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.
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
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 www.comsol.com. TEL's website is located at www.tel.com.