Thermal transport in phase-change materials from atomistic simulations

We computed the thermal conductivity ($\kappa$) of amorphous GeTe by means of classical molecular dynamics and lattice dynamics simulations. GeTe is a phase change material of interest for applications in nonvolatile memories. An interatomic potential with close-to-ab initio accuracy was used as generated by fitting a huge ab initio database with a neural network method. It turns out that the majority of heat carriers are nonpropagating vibrations (diffusons), the small percentage of propagating modes giving a negligible contribution to the total value of $\kappa$. This result is in contrast with the properties of other amorphous semiconductors such as Si for which nonpropagating and propagating vibrations account for about one half of the value of $\kappa$ each. This outcome suggests that the value of $\kappa$ measured for the bulk amorphous phase can be used to model the thermal transport of GeTe and possibly of other materials in the same class also in nanoscaled memory devices. Actually, the contribution from propagating modes, which may endure ballistic transport at the scale of 10–20 nm, is negligible.

Figure 1

(a) Phonon density of states of amorphous GeTe from the 4096-atom NN model. Results for a single 216-atom DFT model (Ref. 17) are also reported. Only phonons at the supercell $\Gamma$ point are considered. The higher smoothness of 4096-atom data is due to the larger supercell used. Projections of the DOS on the different atomic species (Te atoms and Ge atoms in tetrahedral and defective octahedral geometries) are also shown. (b) Inverse participation ratio of phonons in a-GeTe from the 4096-atom NN model and for a single 216-atom DFT model (Refs. 17 and 19).

Figure 2

(a) Group velocities, (b) lifetimes, and (c) mean free paths of normal modes in a-GeTe.

Figure 3

Cumulative thermal conductivity $\kappa$ of a-GeTe as a function of phonon frequency. The value of $\kappa$ at a given frequency $\omega$ is due to the sum of the contribution of all phonons with frequency below $\omega$. Contribution from propagating modes (${\kappa }_{\mathrm{BTE}}$) is shown together with his sum ($\mathrm{AF}+\mathrm{BTE}$) with the contribution coming from nonpropagating modes (${\kappa }_{\mathrm{AF}}$) and the result obtained from equilibrium MD simulations (EMD). The width of the AF+BTE function corresponds to the error bar in the AF term (see text).