The role of interface thermal boundary resistance in the overall thermal conductivity of Si–Ge multilayered structures

Abstract

Nanoscale engineered materials with tailored thermal properties are desirable for applications such as highly efficient thermoelectric, microelectronic and optoelectronic devices. It has been shown earlier that by judiciously varying the interface thermal boundary resistance (TBR), thermal conductivity in nanostructures can be controlled. In the presented investigation, the role of TBR in controlling thermal conductivity at the nanoscale is analyzed by performing non-equilibrium molecular dynamics (NEMD) simulations to calculate thermal conductivity of a range of Si-Ge multilayered structures with 1-3 periods, and with four different layer thicknesses. The analyses are performed at three different temperatures (400, 600 and 800 K). As expected, the thermal conductivity of all layered structures increases with the increase in the number of periods as well as with the increase in the monolayer thickness. Invariably, we find that the TBR offered by the interface nearest to the hot reservoir is the highest. This effect is in contrast to the usual notion that each interface contributes equally to the heat transfer resistance in a layered structure. Findings also suggest that for high period structures the average TBR offered by the interfaces is not equal. Findings are used to derive an analytical expression that describes period-length-dependent thermal conductivity of multilayered structures.

Heat conduction across a solid-solid interface: Understanding nanoscale interfacial effects on thermal resistance

“…The simulated R k values agree with the literature. 21 With increasing L xÀSi , R k decreases, which follows from our argument about the length dependence of thermal conductivity. The reduction in R k is relatively large between 1 and 40 nm, which are lengths smaller than the mean free paths of phonons.…”

“…4 Here, the total thermal resistance R TOTAL ¼ L xÀSi /k Si þ R k þ L xÀGe /k Ge accounts for resistances due to the length-dependent thermal conductivities of Si and Ge as well at the Kapitza resistance of the assumed interfacial material. 4,21,28 Again, the flux q ¼ ( The reduction in R k with increasing L follows a similar relation for both cases. The decrease is relatively large for system dimensions smaller than the mean free path of phonons, 1 but R k assumes a constant value at larger lengths.…”

“…The interfacial thermal resistance at $ 10 nm produces a temperature discontinuity of $5 K across the Si-Ge interface. 21 Higher temperatures enhance lattice vibrations since the local atoms also possess larger kinetic energies. The vibrations in the Si lattice propagate, transferring energy to cooler regions in the superlattice and also scattering internally.…”

“…The net heat flux through the interface is calculated by time averaging the energy supplied to the warmer Si and removed from the cooler Ge atoms to maintain their temperatures at constant values. 21 Figure 2(a) presents the change in R k with respect to the system length. The simulated R k values agree with the literature.…”

Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers

“…The thermal conductivity of a multilayered structure can be approximated according to the rule of mixtures Samvedi & Tomar (2009);Zhou et al (2007):…”