3.9 Lateral Non-Uniform Doping Model

Lateral non-uniform doping along the length of the channel leads to I-V and C-V displaying different threshold voltages. However, the consistent surface potential based I-V and C-V model doesn’t allow for the usage of different $V_{th}$ values. A straightforward method would be to re-compute the surface potentials at the source and drain ends twice for I-V and C-V separately, breaking the consistency but at the expense of computation time. The below model has been introduced as a multiplicative factor to the drain current (I-V) to allow for that $V_{th}$ shift. This model should be exercised after the C-V extraction step to match the $V_{th}$ for the subthreshold region $I_{d,lin}-V_g$ curve. Parameter $K0$ is used to fit the subthresold region, while parameter $K0SI$ and $K0SISAT$ helps reclaim the fit in the strong inversion region.

$M_{nud} = exp \Bigg[- \dfrac{K0(T)}{\Big( max(0, K0SI(T) + K0SISAT(T) \cdot dqi \cdot dqi) \cdot q_{ia} + 2.0 \cdot \frac{nKT}{q} \Big)} \Bigg]$

$(3.349)$