As a prerequisite for all further analysis, a design has to be able to be modified in order to be subjected to automatic exploration of the design space. If the modification affects only the value of certain parameter settings while leaving the structure of the problem untouched, we speak of a parameterized design . In the case where the structure of the problem is modified, e.g., the sequence of process steps is altered or different paths are taken from the beginning to the end of the flow, we call it structurally variational, or variational for short.
Obviously, this difference depends on the level of abstraction at which the design is described. In many cases, and, most prominently, in geometry modeling, the modification of parameter values leads to structurally different results, e.g., changing layout parameters such as line widths or distances between lines may lead to completely different lithography masks, resulting in wafer geometries that are topologically dissimilar (Figure 8.3). In an analogous fashion, the modification of an etch rate in an etch process step, e.g., may lead to completely distinct wafer topologies.
Figure 8.3:
Layout parameter modifications cause
topologically distinct wafer geometries.
For process-flow related task-level applications, no structural changes in the process flow, i.e., the structure of the design, are admitted. In the case where comparisons between process flows with different step sequences have are to be made, the difference in the sequence has to be mapped to differences in some parameter values that modulate the impact of a given step. For example, if a comparison is to be made between two different process options, one including an additional implantation step that the other one is lacking, the problem is most conveniently modeled by using a very low value for the dose parameter of the implantation step in the flow that, in reality, entirely lacks that step.
There are two justifications for this approach. Firstly, instabilities of the numerical solution of the overall problem are likely to blur the results due to different grids generated for the two different sequences. Secondly, most task-level applications are aimed at adjusting parameter settings of a given process sequence to meet a given target rather than changing the sequence itself.