Abstract

We demonstrated a conformal phosphor coating method for phosphor-converted white light-emitting diodes (LEDs) using capillary microchannel formed by a fixture. The mixture of the phosphor particles and the silicone spontaneously flows in capillary microchannel and was pinned at the edge of the fixture due to the surface tension effect. The present coating method was applied to different packaging types with both the conventional chip and the vertical injection chip. Experimental results show this method can efficiently improve the angular color uniformity (ACU). Compared with those samples packaged by conventional dispensing coating, angular color correlated temperature (CCT) deviation of the test samples by the present method can reduce from 1500K to 200K for the average CCT 5200K from −90°to +90 view angles, and reduce from 5000K to 1000K for the average CCT 9150K. Additionally, this method can prevent the packaging non-consistency that the average CCT varies from package to package due to the deviation of phosphor-silicone mixture volume. In the experiments, even when the phosphor-silicone mixture volume varies from 0.3µl to 0.5µl, the deviation of the average CCT is less than 80K.

© 2012 OSA

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2011

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

2010

2009

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

2008

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008).
[CrossRef] [PubMed]

N. T. Tran and F. G. Shi, “Studies of phosphor concentration and thickness for phosphor-based white light-emitting-diodes,” J. Lightwave Technol. 26(21), 3556–3559 (2008).
[CrossRef]

2007

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

2004

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

M. Brinkmann and R. Blossey, “Blobs, channels and “cigars”: morphologies of liquids at a step,” Eur. Phys. J. E Soft Matter 14(1), 79–89 (2004).
[CrossRef] [PubMed]

2002

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

2001

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

Arscott, S.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Bhat, J.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Bhat, J. C.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

Blossey, R.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

M. Brinkmann and R. Blossey, “Blobs, channels and “cigars”: morphologies of liquids at a step,” Eur. Phys. J. E Soft Matter 14(1), 79–89 (2004).
[CrossRef] [PubMed]

Braune, B.

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Brinkmann, M.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

M. Brinkmann and R. Blossey, “Blobs, channels and “cigars”: morphologies of liquids at a step,” Eur. Phys. J. E Soft Matter 14(1), 79–89 (2004).
[CrossRef] [PubMed]

Collins, D.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Cook, L.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Craford, M. G.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Druon, C.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Fletcher, R.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Fletcher, R. M.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

Gan, Z. Y.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Gardner, N.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Gardner, N. F.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Goetz, W.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Gotz, W.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Grillot, P.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Harbers, G.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Hartmann, P.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

He, Y.

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

Holcomb, M. O.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

Huang, H. T.

Huang, Y. P.

Kaempf, M.

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Keuper, M.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Khare, R.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Kim, A.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Kim, J. K.

Krames, M.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Krames, M. R.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Krenn, J. R.

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Kromotis, P.

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Le Gac, S.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Lee, S.

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

Leising, G.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Liu, S.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

Liu, Z. Y.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Lowery, C. H.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Ludowise, M.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Ludowise, M. J.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

Luo, X. B.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

Martin, P. S.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Misra, M.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Mueller, G.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Mueller-Mach, R.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Pachler, P.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Petersen, K.

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Rolando, C.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Rudaz, S.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Rudaz, S. L.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

Schubert, E. F.

Schweighart, M.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Seo, S. Y.

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

Shen, Y.-C.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Shi, F. G.

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

N. T. Tran and F. G. Shi, “Studies of phosphor concentration and thickness for phosphor-based white light-emitting-diodes,” J. Lightwave Technol. 26(21), 3556–3559 (2008).
[CrossRef]

Shuai, Y.

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

Sommer, C.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Steigerwald, D.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Steigerwald, D. A.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Steranka, F. M.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Stockman, S.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Stockman, S. A.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

Strauss, J.

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Subramanya, S.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Sung, Y. E.

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

Tabourier, P.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Tasch, S.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Tran, N. T.

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

N. T. Tran and F. G. Shi, “Studies of phosphor concentration and thickness for phosphor-based white light-emitting-diodes,” J. Lightwave Technol. 26(21), 3556–3559 (2008).
[CrossRef]

Trottier, T.

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Tsai, C. C.

Wang, K.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Wenzl, F. P.

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

Wierer, J. J.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Yum, J. H.

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

Zhou, B.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Appl. Phys. Lett.

M. Brinkmann, R. Blossey, S. Arscott, C. Druon, P. Tabourier, S. Le Gac, and C. Rolando, “Microfluidic design rules for capillary slot-based electrospray sources,” Appl. Phys. Lett. 85(11), 2140–2142 (2004).
[CrossRef]

Eur. Phys. J. E Soft Matter

M. Brinkmann and R. Blossey, “Blobs, channels and “cigars”: morphologies of liquids at a step,” Eur. Phys. J. E Soft Matter 14(1), 79–89 (2004).
[CrossRef] [PubMed]

IEEE J Sel Top Quantum Electron.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J Sel Top Quantum Electron. 8(2), 310–320 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20(24), 2027–2029 (2008).
[CrossRef]

Y. Shuai, Y. He, N. T. Tran, and F. G. Shi, “Angular CCT uniformity of phosphor converted white LEDs: effects of phosphor materials and packaging structures,” IEEE Photon. Technol. Lett. 23(3), 137–139 (2011).
[CrossRef]

J. Lightwave Technol.

Jpn. J. Appl. Phys.

C. Sommer, J. R. Krenn, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “On the requirements for achieving angular homogeneity in phosphor converted high power flip-chip light-emitting diodes,” Jpn. J. Appl. Phys. 48(7), 070208 (2009).
[CrossRef]

Opt. Eng.

K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80W light-emitting-diode street lamp,” Opt. Eng. 47(1), 013002 (2008).
[CrossRef]

Opt. Express

Opt. Mater.

C. Sommer, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, G. Leising, and F. P. Wenzl, “A detailed study on the requirements for angular homogeneity of phosphor converted high power white LED light sources,” Opt. Mater. 31(6), 837–848 (2009).
[CrossRef]

Phys. Status Solidi A.

M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Gotz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman, and J. J. Wierer, “High-power III-nitride emitters for solid-state lighting,” Phys. Status Solidi A. 192, 237–245 (2002).
[CrossRef]

F. M. Steranka, J. Bhat, D. Collins, L. Cook, M. G. Craford, R. Fletcher, N. Gardner, P. Grillot, W. Goetz, M. Keuper, R. Khare, A. Kim, M. Krames, G. Harbers, M. Ludowise, P. S. Martin, M. Misra, G. Mueller, R. Mueller-Mach, S. Rudaz, Y.-C. Shen, D. Steigerwald, S. Stockman, S. Subramanya, T. Trottier, and J. J. Wierer, “High power LEDs - Technology status and market applications,” Phys. Status Solidi A. 194(2), 380–388 (2002).
[CrossRef]

Proc. SPIE

J. H. Yum, S. Y. Seo, S. Lee, and Y. E. Sung, “Comparison of Y3Al5O12:Ce0.05 phosphor coating methods for white light emitting diode on gallium nitride,” Proc. SPIE 4445, 60–69 (2001).
[CrossRef]

B. Braune, K. Petersen, J. Strauss, P. Kromotis, and M. Kaempf, “A new wafer level coating technique to reduce the color distribution of LEDs,” Proc. SPIE 6486, 68460x (2007).

Other

A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-State Lighting (John Wiley & Sons, 2002).

S. Liu and X. B. Luo, LED Packaging for Lighting Applications: Design, Manufacturing and Testing (John Wiley & Sons, 2011).

W. D. Collins, M. R. Krames, G. J. Verhoeckx, and N. J. M. Leth, “Using electrophoresis to produce a conformally coated phosphor-converted light emitting semiconductor,” U.S. patent 6 576 488 (2003).

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Figures (6)

Fig. 1
Fig. 1

(a) Flow schematic of phosphor particles and silicone mixture in capillary microchannel. (b) Pressure difference inducing the liquid spontaneous imbibition and (c) liquid pinned at step edge of the fixture.

Fig. 2
Fig. 2

Schematic of conformal phosphor coating using capillary microchannel.

Fig. 3
Fig. 3

Schematic of angular CCT measurement.

Fig. 4
Fig. 4

Geometries of phosphor layer by present coating method.

Fig. 5
Fig. 5

Angular CCT distribution comparison between conventional coating and the present coating method at the average CCT around 5200K, (a) for the conventional chip and (b) for the vertical injection chip.

Fig. 6
Fig. 6

Angular CCT distribution comparison between conventional coating and the present coating method at the average CCT around 9150K, (a) for the conventional chip and (b) for the vertical injection chip.

Tables (1)

Tables Icon

Table 1 Average CCT variation with different phosphor-silicone mixture volumes

Equations (4)

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

ΔP=γ LG ( 1 R 1 + 1 R 2 )
ΔP=γ LG 1 R 2 .
R 2 = h 2cos(180θ)
ΔP=γ LG 2cos(180θ) h

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