Alternating space charge and ambiguity of quantum states in double-barrier structures

Summation of a series of perturbation theory was used to obtain a solution to the time-dependent self-consistent Schrödinger and Poisson equations describing the resonance interaction of electrons that tunnel through asymmetric double-barrier structures with a high-frequency electric field. In the case where electrons are uniformly distributed in energy within the width of the quasi-level, the solution is obtained analytically; if the beam is monoenergetic, solution of the equation is reduced to finding the roots of a fifth-degree algebraic polynomial. It is shown that, in a number of cases, the influence of alternating space charge gives rise to an effect that is quite new for the systems under consideration: several different wave functions may correspond to the same amplitude of the high-frequency voltage applied to the structure; consequently, the values obtained for the high-frequency conductivity and the coefficients of transmission and reflection can differ by several times. As a result, instability of the current flow and hysteresis of the current-voltage characteristics can be observed in these structures. Furthermore, the dependence of the coefficients of transmission and reflection of the electrons and high-frequency conductivity on the voltage amplitude are combinations of the N-and S-shaped characteristics for uniform distribution of electrons and are looplike in the case of a monoenergetic beam.