This article concerns the microstructure of self-assembled ErAs islands embedded in GaAs. The material is grown by molecular beam epitaxy. The nucleation of ErAs on GaAs occurs in an island growth mode leading to spontaneous formation of nanometer-sized islands. Several layers of ErAs islands separated by GaAs can be stacked on top of each other to form a superlattice. A series of such samples were grown with different depositions of ErAs at a growth temperature of 535 degrees C. The microstructure of these samples was investigated by x-ray diffraction and transmission electron microscopy. We find that initially isolated ErAs islands with a diameter of 2 nm are nucleated. With increasing ErAs deposition, these islands branch out and form extended structures. The samples are coherent in growth directions for ErAs depositions up to 1.8 monolayers. At higher ErAs depositions defects are incorporated into the GaAs matrix.