High-resolution three-dimensional reconstruction: A combined scanning
electron microscope and focused ion-beam approach
R. K. Bansal, A. Kubis, R. Hull, and J. M. Fitz-Geralda兲
Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22904
共Received 4 August 2005; accepted 28 December 2005; published 8 February 2006兲
The ability to obtain three-dimensional information has always been important to gain insight and
understanding into material systems. Three-dimensional reconstruction often reveals information
about the morphology and composition of a system that can otherwise be obscured or misinterpreted
by two-dimensional images. In this article, we describe tomographic measurements with 10 nm
scale resolution, combining focused ion-beam processing with field-emission scanning electron
microscopy to obtain a series of high-resolution two-dimensional cross-sectional images. The
images were then concatenated in a computer and interpolated into three-dimensional space to
assess and visualize the structure of the material. The results of this research demonstrate the use of
tomographic reconstruction of Si– Si/ Ge and ␪⬘ Al2Cu samples to reproduce the three-dimensional
morphology with sub-10 nm resolution. © 2006 American Vacuum Society.
关DOI: 10.1116/1.2167987兴
I. INTRODUCTION
Over the last few decades multiple tomography techniques have been developed to work at various length scales.
Serial sectioning in conjunction with optical or electron microscopy has been shown to provide valuable threedimensional information1–7 This has traditionally been accomplished using mechanical polishing techniques to
remove material, followed by surface imaging using a scanning electron microscopy 共SEM兲 or a reflective optical microscope. In 1962, branching of pearlitic ferrite and cementite lamellae was shown by Hillert,8 thereby contradicting the
prevailing theory of sideways growth. Hull et al. performed
serial sectioning to obtain the prior-beta grain volume distribution in Ti alloys and assembled the information present in
each slice into a three-dimensional 共3D兲 volume using a reconstruction algorithm.1 Mangan et al.2 used mechanical polishing in combination with SEM, while Kral and Spanos4
employed optical microscopy, in order to study the Widmanstatten structure in high manganese steels. Fiduciary marks
made using the focused ion beam 共FIB兲 were used to align
the images, while the thickness of the slices removed by
polishing were estimated in some cases by following the
shape of the indentation marks made on the surface of the
sample, or in other cases by Ugelstad beads.7 It was estimated that slices as thin as 300 nm could accurately be removed. Imaging and alignment resolution was determined by
the size of the electron probe used in the SEM.
In addition, electron tomography is a well-established
technique for use with biological systems to recover 3D
structure with high resolution 共e.g., Ref. 9兲. This has proved
particularly useful for imaging systems such as viruses or
cell organelles. Recently, electron tomography has been extended to materials science, primarily utilizing bright field
imaging.10,11 This technique works in a way similar to x-ray
a兲
Electronic mail: jmf8h@virginia.edu
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projection-based tomography with the primary difference being that in electron tomography a much higher resolution
共⬃1 nm兲 can be obtained. Two-dimensional projection images are acquired at small angular increments to obtain 3D
information. More recently, a method of spectroscopic electron tomography has been demonstrated using energy-filtered
transmission electron microscopy 共EFTEM兲.12 In this case,
only signals from inelastic electron-matter interactions are
considered. These are proportional to the local concentration
of the selected chemical component. Energy dispersive spectroscopy 共EDS兲 mapping in TEM can also be used as a useful tool for 3D reconstructions with resolution in the range of
1 – 5 nm. It should be noted that for a single tilt axis tomography experiment the tilt range should be as close to 180° as
possible in order to avoid artifacts and obtain acceptable isotropic resolution. In practice, however, due to the TEM
holder designs and limited pole piece space, the tilt range can
be far below 180°, which can result in insufficient data to
complete a 3D reconstruction. Sample preparation must also
be carefully performed to avoid artifacts arising from
changes in thickness while tilting. The available field of view
on a sample is typically on the order of 100 nm– 1 ␮m, taking into account sample preparation procedures and microscope limitations.
The 3D analysis of inhomogeneous microstructures at microscopic and nanoscopic scales is of great importance to the
field of materials science. The FIB allows investigation into
systems that have critical feature sizes varying from a few
tens of nanometers to tens of microns and has been used to
perform three-dimensional reconstructions.13–21 Dunn et al.18
and Tomiyasu et al.15 found that the achievable lateral resolution varied between 25 and 50 nm when using the FIB to
perform tomography via secondary electron imaging and
secondary-ion-mass spectroscopy 共SIMS兲. It was noted,
however, that the final resolution depends heavily on factors
such as differential sputtering in the material, ionization
yield of chemical species, and alignment of the slices. These
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Bansal et al.: High-resolution three-dimensional reconstruction
problems make it difficult to study features that have dimensions on the order of 10 nm. Some of these problems were
addressed by making slices with the beam parallel to the
surface19,20 to avoid the effect of differential sputtering; however, additional errors were introduced while aligning the
images as the stage had to be moved after every slice. In all
cases, it was found that the smallest probe size 共8 – 10 nm兲
that could be used in the FIB was only one of the factors
limiting reconstruction resolution.
Present state-of-the-art SEMs have an ultimate imaging
resolution of 1 – 1.5 nm;22–25 therefore, if the high-resolution
imaging capabilities of a dedicated SEM are combined with
the precision machining capabilities of the FIB, a potential
for significant improvement in reconstruction resolution exists. The advent of dual-beam 共DB兲 integrated focused
electron-ion and electron-beam systems will make the application of the techniques described in this article easier to
implement in practice. While the ultimate imaging resolution
of a DB system may be somewhat lower than that of a dedicated SEM instrument, the sample will not have the alignment issues associated with multiple machine exchanges.
II. EXPERIMENT
A. Samples
For this research, the features to be reconstructed needed
to be sufficiently small and to have significant topology to
explore and demonstrate the resolution limits of this technique. Keeping these requirements in mind, two different
material systems were studied. The first example is a multilayered structure grown by molecular-beam epitaxy 共MBE兲
with alternating layers of Si and Ge0.4Si0.6 grown on a 共100兲
Si wafer with a bilayer pitch of 28 nm. The second example
is a bulk sample containing ␪⬘ Al2Cu precipitates existing as
plates oriented along the 具100典 directions in an Al matrix.
Typically, plate size primarily depends upon the thermal history of the sample. In the present study, the alloy
共Al0.95Cu0.05兲 was homogenized at 600 ° C and aged at
250 ° C for 24 h.
B. Sample preparation
Preparation of both the Al–Cu and Si– Si/ Ge reconstruction samples was performed starting with mechanical polishing to bring the area of interest close to the edge of the
sample. The samples were then cleaned using acetone and
methanol in an ultrasonic cleaner to remove the mounting
adhesive and other contaminants from the sample surface.
Cross-sectional TEM samples, used to provide complementary information, were prepared using conventional methods.
A schematic of the geometry used to obtain 3D information
about the samples using FIB serial sectioning is shown in
Fig. 1. The samples were introduced into the FIB chamber
and Pt was deposited at the area of interest. The size of the
deposited Pt block was 10 ␮m long⫻ 2 ␮m wide⫻ 500 nm
thick and was deposited using a beam current of 70 pA. This
was done to protect the surface from ion irradiation damage
while milling subsequent slices, especially for cases where
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555
FIG. 1. Three-dimensional schematic illustration of the tomography
technique.
the area of interest was close to the surface, such as for the
Si–Ge multilayered sample. The edge of the sample tended
to be rough on the nanoscale, following cleaving and polishing. In order to obtain a flatter edge, a section of material was
milled away by the FIB. A reference line was milled into the
Pt using a beam current of 1 pA to help determine the distance from the sample edge during sample slicing. The
sample was then rotated 90° such that the edge of the sample
faced upwards. Alignment marks 共shown by rectangular
trenches in the sample兲 measuring 150⫻ 150 nm2 were created to serve as fiduciary marks for subsequent image alignment using a 4 pA beam current. Similar trenches were also
milled in pairs at an angle of 10° relative to the surface
normal and were later used to accurately calculate the distance between slices. The distance from the reference line
was recorded before milling and was used to monitor the
stage drift, if any, during the milling process. A beam current
of 11 pA was used to mill away the final section of the
sample. Processing duration was determined by both the desired slice thickness and the required milling depth, and in
this study tended to be on the order of 3 – 4 min. SEM imaging was performed at an accelerating voltage of 5 kV and
a 3 mm working distance. A moderate probe current
共⬃10 pA兲 was used during imaging to achieve an acceptable
signal-to-noise ratio while utilizing a small diameter probe.
Once satisfactory images were acquired, the sample was removed from the SEM and inserted back into the FIB chamber to mill the next slice. This process was repeated between
the FIB and the SEM until the desired number of slices was
obtained. The images were aligned using the fiduciary marks
and the region of interest 共ROI兲 was cropped from the entire
set of images. Routines developed in MATLAB™ were then
used to concatenate the slices in three dimensions and the
information obtained from the slices were interpolated into
three dimensions.
C. Slice alignment
Cross-sectional transmission electron microscopy
共XTEM兲 was performed to independently study the structure
and morphology of the samples studied and to calculate the
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FIG. 2. 共a兲 Schematic illustration of the technique used for making alignment trenches on TEM membrane. 共b兲 SEM micrograph showing a perspective view of the membrane.
distance between slices. Samples were attached to a Cu ring
to provide additional handling support. The sample was then
mounted vertically on a sample holder and inserted into the
FIB chamber. Figure 2 shows a schematic of the technique
and the TEM membrane showing the alignment trenches
made using the FIB. An area of interest was chosen in the
center of the ring and an electron transparent TEM membrane was made via FIB etching, as shown in Fig. 2共b兲. A
high beam current 共1000– 6500 pA兲 was used to remove the
bulk of material near the edges of the sample while lower
beam currents 共70– 350 pA兲 were used near the TEM membrane. The thickness of the membrane was maintained at
around 200– 300 nm. The trenches were milled to span the
entire thickness of the membrane. Square trenches were
milled by the FIB to be used as fiduciary marks and their
profiles were studied by cross-sectional TEM. The angle of
the sidewall with respect to the direction of milling 共␪兲 was
calculated by measuring the length and width of the trench,
as shown in Fig. 3共a兲. It was found that the sidewall of the
trench was not perfectly linear and the maximum deviation
from linearity was measured 共denoted by ⌬L + ⌬R兲. Measurements were made on six different trenches that were milled
using a 4 pA beam current for 25 s over a 150⫻ 150 nm2
556
FIG. 3. Bright field TEM images taken 共a兲 along the 具110典 zone axis showing
the vertically FIB milled alignment trenches, 共b兲 along the 具110典 zone axis
showing the profile of the z-spacer trenches, and 共c兲 along the 具110典 zone
axis showing a pair of z-spacer trenches along with the measurements made
to determine their profile.
area and are listed in Table I. The slope of the sidewall with
respect to the milling direction can be calculated from the
average W / L ratio, to be 0.175, where W represents the
change in width 共W1 − W2兲, and L is the distance between
slices. The maximum deviation from linearity 共⌬L + ⌬R兲 was
found to be 6.35 nm over a depth 共L兲 of ⬃650 nm. Using the
SEM, it was determined that the alignment mark could be
measured with 3 nm accuracy, defined as ␦共W兲. Therefore if
␦共L兲 and ␦共W兲 represent errors associated in measuring L
and W, respectively, where ␦共L兲 = ␦共W兲 ⫻ L / W ratio, then
␦共L兲 = 3 nm⫻ 5.7= 17.1 nm. These results provide a fundamental limit in the accuracy with which we can predict the
distance between slices, L, by measuring widths of alignment
trenches in cross-sectional images. While this method is a
significant development, the method fails to reach the resolution goal for this work of predicting the distance less than
10 nm accuracy. Since the value of ␦共W兲 is governed by
several factors, such as the resolution of the SEM, it was
realized that in order to improve the accuracy of these measurements, the ratio of W / L needed to be increased. This was
achieved by milling additional trenches on an angle 共termed
TABLE I. Measurements taken to determine the profile of the alignment trenches where 共W兲 refers to the changes
in width as a function of length 共L兲, 共␪兲 represents the angle of the vertically FIB milled sidewalls, and 共⌬L
+ ⌬R兲 represent the maximum measured deviation from linearity.
Serial
no.
W 共W1 − W2兲
共pixels兲
L
共pixels兲
W/L
␪
共°兲
⌬L + ⌬R
共nm兲
1
2
3
4
5
6
158
166
170
145
166
162
932
934
936
880
932
922
0.170
0.178
0.182
0.165
0.178
0.176
4.85
5.08
5.19
4.71
5.09
5.02
8.87
5.74
5.74
6.79
5.22
5.74
0.175
0.006
4.99
0.18
6.35
Average
Standard deviation
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TABLE II. Measurements taken to determine the profile of the z-spacer
trenches where 共W兲 refers to the changes in width as a function of length
共L兲, and 共␾兲 represents the angle between the inner walls.
Serial no.
1
2
3
4
5
6
W 共W2 − W1兲 共pixels兲
L 共pixels兲
W/L
␾/2
1041
826
1067
1041
991
923
0.562
0.585
0.583
0.569
0.585
0.577
15.7
16.3
16.3
15.9
16.3
16.1
0.577
0.010
16.1
0.25
585
483
622
592
580
533
Average
Standarddeviation
z-spacer trenches兲 in the vicinity of the area under investigation for the 3D reconstruction. Figures 3共b兲 and 3共c兲 illustrate the method by which the trenches were made on a TEM
membrane in order to study the trench profiles. The trenches
were made in pairs 共labeled “A” and “B”兲 on a TEM membrane. All the A trenches were milled after tilting the sample
by 10° along the y axis. The B trenches were milled after
tilting in the opposite direction by 10° along the y axis. In
this way, we obtain pairs of trenches as shown in Fig. 3共b兲
with an angle ␾ between the inner walls. In the XTEM image shown in Fig. 3共b兲 the A and B trenches are immediately
adjacent to each other and the inner walls appear to intersect.
On the actual samples, the A and B trenches are milled at a
distance of about 50– 100 nm from each other. The profiles
of the trenches are not affected as a result of this change. The
profile of the z-spacer trenches was studied from the XTEM
images, as shown in Fig. 3共c兲. Measurements from this geometry are listed in Table II. It can be observed that the angle
␾ between the inner walls is greater than 2␪, which governs
the ratio W / L and hence the level of accuracy in predicting
the distance between slices. The average value of W / L was
found to be 0.577, while ␦共W兲 was on the order of 3 – 4 nm,
yielding a ␦共L兲 of 5.2– 6.9 nm, a greater than twofold improvement.
D. Three-dimensional interpolation
1. Intensity-based interpolation
The information obtained by serial sectioning exist as discreet two-dimensional images and must be rendered into
three dimensions for tomographic interpretation. This requires interpolation to reconstruct the region between slices.
Image interpolation for gray scale images generally falls into
two broad categories: intensity based and shape based. In
this work, intensity-based interpolation was used for the
Si–Ge multilayered sample. This process involves analyzing
each image as a two-dimensional array with each node representing a pixel of the image where the value at each node is
translated into a gray scale pixel value 共0–255, 8 bits兲. The
two-dimensional 共2D兲 arrays were then concatenated to form
a 3D array while taking into consideration the interslice distance and the pixel gray scale values are interpolated to obtain a continuous 3D data set.
JVST B - Microelectronics and Nanometer Structures
FIG. 4. Bright field cross-sectional TEM image of 共a兲 Si–Ge multilayered
structure along the 具210典 zone axis. 共b兲 SEM micrograph of the Si–Ge multilayered sample.
2. Shape-based interpolation
While intensity-based interpolation works adequately for
geometrically simple structures with relatively low curvature
along the sectioning direction, it fails to accurately recreate
the data in cases involving geometrically complex features.
In 1990, Ray and Dupe26 described a shape-based interpolation technique and showed its applicability to 3D medical
imaging. This technique has since been extensively used in
the physical sciences.2,7,18,27–30 In the present work, images
from the Al–Cu sample were reconstructed using the shapebased interpolation technique. Features were identified on
the image and it was converted to a binary image 共black and
white兲 by performing image segmentation. The edges of the
features were delineated and each pixel represented by its
distance from the nearest edge. This value was positive if the
pixel was inside the feature, and negative when outside.
These two-dimensional arrays of values were then interpolated into a volume.
III. RESULTS AND DISCUSSION
A. Si–Ge multilayered sample
This sample comprised a multilayered structure with alternating layers of Si and Si0.6 / Ge0.4 grown on a 共100兲 Si
wafer. Each Si and Si0.6 / Ge0.4 layer had a thickness of
⬃14 nm, and a total of ten bilayers were grown. Figure 4共a兲
shows a cross-sectional TEM image of the sample showing
the alternating Si–Ge and Si layers grown on the Si substrate.
It can also be seen that the Si–Ge layers vary in thickness.
This thickness variation can be attributed to the strains induced through lattice mismatch between the Si and Si–Ge
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558
FIG. 5. Scanning electron microscope images for slices taken before 关共a兲 and 共b兲兴 and after 关共c兲 and 共d兲兴 postcontrast normalization along with gray scale image
histograms.
layers. The formation of islands on the film is one of the
strain relieving mechanisms and follows the StranskiKrastanov growth mode.31 The thickness of the layers was
measured from the image and the bilayer thickness was measured to be ⬃28 nm. Figure 4共b兲 shows a cross-sectional
SEM image of the Si–Ge multilayered sample acquired at
5 kV with a probe current of ⬃10 pA at a magnification of
100k⫻. These conditions were subsequently used for acquiring 2D images for 3D reconstructions. The multilayered
structure is clearly visible where Si0.6Ge0.4, generating a
higher secondary electron 共SE兲 yield, appears brighter than
the Si layers. The layers of varying thickness correspond to
those observed in cross-sectional TEM images.
1. Contrast normalization and three-dimensional
reconstruction
The process of acquiring multiple sections requires working alternately on the FIB and the SEM. During each session
the brightness and contrast settings for image acquisition
must be adjusted and it was found that it was difficult to
achieve the same setting for all of the slices. This is imporJ. Vac. Sci. Technol. B, Vol. 24, No. 2, Mar/Apr 2006
tant because the gray scale intensity value of each pixel is
used for the 3D interpolation of the Si/ GeSi data set. Figure
5共a兲 illustrates an as-acquired image of a slice showing the
cropped area of interest along with its respective gray scale
histogram 共b兲. To accommodate variations in imaging conditions, contrast normalization was performed on every image.
This was accomplished by stretching the histogram to cover
the entire gray scale spectrum 共0–255兲. A representative image obtained following normalization is shown in Fig. 5共c兲
along with its respective gray scale histogram 共d兲. This operation was performed using the image processing software
SIS ANALYSIS™. This software has the ability to overlay images and alter the opacity of the images such that features
from both images can be seen simultaneously, allowing for
image alignment using the fiduciary marks. An image of
each slice was added as a new layer and aligned with the
previous image. When all the images were aligned the area
of interest was chosen and cropped from all layers. The
cropped component of each layer was then saved as an individual image and 3D interpolation and visualization was then
performed. This was carried out using functions and routines
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Bansal et al.: High-resolution three-dimensional reconstruction
FIG. 6. 共a兲 Cross-sectional SEM image of a Si–Ge multilayered sample
showing alignment marks. 共b兲 High-resolution SEM image showing
z-spacer trenches.
written
in
the
image
processing
toolbox
of
MATLAB™. Visualization was performed using “slice”
共MATLAB reference function兲 and orthogonal planes in the
x-y-z direction were displayed at predetermined positions.
For this study, the program was used to display both the
slices stacked prior to interpolation and the edge slices representing the interpolated volume.
It was attempted to make slices uniformly 20 nm apart,
but it was observed that the actual distance between the
slices varied significantly 共Fig. 6兲. In order to concatenate
these images into 3D space, the interslice distances were
rounded off to the nearest even number of nanometers, as
2 nm is the smallest unit in the grid 共along the z axis兲 created
for interpolation. This number can be changed to any desired
value but was kept at 2 nm to maintain a balance between
resolution and computation time for interpolation. Figure
7共a兲 shows a perspective view of the 2D slices concatenated
per the interslice distance. A perspective view of the 3D interpolated volume of the Si–Ge multilayered structure is
shown in Fig. 7共b兲. The interpolation was performed in the z
direction and the slice shown in the x-y plane in the figure is
generated as a result of interpolation. As expected, the layers
of Si and Si–Ge were found to be aligned in the x-z plane
which proves the accuracy of the data acquisition and alignment procedures. A modulation of the thickness of the Si–Ge
layers in the z direction was expected as these structures are
known to form roughened surfaces.
B. Al–Cu alloy sample
In the Al–Cu system, the Al2Cu ␪⬘ precipitates form disklike structures along the orthogonal 具100典 directions when
aged.32,33 Figure 8共a兲 shows a TEM image acquired along the
具100典 zone axis. The orthogonal alignment of the precipitates
is clear in the images. The precipitates appear as rods in two
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559
FIG. 7. Three-dimensional rendering showing how the slice images were
concatenated prior to interpolation 共a兲 and a 3D interpolated image of a
Si–Ge multilayered sample shown in a perspective view 共b兲.
directions as the projection is taken along the cross section of
the rod 共precipitate兲 while the face of the plate can be seen in
the third direction. Since these precipitates are thin plates
共10– 20 nm兲 the contrast from the precipitates aligned along
the plane of the image is less than the other two directions. A
representative area is shown in Fig. 8共b兲. The image shown
in Fig. 8共b兲 is similar to the XTEM image shown in Fig. 8共a兲
in that the precipitates oriented in the three orthogonal directions can clearly be seen. The platelike shape of the precipitate can be seen in the bottom-right corner of the image
while the other two orientations are seen in cross section.
FIG. 8. SEM and TEM imagings of the Al2Cu ␪⬘ precipitates in the Al
matrix. 共a兲 A bright field XTEM image along the 具100典 zone axis showing
Al2Cu ␪⬘ precipitates in Al matrix. 共b兲 SEM image of an electrochemically
polished Al–Cu sample acquired at 5 kV accelerating voltage. 共c兲 SEM image of a section of the Al–Cu alloy milled using the FIB showing the ␪⬘
precipitates and alignment marks. 共d兲 3D rendering showing how the Al–Cu
slices were concatenated prior to interpolation.
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560
The viewing direction in Fig. 9共b兲 has been adjusted to show
the orthogonal nature of these precipitates. Two of the orientations appear as rods while the third can be seen face on. It
should be noted that while the orthogonal nature of these
precipitates was not apparent from the 2D cross-sectional
images, it can clearly be seen from the perspective view of
the 3D reconstruction. The faces of the precipitates in Fig. 9
appear to have a distinct rippling morphology, which we believe is due to rendering artifacts.
IV. SUMMARY
FIG. 9. Perspective views are shown in 共a兲 and 共b兲 of the ␪⬘ precipitates in
an Al matrix reconstructed using shape-based interpolation and rendered in
MATLAB. The orthogonal nature of the precipitates indicates that the viewing
direction is 具100典.
This suggests that the surface of this grain is also oriented
along the 共100兲 plane. Figure 8共c兲 shows a SEM image of a
FIB milled section of the same sample. Fiduciary alignment
marks are also shown in the image. In this case the section
was oriented such that the precipitates along all three orthogonal directions would be seen in the cross section as
rods. It was found that the ␪⬘ precipitates could clearly be
seen in the FIB sectioned images; however, a distinct difference can be noticed as compared to the electropolished section images: the edges of the precipitates appear blurred. A
careful study of the images and an understanding of the
sample preparation technique utilized can offer a possible
explanation for this observation. Precipitates have been classified as A, B, or C depending on their orientation in Fig.
8共c兲. It can clearly be seen that the A set of precipitates
appear discreet while in the case of the B and C precipitates
the contrast seems to fade as the distance from the precipitate
increases. It can also be seen that the gradual fading of contrast appears preferentially on only one side of the B and C
precipitates. After studying multiple sections, it was found
that the B and C orientations of precipitates intersect the
surface at low angles. Since the SE signal originates from a
depth of 1 – 10 nm below the surface, a gradual fading of
contrast is thus geometrically expected.
1. Three-dimensional reconstructions
Shape-based interpolation was performed using a code
written in MATLAB™. The input to the program was two sets
of binary images. The first set contained a 1 pixel wide continuous white border along the edge of the precipitates,
where all of the other pixels were black. The second set
showed all precipitates as solid white pixels. A 3D perspective view showing the concatenated slices is shown in Fig.
8共d兲. A 3D isosurface reconstruction is shown in Fig. 9 from
two different viewing angles. The platelike structures can be
observed in Fig. 9共a兲 oriented in three different directions.
J. Vac. Sci. Technol. B, Vol. 24, No. 2, Mar/Apr 2006
In this research, sub-20 nm features were reconstructed in
Si– Si/ Ge and Al–Cu systems, using focused ion-beam nanomachining, combined with high-resolution secondary electron imaging. A procedure was developed to estimate the
interslice distance with high accuracy by studying the profile
of spacer trenches, which further improves the resolution and
accuracy of the technique. It was found that the interslice
distance tended to be unequal from slice to slice even though
equidistant slices were attempted while milling using the
FIB. While this could be partially improved by letting the
FIB stage drift stabilize for longer periods of time, it would
be difficult to get exactly equidistant slices since this distance is comparable to the resolution of the FIB for the probe
current used 共11 pA兲.
ACKNOWLEDGMENTS
The authors gratefully acknowledge support from Materials Structures and Devices 共MSD兲 Focus Centre under the
MARCO grant by the semiconductor research corporation
共SRC兲 共Project No. 887.001兲. At the University of Virginia
the authors would like to acknowledge Professor John Bean
for providing them with the Si/ SiGe multilayered sample,
Professor Gary Shiflet and Dr. Brian Gable for providing the
Al–Cu alloy samples, and Professor James Howe for insightful discussions.
1
D. A. Hull, D. McCammond, D. W. Hoeppner, and W. G. Hellier, Mater.
Charact. 26, 63 共1991兲.
M. A. Mangan, P. D. Lauren, and G. J. Shiflet, J. Microsc. 188, 36
共1997兲.
3
M. A. Mangan and G. J. Shiflet, Scr. Mater. 37, 517 共1997兲.
4
M. V. Kral and G. Spanos, Acta Mater. 47, 711 共1999兲.
5
R. E. Hackenburg, D. P. Nordstrom, and G. J. Shiflet, Scr. Mater. 47, 357
共2002兲.
6
M. V. Kral and G. Spanos, Acta Mater. 47, 711 共1999兲.
7
G. Chinga, P. O. Johnsen, and O. Diserud, J. Microsc. 214, 13 共2004兲.
8
M. Hillert, in Decomposition of Austenite by Diffusional Processes, B.
Zackay and H. I. Aaronson 共Interscience, New York, 1962兲, pp. 197–247.
9
A. J. Koster, R. Grimm, D. Typke, R. Hegerl, A. Stoschek, J. Walz,
and W. Baumeister, J. Struct. Biol. 120, 276 共1997兲.
10
A. J. Koster, U. Ziese, A. J. Verkleij, A. H. Janssen, and K. P. de Jong, J.
Phys. Chem. B 104, 9368 共2000兲.
11
A. Argyros, S. Manos, M. C. J. Large, D. R. McKenzie, G. C. Cox,
and D. M. Dwarte, Micron 33, 483 共2002兲.
12
G. Mobus, R. C. Doole, and B. J. Inkson, Ultramicroscopy 96, 433
共2003兲.
13
H. Satoh, M. Owari, and Y. Nihei, J. Vac. Sci. Technol. B 9, 2638 共1991兲.
14
T. Sakamoto, Z. Cheng, M. Takahashi, M. Owari, and Y. Nihei, Jpn. J.
Appl. Phys., Part 1 37, 2051 共1998兲.
15
B. Tomiyasu, I. Fukuju, H. Komatsubara, M. Owari, and Y. Nihei, Nucl.
Instrum. Methods Phys. Res. B 137, 1028 共1998兲.
2
561
Bansal et al.: High-resolution three-dimensional reconstruction
D. N. Dunn and R. Hull, Appl. Phys. Lett. 75, 3414 共1999兲.
B. J. Inkson, M. Mulvihill, and G. Mobus, Scr. Mater. 45, 753 共2001兲.
18
D. N. Dunn, G. J. Shiflet, and R. Hull, Rev. Sci. Instrum. 73, 330 共2002兲.
19
H. Z. Wu, S. G. Roberts, G. Mobus, and B. J. Inkson, Acta Mater. 51,
149 共2003兲.
20
A. J. Kubis, G. J. Shiflet, D. N. Dunn, and R. Hull, Metall. Mater. Trans.
A 35A, 1935 共2004兲.
21
E. Zschech, E. Langer, H. Engelmann, and K. Dittmar, Mater. Sci. Semicond. Process. 5, 457 共2003兲.
22
P. G. Merli, A. Migliori, M. Nacucchi, D. Govoni, and G. Mattei,
Ultramicroscopy 60, 229 共1995兲.
23
D. C. Joy and C. S. Joy, Micron 27, 247 共1996兲.
24
P. G. Merli, A. Migliori, M. Nacucchi, and M. V. Antisari,
Ultramicroscopy 65, 23 共1996兲.
J. Liu, Mater. Charact. 44, 353 共2000兲.
S. P. Ray and J. K. Dupe, IEEE Trans. Med. Imaging 9, 32 共1990兲.
27
G. T. Herman, J. Zheng, and C. A. Bucholtz, IEEE Comput. Graphics
Appl. 12, 69 共1992兲.
28
V. Chatzis and I. Pitas, IEEE Trans. Med. Imaging 19, 699 共2000兲.
29
T. Y. Lee and C. H. Lin, IEEE Trans. Med. Imaging 21, 1479 共2002兲.
30
G. J. Grevera and J. K. Dupe, IEEE Trans. Med. Imaging 15, 881 共1996兲.
31
I. N. Stranski and L. Krastanov, Sitzungsber. Akad. Wiss. Wien, Math.Naturwiss. Kl., Abt. 2B 146, 797 共1938兲.
32
Aluminum Properties and Physical Metallurgy, edited by J. E. Hatch
共American Society of Metals, Metals Park, OH, 1984兲, p. 141.
33
J. W. Christian, The Theory of Transformation in Metals and Alloys
共Permagon, Oxford, 1965兲, p. 6.
16
25
17
26
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