A new simplified two-dimensional model for the threshold voltage of MOSFET's with nonuniformly doped substrate

Pole-Shang Lin, Ching-Yuan Wu
1991 IEEE Transactions on Electron Devices  
A new simplified two-dimensional model for the threshold voltage of MOSFET's is derived in terms of simple characteristic functions. These characteristic functions are transformed from the exact series solution of the two-dimensional Poisson's equation, in which the effects of a nonuniformly doped substrate and a finite graded source-drain junction depth have been included. The attractive features of the developed model are: 1) charge-screening effects are proposed to account for the weak
more » ... for the weak dependence of the threshold voltage on the substrate bias for short-channel MOSFET's, and 2) exact source and drain boundary potentials can be approximated by their equivalent power functions. The accuracy of the simplified 2-D model has been verified by 2-D numerical analysis. Moreover, comparisons between the simplified 2-D model and the experimental results have been made, and good agreement has been obtained for wide ranges of channel lengths, applied substrate, and drain biases.
doi:10.1109/16.81629 fatcat:wdnjdvkld5bzni37xcd55zjrgi