We see that the quantized thermal conductance, which does not depend on the wire diameter, appears below 5 K. With increasing temperature, the thermal conductance comes to depend on its diameter. For over 100 K, we see that the thick

SiNW with a large diameter has a larger thermal conductance proportional to the cross-sectional area, which reflects its atomic structure since the SiNW has the columnar shape and the total number of silicon atoms in the SiNW is proportional to its Autophagy Compound Library ic50 cross-sectional area. This indicates that the thermal conductance in the defect-free clean limit is determined by the total number of atoms in the nanowire structures. The right panel of Figure 3 shows the phonon dispersion relation of 〈100〉 SiNW with 1.5 nm in diameter. We see that

the phonon dispersion of SiNW spreads up to 70 meV, which is determined by the interaction between silicon atoms. As the thickness of the wire becomes larger and larger, the number of phonon subbands increases in proportion to the number of silicon atoms. Figure 3 Thermal conductance of SiNW and phonon dispersion relation. Thermal conductance PCI-34051 as a function of the diameter of SiNW without vacancy defects for several temperature. Inset is the exponent n of diameter dependence of thermal conductance for several temperature. (right) Phonon dispersion relation of 〈100〉 SiNW with 1.5 STK38 nm in diameter for the wave vector q. Here a=5.362 Å. Red and purple solid lines show weight functions in thermal conductance for 100 and 5 K. The left panel of Figure 4 shows the thermal conductance of DNWs as a function of the diameter at various temperatures from 5 K up to 300 K, and the inset shows an exponent of the diameter dependence of thermal conductance. Similarly as in Figure 3, we can see the quantized thermal conductance below 5 K and the thermal conductance comes to depend on its diameter with an increase of temperature. We also see that the thick wire with the large diameter has the larger

thermal conductance, which is proportional to the cross-sectional area of the DNW at the temperature over 300 K. Since the DNW also has the columnar shape, the total number of carbon atoms in the DNW is also proportional to its cross-sectional area. Then, we can say that the thermal conductance of DNW in the defect free-clean limit is determined by the total number of atoms in the nanowire structures. The right panel of Figure 4 shows the phonon dispersion relation of 〈100〉 DNW with 1.0 nm in diameter. We see that the phonon dispersion of DNW spreads up to 180 meV, which is determined by the interaction between the carbon atoms. As the thickness of the wire becomes larger and larger, the number of phonon subbands also increases in proportion to the number of carbon atoms.