Yao N. Focused Ion Beam Systems: Basics and Applications
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positions of feature edges can be determined within experimentally measured
slices. Typically, standard image processing and edge detection methods are
applied to each experimentally measured slice prior to reconstruction. The
particular methods used for each reconstruction require some investigator
input to determine which features will be reconstructed and which methods
are best suited to determining edge positions within each slice. An in depth
discussion of image processing and edge detection methods are beyond the
scope of this chapter, but the reader is encouraged to consult standard image
processing text books to determine which methods are best for his or her
particular data [58].
SIMS elemental maps can be processed using shape based interpolation
methods similar to those described for image data. In some cases, however,
SIMS elemental maps have a low signal to background ratio making it dif-
ficult to find edges using typical edge detection methods. In these cases, a
combination of shape based interpolation methods and intensity interpola-
tion are used to analyze these data. In particular, SIMS data are con-
catenated into a three-dimensional array and volume between slices is
linearly interpolated to produce a three-dimensional map of SIMS intensities
[50]. These data are then further processed to determine the chemical dis-
tribution of selected elements within or outside the edges of features of
interest. Since the volumes reconstructed from image data have positive voxel
values for voxels inside a feature and zero for those outside of a feature, these
volumes can be used as masks to select SIMS intensities inside a given feature
by logical AND operations. In addition, the chemical distribution outside of
+1
+1
Edge of feature
in this slice
Inside
Outside
–1
+1
+1+1+1
–1
–1–1–10
0
0
Figure 11.3 A schematic diagram of a typical slice of an object in which the
distances to the edges have been calculated and placed in each pixel position.
Pixels that land on an edge have 0 distance, pixels inside an edge ha ve
positive distances and those outside of object edges have negative distances
to an edge.
Focused ion beam systems308
selected features can be selected by NAND logical operations. Logical
operations can then be used to investigate changes in chemistry across the
interfaces of selected features.
As an example of shape based volume reconstructions, we now present
volume reconstructions of the structure and chemistry of lamellar structures
from Cu-15In colonies [59]. Shown in Figure 11.4 is a typical SEM image
taken from a Cu-15In colony. These colonies consist of lamellar In rich
regions, which are marked by arrows in Figure 11.4(a). Figure 11.4(b) shows
an image that consists of edges for Cu-15In lamellae determined from the
SEM image in Figure 11.4(a). These edges and others from consecutive slices
through this colony were used to reconstruct a three-dimensional volume
from this colony using shape based interpolation.
Figure 11.5 shows a montage of shape based volume reconstructions cal-
culated from slices similar to those shown in Figure 11.4(b). In Figure 11.5(a ),
the entire set of Cu-15In lamellae shown in Figure 11.4 have been recon-
structed. In this reconstruction, all positive distances and interfaces have
been colored gray showing the spatial variation of lamellae within this colony
structure. In Figures 11.5(b) and 11.5(c), a set of lamellae have been extracted
from this colony for further investigation. It has long been thought that these
colonies consist of disconnected plates. It is clear from this reconstruction,
however, that these lamellae are connected in Figure 11.5(c). If this colony
were viewed only from a two-dimensional projection of Figure 11.5(c), an
investigator might erroneously assume that this colony was made up of
disconnected plates.
There is a great deal of geometric and spatial information available in
shape based volume reconstructions like those shown in Figure 11.5. From
(a) (b)
Figure 11.4 Typical SEM images and edges collected as part of a serial
section experiment to investigate Cu-15In colonies. (a) An SEM image of a
sample showing Cu-15In colonies. White arrows in this image point to
examples of lamellae that make up a colony. (b) Edges determined from the
SEM image shown in (a) [59].
Three-dimensional visualization of nanostructured materials 309
these reconstructions, volume, volume fraction, and connectivity relation-
ships are easily calculated. These reconstructions can also be used to help
understand the spatial variation of chemical species measured by SIMS.
Figure 11.6 shows a montage of reconstructed volumes and three-dimen-
sional In SIMS elemental maps taken from cellular colonies. Figure 11.6(a)
shows a shape based volume reconstruction of several cellular structures
taken from the colony in Figure 11.5(a). This reconstruction shows connected
lamellae that diverge near the top surface of the reconstruction.
Figure 11.6(b) is a three-dimensional In elemental map showing the spatial
variation of In both in lamellae and the matrix. This chemical reconstruction
was done using linear interpolation of the In signal between slices. If the
elemental map shown in Figure 11.6(b) is operated on using a logical AND
operation with the volume in Figure 11.6(a), the spatial variation of In within
lamellae is obtained as shown in Figure 11.6(c). This operation shows not
only the variation of In concentration within lamellae but also yields the
position of interfaces between lamellae and the surrounding matrix. Using
this position, one can extract data across a specific interface and investigate
the chemical and spatial variation of interfaces.
Another example of the power of shape based reconstructions is their
application to quantum dot structures. Recently, Kubis et al.[59] have
applied these techniques to investigate growth characteristics of Ge/Si
quantum dots (QD). One of the most important problems investigated in these
systems is how dots are arranged in the matrix during growth. Figure 11.7
shows a shape based volume reconstruction from a Ge/Si quantum dot
(a)
(b)
(c)
2 µm
Figure 11.5 Reconstructed volumes from Cu-15In colonies. (a) A volume
reconstruction calcul ated from SEM images using shape based inter pola-
tion. (b) A few selec t lamellae from the colony shown in (a). This set of
lamellae appear to be connected in this view. (c) The same lamellae from (b)
but at a different depth. At the depth shown in (c), these lamellae appear to
separate as a function of depth. If a single slice is observed at the last slice
for (c), these lamellae might be mistakenly reported as not connected [64].
Focused ion beam systems310
superlattice. In the near left-hand corner as highlighted in the reconstruction
is an example of a QD column that has terminated during growth of the
superlattice and does not continue through the entire structure.
In many cases tomographic reconstructions have been used empirically to
visually inspect spatial distributions of quantum dots. In the case of the QD
superlattice shown in Figure 11.7, close examination shows that all of the QD
(a) (b)
(c)
Figure 11.6 A montage of volume reconstructions from a Cu-15In colony.
(a) A volume reconstruction calculated using shape based interpolation in
In rich colony regions. (b) An SIMS volume reconstruction using positive
In ions and direct interpolation of intensities. Dark and light gray represent
different concentrations of In and black defines background. (c) A volume
reconstruction that is the result of a logical AND operation of the shape
based reconstruction shown in (a) with the In SIMS elemental map shown in
(b). This reconstruction yields a clearer view of the variation of In within
colony lamellae [64].
2.0 µm
1.7 µm
5.6 µm
Figure 11.7 A shape based volume reconstruction of quantum dots in a Ge/
Si quantum dot superlattice. In the near left-hand corner is an example of a
QD column that has terminated during growth. Spatial resolution between
the layers was intentionally decreased so that the evolution of the columns
could more easily be observed.
Three-dimensional visualization of nanostructured materials 311
columns in the reconstruction do emanate from the first layer grown and in
some cases are extinguished prior to the 20th layer. The termination of QD
columns after several layers of growth was predicted by Tersoff et al.[60] and
Liu et al.[61] for QD columns that were too closely spaced. While this
observation is important when studying the evolution of ordering in these
structures it does not lend itself to quantifying differences in comparably
grown structures.
To gain a better understanding of the ordering of this superlattice, these
data were further analyzed and compiled as a function of layer number. The
number density of the QDs on each layer was calculated by analyzing the
reconstructed volume perpendicular to the sectioning direction. Figure 11.8
shows a graph of the number density of QDs on each of the grown layers.
The number of QDs on each successive layer decreases until a minimum is
reached at the 17th layer. As can be seen in the inset of Figure 11.8 the lower
layers consist of a high number density of small QDs while the upper layers
have a lower density of larger QDs. As some columns disappear in Figure 11.7,
QDs in other columns increase in size. This clearly shows one effect of the
self-assembly process. This size distribution and volume relationships shown
in Figures 11.7 and 11.8 would not have been easily accessible without shape
based volume reconstructions.
Volume reconstructions using FIB microscopy and shape based inter-
polation can provide a wealth of critical information for problems in mate-
rials science and condensed matter physics. In problems involving solid state
4.5
Number density of QDs
Growth la
y
er
0 5 10 15 20
(a)
(b)
Number density (QDs/µm
2
)
4
3.5
3
2.5
2
Figure 11.8 A plot of the number density of QDs as a function of growth
layer in this superlattice structure. Inset (a) is a processed slice through the
lowest layer and (b) shows a slice through the uppermost layer.
Focused ion beam systems312
phase transformations and reaction kinetics, it is important to ascertain the
connectivity of component phases and their respective volume fractions,
surface to volume ratios, etc. Typically, this type of information is obtained
through stereological analyses. One drawback to stereological analyses is that
feature geometry must be assumed. Features are typically assumed to take on
model shapes such as plates, cylinders, spheres, and oblate and prolate
spheroids, and then methods of geometric probability are used to infer mean
feature dimensions, volume fractions, surface areas, etc. By using FIB three-
dimensional reconstruction techniques, one can measure these quantities
directly without having to assume model feature shapes.
11.3 Summary and future work
Focused ion beam tomography is proving to be a very powerful technique
for investigating three-dimensional relationships in a number of materials
systems. Volume reconstructions for a wide array of materials can be cal-
culated with lateral resolutions as high as 20 nm and depth resolutions of
10 nm. When combined with accurate reconstruction algorithms such as
shape based interpolation, FIB tomography is capable of yielding quantita-
tive information such as surface area, volume, perimeter, volume fraction,
and connectivity. In addition, three-dimensional variations in chemistry can
also be investigated if SIMS, AES, or EDX mapping techniques are incor-
porated into volume reconstructions. If image volume reconstructions are
used as masks to process chemical reconstructions, it is possible to investigate
three-dimensional distributions of chemical species within features of interest
and their variation across interfaces.
In this chapter, we have shown examples from metallurgy and solid state
physics in which FIB tomography has yielded new insight that would have
been difficult to obtain using traditional two dimensional methods of char-
acterization. FIB tomography will continue to be an important technique for
objects with critical dimensions ranging from 10 nm to 10 mm and beyond.
There are however, several advances in FIB microscopy systems that will
undoubtedly increase the range of applicability of FIB tomography and may
well extend its range of critical length scales below 10 nm. Perhaps the most
important change can be seen in the maturity of dual-beam FIB micro-
machines. In dual-beam systems, an SEM column is included in addition to
the ion column. Using this dual-beam configuration, a sample can be sec-
tioned using the primary ion beam and imaged with the SEM column. In this
type of FIB, lateral resolution is no longer confined by the beam char-
acteristics and contrast transfer function of the primary ion column, thus the
Three-dimensional visualization of nanostructured materials 313
ultimate resolution of image slices can be increased to that of a current state
of the art SEM. In addition, since sputtering is not occurring during image
collection, less material is lost making it possible to achieve much finer depth
resolution when collecting slices.
Outside of higher resolutions attainable with SEM imaging on dual-beam
FIBs, most modern dual-beam systems allow for SEM imaging with electron
accelerating voltages less than 2.0 keV. Low voltage imaging modes also
extend the applicability of FIB tomography to organic systems and those
materials systems that are easily damaged by electron radiation. In parti-
cular, low voltage SEM imaging modes make it possible to investigate
organic dielectrics in the semiconductor industry and many polymer systems
in other fields of materials science. Limitations for these materials systems
will most probably be confined to ion effects such as differential sputtering
and whether these materials can be sectioned with sufficient accuracy via
sputter processes to allow for volume reconstruction.
In addition to dual -beam systems with high-resolut ion SEM columns, a
great deal of work is currentl y being done on ion so urces to attain smaller
probe sizes. In particular, there are e fforts to develop gas ion s ources
[62,63], which, in theory, should yield smaller virtual source sizes and lead
to effective ion beam sizes of less than 10 nm. If successful, these sources
could be mass-matched to materials of interest and allow for greater
control o f sputtering, and th erefor e much finer slice sampling d urin g data
collection. While these sources are unlikely to improve lateral resolutions
for single beam FIB systems, they could make a great difference in the
depth resolution of volume reco ns truct ion s done using du al- beam FIB
systems. In addition, thes e sourc es m ight offer the pos sibilit y of increasing
ionization yield for SIMS in fo cused ion beam systems, thereby increasin g
sensitivity and si gnal to noise c hara cteris tics of chemical element volume
reconstructions. These sourc es are st ill at the development stage, however,
and will probably not be incorporated into production FIB systems for
some time.
In summary, techniques for FIB tomography using serial sectioning with
a lateral resolution of approximately 20 nm and a depth resolution of 10 nm
have been presented. This critical dimension scale is well within the realm
of application for many nanotechnology applications. When coupled with
chemically sensitive analytical techniques such as SIMS, AES, and EDX,
structural and chemical relationships can be readily developed in three-
dimensions from volume reconstructions for nanostructured materials
systems.
Focused ion beam systems314
Acknowledgements
The authors would like to acknowledge G. Shiflet (University of Virginia)
and G. Gilmer (Bell Laboratories) for provision of samples used to generate
tomographic reconstructions presented in this article. Funding from IBM,
the Defense Advanced Research Projects Agency (Virtual Integrated Proto-
typing Program), and the National Science Foundation (Materials Research
Science and Engineering Center) is gratefully acknowledged.
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