The photoconductive antenna is a kind of widely used broadband terahertz (THz) radiation source in THz time-domain spectroscopy systems, and the substrate material of the antenna is crucial for the characteristics of generated THz wave. The widely used photoconductive antenna material is the second-generation semiconductor of GaAs, while the third-generation semiconductor has a larger band gap, which is more advantageous for improving the power of THz wave from photoconductive antenna. In this work, the current surge model of large-aperture photoconductive antennas was used to simulate the characteristics of THz waves radiated by the photoconductive antenna made from commonly used SI-GaAs and LT-GaAs, and the third-generation semiconductors (ZnSe, GaN, SiC) that are expected to be used in the future for photoconductive antennas. The results show that under the same bias electric field and their respective highest pump laser flux, LT-GaAs antenna generates THz waves with the highest amplitude and widest frequency. The photoconductive antenna made by the third-generation semiconductor materials can withstand higher bias electric fields, and the intensity of radiated THz waves is much greater than that from GaAs antennas under their respective maximum bias electrical fields. This work provides theoretical guidance for the development of new third-generation semiconductor photoconductive antennas.