A Statistical Model for the Headed and Tail Distributions of Random Telegraph Signal Magnitudes in Nanoscale MOSFETs

Abstract

Trapping-detrapping of a single electron via an individual trap in metal-oxide-semiconductor field-effect transistor (MOSFET) gate dielectric constitutes two-level random telegraph signals. Recent 3-D technology computer-aided design (TCAD) simulations, on an individual MOSFET, revealed that with the position of the trap as a random variable, resulting random telegraph signals relative magnitude Delta I-d/I-d in the subthreshold current at low drain voltage can have two distinct distributions: a headed one for a percolation-free channel and a tail one for a percolative channel. The latter may be effectively treated by a literature formula: (Delta I-d/I-d) = (I-loc/I-d)(2), where I-loc is the local current around the trap. In this paper, we show how to make this formula practically useful. First, we conduct 3-D TCAD simulations on a 35 x 35-nm(2) channel to provide Delta I-d/I-d for a few positions of the trap. This leads to a new statistical model in closed form, which can reproduce headed distributions. Straightforwardly, key criteria are drawn from the model, which can act as guidelines for the adequate use of the I-loc/I-d formula. Extension to threshold voltage shift counterparts, from subthreshold through transition to inversion, is successfully achieved. Importantly, use of the model may overcome the drawbacks of the statistical experiment or simulation in the field.