3.1.2 Effective Channel Width, Channel Length and Fin Nuember

$\Delta L = LINT + \frac{LL}{(L + XL)^{LLN}} \qquad (3.11)$

$L_{eff} = L + XL - 2 \Delta L \qquad (3.12)$

Here, $\Delta L$ is the overlap/underlap between the gate and the source/drain diffusions; $LINT$ is the $\Delta L$ for large devices; $L$ is the designed (drawn) length; $XL$ is the length variation due to the process effects; $LL$ and $LLN$ are the fitting parameters.

$\Delta L_{CV} = DLC + \frac{LLC}{(L + XL)^{LLN}} \qquad (3.13)$

$L_{eff, CV} = L + XL - 2 \Delta L_{CV} \qquad (3.14)$

Here, $\Delta L_{CV}$ is the overlap/underlap between the gate and the source/drain diffusions for C-V calculations; $DLC$ is the $\Delta L_{CV}$ for large devices; $LLC$ is a fitting parameter.

If $BULKMOD = 1$ and $CAPMOD = 1$ then

$L_{eff,CV,acc} = L_{eff,CV} - DLCACC \qquad (3.15)$

If $GEOMOD = 0$ then

$W_{eff0} = 2 \cdot HFIN - DELTAW \qquad (3.16)$

$W_{eff,CV0} = 2 \cdot HFIN - DELTAWCV \qquad (3.17)$

If $GEOMOD = 1$ then

$W_{eff0} = 2 \cdot HFIN + FECH \cdot TFIN - DELTAW \qquad (3.18)$

$W_{eff,CV0} = 2 \cdot HFIN + FECH \cdot TFIN - DELTAWCV \qquad (3.19)$

If $GEOMOD = 2$ then

$W_{eff0} = 2 \cdot HFIN + 2 \cdot FECH \cdot TFIN - DELTAW \qquad (3.20)$

$W_{eff,CV0} = 2 \cdot HFIN + 2 \cdot FECH \cdot TFIN - DELTAWCV \qquad (3.21)$

If $GEOMOD = 3$ then

$R = \frac{D}{2} \qquad (3.22)$

$W_{eff0} = \pi \cdot D - DELTAW \qquad (3.23)$

$W_{eff,CV0} = \pi \cdot D - DELTAWCV \qquad (3.24)$

$NFIN_{total} = NFIN \cdot NF \qquad (3.25)$

If $BULKMOD \ne 0$,

$COX_{ACC} = COX \cdot \frac{EOT}{EOTACC} \qquad (3.26)$

Case $GEOMOD = 0$ (double gate):

If the values of $TFIN\_TOP$ (top fin thickness of a trapezoidal FinFET) or $TFIN\_BASE$ (base fin thickness of a trapezoidal FinFET) are provided as the model parameters and not passed as the instance parameters,

$W\_UFCM = 2 \cdot HFIN \qquad (3.27)$

$ACH\_UFCM = HFIN \cdot TFIN \qquad (3.28)$

If the values of $TFIN\_TOP$ and $TFIN\_BASE$ are overwritten by the instance parameters passed from the netlist,

$W\_UFCM = 2 \cdot \sqrt{HFIN^2 + \frac{1}{4} \cdot (TFIN\_TOP - TFIN\_BASE)^2} \qquad (3.29)$

$ACH\_UFCM = HFIN \cdot (\frac{TFIN\_TOP + TFIN\_BASE}{2}) \qquad (3.30)$

In both cases,

$CINS\_UFCM = W\_UFCM \cdot EPSROX \cdot \frac{\epsilon_0}{EOT} \qquad (3.31)$

$rc = \frac{2 \cdot CINS\_UFCM}{W\_UFCM^2 \cdot \Big( \dfrac{\epsilon_{sub}}{ACH\_UFCM} \Big)} \qquad (3.32)$

$qdep = -q \cdot NBODY_i \cdot \frac{ACH\_UFCM}{CINS\_UFCM} \qquad (3.33)$

Case $GEOMOD = 1$ (triple gate):

If the values of $TFIN\_TOP$ or $TFIN\_BASE$ are provided as the model parameters and not passed as the instance parameters,

$W\_UFCM = 2 \cdot HFIN + TFIN \qquad (3.34)$

$ACH\_UFCM = HFIN \cdot TFIN \qquad (3.35)$

If the values of $TFIN\_TOP$ and $TFIN\_BASE$ are overwritten by the instance parameters passed from the netlist,

$\begin{aligned} W\_UFCM &= 2 \cdot \sqrt{HFIN^2 + \frac{1}{4} \cdot (TFIN\_TOP - TFIN\_BASE)^2} \qquad (3.36) \\ \\ &+ TFIN\_TOP \end{aligned}$

$ACH\_UFCM = HFIN \cdot (\frac{TFIN\_TOP + TFIN\_BASE}{2}) \qquad (3.37)$

In both cases,

$CINS\_UFCM = W\_UFCM \cdot EPSROX \cdot \frac{\epsilon_0}{EOT} \qquad (3.38)$

$rc = \frac{2 \cdot CINS\_UFCM}{W\_UFCM^2 \cdot \Big( \dfrac{\epsilon_{sub}}{ACH\_UFCM} \Big) } \qquad (3.39)$

$qdep = -q \cdot NBODY_i \cdot \frac{ACH\_UFCM}{CINS\_UFCM} \qquad (3.40)$

Case $GEOMOD = 2$ (quadruple gate):

If the values of $TFIN\_TOP$ or $TFIN\_BASE$ are provided as the model parameters and not passed as the instance parameters,

$W\_UFCM = 2 \cdot HFIN + 2 \cdot TFIN \qquad (3.41)$

$ACH\_UFCM = HFIN \cdot TFIN \qquad (3.42)$

If the values of $TFIN\_TOP$ and $TFIN\_BASE$ are overwritten by the instance parameters passed from the netlist,

$\begin{aligned} W\_UFCM &= 2 \cdot \sqrt{HFIN^2 + \frac{1}{4} \cdot (TFIN\_TOP - TFIN\_BASE)^2} \qquad (3.43) \\ \\ &+ (TFIN\_TOP + TFIN\_BASE) \end{aligned}$

$ACH\_UFCM = HFIN \cdot (\frac{TFIN\_TOP + TFIN\_BASE}{2}) \qquad (3.44)$

In both cases,

$CINS\_UFCM = W\_UFCM \cdot EPSROX \cdot \frac{\epsilon_0}{EOT} \qquad (3.45)$

$rc = \frac{2 \cdot CINS\_UFCM}{W\_UFCM^2 \cdot \Big( \dfrac{\epsilon_{sub}}{ACH\_UFCM} \Big) } \qquad (3.46)$

$qdep = -q \cdot NBODY_i \cdot \frac{ACH\_UFCM}{CINS\_UFCM} \qquad (3.47)$

Case $GEOMOD = 3$ (cylindrical gate):

If the values of $TFIN\_TOP$ or $TFIN\_BASE$ are provided as the model parameters and not passed as the instance parameters,

$W\_UFCM = \pi \cdot D \qquad (3.48)$

$CINS\_UFCM = 2 \cdot \pi \cdot EPSROX \cdot \frac{\epsilon_0}{\log_e1 + 2 \cdot \frac{EOT}{D}} \qquad (3.49)$

$ACH\_UFCM = \pi \cdot D \cdot \frac{D}{4} \qquad (3.50)$

$rc = \frac{2 \cdot CINS\_UFCM}{W\_UFCM^2 \cdot \Big( \dfrac{\epsilon_{sub}}{ACH\_UFCM} \Big) } \qquad (3.51)$

$qdep = -q \cdot NBODY_i \cdot \frac{ACH\_UFCM}{CINS\_UFCM} \qquad (3.52)$

Case $GEOMOD = 4$ (unified model):

$rc = \frac{2 \cdot CINS\_UFCM}{W\_UFCM^2 \cdot \Big( \dfrac{\epsilon_{sub}}{ACH\_UFCM} \Big) } \qquad (3.53)$

$qdep = -q \cdot NBODY_i \cdot \frac{ACH\_UFCM}{CINS\_UFCM} \qquad (3.54)$

$C_{ox} = \frac{CINS\_UFCM}{W\_UFCM} \qquad (3.55)$