Abstract

We show an increase of the luminous power efficiency of a white organic light-emitting diode (LED) with three emitters by optimizing its spectrum and its extraction efficiency. To calculate this efficiency we use a model with four parameters: the spectra, extraction efficiencies, internal quantum efficiencies of three emitters, and the driving voltage. This luminous power efficiency increases by 30% by use of a spectrum close to the spectrum of the MacAdam limit. This limit gives the highest luminous efficacy for a given chromaticity. We also show that a white organic LED with an inefficient deep blue emitter can give the same luminous power efficiency as a white organic LED with a more efficient light blue emitter, because of their different fractions in the radiant flux. Tuning the extraction efficiency with a microcavity to the spectrum also increases the luminous power efficiency by 10%.

© 2008 Optical Society of America

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2007 (3)

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

C. L. Mulder, K. Celebi, and K. M. Milaninia, “Saturated and efficient blue phosphorescent organic light emitting devices with Lambertian angular emission,” Appl. Phys. Lett. 90, 211109 (2007).
[CrossRef]

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

2006 (9)

J. Lim, S. S. Oh, D. Y. Kim, S. H. Cho, I. T. Kim, S. H. Han, H. Takezoe, E. H. Choi, G. S. Cho, Y. H. Seo, S. O. Kang, and B. Park, “Enhanced out-coupling factor of microcavity organic light-emitting devices with irregular microlens array,” Opt. Express 14, 6564-6571 (2006).
[CrossRef] [PubMed]

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

2005 (3)

2004 (3)

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

B. W. D'Andrade and S. R. Forrest, “White organic light-emitting devices for solid-state lighting,” Adv. Mater. 16 (18), 1585-1595 (2004).
[CrossRef]

2003 (3)

S. R. Forrest, D. C. Bradley, and M. E. Thompson, “Measuring the efficiency of organic light-emitting diodes,” Adv. Mater. 15, 1043-1048 (2003).
[CrossRef]

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

2002 (3)

N. K. Patel, S. Cina, and J. H. Burroughes, “High-efficiency organic light-emitting diodes,” IEEE J. Sel. Top. Quantum Electron. 8, 346-361 (2002).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

2001 (2)

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

E. Thompson Chihaya Adachi, Marc A. Baldo, and Stephen R. Forrest, “Nearly 100% internal phosphorescence efficiency in an organic light emitting diode.J. Appl. Phys. 90, 5048-5051(2001).
[CrossRef]

2000 (1)

P. Bienstman and R. Baets, “The RC2 LED: a novel resonant-cavity LED design using a symmetric resonant cavity in the outcoupling reflector,” IEEE J. Quantum Electron. 36, 669-673 (2000).
[CrossRef]

1994 (1)

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

1950 (1)

Adati, R. D.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Adawi, A. M.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Agata, Y.

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

Athanassopoulou, N.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Baets, R.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

P. Bienstman and R. Baets, “The RC2 LED: a novel resonant-cavity LED design using a symmetric resonant cavity in the outcoupling reflector,” IEEE J. Quantum Electron. 36, 669-673 (2000).
[CrossRef]

Baldo, Marc A.

E. Thompson Chihaya Adachi, Marc A. Baldo, and Stephen R. Forrest, “Nearly 100% internal phosphorescence efficiency in an organic light emitting diode.J. Appl. Phys. 90, 5048-5051(2001).
[CrossRef]

Benisty, H.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Bienstman, P.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

P. Bienstman and R. Baets, “The RC2 LED: a novel resonant-cavity LED design using a symmetric resonant cavity in the outcoupling reflector,” IEEE J. Quantum Electron. 36, 669-673 (2000).
[CrossRef]

Birnstock, Jan

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

Bockstaele, R.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Bradley, D. C.

S. R. Forrest, D. C. Bradley, and M. E. Thompson, “Measuring the efficiency of organic light-emitting diodes,” Adv. Mater. 15, 1043-1048 (2003).
[CrossRef]

Burroughes, J. H.

N. K. Patel, S. Cina, and J. H. Burroughes, “High-efficiency organic light-emitting diodes,” IEEE J. Sel. Top. Quantum Electron. 8, 346-361 (2002).
[CrossRef]

Celebi, K.

C. L. Mulder, K. Celebi, and K. M. Milaninia, “Saturated and efficient blue phosphorescent organic light emitting devices with Lambertian angular emission,” Appl. Phys. Lett. 90, 211109 (2007).
[CrossRef]

Chandra, S.

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

Chen, C. H.

Chihaya Adachi, E. Thompson

E. Thompson Chihaya Adachi, Marc A. Baldo, and Stephen R. Forrest, “Nearly 100% internal phosphorescence efficiency in an organic light emitting diode.J. Appl. Phys. 90, 5048-5051(2001).
[CrossRef]

Cho, G. S.

Cho, S. H.

Cho, S.-H.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Choi, E. H.

Cina, S.

N. K. Patel, S. Cina, and J. H. Burroughes, “High-efficiency organic light-emitting diodes,” IEEE J. Sel. Top. Quantum Electron. 8, 346-361 (2002).
[CrossRef]

Connolly, L. G.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Cremona, M.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

D'Andrade, B. W.

B. W. D'Andrade and S. R. Forrest, “White organic light-emitting devices for solid-state lighting,” Adv. Mater. 16 (18), 1585-1595 (2004).
[CrossRef]

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

Davolos, M. R.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Delbeke, D.

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

Do, Y. R.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Fehse, Karsten

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Foden, C.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Forrest, S. R.

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

S. R. Forrest, D. C. Bradley, and M. E. Thompson, “Measuring the efficiency of organic light-emitting diodes,” Adv. Mater. 15, 1043-1048 (2003).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

Forrest, S. W.

B. W. D'Andrade and S. R. Forrest, “White organic light-emitting devices for solid-state lighting,” Adv. Mater. 16 (18), 1585-1595 (2004).
[CrossRef]

Forrest, Stephen R.

E. Thompson Chihaya Adachi, Marc A. Baldo, and Stephen R. Forrest, “Nearly 100% internal phosphorescence efficiency in an organic light emitting diode.J. Appl. Phys. 90, 5048-5051(2001).
[CrossRef]

Fujii., H.

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

Giebink, N. C.

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

Han, S. H.

He, G.

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

Ho, Y. L.

Hofmann, Michael

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

Holmes, R. J.

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

Hongawa, K.

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

Iijima, T.

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

Jafelicci, M.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Juni, N.

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

Kamalasanan, M N.

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

Kang, S. O.

Kanno, H.

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

Kawano, K.

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

Kido, J.

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

Kim, D. Y.

Kim, I. T.

Kim, Y.-C.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Kumar, P.

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

Kwok, H.-S.

Lee, M.-T.

Lee, Y.-H.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Lee, Y.-J.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Legnani, C.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Leo, K.

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

Leo, Karl

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Leo., K.

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

Li, J.

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

Lidzey, D. G.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Lim, J.

Lima, S. A. M.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Ma, B.

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

MacAdam, D. L.

Maennig, B.

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

Meerhiem, R.

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

Milaninia, K. M.

C. L. Mulder, K. Celebi, and K. M. Milaninia, “Saturated and efficient blue phosphorescent organic light emitting devices with Lambertian angular emission,” Appl. Phys. Lett. 90, 211109 (2007).
[CrossRef]

Misra, A.

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

Mulder, C. L.

C. L. Mulder, K. Celebi, and K. M. Milaninia, “Saturated and efficient blue phosphorescent organic light emitting devices with Lambertian angular emission,” Appl. Phys. Lett. 90, 211109 (2007).
[CrossRef]

Nagai, K.

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

Nakamura, T.

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

Neyts, K.

K. Neyts, “Microcavity effects and the outcoupling of light in displays and lighting applications based on thin emitting films,” Appl. Surf. Sci. 244, 517-523 (2005).
[CrossRef]

Oh, S. S.

Okuyama, K.

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

Park, B.

Patel, N. K.

N. K. Patel, S. Cina, and J. H. Burroughes, “High-efficiency organic light-emitting diodes,” IEEE J. Sel. Top. Quantum Electron. 8, 346-361 (2002).
[CrossRef]

Peng, H.

Pfeiffer, M.

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

Pfeiffer, Martin

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Pudzich, R.

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

Quirino, W. G.

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Qureshi, F.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Ren, X.

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

Roberts, M.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Salbeck, J.

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

Sato, F.

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

Schwartz, Gregor

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Seo, Y. H.

Smith, E.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Song, Y.-W.

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

Sun, Y.

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

Takeda, T.

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

Takezoe, H.

Tanaka, D.

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

Thompson, M. E.

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

S. R. Forrest, D. C. Bradley, and M. E. Thompson, “Measuring the efficiency of organic light-emitting diodes,” Adv. Mater. 15, 1043-1048 (2003).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

Tokito, S.

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

Tsutsui, T.

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

Tsutsumi, N.

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

Tsuzuki, T.

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

Walzer, K.

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

Walzer, Karsten

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Watanabe, S.

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

Wen, S.-W.

Whittaker, D. M.

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

Wong, M.

Yahiro, M.

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

Yokogawa, H.

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

Yokoyama, M.

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

Yu , X.-J.

Adv. Mater. (4)

S. R. Forrest, D. C. Bradley, and M. E. Thompson, “Measuring the efficiency of organic light-emitting diodes,” Adv. Mater. 15, 1043-1048 (2003).
[CrossRef]

B. W. D'Andrade and S. R. Forrest, “White organic light-emitting devices for solid-state lighting,” Adv. Mater. 16 (18), 1585-1595 (2004).
[CrossRef]

T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, and M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149-1152 (2001).
[CrossRef]

M. Pfeiffer, S. R. Forrest, K. Leo, and M. E. Thompson, “Electrophosphorescent p-i-n organic light emitting devices for very high efficiency flat panel displays,” Adv. Mater. 14, 1633-1636(2002).
[CrossRef]

Appl. Phys. Lett. (8)

Y.-C. Kim, S.-H. Cho, Y.-W. Song, Y.-J. Lee, Y.-H. Lee, and Y. R. Do, Planarized sinx/spin-on-glass photonic crystal organic light-emitting diodes,” Appl. Phys. Lett. 89, 173502 (2006).
[CrossRef]

S. Tokito, T. Iijima, T. Tsuzuki, and F. Sato, “High-efficiency white phosphorescent organic light-emitting devices with greenish-blue and red-emitting layers,” Appl. Phys. Lett. 83, 2459-2461 (2003).
[CrossRef]

J. Kido, K. Hongawa, K. Okuyama, and K. Nagai, “White light-emitting organic electroluminescent devices using the poly(N-vinylcarbazole) emitter layer doped with three fluorescent dyes,” Appl. Phys. Lett. 64, 815-817, (1994).
[CrossRef]

G. He, M. Pfeiffer, K. Leo, Michael Hofmann, Jan Birnstock, R. Pudzich, and J. Salbeck, “High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with double-emission layers,” Appl. Phys. Lett. 85, 3911-3913 (2004).
[CrossRef]

S. R. Forrest, X. Ren, J. Li, R. J. Holmes, B. W. D'Andrade, and M. E. Thompson, “Efficient, deep-blue organic electrophosphorescence by guest charge trapping,” Appl. Phys. Lett. 83, 3818-3820 (2003).
[CrossRef]

C. L. Mulder, K. Celebi, and K. M. Milaninia, “Saturated and efficient blue phosphorescent organic light emitting devices with Lambertian angular emission,” Appl. Phys. Lett. 90, 211109 (2007).
[CrossRef]

H. Kanno, N. C. Giebink, Y. Sun, and S. R. Forrest, “Stacked white organic light-emitting devices based on a combination of fluorescent and phosphorescent emitters,” Appl. Phys. Lett. 89, 023503 (2006).
[CrossRef]

Gregor Schwartz, Karsten Fehse, Martin Pfeiffer, Karsten Walzer, and Karl Leo, “Highly efficient white organic light emitting diodes comprising an interlayer to separate fluorescent and phosphorescent regions,” Appl. Phys. Lett. 89, 083509 (2006).
[CrossRef]

Appl. Surf. Sci. (1)

K. Neyts, “Microcavity effects and the outcoupling of light in displays and lighting applications based on thin emitting films,” Appl. Surf. Sci. 244, 517-523 (2005).
[CrossRef]

Chem. Rev. (1)

K. Walzer, B. Maennig, M. Pfeiffer, and K. Leo., “Highly efficient organic devices based on electrically doped transport layers,” Chem. Rev. 107, 1233-1271 (2007).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

P. Bienstman and R. Baets, “The RC2 LED: a novel resonant-cavity LED design using a symmetric resonant cavity in the outcoupling reflector,” IEEE J. Quantum Electron. 36, 669-673 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

N. K. Patel, S. Cina, and J. H. Burroughes, “High-efficiency organic light-emitting diodes,” IEEE J. Sel. Top. Quantum Electron. 8, 346-361 (2002).
[CrossRef]

IEEE J.Sel. Top. Quantum Electron. (1)

D. Delbeke, R. Bockstaele, P. Bienstman, R. Baets, and H. Benisty, “High-efficiency semiconductor resonant-cavity light-emitting diodes: a review.,” IEEE J.Sel. Top. Quantum Electron. 8, 189-206 (2002).
[CrossRef]

J. Appl. Phys. (3)

A. M. Adawi, L. G. Connolly, D. M. Whittaker, D. G. Lidzey, E. Smith, M. Roberts, F. Qureshi, C. Foden, and N. Athanassopoulou, “Improving the light extraction efficiency of red-emitting conjugated polymer light emitting diodes,” J. Appl. Phys. 99, 054505 (2006).
[CrossRef]

E. Thompson Chihaya Adachi, Marc A. Baldo, and Stephen R. Forrest, “Nearly 100% internal phosphorescence efficiency in an organic light emitting diode.J. Appl. Phys. 90, 5048-5051(2001).
[CrossRef]

T. Nakamura, N. Tsutsumi, N. Juni, and H. Fujii., “Improvement of coupling-out efficiency in organic electroluminescent devices by addition of a diffusive layer,” J. Appl. Phys. 96, 6016-6024 (2004).
[CrossRef]

J. Display Technol. (2)

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

D. Tanaka, Y. Agata, T. Takeda, S. Watanabe, and J. Kido, “High luminous efficiency blue organic light-emitting devices using high triplet excited energy materials,” Jpn. J. Appl. Phys. 46, L117-L119 (2007).
[CrossRef]

Nature (1)

Y. Sun, N. C. Giebink, H. Kanno, B. Ma, M. E. Thompson, and S. R. Forrest, “Management of singlet and triplet excitons for efficient white organic light-emitting devices,”Nature 440, 908-912 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Proc. SPIE (1)

R. Meerhiem, K. Walzer, G. He, M. Pfeiffer, and K. Leo, “Highly efficient organic light emitting diodes (OLED) for displays and lighting,” Proc. SPIE 6192, 61920P (2006).
[CrossRef]

Semicond. Sci. Technol. (1)

A. Misra, P. Kumar, M N. Kamalasanan, and S. Chandra, White organic LEDs and their recent advancements,” Semicond. Sci. Technol. 21, R35-R46 (2006).
[CrossRef]

Thin Solid Films (1)

W. G. Quirino, R. D. Adati, S. A. M. Lima, C. Legnani, M. Jafelicci Jr, M. R. Davolos, and M. Cremona, Electroluminescence of a device based on europium β-diketonate with phosphine oxide complex,”Thin Solid Films 515, 927-931(2006).
[CrossRef]

Other (3)

CIE 13.3-1995, “Method of measuring and specifying colour rendering properties of light sources,” ISBN: 3 900 734 57 7.

CIE 15:2004, Colorimetry, 3rd ed. www.cie.co.at.

CIE 177:2007, “Colour rendering of white LED light sources,” ISBN 978 3 901 906 57 2.

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Figures (6)

Fig. 1
Fig. 1

Maximal luminous efficacy of a color point in CIE 1931 x y color space; for example, illuminant A can achieve 512 lm / W [8].

Fig. 2
Fig. 2

Spectra of three emitters that yields illuminant A. (a) Spiro-DPVBi, Ir(ppy)3 in TCTA, and Ir(MDQ)(acac) in alpha-NPD. (b) The red emitter was replaced by a monochromatic emitter at 585 nm .

Fig. 3
Fig. 3

(a) Shifting and (b) stretching of the spectra of the blue emitter were obtained, respectively, with expressions (9, 10).

Fig. 4
Fig. 4

Variation of the spectral intensity of each of three emitters, as defined in Fig. 3. These variations affect the luminous efficacy, the CRI, and the luminous power efficiency.

Fig. 5
Fig. 5

Monochrome emitters found in the literature for the CIE x y 1931 chromaticity diagram. The luminous power efficiencies of these emitters are also shown.

Fig. 6
Fig. 6

Wavelength-dependent extraction efficiency that corresponds with the values listed in Tables 4, 5 for different stack configurations. Basic WOLED with (a) a blue phosphorescent emitter and (b) a blue fluorescent emitter. WOLEDs with additional interference layers with (c) a blue phosphosrescent and (d) a blue fluorescent emitter. The green and red emitters are always phosphorescent.

Tables (5)

Tables Icon

Table 1 Luminous Properties of the Spectra in Fig. 2a a

Tables Icon

Table 2 Properties of the Emitters shown in Fig. 5

Tables Icon

Table 3 Luminous Power Efficiency of the Composed WOLEDs

Tables Icon

Table 4 Typical stack of a three color White OLED a

Tables Icon

Table 5 Basic White OLEDs with and without Interference Layers a

Equations (10)

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

η P = i = b , g , r F i i = b , g , r P el , i .
E op , i ( λ ) = E el , i ( λ ) η c , i ( λ ) .
X i = E op , i ( λ ) x ¯ ( λ ) d λ , Y i = E op , i ( λ ) y ¯ ( λ ) d λ , Z i = E op , i ( λ ) z ¯ ( λ ) d λ .
X w = i = b , g , r A i X i , Y w = i = b , g , r A i Y i , Z w = i = b , g , r A i Z i .
F i = 683.0 A i E op , i ( λ ) V ( λ ) d λ .
P el , i = A i E el , i ( λ ) 1 η int , i qV λ hc d λ .
η W / W = i = b , g , r A i i = b , g , r A i η W / W , i .
η P = 683 E op ( λ ) V ( λ ) d λ E op d λ η W / W .
ϕ i ( λ ) ϕ ( λ λ 0 ) ,
ϕ i ( λ ) ϕ ( λ max + λ λ max narrow factor ) .

Metrics