Potential profiles near the Schottky nanocontacts

The conventional Schottky model describes in the mean-field approximation the electrostatic potential appearing in a doped semiconductor during its flat contact with a metal. More recently, the Schottky model has been used to describe the mean-field potential profile near a metallic nanosphere surrounded by or located on the surface of a semiconductor. We present the corresponding results for a metallic nanowire. In these three cases, the shape of the potential profiles and their scalings are very different. In particular, the full width at half maximum of the potential barrier dramatically shrinks if the geometry changes from linear to cylindrical and then to spherical. In addition, we scrutinize the effect of the discreteness of the dopant charges on the potential near a metallic nanosphere.