Computational study of power conversion and luminous efficiency performance for semiconductor quantum dot nanophosphors on light-emitting diodes

Talha Erdem; Sedat Nizamoglu; Hilmi Volkan Demir

doi:10.1364/OE.20.003275

Computational study of power conversion and luminous efficiency performance for semiconductor quantum dot nanophosphors on light-emitting diodes

Talha Erdem, Sedat Nizamoglu, and Hilmi Volkan Demir

Optics Express
Vol. 20,
Issue 3,
pp. 3275-3295
(2012)
•https://doi.org/10.1364/OE.20.003275

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Talha Erdem, Sedat Nizamoglu, and Hilmi Volkan Demir, "Computational study of power conversion and luminous efficiency performance for semiconductor quantum dot nanophosphors on light-emitting diodes," Opt. Express 20, 3275-3295 (2012)

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Related Topics
Table of Contents Category
- Optical Devices
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Optical materials (160.4670)
- Optical properties (160.4760)
- Light-emitting diodes (230.3670)
- Quantum-well, -wire and -dot devices (230.5590)

About this Article
History
- Original Manuscript: November 28, 2011
- Revised Manuscript: January 18, 2012
- Manuscript Accepted: January 25, 2012
- Published: January 27, 2012

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Open Access

Abstract

We present power conversion efficiency (PCE) and luminous efficiency (LE) performance levels of high photometric quality white LEDs integrated with quantum dots (QDs) achieving an averaged color rendering index of ≥90 (with R9 at least 70), a luminous efficacy of optical radiation of ≥380 lm/W_opt a correlated color temperature of ≤4000 K, and a chromaticity difference dC <0.0054. We computationally find that the device LE levels of 100, 150, and 200 lm/W_elect can be achieved with QD quantum efficiency of 43%, 61%, and 80% in film, respectively, using state-of-the-art blue LED chips (81.3% PCE). Furthermore, our computational analyses suggest that QD-LEDs can be both photometrically and electrically more efficient than phosphor based LEDs when state-of-the-art QDs are used.

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References

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Publication

Energy Savings Estimates of Light Emitting Diodes in Niche Lighting Applications, Building Technologies Program, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy (2011).
J. M. Phillips, M. F. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1(4), 307–333 (2007).
[Crossref]
S. Nizamoglu, T. Erdem, X. W. Sun, and H. V. Demir, “Warm-white light-emitting diodes integrated with colloidal quantum dots for high luminous efficacy and color rendering,” Opt. Lett. 35(20), 3372–3374 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=ol-35-20-3372 .
[Crossref] [PubMed]
M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]
DEMA Electronic AG, http://www.zenigata.de (accessed on August 17, 2011).
Cree Inc, http://www.cree.com/press/enlarge.asp?i=1174480795673 (accessed on August 17, 2011).
OSRAM Opto Semiconductors GmbH, http://www.osram-os.com/osram_os/EN/Press/Press_Releases/Solid_State_Lighting/2011/From_the_OSRAM_laboratory_-_efficiency_record_for_warm_white.html (accessed on August 17, 2011).
O. Graydon, “The new oil?” Nat. Photonics 5(1), 1 (2011).
[Crossref]
T. Erdem and H. V. Demir, “Semiconductor nanocrystals as rare-earth alternatives,” Nat. Photonics 5(3), 126 (2011).
[Crossref]
T. Erdem, S. Nizamoglu, X. W. Sun, and H. V. Demir, “A photometric investigation of ultra-efficient LEDs with high color rendering index and high luminous efficacy employing nanocrystal quantum dot luminophores,” Opt. Express 18(1), 340–347 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-1-340 .
[Crossref] [PubMed]
K. Sanderson, “Quantum dots go large,” Nature 459(7248), 760–761 (2009).
[Crossref] [PubMed]
E. Jang, S. Jun, H. Jang, J. Lim, B. Kim, and Y. Kim, “White-light-emitting diodes with quantum dot color converters for display backlights,” Adv. Mater. (Deerfield Beach Fla.) 22(28), 3076–3080 (2010).
[Crossref] [PubMed]
E. Matioli, E. Rangel, M. Iza, B. Fleury, N. Pfaff, J. Speck, E. Hu, and C. Weisbuch, “High extraction efficiency light-emitting diodes based on embedded air-gap photonic-crystals,” Appl. Phys. Lett. 96(3), 031108 (2010).
[Crossref]
M.-A. Tsai, H.-W. Wang, P. Yu, H.-C. Kuo, and S.-H. Lin, “High extraction efficiency of GaN-based vertical-injection light-emitting diodes using distinctive indium–tin-oxide nanorod by glancing-angle deposition,” Jpn. J. Appl. Phys. 50(5), 052102 (2011).
[Crossref]
Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]
K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]
D. S. Ginger and N. C. Greenham, “Charge injection and transport in films of CdSe nanocrystals,” J. Appl. Phys. 87(3), 1361–1368 (2000).
[Crossref]

2011 (3)

O. Graydon, “The new oil?” Nat. Photonics 5(1), 1 (2011).
[Crossref]

T. Erdem and H. V. Demir, “Semiconductor nanocrystals as rare-earth alternatives,” Nat. Photonics 5(3), 126 (2011).
[Crossref]

M.-A. Tsai, H.-W. Wang, P. Yu, H.-C. Kuo, and S.-H. Lin, “High extraction efficiency of GaN-based vertical-injection light-emitting diodes using distinctive indium–tin-oxide nanorod by glancing-angle deposition,” Jpn. J. Appl. Phys. 50(5), 052102 (2011).
[Crossref]

2010 (5)

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

T. Erdem, S. Nizamoglu, X. W. Sun, and H. V. Demir, “A photometric investigation of ultra-efficient LEDs with high color rendering index and high luminous efficacy employing nanocrystal quantum dot luminophores,” Opt. Express 18(1), 340–347 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-1-340 .
[Crossref] [PubMed]

S. Nizamoglu, T. Erdem, X. W. Sun, and H. V. Demir, “Warm-white light-emitting diodes integrated with colloidal quantum dots for high luminous efficacy and color rendering,” Opt. Lett. 35(20), 3372–3374 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=ol-35-20-3372 .
[Crossref] [PubMed]

E. Jang, S. Jun, H. Jang, J. Lim, B. Kim, and Y. Kim, “White-light-emitting diodes with quantum dot color converters for display backlights,” Adv. Mater. (Deerfield Beach Fla.) 22(28), 3076–3080 (2010).
[Crossref] [PubMed]

E. Matioli, E. Rangel, M. Iza, B. Fleury, N. Pfaff, J. Speck, E. Hu, and C. Weisbuch, “High extraction efficiency light-emitting diodes based on embedded air-gap photonic-crystals,” Appl. Phys. Lett. 96(3), 031108 (2010).
[Crossref]

2009 (1)

K. Sanderson, “Quantum dots go large,” Nature 459(7248), 760–761 (2009).
[Crossref] [PubMed]

2007 (2)

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

J. M. Phillips, M. F. Coltrin, M. H. Crawford, A. J. Fischer, M. R. Krames, R. Mueller-Mach, G. O. Mueller, Y. Ohno, L. E. S. Rohwer, J. A. Simmons, and J. Y. Tsao, “Research challenges to ultra-efficient inorganic solid-state lighting,” Laser Photon. Rev. 1(4), 307–333 (2007).
[Crossref]

2005 (1)

K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]

2000 (1)

D. S. Ginger and N. C. Greenham, “Charge injection and transport in films of CdSe nanocrystals,” J. Appl. Phys. 87(3), 1361–1368 (2000).
[Crossref]

Boatman, E. M.

K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]

Coltrin, M. F.

Craford, M. G.

Crawford, M. H.

Demir, H. V.

T. Erdem and H. V. Demir, “Semiconductor nanocrystals as rare-earth alternatives,” Nat. Photonics 5(3), 126 (2011).
[Crossref]

Erdem, T.

T. Erdem and H. V. Demir, “Semiconductor nanocrystals as rare-earth alternatives,” Nat. Photonics 5(3), 126 (2011).
[Crossref]

Fischer, A. J.

Fleury, B.

Ginger, D. S.

D. S. Ginger and N. C. Greenham, “Charge injection and transport in films of CdSe nanocrystals,” J. Appl. Phys. 87(3), 1361–1368 (2000).
[Crossref]

Graydon, O.

O. Graydon, “The new oil?” Nat. Photonics 5(1), 1 (2011).
[Crossref]

Greenham, N. C.

D. S. Ginger and N. C. Greenham, “Charge injection and transport in films of CdSe nanocrystals,” J. Appl. Phys. 87(3), 1361–1368 (2000).
[Crossref]

Harbers, G.

Hu, E.

Ichikawa, M.

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Iza, M.

Jang, E.

Jang, H.

Jun, S.

Kim, B.

Kim, Y.

Krames, M. R.

Kuo, H.-C.

Lim, J.

Lin, S.-H.

Lisensky, G. C.

K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]

Matioli, E.

Mueller, G. O.

Mueller-Mach, R.

Mukai, T.

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Narukawa, Y.

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Nizamoglu, S.

Nordell, K. J.

K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]

Ohno, Y.

Pfaff, N.

Phillips, J. M.

Rangel, E.

Rohwer, L. E. S.

Sanderson, K.

K. Sanderson, “Quantum dots go large,” Nature 459(7248), 760–761 (2009).
[Crossref] [PubMed]

Sanga, D.

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Sano, M.

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Shchekin, O. B.

Simmons, J. A.

Speck, J.

Sun, X. W.

Tsai, M.-A.

Tsao, J. Y.

Wang, H.-W.

Weisbuch, C.

Yu, P.

Zhou, L.

Adv. Mater. (Deerfield Beach Fla.) (1)

Appl. Phys. Lett. (1)

J. Appl. Phys. (1)

D. S. Ginger and N. C. Greenham, “Charge injection and transport in films of CdSe nanocrystals,” J. Appl. Phys. 87(3), 1361–1368 (2000).
[Crossref]

J. Chem. Educ. (1)

K. J. Nordell, E. M. Boatman, and G. C. Lisensky, “A safer, easier, faster synthesis for CdSe quantum dot nanocrystals,” J. Chem. Educ. 82(11), 1697–1699 (2005).
[Crossref]

J. Disp. Technol. (1)

J. Phys. D Appl. Phys. (1)

Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010).
[Crossref]

Jpn. J. Appl. Phys. (1)

Laser Photon. Rev. (1)

Nat. Photonics (2)

O. Graydon, “The new oil?” Nat. Photonics 5(1), 1 (2011).
[Crossref]

T. Erdem and H. V. Demir, “Semiconductor nanocrystals as rare-earth alternatives,” Nat. Photonics 5(3), 126 (2011).
[Crossref]

Nature (1)

K. Sanderson, “Quantum dots go large,” Nature 459(7248), 760–761 (2009).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Other (4)

DEMA Electronic AG, http://www.zenigata.de (accessed on August 17, 2011).

Cree Inc, http://www.cree.com/press/enlarge.asp?i=1174480795673 (accessed on August 17, 2011).

OSRAM Opto Semiconductors GmbH, http://www.osram-os.com/osram_os/EN/Press/Press_Releases/Solid_State_Lighting/2011/From_the_OSRAM_laboratory_-_efficiency_record_for_warm_white.html (accessed on August 17, 2011).

Energy Savings Estimates of Light Emitting Diodes in Niche Lighting Applications, Building Technologies Program, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy (2011).

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Fig. 1 Illustration of layered (A) and blend (B) architectures.

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Fig. 2 Fraction of the blue photons transferred to the green QDs (bg), to the yellow QDs (by), to the red QDs (br), and being extracted (be); fraction of the green photons self-absorbed (gg), transferred to the yellow QDs (gy), to the red QDs (gr), and being extracted (ge); fraction of the yellow photons self-absorbed (yy), transferred to the red QDs (yr), and being extracted (ye); and fraction of the red photons self-absorbed (rr) and being extracted (re) in A and B at η = 100%.

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Fig. 3 Fraction of the blue photons transferred to the green QDs (bg), to the yellow QDs (by), to the red QDs (br), and being extracted (be); fraction of the green photons self-absorbed (gg), transferred to the yellow QDs (gy), to the red QDs (gr), and being extracted (ge); fraction of the yellow photons self-absorbed (yy), transferred to the red QDs (yr), and being extracted (ye); and fraction of the red photons self-absorbed (rr) and being extracted (re) in A and B at η = 50%.

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Fig. 4 The luminous efficiency as a function of the variation in quantum efficiency for architectures A and B. In this analysis, η_QD of two of the QD luminophors is fixed at 100%, 80%, 50%, and 20%; η_QD of the remaining QD luminophor is changed between 20% and 100%. The points shown in the figure correspond to the luminous efficiency of QD color component whose efficiency spans this range.

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Fig. 5 Illustration of optical mechanisms using system box model for architecture A.

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Fig. 6 Illustration of optical mechanisms using system boxes for A_rev.

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Fig. 7 Illustration of optical mechanisms using system boxes for B.

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Tables (4)

Table 1 Maximum, Minimum, Average and Standard Deviation of PCE (Taking Unity PCE of the Blue LED) and LE (Taking a PCE of 81.3% for the Blue LED) for the Photometrically Efficient Spectra

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Table 2 Maximum, minimum, average and standard deviation of LE (with PCE of the blue LED taken as 81.3%) in lm/W_elect for the photometrically efficient spectra with QD’s η = 80%, 50% and 20% for two different architectures: A and B. The effect of self-absorption (SA) is also investigated for architecture A.

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Table 3 Maximum, minimum, average and standard deviation of PCE (with PCE of the blue LED taken as 100%) in percentages for the photometrically efficient spectra with QD’s η = 80%, 50% and 20% for two different architectures. The effect of self-absorption (SA) is also investigated for architecture A.

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Table 4 Average of the spectral parameters belonging to the spectra whose PCE is larger than the average PCE of the photometrically efficient spectra in A and B while varying quantum efficiencies. λ_i: peak emission wavelength, Δλ_i: full-width at half-maximum, a_i: weight of the color component i. i is either blue (b), green (g), yellow (y) or red (r).

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Equations (93)

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L E R = 683 l m / w_{o p t} \frac{\int v (λ) s (λ) d λ}{\int s (λ) d λ}

L E = 683 l m / W_{o p t} \frac{\int V (λ) s (λ) d λ}{P_{e l e c t}}

λ_{a b s} = \frac{λ_{e m} - 8.3045}{1.0308}

P_{o p t, L E D} = γ \int S_{b 1} g_{L E D} (λ, λ_{b}, Δ λ_{b}) d λ

γ = \frac{P_{o p t, L E D}}{\int S_{b 1} g_{L E D} (λ, λ_{b}, Δ λ_{b}) d λ}

S_{b, f i n a l} = γ S_{b}

S_{y, f i n a l} = γ S_{g}

S_{r, f i n a l} = γ S_{y}

S_{r, f i n a l} = γ S_{r}

\begin{matrix} s (λ) = S_{b, f i n a l} g (λ, λ_{b}, Δ λ_{b}) + S_{g, f i n a l} g (λ, λ_{g}, Δ λ_{g}) \\ + S_{y, f i n a l} g (λ, λ_{y}, Δ λ_{y}) + S_{r, f i n a l} g (λ, λ_{r}, Δ λ_{r}) \end{matrix}

P C E = \frac{\int^{​} s (λ) d λ}{P_{e l e c t}}

L E = P C E \times L E R

c_{4} \approx 1 - (1 - c_{2}) \frac{α_{y} (λ_{g})}{α_{y} (λ_{b})}

c_{5} \approx 1 - (1 - c_{3}) \frac{α_{r} (λ_{g})}{α_{r} (λ_{b})}

c_{6} \approx 1 - (1 - c_{3}) \frac{α_{r} (λ_{y})}{α_{r} (λ_{b})}

E = \frac{k (1 - c^{'}) + (1 - k) (1 - c_{a}^{"}) {(1 - c_{t})}^{2} (1 - c_{b}^{"})}{1 - k c^{'} η - (1 - k) c_{a}^{"} η - (1 - k) (1 - c_{a}^{"}) {(1 - c_{t})}^{2} c_{b}^{"} η}

T = \frac{(1 - k) (1 - c_{a}^{"}) c_{t} [1 + (1 - c_{t})]}{1 - k c^{'} η - (1 - k) c_{a}^{"} η - (1 - k) (1 - c_{a}^{"}) {(1 - c_{t})}^{2} c_{b}^{"} η}

L = \frac{(1 - η) [k c^{'} + (1 - k) (1 - c_{a}^{"}) {(1 - c_{t})}^{2} c_{b}^{"} + (1 - k) c_{a}^{"}]}{1 - k c^{'} η - (1 - k) c_{a}^{"} η - (1 - k) (1 - c_{a}^{"}) {(1 - c_{t})}^{2} c_{b}^{"} η}

c_{m j a}^{''} = \int_{0}^{z_{m}} d_{m j} (z) (1 - e^{- α_{m} (λ_{m}) (z_{m} - z)}) d z

c_{m j a}^{''} = \int_{0}^{z_{m}} d_{m j} (z) (1 - e^{- α_{m} (λ_{m}) z}) d z

c_{m j b}^{''} = 1 - e^{- α_{m} (λ_{m}) z_{m}}

d_{m 0} (z) = κ_{m 0} e^{- α_{m} (λ_{b}) z}

d_{y g} (z) = κ_{yg} {\begin{cases} [e^{- α_{y} (λ_{g}) (z_{y} - z)} + (1 - c_{4}) {(1 - c_{5})}^{2} e^{- α_{y} (λ_{g}) z}] e^{- α_{y} (λ_{g}) (z_{y} - z)} \\ + (1 - c_{4}) {(1 - c_{5})}^{2} e^{- α_{y} (λ_{g}) z} \end{cases}}

d_{r g} (z) = κ_{rg} {[e^{- α_{r} (λ_{g}) (z_{r} - z)} + (1 - c_{5}) e^{- α_{r} (λ_{g}) z}] e^{- α_{r} (λ_{g}) (z_{r} - z)} + (1 - c_{5}) e^{- α_{r} (λ_{g}) z}}

d_{r y} (z) = κ_{ry} {[e^{- α_{r} (λ_{y}) (z_{r} - z)} + (1 - c_{6}) e^{- α_{r} (λ_{y}) z}] e^{- α_{r} (λ_{y}) (z_{r} - z)} + (1 - c_{6}) e^{- α_{r} (λ_{y}) z}}

c_{t g} = c_{4} + (1 - c_{4}) {(1 - c_{5})}^{2} c_{4} + (1 - c_{4}) c_{5} + (1 - c_{4}) (1 - c_{5}) c_{5}

c_{t y} = c_{6} + c_{6} (1 - c_{6})

c_{t r} = 0

s_{g 0} = s_{b 1} c_{1} (1 - c_{2}) (1 - c_{3}) η_{g}

s_{g n} = s_{g 0} E_{g 0}

s_{y 0} = s_{b 1} (1 - c_{3}) c_{2} η_{y}

s_{y g 0} = s_{g 0} T_{g 0} \frac{c_{4} + (1 - c_{4}) {(1 - c_{5})}^{2} c_{4}}{c_{4} + (1 - c_{4}) {(1 - c_{5})}^{2} c_{4} + c_{5} (1 - c_{4}) + c_{5} (1 - c_{4}) (1 - c_{5})} η_{y}

s_{y n} = s_{y 0} E_{y 0} + s_{y g 0} E_{y g}

s_{r 0} = s_{b 1} c_{3}) η_{r}

s_{r g 0} = s_{g 0} T_{g 0} \frac{c_{5} + (1 - c_{4}) + c_{5} (1 - c_{4}) (1 - c_{5})}{c_{4} + (1 - c_{4}) {(1 - c_{5})}^{2} c_{4} + c_{5} (1 - c_{4}) + c_{5} (1 - c_{4}) (1 - c_{5})} η_{y}

s_{r y 0} = s_{y 0} T_{y g} η_{r}

s_{r y g 0} = s_{y g 0} T_{y g} η_{r}

s_{r n} = s_{r 0} E_{r 0} + s_{r g 0} E_{r g} + s_{r y 0} E_{r y} + s_{r y g 0} E_{r y}

s_{b n} = s_{b 1} (1 - c_{1}) (1 - c_{2}) (1 - c_{3})

E = \frac{(1 - c_{t}) [k (1 - c') + (1 - k) (1 - c_{a}'') (1 - c_{b}'')]}{1 - k c' η - (1 - k) c_{a}'' η - (1 - k) (1 - c_{a}'') c_{b}'' η}

T = \frac{c_{t} [k (1 - c') + (1 - k) (1 - c_{a}'') (1 - c_{b}'')]}{1 - k c' η - (1 - k) c_{a}'' η - (1 - k) (1 - c_{a}'') c_{b}'' η}

L = \frac{(1 - η) [k c' + (1 - k) (1 - c_{a}'') c_{b}'' + (1 - k) c_{a}'']}{1 - k c' η - (1 - k) c_{a}'' η - (1 - k) (1 - c_{a}'') c_{b}'' η}

d_{m j} (z) = κ_{m j} e^{- α_{m} (λ_{j}) z}

S_{g 0} = S_{b 1} c_{1} η_{g}

S_{g n} = S_{g 0} E_{g 0}

S_{y 0} = S_{b 1} (1 - c_{1}) c_{2} η_{y}

S_{y g 0} = S_{g 0} T_{g 0} \frac{c_{4}}{c_{4} + (1 - c_{4}) c_{5}} η_{y}

S_{y n} = S_{y 0} E_{y 0} + S_{y g 0} E_{y g}

S_{r 0} = S_{b 1} (1 - c_{1}) (1 - c_{2}) c_{3} η_{r}

S_{r g 0} = S_{g 0} T_{g 0} \frac{c_{5} (1 - c_{4})}{c_{4} + (1 - c_{4}) c_{5}} η_{r}

S_{r y 0} = S_{y 0} T_{y o} η_{r}

S_{r y g 0} = S_{y g 0} T_{y g} η_{r}

S_{r n} = S_{r 0} E_{r 0} + S_{r g 0} E_{r g} + S_{r y 0} E_{r y} + S_{r y g 0} E_{r y}

S_{b n} = S_{b 1} (1 - c_{1}) (1 - c_{2}) (1 - c_{3})

E = \frac{k (1 - c') (1 - c'_{t}) + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') (1 - c_{b}'') (1 - c_{t b}'')}{1 - η [k c' + (1 - k) c_{a}'' + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') c_{b}'']}

T = \frac{k (1 - c') c'_{t} + (1 - k) (1 - c_{a}'') c_{t a}'' + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') (1 - c_{b}'') c_{t b}''}{1 - η [k c' + (1 - k) c_{a}'' + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') c_{b}'']}

L = \frac{(1 - η) [k c' + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') c_{b}'' + (1 - k) c_{a}'']}{1 - η [k c' + (1 - k) c_{a}'' + (1 - k) (1 - c_{a}'') (1 - c_{t a}'') c_{b}'']}

{c^{'}}_{m j} = \int_{0}^{z_{l}} f_{m} d_{m} (z) (1 - e^{- α_{m} (λ_{m}) (z_{1} - z)}) d z

c_{m j a}^{''} = \int_{0}^{z_{l}} f_{m} d_{m j} (z) (1 - e^{- α_{m} (λ_{m}) z}) d z

c_{m j b}^{''} = f_{m} (1 - e^{- α_{m} (λ_{m}) z_{l}})

d_{m 0} (z) = κ_{m 0} e^{- α_{m} (λ_{b}) z}

d_{y g 0} (z) = k_{y g 0} d_{g 0} (z) [\begin{matrix} \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{g}) (z - z_{i})} d z_{i} + \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{g}) (z_{i} - z)} d z_{i} + \\ f_{y} e^{- α_{y} (λ_{g}) z} \int_{0}^{z_{l}} f_{g} e^{- α_{g} (λ_{g}) z_{i}} d z_{i} + \\ f_{y} e^{- α_{y} (λ_{g}) z} \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{g}) z_{i}} d z_{i} + f_{y} e^{- α_{y} (λ_{g}) z} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{g}) z_{i}} d z_{i} \end{matrix}]

d_{r g 0} (z) = k_{r g 0} d_{g 0} (z) [\begin{matrix} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{g}) (z - z_{i})} d z_{i} + \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{g}) (z_{i} - z)} d z_{i} + \\ f_{r} e^{- α_{r} (λ_{g}) z} \int_{0}^{z_{l}} f_{g} e^{- α_{g} (λ_{g}) z_{i}} d z_{i} + f_{r} e^{- α_{r} (λ_{g}) z} \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{g}) z_{i}} d z_{i} + \\ f_{r} e^{- α_{r} (λ_{g}) z} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{g}) z_{i}} d z_{i} \end{matrix}]

d_{r y 0} (z) = k_{r y 0} d_{y 0} (z) [\begin{matrix} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) (z - z_{i})} d z_{i} + \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) (z_{i} - z)} d z_{i} + \\ f_{r} e^{- α_{r} (λ_{y}) z} \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{y}) z_{i}} d z_{i} + f_{r} e^{- α_{r} (λ_{y}) z} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) z_{i}} d z_{i} + \end{matrix}]

d_{r y g 0} (z) = k_{r y g 0} d_{y g 0} (z) [\begin{matrix} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) (z - z_{i})} d z_{i} + \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) (z_{i} - z)} d z_{i} + \\ f_{r} e^{- α_{r} (λ_{y}) z} \int_{0}^{z_{l}} f_{y} e^{- α_{y} (λ_{y}) z_{i}} d z_{i} + f_{r} e^{- α_{r} (λ_{y}) z} \int_{0}^{z_{l}} f_{r} e^{- α_{r} (λ_{y}) z_{i}} d z_{i} + \end{matrix}]

c_{t g 0}^{'} = \int_{0}^{z_{l}} d_{g 0} (z) f_{y} (1 - e^{- α_{y} (λ_{g}) z}) d z + \int_{0}^{z_{l}} d_{g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{g}) (z_{l} - z)}) d z

c_{t g 0 a}^{"} = \int_{0}^{z_{l}} d_{g 0} (z) f_{y} (1 - e^{- α_{y} (λ_{g}) z}) d z + \int_{0}^{z_{l}} d_{g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{g}) z}) d z

c_{t g 0 b}^{"} = f_{r} (1 - e^{- α_{y} (λ_{g}) z_{l}}) + f_{y} (1 - e^{- α_{r} (λ_{y}) z_{l}})

c_{t y g 0}^{'} = \int_{0}^{z_{l}} d_{y g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{y}) (z_{l} - z)}) d z

c_{t y 0 a}^{''} = \int_{0}^{z_{l}} d_{y 0} (z) f_{r} (1 - e^{- α_{r} (λ_{y}) z}) d z

c_{t y 0 b}^{''} = f_{r} (1 - e^{- α_{r} (λ_{y}) z_{l}})

{c^{'}}_{t y g 0} \int_{0}^{z_{l}} d_{y g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{y}) (z_{l} - z)}) d z

c_{t y g 0 a}^{''} = \int_{0}^{z_{l}} d_{y g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{y}) z}) d z

c_{t y g 0 b}^{''} = f_{r} (1 - e^{- α_{r} (λ_{y}) z_{l}})

t_{y} = \frac{k (1 - c^{'}) c_{y}^{'} + (1 - k) (1 - c_{a}^{''}) c_{y}^{''} + (1 - k) (1 - c_{a}^{''}) (1 - c_{t a}^{''}) (1 - c_{b}^{''}) c_{y b}^{''}}{k (1 - c^{'}) (c_{y}^{'} + c_{r}^{'}) + (1 - k) (1 - c_{a}^{''}) (c_{y}^{''} + c_{r}^{''}) + (1 - k) (1 - c_{a}^{''}) (1 - c_{t a}^{''}) (1 - c_{b}^{''}) (c_{y b}^{''} + c_{r b}^{''})}

t_{r} = 1 - t_{y}

c_{y}^{'} = \int_{0}^{z_{l}} d_{g 0} (z) f_{y} (1 - e^{- α_{y} (λ_{g}) (z_{l} - z)}) d z

c_{y}^{''} = \int_{0}^{z_{l}} d_{g 0} (z) f_{y} (1 - e^{- α_{y} (λ_{g}) z}) d z

c_{y b}^{''} = f_{y} (1 - e^{- α_{y} (λ_{g}) z_{l}})

c_{y}^{'} = \int_{0}^{z_{l}} d_{g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{g}) (z_{l} - z)}) d z

c_{r}^{''} = \int_{0}^{z_{l}} d_{g 0} (z) f_{r} (1 - e^{- α_{r} (λ_{g}) z}) d z

c_{r b}^{''} = f_{y} (1 - e^{- α_{r} (λ_{g}) z_{l}})

S_{g 0}^{} = S_{b 1} f_{g} (1 - e^{- α_{g} (λ_{b}) z_{l}}) η_{g}

S_{y 0}^{} = S_{b 1} f_{y} (1 - e^{- α_{y} (λ_{b}) z_{l}}) η_{y}

S_{r 0}^{} = S_{b 1} f_{r} (1 - e^{- α_{r} (λ_{b}) z_{l}}) η_{r}

S_{g n} = S_{g 0} E_{g 0}

S_{y g 0} = η_{y} S_{g 0} T_{g 0} t_{y}

S_{r g 0} = η_{r} S_{g 0} T_{g 0} t_{r}

S_{y n} = S_{y 0} E_{y 0} + S_{y g 0} E_{y g 0}

S_{r y 0} = S_{y 0} T_{y 0} η_{r}

S_{r y g 0} = S_{y g 0} T_{y g 0} η_{r}

S_{r n} = S_{r 0} E_{r 0} + S_{r g 0} E_{r g 0} + S_{r y 0} E_{r y 0} + S_{r y g 0} E_{r y g 0}

S_{b n} = S_{b 1} [f_{g} e^{- α_{g} (λ_{b}) z_{l}} + f_{y} e^{- α_{y} (λ_{b}) z_{l}} + f_{r} e^{- α_{r} (λ_{b}) z_{l}}]

	max.	min.	aver.	st. dev.
PCE (%) (with 100% PCE of blue LED)	82.7	81.6	82.1	0.3
LE (lm/W_elect) (with 81.3% PCE of blue LED)	256.1	253.2	254.3	0.8

LE (lm/W_elect)	η = 80%				η = 50%				η = 20%
LE (lm/W_elect)	max.	min.	avg.	st. dev.	max.	min.	avg.	st. dev.	max.	min.	avg.	st. dev
A without SA	204.2	201.4	202.7	0.9	126.9	124.6	125.5	0.9	50.4	49.1	49.6	0.5
A with SA	200.6	197.5	199.0	1.0	120.0	116.7	118.6	1.1	44.1	41.7	43.6	0.7
B	193.9	190.5	192.0	1.2	108.0	104.5	106.1	1.1	36.3	34.5	35.3	0.6
A without SA – A w. SA	3.9	3.0	3.7	0.3	7.9	6.2	7.0	0.7	7.4	5.2	6.0	0.7
A w. SA – B	7.8	6.5	7.0	0.4	13.4	11.7	12.5	0.5	9.1	7.2	8.3	0.6

PCE (%)	η = 80%				η = 50%				η = 20%
PCE (%)	max.	min.	avg.	st. dev.	max.	min.	avg.	st. dev.	max	min.	avg	st. dev
A without SA	64.9	63.8	64.3	0.4	42.9	37.4	39.8	0.3	17.2	14.4	15.6	0.2
A w. SA	66.0	65.0	65.5	0.4	41.1	31.9	36.0	0.4	15.6	9.7	12.4	0.3
B	62.7	61.3	62.0	0.5	37.2	30.0	32.8	0.4	12.4	9.4	10.8	0.2
A without SA – A w. SA	1.3	1.0	1.2	0.1	2.6	2.0	2.3	0.2	2.4	1.7	1.9	0.2
A w. SA – B	2.5	2.1	2.2	0.1	4.3	3.8	4.0	0.2	2.9	2.3	2.7	0.2

Architecture	η_QD	100%	80%	50%	20%
A	λ_b, λ_g, λ_y, λ_r (nm)	472, 542, 559, 620	472, 542, 559, 620	471, 541, 559, 620	471, 542, 559, 620
	Δλ_b, Δλ_g, Δλ_y, Δλ_r (nm)	28.4, 30.8, 54.8, 27.6	28.4, 30.8, 54.8, 27.6	29.0, 31.0, 56.0, 28.0	27.7, 31.7, 54.0, 27.1
	a_b, a_g, a_y, a_r (/1000)	153, 153, 153, 541	153, 153, 153, 541	155, 155, 155, 535	150, 150, 150, 550
B	λ_b, λ_g, λ_y, λ_r (nm)	472, 542, 559, 620	472, 542, 559, 620	472, 543, 558, 620	471, 541, 559, 620
	Δλ_b, Δλ_g, Δλ_y, Δλ_r (nm)	28.4, 30.8, 54.8, 27.6	28.4, 30.8, 54.8, 27.6	30.0, 32.7, 55.3, 27.3	29.0, 31.0, 56.0, 28.0
	a_b, a_g, a_y, a_r (/1000)	153, 153, 153, 541	153, 153, 153, 541	151, 151, 151, 547	155, 155, 155, 535

	max.	min.	aver.	st. dev.
PCE (%) (with 100% PCE of blue LED)	82.7	81.6	82.1	0.3
LE (lm/W_elect) (with 81.3% PCE of blue LED)	256.1	253.2	254.3	0.8

Abstract

References

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