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

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 ΔI_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: (ΔI_d/I_d) = (I_loc/I_d)², where Iloc 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 × 35-nm² channel to provide ΔI_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.