Critical distance method for predicting the tail part of the threshold voltage distribution

As a source of the tail of the statistical distribution of MOSFET threshold voltage distributions, we identified how the potential chain extending from one width edge of the channel to the other width edge creates an abnormally large V_T shift, using 3-D TCAD simulations. The critical distance between two adjacent fixed charges in a potential chain that is required to block the channel current has been identified, and its dependence on parameters has been verified. Using the critical distance, the probability of the occurrence of the worst case scenario, in which source to drain current is blocked by the potential chain, for 1 billion transistors has been predicted through percolation method.