Forming of wave packets by one-dimensional tunneling structures having a time-dependent potential

Abstract

We study the influence of a relatively small (in a classical sense) arbitrary time-dependent electrical pulse on the transmission amplitude of one-dimensional tunneling and resonant-tunneling structures. The transmission amplitude is found with use of semiclassical perturbation theory. First, the simplest tunneling structure\char22{}a potential barrier\char22{}is considered. It is shown that the form of the outgoing wave packet is sensitive to the presence of poles of the potential in the complex plane of time. For instance, a potential pulse with a single-peak time dependence can generate an outgoing wave packet with a number of peaks related to complex poles. Next, an expression for the transmission amplitude of arbitrary one-dimensional structure is obtained under the assumption that the time-dependent part of the potential is independent of the coordinate inside the structure. Then a resonant-tunneling double-barrier structure is considered. The expression for the transmission amplitude is simplified in this case, making use of the Breit-Wigner approximation. As examples we consider the switching-on of a potential, constant in time, and a potential with a linear time dependence. It is shown, in the nonadiabatic case, that at the moment of switching the outgoing flux begins to oscillate, with the amplitude of oscillation vanishing with time. We consider also the charge-accumulation process during one-dimensional resonant tunneling of monoenergetic electrons and study the conditions of intrinsic stability of a double-barrier structure.