Thermal conductivity of Si nanostructures containing defects: Methodology, isotope effects, and phonon trapping

Abstract

A first-principles method to calculate the thermal conductivity in nanostructures that may contain defects or impurities is described in detail. The method mimics the so-called "laser-flash" technique to measure thermal conductivities. It starts with first-principles density-functional theory and involves the preparation of various regions of a supercell at slightly different temperatures. The temperature fluctuations are minimized without using a thermostat and, after averaging over random initial conditions, temperature changes as small as 5 K can be monitored (from 120 to 125 K). The changes to the phonon density of states and the specific heat induced by several atomic percent of impurities are discussed. The thermal conductivity of Si supercells is calculated as a function of the temperature and of the impurity content. For most impurities, the drop in thermal conductivity is unremarkable. However, there exist narrow ranges of impurity parameters (mass, bond strength, etc.) for which substantial drops in the thermal conductivity are predicted. These drops are isotope dependent and appear to be related to the vibrational lifetime of specific impurity-related modes.

Impact of screw and edge dislocations on the thermal conductivity of individual nanowires and bulk GaN: a molecular dynamics study

“…The different behavior of phonons within structures with dislocations might be related with different spatially localized modes associate with the different types of dislocations [27]. It is not on the scope of the current study, but it will be interesting to investigate the dynamic properties of defects as the vibrational lifetimes of phonons trapped in each kind of dislocations [26,27,28,65].…”

“…In the three previous studies, phonon scattering by dislocations has been suggested as an explanation for the thermal conductivity reduction. Gibbons et al [26] claimed that, in covalent crystals, impurities introduce localized vibrational modes which may absorb energy. These spatially localized vibrational modes can trap not only electric charges [27] but also phonons with vibrational lifetimes several hundred periods of oscillation [27,28].…”

Mechanism of thermal conductivity suppression in doped silicon studied with nonequilibrium molecular dynamics

“…While heat conduction in Si is mainly governed by phonon transport, recently, many attempts have been made to suppress the thermal conductivity by introducing phonon scattering through nanostructuring, doping, and alloying. [15][16][17][18] Phonon-boundary scattering has been found to bring about a substantial reduction of thermal conductivity in Si nanostructures, such as nanowire and thin film. In addition, the presence of isotopes, intrinsic lattice defects, and chemical impurities in Si would lead to scattering of phonons, which can in turn significantly influence thermal conductivity suppression.…”

Effects of impurities on the lattice dynamics of nanocrystalline silicon for thermoelectric application

“…Furthermore, the addition of impurities and/or defects was shown to result in a favorable decrease of the lattice thermal conductivity of silicon. Gibbons et al [10] used first-principle methods to calculate the thermal conductivity of nanostructured Si which contained defects and/or impurities and concluded that there exist narrow ranges of impurity parameters (mass, bond strength, etc.) for which a reduction in the thermal conductivity was predicted.…”