Abstract
The vibrational modes of acoustic phonons and their corresponding eigenfrequencies in CdS/CdSe/CdS quantum-dot quantum wells (QDQWs) are obtained by taking on the continuum model. The energy spectra of the phonons in nanocrystals from the analytic solutions are checked by the finite-element method. 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 the size-dependent effects. The 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 plays an important role in the calculation of specific heat, and the modification of the effective sound velocity in the nanocrystal is also suggested.
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