[User Tip]Trend Based Analysis

[cfdace]

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.