4.1 Target and Constraint Definition

As already mentioned in Section 3.2 the target will be minimized during the optimization procedure. For our optimization task it is defined in a way to maximize the drive current. There are several different ways to accomplish this, for example, defining the target as the negative drive current or the inverse drive current. But amongst all these the linear definition (negative drive current) has proven to have the best convergence behavior of the optimization procedure:

$$\mathrm{target} = -\frac{ {I_{\mathrm{on}}}}{1 \mathrm{\,\mu A}} \hspace{0.5cm} \rightarrow \mathrm{min.}$$ (4.1)

To set an upper limit for the channel leakage current one inequality constraint is used which reads

$$\mathrm{constraint} = - \log \left( \frac{{ {I_{\mathrm{off}}}}}{1 \mathrm{\,pA}} \right) \hspace{0.5cm} > 0 \; ,$$ (4.2)

and keeps the leakage below 1 pA. Usually, a change in channel doping has an exponential-like impact on the leakage current. Therefore, the use of a logarithmic transformation reduces this nonlinearity and leads to a better convergence of the optimization procedure.