Probing a nonuniform two-dimensional electron gas with random telegraph signals

We observe a sequence of two-level random telegraph signals (RTSs) in the drain/source current of a 1.7nm gate oxide silicon metal-oxide-semiconductor field-effect transistor. The RTS magnitude is transformed into the apparent Debye length around a negatively charged oxide trap. We achieve excellent reproduction of the Debye data (40 down to 5nm). This leads to the quantified area spanned by the dominant conductive percolation paths in the underlying two-dimensional electron gas (2DEG). We find that most of the 2DEG in inversion is recovered in a largest threshold voltage sample (∼0.35V), while for the lowest threshold (∼0.15V), a certain conductive filament is likely to occur. The gate direct tunneling current further corroborates the percolation picture.