Heterostructures consisting of alternating GaN/AlN epitaxial layers represent the building-blocks of state-of-the-art devices employed for active cooling and energy-saving lightning. Insights into the heat conduction of these structures are essential in the perspective of improving the heat management for prospective applications. Here, the cross-plane (perpendicular to the samples surface) thermal conductivity of GaN/AlN superlattices as a function of the layers thickness is established by employing the $3omega$-method. Moreover, the role of interdiffusion at the interfaces on the phonon scattering is taken into account in the modelling and data treatment. It is found, that the cross-plane thermal conductivity of the epitaxial heterostructures can be driven to values as low as 5.9 W/(m$cdot$K) comparable with those reported for amorphous films, thus opening wide perspectives for optimized heat management in III-nitride-based epitaxial multilayers.
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