We have theoretically investigated steady-state carrier transport and current self-oscillation in negative-effective-mass (NEM) p$^$+/pp$^$+/diodes. The current self-oscillation here is a result of the formation and traveling of electric field domains in the p base having a NEM. The dependence of self-oscillating frequency on the applied dc voltage is obtained by detailed numerical simulations. In the calculations, we have considered the scatterings by carrier-impurity, carrier-acoustic phonon, carrier-polar-phonon, and carrier-nonpolar-phonon-hole interactions . This kind of NEM oscillator allows us to reach a current oscillation with terahertz frequency, thus it may be used as a broadband source of terahertz radiation.