Analytical explanation to double-hump substrate current in funnel-shape transistors

Measurements of double-hump substrate current and enhanced gate current in funnel-shape (FS) MOSFET´s have been recently reported [1]. In this letter an analytical explanation of these observations is given. It is shown that contrary to conventional transistors, the maximum lateral field along the channel of FS transistors operated in the wide-drain mode, and therefore the hot-carrier generation region, is shifted towards the source side as the gate voltage is increased. In addition, the maximum lateral field is increased at high gate voltages, giving rise to the abnormal increase of the substrate current. These results are derived from a simple one-dimensional solution of FS transistor characteristics.