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Analysis of Reduced Built-In Polarization Fields and Electronic Structure of InGaN/GaN Quantum Dot Molecules

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Quantum Dot Molecules

Part of the book series: Lecture Notes in Nanoscale Science and Technology ((LNNST,volume 14))

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Abstract

Nitride-based semiconductor materials InN, GaN, AlN, and their alloys are attracting great attention due to their promising applications in optoelectronic devices. However, the emission efficiency of c-plane InGaN/GaN quantum wells (QWs) drops significantly when going to longer wavelengths due to the strong electrostatic built-in fields in such heterostructures. We present a surface integral method to show and explain why the polarization potential in an InGaN/GaN quantum dot (QD) grown along the [0001]-direction is strongly reduced compared to that in a QW of the same height. We show that the sign of the shear strain piezoelectric coefficient e 15 strongly affects the built-in field and therefore the electronic structure both of an isolated QD and also of a system of stacked c-plane InGaN/GaN dots. Based on two different approaches we conclude e 15 < 0, in agreement with recent independent studies. We then use a tight-binding model and include strain and polarization fields, to study the electronic structure of InGaN/GaN quantum dot molecules grown along the c-axis. This analysis is carried out as a function of the barrier thickness firstly between identical and then between two non-identical dots. Our results show that the built-in field can be further reduced in systems of coupled nitride quantum dots, leading to an increased spatial overlap of electron and hole wave functions compared to an isolated dot. This finding is in agreement with experimental data reported in the literature and is directly related to the behavior of the built-in potential outside an isolated dot.

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Notes

  1. 1.

    Note that the quantities a 2 and a 1 given by Vurgaftman and Meyer in their 2003 review article [44] are not the conduction-band deformation potentials a cp and a ct , respectively. The quantities denoted by a 1 and a 2 in [44] are the band gap deformation potentials, e.g. a 1 = a cp − D 1 and a 2 = a ct − D 2.

  2. 2.

    Note that the term \(\mp 2\pi \text{sgn}(z \pm b)(z \pm b)\frac{{a}^{2}} {{c}^{2}} \left (\frac{3{b}^{2}} {{c}^{2}} + \frac{{c}^{2}-{b}^{2}+z(z\pm b)} {{c}^{2}+{z}^{2}} \right )\) is missing in Eq. (B13) for I 1 given in the appendix of Ref. [38] for an ellipsoid-shaped system.

References

  1. Jarjour, A.F., Oliver, R.A., Taylor, R.A.: Phys. Status Solid A 206, 2510 (2009)

    Article  CAS  Google Scholar 

  2. Humphreys, C.J.: MRS Bull. 33, 459 (2008)

    Article  Google Scholar 

  3. Nakamura, S., Mukai, T., Senoh, M.: Appl. Phys. Lett. 64, 1687 (1994)

    Article  CAS  Google Scholar 

  4. Nakamura, S.: J. Sel. Top. Quant. Electron. 3, 712 (1997)

    Article  CAS  Google Scholar 

  5. Yang, W., Lee, H., Johnson, T.J., Sercel, P.C., Norman, A.G.: Phys. Rev. B 61, 2784 (2000)

    Article  CAS  Google Scholar 

  6. Simon, J., Pelekanos, N.T., Adelmann, C., Martinez-Guerrero, E., Andre, R., Daudin, B., Dang, L.S., Mariette, H.: Phys. Rev. B 68, 035312 (2003)

    Article  Google Scholar 

  7. Andreev, A.D., O’Reilly, E.P.: Phys. Rev. B 62, 15851 (2000)

    Article  CAS  Google Scholar 

  8. Schulz, S., Caro, M.A., O’Reilly, E.P., Marquardt, O.: Phys. Status Solid B 249, 521 (2012)

    Article  CAS  Google Scholar 

  9. Waltereit, P., Brandt, O., Trampert, A., Grahn, H.T., Menniger, J., Ramsteiner, M., Ploog, K.H.: Nature 406, 865 (2000)

    Article  CAS  Google Scholar 

  10. Founta, S., Rol, F., Bellet-Amalric, E., Bleuse, J., Daudin, B., Gayral, B., Mariette, H., Moisson, C.: Appl. Phys. Lett. 86, 171901 (2005)

    Article  Google Scholar 

  11. Schulz, S., Caro, M.A., O’Reilly, E.P.: Appl. Phys. Lett. 101, 113107 (2012)

    Article  Google Scholar 

  12. Kim, K.C., Schmidt, M.C., Sato, H., Wu, F., Fellows, N., Saito, M., Fujito, K., Speck, J.S., Nakamura, S., DenBaars, S.P.: Phys. Stat. Sol. (RRL) 1, 125 (2007)

    Google Scholar 

  13. Caro, M.A., Schulz, S., Healy, S.B., O’Reilly, E.P.: J. Appl. Phys. 109, 084110 (2011)

    Article  Google Scholar 

  14. Zhang, M., Banerjee, A., Lee, C.S., Hinckley, J.M., Bhattacharya, P.: Appl. Phys. Lett. 98, 221104 (2011)

    Article  Google Scholar 

  15. Wu, Y.R., Lin, Y.Y., Huang, H.H., Singh, J.: J. Appl. Phys. 105, 013117 (2009)

    Article  Google Scholar 

  16. Schulz, S., O’Reilly, E.P.: Phys. Rev. B 82, 033411 (2010)

    Article  Google Scholar 

  17. Zhang, M., Bhattacharya, P., Guo, W.: Appl. Phys. Lett. 97, 011103 (2010)

    Article  Google Scholar 

  18. Soh, C.B., Liu, W., Chua, S.J., Ang, S.S., Tan, R.J.N., Chow, S.Y.: J. Appl. Phys. 108, 093501 (2010)

    Article  Google Scholar 

  19. Schmidt, O.G., Kirstaedter, N., Ledentsov, N.N., Mao, M.H., Bimberg, D., Ustinov, V.M., Egorov, A.Y., Zhukov, A.E., Maximov, M., Kop’ev, P.S., Alferov, Z.I.: Electron. Lett. 32, 1302 (1996)

    Article  CAS  Google Scholar 

  20. Ledentsov, N.N., Shchukin, V.A., Grundmann, M., Kirstaedter, K., Bohrer, J., Schmidt, O., Bimberg, D., Ustinov, V.M., Egorov, A.Y., Zhukov, A.E., Kop’ev, P.S., Zaitsev, S.V., Gordeev, N.Y., Alferov, Z.I., Borovkov, A.I., Kosogov, A.O., Ruvimov, S.S., Werner, P., Gösele, U., Heydenreich, J.: Phys. Rev. B 54, 8743 (1996)

    Article  CAS  Google Scholar 

  21. Neogi, A., Morkoc, H., Kuroda, T., Tackeuchi, A., Kawazoe, T., Ohtsu, M.: Nano Lett. 5, 213 (2004)

    Article  Google Scholar 

  22. Davies, S.C., Mowbray, D.J., Ranalli, F., Wang, T.: Appl. Phys. Lett. 96, 251904 (2010)

    Article  Google Scholar 

  23. Bernardini, F., Fiorentini, V., Vanderbilt, D.: Phys. Rev. B 56, R10024 (1997)

    Article  CAS  Google Scholar 

  24. Schulz, S., Berube, A., O’Reilly, E.P.: Phys. Rev. B 79, 081401(R) (2009)

    Google Scholar 

  25. Skylaris, C.K., Haynes, P.D., Mostofi, A.A., Payne, M.C.: J. Chem. Phys. 122, 084119 (2005)

    Article  Google Scholar 

  26. Hine, N.D.M., Robinson, M., Haynes, P.D., Skylaris, C.K., Payne, M.C., Mostofi, A.A.: Phys. Rev. B 83, 195102 (2011)

    Article  Google Scholar 

  27. Pryor, C., Kim, J., Wang, L.W., Williamson, A.J., Zunger, A.: J. Appl. Phys. 83, 2548 (1998)

    Article  CAS  Google Scholar 

  28. Klimeck, G., Ahmed, S.S., Bae, H., Kharche, N., Rahman, R., Clark, S., Haley, B., Lee, S., Naumov, M., Ryu, H., Saied, F., Prada, M., Korkusinski, M., Boykin, T.B.: IEEE Trans. Electron Dev. 54, 2079 (2007)

    Article  CAS  Google Scholar 

  29. Bester, G.: J. Phys. Condens. Matter 21, 023202 (2009)

    Article  Google Scholar 

  30. Caro, M.A., Schulz, S., O’Reilly, E.P.: Phys. Status Solid B 249, 526 (2012)

    Article  CAS  Google Scholar 

  31. Schliwa, A., Winkelnkemper, M., Bimberg, D.: Phys. Rev. B 76, 205324 (2007)

    Article  Google Scholar 

  32. Marquardt, O., Schulz, S., Freysoldt, C., Boeck, S., Hickel, T., O’Reilly, E.P., Neugebauer, J.: Opt. Quant. Electron. 44, 183 (2012)

    Article  CAS  Google Scholar 

  33. Faux, D.A., Downes, J.R., O’Reilly, E.P.: J. Appl. Phys. 80, 2515 (1996)

    Article  CAS  Google Scholar 

  34. Faux, D.A., Downes, J.R., O’Reilly, E.P.: J. Appl. Phys. 82, 3754 (1997)

    Article  CAS  Google Scholar 

  35. Downes, J.R., Faux, D.A., O’Reilly, E.P.: J. Appl. Phys. 81, 6700 (1997)

    Article  CAS  Google Scholar 

  36. Andreev, A.D., Downes, J., Faux, D.A., O’Reilly, E.P.: J. Appl. Phys. 86, 297 (1999)

    Article  CAS  Google Scholar 

  37. Davies, J.H.: J. Appl. Phys. 84, 1358 (1998)

    Article  CAS  Google Scholar 

  38. Williams, D.P., Andreev, A.D., O’Reilly, E.P., Faux, D.A.: Phys. Rev. B 72, 235318 (2005)

    Article  Google Scholar 

  39. Eshelby, J.D.: Proc. R. Soc. Lond. Ser. A 241, 376 (1957)

    Article  Google Scholar 

  40. Ridha, P., Li, L.H., Mexis, M., Smowton, P.M., Andrzejewski, J., Sek, G., Misiewicz, J., O’Reilly, E.P., Patriarche, G., Fiore, A.: IEEE J. Quant. Electron. 46, 197 (2010)

    Article  CAS  Google Scholar 

  41. Williams, D.P., Schulz, S., Andreev, A.D., O’Reilly, E.P.: J. Sel. Top. Quant. Electron. 15, 1092 (2009)

    Article  CAS  Google Scholar 

  42. Ambacher, O.: J. Phys. D Appl. Phys. 31, 2653 (1998)

    Article  CAS  Google Scholar 

  43. Kittel, C.: Introduction to Solid State Physics. Wiley, New York (1995)

    Google Scholar 

  44. Vurgaftman, I., Meyer, J.R.: J. Appl. Phys. 94, 3675 (2003)

    Article  CAS  Google Scholar 

  45. Baer, N., Gartner, P., Jahnke, F.: Eur. Phys. J. B 42, 231 (2004)

    Article  CAS  Google Scholar 

  46. Wojs, A., Hawrylak, P., Fafard, S., Jacak, L.: Phys. Rev. B 54, 5604 (1996)

    Article  CAS  Google Scholar 

  47. Winkelnkemper, M., Schliwa, A., Bimberg, D.: Phys. Rev. B 74, 155322 (2006)

    Article  Google Scholar 

  48. Marquardt, O., Mourad, D., Schulz, S., Hickel, T., Czycholl, G., Neugebauer, J.: Phys. Rev. B 78, 235302 (2008)

    Article  Google Scholar 

  49. Marquardt, O., Hickel, T., Neugebauer, J.: J. Appl. Phys. 106, 083707 (2009)

    Article  Google Scholar 

  50. Bester, G., Zunger, A.: Phys. Rev. B 71, 045318 (2005)

    Article  Google Scholar 

  51. Bester, G., Zunger, A., Shumway, J.: Phys. Rev. B 71, 075325 (2005)

    Article  Google Scholar 

  52. Singh, R., Bester, G.: Phys. Rev. Lett. 103, 063601 (2009)

    Article  Google Scholar 

  53. Santoprete, R., Koiller, B., Capaz, R.B., Kratzer, P., Liu, Q.K.K., Scheffler, M.: Phys. Rev. B 68, 235311 (2003)

    Article  Google Scholar 

  54. Ranjan, V., Allan, G., Priester, C., Delerue, C.: Phys. Rev. B 68, 115305 (2003)

    Article  Google Scholar 

  55. Schulz, S., Schumacher, S., Czycholl, G.: Phys. Rev. B 73, 245327 (2006)

    Article  Google Scholar 

  56. Schulz, S., Schumacher, S., Czycholl, G.: Eur. Phys. J. B 64, 51 (2008)

    Article  CAS  Google Scholar 

  57. Lee, S.J., Chung, H.S., Nahm, K., Kim, C.K.: Phys. Rev. B 42, 1452 (1990)

    Article  Google Scholar 

  58. Bouhafs, B., Aourag, A., Ferhat, M., Zaoui, A., Certier, M.: J. Appl. Phys. 82, 4923 (1997)

    Article  CAS  Google Scholar 

  59. Fredj, A.B., Debbichi, M., Said, M.: Microelectron. J. 38, 860 (2007)

    Article  Google Scholar 

  60. Jancu, J.M., Scholz, R., Beltram, F., Bassani, F.: Phys. Rev. B 57, 6493 (1998)

    Article  CAS  Google Scholar 

  61. Boykin, T.B., Klimeck, G., Bowen, R.C., Oyafuso, F.: Phys. Rev. B 66, 125207 (2002)

    Article  Google Scholar 

  62. Schulz, S., Badcock, T.J., Moram, M.A., Dawson, P., Kappers, M.J., Humphreys, C.J., O’Reilly, E.P.: Phys. Rev. B 82, 125318 (2010)

    Article  Google Scholar 

  63. Yan, Q., Rinke, P., Scheffler, M., Van de Walle, C.G.: Appl. Phys. Lett. 95, 121111 (2009)

    Article  Google Scholar 

  64. Saito, T., Arakawa, Y.: Phys. E (Amsterdam) 15, 169 (2002)

    Google Scholar 

  65. Zielinski, M., Jaskolski, W., Aizpurua, J., Bryant, G.W.: Acta Phys. Pol. A 108, 929 (2005)

    CAS  Google Scholar 

  66. Schuh, K., Barthel, S., Marquardt, O., Hickel, T., Neugebauer, J., Czycholl, G., Jahnke, F.: Appl. Phys. Lett. 100, 092103 (2012)

    Article  Google Scholar 

  67. Schulz, S., O’Reilly, E.P.: Phys. Stat. Sol. (c) 7, 1900 (2010)

    Google Scholar 

  68. Strittmatter, A., Reißmann, L., Seguin, R., Rodt, S., Brostowski, A., Pohl, U., Bimberg, D., Hahn, E., Gerthsen, D.: J. Cryst. Growth 272, 415 (2004)

    Article  CAS  Google Scholar 

  69. Gerthsen, D., Hahn, E., Neubauer, B., Potin, V., Rosenauer, A., Schowalter, M.: Phys. Stat. Sol. (c) 0, 1668 (2003)

    Google Scholar 

  70. Senes, M., Smith, K.L., Smeeton, T.M., Hooper, S.E., Heffernan, J.: Phys. Rev. B 75, 045314 (2007)

    Article  Google Scholar 

  71. Schulz, S., O’Reilly, E.P.: Phys. Status Solid C 7, 80 (2010)

    Article  CAS  Google Scholar 

  72. Moriwaki, O., Someya, T., Tachibana, K., Ishida, S., Arakawa, Y.: Appl. Phys. Lett. 76, 2361 (2000)

    Article  CAS  Google Scholar 

  73. Robinson, J.W., Rice, J.H., Lee, K.H., Na, J.H., Taylor, R.A., Hasko, D.G., Oliver, R.A., Kappers, M.J., Humphreys, C.J., Briggs, G.A.D.: Appl. Phys. Lett. 86, 213103 (2005)

    Article  Google Scholar 

  74. Zhang, Q., Zhu, J., Ren, X., Li, H., Wang, T.: Appl. Phys. Lett. 78, 3830 (2001)

    Article  CAS  Google Scholar 

  75. Neogi, A., Gorman, B.P., Morkoc, H., Kawazoe, T., Ohtsu, M.: Appl. Phys. Lett. 86, 043103 (2005)

    Article  Google Scholar 

  76. Christmas, U.M.E., Andreev, A.D., Faux, D.A.: J. Appl. Phys. 98, 073522 (2005)

    Article  Google Scholar 

  77. Bernardini, F., Fiorentini, V.: Appl. Phys. Lett. 80, 4145 (2002)

    Article  CAS  Google Scholar 

  78. Shimada, K.: Jpn. J. Appl. Phys. 45, L358 (2006)

    Article  CAS  Google Scholar 

  79. Romanov, A.E., Baker, T.J., Nakamura, S., Speck, J.S.: J. Appl. Phys. 100, 023522 (2006)

    Article  Google Scholar 

  80. Shen, H., Wraback, M., Zhong, H., Tyagi, A., DenBaars, S.P., Nakamura, S., Speck, J.S.: Appl. Phys. Lett. 95, 033503 (2009)

    Article  Google Scholar 

  81. Pal, J., Tse, G., Haxha, V., Migliorato, M.A., Tomic, S.: Phys. Rev. B 84, 085211 (2011)

    Article  Google Scholar 

  82. Garro, N., Cros, A., Budagosky, J.A., Cantarero, A., Vinattieri, A., Gurioli, M., Founta, S., Mariette, H., Daudin, B.: Appl. Phys. Lett. 87, 011101 (2005)

    Article  Google Scholar 

  83. Founta, S., Rol, F., Bellet-Amalric, E., Sarigiannidou, E., Gayral, B., Moisson, C., Mariette, H., Daudin, B.: Phys. Stat. Sol. (b) 243, 3968 (2006)

    Google Scholar 

  84. Founta, S., Coraux, J., Jalabert, D., Bougerol, C., Rol, F., Mariette, H., Renevier, H., Daudin, B., Oliver, R.A., Humphreys, C.J., Noakes, T.C.Q., Bailey, P.: J. Appl. Phys. 101, 063541 (2007)

    Article  Google Scholar 

  85. Yang, X., Arita, M., Kako, S., Arakawa, Y.: Appl. Phys. Lett. 99, 061914 (2011)

    Article  Google Scholar 

  86. Schulz, S., Caro, M.A., O’Reilly, E.P., Marquardt, O.: Phys. Rev. B 84, 125312 (2011)

    Article  Google Scholar 

  87. Dimastrodonato, V., Mereni, L.O., Juska, G., Pelucchi, E.: Appl. Phys. Lett. 97, 072115 (2010)

    Article  Google Scholar 

  88. Mohan, A., Felici, M., Gallo, P., Dwir, B., Rudra, A., Faist, J., Kapon, E.: Nat. Photon. 4, 302 (2010)

    Article  CAS  Google Scholar 

  89. Yeh, C.Y., Lu, Z.W., Froyen, S., Zunger, A.: Phys. Rev. B 46, 10086 (1992)

    Article  CAS  Google Scholar 

  90. Schulz, S., O’Reilly, E.P.: Phys. Status Solid A 208, 1551 (2011)

    Article  CAS  Google Scholar 

  91. Schulz, S., O’Reilly, E.P.: Phys. Status Solid B 249, 516 (2012)

    Article  CAS  Google Scholar 

  92. Schulz, S., O’Reilly, E.P.: Appl. Phys. Lett. 99, 223106 (2011)

    Article  Google Scholar 

  93. Schulz, S., Mourad, D., Schumacher, S., Czycholl, G.: Phys. Status Solid B 248, 1853 (2011)

    Article  CAS  Google Scholar 

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Acknowledgments

The authors acknowledge the financial support from Science Foundation Ireland. S. Schulz was further supported by the Irish Research Council for Science, Engineering and Technology (IRCSET).

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Authors and Affiliations

  1. Tyndall National Institute, Lee Maltings, Cork, Ireland

    Stefan Schulz & Eoin P. O’Reilly

  2. Department of Physics, University College Cork, Cork, Ireland

    Eoin P. O’Reilly

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  1. Stefan Schulz
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  2. Eoin P. O’Reilly
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Correspondence to Stefan Schulz .

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Editors and Affiliations

  1. State Key Laboratory of Electronic Thin, University of Electronic Science and Technology of China, Chengdu, People's Republic of China

    Jiang Wu

  2. State Key Laboratory of Electronic, University of Electronic Science and Technology, Chengdu, People's Republic of China

    Zhiming M. Wang

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Schulz, S., O’Reilly, E.P. (2014). Analysis of Reduced Built-In Polarization Fields and Electronic Structure of InGaN/GaN Quantum Dot Molecules. In: Wu, J., Wang, Z. (eds) Quantum Dot Molecules. Lecture Notes in Nanoscale Science and Technology, vol 14. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8130-0_6

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