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ebeam.html
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<HTML>
<CENTER><A HREF = "main.html">Return to Steve Plimpton's home page</A>
</CENTER>
<HR>
<H3>Electron Microscopy - Monte Carlo trajectory simulation
</H3>
<P>Monte Carlo trajectory simulation is an effective means of modeling
high- resolution microscopes. I worked with Joe Michael and Al Romig
from Sandia's materials center to create a parallel code for modeling
beam/substrate interactions in an electron-beam microscope. We started
with a serial code written by Dale Newbury and Bob Myklebust from
NIST. The basic idea is shown in the following figure. Individual
electron trajectories are tracked as they hit the surface and travel
thru the substrate. Inelastic energy loss is computed as well as
scattering events that may produce secondary electrons. The latter
occurs in a random way via Monte Carlo rules. The trajectories of all
the electrons are followed until they die out, transmit thru a
thin-film sample, or backscatter from the incident surface. X-ray
emission from primary and secondary electrons that would reach a
detector is tallied along the way.
</P>
<CENTER><IMG SRC = "images/ebeam_schematic.gif">
</CENTER>
<P>The obvious parallel algorithm for this model is to have each
processor simulate one or more independent trajectories. For
load-balancing we used a master-slave approach where each processor
simulates a set of trajectories, then requests another set. A large
parallel machine can rapidly accumulate good statistics for many
millions of trajectories interacting with complex substrates. A bit of
care must be taken to insure the random number stream used by each
processor is truly independent. We experimented with several schemes
for this which are discussed in the papers below.
</P>
<P>Here are some examples of how the Monte Carlo simulations can help
calibrate or design microscopes and also be used to analyze
experimental data. The scanning- electron micrograph is an Al thin
film with 2% Cu. Some of the Cu has segragated to the Al grain
boundaries (dark spots). The question is how sharply can these regions
of Cu be resolved? Even if the interface between 2 materials is
atomistically sharp, scanning the microscope beam across the interface
will give a smeared-out profile due to beam spreading. The graph below
shows a comparison between experiment and the Monte Carlo code for
scanning a beam across a sharp interface between Ni-Fe-Cr alloys of
different composition. In the simulation this "scanning" is done by
simulating 100,000 or more electron trajectories at each of the data
points shown. The excellent agreement between the 2 data sets is an
example of how the simulation results can be used to deconvolve actual
microscope data.
</P>
<CENTER><IMG SRC = "images/ebeam_alcu.gif">
</CENTER>
<CENTER><IMG SRC = "images/ebeam_graph.gif">
</CENTER>
<P>A large-scale calculation was also done of void imaging in Al
metallization lines due to electromigration. These voids can be viewed
in situ beneath an overlayer of passivation oxide if the beam voltage
is within the proper range. The following 2 micrographs show the
difference in void resolution with beam voltages of 40 KeV and 120
KeV.
</P>
<CENTER><IMG SRC = "images/ebeam_void_40kev.gif">
</CENTER>
<CENTER><IMG SRC = "images/ebeam_void_120kev.gif">
</CENTER>
<CENTER><IMG SRC = "images/ebeam_void_sim.gif">
</CENTER>
<P>The bottom 2 images are simulated pictures of a rectangular void
beneath the same thickness of passivation at 40 KeV and 80 KeV. The
actual void extent is shown as the rectangular box. This is an immense
computation since many trajectories must be simulated at each pixel
point in the 2-d image (actually only 1/4 of the pixels due to
symmetry). We see the same kind of contrast dependence on beam voltage
as in the actual microscope. These kinds of calculations can serve to
optimize the contrast for a particular microscope as well as determine
the ultimate resolution of what size voids can be "seen" thru a given
passivation thickness.
</P>
<P>Collaborators on this project:
</P>
<UL><LI>Joe Michael, Sandia
<LI>Al Romig, Sandia
<LI>Dale Newbury, NIST
<LI>Bob Myklebust, NIST
</UL>
<HR>
<P>The 1st of these papers focuses on the physics of the computational
model and some interesting results. The 2nd has more discussion of the
parallel issues along with parallel performance results. A discussion
of the different techniques for parallel random number generation we
tried is also included in the 2nd paper.
</P>
<P><B>Parallel Simulation of Electron-Solid Interactions: A Rapid Aid for
Electron- Microscope Data Interpretation</B>, J. R. Michael,
S. J. Plimpton, A. D. Romig Jr., Ultramicroscopy, 51, 160-167
(1993). (<A HREF = "abstracts/ultra93.html">abstract</A>)
</P>
<P><B>Parallel Simulation of Electron-Solid Interactions for
Electron-Microscopy Modeling</B>, S. J. Plimpton, J. R. Michael,
A. D. Romig, Jr., J of SuperComputing, 6, 139-151
(1992). (<A HREF = "abstracts/jsc92.html">abstract</A>)
</P>
</HTML>