Phonon Thermal Boundary Conductance in 1-D Chains: Comparison Between the Semiclassical and Nonequilibrium Green’s Function Formalisms

Thermal boundary conductance (h_BD) across solid interfaces is a limiting factor in many applications, especially as characteristic length scales of devices are decreasing to the nanoscale. Accurate prediction of this interfacial energy transfer, however, is difficult. The most widely used model for h_BD prediction is the diffuse mismatch model (DMM), which considers the transmission of the incident phonon intensity across the interface for the case of thermal equilibrium between the two materials adjacent to the interface. This semi-classical model is limited by the equilibrium assumption, and breaks down for the case of two similar materials comprising the interface. Recently, the Nonequilibrium Green’s Function (NEGF) formalism has been extended to phonon transport. The NEGF formalism is rooted in nonequilibrium transport theory, making it ideal to study energy transfer applications, especially in nanosystems where the concept of thermal equilibrium breaks down due to the small dimensions of the transport regions. The purpose of this paper is to derive, from first principles, the NEGF formalism of thermal conductance, and compare the assumptions of this formalism to the semi-classical DMM assumptions. The NEGF formalism is derived for two simple 1-D examples, and the 1-D conductance and phonon transmission is calculated for a 1-D atomic chains of Si and compared to DMM calculations and experimental data.