We present a systematic analysis of the hole transport over heterobarriers in the InGaAs(P)/InP material system. The experiments have been performed on our recently developed all-optical switching structures [C. Knorr &etal;, Appl. Phys. Lett.69, 4212 (1996)], which offer an elegant access to hole transport rates. We have varied barrier thickness, barrier height, bias voltage, and temperature. The time constants vary from 30 &mgr;s to 30 ns. Our model calculations, including all heavy and light hole subbands, show that only thermally assisted tunneling can explain both the temperature and electric field dependence of the transport rates. We have extracted the activation energies. The hole capture time is determined as250±50 fs.©1998 American Institute of Physics.