Multiscale Modeling in Wafer Processing

In semiconductor applications, many of the tasks involve a number of complex factors requiring analysis. “First it is necessary to prepare and process materials and thin films, typically in a plasma environment,” noted Dr. Jozef Brcka, Tokyo Electron Ltd (TEL) Technology Center in Albany, NY in a recent paper for Comsol. “Then, manufacturers must deal with flowing and reacting gas mixtures, where it is vital to account for static or RF electromagnetic fields and their couplings to the processing media. A wafer fab represents a true multiscale challenge because the reactors in which the wafers are placed can be more than a meter wide, whereas you must account for molecular activity happening in the nanometer range. Further, time scales of interest can range from milliseconds to hours.”

Computational modeling can significantly reduce overall development time and cost. Without it, it’s a trial and error process to find a part that does the job exactly as required under complex chemistry environments, as well as heat or electromagnetic field loads. A good model will let you test 10 or 20 cases in just days and get a new process online as quickly as possible.

Brcka and other engineers at TEL turned to Comsol Multiphysics for many of their projects. TEL, founded in 1963, introduced American semiconductor production equipment and integrated circuit testers to Japan.

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In the analysis of a reactor geometry, a study of the velocity field shows possible spots of low flow rates on the wafer.

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This picture shows the measure of the hydrogen radical distribution and nonuniformity (NUwafer) on the wafer surface for the case of reactor walls made from a metallic and ceramic material.
The parameter, NUwafer, is the min-max deviation of the distribution from the average value. The corresponding hydrogen dissociation ratio for metallic and ceramic walls reactor  as surface isoplots are also shown.

Said Brcka, “In the use of hydrogen for surface preparation and cleaning of silicon wafers and thin films, we worked with a commercial package dedicated to EM simulations. I used my own custom code for the bulk plasma model. It was also necessary to develop a sheath model that examined the transport of the chemically active species during the manufacturing process, and here we typically worked with an analytical model. Finally, to look at the feature model that describes events at the molecular level, we again worked with my own code. I found this combination quite annoying and counterproductive. I’m dealing with different codes, on different platforms and operating systems, in different time scales.”

Comsol Multiphysics streamlined Brcka’s process. “Without extra coding of my own, the software shows how the gas flows into a generic hydrogen remote plasma reactor, and makes it easy to describe the flow and use this information to investigate the actual plasma distribution.
“Even though I was a new user of Comsol,” continued Brcka, “I felt comfortable modeling the hydrogen’s chemistry and potential interaction with the wafer surface; and in this study I looked at 15 reactions. The important thing with the chemistry is to achieve as uniform a distribution of hydrogen radicals as possible. Reactors made with a metallic surface on the walls, typically an aluminum alloy; result in process performance at the wafer surface that is less uniform than those made with a ceramic wall surface. Further, metallic walls react more with the intermediate species so that there are fewer hydrogen radicals available and the overall chemistry in complex molecular plasma can be negatively affected.”

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