Polarization Effect Due to Discreteness of Dopants in Nanoscale MOSFETs

We study the polarization effects associated with the discreteness of dopants at the interface in metal-oxide-semiconductor field-effect-transistors (MOSFETs) by drift-diffusion simulations. A charge distribution model, which reproduces the long-range Coulomb potential consistently with a dielectric mismatch at the interface between semiconductor substrate and oxide, is incorporated into simulations, and the impact on statistical variability in threshold voltage in nanoscale MOSFETs is clarified. We explicitly and quantitatively show, for the first time, that the threshold voltage is shifted due to the polarization charge at the interface induced by the discreteness of dopants in the semiconductor substrate.