In the first part of this thesis, I will present a study of the vibrational modes of acoustic
phonons and their corresponding eigenfrequencies in CdS/CdSe/CdS quantum-dot
quantum wells (QDQWs) obtained on the continuum model. The energy spectra of
the phonons in nanocrystals from the analytic solutions are checked by the Finite-
Element Method (FEM). Based on the spectrum of acoustic phonons and the Debye
model, the temperature dependences of the specific heat contributed from lattice
phonons are calculated to investigate their size-dependent effects. Lattice softening
is also demonstrated and the results qualitatively agree with the experimental observations
for fine particles and quantum dots. We found that the phonon density of
states of a QDQW is important for calculating specific heat, and, perhaps, also for
modifying the effective sound velocity in the nanocrystal.
In the second part of the thesis, I will describe an investigation of the Raman
light-to-vibration coupling coefficients Cαβ of the l=0 and the l=2 spheroidal phonon
modes of quasi-free spherical CdSe/CdS core/shell nanoparticles calculated. Based on
the Lamb model, the displacement vectors of acoustic phonon modes are obtained and
the Cαβ is also derived. The Raman scattering from quasi-free CdSe/CdS nanoparticles
with various inner radii is investigated. For the l=0 acoustic modes, the bond
polarizability model is adopted to calculate Cαβ, whose peak positions shift toward
lower frequencies with the increase of the inner radius. This could be accounted for
by the decrease of the averaged longitudinal and transverse sound velocities. Moreover,
the ratio of the coefficients Aαβγδ [Montagna and Dusi, Phys. Rev. B 52, 10080
(1995)] between layers characterizes behaviors of peak heights of Cαβ. For the l=2
modes based on the dipole-induced-dipole model, the behaviors of peak positions are
obtained by varying the values of vL and vT of materials in both layers. Because we
treat the core/shell nanoparticle as a whole, the behavior of Cαβ peak positions on a
CdSe/CdS core/shell nanoparticle is consistent with its dependence on the averaged
sound velocities of the whole nanoparticle. At the same time, it also agrees with the
calculated results for a CdSxSe1¡x nanoparticle [Risti´c et al., J. Appl. Phys. 104,
073519 (2008)]. However, we observed that some peaks reach dramatically high values
for given inner radii of the CdSe/CdS nanoparticles, which occur only in spherical
core/shell nanoparticles.

Table of Contents iv
List of Tables vi
List of Figures vii
Acknowledgements x
Abstract xi
1 Introduction 1
2 Theoretical Backgrounds: Elasticity Theory, Raman Spectrum 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Elasticity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 The Generalized Hook’s Law . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 The Autocorrelation Functions of Statistical Mechanics . . . . . . . . 29
2.5 Raman Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Specific heat of CdS/CdSe/CdS quantum-dot quantum wells 44
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Spectrums of vibrational modes . . . . . . . . . . . . . . . . . . . . . 47
3.3 Lattice specific heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Low-frequency Raman scattering from acoustic vibrations of spherical
CdSe/CdS nanoparticles 64
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 The Vibrational Modes of a spherical core/shell nanoparticle . . . . . 67
4.3 The Light to Vibration Coupling Coefficient for CdSe/CdS nanoparticles 71
4.3.1 Bond polarizability model for l=0 vibrational modes . . . . . 72
4.3.2 Dipole-induced-dipole model for the l=2 vibrational modes . . 78
4.3.3 The difference in light to vibration coupling coefficients between
CdSe/CdS and CdSxSe1¡x nanoparticles . . . . . . . . . . . . 82
4.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Conclusion 87
Appendix 90
A Elements of the secular equations for a QDQW 90
A.1 Elements of the 5£5 secular equation for the torsional mode in a QDQW 91
A.2 Elements of the 5 £ 5 secular equation for the spheroidal mode and
L = 0 in a QDQW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A.3 Elements of the 10 £ 10 secular equation for the spheroidal mode and
L 6= 0 in a QDQW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
B The functions in the linear equations 97
Bibliography 99

[1] T. M. Atanackovic and A. Guran, Theory of Elasticity for Scientists and Engineers
(Birkh¨auser, Boston, 2000).
[2] L. D. Landau, and E. M. Lifshitz, Institute of Physical Problems, U.S.S.R.
Academy of Sciences, Theory of Elasticity, Volume 7 of Course of Theoretical
Physics.
[3] J. B. Marion and S. T. Thornton, Classical dynamics of particles and system,
4th Ed.
[4] D. Risti´c, M. Ivanda, K. Furi´c, U. V. Desnica, M.Buljan, M. Montagna,
M.Ferrari, A. Chiasera, and Y.Jestin, JAP. 104, 073519 (2008)
[5] B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
[6] M. Montagna and R. Dusi, Phys. Rev. B 52, 1008 (1995).
[7] M. Mattarelli, M. Montagna, F. Rossi, A. Chiasera, and M.Ferrari, Phys. Rev.
B 74, 153412 (2006).
[8] M. Montagna, Phys. Rev. B 77, 045418 (2008).
[9] H. Lamb, Proc. London Math. Soc. 13, 187 (1882).
[10] M. A. Stroscio and M.Dutta, Phonons in Nanostructures (Cambridge University
Press, Cambridge, UK, 2001).
[11] R. Shuker and R. W. Gammon, Phys. Rev. Lett. 25, 222 (1970).
[12] X. Peng, M. Schlamp, A. Kadavanish, and A. Alivisatos, J. Am. Chem. Soc.
119, 7019 (1997).
[13] D. Talapin, R. Koeppe, S. Gotzinger, A. Kornowski, J. Lupton, A. Rogach, O.
Benson, J. Feldmann, and H. Weller, Nano Lett. 3, 1677 (2003).
[14] J. Li and L.-W. Wang, Appl. Phys. Lett. 84, 3648 (2004).
[15] M. Hines and P. Guyot-Sionnest, J. Phys. Chem. 100, 468 (1996).
[16] D. Battaglia, B. Blackman, and X. Peng, J. Am. Chem. Soc. 127, (2005).
[17] D. Battaglia, J. J. Li, Y. Wang, and X. Peng, Angew. Chem. Int. Ed. 42, 5035
(2003).
[18] R. B. Little, M. A. El-Sayed, G. W. Bryant, and S. Burke, J. Chem. Phys. 114,
1813 (2001).
[19] L. Cao, S. Huang, and J. Lin, J. Colloid Interface Sci. 284, 516 (2005).
[20] D. Schooss, A. Mews, A. Eychm¨uller, and H. Weller, Phys. Rev. B 49, 17072
(1994).
[21] S. Neeleshwar, C. L. Chen, C. B. Tsai, Y. Y. Chen, S. G. Shyu, and M. S. Seehra,
Phys. Rev. B 71, 201307 (2005).
[22] V. Mazzacurati and G. Ruocco, Mol. Phys. 61, 1391 (1987).
[23] H. P. Baltes and E. R. Hilf, Solid State Commun. 12, 369 (1973).
[24] W. P. Halperin, Rev. Mod. Phys. 58, 533 (1986).
[25] N. Nishiguchi and T. Sakuma, Solid State Commun.58, 533 (1986).
[26] A. Tamura, K. Higeta, and T. Ichinokawa, J. Phys. C: Solid State Phys. 15, 4975
(1982).
[27] P. Swaminathan, V. N. Antonov, J. A. N. Soares, J.S. Palmer, and H. H. Weaver,
Phys. Rev. B 73, 125430 (2006).
[28] J. Schrier and L.-W. Wang, Phys. Rev. B 73, 245332 (2006).
[29] J. Xu, M. Xiao, D. Battaglia, and X. Peng, Appl. Phys. Lett 87, 043107 (2005).
[30] J. Berezovsky, M. Ouyang, F. Meier, D. D. Awschalom, D. Battaglia, and X.
Peng, 71, 081309 (2005).
[31] F. Meier and D. D. Awschalom, Phys. Rev. B 71, 205315 (2005).
[32] J. Xu and M. Xiao, Appl. Phys. Lett 87, 173117 (2005).
[33] J. P. Hirth and J. Lothe, Theory of Dislocations, 2nd Ed. (John Wiley and Sons,
New York, 1982).
[34] N. W. Ashcroft and N. D. Mermin, Solid State Physics. (Saunders College, 1976).
[35] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity. (Dover, New
York, 1944).
[36] S. Adachi, Optical Properties of Crystalline Amorphous Semiconductors, (Kluwer
Academic, Massachusetts, 1999).
[37] O. Madelung, Semiconductors: Data Handbook, 3rd Ed. (Springer, Berlin Heidelberg,
2004).
[38] M. Schultz, Semiconductors, Landolt-B¨ornstein, New Series, Group III, Vol. 4,
(Springer, New York, 1998).
[39] T. Takagahara, J. Lumin. 70, 129 (1996).
[40] Y. Masumoto, ed., Semiconductor Quantum Dots. (Springer, Berlin Heidelberg,
2002).
[41] C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in
Solids. (Oxford University Press, London 1972).
[42] J. R. Childress, C. L. Chien, M. Y. Zhou, and P. Sheng, Phys. Rev. B. textbf44,
11689 (1991).
[43] A. P. Alivisatos, T. D. Harris, P. J. Carroll, M. L. Steigerwald, and L. E. Brus,
J. Chem. Phy. 90, 3463 (1989).
[44] M. C. Klein, F. Hache, D. Ricard, and C. Flytzanis, Phy. Rev. B 42, 11123
(1990).
[45] A. Tanaka, S. Onari, and T. Arai, Phys. Rev. B 45, 6587 (1992).
[46] A. Tanaka, S. Onari, and T. Arai, Phys. Rev. B 47, 1237 (1993).
[47] M. Rajalakshmi, T. Sakuntala, and A. K. Arora, J. Phys.: Condensed Matter 9,
9745 (1997).
[48] T. R. Ravindran, A. K. Arora, B. Balamurugan, and B. R. Mehta, Nanostruct.
Mater. 11, 603 (1999).
[49] I. H. Campbell and P. M. Fauchet, Solid State Commun. 58, 739 (1986).
[50] R. J. Nemanich and S. A. Solin, Phys. Rev. B 20, 392 (1979).
[51] E. Duval, A. Boukenter, and B. Champagnon, Phys. Rev. Lett. 56, 2052 (1986).
[52] G. Mariotto, M. Montagna, G. Viliani, E. Duval, S. Lefrant, E. Rzepka, and C.
Mai, Europhys. Lett. 6, 239 (1988).
[53] M. Fujii, T. Nagareda, S. Hayashi, and K. Yamamoto, Phys. Rev. B 44, 6243
(1991).
[54] R. Ceccato, R. D. Maschio, S. Gialanella, G. Maritto, M. Montagna, F. Rossi,
M. Ferrari, K. E. Lipinska-Kalita, and Y. Ohki, J. Appl. Phys. 90, 2522 (2001).
[55] Y. Jestin, N. Afify, C. Armellini, S. Berneschi, S. N. B. Bhaktha, B. Boulard,
A. Chiappini, A. Chiasera, G. Dalba, C. Duverger, et al., Proc. SPIE 6183, 438
(2006).
[56] V. K. Tikhomirov, D. Furniss, A. B. Seddon, M. Ferrari, and R. Rolli, Appl.
Phys. Lett. 81, 1937 (2002).
[57] M. Montagna, E. Moser, F. Visintainer, L. Zampedri, M. Ferrari, A. Martucci,
M. Guglielmi, and M. Ivanda, J. Sol-Gel Sci. Technol. 26, 241 (2003).
[58] M. Ivanda, A. Hohl, M. Montagna, G. Mariotto, M. Ferrari, Z. C. Orel, A.
Turkovic, and K. Furic, J. Raman Spectrosc. 37, 161 (2006).
[59] M. Ivanda, K. Babosci, C. Dem, M. Schmitt, M. Montagna, and W. Kiefer, Phys.
Rev. B 67, 235329 (2003).
[60] M. Ivanda, K. Furi´c, S. Musi´c, M. Risti´c, M. Goti´c, D. Risti´c, A. M. Tonejc, I.
Djerdj, and M. Montagna, J. Raman Spectrosc. 38, 161647 (2007).
[61] S. Adichtchev, S. Sirotkin, G. Bachelier, L. Saviot, S. Etienne, B. Stephanidis,
E. Duval, and A. Mermet, Phys. Rev. B 79, 201402 (2009).
[62] A. L. Efros and A. L. Efros, Sov. Phys.-Semicomd 16, 772 (1982).
[63] A. I. Ekimov and A. A. Onushchenko, JETP Lett. 40, 1136 (1984).
[64] A. I. Ekimov, F. Hache, M. C. Schanne-Klein, D. Ricard, C. Flyt-zanis, I. A.
Kudryavtsev, T. V. Yazeva, A. V. Rodina, and A. L. Efros, J. Opt, Soc. Am. B
10, 100 (1993).
[65] A. I. Ekimov, J. Lumin. 70, 1 (1996).
[66] M. Rajalakshmi and A. K. Arora, Solid State Commun. 110, 75 (1999).
[67] A. V. Gomonnai, Y. M. Azhniuk, V. V. Lopushansky, I. G. Megela, I. I. Turok,
M. Kranjˇcec, and V. O. Yukhymchuk, Phys. Rev. B 65, 245327 (2002).
[68] S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, Phys. Rev. B 35, 8113
(1987).
[69] J. Schroeder and P. D. Persans, J. Lumin. 70, 69 (1996).
[70] P. D. Persans, L. B. Lurio, J. Pant, H. Y¨ukselici, G. Lian, and T. M. Hayes, J.
Appl. Phys. 87, 3850 (2000).
[71] S. K. Gupta, S. Sahoo, P. K. Jha, A. K. Arora, and Y. M. Azhniuk, J. Appl.
Phys. 106, 024307 (2009).
[72] L. Saviot and D. B. Murray, Phys. Rev. B 72, 205433 (2005).
[73] H. Portal´es, L. Saviot, E. Duval, M. Gaudry, E. Cottancin, M. Pellarin, J.Lerm´e,
and M. Broyer, Phys. Rev. B 65, 165422 (2002).
[74] S. K. Gupta, P. K. Jha, and A. K. Arora, Journal of Applied Physics 103, 124307
(2008).
[75] L. Saviot and D. B. Murray, Phys. Rev. Lett. 93, 055506 (2004).
[76] D. B. Murray and L. Saviot, Phys. Rev. B 69, 094305 (2004).
[77] L. Saviot, D. B. Murray, and M. d. C. M. de Lucas, Phys. Rev. B 69, 113402
(2004).
[78] M. Montagna, Phys. Rev. B 77, 167401 (2008).
[79] M. Kanehisa, Phys. Rev. B 72, 241405 (2005).
[80] M. Kanehisa, Phys. Rev. B 74, 197402 (2006).
[81] S. V. Goupalov, L. Saviot and E. Duval, Phys. Rev. B 74, 197401 (2006).
[82] E. Duval, Phys. Rev. B 46, 5795 (1992).
[83] W. U. Huynh, J. J. Dittmer, and A. P. Alivisatos, Science 295, 2425 (2002).
[84] P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill,
New York, 1953).