We demonstrate the generation of terahertz (THz) pulses with electric field strength reaching 34 kV/cm from low-temperature-grown GaAs (LT-GaAs) interdigitated photoconductive antennas driven by 1030 nm optical pulses delivered by a commercial ytterbium-doped fiber laser operating at a repetition rate of 200 kHz. By probing the Urbach absorption in LT-GaAs layers, we show that the THz generation mechanism predominantly relies on the photoexcitation of electrons from the valence band to shallow defect states arising from the incorporation of excess As during the growth process. Our THz source opens the route toward nonlinear time-resolved study of low-energy excitations in matter with high signal-to-noise ratios.