We analyze electron tunneling between semiconductor bands and insulator traps at a semiconductor-insulator interface in terms of a Born-Oppenheimer model. For insulator traps which exhibit large electron-phonon interactions this model predicts tunneling processes analogous to optical Franck-Condon transitions, i.e., tunneling followed by atomic relaxation at the defect. Such ideas go back to Gurneys treatment of electrolysis, but have not appeared in the current interface literature. We estimate the relaxation energies for a model of the E center in silicon dioxide and argue that the hysteresis observed by Zvanut et al. in band-to-trap tunneling in Si-SiO2 most likely arises from such a process, which we call hysteretic tunneling. We suggest that such processes should occur in other cases involving insulating defects which exhibit large electron-lattice coupling. © 1990 The American Physical Society.