Graphically Transforming Mueller-Schulz Percolation Criteria to Random Telegraph Signal Magnitudes in Scaled FETs

We propose a novel graphic method to enable the analysis of the field-effect transistor (FET) threshold voltage variation ΔV
_th
due to random telegraph signals in a percolative channel. First, through technology computer-aided design simulation with no percolation, both a minimum ΔV
_th
and a critical curve in a m
_loc
- σ
_loc
plot are produced. The former constitutes a statistical distribution far away from the conventional log-normal one. In the latter, m
_loc
and σ
_loc
are the mean and the standard deviation, respectively, of a well-known normal variable in Mueller-Schulz's percolation theory. The critical m
_loc
- σ
_loc
curve divides the plot into the allowed region and the forbidden region and will go down with increasing gate size. Then, ΔV
_th
contours in the allowed region are graphically created. While applying to existing experimental ΔV
_th
statistical distributions of SiON- and high-k metal gate (HKMG)-scaled FETs, resulting paired m
_loc
and σ
_loc
at high ΔV
_th
remain intact, regardless of gate size or gate stack type. This means that the underlying percolation patterns resemble each other, due to the same manufacturing process used. However, if these paired m
_loc
and σ
_loc
fall in the forbidden region, it is the critical m
_loc
- σ
_loc
curve dominating. Application to bias and temperature instability statistical data in literature is straightforwardly well done.