We present an analytical theory of the experimentally observed enhanced impact ionization rate in multiquantum well structures, which is based on a modification of Schockley’s [Solid State Electron.2, 35 (1961)] lucky electron theory. The general expression always predicts an enhancement in the ionization rate over the corresponding bulk value. The model is compared to both Monte Carlo calculations and recent experimental results. It is concluded that owing to the nonlinear aspects of impact ionization, the ionization rate can be significantly enhanced by the superposition of a uniform electric field and any spatially periodic electric field.