Limits of size confinement in silicon thin films and wires - Pascual-Gutiérrez, José A.; Murthy, Jayathi Y.; Viskanta, Raymond (Journal of applied physics, 2007)
Physically confined structures such as thin films and nanowires are becoming increasingly important in nanoscale energy conversion and nanoelectronics. The main focus of this work is to determine the size threshold below which the volumetric specific heat and group velocity of one- and two-dimensionally confined silicon nanostructures begin to differ significantly with respect to bulk silicon and to quantify these changes. The dynamical matrix approach subject to free-standing boundary conditions is employed to determine the phonon normal modes of vibration of the structures. The environment-dependent interatomic potential under the harmonic approximation is used to model interatomic forces. We find that above 10 nm thickness, silicon [111]-films yield specific heats and group velocities which exhibit size-invariant behavior; for [111]-silicon nanowires, the limit is approximately 5 nm . Moreover, we show that computed phonon group velocities using the dynamical matrix approach are affected by geometry-specific modes beyond confinement, and that size effects are mainly manifested through the volumetric specific heat at low temperatures. Furthermore, we conclude that confinement effects, when present, are only relevant at low temperatures, below 100 K , when the predominant phonon wavelength becomes larger than the confined dimension.