The necessary conditions for the occurrence of current oscillation, observed in the current-saturation regime regarding the current-voltage characteristics of semiconductors with a dumbbell-shaped structure, have been investigated by varying the carrier densities through illumination and heat. It is necessary to establish an oscillation of the space-charge layer in the wide region at the anode side at the devices. It is also necessary that the electric field at the boundary between the wide region on the anode side and the narrow region exceeds a critical value, above which the velocity of electrons or holes deviates from Ohm's law and becomes saturated.