Stark effect of electrons in a semiconducting quantum disk

We investigate the effect of an electric field on the electronic energy levels in a semiconducting quantum disk. When the field is applied perpendicular to the axis of the disk, the Stark shift in the electron energy levels depends upon the radius of the disk but not on its height while if the field is applied parallel to the axis of the disk, the Stark shift depends upon the height of the disk but not upon its radius. When the electric field is neither parallel or perpendicular to the axis of the disk, the Stark shift depends upon both the radius and height of the disk as well as the angle between the field and the disk axis. This Stark shift of the electron energy levels leads to an increase in the band gap with electric field.