The dependencies in modern semiconductor devices are difficult to predict. So the question of how to choose, for example, the energy of a particular implant in order to obtain a certain electrical output characteristic of the device is nearly impossible to answer. There are also several side effects which have to be considered. An approach to the improvement of the device characteristics is to evaluate statistical variations of a set of selected device parameters and examine their results.
The statistical methods for the generation of the values of the parameters for several designs are known as Design of Experiments methods. The results of the simulations can be used to fit an analytical model of them. What one gets is an easily evaluated approximated model of the parameters and the results. This concept is known as Response Surface Methodology.
The concept of response surfaces and experimental designs began in the chemical industry. The early work was done by statisticians and chemical engineers in the imperial chemical industry in the 50's.
These methods are adapted for microelectronics applications. In the special case of computer simulation of the fabrication process of the microelectronic devices some restrictions can be made for the statistical designs. This will be explained in Section 3.1.
How response surfaces are fitted to the extracted results and what has to be mentioned is explained in Section 3.2.