Thermal conductivity reduction in core-shell nanowires

Nanostructuring of thermoelectric materials bears promise for manipulating physical parameters to improve the energy conversion efficiency of thermoelectrics. Using nonequilibrium molecular dynamics, we investigate how the thermal conductivity can be altered in core-shell nanocomposites of Si and Ge. By calculating the phonon vibrational density of states and performing normal mode analysis, we show that the thermal conductivity decreases when phonon-transport becomes diffusion-dominated and unveil a competition between modes from the various regions of the nanocomposite (core, interface, and shell). The effects of nanowire length, cross section, and temperature on thermal conductivity are explicitly considered. Surprisingly, the thermal conductivity variation with nanowire length is much weaker than in pure nanowires. Also, the thermal conductivity is almost independent of temperature in the wide region between 50 and 600 K, a direct result of confinement of the core by the shell. These results suggest that core-shell nanowires are promising structures for thermoelectrics.

Figure 1

(a) Calculated thermal conductivity for a Si-core/Ge-shell structure vs nanowire length at 300 K with comparison to that of a pure Si nanowire. (b) Relationship between the reciprocal of thermal conductivity and the reciprocal of length. The dotted line represents a fitting to the MD results, while the black dashed line in panel (a) denotes the upper limit of the thermal conductivity of an infinitely long NW with the same cross section. The green dashed lines mark the suggested ballistic and diffusive regimes. The right axis in panel (a) shows the percent reduction in thermal conductivity of the Si core relative to that of a pure Si nanowire.

Figure 2

Comparison of vibrational density of states of Si atoms located on the nanowire surface in the absence and presence of a Ge shell of 2-unit-cell thickness. The core Si is a matrix of (a) 9 × 9 × 52 u.c.; (b) 9 × 9 × 502 u.c.; (c) 9 × 9 × 2002 u.c.

Figure 3

Thermal conductivity of 9 × 9 × 302 u.c. (164 nm long) nanowire as a function of temperature. The Ge layer on the core-shell structure is 2 unit cells thick.

Figure 4

Calculated thermal conductivity of a square cross section Si/Ge core-shell nanowire as a function of thickness at 300 K. Results are also shown for a pure Si nanowire. All nanowires are 164 nm long and the Ge layer is 2 unit cells thick. The dashed lines are linear fits to the log κ ∼ β log $D$ relationship with exponent β indicated.

Figure 5

Participation ratio of each vibrational eigenmode for Si/Ge core-shell nanowires with different core thickness. Red: $D$ $=$ 0.77 nm; green: 1.54 nm; blue: 2.31 nm; and black: 3.46 nm. In all cases, the Ge layer is 2 unit cells thick.

Figure 6

Fraction of each mode contained in Si core (blue dots), Si-Ge interface (black dots), and Ge shell (red dots) for different Si core thickness, (a) 0.77 nm, (b) 1.54 nm, (c) 2.31 nm, and (d) 3.46 nm. In all cases the Ge layer is 2 unit cells thick.

Figure 7

Thermal conductivity of 9 × 9 × 302 u.c. (165 nm long) Si-core/Ge-shell NW as a function of the normalized interfacial strength. The right axis indicates the percent reduction in thermal conductivity of the Si core relative to that of a pure Si NW. The Ge layer is 2 unit cells thick.

Figure 8

Calculated thermal conductivity for a Ge-core/Si-shell structure vs nanowire length at 300 K with comparison to that of a pure Ge nanowire. The dotted line is fitting to the MD results, and the dashed line denotes the upper limit of the thermal conductivity of an infinitely long pure Ge NW with same cross section size. The right axis shows the percent reduction in thermal conductivity of the Ge core relative to that of pure Ge NW.

Figure 9

Thermal conductivity of 9 × 9 × 292 u.c. (165 nm long) Ge-core/Si-shell NW as a function of temperature. For all the NWs, the Si layer is 2 unit cells thick.