Confinement effect on the low temperature specific heat for ultrathin silicon nanowires: a first principles study

This work studied the phonon confinement effects at the low temperature specific heat of Si nanowires from first principles using density functional perturbation theory. The nanowires were modeled in the [0 0 1] direction for three different diameters, with the largest cross section being approximately 10 Å. The results indicate the specific heat can be described at low temperatures using a third-grade polynomial of the form c _v  =  λT  +  βT ²  +  γT³, where the coefficients of quadratic and cubic terms are almost nonexistent for small diameters. These terms begin to have relevance at larger diameters. Further analysis shows λ  >  β  >  γ, which shows the phonon confinement (λ) and surface atoms (β) become more important than the volumetric contribution (γ) for ultrathin nanowires at low temperatures.