Statistical Enhancement of the Evaluation of Combined RDD- and LER-Induced $V_{T}$ Variability: Lessons From $\hbox{10}^{5}$ Sample Simulations

Using full-scale 3-D simulations of 100 000s of devices, enabled by “push-button” cluster technology, we study in detail statistical threshold voltage variability in a state-of-the-art n-channel MOSFET introduced by the combined effect of random discrete dopants (RDDs) and line edge roughness (LER) and demonstrate that the resulting distribution is non-normal. Based on careful statistical analysis of the results, we show how the resulting distribution of V
_T
can be constructed from the distributions arising from the individual simulation of RDD and LER variability. In accomplishing this task, we have deployed computationally efficient statistical enhancement techniques that drastically reduce the computational effort needed to accurately characterize threshold voltage variability under the combined influence of RDD and LER.