4.3.2 Results

The body contact provides a current path in the third-dimension. Since the resistance of this current path cannot be arbitrarily reduced without degrading the transistor performance, the body potential depends on the position under the gate and the devices can no longer be considered two-dimensional.

In CMOS technology higher drain currents are obtained by increasing the width

of the devices. When this approach is applied to body contacted SOI MOSFETs [156,157] a scaling limit can be found given by the potential drop in the body area. A comparison of two- and three-dimensional simulation results with and without impact ionization (II) for SOI MOSFETs is shown in Fig. 4.15, Fig. 4.16, and Fig. 4.17 for gate widths of $w=1\,\mathrm{\mu m}$ , $w=5\,\mathrm{\mu m}$ , and $w=10\,\mathrm{\mu m}$ , respectively.

For $w=1\,\mathrm{\mu m}$ no kink is visible in the drain current but slight differences compared to the two-dimensional result are obtained (introduced by narrow channel effects). For $w=5\,\mathrm{\mu m}$ still no kink is visible in the drain current but a slightly higher drain current is obtained for higher bias. However, for low bias, the two- and three-dimensional results are identical which means that the narrow channel effect can be neglected for this device width. For $w=10\,\mathrm{\mu m}$ , however, the resistance of the current path in the substrate is too high and the excess carriers cannot be sufficiently drained off. Thus, the threshold voltage of the device is reduced which causes a strong kink in the drain current.

Fig. 4.18, Fig. 4.19, and Fig. 4.20 show the potential drop for the three devices below the gate along the

-coordinate. Whereas only a small potential drop is observed for $w=1\,\mathrm{\mu m}$ even after the onset of impact-ionization, the potential drop is quite significant for $w=5\,\mathrm{\mu m}$ . However, both devices show good output characteristics. For $w=10\,\mathrm{\mu m}$ the potential drop is dramatically high resulting in a perturbed output characteristic.

**Figure 4.15:** Comparison of two- and three-dimensional simulations with and without impact ionization (II) for a gate width of $w=1 {\mu }\textrm {m}$ and $V_{\textrm {DS}}=1.2 \textrm {V}$ .
$\begin{figure}\vspace*{0.4cm} \begin{center} \psfig{file=figures/soikink/IdVg_soi9_xcrv_rot, width=11.5cm}\end{center}\end{figure}$

**Figure 4.16:** Comparison of two- and three-dimensional simulations with and without impact ionization (II) for a gate width of $w=5 {\mu }\textrm {m}$ and $V_{\textrm {DS}}=1.2 \textrm {V}$ .
$\begin{figure}\begin{center} \psfig{file=figures/soikink/IdVg_soi10_xcrv_rot, width=11.5cm}\end{center}\end{figure}$

**Figure 4.17:** Comparison of two- and three-dimensional simulations with and without impact ionization (II) for a gate width of $w=10 {\mu }\textrm {m}$ and $V_{\textrm {DS}}=1.2 \textrm {V}$ .
$\begin{figure}\vspace*{0.4cm} \begin{center} \psfig{file=figures/soikink/IdVg_soi11_xcrv_rot, width=11.5cm}\end{center}\end{figure}$

**Figure 4.18:** The potential along the floating body under the gate for $w=1 {\mu }\textrm {m}$ . A small potential drop is observed, even after the onset of impact-ionization.
$\begin{figure}\begin{center} \psfig{file=figures/soikink/potSoi9_xcrv_rot, width=11.5cm}\end{center}\end{figure}$

**Figure 4.19:** The potential along the floating body under the gate for $w=5 {\mu }\textrm {m}$ . Quite a significant potential drop is observed along the gate.
$\begin{figure}\vspace*{0.4cm} \begin{center} \psfig{file=figures/soikink/potSoi1... ..., however, the average device is still 'well-behaved'.} \end{center}\end{figure}$

**Figure 4.20:** The potential along the floating body under the gate for $w=10 {\mu }\textrm {m}$ . A dramatic potential drop is observed along the gate, which renders the device useless.
$\begin{figure}\begin{center} \psfig{file=figures/soikink/potSoi11_xcrv_rot, width=11.5cm}\end{center}\end{figure}$