Enhancing and tuning phonon transport at vibrationally mismatched solid-solid interfaces

The thermal conductance of interfaces plays a major role in defining the thermal properties of nanostructured materials in which heat transfer is predominantly phonon mediated. Ongoing research has improved the understanding of factors that govern interfacial phonon transport as well as the ability to predict thermal interface conductance. However, despite this progress, the ability to control interface conductance remains a major challenge. In this manuscript, we present a method to enhance and tune thermal interface conductance at vibrationally mismatched solid-solid interfaces. Enhancement is achieved through the insertion of an interfacial film with mediating vibrational properties, such that the vibrational mismatch at the interface is bridged, and consequently, the total interface conductance is enhanced. This phenomena is explored using nonequilibrium molecular dynamics simulations, where the effects of altering the interfacial film thickness, vibrational spectrum, and the temperature of the system are investigated. A systematic study of these pertinent design parameters explores the ability to enhance and tune phonon transport at both ideal (sharp) and nonideal (compositionally disordered) interfaces. Results show that interface conductance can be broadly enhanced by up to 53$\%$ in comparison to the vibrationally mismatched baseline interface. Additionally, we find that compositional disorder at an interface does not imply a deterministic change in interface conductance, but instead, that the influence of compositional disorder depends on the characteristics of the disordered region itself. These results, in contrast to macroscopic thermal transport theory, imply that it is possible to increase thermal conductance associated with interface scattering by adding more material along the direction of heat flux.

Figure 1

Phonon dispersion in the [100] direction and DOS of materials A and B calculated using harmonic lattice dynamics. The difference in cutoff frequencies is shown with respect to both the dispersion relationship and DOS. The red region demonstrates the vibrational mismatch and shows the density of phonon states in material A that do not exist in material B.

Figure 2

Schematic of computational domains representing (a) the baseline interface and (b) the enhanced interface structures with an 8-UC-thick interfacial film.

Figure 3

Schematics of the computational domain and geometric definition of $\Delta T=T_2-T_1$ at (a) baseline and (b) enhanced interface structures. The hatched regions are excluded from the LLSFs to ensure that nonlinear effects near the interface and baths are not considered in the LLSFs. (c) Thermal conductivity is plotted vs reduced temperature from 6$\%$ to 50$\%$ of $T_{\mathrm{m}}$. The thermal conductivities from a subset of the LLSFs used to determine $h_{\mathrm{BD}}$ throughout the study are compared to the bulk thermal conductivities predicted from additional MD simulations. The average temperatures over which the LLSFs are fit in each material are shown to provide a measure of the temperature drop, $\Delta \left(\overline{T}\right)=\left(\overline{T_2}\right)-(\overline{T_1}$), over the computational domain.

Figure 4

Raw temperature profiles at 0.1 $T_{\mathrm{m}}$, (a) baseline interface, (b) sharp, 6 UC thick interfacial film with atomic mass of 80 amu, and (c) medium disorder, 6 UC thick interfacial film with atomic mass of 80 amu. Solid black lines show the LLSF in each material.

Figure 5

Normalized $h_{\mathrm{BD}}$ as a function of varying domain length (a) and width (b).

Figure 6

Plots of occupied DOS calculated for material B for each principal direction of the sample at 0.1 $T_{\mathrm{m}}$ and 0.5 $T_{\mathrm{m}}$. The isotropic nature of the DOS in each direction indicates that phonon modes are not suppressed due to size effects.

Figure 7

Contour plot of $h_{\mathrm{BD}}$ values for varying interfacial film thickness and mass values. (a) Results of the 0.1 $T_{\mathrm{m}}$ study, which shows enhancement of $h_{\mathrm{BD}}$ of up to 23$\%$ and a nearly symmetric dependence on interfacial film mass. (b) Results of the 0.5 $T_{\mathrm{m}}$ study, for which enhancement of $h_{\mathrm{BD}}$ is found to be minimal and only for interfacial film thicknesses $<$4 UC.

Figure 8

The phonon dispersion is shown for several directions of major symmetry. The solid lines show analytical calculations from harmonic lattice dynamics. The points are the anharmonic dispersion relationships from an MD simulation consisting of 512 atoms at 0.5 $T_{\mathrm{m}}$ and zero pressure.

Figure 9

(a) Bulk and isotropic occupied DOS for material A (40 amu) and material B (120 amu). The shaded region outlines the overlap between the bulk DOS. (b) Occupied DOS along the $z$ axis calculated from monolayers containing 72 atoms of material A and B, which reside on either side of the sharp baseline interface.

Figure 10

(a) DOS along the $z$ axis calculated from monolayers containing 72 atoms of material A and C in the enhanced (8 UC, 80 amu) interface (dashed lines) in comparison to the baseline interface. The added overlap in the DOS is shown by the hatched region. (b) Integrated difference in the DOS area at each of the A:C and C:B interfaces for the 8-UC thickness interfacial film and varying mass values. The metric displays the tradeoffs in spreading the vibrational mismatch, which formerly occurs at a single interface, between the two new interfaces. An optimal value of the interfacial mass (80 amu) is observed, reflecting a maximum in the combined DOS overlap of both interfaces.

Figure 11

(a) Plot of the log-ratio Laplace distribution function for various values of $\alpha$ with ${\eta }_L=-1$ and ${\eta }_U=1$. Compared to the step function associated with the sharp reference interface, the distribution function is capable of modeling more gradual transitions. (b) Schematic demonstrating the probability of atom type across the interfacial film region. Two distinct mixing regions are shown centered around the location of the A:C and C:B interfaces in the comparable sharp interface structures.

Figure 12

Computational domains showing the low, medium, and high levels of disorder for both the 2- and 8-UC-thick interfacial films in comparison to the sharp interface structure.

Figure 13

Interface conductance values as a function of interfacial film mass for the three disordered interfaces are plotted along with the comparable sharp interface at 0.1 $T_{\mathrm{m}}$. Error bars represent one standard deviation of three independent simulations.

Figure 14

Comparison of the monolayer-resolved DOS along the $z$ axis at the sharp A:B interface with the DOS in a monolayer of the mixing region for a medium-disordered interface with an interfacial atomic mass equal to 80 amu. The DOS in the disordered monolayer spans a much wider range of frequencies up to nearly the cutoff frequency in bulk material B.