Abstract

There is common agreement that dimensional downscaling of III-nitride light-emitting diodes leads to spectral blue shifts due to strain relaxation of the quantum wells (QWs). Near-field photoluminescence (nf-PL) mapping of micropillars with InGaN/GaN QWs of different indium compositions using scanning near-field optical spectroscopy reveals that the nf-PL spectrum blue-shifts at the edge of a micropillar with respect to the center for QWs with a high indium composition, whereas a relative red shift is observed for QWs with a low indium composition. This observation suggests that the strain relaxation mechanism in micropillars is dependent on the indium composition, evident from changes in lattice parameters determined from calibrated diffraction patterns obtained by transmission electron microscopy. As indicated by molecular dynamics simulations, the strain of a micropillar is influenced by competing strain relaxation mechanisms between the lattice mismatch strain from the QWs, and residual strain from other layers and their interactions with the edge of the micropillar. First-principle calculations of GaN/InGaN/GaN heterostructures confirmed the effect of strain relaxation on the potential profiles, and, thus, on the spectral shifts from the micropillars. The findings of this work provide insight into strain-induced band profile engineering in optoelectronic devices built on lattice-mismatched systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. S. Plimpton, “Fast parallel algorithms for short-range molecular-dynamics,” J. Comput. Phys. 117, 1–19 (1995).
    [Crossref]
  21. F. H. Stillinger and T. A. Weber, “Computer-simulation of local order in condensed phases of silicon,” Phys. Rev. B 31, 5262–5271 (1985).
    [Crossref]
  22. A. Bere and A. Serra, “On the atomic structures, mobility and interactions of extended defects in GaN: dislocations, tilt and twin boundaries,” Philos. Mag. 86(15), 2159–2192 (2006).
    [Crossref]
  23. H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
    [Crossref]
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    [Crossref]
  25. Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
    [Crossref]
  26. A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
    [Crossref]
  27. S. L. Chuang and C. S. Chang, “A band-structure model of strained quantum-well wurtzite semiconductors,” Semicond. Sci. Technol. 12, 252–263 (1997).
    [Crossref]
  28. J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
    [Crossref]
  29. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
    [Crossref]
  30. N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43, 1993–2006 (1991).
    [Crossref]

2016 (2)

C. Feng, J.-A. Huang, and H. W. Choi, “Monolithic broadband InGaN light-emitting diode,” ACS Photon. 3, 1294–1300 (2016).
[Crossref]

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
[Crossref]

2014 (3)

Y. D. Zhuang, J. Bruckbauer, P. A. Shields, P. R. Edwards, R. W. Martin, and D. W. E. Allsopp, “Influence of stress on optical transitions in GaN nanorods containing a single InGaN/GaN quantum disk,” J. Appl. Phys. 116, 174305 (2014).
[Crossref]

W. Li, K. Li, F.-M. Kong, Q.-Y. Yue, X.-L. Chen, and X.-J. Yu, “Study of light extraction efficiency of GaN-based light emitting diodes by using top micro/nanorod hybrid arrays,” Opt. Quantum Electron. 46, 1413–1423 (2014).
[Crossref]

Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
[Crossref]

2012 (4)

C. Kolper, M. Sabathil, M. Mandl, M. Strassburg, and B. Witzigmann, “All-InGaN phosphorless white light emitting diodes: an efficiency estimation,” J. Lightwave Technol. 30, 2853–2862 (2012).
[Crossref]

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

J. Bai, Q. Wang, and T. Wang, “Characterization of InGaN-based nanorod light emitting diodes with different indium compositions,” J. Appl. Phys. 111, 113103 (2012).
[Crossref]

C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
[Crossref]

2011 (3)

Q. Wang, J. Bai, Y. P. Gong, and T. Wang, “Influence of strain relaxation on the optical properties of InGaN/GaN multiple quantum well nanorods,” J. Phys. D 44, 395102 (2011).
[Crossref]

C. Hahn, Z. Zhang, A. Fu, C. H. Wu, Y. J. Hwang, D. J. Gargas, and P. Yang, “Epitaxial growth of InGaN nanowire arrays for light emitting diodes,” ACS Nano 5, 3970–3976 (2011).
[Crossref]

Y.-J. Lu, H.-W. Lin, H.-Y. Chen, Y.-C. Yang, and S. Gwo, “Single InGaN nanodisk light emitting diodes as full-color subwavelength light sources,” Appl. Phys. Lett. 98, 233101 (2011).
[Crossref]

2010 (3)

Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
[Crossref]

V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
[Crossref]

C. Böcklin, R. G. Veprek, S. Steiger, and B. Witzigmann, “Computational study of an InGaN/GaN nanocolumn light-emitting diode,” Phys. Rev. B 81, 155306 (2010).
[Crossref]

2009 (1)

Y. R. Wu, C. H. Chiu, C. Y. Chang, P. C. Yu, and H. C. Kuo, “Size-dependent strain relaxation and optical characteristics of InGaN/GaN nanorod LEDs,” IEEE J. Sel. Top. Quantum Electron. 15, 1226–1233 (2009).
[Crossref]

2007 (1)

C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
[Crossref]

2006 (2)

A. Bere and A. Serra, “On the atomic structures, mobility and interactions of extended defects in GaN: dislocations, tilt and twin boundaries,” Philos. Mag. 86(15), 2159–2192 (2006).
[Crossref]

H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
[Crossref]

2003 (2)

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94, 3675–3696 (2003).
[Crossref]

H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
[Crossref]

2002 (1)

J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
[Crossref]

2001 (1)

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field fibre probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
[Crossref]

2000 (1)

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

1999 (1)

T. Saiki and K. Matsuda, “Near-field optical fiber probe optimized for illumination collection hybrid mode operation,” Appl. Phys. Lett. 74, 2773–2775 (1999).
[Crossref]

1997 (1)

S. L. Chuang and C. S. Chang, “A band-structure model of strained quantum-well wurtzite semiconductors,” Semicond. Sci. Technol. 12, 252–263 (1997).
[Crossref]

1996 (1)

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

1995 (1)

S. Plimpton, “Fast parallel algorithms for short-range molecular-dynamics,” J. Comput. Phys. 117, 1–19 (1995).
[Crossref]

1991 (1)

N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43, 1993–2006 (1991).
[Crossref]

1985 (1)

F. H. Stillinger and T. A. Weber, “Computer-simulation of local order in condensed phases of silicon,” Phys. Rev. B 31, 5262–5271 (1985).
[Crossref]

Allsopp, D. W. E.

Y. D. Zhuang, J. Bruckbauer, P. A. Shields, P. R. Edwards, R. W. Martin, and D. W. E. Allsopp, “Influence of stress on optical transitions in GaN nanorods containing a single InGaN/GaN quantum disk,” J. Appl. Phys. 116, 174305 (2014).
[Crossref]

Artacho, E.

J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
[Crossref]

Bai, D.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
[Crossref]

Bai, J.

J. Bai, Q. Wang, and T. Wang, “Characterization of InGaN-based nanorod light emitting diodes with different indium compositions,” J. Appl. Phys. 111, 113103 (2012).
[Crossref]

Q. Wang, J. Bai, Y. P. Gong, and T. Wang, “Influence of strain relaxation on the optical properties of InGaN/GaN multiple quantum well nanorods,” J. Phys. D 44, 395102 (2011).
[Crossref]

Bere, A.

A. Bere and A. Serra, “On the atomic structures, mobility and interactions of extended defects in GaN: dislocations, tilt and twin boundaries,” Philos. Mag. 86(15), 2159–2192 (2006).
[Crossref]

Böcklin, C.

C. Böcklin, R. G. Veprek, S. Steiger, and B. Witzigmann, “Computational study of an InGaN/GaN nanocolumn light-emitting diode,” Phys. Rev. B 81, 155306 (2010).
[Crossref]

Bonfiglio, A.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

Botchkarev, A.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

Bruckbauer, J.

Y. D. Zhuang, J. Bruckbauer, P. A. Shields, P. R. Edwards, R. W. Martin, and D. W. E. Allsopp, “Influence of stress on optical transitions in GaN nanorods containing a single InGaN/GaN quantum disk,” J. Appl. Phys. 116, 174305 (2014).
[Crossref]

Burke, K.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

Chang, C. H.

C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
[Crossref]

Chang, C. S.

S. L. Chuang and C. S. Chang, “A band-structure model of strained quantum-well wurtzite semiconductors,” Semicond. Sci. Technol. 12, 252–263 (1997).
[Crossref]

Chang, C. Y.

Y. R. Wu, C. H. Chiu, C. Y. Chang, P. C. Yu, and H. C. Kuo, “Size-dependent strain relaxation and optical characteristics of InGaN/GaN nanorod LEDs,” IEEE J. Sel. Top. Quantum Electron. 15, 1226–1233 (2009).
[Crossref]

Chen, H.-Y.

Y.-J. Lu, H.-W. Lin, H.-Y. Chen, Y.-C. Yang, and S. Gwo, “Single InGaN nanodisk light emitting diodes as full-color subwavelength light sources,” Appl. Phys. Lett. 98, 233101 (2011).
[Crossref]

Chen, J.

H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
[Crossref]

Chen, L. Y.

C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
[Crossref]

Chen, X.-L.

W. Li, K. Li, F.-M. Kong, Q.-Y. Yue, X.-L. Chen, and X.-J. Yu, “Study of light extraction efficiency of GaN-based light emitting diodes by using top micro/nanorod hybrid arrays,” Opt. Quantum Electron. 46, 1413–1423 (2014).
[Crossref]

Chen, Y. J.

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

Chen, Z. Z.

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

Chiu, C. H.

Y. R. Wu, C. H. Chiu, C. Y. Chang, P. C. Yu, and H. C. Kuo, “Size-dependent strain relaxation and optical characteristics of InGaN/GaN nanorod LEDs,” IEEE J. Sel. Top. Quantum Electron. 15, 1226–1233 (2009).
[Crossref]

Choi, H. W.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
[Crossref]

C. Feng, J.-A. Huang, and H. W. Choi, “Monolithic broadband InGaN light-emitting diode,” ACS Photon. 3, 1294–1300 (2016).
[Crossref]

H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
[Crossref]

Chuang, S. L.

S. L. Chuang and C. S. Chang, “A band-structure model of strained quantum-well wurtzite semiconductors,” Semicond. Sci. Technol. 12, 252–263 (1997).
[Crossref]

Cingolani, R.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

Dawson, M. D.

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
[Crossref]

Della Sala, F.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

Di Carlo, A.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

Edwards, P. R.

Y. D. Zhuang, J. Bruckbauer, P. A. Shields, P. R. Edwards, R. W. Martin, and D. W. E. Allsopp, “Influence of stress on optical transitions in GaN nanorods containing a single InGaN/GaN quantum disk,” J. Appl. Phys. 116, 174305 (2014).
[Crossref]

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
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J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
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Feng, C.

C. Feng, J.-A. Huang, and H. W. Choi, “Monolithic broadband InGaN light-emitting diode,” ACS Photon. 3, 1294–1300 (2016).
[Crossref]

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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
[Crossref]

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C. Hahn, Z. Zhang, A. Fu, C. H. Wu, Y. J. Hwang, D. J. Gargas, and P. Yang, “Epitaxial growth of InGaN nanowire arrays for light emitting diodes,” ACS Nano 5, 3970–3976 (2011).
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Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
[Crossref]

V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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C. Hahn, Z. Zhang, A. Fu, C. H. Wu, Y. J. Hwang, D. J. Gargas, and P. Yang, “Epitaxial growth of InGaN nanowire arrays for light emitting diodes,” ACS Nano 5, 3970–3976 (2011).
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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
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Y.-J. Lu, H.-W. Lin, H.-Y. Chen, Y.-C. Yang, and S. Gwo, “Single InGaN nanodisk light emitting diodes as full-color subwavelength light sources,” Appl. Phys. Lett. 98, 233101 (2011).
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C. Hahn, Z. Zhang, A. Fu, C. H. Wu, Y. J. Hwang, D. J. Gargas, and P. Yang, “Epitaxial growth of InGaN nanowire arrays for light emitting diodes,” ACS Nano 5, 3970–3976 (2011).
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C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
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Huang, J.-A.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
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C. Feng, J.-A. Huang, and H. W. Choi, “Monolithic broadband InGaN light-emitting diode,” ACS Photon. 3, 1294–1300 (2016).
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C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
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C. Hahn, Z. Zhang, A. Fu, C. H. Wu, Y. J. Hwang, D. J. Gargas, and P. Yang, “Epitaxial growth of InGaN nanowire arrays for light emitting diodes,” ACS Nano 5, 3970–3976 (2011).
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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
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Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
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H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
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H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
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V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
[Crossref]

Kikuchi, A.

V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
[Crossref]

Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
[Crossref]

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Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
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V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
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Kong, F.-M.

W. Li, K. Li, F.-M. Kong, Q.-Y. Yue, X.-L. Chen, and X.-J. Yu, “Study of light extraction efficiency of GaN-based light emitting diodes by using top micro/nanorod hybrid arrays,” Opt. Quantum Electron. 46, 1413–1423 (2014).
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Y. R. Wu, C. H. Chiu, C. Y. Chang, P. C. Yu, and H. C. Kuo, “Size-dependent strain relaxation and optical characteristics of InGaN/GaN nanorod LEDs,” IEEE J. Sel. Top. Quantum Electron. 15, 1226–1233 (2009).
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H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
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W. Li, K. Li, F.-M. Kong, Q.-Y. Yue, X.-L. Chen, and X.-J. Yu, “Study of light extraction efficiency of GaN-based light emitting diodes by using top micro/nanorod hybrid arrays,” Opt. Quantum Electron. 46, 1413–1423 (2014).
[Crossref]

Li, K. H.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
[Crossref]

Li, W.

W. Li, K. Li, F.-M. Kong, Q.-Y. Yue, X.-L. Chen, and X.-J. Yu, “Study of light extraction efficiency of GaN-based light emitting diodes by using top micro/nanorod hybrid arrays,” Opt. Quantum Electron. 46, 1413–1423 (2014).
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Y.-J. Lu, H.-W. Lin, H.-Y. Chen, Y.-C. Yang, and S. Gwo, “Single InGaN nanodisk light emitting diodes as full-color subwavelength light sources,” Appl. Phys. Lett. 98, 233101 (2011).
[Crossref]

Liu, N. Y.

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
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A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
[Crossref]

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C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
[Crossref]

Lu, Y.-J.

Y.-J. Lu, H.-W. Lin, H.-Y. Chen, Y.-C. Yang, and S. Gwo, “Single InGaN nanodisk light emitting diodes as full-color subwavelength light sources,” Appl. Phys. Lett. 98, 233101 (2011).
[Crossref]

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A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
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Martin, R. W.

Y. D. Zhuang, J. Bruckbauer, P. A. Shields, P. R. Edwards, R. W. Martin, and D. W. E. Allsopp, “Influence of stress on optical transitions in GaN nanorods containing a single InGaN/GaN quantum disk,” J. Appl. Phys. 116, 174305 (2014).
[Crossref]

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
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N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43, 1993–2006 (1991).
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T. Saiki and K. Matsuda, “Near-field optical fiber probe optimized for illumination collection hybrid mode operation,” Appl. Phys. Lett. 74, 2773–2775 (1999).
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I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94, 3675–3696 (2003).
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Morkoc, H.

A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
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H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field fibre probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
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H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
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Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
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J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
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H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
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V. Ramesh, A. Kikuchi, K. Kishino, M. Funato, and Y. Kawakami, “Strain relaxation effect by nanotexturing InGaN/GaN multiple quantum well,” J. Appl. Phys. 107, 114303 (2010).
[Crossref]

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Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
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C. Rivera, U. Jahn, T. Flissikowski, J. L. Pau, E. Munoz, and H. T. Grahn, “Strain-confinement mechanism in mesoscopic quantum disks based on piezoelectric materials,” Phys. Rev. B 75, 045316 (2007).
[Crossref]

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H. P. Lei, J. Chen, S. Petit, R. Ruterana, X. Y. Jiang, and G. Nouet, “Stillinger–Weber parameters for In and N atoms,” Superlattices Microstruct. 40, 464–469 (2006).
[Crossref]

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Saiki, T.

H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field fibre probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
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T. Saiki and K. Matsuda, “Near-field optical fiber probe optimized for illumination collection hybrid mode operation,” Appl. Phys. Lett. 74, 2773–2775 (1999).
[Crossref]

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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field fibre probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
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H. Nakamura, T. Sato, H. Kambe, K. Sawada, and T. Saiki, “Design and optimization of tapered structure of near-field fibre probe based on finite-difference time-domain simulation,” J. Microsc. 202, 50–52 (2001).
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Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
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J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon, and D. Sanchez-Portal, “The SIESTA method for ab initio order-N materials simulation,” J. Phys. Condens. Matter 14, 2745–2779 (2002).
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C. Böcklin, R. G. Veprek, S. Steiger, and B. Witzigmann, “Computational study of an InGaN/GaN nanocolumn light-emitting diode,” Phys. Rev. B 81, 155306 (2010).
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F. H. Stillinger and T. A. Weber, “Computer-simulation of local order in condensed phases of silicon,” Phys. Rev. B 31, 5262–5271 (1985).
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Su, L.

Y. Kawakami, A. Kaneta, L. Su, Y. Zhu, K. Okamoto, M. Funato, A. Kikuchi, and K. Kishino, “Optical properties of InGaN/GaN nanopillars fabricated by postgrowth chemically assisted ion beam etching,” J. Appl. Phys. 107, 023522 (2010).
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E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
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A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoc, “Well-width dependence of the ground level emission of GaN/AlGaN quantum wells,” J. Appl. Phys. 87, 2289–2292 (2000).
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H. W. Choi, C. W. Jeon, M. D. Dawson, P. R. Edwards, R. W. Martin, and S. Tripathy, “Mechanism of enhanced light output efficiency in InGaN-based microlight emitting diodes,” J. Appl. Phys. 93, 5978–5982 (2003).
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N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43, 1993–2006 (1991).
[Crossref]

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Q. M. Yan, P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, “Effects of strain on the band structure of group-III nitrides,” Phys. Rev. B 90, 125118 (2014).
[Crossref]

Veprek, R. G.

C. Böcklin, R. G. Veprek, S. Steiger, and B. Witzigmann, “Computational study of an InGaN/GaN nanocolumn light-emitting diode,” Phys. Rev. B 81, 155306 (2010).
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I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94, 3675–3696 (2003).
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J. Bai, Q. Wang, and T. Wang, “Characterization of InGaN-based nanorod light emitting diodes with different indium compositions,” J. Appl. Phys. 111, 113103 (2012).
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Q. Wang, J. Bai, Y. P. Gong, and T. Wang, “Influence of strain relaxation on the optical properties of InGaN/GaN multiple quantum well nanorods,” J. Phys. D 44, 395102 (2011).
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Wang, T.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
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J. Bai, Q. Wang, and T. Wang, “Characterization of InGaN-based nanorod light emitting diodes with different indium compositions,” J. Appl. Phys. 111, 113103 (2012).
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Q. Wang, J. Bai, Y. P. Gong, and T. Wang, “Influence of strain relaxation on the optical properties of InGaN/GaN multiple quantum well nanorods,” J. Phys. D 44, 395102 (2011).
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Wang, Y.

Y. Zhang, J.-A. Huang, K. H. Li, D. Bai, Y. Wang, T. Wang, and H. W. Choi, “Influence of strain on emission from GaN-on-Si microdisks,” J. Phys. D 49, 375103 (2016).
[Crossref]

Wang, Y. T.

C. H. Chang, L. Y. Chen, L. C. Huang, Y. T. Wang, T. C. Lu, and J. J. Huang, “Effects of strains and defects on the internal quantum efficiency of InGaN/GaN nanorod light emitting diodes,” IEEE J. Quantum Electron. 48, 551–556 (2012).
[Crossref]

Watson, I. M.

E. Y. Xie, Z. Z. Chen, P. R. Edwards, Z. Gong, N. Y. Liu, Y. B. Tao, Y. F. Zhang, Y. J. Chen, I. M. Watson, E. Gu, R. W. Martin, G. Y. Zhang, and M. D. Dawson, “Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging,” J. Appl. Phys. 112, 013107 (2012).
[Crossref]

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F. H. Stillinger and T. A. Weber, “Computer-simulation of local order in condensed phases of silicon,” Phys. Rev. B 31, 5262–5271 (1985).
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C. Kolper, M. Sabathil, M. Mandl, M. Strassburg, and B. Witzigmann, “All-InGaN phosphorless white light emitting diodes: an efficiency estimation,” J. Lightwave Technol. 30, 2853–2862 (2012).
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Supplementary Material (1)

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Figures (8)

Fig. 1.
Fig. 1. SNOS measurement results of micropillars of 2 μm diameter and 1 μm height, on (a) sample Bl (blue emission), (b) sample Cy (cyan emission), and (c) sample Gn (green emission), showing the corresponding plot of nf-PL peak wavelengths and peak intensity w.r.t. the SNOS probe position from the center of the micropillars. The black dotted line at 1 μm corresponds to the edge of a micropillar. The inset on the bottom left in (c) shows a schematic diagram of the micropillar structure.
Fig. 2.
Fig. 2. SNOS measurements of nf-PL from micropillars on samples Bl, Cy, and Gn. nf-PL spectra maps were collected using SNOS from randomly picked micropillars on each sample. The relative spectral shift in this figure is the difference between the averaged peak wavelength at the center and at the edge from a PL map. The trend of relative spectral shift is shown by a fitted line (dashed line). The error bar indicates the total spread of peak emission wavelengths at the center and at the edge.
Fig. 3.
Fig. 3. nf-TRPL measurement results of micropillars (a) Bl and (b) Gn, of 2 μm diameter and 1 μm height, showing the corresponding plot of nf-TRPL decay lifetime w.r.t. distance from the center of the micropillars.
Fig. 4.
Fig. 4. Temperature-dependent μ -PL results of micropillars (a) Bl and (b) Gn, of 2 μm diameter and 1 μm height. The insets show the μ -PL of the corresponding as-grown samples. Panels (c) and (d) show the results of fitting a Gaussian to the data from (a) and (b), respectively. Note that the Fabry–Perot fringes in the PL spectra have been removed by FFT filtering.
Fig. 5.
Fig. 5. Cross-sectional bright-field TEM images and (inset) selective area diffraction patterns obtained along the 11 2 ¯ 0 zone axis of micropillars (a) Bl and (c) Gn. Panels (b) and (d) show the corresponding high-resolution TEM images of the QWs of Bl and Gn, respectively, and (inset) the SEM images of micropillars from the corresponding samples for reference. The white lines in the insets correspond to a length of 5    nm 1 for the diffraction patterns and 1 μm for the SEM images.
Fig. 6.
Fig. 6. Strain fields calculated from relaxed atomic positions simulated by molecular dynamics simulations. The center and the edge of the simulated micropillars are at X = 0    nm and X = 1000    nm , respectively. (a) In-plane strain and (b) out-of-plane strain of micropillar Bl, and (d) in-plane strain and (e) out-of-plane strain of micropillar Gn. Panels (c) and (f) show the averaged strain profiles, ε xx , ε yy , and ε zz , of the QWs and barriers in micropillars Bl and Gn, respectively.
Fig. 7.
Fig. 7. Averaged potential energy profiles (solid blue line) of the GaN/InGaN/GaN heterostructure calculated from ab initio calculations at the band edge for [(a), (b)] sample Bl and [(c), (d)] sample Gn. The dotted lines are the smoothed individual potential profiles with different indium distributions calculated from DFT simulations before averaging. (e) Peak emission wavelengths w.r.t. strain relaxation, comparing the results calculated using the potential profiles in (a)–(d) [“Bl (DFT)” and “Gn (DFT)”] with conventional k · p calculations, both under out-of-plane strain relaxation, with [“Bl (out-of-plane)” and “Gn (out-of-plane)”] and without the effect of DP [“Bl (out-of-plane), no DP” and “Gn (out-of-plane), no DP”]. Calculation results with full (in-plane and out-of-plane) strain relaxation are shown as reference [“Bn (full)”; “Gn (full)”; “Bn (full), no DP”; “Gn (full), no DP”]. Note that the negative sign indicates a blue shift.
Fig. 8.
Fig. 8. Peak emission wavelengths calculated for micropillars (a) Bl and (b) Gn, using simulated strain fields obtained from the molecular dynamics simulations shown in Fig. 6. For reference purpose, calculation results without the effect of DP (green short-dash line) are also shown.

Tables (1)

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Table 1. Lattice Parameters Extracted from the 0002 and 1 1 ¯ 00 Spots of the Calibrated Selective Area Diffraction Images in Fig. 5

Equations (2)

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1 d h k i l = a 2 h 2 + 3 a 2 ( h + 2 k 2 ) 2 + c 2 l 2 ,
ε = ε C 33 C 13 ε zz .

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