Abstract

Room temperature electrically pumped exciton-polariton light-emitting diode (LED) based on the n-ZnO microwire/MgO/p-GaN heterojunction was fabricated. With the injection current of 1.5 mA, the ultraviolet electroluminescence centered at wavelength of 400 nm is obtained. The whispering gallery cavity model combined with the coupling oscillator model is used to describe the emission intensity modulation, from which the strong coupling regime of the system is proved to be surviving at room temperature.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
    [Crossref]
  3. A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
    [Crossref]
  4. K.J. Chen, F.Y. Hung, S.J. Chang, and S.J. Young, “Optoelectronic characteristics of UV photodetector based on ZnO nanowire thin films,” J. Alloys and Compounds 479, 674 (2009).
    [Crossref]
  5. Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
    [Crossref]
  6. A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
    [Crossref]
  7. A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
    [Crossref]
  8. M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
    [Crossref]
  9. W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
    [Crossref] [PubMed]
  10. L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
    [Crossref] [PubMed]
  11. Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
    [Crossref]
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  14. Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
    [Crossref]
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    [Crossref]
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    [Crossref]
  17. D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
    [Crossref]
  18. E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89, 221109 (2006).
    [Crossref]
  19. X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
    [Crossref]
  20. C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
    [Crossref] [PubMed]
  21. P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
    [Crossref] [PubMed]
  22. D. Sanvitto and S. Kéna-Cohen, “The road towards polaritonic devices,” Nat. Mater. 15, 1061 (2016).
    [Crossref] [PubMed]
  23. J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
    [Crossref] [PubMed]
  24. A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
    [Crossref]
  25. S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
    [Crossref] [PubMed]
  26. H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
    [Crossref]
  27. L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
    [Crossref]
  28. L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
    [Crossref] [PubMed]
  29. L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
    [Crossref] [PubMed]
  30. J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511 (1981).
    [Crossref]

2016 (1)

D. Sanvitto and S. Kéna-Cohen, “The road towards polaritonic devices,” Nat. Mater. 15, 1061 (2016).
[Crossref] [PubMed]

2015 (2)

Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
[Crossref]

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

2014 (1)

P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
[Crossref] [PubMed]

2013 (2)

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
[Crossref]

2012 (1)

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

2011 (1)

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

2010 (1)

2009 (3)

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

K.J. Chen, F.Y. Hung, S.J. Chang, and S.J. Young, “Optoelectronic characteristics of UV photodetector based on ZnO nanowire thin films,” J. Alloys and Compounds 479, 674 (2009).
[Crossref]

2008 (3)

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
[Crossref]

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
[Crossref] [PubMed]

2007 (2)

X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
[Crossref]

R. W. Chuang, R. Wu, L.-W. Lai, and C.-T. Lee, “ ZnO-on-GaN heterojunction light-emitting diode grown by vapor cooling condensation technique,” Appl. Phys. Lett. 91, 231113 (2007).
[Crossref]

2006 (4)

D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
[Crossref]

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89, 221109 (2006).
[Crossref]

S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
[Crossref]

L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

2005 (5)

J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
[Crossref] [PubMed]

T. M. Barnes, K. Olson, and C. A. Wolden, “On the formation and stability of p-type conductivity in nitrogen-doped zinc oxide,” Appl. Phys. Lett. 86, 112112 (2005).
[Crossref]

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
[Crossref]

A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
[Crossref]

2003 (1)

Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
[Crossref]

2002 (1)

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

2001 (1)

E.-C. Lee, Y.-S. Kim, Y.-G. Jin, and K. J. Chang, “ Compensation mechanism for N acceptors in ZnO,” Phys. Rev. B 64, 085120 (2001).
[Crossref]

1981 (1)

J. Lagois, “Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23, 5511 (1981).
[Crossref]

Alivov, Ya. I.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
[Crossref]

Amthor, M.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

An, Z.

Ataev, B. M.

Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
[Crossref]

Avrutin, V.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Bai, L.

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Barnes, T. M.

T. M. Barnes, K. Olson, and C. A. Wolden, “On the formation and stability of p-type conductivity in nitrogen-doped zinc oxide,” Appl. Phys. Lett. 86, 112112 (2005).
[Crossref]

Baten, Md Z.

P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
[Crossref] [PubMed]

Bhattacharya, P.

P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
[Crossref] [PubMed]

Bradley, M. S.

J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
[Crossref] [PubMed]

Bulovic, V.

J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
[Crossref] [PubMed]

Chang, K. J.

E.-C. Lee, Y.-S. Kim, Y.-G. Jin, and K. J. Chang, “ Compensation mechanism for N acceptors in ZnO,” Phys. Rev. B 64, 085120 (2001).
[Crossref]

Chang, S.J.

K.J. Chen, F.Y. Hung, S.J. Chang, and S.J. Young, “Optoelectronic characteristics of UV photodetector based on ZnO nanowire thin films,” J. Alloys and Compounds 479, 674 (2009).
[Crossref]

Chen, K.J.

K.J. Chen, F.Y. Hung, S.J. Chang, and S.J. Young, “Optoelectronic characteristics of UV photodetector based on ZnO nanowire thin films,” J. Alloys and Compounds 479, 674 (2009).
[Crossref]

Chen, P.

X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
[Crossref]

Chen, Z.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
[Crossref] [PubMed]

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Chichibu, S. F.

A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
[Crossref]

Cho, S.-J.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Chuang, R. W.

R. W. Chuang, R. Wu, L.-W. Lai, and C.-T. Lee, “ ZnO-on-GaN heterojunction light-emitting diode grown by vapor cooling condensation technique,” Appl. Phys. Lett. 91, 231113 (2007).
[Crossref]

Chukichev, M. V.

Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
[Crossref]

Dang, Le Si

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

Das, A.

P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
[Crossref] [PubMed]

Datta, S.

A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
[Crossref]

Deshpande, S.

P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
[Crossref] [PubMed]

Dogan, S.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Dong, H.

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
[Crossref] [PubMed]

Dou, B.

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H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
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Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
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S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
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P. Bhattacharya, T. Frost, S. Deshpande, Md Z. Baten, A. Hazari, and A. Das, “Room temperature electrically injected polariton laser,” Phys. Rev. Lett. 112, 236802 (2014).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
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S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
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E.-C. Lee, Y.-S. Kim, Y.-G. Jin, and K. J. Chang, “ Compensation mechanism for N acceptors in ZnO,” Phys. Rev. B 64, 085120 (2001).
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Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
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M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
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M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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E.-C. Lee, Y.-S. Kim, Y.-G. Jin, and K. J. Chang, “ Compensation mechanism for N acceptors in ZnO,” Phys. Rev. B 64, 085120 (2001).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
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A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
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L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
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E.-C. Lee, Y.-S. Kim, Y.-G. Jin, and K. J. Chang, “ Compensation mechanism for N acceptors in ZnO,” Phys. Rev. B 64, 085120 (2001).
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S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
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H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
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X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
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Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
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Li, H.

Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
[Crossref]

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D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
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W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
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Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
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Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
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S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
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A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
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W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
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S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
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H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
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X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
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M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
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A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
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Minder, K.

D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
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A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
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Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
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D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
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[Crossref]

Park, S.-J.

D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
[Crossref]

Pavlovic, G.

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

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S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
[Crossref] [PubMed]

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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

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D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
[Crossref]

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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
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L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Reshchikov, M. A.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Richard, M.

A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
[Crossref]

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

Roberts, J. S.

A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
[Crossref]

Rogers, D. J.

D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
[Crossref]

Rühle, S.

L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Sanvitto, D.

D. Sanvitto and S. Kéna-Cohen, “The road towards polaritonic devices,” Nat. Mater. 15, 1061 (2016).
[Crossref] [PubMed]

Savenko, I. G.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Savvidis, P. G.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
[Crossref] [PubMed]

Schneider, C.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Segawa, Y.

A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
[Crossref]

Shan, C.-X.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Shelykh, I. A.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Shen, D. Z.

S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
[Crossref]

Shen, De-Z.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Shen, X.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
[Crossref] [PubMed]

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Skolnick, M. S.

A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
[Crossref]

Song, J. H.

J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
[Crossref] [PubMed]

Sumiya, M.

A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
[Crossref]

Sun, L.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
[Crossref] [PubMed]

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Tang, Zi-K.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Teherani, F. H.

D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
[Crossref]

Teke, A.

Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98, 041301 (2005).
[Crossref]

Tischler, J. R.

J. R. Tischler, M. S. Bradley, V. Bulović, J. H. Song, and A. Nurmikko, “Strong coupling in a microcavity LED,” Phys. Rev. Lett. 95, 036401 (2005).
[Crossref] [PubMed]

Trichet, A.

A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, and M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate,” Phys. Rev. B 88, 121407 (2013).
[Crossref]

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

Tsintzos, S. I.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372 (2008).
[Crossref] [PubMed]

Tsukazaki, A.

A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, “Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO,” Nat. Mater. 4, 42 (2005).
[Crossref]

Van Nostrand, J. E.

Ya. I. Alivov, J. E. Van Nostrand, D. C. Look, M. V. Chukichev, and B. M. Ataev, “Observation of 430 nm electroluminescence from ZnO/GaN heterojunction light-emitting diodes,” Appl. Phys. Lett. 83, 2943 (2003).
[Crossref]

Vanmaekelbergh, D.

L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Vugt, L. K. v.

L. K. v. Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97, 147401 (2006).
[Crossref] [PubMed]

Wang, J.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

Wang, Y.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
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T. M. Barnes, K. Olson, and C. A. Wolden, “On the formation and stability of p-type conductivity in nitrogen-doped zinc oxide,” Appl. Phys. Lett. 86, 112112 (2005).
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C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Worschech, L.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Wu, C.

Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
[Crossref]

Wu, L.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

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R. W. Chuang, R. Wu, L.-W. Lai, and C.-T. Lee, “ ZnO-on-GaN heterojunction light-emitting diode grown by vapor cooling condensation technique,” Appl. Phys. Lett. 91, 231113 (2007).
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Xie, W.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

A. Trichet, L. Sun, G. Pavlovic, N.A. Gippius, G. Malpuech, W. Xie, Z. Chen, M. Richard, and Le Si Dang, “One-dimensional ZnO exciton polaritons with negligible thermal broadening at room temperature,” Phys. Rev. B 83, 041302 (2011).
[Crossref]

L. Sun, H. Dong, W. Xie, Z. An, X. Shen, and Z. Chen, “Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod,” Opt. Express 18, 15371 (2010).
[Crossref] [PubMed]

Xiong, H.

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Yamamoto, Y.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. D. Kulakovskii, I. A. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “ An electrically pumped polariton laser,” Nature 497, 348 (2013).
[Crossref] [PubMed]

Yang, D.

X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
[Crossref]

Yang, E.-J.

D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
[Crossref]

Yang, J.-H.

D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
[Crossref]

Yao, B.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
[Crossref]

Yasan, A.

D. J. Rogers, F. H. Teherani, A. Yasan, K. Minder, P. Kung, and M. Razeghi, “ Electroluminescence at 375 nm from a Zn O/Ga N: Mg/ c-Al2O3 heterojunction light emitting diode,” Appl. Phys. Lett. 88, 141918 (2006).
[Crossref]

Young, S.J.

K.J. Chen, F.Y. Hung, S.J. Chang, and S.J. Young, “Optoelectronic characteristics of UV photodetector based on ZnO nanowire thin films,” J. Alloys and Compounds 479, 674 (2009).
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Yu, K.

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Yu, Ke

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

Yu, S. F.

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89, 221109 (2006).
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Zamfirescu, M.

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for the realization of room-temperature polariton lasers,” Phys. Rev. B 65, 161205 (2002).
[Crossref]

Zhang, J. Y.

S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
[Crossref]

Zhang, Ji-Y.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Zhang, L.

Y. Wang, T. Hu, W. Xie, L. Sun, L. Zhang, J. Wang, J. Gu, L. Wu, J. Wang, X. Shen, and Z. Chen, “Polarization-coupled polariton pairs in a birefringent microcavity,” Phys. Rev. B 91, 121301 (2015).
[Crossref]

Zhang, S.

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

Zhang, W.

Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
[Crossref]

Zhang, Y.

X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91, 251109 (2007).
[Crossref]

Zhang, Z. Z.

S. J. Jiao, Y. M. Lu, D. Z. Shen, Z. Z. Zhang, B. H. Li, J. Y. Zhang, B. Yao, Y. C. Liu, and X. W. Fan, “Ultraviolet electroluminescence of ZnO based heterojunction light emitting diode,” Physica Status Solidi (c) 3, 972 (2006).
[Crossref]

Zhang, Z.-Z.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Zhao, D.-Xu

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Zhou, W.

W. Xie, H. Dong, S. Zhang, L. Sun, W. Zhou, Y. Ling, J. Lu, X. Shen, and Z. Chen, “Room-temperature polariton parametric scattering driven by a one-dimensional polariton condensate,” Phys. Rev. Lett. 108, 166401 (2012).
[Crossref] [PubMed]

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Zhu, H.

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Zhu, Z. Q.

L. Sun, Z. Chen, Q. Ren, Ke Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Physica Status Solidi (c) 6, 133 (2009).
[Crossref]

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100, 156403 (2008).
[Crossref] [PubMed]

Adv. Mater. (1)

H. Zhu, C.-X. Shan, B. Yao, B.-H. Li, Ji-Y. Zhang, Z.-Z. Zhang, D.-Xu Zhao, De-Z. Shen, Xi-Wu Fan, Y.-M. Lu, and Zi-K. Tang, “Ultralow-Threshold Laser Realized in Zinc Oxide,” Adv. Mater. 21, 1613 (2009).
[Crossref]

Appl. Phys. Lett. (9)

A. A. Khalifa, A. P. D. Love, D. N. Krizhanovskii, M. S. Skolnick, and J. S. Roberts, “Electroluminescence emission from polariton states in GaAs-based semiconductor microcavities,” Appl. Phys. Lett. 92, 061107 (2008).
[Crossref]

D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, and S.-J. Park, “p-ZnO/n-GaN heterostructure ZnO light-emitting diodes,” Appl. Phys. Lett. 86, 222101 (2005).
[Crossref]

Z. Feng, R. Jia, B. Dou, H. Li, Z. Jin, X. Liu, F. Li, W. Zhang, and C. Wu, “Fabrication and properties of ZnO nanorods within silicon nanostructures for solar cell application,” Appl. Phys. Lett. 106, 053118 (2015).
[Crossref]

T. M. Barnes, K. Olson, and C. A. Wolden, “On the formation and stability of p-type conductivity in nitrogen-doped zinc oxide,” Appl. Phys. Lett. 86, 112112 (2005).
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J. Alloys and Compounds (1)

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Nat. Mater. (2)

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[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a) The scanning electron microscope image of a single ZnO microwire. (b) Photoluminescence(PL) spectra of ZnO microwire and GaN layer.
Fig. 2
Fig. 2 (a) Schematic illustration of the n-ZnO microwire/MgO/p-GaN structure. (b) IV curve of the diode, revealing obvious rectifying behavior with a turn-on voltage of about 5 V. (c) Schematic diagram showing the band alignment of the n-ZnO/MgO/p-GaN heterojunction under forward bias. (d) I–V curves of Au/Ni ohmic contact on p-GaN.
Fig. 3
Fig. 3 (a) The real-space electroluminescence (EL) emission image of the ZnO microwire. (b) The room temperature EL emission spectra of the device at different applied currents. (c) The integrated spectrum intensity as a function of injection current.
Fig. 4
Fig. 4 The comparison between the theoretically calculated dispersions and experimental. The energies of B-, C-exciton and dispersion of pure WGM are shown with black lines respectively. Red and green lines represent the lower and upper branch of polariton. And the blue squares are the experimental data extracted from the Fig. 3(a).

Equations (2)

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E = h c 3 3 n R [ N + 6 π arctan ( 1 n 3 n 2 4 ) ] .
n 2 = ( 1 + i = A , B , C Ω i ω i , L 2 ω i , T 2 ω i , T 2 ω 2 i ω Γ i ) = c 2 k 2 ω 2 .

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