Change in low-temperature thermodynamic functions of a semiconductor due to a quantum dot

A phonon Green’s function method is developed for modeling the phonon modes of a semiconductor perturbed by a quantum dot. Simple expressions are derived for the frequency spectrum of perturbed low-frequency phonon modes and changes in the Helmholtz-free energy and the constant-volume specific heat at low temperatures using the Debye model. The changes are found to be significant and can be used to characterize the material properties of the quantum dot. The theory is also applicable to nanocrystals and other nanoinclusions in solids.