We have experimentally measured the terahertz radiation from a series of ion-implanted semiconductors, both from the bare semiconductor surface and from photoconductive switches fabricated on them. GaAs was implanted with arsenic ions, and InGaAs and InP with Fe+ iron ions, and all samples were annealed post implantation. An increase in emission power is observed at high frequencies, which we attribute to the ultrafast trapping of carriers. We use a three-dimensional carrier dynamics simulation to model the emission process. The simulation accurately predicts the experimentally observed bandwidth increase, without resorting to any fitting parameters. Additionally, we discuss intervalley scattering, the influence of space-charge fields, and the relative performance of InP, GaAs and InAs based photoconductive emitters.