Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces

Abstract

Detailed phonon scattering at an ideal Si-Ge interface is studied with a linear lattice dynamics model. Frequency dependent transmission coefficients indicate the significance of acoustic-optical phonon mode conversion at the interface. Applied to multiple interfaces, the method shows how the overall thermal resistance approaches a finite (Bloch mode) limit with the increasing number of interfaces in absence of other scattering mechanisms. The dependence of thermal resistance on the superlattice layer thickness is not significant even in the interface-scattering-only limit we study. We also assess errors incurred by the finite domain size and classical statistics in molecular dynamics simulations of interface thermal resistance. Results suggest that using 6 ϫ 6 unit cells in the transverse directions, a tractable size for such simulations, will incur only a 5% error in the predicted thermal resistance. Similarly, the error due to the classical (Boltzmann) phonon distribution in molecular dynamics simulations is predicted to be less than 10% for temperatures above 300 K.

Effect of lattice mismatch on phonon transmission and interface thermal conductance across dissimilar material interfaces

“…In contrast, the phonon transmission at low frequency from Ge-like to Si will be much smaller (about 0.45, not shown here) due to the much less phonons at similar frequencies available in Si side to match those from Ge-like materials side. 25,30 Figure 4(a) clearly shows that phonon transmission decreases with the increasing percentage of lattice mismatch. Phonon transmission across the relaxed lattice-mismatched interfaces is affected by several factors.…”

“…In addition to lattice mismatch, vacancies, defects and species mixing could all happen in material interfaces due to manufacturing/processing constraints, which could significantly change the phonon scattering at interfaces. There is not much work using either lattice dynamics 25,34 or other methods to study phonon transmission across realistic material interfaces due to the physical and numerical complexity.…”

“…Significant progresses have been made recently for studying phonon transmission using atomistic simulation methods, including the phonon wave-packet method 23 based on molecular dynamics simulations, the linear lattice dynamics, 24,25 and the atomistic Green's function (AGF) approach which solves the phonon dynamical equation under the harmonic approximation. In particular, the frequency-dependent phonon transmission across a variety of material interfaces has been studied using the AGF approach, such as the interface in low dimensional atomic chains, 26 strained Si/Ge interface, 27 metal/graphene nanoribbon (GNR) interface, 28 rough interface between two face-centered cubic (FCC) crystals, 29 and more recently across confined material interfaces.…”

Role of crystal structure and junction morphology on interface thermal conductance

“…1b), which can be a frequent byproduct of nanostructure fabrication. The addition of random atoms at an abrupt interface generates two effects in the harmonic regime: 1) it changes phonon transmission [13][14][15][16]; and, 2) it couples phonons with different transverse wavevectors (k ⊥ ) by breaking the translational symmetry at the interfacial plane [17]. Some papers focused on the effect of mixing on transmission (Effect 1) and showed the importance of the frequency dependence [13], the correlation length of the random distribution [14,15] and the acoustic-optic coupling [16].…”

Phononic thermal resistance due to a finite periodic array of nano-scatterers

“…Other strategies have been highlighted, such as the addition of a new material to the solid/solid coupling or modulating the roughness [10]. Lattice dynamics [11,12], Green"s functions [13] and molecular dynamics are often employed for the calculations [14][15][16]. We observe that the two commonly applied models, the acoustic mismatch model (AMM) and diffuse mismatch model (DMM), do not necessarily lead to values that are comparable to the available experimental data [1,15,17,18].…”