Green's function studies of phonon transport across Si/Ge superlattices

Abstract

Understanding and manipulating coherent phonon transport in solids is of interest both for enhancing the fundamental understanding of thermal transport as well as for many practical applications, including thermoelectrics. In this study, we investigate phonon transmission across Si/Ge superlattices using the Green's function method with first-principles force constants derived from ab initio density functional theory. By keeping the period thickness fixed while changing the number of periods, we show that interface roughness partially destroys coherent phonon transport, especially at high temperatures. The competition between the low-frequency coherent modes and high-frequency incoherent modes leads to an optimum period length for minimum thermal conductivity. To destroy coherence of the low-frequency modes, scattering length scale on the order of period length is required. This finding is useful to guide the design of superlattices to reach even lower thermal conductivity.

Thermal conductance of superlattice junctions

“…Disorder at the intrajunction interfaces, however, does act as a scattering source for these emergent modes. Hence, in agreement with earlier work, 34 the introduction of species disorder at interfaces also leads to diffusive transport.…”

“…Previous works on superlattices 17,19 and superlattice junctions 16,34 suggest that thermal transport in superlattice junctions depends on both period length and junction length, and is modified by disorder. In this work, we vary both period length and junction length, and consider the effects of lead composition, finite temperature, and disorder.…”

“…In particular, they studied the dependence of junction thermal conductance on junction length using both SBM calculations and NEMD simulations. 33 Tian et al 34 studied Si-Ge superlattice junctions using a harmonic lattice-based technique, 35,36 where they found that the introduction of disorder at interfaces destroyed coherent transport of phonons, particularly those with high frequencies.…”

Numerical Study of Thermal Conductivity Reduction in Nanolayered Si-Ge Structures by Solving the Equation of Phonon Radiative Transfer

“…Garg and Chen computed the thermal conductivity of Si-Ge superlattice from density functional perturbation theory, using relaxation times that include both anharmonic and interface roughness effects (Garg et al 2013). Tian et al (2014) applied the atomistic Green's function method to calculate the phonon transmission across Si-Ge superlattices. They have shown that there is an optimum length, resulting from the competition between the coherence of lowfrequency phonons and incoherence of high-frequency phonons caused by interface scattering when anharmonicity is negligible (Tian et al 2014).…”

“…Tian et al (2014) applied the atomistic Green's function method to calculate the phonon transmission across Si-Ge superlattices. They have shown that there is an optimum length, resulting from the competition between the coherence of lowfrequency phonons and incoherence of high-frequency phonons caused by interface scattering when anharmonicity is negligible (Tian et al 2014). Sellitto used a phonon-hydrodynamic approach to obtain a simple mesoscopic model allowing estimating the effective thermal conductivity of a quantum dot superlattice, sketched as a solid matrix of silicon with inclusions of small ellipsoidal obstacles of germanium (Sellitto 2015).…”