Modeling the phonon heat transport in semiconductor superlattices -

Abstract

Understanding the laws that govern the phonon heat transport at atomic interfaces in crystalline superlattices has long been viewed as a key step toward efficient thermal-management strategy for high-performance superlattice-based thermoelectric, microelectronic, and optoelectronic devices. Therefore, several experimental studies on the phonon thermal conductivity in superlattice structures have been carried out, and many numerical techniques describing the phonon heat transport in multi-layer systems have been developed. Experimental studies have demonstrated that, in some circumstances, the phonons in a superlattice can propagate ballistically without being scattered at the interfaces as if the superlattice is a bulk material with no interfaces. This phonon mechanism is known as the coherent phonon transport mode, while the phonon heat transport mode in which phonons experience scattering at the interfaces is known as the incoherent phonon transport mode. Experiments have also demonstrated that when the interfaces between the layers that form the superlattice contain low amounts of irregularities, the superlattice cross-plane thermal conductivity presents a minimum value for a particular period thickness. However, in the case of diffusive interfaces, the cross-plane thermal conductivity increases monotonically with increasing the period thickness. Most theories for the superlattice thermal conductivity either rely on the solution of the Boltzmann transport equation that treats the phonons as particles or are based on the assumption that the phonons are plane waves. The existing Boltzmann models involve a rate at which particle-like phonons are scattered by interfaces. Thus, according to all Boltzmann models, the superlattice cross-plane thermal conductivity decreases monotonously as the interface density increases, which disagrees with the experimental measurements that demonstrated a minimum in the curve describing the cross-plane thermal conductivity versus the period thickness. On the other hand, by invokin