It is generally accepted that heat-carrying phonons in materials scatter off each other (normal or Umklapp scattering) as well as off defects. This assumes static defects, implies quasi-instantaneous interactions and at least some momentum transfer. However, when defect dynamics are explicitly included, the nature of phonon-defect interactions becomes more subtle. Ab initio microcanonical molecular-dynamics simulations show that (1) spatially localized vibrational modes (SLMs), associated with all types of defects in semiconductors, can trap thermal phonons; (2) the vibrational lifetimes of excitations in SLMs are one to two orders of magnitude longer (dozens to hundreds of periods of oscillation) than those of bulk phonons of similar frequency; (3) it is phonon trapping by defects (in SLMs) rather than bulk phonon scattering, which reduces the flow of heat; and (4) the decay of trapped phonons and therefore heat flow can be predicted and controlled—at least to some extent—by the use of carefully selected interfaces and δ layers.

Defects in semiconductors introduce vibrational modes that are distinct from bulk modes because they are spatially localized in the vicinity of the defect. Light impurities produce high-frequency modes often visible by Fourier-transform infrared absorption or Raman spectroscopy. Their vibrational lifetimes vary by orders of magnitude and sometimes exhibit unexpectedly large isotope effects. Heavy impurities introduce low-frequency modes sometimes visible as phonon replicas in photoluminescence bands. But other defects such as surfaces or interfaces exhibit spatially localized modes (SLMs) as well. All of them can trap phonons, which ultimately decay into lower-frequency bulk phonons. When heat flows through a material containing defects, phonon trapping at localized modes followed by their decay into bulk phonons is usually described in terms of phonon scattering: defects are assumed to be static scattering centers and the properties of the defect-related SLMs modes are ignored. These dynamic properties of defects are important. In this paper, we quantify the concepts of vibrational localization and phonon trapping, distinguish between normal and anomalous decay of localized excitations, discuss the meaning of phonon scattering in real space at the atomic level, and illustrate the importance of phonon trapping in the case of heat flow at Si/Ge and Si/C interfaces. V

We present the details of a method to perform molecular-dynamics (MD) simulations without thermostat and with very small temperature fluctuations ±ΔT starting with MD step 1. It involves preparing the supercell at the time t = 0 in physically correct microstates using the eigenvectors of the dynamical matrix. Each initial microstate corresponds to a different distribution of kinetic and potential energies for each vibrational mode (the total energy of each microstate is the same). Averaging the MD runs over many initial microstates further reduces ΔT. The electronic states are obtained using first-principles theory (density-functional theory in periodic supercells). Three applications are discussed: the lifetime and decay of vibrational excitations, the isotope dependence of thermal conductivities, and the flow of heat at an interface.

The interactions between thermal phonons and defects are conventionally described as scattering processes, an idea proposed almost a century ago. In this contribution, ab-initio molecular-dynamics simulations provide atomic-level insight into the nature of these interactions. The defect is the Si|X interface in a nanowire containing a δ-layer (X is C or Ge). The phonon-defect interactions are temperature dependent and involve the trapping of phonons for meaningful lengths of time in defect-related, localized, vibrational modes. No phonon scattering occurs and the momentum of the phonons released by the defect is unrelated to the momentum of the phonons that generated the excitation. The results are extended to the interactions involving only bulk phonons and to phonon-defect interactions at high temperatures. These do resemble scattering since phonon trapping occurs for a length of time short enough for the momentum of the incoming phonon to be conserved.

The most commonly used first-principles technique to predict the properties of impurities in semiconductors involves periodic supercells to represent the host crystal, classical molecular dynamics (MD) to describe the nuclear motion, with ab initio-type pseudopotentials and density-functional theory to treat the electronic problem. Calculating the entire dynamical matrix of the supercell is most useful. Indeed, the eigenvalues of this matrix give all the local, pseudolocal, and resonant vibrational modes associated with the impurity, and allow the calculation of the phonon density of states, from which the vibrational free energy can be obtained. Further, the eigenvectors of the dynamic matrix are used to quantify the ‘localization’ of specific vibrational modes and prepare the supercell in thermal equilibrium at a temperature T, up to a few hundred degrees kelvin. This supercell preparation allows non-equilibrium MD simulations to be performed. Applications include the calculation of vibrational lifetimes and of thermal conductivities. This paper describes the essential ingredients of such calculations.