Characteristics of the propagation of electron waves in coupled-quantum-well waveguides in a transverse electrostatic field

We investigate how the presence of a transverse electrostatic field influences the propagation properties of guided electron waves in coupled-quantum-well waveguides. The basis eigenstates of electrons in the uncoupled quantum well in the presence of a transverse electric field are calculated by using the Airy-function approach and the transfer-matrix method. By decomposing the eigenfunctions of electrons in the coupled double quantum wells in terms of the basis eigenfunctions of the individual wells, the expression for the mode-amplitude functions (MAF) for various bare states in the wells is presented. By setting up appropriate initial boundary conditions one can simulate different electron-injection conditions for the system and study how the electron waves evolve among the various states. By varying the bias, different configurations of electron-state structure can be formed. When a pair of matching states are produced in the wells, the electron-wave transfer takes place mainly between these matching bare states. The particular patterns of the transfer depend on the injection conditions and the energy of the incident electron. The variation of the magnitude of the MAF’s can have a sinusoidal-like oscillation or the profile of a rapid decay (growth) from unity (zero) to a plateau imposed upon a small-amplitude oscillation. When all the bare states are mismatched the transfer of electron waves may still occur between two states with close energy levels in the channels. We also show the influence of multimodes on the variation of the magnitude of MAF. This leads to some oscillations imposed on the original sinusoidal-like function and causes incomplete transfer between pairs of states in the channels. Therefore, the pattern of the electron-wave transfer in channels may be controlled and modified by applying a transverse electrostatic field in the coupled-quantum-well waveguide.