Simulations of photon-assisted tunneling using the Fokker–Planck equation to model the scattering of electrons within the emitting metal tip

A method to simulate photon-assisted tunneling is developed, and applied to model laser-assisted field emission from metals. Our simulations show that most of the exchange of quanta between the electrons and the radiation occurs within the emitting metal tip. In typical experiments (λ=670 nm with tungsten metal) the depth of penetration for the radiation is four times the mean free path for electrons at the Fermi level, so it is necessary to allow for scattering. We use a Floquet expansion with the time-dependent Schrödinger equation to allow for the exchange of quanta between the electrons and the radiation field. Multiparticle effects are modeled with the density functional theory within the local density approximation for the Kohn–Sham exchange and correlation, and the Fokker–Planck formulation is used to determine the effects of scattering on the energy distribution of the electrons.