Quantum States of an Electron Interacting with Various Dielectric Plate Geometries

The tunability of binding energies is explored by modulating a finite dielectric slab width in a planar, three dielectric system. After verifying the equivalence of the field method and method of images, three different configurations are explored for possible control of electronic binding energy: A vacuum gap between a Schottky diode, noble gas layers on a metal wall, and an electron confined between two metal plates. In each, varying the width of the finite, middle dielectric was shown to provide control over the binding energy and Bohr radius of the electron. In the case of an electron confined between two plates, it was found that the bound states smoothly connect to the box states as the gap separation was varied. Lastly, forces on the two parallel plates were examined for a possible source of significant repulsion. All numerical calculations were done in MATLAB.