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One of the most powerful uses for CFD modeling
efforts is trend based analysis. As the name
suggests, this type of analysis work focuses on the
TRENDS of simulations rather than concentrating on
the absolute result of a single simulation.
While CFD technology has advanced by orders of
magnitude there are still questions about the
accuracy of any one simulation. When comparing
results from your simulation to results obtained in
an experiment there are many issues that can affect
the validity of the comparison (click
here to see more details about each of these
issues):
- Do the boundary conditions exactly match that of
the experiment?
- Do the material properties exactly match that of
the experiment?
- Did you simplify the geometry to make gridding
easier?
- How accurate are the experimental measurements?
- Are the experimental results repeatable?
- Did the measurements in the experiment affect the
results?
- Do the proper computational models exist and have
they been used?
- Is the solution grid independent?
- Is the solution fully converged?
Uncertainty in any of the above issues leads to a
good chance that the simulation results will not be a
100% match with the experiment results. In many cases
getting simulation results within 10% of the
experimental results is considered very good
agreement. Getting simulation results within 1% of
the experiment is often impossible due to the issues
outlined above. Exceptions are academic cases which
have simple geometry and physics.
The good news is that trend based analysis can make
excellent engineering use of simulation results even
if the comparison to experiments is off by as much as
20%. The key is that trend based analysis does not
look at a single result, but rather at the TRENDS
found in the results.
Example: Semiconductor Wafer Deposition Process
One of the biggest application areas for CFD-ACE+
is the modeling of semiconductor wafer processing. In
these efforts the goal is very often to minimize the
non-uniformity of the wafer deposition or etching
process. If you are not familiar with how semiconductor
chips are made, then visit http://www.appliedmaterials.com/HTMAC/
for an introduction. You will learn that over 250 wafer
processes are required to make a chip. Each of these
processes must produce uniform results across the
entire area of the wafer in order to ensure that all
chips on the wafer will be acceptable.
In this example a particular process tool is
producing results that are outside of acceptable
range for uniformity (see triangles in the image
below) higher deposition at the center of the wafer
as compared to the edge. The uniformity goal is shown
by the green lines. The analyst ran a CFD-ACE+
simulation of the same process and produced the
results shown by the red curve.
Now let's examine the above results. It is obvious
that the experiment and computations do not match
exactly (they are off by ~10%). But it is also
apparent that the TREND is similar (the computation
also shows higher deposition at the center of the
wafer). At this point the analyst could try to figure
out the cause for the mismatch in results. Some
reasons could be;
geometric simplifications made to model the complex
tool geometry,
inaccurate knowledge of the boundary conditions and
properties,
solution not grid independent,
surface reaction mechanism not fully
understood.
By investigating the above issues, I'm
sure the analyst could improve the results and maybe
even get within 1% match, but this would take
significant effort. The analyst realized that the
computations were matching the TRENDS very well and
instead of spending time trying to get a closer match
to experimental data he spent that time more wisely by
trying to solve the problem at hand. Namely, how to get
a more uniform deposition. In this case he had some 10
parameters that could be varied in the model. These
parameters match those used in the operation of the
tool. He made over 50 simulations to investigate which
combination of parameters produced the most uniform
deposition, the best combination is shown in the graph
below as the red curve.
Here it is seen that the computation shows much more
uniform deposition. The parameters were given to the
tool operator to run a test experiment and those
results are shown by the triangles above. It is clear
that the experimental results are now much more
uniform than before and in fact even more uniform
than the target goal. Note again that the experiment
and computational results are still ~10% different,
however the problem has been solved! This success led
to the quote that "we are now two-years ahead of
schedule". As the semiconductor chips and hence their
features keep getting smaller and smaller it will not
be long before even this level of non-uniformity is
not acceptable!
Lesson Learned
The lesson learned here is that good engineering work
can be done and problems solved without ever having
to match the experimental results to high accuracy.
Remember that CFD is a tool and the power of the tool
can often best be exploited by using it in the
simplest possible way. Think about how trend based
analysis can help you solve your engineering
problems. Let me know if you have a similar success
story.
Regards,
Richard Thoms
Manager
ESI CFD Customer Support
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