 
Summary: Calculation of thermodynamic and mechanical properties of silicon nanostructures using the
local phonon density of states
Z. Tang and N. R. Aluru
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at
UrbanaChampaign, Urbana, Illinois 61801, USA
Received 28 August 2006; revised manuscript received 30 October 2006; published 27 December 2006
We investigate thermodynamic and mechanical properties of silicon nanostructures at finite temperature.
Thermodynamic properties for finitetemperature 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 onsite phonon Green's function by using a
recursion technique based on a continued fraction representation. The CauchyBorn hypothesis is employed to
compute the mechanical properties. By considering ideal Si 001 , 2 1 reconstructed Si 001 , and
monolayerhydrogenpassivated 2 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.
DOI: 10.1103/PhysRevB.74.235441 PACS number s : 63.22. m, 68.35.Md, 62.25. g, 02.70. c
I. INTRODUCTION
In recent years, silicon nanostructures have attracted con
