Abstract

The far-field pattern of light-emitting diodes (LEDs) is an important issue in practical applications. We used a Monte Carlo photon-tracing method for the package design of flip-chip bonded power LEDs. As a first-order approximation, we propose using a plane light source model to calculate the far-field pattern of encapsulated LEDs. The far-field pattern is also studied by use of a more detailed model, which takes the structure of all epitaxial layers of a flip-chip bonded power LED into consideration. By comparing the simulation results with the experimental data, we have concluded that the plane light source model is much less time-consuming and offers fairly good precision for package design.

© 2005 Optical Society of America

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References

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  1. D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
    [CrossRef]
  2. R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
    [CrossRef]
  3. J. K. Roberts, “Binary complementary white LED illumination,” in Solid State Lighting and Displays, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4445, 23–38 (2001).
    [CrossRef]
  4. S. J. Lee, “Design rules for high-brightness light-emitting diodes grown on GaAs substrate,” Jpn. J. Appl. Phys. 37, 509–516 (1998).
    [CrossRef]
  5. S. J. Lee, “Analysis of light-emitting diodes by Monte Carlo photon simulation,” Appl. Opt. 40, 1427–1437 (2001).
    [CrossRef]
  6. S. J. Lee, “Light-emitting diode lamp design by Monte Carlo photon simulation,” in Light-Emitting Diodes: Research, Manufacturing, and Applications V, H. W. Yao, E. F. Schubert, eds., Proc. SPIE4278, 99–108 (2001).
  7. J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
    [CrossRef]
  8. E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
    [CrossRef]
  9. J. M. Hammersley, D. C. Handscomb, “Random, pseudorandom, and quasirandom numbers,” in Monte Carlo Methods (Wiley, New York, 1964), pp. 25–42.
    [CrossRef]
  10. A. Badano, J. Kanicki, “Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light-emitting devices,” J. Appl. Phys. 90, 1827–1830 (2001).
    [CrossRef]
  11. D. L. MacAdam, “Spectrophotometry,” in Color Measurement (Springer-Verlag, Berlin, 1981), pp. 36–45.
    [CrossRef]

2002 (2)

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

2001 (3)

S. J. Lee, “Analysis of light-emitting diodes by Monte Carlo photon simulation,” Appl. Opt. 40, 1427–1437 (2001).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

A. Badano, J. Kanicki, “Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light-emitting devices,” J. Appl. Phys. 90, 1827–1830 (2001).
[CrossRef]

1998 (1)

S. J. Lee, “Design rules for high-brightness light-emitting diodes grown on GaAs substrate,” Jpn. J. Appl. Phys. 37, 509–516 (1998).
[CrossRef]

Badano, A.

A. Badano, J. Kanicki, “Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light-emitting devices,” J. Appl. Phys. 90, 1827–1830 (2001).
[CrossRef]

Bhat, J. C.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

Christenson, G.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Collins, D.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

Eliashevich, I.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

Fletcher, R. M.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

Gardner, N. F.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Götz, W.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Hammersley, J. M.

J. M. Hammersley, D. C. Handscomb, “Random, pseudorandom, and quasirandom numbers,” in Monte Carlo Methods (Wiley, New York, 1964), pp. 25–42.
[CrossRef]

Handscomb, D. C.

J. M. Hammersley, D. C. Handscomb, “Random, pseudorandom, and quasirandom numbers,” in Monte Carlo Methods (Wiley, New York, 1964), pp. 25–42.
[CrossRef]

Kanicki, J.

A. Badano, J. Kanicki, “Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light-emitting devices,” J. Appl. Phys. 90, 1827–1830 (2001).
[CrossRef]

Kern, R. S.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Krames, M. R.

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Lee, S. J.

S. J. Lee, “Analysis of light-emitting diodes by Monte Carlo photon simulation,” Appl. Opt. 40, 1427–1437 (2001).
[CrossRef]

S. J. Lee, “Design rules for high-brightness light-emitting diodes grown on GaAs substrate,” Jpn. J. Appl. Phys. 37, 509–516 (1998).
[CrossRef]

S. J. Lee, “Light-emitting diode lamp design by Monte Carlo photon simulation,” in Light-Emitting Diodes: Research, Manufacturing, and Applications V, H. W. Yao, E. F. Schubert, eds., Proc. SPIE4278, 99–108 (2001).

Lowery, C.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Ludowise, M. J.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

MacAdam, D. L.

D. L. MacAdam, “Spectrophotometry,” in Color Measurement (Springer-Verlag, Berlin, 1981), pp. 36–45.
[CrossRef]

Martin, P. S.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Mueller, G. O.

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

Mueller-Mach, R.

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

Ochiai Holcomb, M.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

O'Shea, J. J.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Roberts, J. K.

J. K. Roberts, “Binary complementary white LED illumination,” in Solid State Lighting and Displays, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4445, 23–38 (2001).
[CrossRef]

Rudaz, S. L.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

Shelton, B. S.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

Shen, Y.-C.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Stefanov, E.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

Steigerwald, D. A.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Stockman, S. A.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Subramanya, S.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Trottier, T.

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

Venugopalan, H. S.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

Wierer, J. J.

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

Zhang, T.

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. J. Wierer, D. A. Steigerwald, M. R. Krames, J. J. O'Shea, M. J. Ludowise, G. Christenson, Y.-C. Shen, C. Lowery, P. S. Martin, S. Subramanya, W. Götz, N. F. Gardner, R. S. Kern, S. A. Stockman, “High-power AlGaInN flip-chip light-emitting diodes,” Appl. Phys. Lett. 78, 3379–3381 (2001).
[CrossRef]

J. Appl. Phys. (1)

A. Badano, J. Kanicki, “Monte Carlo analysis of the spectral photon emission and extraction efficiency of organic light-emitting devices,” J. Appl. Phys. 90, 1827–1830 (2001).
[CrossRef]

J. Sel. Top. Quantum Electron. (2)

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. Ochiai Holcomb, M. J. Ludowise, P. S. Martin, S. L. Rudaz, “Illumination with solid state lighting technology,” J. Sel. Top. Quantum Electron. 8, 310–320 (2002).
[CrossRef]

R. Mueller-Mach, G. O. Mueller, M. R. Krames, T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” J. Sel. Top. Quantum Electron. 8, 339–345 (2002).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S. J. Lee, “Design rules for high-brightness light-emitting diodes grown on GaAs substrate,” Jpn. J. Appl. Phys. 37, 509–516 (1998).
[CrossRef]

Other (5)

J. K. Roberts, “Binary complementary white LED illumination,” in Solid State Lighting and Displays, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4445, 23–38 (2001).
[CrossRef]

S. J. Lee, “Light-emitting diode lamp design by Monte Carlo photon simulation,” in Light-Emitting Diodes: Research, Manufacturing, and Applications V, H. W. Yao, E. F. Schubert, eds., Proc. SPIE4278, 99–108 (2001).

D. L. MacAdam, “Spectrophotometry,” in Color Measurement (Springer-Verlag, Berlin, 1981), pp. 36–45.
[CrossRef]

E. Stefanov, B. S. Shelton, H. S. Venugopalan, T. Zhang, I. Eliashevich, “Optimizing the external light extraction of nitride LEDs,” in Solid State Lighting II, L. T. Ferguson, Y.-S. Park, N. Narendran, S. P. DenBaars, eds., Proc. SPIE4776, 223–234 (2002).
[CrossRef]

J. M. Hammersley, D. C. Handscomb, “Random, pseudorandom, and quasirandom numbers,” in Monte Carlo Methods (Wiley, New York, 1964), pp. 25–42.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Package model.

Fig. 2
Fig. 2

Schematic diagram of model II.

Fig. 3
Fig. 3

Flowchart for the program using model II. In the chart, vectors r and n are adopted to describe the location and the direction of a photon, respectively. When a photon reaches the interface of two materials, such as dielectric–dielectric or dielectric–metal, the boundary conditions are used to determine the photon's fate: reflected, refracted, or absorbed.

Fig. 4
Fig. 4

Simulation results of two models together with experiment results for four package forms: (a) form 1, (b) form 2, (c) form 3, (d) form 4.

Tables (1)

Tables Icon

Table 1 Comparison of Simulation and Experiment Results on θ1/2

Equations (2)

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

n 1 = [ 1 ( 1 2 ξ 1 ) 2 ] 1 / 2 cos ( 2 π ξ 2 ) , n 2 = [ 1 ( 1 2 ξ 1 ) 2 ] 1 / 2 sin ( 2 π ξ 2 ) , n 3 = 1 2 ξ 1 ,
T = exp ( α d ) ,

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