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Size Dependence of Optical Properties in Semiconductor Nanocrystals
Abstract:
An extension of the classic thermodynamic theory to nanometer scale has generated a new interdisciplinary theory - nanothermodynamics. It is the critical tool for the investigation of the size-dependent physicochemical properties in nanocrystals. A simple and unified nanothermodynamic model for the melting temperature of nanocrystals has been established based on Lindemann’s criterion for the melting, Mott’s expression for the vibrational melting entropy, and Shi’s model for the size dependence of the melting point. The developed model has been extensively verified in calculating a variety of size- and dimensionality-dependent phase transition functions of nanocrystals. In this work, such a model was extended to explain the underlying mechanism behind the bandgap energy enhancement and Raman red shifts in semiconductor nanocrystals by (1) investigating the crystal size r, dimensionality d, and constituent stoichiometry x dependences of bandgap energies Eg in semiconductor quantum dots (QDs) and quantum wires (QWs); and (2) revealing the origin of size effect on the Raman red shifts in low dimensional semiconductors by considering the thermal vibration of atoms. For Eg, it is found that: (1) Eg increases with a decreasing r for groups IV, III-V and II-VI semiconductors and the quantum confinement effect is pronounced when r becomes comparable to the exciton radius; (2) the ratio of Eg(r, d)QWs/Eg(r, d)QDs is size-dependent, where Eg(r, d) denotes the change in bandgap energy; (3) the crystallographic structure (i.e. zinc-blende and wurtzite) effect on Eg of III-V and II-VI semiconductor nanocrystals is limited; and (4) for both bulk and nanosized III-V and II-VI semiconductor alloys, the composition effects on Eg are substantial, having a common nonlinear (bowing) relationship. For the Raman red shifts, the lower limit of vibrational frequency was obtained by matching the calculation results of the shifts with the experimental data of Si, InP, CdSe, CdS0.65Se0.35, ZnO, CeO2, as well as SnO2 nanocrystals. It shows that: (1) the Raman frequency (r) decreases as r decreases in both narrow and wide bandgap semiconductors; (2) with the same r, the sequence of size effects on (r) from strong to weak is nanoparticles, nanowires, and thin films; and (3) the Raman red shift is caused by the size-induced phonon confinement effect and surface relaxation. These results are consistent with experimental findings and may provide new insights into the size, dimensionality, and composition effects on the optical properties of semiconductors as well as fundamental understanding of high-performance nanostructural semiconductors towards their applications in optoelectronic devices.
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[1] H. Gleiter: Acta Mater. Vol. 48 (2000), p.1.
[2] Q. Jiang and C.C. Yang: Curr. Nanosci. Vol. 4 (2008), p.179.
[3] C.Q. Sun: Prog. Solid State Chem. Vol. 35 (2007), p.1.
[4] A.D. Yoffe: Adv. Phys. Vol. 50 (2001), p.1.
[5] J.B. Li and L.W. Wang: Phys. Rev. B Vol. 72 (2005), p.125325.
[6] C.C. Yang and S. Li: J. Phys. Chem. C Vol. 112 (2008), p.2851.
[7] H. Takagi, H. Ogawa, Y. Yamazaki, A. Ishizaki and T. Nakagiri: Appl. Phys. Lett. Vol. 56 (1990), p.2379.
[8] L. Pavesi, G. Giebel, F. Ziglio, G. Mariotto, F. Priolo, S.U. Campisano and C. Spinella: Appl. Phys. Lett. Vol. 65 (1994), p.2182.
DOI: 10.1063/1.112755
[9] T. van Buuren, L.N. Dinh, L.L. Chase, W.J. Siekhaus and L.J. Terminello: Phys. Rev. Lett. Vol. 80 (1998), p.3803.
[10] L.K. Pan, C.Q. Sun, B.K. Tay, T.P. Chen and S. Li: J. Phys. Chem. B Vol. 106 (2002), p.11725.
[11] Y.G. Cao, X.L. Chen, J.Y. Li, Y.C. Lan and J.K. Liang: Appl. Phys. A Vol. 71 (2000), p.229.
[12] R. Viswanatha, S. Sapra, T. Saha-Dasgupta and D.D. Sarma: Phys. Rev. B Vol. 72 (2005), p.045333.
[13] S.M. Gao, J. Lu, N. Chen, Y. Zhao and Y. Xie: Chem. Commun. Vol. 2002 (2002), p.3064.
[14] O.I. Mićić and A.J. Nozik: J. Lumin. Vol. 70 (1996), p.95.
[15] S.S. Kher and R.L. Wells: Nanostruct. Mater. Vol. 7 (1996), p.591.
[16] M.A. Malik, P. O'Brien, S. Norager and J. Smith: J. Mater. Chem. Vol. 13 (2003), p.2591.
[17] J.P. Xiao, Y. Xie, R. Tang and W. Luo: Inorg. Chem. Vol. 42 (2003), p.107.
[18] O.I. Mićić, S.P. Ahrenkiel and A.J. Nozik: Appl. Phys. Lett. Vol. 78 (2001), p.4022.
[19] D.V. Talapin, S.K. Poznyak, N.P. Gaponik, A.L. Rogach and A. Eychmüller: Physica E Vol. 14 (2002), p.237.
[20] H. Yu, J.B. Li, R.A. Loomis, L.W. Wang and W.E. Buhro: Nature Mater. Vol. 2 (2003), p.517.
[21] A.A. Guzelian, U. Banin, A.V. Kadavanich, X. Peng and A.P. Alivisatos: Appl. Phys. Lett. Vol. 69 (1996), p.1432.
[22] M. Bruchez Jr., M. Moronne, P. Gin, S. Weiss and A.P. Alivisatos: Science Vol. 281 (1998), p. (2013).
[23] U. Banin, C.J. Lee, A.A. Guzelian, A.V. Kadavanich, A.P. Alivisatos, W. Jaskolski, G.W. Bryant, A.L. Efros and M. Rosen: J. Chem. Phys. Vol. 109 (1998), p.2306.
DOI: 10.1063/1.476797
[24] U. Banin, Y.W. Cao, D. Katz and O. Millo: Nature Vol. 400 (1999), p.542.
[25] S.H. Kan, T. Mokari, E. Rothenberg and U. Banin: Nature Mater. Vol. 2 (2003), 155.
[26] R. Rossetti, R. Hull, J.M. Gibson and L.E. Brus: J. Chem. Phys. Vol. 82 (1985), p.552.
[27] S. Yanagida, T. Yoshiya, T. Shiragami and C. Pac: J. Phys. Chem. Vol. 94 (1990), p.3104.
[28] H. Inoue, N. Ichiroku, T. Torimoto, T. Sakata, H. Mori and H. Yoneyama: Langmuir Vol. 10 (1994), p.4517.
DOI: 10.1021/la00024a022
[29] Y. Nakaoka and Y. Nosaka: Langmuir Vol. 13 (1997), p.708.
[30] J. Nanda, S. Sapra, D.D. Sarma, N. Chandrasekharan and G. Hodes: Chem. Mater. Vol. 12 (2000), p.1018.
[31] M.A. Hines and P. Guyot-Sionnest: J. Phys. Chem. B Vol. 102 (1998), p.3655.
[32] F.T. Quinlan, J. Kuther, W. Tremel, W. Knoll, S. Risbud and P. Stroeve: Langmuir Vol. 16 (2000), p.4049.
DOI: 10.1021/la9909291
[33] J. Mazher, A.K. Shrivastav, R.V. Nandedkar and R.K. Pandey: Nanotechnology Vol. 15 (2004), p.572.
[34] Y. -W. Jun, C. -S. Choi and J. Cheon: Chem. Commun. Vol. 2001 (2001), p.101.
[35] Y. Wang and N. Herron: Phys. Rev. B Vol. 42 (1990), p.7253.
[36] D. -S. Chuu and C. -M. Dai: Phys. Rev. B Vol. 45 (1992), p.11805.
[37] T. Vossmeyer, L. Katsikas, M. Giersig, I.G. Popovic, K. Diesner, A. Chemseddine, A. Eychmüller and H. Weller: J. Phys. Chem. Vol. 98 (1994), p.7665.
DOI: 10.1021/j100082a044
[38] A. Tomasulo and M.V. Ramakrishna: J. Chem. Phys. Vol. 105 (1996), p.3612 and references therein.
[39] J. Nanda, B.A. Kuruvilla and D.D. Sarma: Phys. Rev. B Vol. 59 (1999), p.7473.
[40] T. Torimoto, H. Kontani, Y. Shibutani, S. Kuwabata, T. Sakata, H. Mori and H. Yoneyama: J. Phys. Chem. B Vol. 105 (2001), p.6838.
DOI: 10.1021/jp0109271
[41] C.N.R. Rao, G.U. Kulkarni, P.J. Thomas and P.P. Edwards: Chem. Eur. J. Vol. 8 (2002), p.29.
[42] C.Q. Sun, S. Li, B.K. Tay and T.P. Chen: Acta Mater. Vol. 50 (2002), p.4687 and references therein.
[43] B.O. Dabbousi, C.B. Murray, M.F. Rubner and M.G. Bawendi: Chem. Mater. Vol. 6 (1994), p.216.
[44] A.L. Rogach, A. Kornowski, M. Gao, A. Eychmüller and H. Weller: J. Phys. Chem. B Vol. 103 (1999), p.3065.
[45] S. Gorer and G. Hodes: J. Phys. Chem. Vol. 98 (1994), p.5338.
[46] L.S. Li, J.T. Hu, W.D. Yang and A.P. Alivisatos: Nano. Lett. Vol. 1 (2001), p.349.
[47] H. Yu, J.B. Li, R.A. Loomis, P.C. Gibbons, L.W. Wang and W.E. Buhro: J. Am. Chem. Soc. Vol. 125 (2003), p.16168.
[48] Y. Mastai and G. Hodes: J. Phys. Chem. B Vol. 101 (1997), p.2685.
[49] Y. Masumoto and K. Sonobe: Phys. Rev. B Vol. 56 (1997), p.9734.
[50] L.A. Swafford, L.A. Weigand, M.J. Bowers II, J.R. McBride, J.L. Rapaport, T.L. Watt, S.K. Dixit, L.C. Feldman and S.J. Rosenthal: J. Am. Chem. Soc. Vol. 128 (2006), p.12299.
DOI: 10.1021/ja063939e
[51] S.C. Ray, M.K. Karanjai and D. DasGupta: Thin Solid Films Vol. 322 (1998), p.117.
[52] A.H. Ammar: Vacuum Vol. 60 (2001), p.355.
[53] X.H. Zhong, Y.Y. Feng, W. Knoll and M.Y. Han: J. Am. Chem. Soc. Vol. 125 (2003), p.13559.
[54] J.R. Müllhäuser, B. Jenichen, M. Wassermeier, O. Brandt and K.H. Ploog: Appl. Phys. Lett. Vol. 71 (1997), p.909.
DOI: 10.1063/1.119685
[55] R. Goldhahn, J. Scheiner, S. Shokhovets, T. Frey, U. Köhler, D.J. As and K. Lischka: Appl. Phys. Lett. Vol. 76 (2000), p.291.
DOI: 10.1063/1.125725
[56] X.L. Sun, Y.T. Wang, H. Yang, L.X. Zheng, D.P. Xu, J.B. Li and Z.G. Wang: J. Appl. Phys. Vol. 87 (2000), p.3711.
[57] Y.S. Park, B.R. Hwang, J.C. Lee, H. Im, H.Y. Cho, T.W. Kang, J.H. Na and C.M. Park: Nanotechnology Vol. 17, (2006), p.4640.
[58] J. Kamimura, T. Kouno, S. Ishizawa, A. Kikuchi and K. Kishino: J. Cryst. Growth Vol. 300, (2007), p.160.
[59] D. Barreca, A. Gasparotto, C. Maragno, E. Tondello and C. Sada: Chem. Vap. Deposition Vol. 10 (2004), p.229.
[60] X.H. Zhong, M.Y. Han, Z.L. Dong, T.J. White and W. Knoll: J. Am. Chem. Soc. Vol. 125 (2003), p.8589.
[61] J. P. Ge, S. Xu, J. Zhuang, X. Wang, Q. Peng and Y. D. Li: Inorg. Chem. Vol. 45 (2006), p.4922.
[62] Al.L. Efros and A.L. Efros: Sov. Phys. Semicond. Vol. 16 (1982), p.772.
[63] J.E. Brus: J. Lumin. Vol. 31 (1984), p.381.
[64] Y. Kayanuma: Phys. Rev. B Vol. 38 (1988), p.9797.
[65] Y.D. Glinka, S.H. Lin, L.P. Hwang, Y.T. Chen and N.H. Tolk: Phys. Rev. B Vol. 64 (2001), p.085421.
[66] G.G. Qin, H.Z. Song, B.R. Zhang, J. Lin, J.Q. Duan and G.Q. Yao: Phys. Rev. B Vol. 54 (1996), p.2548.
[67] X. Wang, L. Qu, J. Zhang, X. Peng and M. Xiao: Nano Lett. Vol. 3 (2003), p.1103.
[68] F. Koch, V. Petrova-Koch, T. Muschik, A. Nikolov, V. Gavrilenko: Microcrystalline Semiconductors: Materials Science and Devices (Vol. 283, Pittsburgh, PA: Materials Research Society 1993, p.197).
[69] T.S. Iwayama, D.E. Hole and I.W. Boyd: J. Phys.: Condens. Matter Vol. 11 (1999), p.6595.
[70] N.P. Gurusinghe, N.N. Hewa-Kasakarage and M. Zamkov: J. Phys. Chem. C Vol. 112 (2008), p.12795.
[71] Z. Deng, F.L. Lie, S. Shen, I. Ghosh, M. Mansuripur and A.J. Muscat: Langmuir Vol. 25 (2009), p.434.
[72] Y.F. Zhu, X.Y. Lang and Q. Jiang: Adv. Funct. Mater. Vol. 18 (2008), p.1422.
[73] Y. Wang, G. Ouyang, L.L. Wang, L.M. Tang, D.S. Tang and C.Q. Sun: Chem. Phys. Lett. Vol. 463 (2008), p.383.
[74] G. Guisbiers, G. Abudukelimu, M. Wautelet and L. Buchaillot: J. Phys. Chem. C Vol. 112 (2008), p.17889.
DOI: 10.1021/jp805760h
[75] C.C. Yang and S. Li: J. Phys. Chem. B Vol. 112 (2008), p.14193.
[76] P.M. Fauchet and I.H. Campbell: Crit. Rev. Solid State Mater. Sci. Vol. 14 (1988), p. S79.
[77] W.Z. Wang and L. Ao: Cryst. Growth Des. Vol. 8 (2008), p.358.
[78] Z. Iqbal and S. Vepřek: J. Phys. C: Solid State Phys. Vol. 15 (1982), p.377.
[79] G. -X. Cheng, H. Xia, K. -J. Chen, W. Zhang and X. -K. Zhang: Phys. Status Solidi A Vol. 118 (1990), p. K51.
[80] C. Ossadnik, S. Vepřek and I. Gregora: Thin Solid Films Vol. 337 (1999), p.148.
[81] M. J. Seong, O.I. Mićić, A.J. Nozik, A. Mascarenhas and H.M. Cheong: Appl. Phys. Lett. Vol. 82 (2003), p.185.
[82] A. Tanaka, S. Onari and T. Arai: Phys. Rev. B Vol. 45 (1992), p.6587.
[83] P. Verma, L. Gupta, S.C. Abbi and K.P. Jain: J. Appl. Phys. Vol. 88 (2000), p.4109.
[84] H. -M. Cheng, K. -F. Lin, H. -C. Hsu, C. -J. Lin, L. -J. Lin and W. -F. Hsieh: J. Phys. Chem. B Vol. 109 (2005), p.18385.
[85] J.E. Spanier, R.D. Robinson, F. Zhang, S. -W. Chan and I.P. Herman: Phys. Rev. B Vol. 64 (2001), p.245407.
[86] C.H. Shek, G.M. Lin and J.K.L. Lai: Nanostruct. Mater. Vol. 11 (1999), p.831.
[87] A. Diéguez, A. Romano-Rodríguez, A. Vilà and J.R. Morante: J. Appl. Phys. Vol. 90 (2001), p.1550.
[88] J.K. Jian, X.L. Chen, Q.Y. Tu, Y.P. Xu, L. Dai and M. Zhao: J. Phys. Chem. B Vol. 108 (2004), p.12024.
[89] C.C. Chen, R.S. Chen, T.Y. Tsai, Y.S. Huang, D.S. Tsai and K.K. Tiong: J. Phys.: Condens. Matter Vol. 16 (2004), p.8475.
[90] D.F. Zhang, L.D. Sun and C.H. Yan: Chem. Phys. Lett. Vol. 422 (2006), p.46.
[91] Y.Q. Chen, B. Peng and B. Wang: J. Phys. Chem. C Vol. 111 (2007), p.5855.
[92] D. Wang, J. Zhao, B. Chen and C. Zhu: J. Phys.: Condens. Matter Vol. 20 (2008), p.085212.
[93] A.K. Sood, K. Jayaram and D.V.S. Muthu: J. Appl. Phys. Vol. 72 (1992), p.4963.
[94] J. Zi, H. Büscher, C. Falter, W. Ludwig, K.M. Zhang and X.D. Xie: Appl. Phys. Lett. Vol. 69 (1996), p.200.
DOI: 10.1063/1.117371
[95] G. Viera, S. Huet and L. Boufendi: J. Appl. Phys. Vol. 90 (2001), p.4175.
[96] W. Cheng and S. -F. Ren: Phys. Rev. B Vol. 65 (2002), p.205305.
[97] H. Richter, Z.P. Wang and L. Ley: Solid State Commun. Vol. 39 (1981), p.625.
[98] I.H. Campbell and P.M. Fauchet: Solid State Commun. Vol. 58 (1986), p.739.
[99] E. Anastassakis and E. Liarokapis: J. Appl. Phys. Vol. 62 (1987), p.3346.
[100] C.C. Yang and S. Li: Phys. Rev. B Vol. 75 (2007), p.165413.
[101] F.G. Shi: J. Mater. Res. Vol. 9 (1994), p.1307.
[102] Q. Jiang, H.X. Shi and M. Zhao: J. Chem. Phys. Vol. 111 (1999), p.2176.
[103] F.A. Lindemann: Z. Phys. Vol. 11 (1910), p.609.
[104] C.C. Yang and S. Li: J. Phys. Chem. C Vol. 112 (2008), p.1423.
[105] N.F. Mott: Proc. R. Soc. A Vol. 146 (1934), p.465.
[106] A.R. Regel' and V.M. Glazov: Semiconductors Vol. 29 (1995), p.405.
[107] C.C. Yang and S. Li: J. Phys. Chem. C Vol. 113 (2009), p.14207.
[108] C.C. Yang and S. Li: J. Phys. Chem. B Vol. 112 (2008), p.1482.
[109] C.C. Yang and Q. Jiang: Mater. Sci. Eng. B Vol. 131 (2006), p.191.
[110] T.G. Fox: Bull. Am. Phys. Soc. Vol. 1 (1956), p.123.
[111] D.J. Gillespie: Phys. Rev. B Vol. 14 (1976), p.4021.
[112] B.L. Wang, S.Y. Yin, G.H. Wang, A. Buldum and J.J. Zhao: Phys. Rev. Lett. Vol. 86 (2001), p. (2046).
[113] J.X. Fang, H.J. You, P. Kong, B.J. Ding and X.P. Song: Appl. Phys. Lett. Vol. 92 (2008), p.143111.
[114] Information on http: /www. webelements. com/ Web Elements Periodic Table.
[115] R.C. Weast: CRC Handbook of Chemistry and Physics (69th ed., CRC Press: Boca Raton, FL, 1988-1989, pp. B188 and E112).
[116] S. Sapra and D.D. Sarma: Phys. Rev. B Vol. 69 (2004), p.125304.
[117] Information on http: /www. semiconductors. co. uk/ The Semiconductors Information Website.
[118] I. Vurgaftman, J.R. Meyer and L.R. Ram-Mohan: J. Appl. Phys. Vol. 89 (2001), p.5815.
[119] Information on http: /www. ioffe. ru/SVA/NSM/Semicond/ Semiconductors on NSM.
[120] C.C. Yang, S. Li and J. Armellin: J. Phys. Chem. C Vol. 111 (2007), p.17512.
[121] R. Venugopal, P. Lin and Y. -T. Chen: J. Phys. Chem. B Vol. 110 (2006), p.11691.
[122] R. Hill and D. Richardson: J. Phys. C: Solid State Phys. Vol. 6 (1973), p. L115.
[123] J. Haines and J.M. Léger, Phys. Rev. B Vol. 55 (1997), p.11144.
[124] D.R. Lide: CRC Handbook of Chemistry and Physics (88th ed., CRC Press/Taylor and Francis, Boca Raton, FL, Internet Version 2008, pp.6-115, 6-111, 6-114, 4-158 and 4-162).
DOI: 10.1021/ja077011d
[125] O. Gülseren, F. Ercolessi and E. Tosatti: Phys. Rev. Lett. Vol. 80 (1998), p.3775.
[126] S. Iijima: Nature Vol. 354 (1991), p.56.
[127] Y. Kondo and K. Takayanagi: Science Vol. 289 (2000), p.606.
[128] K. -M. Ho, A.A. Shvartsburg, B. Pan, Z. -Y. Lu, C. -Z. Wang, J. G. Wacker, J.L. Fye and M.F. Jarrold: Nature Vol. 392 (1998), p.582.
DOI: 10.1038/33369
[129] G. Seifert: Nature Mater. Vol. 3 (2004), p.77.
[130] A. Kasuya, R. Sivamohan, Y.A. Barnakov, I.M. Dmitruk, T. Nirasawa, V.R. Romanyuk, V. Kumar, S.V. Mamykin, K. Tohji, B. Jeyadevan, K. Shinoda, T. Kudo, O. Terasaki, Z. Liu, R.V. Belosludov, V. Sundararajan and Y. Kawazoe: Nature Mater. Vol. 3 (2004).
DOI: 10.1038/nmat1056
[131] S. Yoo, J. Zhao, J. Wang and X.C. Zeng: J. Am. Chem. Soc. Vol. 126 (2004), p.13845.
[132] P. Gruene, D.M. Rayner, B. Redlich, A.F.G. van der Meer, J.T. Lyon, G. Meijer and A. Fielicke: Science Vol. 321 (2008), 674.
[133] S.A. Claridge, A.W. Castleman Jr., S.N. Khanna, C.B. Murray, A. Sen and P.S. Weiss: ACS Nano Vol. 3 (2009), p.244.