The terahertz wave generation by spiral photoconductive antennas fabricated on low-temperature In_0.5Ga_0.5As films and In_0.5Ga_0.5As/In_0.5Al_0.5As superlattices is studied by the terahertz time-domain spectroscopy method. The structures were obtained by molecular beam epitaxy on GaAs and InP substrates with surface crystallographic orientations of (100) and (111)A. The pump-probe measurements in the transmission geometry and Hall effect measurements are used to characterize the properties of LT-InGaAs and LT-InGaAs/InAlAs structures. It is found that the terahertz radiation power is almost four times higher for LT-InGaAs samples with the (111)A substrate orientation as compared to (100). Adding of LT-InAlAs layers into the structure with (111)A substrate orientation results in two orders of magnitude increase of the structure resistivity. The possibility of creating LT-InGaAs/InAlAs-based photoconductive antennas with high dark resistance without compensating Be doping is demonstrated.