5.1.4 Device Changes and Optimizations

Circuit design relies on model values from a mean device with a given low sensitivity towards process variations. Thus, device fabrication and optimization requires to account for statistical decision principles in the optimization process as shown in Fig. 5.4. Mathematically, a desired change to a device is a multivariate problem where only very few of the variables are actually known and can be influenced. To include external variables in a more abstract optimization process, external decision loops are added. The inner loop of the actual change procedure addresses whether the specific device properties are reached. However, a change can be called optimization, if the external requirements are added by additional loops to account for the unknowns in this multivariate problem. The two most important loops are:

• Does the sensitivity towards critical parameters increase and thus does the yield decrease below an acceptable limit ?
• Is the proposed device manufacturable within the constraints of the given process ?

Only if the external considerations are fulfilled, a device change can be truly called optimization.

Figure 5.4: Inclusion of external variables into the optimization process.

Figure 5.5: Sensitivity analysis of a $S_{21}$ towards $d_{gc}$ variations as a function of frequency.