3.15.6 Fringe Capacitances and Capacitance Model Selectors

The fringing capacitance consists of a bias-independent outer fringing capacitance and a bias-dependent inner fringing capacitance. Only the bias-independent outer fringing capacitance is modeled.

BSIM-CMG offers 3 models for the outer fringe capacitance, selected by $CGEOMOD$:

For $CGEOMOD = 0$, the fringe and overlap capacitances are proportional to the number of fins and the effective width. The fringe capacitances is given by:

$C_{gs,fr} = NFIN_{total} \cdot W_{eff,CV0} \cdot CFS_i \qquad (3.486)$

$C_{gd,fr} = NFIN_{total} \cdot W_{eff,CV0} \cdot CFD_i \qquad (3.487)$

Figure 7 illustrates the parasitic resistance and capacitance network used for $CGEOMOD = 0$.

Figure 7: R-C network for $CGEOMOD = 0$, $NQSMOD = 1$, and $RGATEMOD = 1$. If $NQSMOD$ or $RGATEMOD$ is 0, then the corresponding resistances become 0 and the nodes collapse.

In some multi-gate applications the parasitic capacitances are not directly proportional to the width of the device. BSIM-CMG offers $CGEOMOD = 1$ so that the fringe and overlap capacitance values can be directly specified without assuming any width dependencies. The simple expressions for fringe and overlap capacitances in $CGEOMOD = 1$ are:

$C_{gs,ov} = COVS_i \qquad (3.488)$

$C_{gd,ov} = COVD_i \qquad (3.489)$

$C_{gs,fr} = CGSP \qquad (3.490)$

$C_{gd,fr} = CGDP \qquad (3.491)$

Note: The switch $CGEO1SW$ can be used to enable the parameters $COVS$, $COVD$, $CGSP$, and $CGDP$ to be in F per fin, per gate-finger, per unit channel width.

The parasitic resistance and capacitance network for $CGEOMOD = 1$ is illustrated in Fig. 8.

Figure 8: R-C network for $CGEOMOD = 1$, $NQSMOD = 1$, and $RGATEMOD = 1$. If $NQSMOD$ or $RGATEMOD$ is 0, then the corresponding resistances become 0 and the nodes collapse.

If $CGEOMOD = 2$, an outer fringe capacitance model for variability modeling which address the complex dependencies on the FinFET geometry will be invoked. $RGEOMOD = 1$ and $CGEOMOD = 2$ share the same set of input parameters and can be used at the same time. Both models are derived based on the FinFET structure (single-fin or multi-fin with merged source/drain).

In $CGEOMOD = 2$ the fringe capacitance is partitioned into a top component, a corner component and a side component (Fig. 9). The top and side components are calculated based on a 2-D fringe capacitance model, which has been derived and calibrated to numerical simulation in [14]. The corner component is calculated based on the formula of parallel plate capacitors.

$C_{fr,top} = C_{fringe,2D}(H_g, H_{rsd}, LRSD) \times TFIN \times NFIN \qquad (3.492)$

$C_{fr,side} = 2 \times C_{fringe,2D}(W_g, T_{rsd}, LRSD) \times HFIN \times NFIN \qquad (3.493)$

$C_{corner} = \dfrac{\epsilon_{sp}}{LSP} \cdot [A_{corner} \times NFIN + ARSDEND + ASILIEND] \qquad (3.494)$

where

$H_g = TGATE + TMASK \qquad (3.495)$

$T_{rsd} = \dfrac{1}{2} (FPITCH - TFIN) \qquad (3.496)$

$W_g = T_{rsd} - TOXP \qquad (3.497)$

$H_{rsd} = HEPI + TSILI \qquad (3.498)$

$ARSDEND$ and $ASILIEND$ are the additional area of silicon and silicide, respectively, at the two ends of a multi-fin FinFET.

The three components are summed up to give the total fringe capacitance. Several fitting parameters are added to aid fitting. The final expression is:

$\begin{aligned} C_{fr,geo} &= (C_{corner} + C_{fr,top} + CGEOE \cdot C_{fr,side}) \times NF \times \\ &[CGEOA + CGEOB \cdot TFIN + CGEOC \cdot FPITCH + CGEOD \cdot LRSD] \end{aligned}$

$(3.499)$

Figure 9: Illustration of top, corner and side components of the outer fringe capacitance.

For the case of $TMASK > 0$ the fringe capacitances are calculated a little differently, since the 2D model is valid only for a thin $T_{ox}$. $C_{corner}$ is set to 0. $C_{fr,top}$ is proportional to $FPITCH$ and is given by

$\begin{aligned} C_{fr,top} &= \Bigg[ 3.467 \times 10^{-11} \cdot ln \Bigg( \dfrac{EPSRSP \cdot 10^{-7}}{3.9 \cdot LSP} \Bigg) + 0.942 \cdot H_{rsd} \cdot \dfrac{\epsilon_{sp}}{LSP} \Bigg] \times \\ &[TFIN + (FPITCH - TFIN) \cdot CRATIO] \cdot NFIN \end{aligned}$

$(3.500)$

The RC network has the same topology as $CGEOMOD = 0$.

And finally,

$C_{ds,fr} = CDSP$

for all $CGEOMOD$.

References

[14] W.-M. Lin, F. Li, D. D. Lu, A. M. Niknejad, and C. Hu, "A Compact Fringe Capacitance Model for FinFETs," unpublished.