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We investigate the evolution of the cross-plane thermal conductivity $\kappa$of superlattices (SLs) as interfaces change from perfectly abrupt to totallyintermixed, by using non-equilibrium molecular dynamics simulations incombination with the spectral heat current calculations. We highlight the roleof surface-interdiffusion-driven intermixing by calculating the $\kappa$ of SLswith changing interface roughness, whose tuning allows for the $\kappa$ valuesmuch lower than the "alloy limit" and the abrupt interface limit in same cases.The interplay between alloy and interface scattering in different frequencyranges provides a physical basis to predict a minimum of thermal conductivity.More specifically, we also explore how the interface roughness affects thethermal conductivities for SLs materials with a broad span of atomic mass andbond strength. In particular, we find that (i) only when the "spacer" thicknessof SLs increases up to a critical value the $\kappa$ of rough SLs can break thecorresponding "alloy limit". (ii) Whether the $\kappa$ changes monotonically asinterface roughness strongly depends on the period length and intrinsicbehavior of phonon transport for SLs materials. Especially, for the SL withlarge period length, there exists an optimal interface roughness which canminimize the thermal conductivity. (iii) Surface-interdiffusion-drivenintermixing is more effective in achieving the low $\kappa$ below the alloylimit for SL materials with large mass mismatch than with small one. (iv) It'spossible for SLs materials with large lattice mismatch (i.e., bond strength) todesign an ideally abrupt interface structure with $\kappa$ much below the"alloy limit". These results have a clear implications for optimization ofthermal transport for heat management and for the development of thermoelectricmaterials.

Optimizing phonon scattering by tuning surface-interdiffusion-driven intermixing to break the random-alloy limit of thermal conductivity