Stationary resonance of electron flows in structures with modulated dielectric permittivity

Abstract

It is demonstrated that the resonant mechanism on inhomogeneities formed for a fixed distribution of dielectric permittivity can underlie the directed self-organization of the electron flow in semiconductors. The behavior of the resonant flow velocity amplitudes depending on the inhomogeneity factors is considered in the ballistic regime.Prigogin and Nicolis [1] considered the self-organizing processes that laid a foundation for the development of thermodynamics of nonequilibrium processes. Among such processes is the formation of spatially-periodic structures (SPS) in the process of electron motion through nonequilibrium plasma. This is due to the fact that the working electric field strength Е, as a rule, is large compared to kТ/еl, where k is the Boltzmann constant, Т is the temperature, е is the electron charge, and l is the characteristic size of the semiconductor structure. In the ballistic (collisionless) regime (BR), this length l is smaller than the momentum relaxation length (l i ). In the quasiballistic regime (QR), when individual scattering events are observed, the above-indicated lengths coincide. At present, GaAs-based structures with total thickness of 1-2 μm can be prepared by the molecular beam epitaxy method in which the BR is observed at temperature Т = 77 K [2]. The BR can also be realized in Ge with thickness of 20 μm at the temperature of liquid helium [3]. At these thicknesses, the main properties of the medium (including its dielectric permittivity) retain their physical meaning, which provides the possibility of application of the classical electrodynamic approach. Bannov et al.[4], who considered the influence of collisions with optical phonons on the dynamics of electron motion, should also be mentioned. When the energy transferred to the electron is higher than the energy of the optical phonon, the electron virtually instantly emits an optical phonon and is scattered on phonons, thereby leading to the transition from the BR to the QR and further to the drift regime. Therefore, low-energy regimes are conventionally used to fulfill the BR and QR conditions.In [5], the influence of a neutralizing positive charge on the SPS formation in an electron flow moving in vacuum was investigated, and the electron response on the inhomogeneous distribution of the neutralizing positive charge was determined. Whereas in vacuum the velocity of directed motion v can be easily made greater than the thermal velocity v t , in semiconductors this condition is realized in the BR, that is, at low temperatures and in highquality structures. The physical reason for the SPS formation during electron beam propagation in vacuum is the Coulomb interaction of electrons with the neutralizing positive charge. In semiconductor structures with variable dielectric permittivity, in addition to the Coulomb mechanism which is much weaker, the SPS formation and resonant properties are caused by the mechanism of forming a built-in gradient of the dielectric permittivity χ and grouping the electron flow due to this effect. In...