Effect of long- and short-range order on SiGe alloy thermal conductivity: Molecular dynamics simulation

We report the role of long- and short-range order on the thermal conductivity and mode relaxation times of a model ${\mathrm{Si}}_{0.5}{\mathrm{Ge}}_{0.5}$ alloy using molecular dynamics simulation. All interactions used the Stillinger-Weber potential and the Si and Ge atoms differed only by their mass. The simulated alloys were generated using a Monte Carlo approach to decouple the short-range order from the long-range order. The thermal conductivity is almost entirely determined by the alloy's nearest-neighbor short-range order. Changes to the mode relaxation times between $\sim 3$ and $\sim 6\mathrm{THz}$ upon short-range ordering, and the observed $f^{-2}$ power law trend, suggest that short-range ordering reduces the anharmonic scattering rate of low frequency modes. The trend of thermal conductivity with short-range order may be transferred to real ${\mathrm{Si}}_{0.5}{\mathrm{Ge}}_{0.5}$ and other semiconductor alloys to the extent that scattering from mass disorder dominates their thermal conductivities.

Figure 1

Short-range order parameters of the $8^3$ unit cell SiGe structures. Each color represents a different long-range order and each line is the average of ten independently generated samples.

Figure 2

Thermal conductivities of the $8^3$ unit cell SiGe structures. The thermal conductivity is constant within the uncertainty ($2\sigma$) along the rows, indicating that the short-range order is the dominant factor. Underlined data were also studied for size effects (Fig. 3).

Figure 3

Size effects on the thermal conductivity for select SiGe structures. Each solid symbol is the average of ten samples. The arcs along the $k$ axis indicate the 95% confidence interval of the intercept based on the 50 total samples for each $(\mathbb{L},{\mathbb{S}}_1)$ pair. The intercepts are ordered by ${\mathbb{S}}_1$ and not $\mathbb{L}$, indicating that, just as in Fig. 2, the bulk $k$ is determined by ${\mathbb{S}}_1$. Previous studies of the $\mathbb{L}={\mathbb{S}}_1=0$ alloy are also plotted.

Figure 4

Mode relaxation times for slices through $\mathbb{L}-{\mathbb{S}}_1$ parameter space. (a) Comparison of our fully disordered SiGe structure to previous results. (b) Constant ${\mathbb{S}}_1$ slice. The majority of modes are unaffected by $\mathbb{L}$. Note the change in ordinate scale. (c) Constant $\mathbb{L}$ slice. All modes are sensitive to ${\mathbb{S}}_1$. (d) $\mathbb{L}={\mathbb{S}}_1$ slice. The relaxation times are nearly identical to those of (c), in agreement with the thermal conductivity trends of Figs. 2 and 3.