Ultra-compact Interference Phonon Nanocapacitor for Storage and Lasing of Terahertz Lattice Waves

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Phonon transmission coefficient

The detailed behaviour of phonons in the scattering events with defects, boundaries and interfaces is crucial to understand and predict the phonon transport at the nanoscale, when the phonon MFP is comparable to the characteristic size of the scatterers. A key quantity in this concern is the phonon transmission coefficient or probability.
In terms of phonon interface scattering, the acoustic mismatch model (AMM) and diffuse mismatch model (DMM) are often used for the calculation of phonon transmission [Swartz and Pohl (1989)]. The AMM, assuming a perfect interface, considers long-wavelength phonons and uses the acoustic impedances Z of the two adjacent materials 1 and 2 for the calculation of phonon transmission
probability, 1;2 = 4Z1Z2 (Z1 + Z2)2.

Phonon wave-packet technique

To probe the phonon transmission coefficient, MD with the phonon wave packet method has been used to provide the per-phonon-mode energy transmission coefficient (!; l) [Schelling et al. (2002a); Schelling et al. (2004)]. This method has been limited to effective 1D systems since all the atoms obey the same atomic movement patterns in the plane normal to the wave vector.
In the present thesis, I extend this 1D method by exciting a realistic 3D Gaussian wave packet centered at the frequency ! and wave vector ~k in the reciprocal space and at ~r0 in the real space, with the spatial width (coherence length) lq in the direction of ~k. The spatial extent l? in the perpendicular directions to ~k can be different from that in the parallel direction. A 3D phonon WP has the displacement ~ui for the atom.

Interface thermal conductance

Phonon wave-packet technique based on MD and atomistic Green’s Function allows us to precisely determine the key quantity that characterizes the phonon transport and scattering across an interface: the phonon transmission coefficient q and transmission function (!). The interface thermal conductance can thereby be determined by following the Landauer’s formalism for phononwave scattering as an analogy to electron-wave scattering. Apart from the Landauer’s formalism that treats phonons as coherent waves, other approaches can be used to determine the interface thermal conductance. Two major approaches are commonly used: a direct non-equilibrium MD method by fitting the Fourier’s law and an indirect equilibrium MD method by using the fluctuation-dissipation theorem.

Phonon relaxation time

To extract the phonon relaxation time for Umklapp phonon processes, two major technique categories exist: equilibrium MD-based spectral energy density method (SED) [Turney et al. (2009); Thomas et al. (2010)] and anharmonic lattice dynamics (LD)-based third-order Hamiltonian method [Srivastava (1990)]. Equilibrium MD simulation employs empirical interatomic potentials that incorporate full anharmonicity, which reproduces inelastic phonon scatterings of all orders. Whereas the existing theoretical formalism of anharmonic LD for predicting phonon lifetimes only includes three-phonon processes since the cubic force constants are required). Higher-order phonon processes are not included and will become important as temperature is further increased. The anharmonic LD method apply for systems at the temperature lower than the Debye temperature.

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Table of contents :

Abstract
Résumé
1 Introduction 
1.1 Phonon as a wave
1.2 Phonon interference in thermal transport
1.3 Basics of phonons
1.3.1 One-dimensional open system of coupled masses
1.3.2 Periodic Boundary Condition
1.3.3 Normal modes and phonon energy
1.4 Organization of the Thesis
2 Atomistic Simulation of Phonon Transport 
2.1 Classical molecular dynamics
2.1.1 Generality
2.1.2 Limitation
2.2 Phonon transmission coefficient
2.2.1 Phonon wave-packet technique
2.2.2 Green’s function and phonon Green’s Function
2.3 Interface thermal conductance
2.3.1 Landauer’s formalism
2.3.2 Molecular dynamics
2.4 Lattice thermal conductivity
2.4.1 Phonon group velocity
2.4.2 Phonon relaxation time
2.4.3 Thermal conductivity from Green-Kubo formulation .
2.5 Conclusions
3 Phonon Interference and Energy Transport in Nonlinear Lattices with Resonance Defects 
3.1 Introduction
3.2 Atomistic model and Methodology
3.2.1 Model Structure
3.2.2 Methodology
3.3 Results and Discussions
3.3.1 Interference Resonance Profile
3.3.2 Isotopic Shift of Resonances
3.3.3 Phonon Screening Effect
3.3.4 Two-Path Phonon Interference in Si crystal with Ge impurities
3.3.5 Random Distribution of Atoms
3.3.6 Nonlinear Effects
3.3.7 Wave Packet Coherence Length Determination
3.4 Conclusions
4 Ultra-compact Interference Phonon Nanocapacitor for Storage and Lasing of Terahertz Lattice Waves 
4.1 Introduction
4.2 Atomistic Model
4.3 Results and Discussions
4.3.1 Linewidth narrowing by adiabatic cooling
4.3.2 Phonon reflection on the mirror
4.3.3 Phonon localization
4.3.4 Controllabe phonon emission
4.4 Conclusions
5 Harmonic Phonon Interferences Reduce Heat Conduction 
5.1 Introduction
5.2 Atomistic Scheme
5.3 Results and Discussions
5.3.1 Harmonic force constants determination from density functional perturbation theory (DFPT) calculations
5.3.2 Phonon transmission
5.3.3 Alloy thermal conductivity
5.3.4 Phonon spectrum of of the diatomic 1D chain and the SiGe alloy
5.3.5 Anharmonic relaxation time
5.4 Conclusions
6 Conclusions and Perspectives 
6.1 Conclusions
6.2 Perspectives
References

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