This work presents a comprehensive detailed comparative study of the three ultra-wideband and high directive antennas for the THz imaging, spectroscopy, and communication applications. Three different types of photoconductive antennas (log-spiral, Vivaldi, and bowtie antennas) are designed and simulated in the frequency range of 1 to 6 THz in the CST microwave studio (MWS). The enhanced directivity of the designed PCAs is achieved with the integration of the hemispherical silicon-based lens with the PCA gold electrode and quartz substrate of the proposed antennas. The performance of the designed PCAs is compared in terms of impedance and axial ratio bandwidths, directivity, and radiation efficiency of the proposed antennas. The reported log spiral, Vivaldi PCAs with added silicon lens exhibit the -10 dB impedance bandwidth of 6 THz, 3dB AR bandwidth of 5 THz, 6 THz, and 6 THz and peak total radiation efficiencies of 45%, 65%, and 95% respectively.