A. Drive Current as the Constraint

For the optimization tasks in Chapter 4 the drive current of an NMOS transistor is maximized under a constant leakage current condition. The question arises whether this optimization task can be reversed and if this would deliver a doping profile which shows the same features as in Chapter 4. Reversed means, in this context, that now the drive current is the constraint and the drain-source leakage current is minimized.

Consequently, the target (4.1) and constraint (4.2) definitions have to be changed in the optimization setup to meet the new optimization goal:

$$\mathrm{target} = 100 \cdot \log \left( \frac{ {I_{\mathrm{off}}}}{1 \mathrm{\,A}} \right) \rightarrow \mathrm{min.} \; ,$$ (A1)

$$\mathrm{constraint} = \frac{{ {I_{\mathrm{on}}}} - 373.7 \mathrm{\,\mu A}}{1 \mathrm{\,mA}} \hspace{0.5cm} > 0 \; .$$ (A2)

The new constraint definition guarantees that the drive current stays above 373.7 $\mu$A which is the result from the two-dimensional drive current optimization for Device Generation A given in Table 4.4. The logarithmic function in the target definition linearizes its response to doping profile variations and, therefore, improves the convergence behavior of the optimization procedure.

When comparing the resulting acceptor doping profile (Fig. A.1) of this new task to the conventional result (Fig. 4.4), it can be seen that they are almost identical. The resulting leakage current of this optimization is 1.2 pA. Therefore, the two optimization tasks can be considered as equivalent as they deliver fairly the same results. Furthermore, it underlines the assumption that the doping profiles found in this work are global optima since they can be obtained by two completely different optimization setups.

Figure A.1: The result of the two-dimensional optimization with the drive current as the constraint.