Specific Heat of Individual Silicon Nanowires

The elastic continuum model is resorted to study the lattice specific heat of individual crystalline silicon nanowires with 22 and 37 nm in diameter. Incorporating both longitudinal and transverse modes, a model based on the power-law phonon dispersion is developed to illustrate the characteristics of phonon density of states (DOS) in bulk and low-dimensional systems. The results show that there exist multiple and explicit van Hove singularities for thin wire and step-like enhancement for thin film, attributing to the quantized phonon modes in the particular dimensionality. Furthermore, we examine the phonon dispersion and DOS of silicon nanowires and find infinite phonon branches. A cutoff frequency based on the reduced phonon group velocity is defined to guarantee that the phonon wavelength can not be shorter than the lattice constant. The softening of vibrational modes in low-frequency region and the deficit in high-frequency region occur, resulting in the excess specific heat of silicon nanowire compared with that of bulk silicon. This phenomena becomes more significant at low temperatures. In addition, the dependence of specific heat of nanowires on temperature departs from that of bulk material in view of the quasi one-dimensional feature. Qualitative support is presented to our present work.