Here, we have designed a novel, to the best of our knowledge, three-terminal AlGaN-based deep-ultraviolet (DUV) laser diode (LD), featuring an AlScN ferroelectric layer beneath the third terminal and a stepped ridge structure. Our findings indicate that when the AlScN layer is negatively polarized by an external bias by the third terminal, the fixed polarization positive charges at the AlScN/p-GaN interface can enhance hole injection efficiency by modulating the energy band in the p-type region near the AlScN layer. The modulation does not deteriorate the electron injection and the optical field confinement, thus effectively increasing the stimulated recombination rate in the active region. As a result, there is a marked reduction in threshold current density, accompanied by a significant rise in output light power. Furthermore, our investigation suggests that the stepped ridge structure can further mitigate the hole lateral diffusion during the hole injection process, ensuring sufficient hole current density. This study, theoretically, offers a novel way to realize high-performance AlGaN-based DUV LD.