5.1.5 Results

For the calculation of the response surface, 9 runs with 28 simulation steps have been executed, and the optimizer needed about 250 evaluations of this response surface.

Figure 5.4 shows the target function (on-resistance R_{DS on}) versus the parameter space of the control variables (epi-doping concentration n_epi and epi-layer thickness d_epi). The minimum value of the on-resistance was found on the constraint where the breakdown voltage reaches the lower limit of $105 \ {\rm V}$.

Figure 5.4: Response surface of the target function.

The optimum process parameters found are listed in Table 5.2. The on-resistance of the optimal VDMOS transistor is $R_{DS(on)}= 0.614 \ {\rm\Omega}$ . In Figure 5.5 the source region of the optimum VDMOS transistor is shown.

Table 5.2: Parameters of the optimization problem.

Parameter	Minimum	Maximum	Optimum
depi	$8.0 \ {\rm\mu m}$	$14.0 \ {\rm\mu m}$	$10.37 \ {\rm\mu m}$
nepi	$7.25 \cdot 10^{14} \ {\rm cm^{-3}}$	$2.9 \cdot 10^{15} \ {\rm cm^{-3}}$	$1.9 \cdot 10^{15} \ {\rm cm^{-3}}$

Figure 5.5: Net-doping concentration (in $\ {\rm cm^{-3}}$) of the optimized VDMOS transistor.