We developed the scheme of terahertz (THz) surface magnetoplasmons (SMPs) over n-type semiconductor by an electron beam in the presence of an external magnetic field. Electron beam bunching by SMPs generates perturbed current density and develops THz SMPs by resonant Cherenkov interaction. More beam energy is required for the generation of high-frequency THz SMPs in the presence of large applied magnetic field. Growth rate of Cherenkov THz SMPs grows with THz frequency and attains a maximum value and then falls off with THz frequency. It grows with temperature and decreases with the electron cyclotron frequency. Growth rate is directly proportional to beam density's cube root and inversely proportional to [Formula: see text], where [Formula: see text] is relativistic factor of incident electron beam. The proposed mechanism may develop an actively tunable device for the generation of THz SMPs due to growth rate dependence on semiconductor temperature, applied magnetic field, and electron beam energy. The beam energy of [Formula: see text]–[Formula: see text] is used for the excitation of SMPs 0.81–2.3 THz.