Molecular Dynamics Prediction of the Thermal Resistance of Solid-solid Interfaces in Superlattices

Molecular dynamics simulations are used to predict the thermal resistance of solid-solid interfaces in crystalline superlattices using a new Green-Kubo formula. The materials on both sides of the interfaces studied are modeled with the LennardJones potential and are only differentiated by their masses. To obtain the interface thermal resistance, a correlation length in the bulk materials is first predicted, which approaches a systemsize independent value for larger systems. The interface thermal resistance is found to initially increase as the layer length is increased, and then to decrease as the phonon transport shifts from a regime dominated by ballistic transport to one dominated by diffusive transport. NOMENCLATURE A area E energy F force vector k thermal conductivity kB Boltzmann constant L length m mass r particle position vector, particle separation vector q planar energy flux R thermal resistance Rm mass ratio ∗Address all correspondence to this author. S, S heat current, heat current vector t time T temperature v particle velocity vector V volume x position Greek ∆ length λ correlation length φ potential energy Φ spatial correlation function Subscripts A material on one side of interface A|B A–B interface B material on other side of interface i summation index, particle label j summation index, particle label K Kapitza l direction (x, y, or z) SL superlattice x composition fraction Superscripts o time average value ∞ large system limit 1 Copyright c © 2006 by ASME INTRODUCTION A superlattice is a periodic composite material composed of layers of metals, semiconductors, and/or insulators. Superlattices built from group IV semiconductors (e.g., Si/SixGe1−x) and Group III-V semiconductors (e.g., AlAs/GaAs) have received considerable attention due to their relevance to the electronics industry. By appropriate choice of the layer compositions (including doping) and thicknesses, it is possible to separately control the transport of electrons and phonons in a superlattice [1]. While the electron transport has been considered extensively, attention has only recently turned to the thermal transport characteristics. The potential anisotropy of the superlattice thermal conductivity tensor may be advantageous in systems where the careful control of heat transfer is needed, and superlattices with low thermal conductivity are of interest in thermoelectric energy conversion applications [2]. Thermal transport modeling in superlattices has typically focused on the prediction of the effective thermal conductivity [3–12]. Here, we report on a molecular dynamics (MD) study aimed at predicting the thermal resistance of the interfaces in a model superlattice. The interface resistance plays an important role in the thermal behavior of many of the new nanocomposites being developed. Prediction of its magnitude is challenging, especially when system interfaces are close together, but is crucial for the development of superlattice design techniques. The nature of phonon transport in a superlattice is first reviewed, followed by a description of modeling methods available. We then propose a method to predict the interface thermal resistance using a Green-Kubo formula, and examine the effects of changing the period length in a superlattice modeled with the Lennard-Jones (LJ) potential. PHONON TRANSPORT IN SUPERLATTICES Consider a superlattice composed of layers of equal thickness of materials A and B with a period length L (i.e., LA = LB = L/2), as shown in Fig 1. From a continuum standpoint, the thermal resistance normal to the layers of one period of such a structure will be RSL = LA kA + LB kB +2RA|B, (1) where ki is the bulk thermal conductivity of material i (i =A,B) and RA|B is the thermal resistance of the A|B interface. Note that RA|B is equal to RB|A. As the period length increases, the contribution of RA|B to RSL will decrease, and beyond a certain size, will be negligible. When the interfaces are far enough apart to be considered isolated, the interface thermal resistance can also be called the Kapitza resistance, RK,A|B. To move from the continuum description of Eq. (1) to the nanoscale superlattices currently being fabricated, we must conA B A A B B L A L B