Statistical Modeling and Simulation of Threshold Variation Under Random Dopant Fluctuations and Line-Edge Roughness

The threshold voltage (
V
_th
) of a nanoscale transistor is severely affected by random dopant fluctuations and line-edge roughness. The analysis of these effects usually requires atomistic simulations which are too expensive in computation for statistical design. In this work, we develop an efficient SPICE simulation method and statistical variation model that accurately predict threshold variation as a function of dopant fluctuations and gate length change caused by lithography and the etching process. By understanding the physical principles of atomistic simulations, we: 1) identify the appropriate method to divide a nonuniform gate into slices in order to map those fluctuations into the device model; 2) extract the variation of
V
_th
from the strong-inversion region instead of the leakage current, benefiting from the linearity of the saturation current with respect to
V
_th
; 3) propose a compact model of
V
_th
variation that is scalable with gate size and the amount of dopant and gate length fluctuations; and 4) investigate the interaction with non-rectangular gate (NRG) and reverse narrow width effect (RNWE). The proposed SPICE simulation method is validated with atomistic simulation results. Given the post-lithography gate geometry, this approach correctly models the variation of device output current in all operating regions. Based on the new results, we further project the amount of
V
_th
variation at advanced technology nodes, helping shed light on the challenges of future robust circuit design.