Abstract

InGaN p-n junction solar cells with various indium composition and thickness of upper p-InGaN and lower n-InGaN junctions are investigated theoretically. The physical properties of InGaN p-n junction solar cells, such as the short circuit current density (JSC), open circuit voltage (Voc), fill factor (FF), and conversion efficiency (η), are theoretically calculated and simulated by varying the device structures, position of the depletion region, indium content, and photon penetration depth. The results indicate that an In0.6Ga0.4N solar cell, with optimal device parameters, can have a JSC ~31.8 mA/cm2, Voc ~0.874 volt, FF ~0.775, and η ~21.5%. It clearly demonstrates that medium-indium-content InGaN materials have the potential to realize high efficiency solar cells. Furthermore, the simulation results, with various thicknesses of the p-InGaN junction but a fixed thickness of the n-InGaN junction, shows that the performance of InGaN solar cells is determined by the upper p-InGaN junction rather than the n-InGaN substrate. This is attributed to the different amount of light absorption in the depletion region and the variation of the collection efficiency of minority carriers.

© 2013 Optical Society of America

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2012 (1)

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

2011 (2)

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

J. Y. Chang and Y. K. Kuo, “Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (0001)-face GaN/InGaN p-i-n solar cells,” IEEE Electron Device Lett.32(7), 937–939 (2011).
[CrossRef]

2010 (7)

J. J. Wierer, A. J. Fischer, and D. D. Koleske, “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN/InGaN photovoltaic devices,” Appl. Phys. Lett.96(5), 051107 (2010).
[CrossRef]

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

2009 (2)

M. J. Jeng, Y. L. Lee, and L. B. Chang, “Temperature dependences of InxGa1-xN multiple quantum well solar cells,” J. Phys. D Appl. Phys.42(10), 105101 (2009).
[CrossRef]

X. M. Cai, S. W. Zeng, and B. P. Zhang, “Fabrication and characterization of InGaN p-i-n homojunction solar cell,” Appl. Phys. Lett.95(17), 173504 (2009).
[CrossRef]

2008 (3)

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

L. Hsu and W. Walukiewicz, “Modeling of InGaN/Si tandem solar cells,” J. Appl. Phys.104(2), 024507 (2008).
[CrossRef]

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

2007 (2)

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

2005 (1)

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

2004 (1)

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

1998 (1)

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Ager, J. W.

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

Akasaki, I.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Amano, H.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Aryal, K.

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

Bandic, Z. Z.

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Bandoh, A.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Bridger, P. M.

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Brown, G. F.

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

Cai, X. M.

X. M. Cai, S. W. Zeng, and B. P. Zhang, “Fabrication and characterization of InGaN p-i-n homojunction solar cell,” Appl. Phys. Lett.95(17), 173504 (2009).
[CrossRef]

Cartwright, A. N.

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

Chang, J. Y.

J. Y. Chang and Y. K. Kuo, “Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (0001)-face GaN/InGaN p-i-n solar cells,” IEEE Electron Device Lett.32(7), 937–939 (2011).
[CrossRef]

Chang, L. B.

M. J. Jeng, Y. L. Lee, and L. B. Chang, “Temperature dependences of InxGa1-xN multiple quantum well solar cells,” J. Phys. D Appl. Phys.42(10), 105101 (2009).
[CrossRef]

Chen, C. H.

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

Chen, F.

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

Chena, F.

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

Chu, M. T.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Cruz, S. C.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Dahal, R.

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

DenBaars, S. P.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Faleev, N. N.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Feezell, D.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Feng, S. W.

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

Ferguson, I.

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

Ferguson, I. T.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Fischer, A. J.

J. J. Wierer, A. J. Fischer, and D. D. Koleske, “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN/InGaN photovoltaic devices,” Appl. Phys. Lett.96(5), 051107 (2010).
[CrossRef]

Fujito, K.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Hashimoto, A.

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

Honsberg, C.

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

Honsberg, C. B.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Horng, R. H.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Hou, Q. F.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Hsu, L.

L. Hsu and W. Walukiewicz, “Modeling of InGaN/Si tandem solar cells,” J. Appl. Phys.104(2), 024507 (2008).
[CrossRef]

Hu, P. S.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Huang, C. Y.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Huang, S. C.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Hurni, C. A.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Iida, D.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Islam, M. R.

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

Iwaya, M.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Jamil, M.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Jampana, B. R.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Jani, O.

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

Jeng, M. J.

M. J. Jeng, Y. L. Lee, and L. B. Chang, “Temperature dependences of InxGa1-xN multiple quantum well solar cells,” J. Phys. D Appl. Phys.42(10), 105101 (2009).
[CrossRef]

Jiang, H. X.

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

Kamiyama, S.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Kang, T.-T.

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

Kawaguchi, Y.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Koleske, D. D.

J. J. Wierer, A. J. Fischer, and D. D. Koleske, “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN/InGaN photovoltaic devices,” Appl. Phys. Lett.96(5), 051107 (2010).
[CrossRef]

Kuo, Y. K.

J. Y. Chang and Y. K. Kuo, “Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (0001)-face GaN/InGaN p-i-n solar cells,” IEEE Electron Device Lett.32(7), 937–939 (2011).
[CrossRef]

Kurtz, S.

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

Lai, C. M.

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

Lang, J. R.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Lee, Y. L.

M. J. Jeng, Y. L. Lee, and L. B. Chang, “Temperature dependences of InxGa1-xN multiple quantum well solar cells,” J. Phys. D Appl. Phys.42(10), 105101 (2009).
[CrossRef]

Li, F.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Li, J.

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Li, J. M.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Liao, W. Y.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Lin, J. Y.

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

Lin, R. M.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Lin, S.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Lu, H.

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

Lu, Y. C.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Makino, T.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Matioli, E.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

McGill, T. C.

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Melton, A. G.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Mishra, U. K.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Nagata, K.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Nakamura, S.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Neufeld, C. J.

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Opila, R. L.

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

Pan, C. C.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Piquette, E. C.

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Ran, J. X.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Schaff, W. J.

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

Shen, X.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Speck, J. S.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

Sun, W. C.

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

Tanaka, S.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Tu, L. W.

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

Udagawa, T.

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Van de Walle, C. G.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Walukiewicz, W.

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

L. Hsu and W. Walukiewicz, “Modeling of InGaN/Si tandem solar cells,” J. Appl. Phys.104(2), 024507 (2008).
[CrossRef]

Wan, H.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Wang, C. M.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Wang, X. L.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Wei, Y.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Wierer, J. J.

J. J. Wierer, A. J. Fischer, and D. D. Koleske, “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN/InGaN photovoltaic devices,” Appl. Phys. Lett.96(5), 051107 (2010).
[CrossRef]

Wu, J.

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

Wu, M. H.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Wuu, D. S.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Xiao, H. L.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Yamamoto, A.

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

Yan, Q.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Yang, C. B.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Zeng, S. W.

X. M. Cai, S. W. Zeng, and B. P. Zhang, “Fabrication and characterization of InGaN p-i-n homojunction solar cell,” Appl. Phys. Lett.95(17), 173504 (2009).
[CrossRef]

Zhang, B. P.

X. M. Cai, S. W. Zeng, and B. P. Zhang, “Fabrication and characterization of InGaN p-i-n homojunction solar cell,” Appl. Phys. Lett.95(17), 173504 (2009).
[CrossRef]

Zhang, X.

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Zhao, Y.

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

Zheng, X.

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

Zhong, S.

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Appl. Phys. Express (1)

D. Iida, K. Nagata, T. Makino, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, A. Bandoh, and T. Udagawa, “Growth of GaInN by raised-pressure metalorganic vapor phase epitaxy,” Appl. Phys. Express3(7), 075601 (2010).
[CrossRef]

Appl. Phys. Lett. (9)

Z. Z. Bandić, P. M. Bridger, E. C. Piquette, and T. C. McGill, “Electron diffusion length and lifetime in p-type GaN,” Appl. Phys. Lett.73(22), 3276–3278 (1998).
[CrossRef]

Y. Zhao, Q. Yan, C. Y. Huang, S. C. Huang, P. S. Hu, S. Tanaka, C. C. Pan, Y. Kawaguchi, K. Fujito, C. G. Van de Walle, J. S. Speck, S. P. DenBaars, S. Nakamura, and D. Feezell, “Indium incorporation and emission properties of nonpolar and semipolar InGaN quantum wells,” Appl. Phys. Lett.100(20), 201108 (2012).
[CrossRef]

O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, “Design and characterization of GaN/InGaN solar cells,” Appl. Phys. Lett.91(13), 132117 (2007).
[CrossRef]

J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, and J. S. Speck, “High external quantum efficiency and fill-factor InGaN/GaN heterojunction solar cells grown by NH3-based molecular beam epitaxy,” Appl. Phys. Lett.98(13), 131115 (2011).
[CrossRef]

X. Zheng, R. H. Horng, D. S. Wuu, M. T. Chu, W. Y. Liao, M. H. Wu, R. M. Lin, and Y. C. Lu, “High-quality InGaN/GaN heterojunctions and their photovoltaic effects,” Appl. Phys. Lett.93(26), 261108 (2008).
[CrossRef]

X. M. Cai, S. W. Zeng, and B. P. Zhang, “Fabrication and characterization of InGaN p-i-n homojunction solar cell,” Appl. Phys. Lett.95(17), 173504 (2009).
[CrossRef]

R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well concentrator solar cells,” Appl. Phys. Lett.97(7), 073115 (2010).
[CrossRef]

J. J. Wierer, A. J. Fischer, and D. D. Koleske, “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN/InGaN photovoltaic devices,” Appl. Phys. Lett.96(5), 051107 (2010).
[CrossRef]

F. Chen, A. N. Cartwright, H. Lu, and W. J. Schaff, “Hole transport and carrier lifetime in InN epilayers,” Appl. Phys. Lett.87(21), 212104 (2005).
[CrossRef]

IEEE Electron Device Lett. (2)

J. Y. Chang and Y. K. Kuo, “Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (0001)-face GaN/InGaN p-i-n solar cells,” IEEE Electron Device Lett.32(7), 937–939 (2011).
[CrossRef]

B. R. Jampana, A. G. Melton, M. Jamil, N. N. Faleev, R. L. Opila, I. T. Ferguson, and C. B. Honsberg, “Design and realization of wide-band-gap (~2.67 eV) InGaN p-n junction solar cell,” IEEE Electron Device Lett.31(1), 32–34 (2010).
[CrossRef]

J. Appl. Phys. (2)

S. W. Feng, C. M. Lai, C. H. Chen, W. C. Sun, and L. W. Tu, “Theoretical simulations of the effects of the indium content, thickness, and defect density of the i-layer on the performance of p-i-n InGaN single homo-junction solar cells,” J. Appl. Phys.108(9), 093118 (2010).
[CrossRef]

L. Hsu and W. Walukiewicz, “Modeling of InGaN/Si tandem solar cells,” J. Appl. Phys.104(2), 024507 (2008).
[CrossRef]

J. Phys. D Appl. Phys. (2)

M. J. Jeng, Y. L. Lee, and L. B. Chang, “Temperature dependences of InxGa1-xN multiple quantum well solar cells,” J. Phys. D Appl. Phys.42(10), 105101 (2009).
[CrossRef]

X. Zhang, X. L. Wang, H. L. Xiao, C. B. Yang, J. X. Ran, C. M. Wang, Q. F. Hou, and J. M. Li, “Simulation of In0.65Ga0.35N single-junction solar cell,” J. Phys. D Appl. Phys.40(23), 7335–7338 (2007).

Phys. Status Solidi C (1)

A. Yamamoto, M. R. Islam, T.-T. Kang, and A. Hashimoto, “Recent advances in InN-based solar cells: status and challenges in InGaN and InAlN solar cells,” Phys. Status Solidi C7(5), 1309–1316 (2010).
[CrossRef]

Physica E (1)

F. Chena, A. N. Cartwright, H. Lu, and W. J. Schaff, “Temperature-dependent optical properties of wurtzite InN,” Physica E20(3–4), 308–312 (2004).
[CrossRef]

Proc. SPIE (1)

X. Shen, S. Lin, F. Li, Y. Wei, S. Zhong, H. Wan, and J. Li, “Simulation of the InGaN-based tandem solar cells,” Proc. SPIE7045, 70450E, 70450E-8 (2008).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

G. F. Brown, J. W. Ager, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells94(3), 478–483 (2010).
[CrossRef]

Other (4)

G. Durkaya, M. Alevli, M. Buegler, R. Atalay, S. Gamage, M. Kaiser, R. Kirste, A. Hoffmann, M. Jamil, I. Ferguson, and N. Dietz, “Growth temperature-phase stability relation in In1-xGaxN epilayers grown by high-pressure CVD,” Mater. Res. Soc. Symp. Proc. 1202, 1202–I5.21 (2010).

J. Nelson, The Physics of Solar Cells (Imperial College Press, 2003), Chap. 6.

M. S. Shur and R. F. Davis, GaN-Based Materials and Device (World Scientific, 2004).

E. F. Schubert, Light Emitting Diodes (Cambridge University Press, 2006).

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Figures (6)

Fig. 1
Fig. 1

The structure of InGaN p-n junction solar cells used for theoretical simulation. Light is incident from the p-InGaN side. wp and wn are the widths of the p- and n-InGaN junctions, respectively. dp and dn are the widths of the depletion region in the p- and n-InGaN junctions, respectively.

Fig. 2
Fig. 2

The J-V characteristic of InGaN p-n junction solar cells with 300 nm p-InGaN and 1,000 nm n-InGaN for various indium compositions.

Fig. 3
Fig. 3

Short circuit current density, Jsc(wp , xp), of InGaN p-n junction solar cells as a function of p-InGaN (a) width (wp) and (b) indium composition (xp). Open circuit voltage, Voc(wp , xp), of InGaN p-n junction solar cells as a function of p-InGaN (c) width (wp) and (d) indium composition (xp). The reported Jsc (* in Figs. 3(a) and 3(b)) and Voc (△ in Figs. 3(c) and 3(d)) of p-In0.168Ga0.832N(35nm)/n-In0.148Ga0.852N(45nm) junction solar cell under AM 1.5 illumination are plotted for comparison [11].

Fig. 4
Fig. 4

Fill factor, FF(wp , xp), of InGaN p-n junction solar cells as a function of p-InGaN (a) width (wp) and (b) indium composition (xp). Conversion efficiency, η(wp , xp), of InGaN p-n junction solar cells as a function of p-InGaN (c) width (wp) and (d) indium composition (xp). The reported FF (* in Figs. 4(a) and 4(b)) and η (△ in Figs. 4(c) and 4(d)) of p-In0.168Ga0.832N(35nm)/n-In0.148Ga0.852N(45nm) junction solar cell under AM 1.5 illumination are plotted for comparison [11].

Fig. 5
Fig. 5

Short circuit current density, Jsc(wn , xn), of InGaN p-n junction solar cells as a function of n-InGaN (a) width (wn) and (b) indium composition (xn). Open circuit voltage, Voc(wn , xn), of InGaN p-n junction solar cells as a function of n-InGaN (c) width (wn) and (d) indium composition (xn).

Fig. 6
Fig. 6

Fill factor, FF(wn , xn), of InGaN p-n junction solar cells as a function of n-InGaN (a) width (wn) and (b) indium composition (xn). Conversion efficiency, η(wn , xn), of InGaN p-n junction solar cells as a function of n-InGaN (c) width (wn) and (d) indium composition (xn).

Tables (1)

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Table 1 The parameters of wurtzite InN and GaN used for theoretical simulations.

Equations (12)

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J= J SCP + J SCN + J G,D ( J DP + J DN )( e q V a /kT 1) J DD ( e q V a /2kT 1)
J= J sc J s1 ( e q V a / kT 1) J s2 ( e q V a / 2kT 1)
Jsc J SCP + J SCN + J G,D
J s1 J DP + J DN
J s2 J DD
J= J sc J s1 ( e q V a / kT 1) J s2 ( e q V a / 2kT 1) J sc J s1 ( e q V a / kT 1) 0
V oc = kT q ln J sc + J s1 J s1
V oc kT q ln J sc J s1
FF= P max V oc I sc = V max I max V oc I sc = V max J max V oc J sc
η= P max P in = FF V oc I sc P in
n i 2 =2.31× 10 31 ( m n m p m e 2 ) 2/3 × T 3 ×exp( E g kT )
E g (x)=0.65x+3.425(1x)1.43x(1x)

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