Molecular dynamics calculation of the thermal conductivity of superlattices

We report on molecular dynamics studies of heat flow in superlattices. The computer simulations are performed using classical mechanics with periodic boundary conditions. The heat flow is in the direction normal to the layers. We have studied the variation of the conductivity with the repeat distance and the effect of interfacial roughness. We discuss the relation of these results to experimental data in the literature. Superlattices are structures composed of alternating layers of two materials that have nearly the same lattice parameter. Semiconductor superlattices have optical, electronic, and thermal properties that vary significantly from those of the bulk constituent materials. These novel properties have led to the use of superlattice structures in a number of applications, including semiconductor lasers 1 and thermoelectric devices. 2,3 The operation of these devices can be greatly af- fected by the thermal conductivity of the superlattice. For instance, the efficiency of a semiconductor laser is reduced when the active region of the device is at high temperature, and so a high thermal conductivity superlattice is preferred. On the other hand, the efficiency of a thermoelectric device is inversely proportional to the thermal conductivity, and so low thermal conductivity materials are preferable. The study of heat flow in a superlattice is also of interest from a fun- damental perspective. The periodicity of the superlattice modifies the phonon dispersion relation. The effects of this modification on the lattice thermal conductivity have been studied by several authors, 4-6 but discrepancies between the- oretical calculations and experimental values have not yet been resolved. Measurements on Si/Ge ~Ref. 7! and GaAs/AlAs ~Ref. 8! superlattices have shown that the thermal conductivity in the direction perpendicular to the layers ~growth direction! is reduced by as much as an order of magnitude compared to the conductivity of the bulk constituents. Part of the decrease in the thermal conductivity can be attributed to the reduction in the group velocity of phonons due to zone folding. 5 How- ever, quantitative calculations show that this effect should lead to a thermal conductivity that decreases as the thickness of the layers making up the superlattice is increased within the range from one to ten monolayers. Experimental results for samples with layer thickness in this range have shown the opposite effect, as can be seen from the data of Capinski et al. 8 shown in Fig. 1, which show a monotonic increase in the thermal conductivity with increasing superlattice period. The disagreement between the zone-folding theory and the data may be due to interface effects, 9 but the extent to which interfacial roughness and other superlattice defects affect the experimentally measured thermal conductivity is not yet known. In order to investigate the effects of the different superlattice parameters on the thermal conductivity in the growth direction, we have performed molecular dynamics simulations on a simple, classical model of a superlattice and present the results here.