Size dependence of electrostatic lens effect in vertical MOSFETs

The size dependence of the electrostatic lens effect in the channel of a nanoscale vertical pillar-type metal-oxide-semiconductor field-effect transistor (V-MOSFET) is studied by quantum dynamics simulation. Our findings indicate that the applicable diameter of the pillar for the efficient current-path control by the electrostatic lens effect on the V-MOSFET is in the range of about 10-30 nm. In the large-diameter pillar (30 nm diameter), the lens effect at the interfaces between the source and the body, and between the body and the source works well owing to the ballistic transport of electrons. On the other hand, in a slim pillar (10nm diameter or less), the lens effect does not work well, because it is difficult to handle the electron dynamics by the analogy of classical geometrical optics, even though the electrons show ballistic transport. Our results indicate that the proposed technique is applicable for many nanoscale pillar-type devices.