OPTIMALLY DESIGNED POTENTIALS FOR CONTROL OF ELECTRON-WAVE SCATTERING IN SEMICONDUCTOR NANODEVICES

Control of plane-wave scattering is examined using designed potential structures in solid-state devices with dimensions of the electron coherence length. Reflection coefficients at specified incident electron energies are controlled by exploiting the quantum interference effects associated with the wavelike nature of the electrons through optimally designed manipulation of the solid-generated scattering potential. This work is motivated by the increasing ability to fabricate semiconductor structures with controlled layer thickness and lateral features, and here the goal is to demonstrate the degree of coherent electron control achievable through the employment of optimal design tools. We examine the case where the potential form is restricted to a fixed number of rectangular barriers. Here, the optimization of the design is performed with respect to the barrier width and spacings in order to achieve the desired reflection coefficients at one or more incident energies. We also examine the case where the potential is not restricted to any particular form, and here optimal control theory is employed to optimize the scattering potential form in order to achieve the desired reflection coefficients over a range of incident electron energies. The possibility of extending this work to controlling electron wave-packet structures is also discussed.