Ballistic scattering of electrons by a parabolic cylinder repeller in two-dimensional structures
The distributions of charge and current density resulting from ballistic electrons incident on a two-dimensional parabolic repeller barrier are obtained. Formulae for incidence at an angle are derived, utilizing as initial electron state a wavepacket locating the particle at the source and carrying the electron momentum. Numerical calculations have been performed with expected electron energies below the barrier height so that the transmitted current is of tunnelling origin. When the electrons leave the source at zero speed the resulting distributions are symmetrical about the perpendicular drawn from the source to the barrier axis. The case of incidence at angle pi /3 and a small initial momentum is also studied. Polar diagrams depicting the current field components and the charge distributions round various circles centred at the point of incidence are given. For each circle there are two current maxima, one corresponding to transmission and the other to reflection. The locus of the positions round the various circles where the magnitude of the current field acquires maximum values coincides with the corresponding locus for the charge distribution, apart from a region in the vicinity of the point of incidence in which case the charge distribution does not exhibit distinct maxima in the transmitted region. The hydrodynamic picture obtained for the electron cloud may be useful to experimenters involved in two-dimensional ballistic arrangements, as can be attained at the interface of certain semiconductors.