Heat transport across a SiGe nanowire axial junction: Interface thermal resistance and thermal rectification

We study thermal transport in SiGe nanowires by means of nonequilibrium molecular dynamics simulations. We calculate the axial interface thermal resistance (ITR) of realistic models of SiGe nanowires that are obtained in different experimental conditions. We study thermal rectification, finding that heat transport from Si to Ge is favored, particularly in sharp junctions, and that this behavior can be explained in terms of the different temperature dependence of the thermal conductivity of the pristine nanowires.

Figure 1

SiGe axial heterojunctions studied in this work. (a) Atomically sharp, flat interface; (b),(c) diffuse interface where the chemical composition switches from Si to Ge within a region of 5 and 15 nm; (d) curved interface. Light yellow spheres and dark blue spheres represent Si and Ge atoms, respectively. A ball-stick model is used for Ge in panel (d) to show the hemispherical shape of the interface.

Figure 2

Time evolution of the temperature along a 40 nm NW with an abrupt interface. The regions whose temperature is plotted in the main graph are illustrated in the sketch on the right hand side of the graph. The red and blue lines indicate the temperature of the hot and cold thermostatted regions. Notice that, because of its larger thermal conductivity, the temperature drop in the Si region of the NW is lower than in the Ge, resulting in more closely spaced lines.

Figure 3

Inverse of $\kappa$ as a function of the inverse of the length of the nanowire $L_z$. Linear interpolation for $1/L_z\to 0$ gives the thermal conductivity $\kappa$ of very long wires $\left(L_z\to \infty \right)$. Lengths refer to the nonthermostatted region of the NW. Notice that a quantitative estimate of the thermal conductivity would require including longer lengths (Refs. [21, 22, 23]), as indicated by nonperfectly linear dependence of $1/\kappa$ vs $1/L_z$.

Figure 4

(a) Steady state temperature along a 80 nm NW with an abrupt interface. The temperature profile discontinuity $\Delta T_{\mathrm{int}}$ at the interface is estimated by linear fits of $T=T\left(z\right)$ nearby the two sides of the interface, so as to avoid artifacts due to the hot and cold thermostats. The ITR can be estimated as $\Delta T_{\mathrm{int}}/J_z$, where $J_z$ is the heat flux. (b) ITR calculated through Eq. (1) for the interfaces of Figs. 1–1(c). The value corresponding to the abrupt junction in a 80 nm NW is in excellent agreement with the estimate made in panel (a). The case $L_z=20$ nm for the $\Delta l=15$ nm was not considered because the nonthermostatted region of the NW was shorter than the nominal length of the junction. Lengths refer to the nonthermostatted region of the NW.

Figure 5

Heat rectification $r$ as a function of $\left|\Delta T\right|$ in a 20 nm SiGe NW with an abrupt (empty black circles) and a diffuse interface, $\Delta l=5$ nm (empty red diamonds) and in a 40 nm SiGe NW with an abrupt interface (filled black circles). Notice that in the case of diffuse junctions, due to random nature of the alloy region, one should in principle average the results over several different configurations.

Figure 6

Thermal rectification of the curved, abrupt interfaces in a 40 nm-long SiGe NW. The flat interface is also included for comparison. The curved interface observed experimentally is the one where Si protrudes into the Ge segment (blue circles).