OPTIMALLY DESIGNED POTENTIALS FOR CONTROL OF ELECTRON-WAVE SCATTERINGIN SEMICONDUCTOR NANODEVICES

Control of plane-wave scattering is examined using designed potential structures in solid-state devices with dimensions of the electron cohe rence length. Reflection coefficients at specified incident electron e nergies 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. Th is work is motivated by the increasing ability to fabricate semiconduc tor structures with controlled layer thickness and lateral features, a nd here the goal is to demonstrate the degree of coherent electron con trol achievable through the employment of optimal design tools. We exa mine the case where the potential form is restricted to a fixed number of rectangular barriers. Here, the optimization of the design is perf ormed with respect to the barrier width and spacings in order to achie ve the desired reflection coefficients at one or more incident energie s. We also examine the case where the potential is not restricted to a ny particular form, and here optimal control theory is employed to opt imize the scattering potential form in order to achieve the desired re flection coefficients over a range of incident electron energies. The possibility of extending this work to controlling electron wave-packet structures is also discussed.