A complete structural and compositional study was carried out for a series of GaN-based lattice-matched HEMT structures. As barrier materials pseudomorphic to GaN, both ternary InAlN and quaternary InAlGaN were investigated. Growths were performed using molecular beam epitaxy on GaN/sapphire or GaN/SiC templates. An abrupt triple-layer AlN/GaN/AlN nanothin spacer at the interface is crucial to improve the structural and electrical properties of the heterostructures. In all cases, this resulted in single-crystalline and single-phase barrier layers.