We report the structural and electrical properties of ultrathin-barrier AlN/GaN heterostructures grown on freestanding GaN substrates by rf plasma-assisted molecular beam epitaxy. Structures with barrier thicknesses between 1.5 nm and 7.5 nm were grown and characterized. We observe that AlN/GaN structures with barriers of 3.0 nm exhibit the highest Hall mobility, approximately 1700 cm(2)/Vs. Furthermore, the Hall mobility is much diminished in heterostructures with AlN barriers thicker than 45 am, coincident with the onset of strain relaxation. Published by Elsevier B.V.