In this study we theoretically and numerically demonstrated a 3-D plasmonic terahertz waveguide made up of two parallel plates of semiconductor sandwiching a thin region of vacuum/air. The semiconductor can reveal conductive properties at the THz regime, making it an appropriate replacement for structured metallic surfaces in plasmonic devices. The proposed waveguide configuration not only offers an extra degree of freedom to tailor the propagation of THz wave but also promises more confinement compared to the planar waveguide configuration. The dispersion relations of the terahertz surface plasmon polaritons as they propagate in the proposed configuration is calculated using the Drude model. It is observed that the dispersion behavior of the modes is altered by the carrier densities of the plates and the separation between them. We also numerically analyze the terahertz surface waves propagation in the proposed geometry and examine terahertz surface modes behavior in conjunction with the theory. For the tapered configuration, we observed that the transmission amplitude increases as the tapering angle increases for the same input width. The present study could be significant in the construction of terahertz active and passive devices that may utilize semiconductors instead of metals.