The field emission current from a carbon fiber is considered. As a model of emission of an elementary carbon tube, tunnel ionization of an electron from a short-range potential is taken. The exact solution for the wave function in such a model allows obtaining an asymptotic expression for electron current. A computer model of transverse distribution of emission current of a carbon fiber is built on the basis of the Monte Carlo method that allows taking into account the random character of distribution of local emitter sources and the distribution of gains of an electric field in carbon nanotubes.

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We discuss the photon emission that occurs due to the radiative recombination of an electron on a nearby center after tunneling ionization. The model of an active electron is used, and analytical solution to three-dimensional problem is obtained. The dependence of the photon emission from a distance between centers of ionization and a recombination, and also the electric field orientation are investigated. The formulas for probability of recombination radiation are derived.

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In the semiclassical approximation, the density of the electron energy spectrum near the metal surface is described, when electron is bound by the image field and the blocking electrostatic field. In the system under consideration, the confinement mechanism is realized, and the energy spectrum for the motion of an electron in the direction perpendicular to the metal surface is completely discrete. The density of states of the energy spectrum is expressed in terms of elliptic integrals, the argument of which is a sigmoidal function. When the field is turned off, it becomes the Heaviside step function. A dimensionless energy parameter is introduced, which determines the intervals with qualitatively different changes in the width of the classically accessible region of motion. For large positive values of the energy parameter, the spectrum density asymptotically tends to the density in the triangular potential with the addition of the Coulomb logarithmic correction, and for negative values of the energy parameter, the spectrum density tends to dependence for a one-dimensional Coulomb potential. Approximate expressions are obtained for the spectrum density in terms of elementary functions in a wide range of electron energies and electric field strength.