Calculation of Fin width for bulk inversion in Si FinFET by applying supersymmetry

Abstract

The transition from surface inversion to bulk inversion in a Si FinFET is investigated in this paper using supersymmetric quantum mechanics. A double quantum well potential, which is the supersymmetric partner of a harmonic oscillator potential, was chosen. The fraction of charge residing inside the bulk was calculated as a function of fin width and electron density. For any electron density, more charge resides in the bulk as the fin width decreases. On the other hand, for a fixed fin width, charges move to the surface as the electron density increases. It was found that in Si FinFET for the electron density of 3×1012 cm−2 bulk inversion occurs when the fin width is about 8 nm.