Selective lateral growth of GaN is a promising technique for producing high quality material for microelectronic and optoelectronic devices. Single-crystal GaN/AIN layers have been grown on Si(111) substrates and subsequently used as the seeding layer for selective lateral overgrowth. GaN pyramids are formed above holes patterned in a Si3N4 mask. Transmission electron microscopy (TEM, which also denotes the microscope) of these structures shows that the GaN pyramid, GaN seed layer, and AIN buffer layer in the samples have the following epitactic relationship with respect to the Si substrate: [1120]GaN || [1120]AIN || [110]Si and (0001)GaN || (0001)AIN || (111)Si. In the core of the pyramid (at or above the seed windows), dislocations thread through the pyramid perpendicular to the interface plane with very high density. Some of these threading dislocations, which originate from the GaN/AIN seed layer, form 90° bends and half loops at the edge of the pyramid core. In the lateral growth part of the GaN pyramid, the dislocation density is relatively low. The majority of dislocations thread through the pyramid parallel to the interface plane. Planar defects, usually parallel to the interface plane, were observed near the interface. The defect density decreases with the distance away from the interface, so that the top several microns of material maybe completely defect free. The mechanism of the growth of GaN pyramids is discussed and related to this defect structure.