A Monte Carlo method-based model of a hot cavity surface ion source with a spherically shaped ionizer is presented. A numerical code enables studies of ion source efficiency as a function of an extraction voltage, geometry of the ionizer and its temperature, the size of extraction aperture and many other factors. The calculation results for a variety of mentioned parameters are presented. A novel configuration of surface ion source is proposed and discussed — the efficiency of the source with an almost spherically shaped ionizer could be much higher than that of currently used constructions of ion sources.