In general, technology characterization problems are more appropriately
solved by nonlinear least squares optimization. On the other hand,
the technology design problem is best formulated in nonlinear programming
terms. This is the approach taken in [63]. As the main focus
of this thesis is TCAD technology characterization, the discussion of
nonlinear programming is limited. It is included for the sake of
completeness and for its usefulness as a mathematical tool in
characterization tasks
.
Given a specified process sequence, TCAD simulation can be used to build models of device characteristics as a function of processing conditions (e.g. the MOSFET saturation current can be modeled as a function of implant doses and energies). The technology design problem can then be formulated in nonlinear programming terms using these models. For example, one would like to find the optimum conditions to maximize an objective function such as the saturation current, while meeting equality constraints such as a target threshold voltage and enforcing inequality constraints such as a maximum value of the off current. It is worth noting that the use of nonlinear programming for process and device design applications is limited by the accuracy of the underlying TCAD simulation tools. Whereas device simulation models are robust and contain parameters that can be characterized from existing electrical device data, process simulation tools lack accurate characterization metrology for calibrating multi-dimensional process models [60][59]. This limits the usefulness of any application of optimization techniques in design application.
A mathematical expression of this problem is:
where 
is the objective function model,
's are given input vectors, and 
's are the models encoding
the set of equality and inequality constraints.
Different techniques exist for the solution of the constrained optimization
problem above [70]. In view of the characteristics
of TCAD models, methods based on sequential linear or quadratic approximation
are the most appropriate to use.