CASE STUDY: Computational Modeling for Semiconductor Wafer Processing

Computational modeling provides a better understanding of the semiconductor wafer manufacturing process, and can significantly reduce overall development time and costs as well.

Optimizing semiconductor processing equipment is a complex task because of the large number of factors that contribute to the whole. It is first necessary to prepare and process materials and thin films, typically in a complex plasma environment. Next, manufacturers must deal with flowing and reacting gas mixtures, where it is vital to account for static or radio frequency (RF) electromagnetic fields and their couplings to the processing media. A wafer fab represents a true multi-scale problem because the reactors the wafers are placed in can be more than a meter wide, whereas molecular activity must be accounted for in the nanometer range. Further, time scales of interest can range from milliseconds to hours.

In the past, the design of chip manufacturing and processing equipment depended mostly on empirical methods due not only to the rapid pace of innovation but also to the incomplete understanding of the fundamental physical and chemical phenomena. Dedicated codes have been developed at universities, but they require users to master their specifics, and they also often use simplified geometries or analytical-approach models.

There is little doubt that computational modeling provides a better understanding of the manufacturing process and can significantly reduce overall development time and costs. Consider that even one component in a complex wafer fab can cost several thousand dollars. Without adequate modeling, finding a part that does the job exactly as required under complex chemistry environments, heat or electromagnetic field loads-and with the predicted final impact on process performance-is primarily trial and error. Not only do non-workable parts turn into expensive scrap, but it can take weeks to get such prototype parts made. With a good model, it's possible to test 10 or 20 cases in just days and thus get a new process online as quickly as possible.

Figure 1. Generic plasma processing for semiconductor manufacturing is characterized by multi-scale and multi-physics processes. Apart from the macro effects within the reactor (reactor model, ~ 40 cm to 1 m), it is also necessary to consider the effects of chemical interactions both within the bulk plasma and at its interface with the wafer (sheath model, ~ several millimeters), as well as what goes on at the molecular level within a specific device geometry (feature model, ~ 10 to 100 nm).

Working with a Hydra

At the TEL Technology Center in Albany, N.Y., our role is to develop new processes and hardware to meet future semiconductor manufacturing requirements. Working closely with process engineers, we bring the nano and macro scales together, and we have found that doing our job is simply not cost effective without modeling. Without simulation results, an equipment designer can't know where to start a development project or how to change tool components to satisfy new process or technology requirements.

However, a problem arose as we adopted a variety of simulation codes and methods for each manufacturing stage. For example, consider the use of hydrogen for the surface preparation and cleaning of silicon wafers and thin films (see Figure 1). The first area to study covers the electromagnetic (EM) interactions with the wafers and the processing materials. Previously, we studied what was going on with a commercial package dedicated to EM simulations. Next is the bulk plasma model, for which I was forced to use my own custom code. It is also necessary to develop a sheath model that examines 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.

Finding a Single Solution

This combination of different codes, platforms and operating systems was quite counterproductive, as were problems we experienced when moving data between these codes. In addition, a flexible simulation tool was needed to create novel technical solutions and implement new ideas in a reasonably short amount of time. I came to believe that it would be far more effective to use an all-in-one simulation package, and I embarked on a feasibility study to see to what extent I could perform plasma reactor simulations using COMSOL Multiphysics.

Figure 2. A study of the velocity field shows possible spots of low flow rates on the wafer.

Some of my initial results are illustrated in Figure 2, which shows the gas flow into a generic hydrogen remote plasma reactor. Most studies of plasma reactors for this type of application simply assume the direction of flow. However, it is easy to describe this flow with COMSOL Multiphysics. Armed with this information, we can investigate the actual plasma distribution, optimize the process and look for possible hot spots that could lead to premature erosion.

Figure 3. A measure of the hydrogen radical distribution and non-uniformity (NUwafer) on the wafer surface for the case of reactor walls made from a metallic and ceramic material (a). The NUwafer parameter is the min-max deviation of the distribution from the average value. The corresponding hydrogen dissociation ratio for metallic and ceramic wall reactors as surface isoplots are also shown (b & c).

The wafer surface can be prepared in a couple of different ways. One method involves using hydrogen radicals' interaction with the wafer surface, and eventually low energy ion bombardment stimulation. Even though I was a new user of COMSOL, I felt comfortable modeling the hydrogen's chemistry (in this study I looked at 15 reactions).

It is important to achieve as uniform a distribution of the hydrogen radicals as possible. Figure 3 shows the effect that the reactor wall has on this parameter. Reactors made with a metallic surface on the walls, typically an aluminum alloy, result in process performance at the wafer surface 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.

Future Modeling

Now that I have completed the bulk-plasma and chemical-reaction model, it's time to include the full sheath and feature-level models. I hope to include even more of the phenomena that describe the process in full and will provide a self-consistent model solution. I am also reworking my first models to include other aspects and more complex geometries. COMSOL Multiphysics gives me one simulation environment for all the phenomena in my multi-scale and multi-physics systems.

For additional information regarding computational modeling, contact COMSOL, Inc., 1 New England Executive Park, Suite 350, Burlington, MA 01803; (781) 273-3322; fax (781) 273-6603; or visit TEL's website is located at


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