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.