We have examined the responses of GaAs, InP, InAs, and AlAs to 30 keV focused ion beam ͑FIB͒ irradiation and applied a unified model that consistently explains the observed effects. Nanodots were observed to form on GaAs, InP, and InAs under irradiation at normal incidence, while nanodots are not observed on AlAs. The FIB response and nanodot formation behavior of each material is discussed with regard to a few basic material properties and a model for nanodot creation and growth by the action of preferential sputtering and Ostwald ripening. The model predicts the development of a stable average nanodot size with increasing ion dose, with the average nanodot size depending on the excess group III adatom yield, adatom surface diffusion rate, and surface tension. These predictions qualitatively agree with the experimentally observed trends for GaAs and InP. They also agree for the initial nanodot formation on InAs, but this material system exhibits a sudden transition in the nanodot size distribution. The model predicts that nanodots will have difficulty forming and growing on AlAs, which is also in agreement with our experimental results.