Place: NVM Workshop, Dublin, Ireland
When reduced to small scale, the thermal transport behavior of devices is not only dependent on the materials’ intrinsic properties. Predicting the thermal conductivity is an inherent multi-scale problem. It requires the quantification of phonon scattering strength caused by various types of defects e.g. vacancies, interfaces and dislocations, inside the materials. For the defects that strongly perturb their atomic environment, the Born approximation of the associated perturbation to the system will fail. The Atomic-Green’s-Function approach has been demonstrated to be an efficient way to evaluate such phonon scattering events.
For one-dimensional line defects, e.g. dislocations, we demonstrate a formalism, where the three-dimensional Brillouin Zone (BZ) is divided into parallel two-dimensional planes perpendicular to the defect line direction. A triangulation mesh is adopted to discretize each of the two-dimensional BZ planes. This treatment allows us to split the three-dimensional domain into independent two-dimensional domains and obtain Greens function in defected super-cell. By summing all the results of the planar sub-domains, the T-matrix and scattering cross section are obtained.
We will illustrate this strategy by setting up an atomic model of a quadrupolar arrangement of edge dislocations in silicon using linear elasticity theory. The frequency frequency dependence of the scattering rate is calculated and it is discussed how this form the basis of a all-scale calculation of the thermal conductivity.