Pumping n-type GaAs and InSb with ultrafast THz pulses having intensities higher than 150 MW/cm^2 shows strong free-carrier absorption saturation at temperatures of 300 K and 200 K, respectively. If the energy imparted to the carriers exceeds the bandgap, impact ionization processes can occur. The dynamics of carrier cooling in GaAs and impact ionization in InSb were monitored using THz-pump/THz probe spectroscopy, which provides both sub-bandgap excitation and probing, eliminating any direct optical electron-hole generation that complicates the evaluation of results in optical pump/THz probe experiments.