**6.1 Modelling rough interfaces for the GaAs/AlAs superlattices**

A new modeling of realistic interfaces is considered with the present study (Termentzidis et al 2010, 2011a). Interfaces with square formed islands of one monolayers and pyramide like islands of two monolayers are modelled. Furthermore there are two characteristic lengths of square islands depending if GaAs or AlAs is on top. It has been proven that large scale islands are formed when an AlAs layer grows on a GaAs layer while small scale islands are formed when a GaAs layer grows on an AlAs layer (Tanaka & Sakaki 1987, Jusserand et al 1990). Furthermore interfaces with interdiffusion parts are also considered. Figure 8 depicts the two kind of interfaces with interface height of one monolayer and in figure 9 with two monolayers (these figures are taken from Termentzidis et al 2010)

Fig. 8. Schematic representation of the two different scale interfaces between the GaAs/AlAs and the AlAs/GaAs, for height of interfaces of one monolayer – square like interfaces.

Fig. 9. Schematic representation of the two different scale interfaces between the GaAs/AlAs and the AlAs/GaAs, for height of interfaces of two monolayers – pyramoidal like interfaces (taken from Termentzidis et al 2010).

#### **6.2 Thermal conductivity of GaAs/AlAs like superlattices with rough interfaces**

Figure 10 shows the predicted cross-plane thermal conductivity as a function of the superlattice period, for a variety of interface configurations. In figure 10 at left the thermal conductivity is plotted for smooth interfaces, for rough interfaces with height of one monolayer and three coverage factors (1%, 10% and 50%) and finally for interfaces with

Molecular Dynamics Simulations and Thermal Transport at the Nano-Scale 97

We hope we have helped in showing the possibilities of the molecular dynamics technique to probe heat transport in solids, and in particular nanomaterials. Molecular dynamics is a relatively simple and flexible method to be used especially today when stable optimized open source codes have become avalaible: LAMMPS, DLPOLY, GROMACS to name a few. The ever increasing number of publications has helped in resolving controversies regarding heat transfer at the nanoscale, and also getting physical insights in classical problems. A physical understanding of energy transport across two solids-a very simple question-still poses a challenge ! MD simulations may help in observing the scattering of phonons at interfaces, which certainly complements experimental investigations. In the context of nanomaterials, MD is well adapted to characterize ballistic heat transport in nano-objects, although care should be taken not to introduce spurious sources of scattering ! Let us hope that further experimental measurements may improve the modeling of the nanomaterials

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**7. Conclusion** 

that we have considered.

doi:10.1063/1.1743957

doi:10.1063/1.1730376

DOI:10.1103/PhysRevLett.84.4613

ISBN: 0-19 855645 4 (Pbk), New York, USA

**8. References** 

height of 2 monolayers. The coverage factor of 1% exhibits the minimum in thermal conductivity as the smooth interfaces. For coverage factor of 10% and 50% the minimum dissapears and the results confirm previous theoretical observations (Daly et al 2002, Imamura et al 2003), while the two defect concentrations do not influence the thermal conductivity. For height of roughness of 2MLs, the thermal conductivity is higher than for smooth interfaces and exhibits a maximum for a 80. In the same figure at the right the influence of interdiffusion of the two species is shown, with similar behavior as the interfaces of height of two MLs. These unexpected results are related with the fact that inelastic scattering could enhance the thermal conductivity through interfaces (Lepi et al 2003). The study shows that the thermal conductivity depends strongly on the detailed description of the interfaces, including height, shape of roughness, interdiffusion of species etc. Changing the structure of the interface can favor or deteriorate the thermal transport through interfaces, and we showed that the interface structure is a relevant parameter which controls the thermal properties of superlattices.

Fig. 10. Cross-plane thermal conductivity as a function of the superlattice period with NEMD for GaAs/AlAs systems. Left: smooth interfaces, rough interfaces of height of 1ML with three different concentrations and rough interfaces of height of 2ML are presented. Right: rough interfaces with interdiffusion. The smooth and rough interfaces with a concentration of 50% are also shown for comparison.
