One-side bound states are very important in vertical resonant tunneling devices which contain either lightly doped spacers or a small band-gap pseudomorphic layer adjacent to the barriers. By a proper choice of the boundary conditions, these states are modeled by stationary wave functions which contain the relevant information of the quasi-two-dimensional system under steady-state conditions. In particular, the wave functions allow the calculation of their contributions to the self-consistent charge density and the electrical current. In qualitative agreement with experimental results, it is demonstrated that the main resonant features of the current-voltage characteristic of these devices are due to resonant tunneling from an emitter two-dimensional electron gas. Finally, the proposed model is compared with a previous picture of other authors. © 1995 American Institute of Physics.