6.4 Using the Modified Energy Transport Model

**Figure 6.10:** Output characteristics of the SOI (Device 1) obtained by anisotropic energy transport simulations without closure modification ( $\beta _0 = 1$ ).
$\includegraphics{gpfigure/ID_SOI_aniso.color.eps}$

By combining the modifications for an anisotropic temperature and a non-MAXWELLian closure relation the artificial current decrease is eliminated (Fig. 6.11). Parameter values roughly estimated from MC simulations can be used, for example $\gamma _{0y}=0.75$ and $\beta _0 = 0.75$ . In the parameter range where the current drop is eliminated the output characteristics are found to be rather insensitive to the exact parameter values.

**Figure 6.11:** Output characteristics of the SOI (Device 1) assuming an anisotropic temperature ( $\gamma _{0y}=0.75$ ) and a modified closure relation at $V_\textrm {GS} = 1 \hspace {.35ex} V$ .
$\includegraphics{gpfigure/ID_SOI_aniso_closure.color.eps}$

When the modified model is applied to a body-contacted MOSFET, the difference in the output characteristic is only marginal compared to the standard energy transport model. For example using the values $\gamma _{0y} = 0.6$ and $\beta _0 = 0.75$ leads to a maximum deviation in the drain current of about $0.3 \, \%$ compared to the standard energy transport model within the bias range.

Using the modified energy transport model good agreement of the electron concentration in vertical direction with Monte Carlo data is obtained (Fig. 6.12 and Fig. 6.13). This confirms that the correction of the SOI output characteristics obtained with the modified model is based on a corrected behavior of the electron distribution in the bulk.

**Figure 6.12:** Electron concentration in a MOSFET (Device 3) obtained by simulations using the modified energy transport model compared to Monte Carlo data.
$\includegraphics[width=.6\textwidth]{eps/2D_eleMCMET_rot}$

**Figure 6.13:** Comparison of the electron concentration in a MOSFET (Device 3) at a vertical cut located in the middle between source and drain obtained by simulations using drift-diffusion (DD), standard energy transport (ET), Monte Carlo (MC), and the modified energy transport (MET) model.
$\includegraphics{gpfigure/n-cut-MC-ET-MET-DD.color.eps}$


Previous: 6.3 Summarizing the Models Up: 6. Modeling and Application Next: 6.5 "Well-Tempered" SOI MOSFET