3.1.10 Short Channel Effects

The degree of $V_{th}$ roll-off has been modeled through the characteristic field penetration ($scl$), which is written in the unified FINFET model formulation, thus it can be used for FINFETs with complex cross sections.

$scl = \sqrt{\Big( \dfrac{EPSRSUB \cdot ACH}{CINS} \Big) \cdot \Big( 1 + \dfrac{ACH \cdot CINS}{2 \cdot EPSRSUB \cdot WEFF\_UFCM \cdot WEFF\_UFCM} \Big)}$

$(3.203)$

$V_{bi} = \dfrac{kT}{q} \cdot ln \Big( \dfrac{NSD_i \cdot NBODY_i}{n_i^2} \Big) \qquad (3.204)$

$H_{eff} = \sqrt{\dfrac{HFIN}{8} \cdot \Big( HFIN + 2 \cdot \epsilon_{ratio} \cdot EOT \Big)} \qquad (3.205)$

$\lambda = \begin{cases} \sqrt{ \Big( \dfrac{\epsilon_{ratio}}{2} \Big) \cdot \Big( 1 + \dfrac{TFIN}{4 \cdot \epsilon_{ratio} \cdot EOT} \Big) \cdot TFIN \cdot EOT} &\text{if GEOMOD = 0} \\ \\ \dfrac{1}{\sqrt{ \Big[ \Big( \dfrac{\epsilon_{ratio}}{2} \Big) \cdot \Big( 1 + \dfrac{TFIN}{4 \cdot \epsilon_{ratio} \cdot EOT} \Big) \cdot TFIN \cdot EOT \Big]^{-1} + \dfrac{1}{4 \cdot H_{eff}^2} }} &\text{if GEOMOD = 1} \\ \\ \dfrac{0.5}{\sqrt{ \Big[ \Big( \dfrac{\epsilon_{ratio}}{2} \Big) \cdot \Big( 1 + \dfrac{TFIN}{4 \cdot \epsilon_{ratio} \cdot EOT} \Big) \cdot TFIN \cdot EOT \Big]^{-1} + \dfrac{1}{4 \cdot H_{eff}^2} }} &\text{if GEOMOD = 2} \\ \\ \sqrt{ \Big( \dfrac{\epsilon_{ratio}}{2} \Big) \cdot \Big( 1 + \dfrac{R}{2 \cdot \epsilon_{ratio} \cdot EOT} \Big) \cdot R \cdot EOT} &\text{if GEOMOD = 3} \end{cases}$

$(3.206)$