Chemistry Reference
In-Depth Information
the general mechanisms observed in the simulation would also be observed in
a corresponding experiment. In general, there is no easy way to assure this cor-
respondence except through careful comparison between experiments and
model predictions. Second, a quantitative model must provide
some
indication
of how accurate a given prediction is. Is the answer correct to within 10% or
1000%? Again, such uncertainty estimates can only come from careful com-
parison with experimental results in carefully chosen situations. For most aca-
demic applications, the large amount of effort required for quantitative
modeling is not worth the trouble. For many industrial applications, however,
quantitative modeling is an absolute requirement.
Coupled mechanism models are becoming increasing important as the
size scales under investigation decrease. A good example is a complementary
symmetry metal-oxide-semiconductor (CMOS) device. At relatively large
length scales (100s of nanometers), the gate, oxide, substrate, source, and
drain can mostly be considered individually for modeling purposes. As the fea-
ture sizes decrease into the 10s of nanometers range, however, effects such as
local diffusion processes, elastic strain, and conductivity become closely
coupled, making modeling much more difficult. Modeling methodologies
that can handle such coupled processes are very limited and improvements
are badly needed. For further discussion of these and related issues, we refer
the reader to two workshop reports.
286,287
Finally, although coupled time-scale models are not within the scope of
this review chapter, this topic is just as important as multiple length scales
when dynamical processes are being considered. As mentioned previously,
models that include atoms must generally use time steps small enough to cap-
ture the vibrational modes of the system. Since the corresponding experiments
almost always occur over time scales
many
orders of magnitude longer than
what can be simulated, the relevance of the models to real-world behavior is
often in doubt. Although good progress has been made in developing multiple
time-scale methodologies, this problem remains a major stumbling block for
people trying to simulate real-world processes.
In summary, tremendous progress has been made over the past couple
of decades in the field of multiscale modeling of solid-state processes.
Nevertheless, existing techniques can only handle a small fraction of the
important problems that require solutions. There is plenty of
opportunity
at
the bottom.
APPENDIX: A LIST OF ACRONYMS
1D
One dimensional
2D
Two dimensional
3D
Three dimensional
