Effect of defects on the thermal conductivity in a nanowire

We investigate the effect of defects on the low temperature thermal conductance in nanowire structure by using the scattering-matrix method. It is found the behavior of the thermal conductance versus temperature is qualitatively different for different types of defects. When the defect is void, the universal quantum thermal conductance and the decrease of the thermal conductance at low temperature can be clearly observed. However, when the structural defect consists of clamped material, the quantized thermal conductance cannot be observed, and the thermal conductance increases monotonically with increasing temperature.

Figure 1

Schematic illustration of a nanowire with defect region $C$. The structure is divided into three regions I, II, and III. Regions I and III are semi-infinite incident and outgoing leads, respectively. Region II consists of three parts $A$, $B$, and $C$. Parts $A$ and $B$ are tunnel regions with widths $w_A$ and $w_B$, respectively; while part C is a structural defect with the width $t$. The length of parts $A$, $B$, and $C$ is $d$. Here, we consider two typical defects: void and clamped material. The rest part of the whole structure consists of GaAs material.

Figure 2

The thermal conductance divided by temperature $K∕T$, which is reduced by the zero-temperature universal value ${\pi }^2{k}_B^2∕3h$, as a function of the reduced temperature $k_{B}T∕\hslash \Delta$ for different width $t$, where $\Delta ={\omega }_{n+1}-{\omega }_n=\pi v∕w_I$ ($v$ is the acoustic wave velocity in region I). Here, the defect $C$ is void. (a)–(c) correspond to $K∕T$ of modes 0, 1, and 2, respectively, and (d) corresponds to the total $K∕T$. Note that the total $K∕T$ should include the contributions of all the propagation modes. By our calculations, however, only the first six modes can make their contributions to the total thermal conductance for the explored temperature scope. The dotted, dashed, and solid curves correspond to $t=30$, 50, and 70 nm. Here, we take $w_a=w_b$, $t+w_a+w_b=100\mathrm{nm}$, and $d=50\mathrm{nm}$.

Figure 3

The thermal conductance divided by temperature $K∕T$, which is reduced by the zero-temperature universal value ${\pi }^2{k}_B^2∕3h$, as a function of the reduced temperature $k_{B}T∕\hslash \Delta$ for different width $t$. Here, the defect $C$ is clamped material. The structural parameters and explanations for curves are the same as for Fig. 2.