We report on an AlN/AlGaN superlattice approach to grow high-Al-content thick n+-AlGaN layers over c-plane sapphire substrates. Insertion of a set of AlN/AlGaN superlattices is shown to significantly reduce the biaxial tensile strain, thereby resulting in 3-μm-thick, crack-free Al0.2Ga0.8N layers. These high-quality, low-sheet-resistive layers are of key importance to avoid current crowding in quaternary AlInGaN multiple-quantum-well deep-ultraviolet light-emitting diodes over sapphire substrates.