Abstract

Indium-rich InGaN epitaxial layers with a p-i-n structure were grown pseudomorphically on a strain-relaxed InGaN template to reduce structural strain induced by lattice mismatch. We applied a nano-sculpting process to improve the crystal quality of the strain-relaxed InGaN template. The results show that the nano-sculpting process can suppress effectively the threading dislocation generation and improves significantly the I-V characteristic of the InGaN p-i-n structure. This InGaN template technique with nano-sculpting process shows great potential for future applications in indium-rich InGaN optic-electron devices.

© 2012 OSA

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  1. J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
    [CrossRef]
  2. E. Muñoz, “(Al,ln,Ga)N-based photodetectors. some materials issues,” Phys. Stat. Solidi B 244(8), 2859–2877 (2007).
    [CrossRef]
  3. R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
    [CrossRef]
  4. J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
    [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]
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    [CrossRef]
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    [CrossRef]
  19. Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
    [CrossRef]
  20. L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
    [CrossRef]

2011 (2)

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

2010 (3)

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

2009 (2)

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

2007 (1)

E. Muñoz, “(Al,ln,Ga)N-based photodetectors. some materials issues,” Phys. Stat. Solidi B 244(8), 2859–2877 (2007).
[CrossRef]

2006 (1)

A. Kobayashi, J. Ohta, and H. Fujioka, “Low temperature epitaxial growth of In0.25Ga0.75N on lattice-matched ZnO by pulsed laser deposition,” J. Appl. Phys. 99(12), 123513 (2006).
[CrossRef]

2005 (1)

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

2002 (2)

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

1999 (2)

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

W. Paszkowicz, “X-ray powder diffraction data for indium nitride,” Powder Diffr. 14, 258–260 (1999).

1997 (2)

A. F. Wright, “Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,” J. Appl. Phys. 82(6), 2833–2839 (1997).
[CrossRef]

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

1996 (1)

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

1994 (1)

S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64(13), 1687–1689 (1994).
[CrossRef]

1992 (1)

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

Ager, J. W.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Akasaki, I.

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

Alves, E.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Araki, T.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Aschenbrenner, T.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Averbeck, R.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Bley, S.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Chen, D. J.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Colby, R.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Correia, M. R.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Dahal, R.

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

Deatcher, C. J.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Detchprohm, T.

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

Dupuis, R. D.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Ewoldt, D. A.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Ferguson, I. T.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Figge, S.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Franco, N.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Fujioka, H.

A. Kobayashi, J. Ohta, and H. Fujioka, “Low temperature epitaxial growth of In0.25Ga0.75N on lattice-matched ZnO by pulsed laser deposition,” J. Appl. Phys. 99(12), 123513 (2006).
[CrossRef]

Fujita, S.

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

Funato, M.

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

García, R. E.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Gervais, P. O.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Gutowski, J.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Haller, E. E.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Hiramatsu, K.

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

Hommel, D.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Hosler, W.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Huang, Y.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Iberl, A.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Itoh, K.

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

Iwasa, N.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Jamil, M.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Jampana, B.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Jiang, H. X.

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

Jiang, R. L.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Jobst, B.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Kalden, J.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Kawakami, Y.

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

Kiyoku, H.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Kobayashi, A.

A. Kobayashi, J. Ohta, and H. Fujioka, “Low temperature epitaxial growth of In0.25Ga0.75N on lattice-matched ZnO by pulsed laser deposition,” J. Appl. Phys. 99(12), 123513 (2006).
[CrossRef]

Kurouchi, M.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Lee, W.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Li, J.

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

Liang, Z. W.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Lin, J. Y.

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

Liu, B.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Lozach, M.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Lu, H.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Matsushita, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Melton, A.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Mukai, T.

S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64(13), 1687–1689 (1994).
[CrossRef]

Muñoz, E.

E. Muñoz, “(Al,ln,Ga)N-based photodetectors. some materials issues,” Phys. Stat. Solidi B 244(8), 2859–2877 (2007).
[CrossRef]

Muto, D.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Nagahama, S.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Nakamura, S.

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64(13), 1687–1689 (1994).
[CrossRef]

Nakayama, Y.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Nanishi, Y.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Naoi, H.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Narukawa, Y.

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

O’Donnell, K. P.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Ohta, J.

A. Kobayashi, J. Ohta, and H. Fujioka, “Low temperature epitaxial growth of In0.25Ga0.75N on lattice-matched ZnO by pulsed laser deposition,” J. Appl. Phys. 99(12), 123513 (2006).
[CrossRef]

Pantha, B.

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

Pantha, B. N.

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

Paszkowicz, W.

W. Paszkowicz, “X-ray powder diffraction data for indium nitride,” Powder Diffr. 14, 258–260 (1999).

Pereira, E.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Pereira, S.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Riechert, H.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Rosenauer, A.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Ryou, J. H.

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

Saito, Y.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Sands, T. D.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Sang, L.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Schaff, W. J.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Schuster, M.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Sebald, K.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Sekiguchi, T.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Senoh, M.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64(13), 1687–1689 (1994).
[CrossRef]

Sequeira, A. D.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Seyfried, M.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Stach, E. A.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Stommer, R.

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Sugimoto, Y.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Sumiya, M.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Takado, S.

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Takeguchi, M.

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Tessarek, C.

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Walukiewicz, W.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Watson, I. M.

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

Wildeson, I. H.

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Wright, A. F.

A. F. Wright, “Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,” J. Appl. Phys. 82(6), 2833–2839 (1997).
[CrossRef]

Wu, J.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Xie, Z. L.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Xue, J. J.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Yamada, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Yu, K. M.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

Zhang, R.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Zheng, Y. D.

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

Appl. Phys. Express (1)

L. Sang, M. Takeguchi, W. Lee, Y. Nakayama, M. Lozach, T. Sekiguchi, and M. Sumiya, “Phase separation resulting from Mg doping in p-InGaN film grown on GaN/Sapphire template,” Appl. Phys. Express 3(11), 111004 (2010).
[CrossRef]

Appl. Phys. Lett. (6)

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, “Unusual properties of the fundamental band gap of InN,” Appl. Phys. Lett. 80(21), 3967–3969 (2002).
[CrossRef]

R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009).
[CrossRef]

S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64(13), 1687–1689 (1994).
[CrossRef]

Y. Narukawa, Y. Kawakami, M. Funato, S. Fujita, S. Fujita, and S. Nakamura, “Role of self-formed InGaN quantum dots for exciton localization in the purple laser diode emitting at 420 nm,” Appl. Phys. Lett. 70(8), 981–983 (1997).
[CrossRef]

S. Pereira, M. R. Correia, E. Pereira, K. P. O’Donnell, E. Alves, A. D. Sequeira, N. Franco, I. M. Watson, and C. J. Deatcher, “Strain and composition distributions in Wurtzite InGaN/GaN layers extracted from x-ray reciprocal space mapping,” Appl. Phys. Lett. 80(21), 3913–3915 (2002).
[CrossRef]

B. N. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “Evolution of phase separation in In-rich InGaN alloys,” Appl. Phys. Lett. 96(23), 232105 (2010).
[CrossRef]

Chin. Phys. Lett. (1)

J. J. Xue, D. J. Chen, B. Liu, Z. L. Xie, R. L. Jiang, R. Zhang, and Y. D. Zheng, “Au/Pt/InGaN/GaN heterostructure Schottky prototype solar cell,” Chin. Phys. Lett. 26(9), 098102 (2009).
[CrossRef]

J. Appl. Phys. (3)

A. Kobayashi, J. Ohta, and H. Fujioka, “Low temperature epitaxial growth of In0.25Ga0.75N on lattice-matched ZnO by pulsed laser deposition,” J. Appl. Phys. 99(12), 123513 (2006).
[CrossRef]

Y. Huang, A. Melton, B. Jampana, M. Jamil, J. H. Ryou, R. D. Dupuis, and I. T. Ferguson, “Compositional instability in strained InGaN epitaxial layers induced by kinetic effects,” J. Appl. Phys. 110(6), 064908 (2011).
[CrossRef]

A. F. Wright, “Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN,” J. Appl. Phys. 82(6), 2833–2839 (1997).
[CrossRef]

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

M. Schuster, P. O. Gervais, B. Jobst, W. Hosler, R. Averbeck, H. Riechert, A. Iberl, and R. Stommer, “Determination of the chemical composition of distorted InGaN GaN heterostructures from x-ray diffraction data,” J. Phys. D Appl. Phys. 32(10A), A56–A60 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (2)

T. Detchprohm, K. Hiramatsu, K. Itoh, and I. Akasaki, “Relaxation process of the thermal strain in the GaN/alpha-Al2O3 heterostructure and determination of the intrinsic lattice constants of GaN free from the strain,” Jpn. J. Appl. Phys. 31(Part 2, No. 10B), L1454–L1456 (1992).

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, “InGaN-based multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 35(Part 2, No. 1B), L74–L76 (1996).
[CrossRef]

Nano Lett. (1)

R. Colby, Z. W. Liang, I. H. Wildeson, D. A. Ewoldt, T. D. Sands, R. E. García, and E. A. Stach, “Dislocation filtering in GaN nanostructures,” Nano Lett. 10(5), 1568–1573 (2010).
[CrossRef] [PubMed]

Phys. Rev. B (1)

C. Tessarek, S. Figge, T. Aschenbrenner, S. Bley, A. Rosenauer, M. Seyfried, J. Kalden, K. Sebald, J. Gutowski, and D. Hommel, “Strong phase separation of strained In(x)Ga(1-x)N layers due to spinodal and binodal decomposition: formation of stable quantum dots,” Phys. Rev. B 83(11), 115316 (2011).
[CrossRef]

Phys. Stat. Solidi B (1)

E. Muñoz, “(Al,ln,Ga)N-based photodetectors. some materials issues,” Phys. Stat. Solidi B 244(8), 2859–2877 (2007).
[CrossRef]

Phys. Status Solidi A (1)

H. Naoi, M. Kurouchi, S. Takado, D. Muto, T. Araki, and Y. Nanishi, “Structural and luminescence properties of In-rich InGaN layers grown on InN templates by RF-MBE,” Phys. Status Solidi A 202(14), 2642–2647 (2005).
[CrossRef]

Powder Diffr. (1)

W. Paszkowicz, “X-ray powder diffraction data for indium nitride,” Powder Diffr. 14, 258–260 (1999).

Other (1)

P. I. Cohen and B. Cui, US patent 20100090311A1 (2010).

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Figures (7)

Fig. 1
Fig. 1

Schematic structure of the InGaN sample.

Fig. 2
Fig. 2

XRD ω/2θ scan of symmetric (0002) reflection for the InGaN sample with nano-sculpting process.

Fig. 3
Fig. 3

Asymmetric (105) RSM of the InGaN sample.

Fig. 4
Fig. 4

SAD patterns from (a) the InGaN template and (b) n-InGaN layer.

Fig. 5
Fig. 5

Cross-sectional TEM image of the InGaN template with (a) and without (b) a nano-sculpting process.

Fig. 6
Fig. 6

XRD ω/2θ scan of symmetric (0002) reflection for the InGaN sample without nano-sculpting process.

Fig. 7
Fig. 7

I-V characteristic of the InGaN structures with and without the nano-sculpting process.

Equations (4)

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

a = 2 π q x 4 ( h 2 + h k + k 2 ) 3
c = 2 π l q z
ε z z = c In x Ga 1-x N c 0 In x Ga 1-x N c 0 In x Ga 1-x N
ε xx = a In x Ga 1-x N a 0 In x Ga 1-x N a 0 In x Ga 1-x N

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