Size-dependent Einstein temperature and linear thermal expansion coefficient of embedded Ge quantum dots

Based on the consideration for the vibrational characteristics of interface atoms, the size-dependent thermal properties of Ge quantum dots embedded in silica (a-SiO2) matrix is modeled. According to the established model without any adjustable parameters, it is found that the matrix can well stabilize the interface atoms of Ge quantum dots due to the coherent or semi-coherent interface effect, which thus results in the increase of Einstein temperature and the decrease of the linear thermal expansion coefficient as D is reduced (D shows the diameter of Ge quantum dots). These conclusions are in good agreement with corresponding experimental results.