The formation of a stable surface morphology of Ge on Si(111) at coverages close to the transition from two-dimensional (2D) to three-dimensional (3D) growth was studied using scanning reflection electron microscopy and energy dispersive X-ray spectroscopy. Regions of the stable surface morphologies of 2D layers and 3D islands are described by a phase diagram as a function of coverage and temperature. Temperatures were determined at which the unstable 2D Ge layer at coverages between 1.5 and 2.3 BL does not transform into islands longer than 10 min. It was found that irradiation by focused e-beam creates points in the unstable 2D layer where 3D islands appear after annealing. These 3D islands probably nucleate on structural defects introduced by the irradiation. This shows that the instability of the 2D layer can be used for controllable nucleation of islands.