Efficient simulations of 6σ VT distributions due to Random Discrete Dopants

Previously published 3D simulations of 10⁵ statistical samples have shown distinct asymmetry in Random Discrete Dopant induced threshold voltage variations in Bulk MOSFETs. Based on detailed statistical analysis of the underlying physical processes that shape such distributions we present a robust method, capable of accurately predicting random discrete dopant induced threshold voltage variation out to 6-7sigma from the mean. This methodology can be used to dramatically reduce the computational cost associated with accurately determining the effect of Random Dopant distribution on threshold voltage in bulk MOSFETs.