Thus, we present thermal conductance calculations of SiNWs with diameters from 1 to 2 nm with vacancy defects, focusing especially on the difference of the position of the vacancies, where we consider two types of a vacancy: a ‘surface defect’ with an atom at
the surface is missing and a ‘center defect’ with an atom at the center of cross section of wires is missing for an example of a simple defect. We found that thermal conductance reduces much more for a center defect than for a surface defect. Finally, we compare thermal transport properties of SiNWs and DNWs and discuss the effects of differences of atomic types. Methods We split the Tozasertib price total Hamiltonian into four pieces: H=H L+H S+H R+H int, where H L(R) is the Hamiltonian for the left (right) lead, H S is for the scattering region, and H int is for the interaction between the scattering region and the left(right) Milciclib price lead (Figure 1). Figure 1 Schematic view of the atomistic model of SiNW for 〈100〉 direction with a diameter of 2 nm. The system is divided into three parts by black lines: left lead, scattering region, and right lead. Vacancy
defects are introduced in the scattering region, while no defects are present in the left and right leads. Red circles represent the vacancy defects. The thermal current J th from the left lead to the scattering region can be expressed by the following formula with the NEGF technique
 (1) Here the bracket 〈…〉 denotes the non-equilibrium statistical average of the physical observable, n(ω,T L(R)) is the Bose-Einstein distribution AZD1480 cell line function of equilibrium phonons with an energy of in the left (right) lead oxyclozanide at temperature T L(R). ζ(ω) is the transmission coefficient for the phonon transport through the scattering region given by (2) Here, G r/a(ω) is the retarded (advanced) Green’s function for the scattering region and Γ L/R(ω) is the coupling constant. In the limit of small temperature difference between left and right regions, the thermal conductance G is given by (3) For the ideal ballistic limit without any scattering, ζ(ω) is equal to the number of phonon subbands at frequency ω. The retarded (advanced) Green’s function for the scattering region is given by (4) where M is the diagonal matrix whose element is a mass of atom and is the retarded (advanced) self-energy due to the coupling to the left (right) semi-infinite lead with the scattering region, which is obtained independently from the atomistic structure of the lead. We use a quick iterative scheme with the surface Green’s function technique  to calculate the self-energy for complex atomic structures of SiNWs.