We study experimentally and theoretically the controlled field evaporation of single atoms from a semiconductor surface by ultrafast laser-assisted atom probe tomography. The conventional physical mechanisms of field evaporation cannot explain the experimental results recently reported for such materials. A new model is presented in which the positive dc field leads to band bending with a high density of laser-generated holes near the surface of the sample. The laser energy absorption by these holes and the subsequent energy transfer to the lattice considerably increase the tip temperature. We show that this heating plays an important role in the field ion emission process. In addition, experiments are carried out for germanium and silicon tips to check the role of the dc field in the absorption processes, as well as the heating of the tip and the following evaporation. Good agreement between the predictions of our model and the experimental data is found.