Simulation of Interfacial Phonon Transport in Si–Ge Heterostructures Using an Atomistic Green’s Function Method

Abstract

An atomistic Green’s function method is developed to simulate phonon transport across a strained germanium (or silicon) thin film between two semi-infinite silicon (or germa-nium) contacts. A plane-wave formulation is employed to handle the translational sym-metry in directions parallel to the interfaces. The phonon transmission function and thermal conductance across the thin film are evaluated for various atomic configurations. The contributions from lattice straining and material heterogeneity are evaluated sepa-rately, and their relative magnitudes are characterized. The dependence of thermal con-ductance on film thickness is also calculated, verifying that the thermal conductance reaches an asymptotic value for very thick films. The thermal boundary resistance of a single Si/Ge interface is computed and agrees well with analytical model predictions. Multiple-interface effects on thermal resistance are investigated, and the results indicate that the first few interfaces have the most significant effect on the overall thermal resistance. DOI: 10.1115/1.270965

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

“…We follow the same atomistic Green's function method [23,27] we applied for a single Si/Ge interface [25]. The only difference is that, in this study, we use Si/Ge superlattices as the center region, as shown in Fig.…”

“…Green's function study on Si/Ge superlattices, however, is scarce. Zhang et al [23] briefly discussed the effect of number of interfaces on the overall thermal resistance across multiple Si/Ge interfaces, while transmission function was not detailed. In this study, we use the Green's function method to investigate coherent phonon transport across Si/Ge superlattices.…”

“…For single Si/Ge interfaces, effects of strain [23], lattice mismatch [24], and interface roughness [25,26] on phonon transmission have been investigated. Green's function study on Si/Ge superlattices, however, is scarce.…”

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

“…For example, Si (or Ge) is strained to have the same lattice constant as Ge (or Si) along the interface plane to study phonon transmission across Si/Ge interface while the inter-atomic distance in the direction perpendicular to the interface is adjusted according to the Poisson's ratio in Ref. 27. A similar numerical technique has been applied to study the phonon transmission across a TiC/graphene nanoribbon (GNR) interface in Ref.…”

“…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. 30 However, all the past AGF-based studies on phonon transmission across interfaces [27][28][29][30][31][32] focused on lattice-matched material interfaces, where the inter-atomic distance of one material is usually adjusted to match that in the other material in the directions parallel to the interface to simplify the calculations. For example, Si (or Ge) is strained to have the same lattice constant as Ge (or Si) along the interface plane to study phonon transmission across Si/Ge interface while the inter-atomic distance in the direction perpendicular to the interface is adjusted according to the Poisson's ratio in Ref.…”