soc. Am. B 2(4), 544–551 (1985).
    [Crossref]
  20. J. B. Khurgin and G. Sun, “Impact of surface collisions on enhancement and quenching of the luminescence near the metal nanoparticles,” Opt. Express 23(24), 30739–30748(2015).
    [Crossref] [PubMed]
  21. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Third Edition) (Wiley, 2012).
  22. C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
    [Crossref] [PubMed]
  23. U. Laor and G. C. Schatz, “The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy,” J. Chem. Phys. 76(6), 2888–2899 (1982).
    [Crossref]
  24. C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
    [Crossref]
  25. C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
    [Crossref]
  26. E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
    [Crossref]
  27. Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).
  28. X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
    [Crossref]
  29. G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
    [Crossref] [PubMed]
  30. M. J. Alam and D. C. Cameron, “Optical and electrical properties of transparent conductive ITO thin films deposited by sol-gel process,” Thin Solid Films 377–378, 455–459 (2000).
    [Crossref]
  31. R. U. Tok and K. Sendur, “Absorption efficiency enhancement in inorganic and organic thin film solar cells via plasmonic honeycomb nanoantenna arrays,” Opt. Lett. 38(16), 3119–3122 (2013).
    [Crossref] [PubMed]

2015 (1)

2014 (2)

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

2013 (4)

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

R. U. Tok and K. Sendur, “Absorption efficiency enhancement in inorganic and organic thin film solar cells via plasmonic honeycomb nanoantenna arrays,” Opt. Lett. 38(16), 3119–3122 (2013).
[Crossref] [PubMed]

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
[Crossref]

2012 (2)

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

2009 (4)

2008 (1)

2007 (3)

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
[Crossref]

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

2004 (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

2000 (1)

M. J. Alam and D. C. Cameron, “Optical and electrical properties of transparent conductive ITO thin films deposited by sol-gel process,” Thin Solid Films 377–378, 455–459 (2000).
[Crossref]

1997 (1)

F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
[Crossref]

1985 (2)

A. C. Pineda and D. Ronis, “Fluorescence quenching in molecules near rough metal surfaces,” J. Chem. Phys. 83(10), 5330–5337 (1985).
[Crossref]

G. Ritchie, E. Burstein, and R. B. Stephens, “Optical phenomena at a silver surface with siibmicroscopic bumps,” J. Opt. Soc. Am. B 2(4), 544–551 (1985).
[Crossref]

1982 (2)

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982).
[Crossref]

U. Laor and G. C. Schatz, “The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy,” J. Chem. Phys. 76(6), 2888–2899 (1982).
[Crossref]

1981 (1)

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys J. Chem. Phys. 75(3), 1139–1152 (1981).

1975 (1)

E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
[Crossref]

1946 (1)

E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
[Crossref]

Adachi, C.

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

Agarwal, R.

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

Aguirov, T.

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

Alam, M. J.

M. J. Alam and D. C. Cameron, “Optical and electrical properties of transparent conductive ITO thin films deposited by sol-gel process,” Thin Solid Films 377–378, 455–459 (2000).
[Crossref]

Aspetti, C.O.

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

Biaglow, T.

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
[Crossref]

Boltasseva, A.

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

Bose, R.

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Brutting, W.

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

Burstein, E.

Cameron, D. C.

M. J. Alam and D. C. Cameron, “Optical and electrical properties of transparent conductive ITO thin films deposited by sol-gel process,” Thin Solid Films 377–378, 455–459 (2000).
[Crossref]

Carras, M.

A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
[Crossref]

Chatterjee, R.

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Cho, C. H.

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

Chong, K. K.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Dai, J.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Danz, N.

Descrovi, E.

Ding, G.

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Dominici, L.

Fang, X.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Gao, J.

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Gersten, J.

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys J. Chem. Phys. 75(3), 1139–1152 (1981).

Griffiths, D. J.

D. J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 1995).

Hattori, H. T.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2007).

Herzog, H. J.

E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
[Crossref]

Hong, X.

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Houng, M. P.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Huang, C. P.

Huang, H.

Huangfu, Y.

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Hung, C. I.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Kasper, E.

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
[Crossref]

Khurgin, J. B.

Kibbel, H.

E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
[Crossref]

Kittler, M.

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

Ku, H.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Laor, U.

U. Laor and G. C. Schatz, “The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy,” J. Chem. Phys. 76(6), 2888–2899 (1982).
[Crossref]

Leung, C. W.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Li, K.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Li, Z.

Liu, C. C.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Liu, D.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).

Mak, C. L.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Mayr, C.

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

Menchini, F.

Michelotti, F.

Mukai, T.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Naik, G. V.

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

Narukawa, Y.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Niki, I.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Nitzan, A.

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys J. Chem. Phys. 75(3), 1139–1152 (1981).

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2007).

Oehme, M.

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

Okamoto, K.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Park, J.

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

Paul, D. J.

A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
[Crossref]

Pineda, A. C.

A. C. Pineda and D. Ronis, “Fluorescence quenching in molecules near rough metal surfaces,” J. Chem. Phys. 83(10), 5330–5337 (1985).
[Crossref]

Premaratne, M.

Proud, R. V.

E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
[Crossref]

Purcell, E. M.

E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
[Crossref]

Ritchie, G.

Ronis, D.

A. C. Pineda and D. Ronis, “Fluorescence quenching in molecules near rough metal surfaces,” J. Chem. Phys. 83(10), 5330–5337 (1985).
[Crossref]

Ross, F. M.

F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
[Crossref]

Rossi, A. D.

A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
[Crossref]

Rukhlenko, I. D.

Ruppin, R.

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982).
[Crossref]

Schatz, G. C.

U. Laor and G. C. Schatz, “The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy,” J. Chem. Phys. 76(6), 2888–2899 (1982).
[Crossref]

Scherer, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Sendur, K.

Shalaev, V. M.

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Soref, R. A.

Sreekanth, K. V.

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
[Crossref]

Stephens, R. B.

Strangi, G.

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
[Crossref]

Stutzman, W. L.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Third Edition) (Wiley, 2012).

Sun, G.

Taneda, M.

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

Tersoff, J.

F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
[Crossref]

Thiele, G. A.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Third Edition) (Wiley, 2012).

Tok, R. U.

Torrey, H. C.

E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
[Crossref]

Tromp, R. M.

F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
[Crossref]

Wang, C. C.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Wang, Y. H.

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

Werner, J.

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

Wong, C. W.

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Yang, X. D.

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Ye, H.

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Yin, X. G.

Zhan, W.

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Zhu, Y. Y.

Adv. Mater. (1)

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

Appl. Mater. & Interfaces (1)

X. Fang, C. L. Mak, J. Dai, K. Li, H. Ye, and C. W. Leung, “ITO/Au/ITO sandwich structure for near-infrared plasmonics,” Appl. Mater. & Interfaces 6(18), 15743–15752 (2014).
[Crossref]

Appl. Phys. (1)

E. Kasper, H. J. Herzog, and H. Kibbel, “A one-dimensional SiGe superlattice grown by UHV epitaxy,” Appl. Phys. 8(3), 199–205 (1975).
[Crossref]

Appl. Phys. Lett. (2)

C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I. Hung, Y. H. Wang, and M. P. Houng, “Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure,” Appl. Phys. Lett. 91(12), 121109 (2007).
[Crossref]

R. Bose, X. D. Yang, R. Chatterjee, J. Gao, and C. W. Wong, “Weak coupling interactions of colloidal lead sulphide nanocrystals with silicon photonic crystal nanocavities near 1.55 m at room temperature,” Appl. Phys. Lett. 90(11), 111117 (2007).
[Crossref]

Front. Optoelectron. (1)

E. Kasper, M. Oehme, J. Werner, T. Aguirov, and M. Kittler, “Direct band gap luminescence from Ge on Si pin diodes,” Front. Optoelectron. 5(3), 256–260 (2012).
[Crossref]

IEEE J. Quantum Elect. (1)

A. D. Rossi, M. Carras, and D. J. Paul, “Low-Loss Surface-Mode Waveguides for Terahertz SiSiGe Quantum Cascade Lasers,” IEEE J. Quantum Elect. 42(12), 1233–1238 (2007).
[Crossref]

J. Appl. Phys. (1)

K. V. Sreekanth, T. Biaglow, and G. Strangi, “Directional spontaneous emission enhancement in hyperbolic metamaterials,” J. Appl. Phys. 114(114), 134306 (2013).
[Crossref]

J. Chem. Phys J. Chem. Phys. (1)

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys J. Chem. Phys. 75(3), 1139–1152 (1981).

J. Chem. Phys. (3)

A. C. Pineda and D. Ronis, “Fluorescence quenching in molecules near rough metal surfaces,” J. Chem. Phys. 83(10), 5330–5337 (1985).
[Crossref]

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76(4), 1681–1684 (1982).
[Crossref]

U. Laor and G. C. Schatz, “The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy,” J. Chem. Phys. 76(6), 2888–2899 (1982).
[Crossref]

J. Opt. Soc. Am. B (3)

Nanotechnology (1)

Y. Huangfu, W. Zhan, X. Hong, X. Fang, G. Ding, and H. Ye, “Optimal growth of Ge-rich dots on Si (001) substrates with hexagonal packed pit patterns,” Nanotechnology 24(3), 635–639 (2012).

Nat. mater. (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Nat. Photonics (1)

C. H. Cho, C.O. Aspetti, J. Park, and R. Agarwal, “Silicon coupled with plasmon nanocavities generates bright visible hot luminescence,” Nat. Photonics,  7(4), 285–289 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Org. Electron. (1)

C. Mayr, M. Taneda, C. Adachi, and W. Brutting, “Different orientation of the transition dipole moments of two similar Pt (II) complexes and their potential for high efficiency organic light-emitting diodes,” Org. Electron. 15(11), 3031–3037 (2014).
[Crossref]

Phys. Rev. (1)

E. M. Purcell, H. C. Torrey, and R. V. Proud, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69(1–2), 37–38 (1946).
[Crossref]

Phys. Rev. Lett. (1)

F. M. Ross, J. Tersoff, and R. M. Tromp, “Coarsening of self-assembled Ge quantum dots on Si (001),” Phys. Rev. Lett. 80(5), 984 (1997).
[Crossref]

Thin Solid Films (1)

M. J. Alam and D. C. Cameron, “Optical and electrical properties of transparent conductive ITO thin films deposited by sol-gel process,” Thin Solid Films 377–378, 455–459 (2000).
[Crossref]

Other (4)

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Third Edition) (Wiley, 2012).

S. A. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).

D. J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 1995).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2007).

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Figures (8)

Fig. 1
Fig. 1 Illustration of the surface plasmonic enhancement, with an isolated NP placed near a layer of active QDs in dielectric, where τ r a d 1 is the radiative decay rate of QDs, F p τ r a d 1 is the energy transferred from emitter into SP modes, τ n r a d 1 is the nonradiative decay rate of QDs, γrad is the radiative decay rate of SPs, and γnrad is the nonradiative decay rate of SPs.
Fig. 2
Fig. 2 Illustration of a pillar ordered array, where a and h represent the radius and the height, respectively, of the pillar, and b is the center-to-center spacing between two neighboring pillars.
Fig. 3
Fig. 3 Illustration of the nano-pillar with a stimulating electric field of horizontal polarization, where ϕ is the angle between the position vector r and the x-axis.
Fig. 4
Fig. 4 Enhancement factor Fsingle (due to a single isolated ITO pillar with the electric field of a horizontal polarization) as a function of the pillar radius a and the height h. In (a), the pillar height ranges from 100 to 500 nm, and the distance d from QD to the bottom of the pillar is 10 nm; In (b), the distance d from QD to the pillar bottom ranges from 10 to 50 nm, and the pillar height h is 200 nm; In (c), the distance d from QD to the pillar bottom ranges from 10 to 50 nm and the radius a of the pillar is 60 nm.
Fig. 5
Fig. 5 Illustration of the nano-pillar with the electric field of a vertical polarization, where ϕ is the angle between the position vector r and the y-axis.
Fig. 6
Fig. 6 Enhancement factor Fsingle (due to a single isolated ITO pillar with the electric field of vertical polarization) as a function of the pillar radius a and the height h. In (a), the height ranges from 100 to 500 nm, and the distance d from QD to the pillar bottom is 10 nm; In (b), the distance d from QD to the bottom of the pillar ranges from 10 to 50 nm, and the height of the pillar is 200 nm; In (c), the distance d from QD to the pillar bottom ranges from 10 to 50 nm, and the radius of the pillar is 60 nm.
Fig. 7
Fig. 7 The field distribution of the ITO pillar. (a) and (b) are the illustrations of the dipoles with two orientations: (a) oriented horizontally and (b) oriented vertically; (c) and (d) show the common logarithm, (lg|E|), of the near field profiles of the silicon based light source with enhancement by ITO pillar. These are the top views of near-field profiles of the horizontally oriented dipole (c) and the vertically oriented dipole (d); (e) and (f) indicate the common logarithm, (lg|E|), of the near field profiles of the same silicon based light source. These are the cross-section near-field profiles of the horizontally oriented dipole (e) and the vertically oriented dipole (f) at 1550 nm. The radius and the height of the ITO pillar are 60 nm and 200 nm, respectively, and the distance from QD to the bottom of the pillar is 10 nm.
Fig. 8
Fig. 8 Enhancement of the device efficiency, as the function of radius a and height h with (a) 1 QD, (b) 3 QDs and (c) 5 QDs, where the distance from QD to the bottom of the pillar is 10 nm and the dipoles are oriented vertically.

Tables (1)

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Table 1 Typical Parameters of Numerical Calculation for Enhancement Factor

Equations (63)

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η r a d = τ r a d 1 τ r a d 1 + τ n r a d 1 ,
η r a d = τ r a d 1 τ n r a d 1 .
η i j = | M i j | 2 ρ ,
ρ s p = 1 V e f f Δ ω .
U = 0.5 ε 0 ε d E m a x 2 V e f f ,
V e f f = in 0.5 ε 0 ω ε M ω E 2 d V + out 0.5 ε 0 ε d E 2 d V 0.5 ε 0 ε d + E m a x 2 ,
ε M = 1 ω p 2 ω 2 + i υ ω ,
V e f f q d = V e f f ( E m a x E Q D ) 2 ,
( d U d t ) n r a d = in 1 2 ε 0 Im ( ω ε M ω ) ω E 2 d V ,
( d U d t ) r a d = S d s .
S = 1 2 Re [ E × H ] = 1 2 r 0 μ 0 ε 0 ε d | k d ω p 4 π r | 2 sin 2 ( θ ) ,
P r = 0 2 π d ϕ 0 π d θ r 2 sin θ S = ω 4 ε d 1.5 12 π ε 0 c 3 | p | 2 ,
γ = ( d U d t ) r a d + ( d U d t ) n r a d U .
Δ ω = ( π / 2 ) γ .
Q = ω 0 / Δ ω ,
ρ r a d = 1 3 π 2 ( 2 π λ d ) 3 / ω 0 ,
F p = 3 8 π λ d 3 Q V e f f q d .
1 τ r a d = F p τ r a d .
η r = γ r a d γ r a d + γ n r a d ,
η s p = τ r a d 1 ( 1 + F p η r ) τ n r a d 1 + τ r a d 1 ( 1 + F p ) .
Δ E = ε μ 2 t 2 E ,
ω 2 = ω 0 2 [ 1 + E m , n 1 o u t E i n cos ( b X n ) + E m , n + 1 o u t E i n cos ( b X n ) + E m 1 , n o u t E i n cos ( b X m ) + E m + 1 , n o u t E i n cos ( b X m ) ] ,
Δ Φ = 1 r ( 1 r 2 ϕ 2 + r ( r r ) ) Φ = 0 ,
Φ = C ln r + B + , n 0 r n ( A n cos n ϕ + B n sin n ϕ ) .
Φ i n s i d e = ( 2 ε d ε M + ε d ) r cos ϕ ,
Φ o u t s i d e = [ ( ε M ε d ε M + ε d ) a 2 r r ] cos ϕ .
ω = ω p 2 1 + ε d ,
E r = { ( ε M ε d ε M + ε d 1 ) cos ϕ r < a ( ε M ε d ε M + ε d a 2 r 2 + 1 ) cos ϕ r > a ,
E ϕ = { ( ε M ε d ε M + ε d 1 ) sin ϕ r < a ( ε M ε d ε M + ε d a 2 r 2 + 1 ) sin ϕ r > a .
E y = R ( r ) Φ ( ϕ ) e j k z z ,
E y = { D J n ( k t 1 r ) J n k t 1 a cos n ϕ e j k z z r < a D K n ( k t 2 r ) K n k t 2 a cos n ϕ e j k z z r > a ,
k t 1 2 = ( 2 π λ 0 ) 2 ε M k z 2 ,
k t 2 2 = ( 2 π λ 0 ) 2 ε d k z 2 ,
k t 1 J n 1 ( k t 1 a ) ε J n ( k t 1 a ) = k t 2 J n 1 ( k t 2 a ) ε J n ( k t 2 a ) ,
H x = E y μ / ε 0 ε ,
E z = j ω ε ( H y x H x y ) j ω ε H x y .
E y = { D J 0 ( k t 1 r ) J 0 k t 1 a cos n ϕ e j k z z r < a D K 0 ( k t 2 r ) K 0 k t 2 a cos n ϕ e j k z z r > a .
k M = ω c ε M ,
U = ( 3 + ε d ) ε 0 E m a x 2 ( 1 e 2 k d h ) π a 2 4 k d = 0.5 ε 0 ε d E m a x 2 V e f f ,
V e f f = ( 1 + 3 ε d ) 1 e 2 h k d 2 h k d π a 2 h .
p = P d V = 0 l 2 ε 0 ε d ( ε d 1 ) ε M + ε d E 0 π a 2 e j k d z d z .
P r = 0 2 π d ϕ 0 2 π d θ r 2 sin θ S = ω 4 ε d 1.5 12 π ε 0 c 3 | p | = ω 4 ε d 1.5 ( π a 2 h ) 2 ( 1 + ε d ) 2 12 π ε 0 c 3 ( 1 e h k d h k d ) 2 E m a x 2 = ( d U d t ) r a d ,
( d U d t ) n r a d = υ ( 1 + ε d ) π a 2 h E m a x 2 1 e 2 k d h 2 k d h .
γ = υ ( 1 + ε d ) + ω 0 4 ε d 1.5 a 2 h 12 c 3 ( 1 + ε d 2 ) 0.5 ( 3 + ε d ) .
η r = ω 0 4 ε d 1.5 a 2 h 12 c 3 ( 1 + ε d ) υ + ω 0 4 ε d 1.5 a 2 h 12 c 3 ( 1 + ε d ) .
V e f f q d = V e f f ( h + d h ) 4 ,
F p = 6 c 3 ( 1 + ε d ) k d ε d 0.5 ω p 2 ( υ + ω 0 4 ε d 1.5 a 2 h 12 c 3 ) ( 1 e 2 h k d ) a 2 ( h h + d ) 4 .
F s i n g l e = ( 1 + ε d ) k d ε d h ω o 2 2 ( υ + ω 0 4 ε d 1.5 a 2 h 12 c 3 ) 2 ( 1 e 2 h k d ) ( h h + d ) 4 + 1.
E z = { J 0 ( k t 1 r ) e γ z z r < a K 0 ( k t 2 r ) e γ z z r > a
k t 1 ε M J 0 ( k t 1 a ) J 1 ( k t 1 a ) = k t 2 ε d K 0 ( k t 2 a ) K 1 ( k t 2 a ) ,
k t 2 2 = k d 2 + γ z 2 ,
E ϕ = 0 h j η 0 k d J ( z ) 4 π r sin ( ϕ ) e j k d r + j k d z cos ( ϕ ) d z ,
P r = a ( π ε 0 k d e k t 2 a a ) 2 32 k t 2 ω 2 0 π sin 3 ( ϕ ) ( e j k d r + j k d z cos ( ϕ ) 1 γ z + j k d cos ( ϕ ) ) 2 d ϕ .
U = π ε 0 1 e 2 γ z h 2 γ z ( 2 ε d ) a 2 2 [ I 0 2 ( a k t 1 ) I 1 2 ( a k t 2 ) ] .
V e f f = π a 2 h 2 ε d ε M 1 e γ z h 2 γ z h [ 1 I 1 2 ( a k t 1 ) I 0 2 ( a k t 1 ) ] ,
( d U d t ) n r a d = 2 π ε 0 ( 1 + ε d ) v 1 e 2 γ z h 2 γ z a 2 2 ( I 0 2 ( a k t 1 ) I 1 2 ( a k t 1 ) ) ,
γ = P r + ( d U d t ) n r a d U ,
η r = P r P r + ( d U d t ) n r a d ,
F p = λ 3 4 π 3 γ ω 0 ε d 2 ε M a 2 ( a + d ) 4 I 0 2 ( a k t 1 ) I 0 2 ( a k t 1 ) I 1 2 ( a k t 1 ) 2 γ z 1 e 2 γ z h .
F s i n g l e = 1 + F p η r .
ω 2 = ω 0 2 [ 1 + 2 ( a a + b ) 2 ] [ cos ( b X n ) + cos ( b X m ) ] .
( ω 0 1 + 4 ( a a + b ) 2 cos ( 2 2 b k d ) , ω 0 1 + 4 ( a a + b ) 2 ) .
Δ ω = 2 1 + ε d ( a a + b ) 2 ( 1 cos 2 b k d ) ω p .

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