Thermal conductivity reduction by interface roughness in AlN$_{x}$-GaN$_{y}$ superlattices.

A reduction of cross-plane thermal conductivity $\Lambda $ by a factor of two is achieved in AlN$_{4 nm}$-GaN$_{52 nm}$ superlattices by varying the plasma power during growth. This reduction is attributed to interface roughness, introducing a new parameter to be considered in the design and fabrication of superlattices for thermoelectric applications. Thermal conductivity of AlN$_{x}$-GaN$_{y}$ superlattices, x $\sim $ 4 nm and 2 $<$ y $<$ 1000 nm, with rough interfaces is then measured by time-domain thermoreflectance. $\Lambda $ decreases monotonically as the GaN thickness y decreases, $\Lambda $ = 6.35 W m$^{-1}$ K$^{-1}$ at y = 2.2 nm. We observe no minimum thermal conductivity as a function of period for these rough superlattices. A continuum model incorporating the effects of interface roughness indicates that diffuse scattering is dominant when y $>$ 20 nm, and significant coherent transmission occurs when y $<$ 20 nm.