Theory of Breakdown Position Determination by Voltage- and Current-Ratio Methods

A theory of the current-ratio (CR) technique in uniform semiconductors, which is widely used to locate gate oxide breakdown (BD) spots in one dimension (i.e., distance from source or drain), is proposed and verified. The theory shows that the CR method is a special case of generalized van der Pauw technique and, as such, can easily be generalized to locate oxide BD spots in two dimensions. We develop the theoretical framework of this new class of BD-spot characterization techniques and then validate the theory by experiments. We conclude by discussing the implications of locating BD spots in two dimensions for reliability projections of ultrathin gate oxides.