Dynamical effects in electron tunneling: Self-consistent semiclassical image potentials

The problem of dynamical screening and local potentials for electrons tunneling in the metal-insulator-metal system is treated in the self-consistent GW approximation. The self-energy is evaluated for electron coupling to the long-wavelength charge-density oscillations. The analytic results for dynamical image potentials, obtained in the semiclassical (local) limit, contain explicitly the competing influences of screening dynamics, tunneling electron energy, and recoil. The role of dynamical image potentials on the tunneling rates for thin barriers is discussed.