DYNAMICAL EFFECTIVE POTENTIALS IN ELECTRON-TUNNELING

Dynamical screening of electrons tunneling in the metal-insulator-meta l system is treated generalizing the Jonson's nonlocal theory of excha nge-correlation potential and the effective barrier concept. The self- energy is evaluated within the GW approximation for electrons coupled to the long-wavelength charge-density oscillations. Potentials are cal culated self-consistently, and compared with non-self-consistent resul ts, and those obtained within the local limit. We show that the concep t of effective potential is valid only for electron energies below the top of the barrier, and for these energies there is usually no need f or a self-consistent treatment. We also show that effective potential does not vary appreciably with electron energy when this energy is bel ow the top of the barrier and far from the surface plasmon energies.