Abstract

We have computed the transmittances of four types of cathode—Yb∕Au, Al∕Au, Yb∕Ag, and Al∕Ag double layers—and the light extraction efficiencies of the top-emission organic light-emitting diodes with these cathodes, respectively, based on the characteristic matrix method and the dissipation spectrum model. Computations show that the Yb∕Au cathode has a markedly higher transmittance than the other three types of cathode when the Yb and Au thicknesses in the Yb∕Au cathode are, respectively, equal to the Al (or Yb) and Au (or Ag) thicknesses in the other three types of cathode. The power lost to the Yb∕Au cathode due to the surface plasmon polaritons is the lowest, and hence the device with the Yb∕Au cathode has the highest extraction efficiency. The transmittances for the four cathodes are also measured experimentally.

© 2006 Optical Society of America

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2004 (5)

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

X. D. Feng, R. Khangura, and Z. H. Lu, "Metal-organic-metal cathode for high-contrast organic light-emitting diodes," Appl. Phys. Lett. 85, 497-499 (2004).
[CrossRef]

R. B. Pode, C. J. Lee, D. G. Moon, and J. I. Han, "Transparent conducting metal electrode for top emission organic light-emitting devices: Ca-Ag double layer," Appl. Phys. Lett. 84, 4614-4616 (2004).
[CrossRef]

Y. Rag Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

L. H. Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

2003 (6)

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Y. Q. Li, J. X. Tang, and L. S. Hung, "Interfacial chemistry of Sm with Alq3 and its implication to organic light-emitting devices," Chem. Phys. Lett. 376, 90-95 (2003).
[CrossRef]

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

X. Jiang, F. L. Wong, M. K. Fung, and S. T. Lee, "Aluminum-doped zinc oxide films as transparent conductive electrode for organic light-emitting devices," Appl. Phys. Lett. 83, 1875-1877 (2003).
[CrossRef]

2002 (1)

L.-S. Hung and J. Madathil, "Radiation damage and transmission enhancement in surface-emitting organic light-emitting diodes," Thin Solid Films 410, 101-106 (2002).
[CrossRef]

2001 (3)

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

P. T. Worthing, J. A. E. Wasey, and W. L. Barnes, "Rate and efficiency of spontaneous emission in metal-clad microcavities," J. Appl. Phys. 89, 615-625 (2001).
[CrossRef]

2000 (5)

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission from planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

G. Parthasarathy, C. Adachi, P. E. Burrows, and S. R. Forrest, "High-efficiency transparent organic light-emitting devices," Appl. Phys. Lett. 76, 2128-2130 (2000).
[CrossRef]

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

D. S. Ginley and C. Bright, "Transparent conducting oxides," Mater. Res. Bull. 25, 15-18 (2000).
[CrossRef]

P. E. Burrows, G. Gu, S. R. Forrest, E. P. Vicenzi, and T. X. Zhou, "Semitransparent cathodes for organic light emitting devices," J. Appl. Phys. 87, 3080-3085 (2000).
[CrossRef]

1999 (2)

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

W. L. Barnes, "Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices," J. Lightwave Technol. 17, 2170-2182 (1999).
[CrossRef]

1998 (2)

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

1996 (1)

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
[CrossRef]

1994 (1)

I. D. Parker and H. H. Kim, "Fabrication of polymer light-emitting diodes using doped silicon electrodes," Appl. Phys. Lett. 64, 1774-1776 (1994).
[CrossRef]

1978 (1)

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

Adachi, C.

G. Parthasarathy, C. Adachi, P. E. Burrows, and S. R. Forrest, "High-efficiency transparent organic light-emitting devices," Appl. Phys. Lett. 76, 2128-2130 (2000).
[CrossRef]

Barnes, W. L.

L. H. Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

P. T. Worthing, J. A. E. Wasey, and W. L. Barnes, "Rate and efficiency of spontaneous emission in metal-clad microcavities," J. Appl. Phys. 89, 615-625 (2001).
[CrossRef]

J. A. E. Wasey and W. L. Barnes, "Efficiency of spontaneous emission from planar microcavities," J. Mod. Opt. 47, 725-741 (2000).
[CrossRef]

W. L. Barnes, "Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices," J. Lightwave Technol. 17, 2170-2182 (1999).
[CrossRef]

Beierlein, T.

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001), pp. 61-64.

Brédas, J. L.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Bright, C.

D. S. Ginley and C. Bright, "Transparent conducting oxides," Mater. Res. Bull. 25, 15-18 (2000).
[CrossRef]

Bulovic, V.

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
[CrossRef]

Burrows, P. E.

G. Parthasarathy, C. Adachi, P. E. Burrows, and S. R. Forrest, "High-efficiency transparent organic light-emitting devices," Appl. Phys. Lett. 76, 2128-2130 (2000).
[CrossRef]

P. E. Burrows, G. Gu, S. R. Forrest, E. P. Vicenzi, and T. X. Zhou, "Semitransparent cathodes for organic light emitting devices," J. Appl. Phys. 87, 3080-3085 (2000).
[CrossRef]

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
[CrossRef]

Chan, M. Y.

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

Chen, C. H.

S.-F. Hsu, C.-C. Lee, S.-W. Hwang, and C. H. Chen, "Highly efficient top-emitting white organic electroluminescent devices," Appl. Phys. Lett 86, 253508 (2005).

Cheng, L. F.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Crisey, D. B.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Ding, X. M.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Do, Y. Rag

Y. Rag Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

dos Santos, D. A.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Feng, X.

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

Feng, X. D.

X. D. Feng, R. Khangura, and Z. H. Lu, "Metal-organic-metal cathode for high-contrast organic light-emitting diodes," Appl. Phys. Lett. 85, 497-499 (2004).
[CrossRef]

Forrest, S. R.

P. E. Burrows, G. Gu, S. R. Forrest, E. P. Vicenzi, and T. X. Zhou, "Semitransparent cathodes for organic light emitting devices," J. Appl. Phys. 87, 3080-3085 (2000).
[CrossRef]

G. Parthasarathy, C. Adachi, P. E. Burrows, and S. R. Forrest, "High-efficiency transparent organic light-emitting devices," Appl. Phys. Lett. 76, 2128-2130 (2000).
[CrossRef]

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
[CrossRef]

Fung, M. K.

X. Jiang, F. L. Wong, M. K. Fung, and S. T. Lee, "Aluminum-doped zinc oxide films as transparent conductive electrode for organic light-emitting devices," Appl. Phys. Lett. 83, 1875-1877 (2003).
[CrossRef]

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

Gao, Y.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Garbuzov, D. Z.

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

Giesen, D. J.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Gilmore, C. M.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Ginley, D. S.

D. S. Ginley and C. Bright, "Transparent conducting oxides," Mater. Res. Bull. 25, 15-18 (2000).
[CrossRef]

Grozea, D.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

Gu, G.

P. E. Burrows, G. Gu, S. R. Forrest, E. P. Vicenzi, and T. X. Zhou, "Semitransparent cathodes for organic light emitting devices," J. Appl. Phys. 87, 3080-3085 (2000).
[CrossRef]

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
[CrossRef]

Han, J. I.

R. B. Pode, C. J. Lee, D. G. Moon, and J. I. Han, "Transparent conducting metal electrode for top emission organic light-emitting devices: Ca-Ag double layer," Appl. Phys. Lett. 84, 4614-4616 (2004).
[CrossRef]

Han, S.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

He, J.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

He, P. M.

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

Horwitz, J. S.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Hou, X. Y.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Hsu, S.-F.

S.-F. Hsu, C.-C. Lee, S.-W. Hwang, and C. H. Chen, "Highly efficient top-emitting white organic electroluminescent devices," Appl. Phys. Lett 86, 253508 (2005).

Huang, C.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

Hung, L. S.

Y. Q. Li, J. X. Tang, and L. S. Hung, "Interfacial chemistry of Sm with Alq3 and its implication to organic light-emitting devices," Chem. Phys. Lett. 376, 90-95 (2003).
[CrossRef]

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

Hung, L.-S.

L.-S. Hung and J. Madathil, "Radiation damage and transmission enhancement in surface-emitting organic light-emitting diodes," Thin Solid Films 410, 101-106 (2002).
[CrossRef]

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Hwang, S.-W.

S.-F. Hsu, C.-C. Lee, S.-W. Hwang, and C. H. Chen, "Highly efficient top-emitting white organic electroluminescent devices," Appl. Phys. Lett 86, 253508 (2005).

Jiang, X.

X. Jiang, F. L. Wong, M. K. Fung, and S. T. Lee, "Aluminum-doped zinc oxide films as transparent conductive electrode for organic light-emitting devices," Appl. Phys. Lett. 83, 1875-1877 (2003).
[CrossRef]

Johnson, D.

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

Kafafi, Z. H.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Karg, S.

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Khalfin, V.

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

Khalfin, V. B.

V. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Z. Garbuzov, and S. R. Forrest, "Weak microcavity effects in organic light-emitting devices," Phys. Rev. B 58, 3730-3740 (1998).
[CrossRef]

Khangura, R.

X. D. Feng, R. Khangura, and Z. H. Lu, "Metal-organic-metal cathode for high-contrast organic light-emitting diodes," Appl. Phys. Lett. 85, 497-499 (2004).
[CrossRef]

Kim, H.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Kim, H. H.

I. D. Parker and H. H. Kim, "Fabrication of polymer light-emitting diodes using doped silicon electrodes," Appl. Phys. Lett. 64, 1774-1776 (1994).
[CrossRef]

Kim, W. Y.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

Kim, Y.-C.

Y. Rag Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Kozlov, V. G.

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

Kushto, G. P.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Lai, S. L.

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

Le, Q. T.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Lee, C. J.

R. B. Pode, C. J. Lee, D. G. Moon, and J. I. Han, "Transparent conducting metal electrode for top emission organic light-emitting devices: Ca-Ag double layer," Appl. Phys. Lett. 84, 4614-4616 (2004).
[CrossRef]

Lee, C. S.

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

Lee, C.-C.

S.-F. Hsu, C.-C. Lee, S.-W. Hwang, and C. H. Chen, "Highly efficient top-emitting white organic electroluminescent devices," Appl. Phys. Lett 86, 253508 (2005).

Lee, S. T.

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
[CrossRef]

X. Jiang, F. L. Wong, M. K. Fung, and S. T. Lee, "Aluminum-doped zinc oxide films as transparent conductive electrode for organic light-emitting devices," Appl. Phys. Lett. 83, 1875-1877 (2003).
[CrossRef]

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Lee, S.-T.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Lee, Y.-H.

Y. Rag Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
[CrossRef]

Li, Y. Q.

Y. Q. Li, J. X. Tang, and L. S. Hung, "Interfacial chemistry of Sm with Alq3 and its implication to organic light-emitting devices," Chem. Phys. Lett. 376, 90-95 (2003).
[CrossRef]

Liao, L. S.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Lu, M.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Lu, Z. H.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

X. D. Feng, R. Khangura, and Z. H. Lu, "Metal-organic-metal cathode for high-contrast organic light-emitting diodes," Appl. Phys. Lett. 85, 497-499 (2004).
[CrossRef]

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

Ma, G. L.

G. L. Ma, G. Z. Ran, A. G. Xu, Y. P. Qiao, and G. G. Qin, "Improving charge-injection balance and cathode transmittance of top-emitting organic light-emitting device with p-type silicon anode," Appl. Phys. Lett. 87, 081106 (2005).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IOP, 2001).
[CrossRef]

Madathil, J.

L.-S. Hung and J. Madathil, "Radiation damage and transmission enhancement in surface-emitting organic light-emitting diodes," Thin Solid Films 410, 101-106 (2002).
[CrossRef]

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

Mason, M. G.

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Moon, D. G.

R. B. Pode, C. J. Lee, D. G. Moon, and J. I. Han, "Transparent conducting metal electrode for top emission organic light-emitting devices: Ca-Ag double layer," Appl. Phys. Lett. 84, 4614-4616 (2004).
[CrossRef]

Murata, H.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Neyts, K.

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Palik, E. D.

E. D. Palik, ed., Handbook of Optical Constants of Solids I, II, & III (Academic, 1998). The refractive indices at 525 nm not given directly in the present reference are deduced by linearly fitting the nearest neighbor data. The refractive index given is anisotropic for the crystalline bulk rare-earth metal materials, so their average values with respect to the crystalline axis directions are adopted in the computation.

Parker, I. D.

I. D. Parker and H. H. Kim, "Fabrication of polymer light-emitting diodes using doped silicon electrodes," Appl. Phys. Lett. 64, 1774-1776 (1994).
[CrossRef]

Parthasarathy, G.

G. Parthasarathy, C. Adachi, P. E. Burrows, and S. R. Forrest, "High-efficiency transparent organic light-emitting devices," Appl. Phys. Lett. 76, 2128-2130 (2000).
[CrossRef]

G. Parthasarathy, P. E. Burrows, V. Khalfin, V. G. Kozlov, and S. R. Forrest, "A metal-free cathode for organic semiconductor devices," Appl. Phys. Lett. 72, 2138-2140 (1998).
[CrossRef]

Píque, A.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Pode, R. B.

R. B. Pode, C. J. Lee, D. G. Moon, and J. I. Han, "Transparent conducting metal electrode for top emission organic light-emitting devices: Ca-Ag double layer," Appl. Phys. Lett. 84, 4614-4616 (2004).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

Qiao, Y. P.

G. L. Ma, G. Z. Ran, A. G. Xu, Y. P. Qiao, and G. G. Qin, "Improving charge-injection balance and cathode transmittance of top-emitting organic light-emitting device with p-type silicon anode," Appl. Phys. Lett. 87, 081106 (2005).

Qin, G. G.

G. L. Ma, G. Z. Ran, A. G. Xu, Y. P. Qiao, and G. G. Qin, "Improving charge-injection balance and cathode transmittance of top-emitting organic light-emitting device with p-type silicon anode," Appl. Phys. Lett. 87, 081106 (2005).

Ran, G. Z.

G. L. Ma, G. Z. Ran, A. G. Xu, Y. P. Qiao, and G. G. Qin, "Improving charge-injection balance and cathode transmittance of top-emitting organic light-emitting device with p-type silicon anode," Appl. Phys. Lett. 87, 081106 (2005).

Raychaudhuri, P.

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Riel, H.

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Rieß, W.

H. Riel, S. Karg, T. Beierlein, W. Rieß, and K. Neyts, "Tuning the emission characteristics of top-emitting organic light-emitting devices by means of a dielectric capping layer: an experimental and theoretical study," J. Appl. Phys. 94, 5290-5296 (2003).
[CrossRef]

Salaneck, W. R.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Schlaf, R.

H. Kim, C. M. Gilmore, J. S. Horwitz, A. Píque, H. Murata, G. P. Kushtǒ, R. Schlaf, Z. H. Kafafi, and D. B. Crisey, "Transparent conducting aluminum-doped zinc oxide thin films for organic light-emitting devices," Appl. Phys. Lett. 76, 259-261 (2000).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, "Molecular fluorescence and energy transfer near interfaces," Adv. Chem. Phys. 37, 1-65 (1978).
[CrossRef]

Smith, L. H.

L. H. Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
[CrossRef]

Song, Y.-W.

Y. Rag Do, Y.-C. Kim, Y.-W. Song, and Y.-H. Lee, "Enhanced light extraction efficiency from organic light emitting diodes by insertion of a two-dimensional photonic crystal structure," J. Appl. Phys. 96, 7629-7636 (2004).
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S. M. Sze, Physics of Semiconductor Devices (Wiley, 1981).

Tang, C. W.

L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, "Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes," Appl. Phys. Lett. 78, 544-546 (2001).
[CrossRef]

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
[CrossRef]

Tang, J. X.

Y. Q. Li, J. X. Tang, and L. S. Hung, "Interfacial chemistry of Sm with Alq3 and its implication to organic light-emitting devices," Chem. Phys. Lett. 376, 90-95 (2003).
[CrossRef]

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

Tao, F. G.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
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Thompson, M. E.

G. Gu, V. Bulovic, P. E. Burrows, S. R. Forrest, and M. E. Thompson, "Transparent organic light emitting devices," Appl. Phys. Lett. 68, 2606-2608 (1996).
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Tong, S. W.

J. X. Tang, S. W. Tong, C. S. Lee, S. T. Lee, and P. M. He, "Photoemission study of interface formation between ytterbium and tris-(8-hydroxyquinoline) aluminum," Chem. Phys. Lett. 380, 63-69 (2003).
[CrossRef]

M. Y. Chan, S. L. Lai, M. K. Fung, S. W. Tong, C. S. Lee, and S. T. Lee, "Efficient CsF/Yb/Ag cathodes for organic light-emitting devices," Appl. Phys. Lett. 82, 1784-1786 (2003).
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Vicenzi, E. P.

P. E. Burrows, G. Gu, S. R. Forrest, E. P. Vicenzi, and T. X. Zhou, "Semitransparent cathodes for organic light emitting devices," J. Appl. Phys. 87, 3080-3085 (2000).
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Wasey, J. A. E.

L. H. Smith, J. A. E. Wasey, and W. L. Barnes, "Light outcoupling efficiency of top-emitting organic light-emitting diodes," Appl. Phys. Lett. 84, 2986-2988 (2004).
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P. T. Worthing, J. A. E. Wasey, and W. L. Barnes, "Rate and efficiency of spontaneous emission in metal-clad microcavities," J. Appl. Phys. 89, 615-625 (2001).
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M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001), pp. 61-64.

Wong, F. L.

X. Jiang, F. L. Wong, M. K. Fung, and S. T. Lee, "Aluminum-doped zinc oxide films as transparent conductive electrode for organic light-emitting devices," Appl. Phys. Lett. 83, 1875-1877 (2003).
[CrossRef]

Wood, R.

S. Han, D. Grozea, C. Huang, Z. H. Lu, R. Wood, and W. Y. Kim, "Al:SiO thin films for organic light-emitting diodes," J. Appl. Phys. 96, 709-714 (2004).
[CrossRef]

S. Han, X. Feng, Z. H. Lu, D. Johnson, and R. Wood, "Transparent-cathode for top-emission organic light-emitting diodes," Appl. Phys. Lett. 82, 2715-2717 (2003).
[CrossRef]

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P. T. Worthing, J. A. E. Wasey, and W. L. Barnes, "Rate and efficiency of spontaneous emission in metal-clad microcavities," J. Appl. Phys. 89, 615-625 (2001).
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Xiong, Z. H.

X. Zhou, J. He, L. S. Liao, M. Lu, Z. H. Xiong, X. M. Ding, X. Y. Hou, F. G. Tao, C. E. Zhou, and S. T. Lee, "Enhanced hole injection in a bilayer vacuum-deposited organic light-emitting device using a p-type doped silicon anode," Appl. Phys. Lett. 74, 609-611 (1999).
[CrossRef]

Xu, A. G.

G. L. Ma, G. Z. Ran, A. G. Xu, Y. P. Qiao, and G. G. Qin, "Improving charge-injection balance and cathode transmittance of top-emitting organic light-emitting device with p-type silicon anode," Appl. Phys. Lett. 87, 081106 (2005).

Yan, L.

M. G. Mason, C. W. Tang, L.-S. Hung, P. Raychaudhuri, J. Madathil, D. J. Giesen, L. Yan, Q. T. Le, Y. Gao, S.-T. Lee, L. S. Liao, L. F. Cheng, W. R. Salaneck, D. A. dos Santos, and J. L. Brédas, "Interfacial chemistry of AlQ3 and LiF with reactive metals," J. Appl. Phys. 89, 2756-2765 (2001).
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Zhou, C. E.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic for the TOLEDs, (b) schematic microcavity model.   denotes the emitter location.

Fig. 2
Fig. 2

(a) Simulated intensity transmittances and (b) reflectances at 525   nm for the Yb∕Au and Al∕Au cathodes as functions of the thicknesses of Yb, Al, and Au.

Fig. 3
Fig. 3

(Color online) (a) Simulated intensity transmittances and (b) reflectances at 525   nm for the Yb∕Au and Yb∕Ag cathodes as functions of the thicknesses of Yb, Au, and Ag.

Fig. 4
Fig. 4

(Color online) (a) Simulated intensity transmittances and (b) reflectances at 525   nm for the Yb∕Au and Al∕Ag cathodes as functions of the thicknesses of Yb, Al, and Ag.

Fig. 5
Fig. 5

(Color online) Comparison between the measured transmittances (scattered) and the simulated data (solid curve) for the Yb∕Au, Al∕Au, Yb∕Ag, and Al∕Au cathodes at a fixed Au or Ag thickness of 15   nm and a varying Yb or Al thickness.

Fig. 6
Fig. 6

Power dissipation spectra I(u) for the TOLEDs with (a) Yb ( 4   nm ) Au ( 15   nm ) , (b) Al   ( 4   nm ) / Au   ( 15   nm ) , (c) Yb   ( 4   nm ) / Ag   ( 15   nm ) , and (d) Al   ( 4   nm ) / Ag   ( 15   nm ) cathodes.

Tables (2)

Tables Icon

Table 1 Refractive Indices n (= n r + ik ) at 525 nm Used in Computations and the Work Functions of the Materials Involved

Tables Icon

Table 2 Light Extraction Efficiency for Some Transparent Cathodes

Equations (9)

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

M = M Yb M Au .
T = p ex p in | 2 p in ( m 11 + m 12 p ex ) p in + ( m 21 + m 22 p ex ) | 2 ,
R = | ( m 11 + m 12 p ex ) p in ( m 21 + m 22 p ex ) ( m 11 + m 12 p ex ) p in + ( m 21 + m 22 p ex ) | 2 ,
p = ε μ   cos   θ .
q = μ ε cos θ .
b , / / b 0 = 1 q + q 0 I , / / ( u ) d u ,
I ( u ) = 3 2 u 3 l 1 [ 1 r 1 , 2 p exp ( 1 , 2 ) ] [ 1 r 1 , 3 p exp ( 1 , 3 ) ] { 1 r 1 , 2 p r 1 , 3 p exp [ i ( β 1 , 2 + β 1 , 3 ) ] } ,
I / / ( u ) = 3 4 u l 1 ( [ 1 r 1 , 2 s exp ( 1 , 2 ) ] [ 1 r 1 , 3 s exp ( 1 , 3 ) ] { 1 r 1 , 2 s r 1 , 3 s exp [ i ( β 1 , 2 + β 1 , 3 ) ] } + ( 1 - u 2 ) [ 1 + r 1 , 2 p exp ( 1 , 2 ) ] [ 1 + r 1 , 3 p exp ( 1 , 3 ) ] { 1 - r 1 , 2 p r 1 , 3 p exp [ i ( β 1 , 2 + β 1 , 3 ) ] } ) .   
b b 0 = 2 3 b / / b 0 + 1 3 b b 0 .

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