To reduce the number of threading dislocations (TDs) in nonpolar a-plane GaN (a-GaN) epi-layers grown on flat r-plane sapphire substrates (r-FSS), we investigated the effects on the crystalline quality of the a-GaN epi-layers of high-density patterned r-plane sapphire substrates (r-HPSS), the patterns of which were placed at intervals of several hundred nanometers. Two types of r-HPSS, the patterns of which had diameters and heights on the order of several hundred nanometers (r-NHPSS) or several micrometers (r-MHPSS), were prepared with conventional r-FSS. The effect of these r-HPSS on the a-GaN epi-layers was demonstrated by evaluating the surface morphology and the crystalline quality of the epi-layers. The surfaces of the a-GaN epi-layer grown on r-FSS and r-NHPSS were pit-free and mirror-like, whereas the surface of the a-GaN epi-layer grown on r-MHPSS was very rough due to the large, irregular GaN islands that grew on the patterns, mainly at the initial growth stage. The crystalline quality of the a-GaN epi-layer grown on r-NHPSS was better than that of the a-GaN epi-layer grown on r-FSS. We confirmed that there were fewer TDs in the a-GaN epi-layer grown on r-NHPSS than there were in the a-GaN epi-layer grown on r-FSS. The TDs propagating to the surface in a-GaN epi-layer grown on r-NHPSS were mainly generated on the flat sapphire regions between the patterns. Interestingly, it was also found that the TDs that propagated to the surface concentrated with a periodic pitch along the c-axis direction. The TD densities of a-GaN epi-layers grown on r-FSS and r-NHPSS were estimated to be approximately 5.0 x 10(10) and 1.5 x 10(9) cm(-2), respectively. This knowledge will contribute to the further development of a-GaN epi-layers for high-performance devices. (C) 2017 Elsevier B.V. All rights reserved.