Calculation of thermodynamic and mechanical properties of silicon nanostructures using the local phonon density of states

Abstract

We investigate thermodynamic and mechanical properties of silicon nanostructures at finite temperature. Thermodynamic properties for finite-temperature solid systems under isothermal conditions are characterized by the Helmholtz free energy density. The static part of the Helmholtz free energy is obtained directly from the interatomic potential, while the vibrational part is calculated by using the theory of local phonon density of states (LPDOS). The LPDOS is calculated efficiently from the on-site phonon Green's function by using a recursion technique based on a continued fraction representation. The Cauchy-Born hypothesis is employed to compute the mechanical properties. By considering ideal Si{001}, $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstructed Si{001}, and monolayer-hydrogen-passivated $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstructed Si{001} surfaces of a silicon nanowire, we calculate the local phonon structure and local thermodynamic and mechanical properties at finite temperature and observe that the surface effects on the local thermal and mechanical properties are localized to within one or two atomic layers of the silicon nanowire.