On the tunnelling of electrons out of the potential well in an electric field

Abstract

The exact solution of the nonstationary problem of the tunnelling of electrons out of the one-dimensional potential well by the steady electric field when it is suddenly switched on is obtained. The formula for the tunnel current density is found. The results obtained are compared with those of stationary tunnelling theory that corresponds to the adiabatic switching on of the electric field. It is noted that the especially strong dependence of the tunnel current on the way the electric field is switched on arises in the case of the well with a few bound states. This dependence should ba taken into account while analysing experimental data on tunnelling (atom ionisation, for example) in an electric field.