5.1.4 Solving the Optimization Problem

The time for the simulation of the process flow and the electric characterization takes about 40 minutes, so a direct optimization is not suitable to solve this problem. But the problem can be solved using Design of Experiments and Response Surface Methodology. This is done by the generation of an experimental design, simulation of the design points, fit of a response surface, and, finally, optimization using the data from this fitted surface (see Figure 5.2).

Figure 5.2: Main steps for solving the optimization problem.

In the simulation framework a complex optimization task consists of several analysis functions. Figure 5.3 shows the task using DoE, RSM, and optimization steps. The numbers in the figure indicate the actions which have to be done by the framework listed below.

Figure 5.3: Structure of the optimization task using DoE and RSM.

1. The framework reads the specification of the analysis task from the file. It consists of the reference of the stored simulation flow, the definition of control and response parameters with their location in the flow, and additional information like default values and ranges. The sequence of analysis steps (from step 2-9) is also read from this file.

2. The input for the DoE module (ranges of the control variables and the specified design) and start the DoE program is prepared.

3. After termination of the program the framework collects the evaluated result of the DoE module and adds the control parameter values of the new experiments to the experiment table.

4. The set of controls from the referenced process flow and the experiment table are used to generate the experiments. An experiment consists of the simulation of a process flow and extraction of the results.

5. The experiments are simulated using the integrated simulators and tools. The responses where extracted from simulation output.

6. All responses are collected from the finished runs and added to the experiment table.

7. After all experiments have been carried out, the complete data of the experiment table are given to the Response Surface Methodology module for evaluation.

8. The ranges, start values and target functions are passed to the optimizer.

9. The optimizer requests evaluations from the RSM module and receives the calculated target function until an optimum is found.

The output values of the device simulation used for the performance qualification are the on-resistance R_{DS on} and the breakdown voltage U_{D b}. Two parameters of the process flow are chosen to improve these properties; the epitaxial doping value n_epi and the thickness of the epi-layer d_epi. The goal of this optimization is to minimize the on-resistance while keeping the breakdown voltage above $105 \ {\rm V}$.