On oscillations of thermionic current in composite systems

Abstract

Thermionic current emitted into vacuum by a composite system consisting of a metal layer of finite thickness L and a metal half-space is investigated. An explicit expression for thermionic current is obtained that takes into account the quantum phenomena of above-barrier reflection and the strong degeneracy of the electron gas in metal at sufficiently low temperatures. Actually, a generalization of the classical Richardson-Dashmen result is obtained for the case of low temperatures. A special emphasis is placed on the effect of impurities contained in the metal half-space and in the layer on the total thermionic current. It is shown that violation of the strictly periodic field of an ideal crystal due to impurities breaks the one-to-one relation between the momenta and the total energy of conductivity electrons. It is shown that the expression for the generalized distribution function depending on independent variables (energy and momentum) is naturally included in the equation for the thermionic current. Numerical analysis shows that the variation in the distribution function of electrons due to the impurity field leads to variation of the total thermionic current emitted from the system. In particular, an oscillating dependence of the thermionic current on the layer thickness and on the impurity concentration in the layer is revealed. All the calculations are performed within the formalism of nonequilibrium Green’s functions.