The structures of high-quality ZnO epitaxial films grown by pulsed-laser deposition on sapphire (0001) without an oxygen gas flow were investigated by X-ray diffraction and transmission electron microscopy. The great disparity of X-ray diffraction line widths between the normal and in-plane reflections reveals the specific threading dislocation geometry of ZnO. Most threading dislocations are pure edge dislocations. From a combination of scattering and microscopic results, it is found that threading dislocations are not uniformly distributed in the ZnO films, but the films consist of columnar epitaxial cores surrounded by annular regions of edge threading dislocations in large density. The local surface morphology and capacitance signal obtained from atomic force and scanning capacitance microscopes indicate that the aggregation of threading dislocations leads to high interface traps at the annular regions.