Role of light and heavy embedded nanoparticles on the thermal conductivity of SiGe alloys

We have used an atomistic ab initio approach with no adjustable parameters to compute the lattice thermal conductivity of Si${}_{0.5}$Ge${}_{0.5}$ with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact Green’s function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in ${\text{Si}}_{0.5}{\text{Ge}}_{0.5}$ provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation, which predicts an equal amount of reduction for the two cases, irrespective of the sign of the mass difference. Despite these differences, we find that the Born approximation still performs remarkably well, and it permits investigation of larger nanoparticle sizes, up to 60 nm in diameter, not feasible with the exact approach.

Figure 1

Comparison of the scattering rates $1/{\tau }_{\lambda }^{\text{np}}$ normalized by nanoparticle volume fraction $f_p$, due to Ge and Si nanoparticles of different sizes, in a Si${}_{0.5}$Ge${}_{0.5}$ matrix. The curves shown correspond to the LA phonon branch along direction (100).

Figure 2

Scattering rate $1/{\tau }_{\lambda }^{\text{np}}$ due to Ge and Si nanoparticles of diameter 3.3 nm, in a Si${}_{0.5}$Ge${}_{0.5}$ matrix, normalized by nanoparticle volume fraction $f_p$. The black dotted line is the Born approximation result from Eq. (9). The curves correspond to the LA phonon branch along direction (100).

Figure 3

Thermal conductivity vs nanoparticle diameter at 1% (top), 3.4% (middle), and 5% (bottom) nanoparticle concentrations, for temperature 300 K. Triangles: Born + geometrical interpolation. Squares: $T$-matrix calculation for Si nanoparticle. Circles: $T$-matrix calculation for Ge nanoparticle.

Figure 4

Thermal conductivity vs nanoparticle diameter at 1% (top), 3.4% (middle), and 5% (bottom) nanoparticle concentrations, for temperature 800 K. Triangles: Born + geometrical interpolation. Squares: $T$-matrix calculation for Si nanoparticle. Circles: $T$-matrix calculation for Ge nanoparticle.

Figure 5

The ratio ${\kappa }_{\text{Si}}/{\kappa }_{\text{Ge}}$, of the thermal conductivity of a SiGe matrix with embedded Si nanoparticles, ${\kappa }_{\text{Si}}$, to the thermal conductivity of a SiGe matrix with embedded Ge nanoparticles, ${\kappa }_{\text{Ge}}$, is shown as a function of nanoparticle diameter, at 300 K, for three different nanoparticle concentrations, $f_p$.