  We consider two possible mechanisms for single-vortex fluctuative entry/exit
through the surface barrier in ultrathin superconducting disk-shaped
nanoislands made of Pb and consisting of just few monoatomic layers, which can
be fabricated using modern techniques. We estimate tunnelling probabilities and
establish criteria for the crossover between these two mechanisms depending on
magnetic field and system sizes. For the case of vortex entry, quantum
tunnelling dominates on the major part of the temperature/flux phase diagram.
For the case of vortex exit, thermal activation turns out to be more probable.
This nontrivial result is due to the subtle balance between the barrier height
and width, which determine rates of the thermal activation and quantum
tunneling, respectively.
