Cross-plane thermal conductivity of superlattices with rough interfaces using equilibrium and non-equilibrium molecular dynamics Konstantinos Termentzidis a,b,c,⇑ , Samy Merabia d , Patrice Chantrenne a,b,c,⇑ , Pawel Keblinski e a INSA Lyon, CETHIL UMR5008, F-69621 Villeurbanne, France b Université de Lyon, CNRS, F-69621 Villeurbanne, France c Université Lyon 1, F-69621 Villeurbanne, France d Laboratoire de Physique de la Matiére Condensée et Nanostructures, LPMCN, UMR 5586, Université Lyon 1, F-69621, France e Materials Science and Engineering Department, RPI, Rensselaer Polytechnic Institute, Troy, NY, USA article info Article history: Received 7 July 2010 Received in revised form 20 December 2010 Accepted 23 December 2010 Available online 1 February 2011 Keywords: Non-equilibrium molecular dynamics Green–Kubo Superlattices Cross-, in- and intra-plane thermal conductivity Rough interfaces Shape of interfaces abstract This paper describes a heat transfer study of binary Lennard Jones superlattices, focusing on the influence of interface topology on cross-plane thermal conductivity, by using both non-equilibrium and equilib- rium molecular dynamics methods. Both methods reveal the same trends of thermal conductivity. In par- ticular, interfacial roughness is shown to slightly increase cross-plane thermal conductivity in comparison to smooth interfaces. Our results highlight paths for optimizing superlattices for thermoelec- tric conversion applications and for thermal management solutions in micro- and nano-systems. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Superlattices are structures made of alternating solid layers with a thickness less than 100 nm. Given this small dimension, the thermal properties of superlattices (SL) may vary drastically from those of the material making up the bulk form [1]. In partic- ular, superlattices can exhibit significant thermal conductivity anisotropy, with the conductivity in the direction perpendicular to the layers (Cross-Plane) generally being lower than the conduc- tivity in the direction parallel to the interfaces (In Plane). This has important practical implications in thermoelectric devices, for in- stance, as a low thermal conductivity (TC) in one direction can be combined with the high electrical conductivity of the SL. Among other things, the superlattice cross-plane TC depends on layer thickness (or superlattice period in the case of periodic mate- rials) and interface topology [1]. Given the dimensions of the superlattice structure, layer thickness can be compared to the pho- non mean free path (PMFP). Under these conditions, heat transport is no longer diffusive but ballistic within the layers while the TC has been shown to decrease with layer thickness [2]. This decrease can be understood in terms of the thermal resistance caused by the interfaces. The combined effects involving phonon scattering from multiple interfaces become substantial when the SL period is sig- nificantly smaller than the phonon mean free path (PMFP). These complex effects make TC predictions extremely hard from a theo- retical point of view. In this context, molecular dynamics (MD) simulations have become the method of choice for predicting superlattice TC over the last decade. MD simulations of superlattic- es of smooth interfaces show minimum cross-plane TC when the SL period decreases, which can be attributed to miniband forma- tion, whereas this minimum disappears for rough interfaces [3,4,1,5,6]. Reduced anisotropy of cross-plane and in-plane TC was predicted [4,7] for superlattices with rough interfaces. Simi- larly, Landry and McGaughey [8] showed that the roughness of the interface decreases cross-plane thermal conductivity. However, all these studies considered very slight roughness, of the order of one atomic layer. However, little attention has been given to greater roughnesses, in particular comparable to the PMFP [9]. Nevertheless, this is important in practices since fabrication pro- cesses allow tailoring interface geometry [10,11] consisting of wavy interfaces of variable height. In a previous study using molec- ular dynamics, we showed that in-plane TC varies significantly 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.01.001 ⇑ Corresponding authors at: INSA Lyon, CETHIL UMR5008, F-69621 Villeurbanne, France. E-mail addresses: konstantinos.termentzidis@gmail.com (K. Termentzidis), smerabia@gmail.com (S. Merabia), patrice.chantrenne@insa-lyon.fr (P. Chantrenne), keblip@rpi.edu (P. Keblinski). International Journal of Heat and Mass Transfer 54 (2011) 2014–2020 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt