Phonon dispersion in silicon nanocrystals

Due to their compatibility with CMOS technology, silicon nanocrystals (NC) are a key element of integrated nanodevices as single-electron transistors. The physical simulation of electron transport in these devices is a challenge and to correctly include the effects of electron-phonon coupling like relaxation into the ground state or collisional broadening of energy levels, the knowledge of phonon modes in silicon NCs is required. With this aim in view, we present a theoretical approach to the determination of phonon dispersion in NCs. It is based on the adiabatic bond charge model. While in small diameter NC the phonon modes are strongly discretized, the density of states becomes quasi continuous and bulk-like for diameter larger than approximately 2.5 nm. A special attention is paid to boundary conditions and two cases are considered: the surface atoms are either free to move or rigidly fixed. In the former case surface modes are formed at low frequency and in the latter case stationary modes appear near 11 THz. By projecting the NC modes on the basis of bulk modes, one can show the increasing correlation between these modes when increasing the dot size.