We can see that the transmission coefficient SB-715992 concentration decreases much more for the SiNW with a center defect than that with a surface defect at several specific energies. This result is related to the details of phonon modes with specific energies. In those modes, the center atom SAR302503 price has an important role in the vibration modes while the corresponding edge atom is not so important. This effect on the phonon mode causes different behaviors of thermal conductance between a center defect and a surface defect for thin SiNWs. Conclusions To conclude, we have applied the NEGF technique with the interatomic Tersoff-Brenner potential for the phonon thermal transport of SiNWs with and without a vacancy defect and

DNWs with no defects. We found that crossover from the quantized thermal conductance to the usual thermal conductance appears with increasing temperature from 5 K up to 300 K for both SiNW and DNW. We also found that thermal conductances Natural Product Library order of SiNW and DNW with no defects were in proportion to their cross-sectional area for 100 and 300 K. This reflects the columnar shape of SiNW and DNW. Compared with the recent experiments, understanding of the effects

of defects is essential for thermal conductance of SiNWs. We found that a center defect reduces the thermal conductance much more than a surface defect. This is due to the effects on the specific phonon modes where a center atom has various covalent bonds with neighbor atoms while an edge atom does not have. This concludes that the effects of vacancy defects on the thermal conductance of nanometer-size SiNW are not simply estimated from the density of vacancy defects, but instead we have to take the effects of vacancy defects on the thermal conductance from precise atomistic structures into account. Acknowledgements This work is supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. References 1. Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A: Thermal conductivity of individual silicon nanowires. Appl Phys Lett 2003, 83:2934.CrossRef 2. Chen R, Hochbaum AI, Marphy P, Moore J, Yang P, Majumdar

A: Thermal conductance of thin silicon nanowires. Phys Rev Lett 2008, 101:105501.CrossRef 3. Mingo N, Yaug L, Li D, Majumdar second A: Predicting the thermal conductivity of Si and Ge nanowires. Nano Lett 2003, 3:1713.CrossRef 4. Saito K, Nakamura J, Natori A: Ballistic thermal conductance of a graphene sheet. Phys Rev B 2007, 76:115409.CrossRef 5. Keldysh LV: Diagram technique for nonequilibrium processes. Sov Phys JETP 1965, 20:1018. 6. Caroli C, Combescot R, Nozieres P, Saint-James D: Direct calculation of the tunneling current. J Phys C: Solid St Phys 1971, 4:916.CrossRef 7. Wingreen NS, Meir Y: Landauer formula for the current through an interacting electron region. Phys Rev Lett 1992, 68:2512.CrossRef 8. Ozpineci A, Ciraci S: Quantum effects of thermal conductance through atomic chains. Phys Rev B 2001, 63:125415.CrossRef 9.