3.9 Optimization and Inverse Modeling

A newer trend in TCAD simulation is the use of automatic optimization and
inverse modeling [137],[138],[139].

A special example for optimization of the manufacturing process flow was already given in
Section 3.4. Additional application of optimization
are the optimization of device layout and of device simulation
parameter classes like outlined in Figure 3.6
for semiconductor process flow optimization.
The typical optimization approach of the commercial TCAD vendors is the
generation of response surfaces [140] via definition of DOEs and the analytical
calculation of the optimization minimum from the generated model [112]. This type of
optimization environment is offered inside the graphical environment of the
user interfaces of the TCAD systems as outlined in
Section 3.1. The advantage of this approach is the stability
of the optimization. Even if one or two simulations fail (e.g. because of mesh
stability or accuracy problems), a good result of the optimization can often be
gained. However, a major drawback of this approach is, that the
input parameter interval cannot be set very broadly, because of the
computational costs (even if DOE methods are applied). Therefore it often
happens (as also with experiments in fabrication), that the final optimum is
outside the defined input parameter limits.

The other approach is the use of real multidimensional optimization algorithms
like *downhill simplex*, *direction set* methods of the class
without calculating derivatives or *conjugate gradient*,
*quasi-Newton* and *variable metric* of the class of methods
calculating first-order derivatives, and, finally, *simulated annealing*
and *genetic algorithm* methods which form a class of their own in
terms of mathematical tools used. Details of these methods can be found in,
e.g., [141],[142],[143].

A special application of optimization is inverse modeling [142],[144],[145]. Basically it is
identical to optimization, however the target is a different one. In
optimization the scope is the optimization of the overall system to gain a
more efficient manufacturing method. Inverse modeling aims not to
gain an optimized system at the end, but to get information not
accessible to forward analysis. Inverse modeling defines an analytical or
numerical model with a certain set of input parameters and compares this model
with a desired result (e.g. a measurement). A score function of
the type as shown in (6.1) in
Section 6.1 may be used for such a setup. After finding a
global minimum of the score function the model is considered to be reflecting
the physical parameters. A good example is the class of convolution problems in
metrology methods. For instance, SIMS or SRP measurements are convoluted with
the internal point response functions of the measurement systems. These point
response functions are defined by the physical effects occurring during
measurement (e.g. ion mixing during SIMS sputtering [146] or carrier spilling [147],[148] during
SRP measurement) and can be modeled with a simulator. The ``real'' doping
profile may be obtained by inverse modeling as above mentioned.

R. Minixhofer: Integrating Technology Simulation into the Semiconductor Manufacturing Environment