We demonstrate the formation of nanoscale volcano-like structures induced by ion-beam irradiation of nanoscale pores in freestanding silicon nitride membranes. Accreted matter is delivered to the volcanoes from micrometer distances along the surface. Volcano formation accompanies nanopore shrinking and depends on geometrical factors and the presence of a conducting layer on the membrane's back surface. We argue that surface electric fields play an important role in accounting for the experimental observations.