Being the most ubiquitous, and at the same time the most mystic, terms in
TCAD applications, they refer essentially to the same thing:
the minimization of the value of a target function that is constructed
from the inputs and outputs of an arbitrary system
. (Figure 8.11).
The minimization starts at a given set of initial values for the
system inputs.
The result of the minimization task are the values of the inputs
and the outputs at the minimum value of the target function.
Figure 8.11:
Optimization as minimization of target function.
For calibration, the output values for the minimization tasks are computed as the fit error that describes the quality of the correspondence of the system with a set of fit data. The fit error is usually defined as the sum over all fit data points of the squares of the differences of fit data and system output data. The input values for the calibration task are the fit parameters of the system to calibrate (Figure 8.12).
Figure 8.12: Calibration as minimization of the fit error.
If a system does not have any parameters to use as fit parameters, it is possible to apply a parameterized transformation of the input variables to calibrate the new system consisting of the original system and transformation (Figure 8.13).
Figure 8.13:
Calibration by transformation of input variables.
The result of the calibration, or the calibration for short, is the set of optimum fit parameters obtained. In the second case, also the optimum transformation pertains to the calibration.
In TCAD, the term optimization refers to the search of a set of process parameters that lead to a desired device behavior. In most cases, the system used for optimization is represented as a response surface model generated from a standard design of experiments, as direct evaluation of a process and device simulation sequence for each step of the optimizer is not feasible.
On the other hand, the term calibration is used to indicate that a set of parameters has to be computed that optimally fits a system to a set of measured data. For tool calibration, the system is represented by a single simulator run including pre-processing and post-processing; for global process calibration, the system is a response surface model the coefficients of which are used as parameters (cf. Section 8.4.3).