Materials Transactions, Vol. 48, No. 10 (2007) pp. 2631 to 2635
Special Issue on Advances in Electron Microscopy for Materials Characterization
#2007 The Japan Institute of Metals
Quantitative Electron Holographic Analysis of Electric
Potential Distribution around FEG-Emitters
J. J. Kim1 , W. X. Xia1 , D. Shindo1; * , T. Oikawa2 and T. Tomita2
1
2
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan
JEOL Ltd., Akishima, Tokyo 196-8558, Japan
By means of electron holography, the electric potential distributions around a cold-type FEG-emitter (field emission gun emitter) are
visualized with a change in the applied voltages. In a biased FEG-emitter, the experimental method for obtaining an unperturbed reference wave
is applied in order to carry out quantitative electron holographic analyses. Further, through comparing the experimental results obtained by
electron holography with those of the simulations taking into account the three dimensional configurations of the FEG-emitter and the anode, it is
found that the experimental technique presented in this study is quite useful in obtaining the quantitative information regarding the electric field
distribution around a biased FEG-emitter. [doi:10.2320/matertrans.MD200719]
(Received May 16, 2007; Accepted July 24, 2007; Published September 5, 2007)
Keywords: field emission gun (FEG)-emitter, electric field, electron holography
1.
Introduction
Field emission gun emitters (FEG-emitters) play an
important role in the development of nanoanalysis techniques
using electron microscopy. Recently, by utilizing FEGemitters, we could obtain an electron beam source at the
subnanometer level with high brightness and an extremely
short energy spread.1) Among the various types of emitters,
the cold-type FEG-emitters have been widely used in
scanning electron microscopy as well as transmission
electron microscopy because of their superior characteristics
with respect to the stability of the electron emission current.
In particular, in order to perform manufacturing inspections
and critical dimension (CD) measurements in semiconductor
industries, where the electron beam stability and the sample
damage due to electron irradiation are very important, they
have been mainly employed as electron beam sources for
scanning electron microscopy.
On the other hand, in order to obtain reliable analysis data
using electron microscopy, the stability of the electron beam
emitted from a FEG-emitter and the performance of the
emitter are of vital importance. Thus, many efforts have been
made on the development of new emitters with improved
emission properties, including the evaluation techniques for
such emitters.2–5) Some of the present authors have extensively carried out electron holography measurements, which
is a unique tool for quantitatively visualizing the electric field
on a nanometer scale, on the various types of field emitters. In
the previous studies, by means of electron holography, we
have reported on not only evaluation techniques for the
emitters in the presence of an applied voltage but also a
useful method to obtain quantitative information on the
microfields around the emitters.6–8)
In this study, on the basis of our previous studies, we carry
out the electron holographic analysis of the electric potential
distribution around a cold-type FEG-emitter with a change in
the applied voltage. Further, we discuss the quantitative
evaluation technique of the electron holography results
obtained from the biased FEG-emitters.
*Corresponding
author, E-mail: shindo@tagen.tohoku.ac.jp
2.
Experimental Procedure
Figure 1 shows the experimental setup used in this study.
Electron holography experiments were carried out with the
configurations of the field emitter and counter anode, as
shown in Figs. 1(a) and (b). We used a cold-typed FEGemitter for a scanning electron microscope (SEM) as the field
emitter and a commercial tungsten needle as the anode. They
were placed in a special specimen holder with which the
distance between the FEG-emitter and the anode could be
controlled, and the biased voltage between them could be
applied within a transmission electron microscope (TEM).6–8)
Electron holography was carried out with a JEM-3000F TEM
equipped with a biprism.9) With a change in the voltage
applied between the FEG-emitter and the anode, the electron
holograms were recorded using a CCD camera. The exposure
time was set to be constant at 6 s. Further, in order to analyze
the electric potential distribution around the biased FEGemitter, the simulations were performed using a commercial
software (JMAG-studio ver. 8.41, JRI solutions) operated on
the basis of the three-dimensional finite element method.
3.
Results and Discussion
Figure 2 shows the SEM and TEM images of the cold-type
FEG-emitter used in this study. The FEG-emitter is made of
tungsten and its tip has a spherical shape with a diameter of
approximately 100 nm. Figure 3 shows the electron holography results showing the electric potential distribution
around a FEG-emitter with a change in the applied voltage.
Electron holography experiments are carried out at the
experimental setup shown in Fig. 1(a), where the distance
between the FEG-emitter and the anode is 2 mm. The electron
holograms and the corresponding reconstructed phase images
are shown in Figs. 3(a)–(c) and Figs. 3(d)–(e), respectively.
In the reconstructed phase image, the white and black lines
denote the equiphase lines formed by the electrons passing
through the electromagnetic field; in the case of the electric
field alone, these lines indicate the equipotential lines,
thereby reflecting the three-dimensional electric potential
distribution integrated along the trajectories of the incident
2632
J. J. Kim, W. X. Xia, D. Shindo, T. Oikawa and T. Tomita
(a)
(b)
Field emitter
Anode
Anode
Field emitter
Interference fringes
Interference fringes
Fig. 1 Experimental setup used in this study. (a) Case in which the reference wave perturbed. (b) Case in which the reference wave
unperturbed. Light-red and blue lines indicate the plane waves of the object wave and the reference wave, respectively. Long-range fields
due to biased field emitters are depicted by the red broken lines around each emitter.
50 µm
(a)
100nm
(b)
Fig. 2 (a) SEM and (b) TEM images of a cold-type FEG-emitter.
electrons.1) Here, it is evident that the equipotential lines due
to the electric potential are visualized; in Fig. 3(d), there is no
change in the electric potential around the FEG-emitter when
the applied voltage is 0 V, while with an increase in the
applied voltage, the change in the electric potential distribution around the FEG-emitter can be observed from the change
in the number of equipotential lines. These results indicate
that the strength of the electric field increases around the
FEG-emitter owing to the applied voltage. However, it
should be noted that these reconstructed phase images exhibit
some artifacts due to the electric field between the biased
FEG-emitter and the anode.10,11) In other words, in this
experimental setup, we encounter a fundamental problem in
the reconstruction process of an electron hologram: the socalled the reference wave perturbation occurs due to a long
range field since the electric field due to the biased FEG-
Quantitative Electron Holographic Analysis of Electric Potential Distribution around FEG-Emitters
(a)
100nm
(c)
(b)
0V
(d)
2633
60V
100V
(f)
(e)
0V
60V
100V
Fig. 3 Electron holography results obtained under the experimental conditions shown in Fig. 1(a). The applied voltage is indicated at the
bottom-right corner of each figure.
emitter extends to the region of the reference wave, which is
illustrated by the red broken lines around the field emitter in
Fig. 1(a).
Here, we discuss this issue in detail. In general, by means
of electron holography, we can obtain the phase shift ðrÞ
between the reference wave and the object wave. In the case
of the electric potential alone, in the reconstructed phase
image, the intensity Iph ðrÞ is represented by the cosine
function of the phase shift ðrÞ, corresponding to the electric
potential integrated along the trajectories of the incident
electrons, i.e., Iph ðrÞ ¼ cos½ðrÞ, as pointed out earlier.
However, it is noted that in the case shown in Fig. 3, when
the reference wave is perturbed by the electric field due to the
biased FEG-emitter, we cannot obtain the direct information
reflecting the electric potential distribution from the reconstructed phase image. In this case, the intensity of the
reconstructed phase image Iph ðrÞ is represented by a cosine
function as follows:
Iph ðrÞ ¼ cos½ðrÞ ð1Þ
Here, we should consider , which corresponds to the
perturbation of the reference wave. This perturbation is
owing to the field leakage around the biased FEG-emitter. In
other words, in order to obtain the quantitative information
regarding the electric potential distribution in the case of the
biased FEG-emitter, we should take into consideration.6)
However, it is very difficult to experimentally determine .
Thus, we have proposed a useful method by which we can
obtain an unperturbed reference wave even in the case of
biased FEG-emitters, as shown in Fig. 1(b). Eventually, it is
possible to obtain an unperturbed reference wave by installing the FEG-emitter and electrode on the same side of the
optical axis in a TEM by utilizing the special specimen
holder in this study.
Figure 4 shows the electron holography results obtained
from the experimental setup shown in Fig. 1(b). In this case,
it is expected that the reference wave is not affected by the
electric field from the biased FEG-emitter, i.e., ¼ 0. In
the Figs. 4(a) and (d), where the applied voltage is 0 V, no
change in the phase is observed in the field of view, except in
the FEG-emitter and the W-anode position. At the W-anode
position, it is noted that the contrast in the reconstructed
phase image appears to be somewhat noisy due to the effect
of the thickness of the W anode, and the equipotential lines
observed within the FEG-emitter result from its mean inner
potential. On the other hand, with an increase in the applied
voltage, the equipotential lines between the FEG-emitter and
the anode are observed while there is no change in the upperleft region of the anode (indicated with an asterisk in
Fig. 4(e)). These results indicate that the reference wave is
not affected by the applied voltage. Further, from the digital
diffractograms shown in the insets of Figs. 4(a)–(c), we can
confirm that the reference wave is not perturbed. Namely, in
the applied voltage of 0 V, we can find only one sideband as
indicated by the white arrow, while with an increase in the
applied voltage, two sidebands (indicated by the white and
yellow arrows) are observed. The sidebands indicated by the
yellow arrow in the insets of Figs. 4(b) and (c) are resulted
from the electric fields between the FEG-emitter and the
anode, and the sidebands indicated by the white arrow are
2634
J. J. Kim, W. X. Xia, D. Shindo, T. Oikawa and T. Tomita
(a)
(c)
(b)
W anode
W anode
W anode
100nm
60V
0V
(e)
(d)
100V
(f)
*
0V
60V
100V
Fig. 4 Electron holography results obtained under the experimental conditions shown in Fig. 1(b). The applied voltage is indicated at the
bottom-right corner of each figure. Insets of Figs. 4(a)–(c) show the digital diffractograms. White arrows indicate the sidebands caused by
the no-field region. Yellow arrows indicate the sidebands caused by the region between the FEG-emitter and the anode.
(a)
(b)
0V
(c)
W anode
W anode
-30V
FEG-emitter
z
y
x
100nm
-60V
FEG-emitter
Fig. 5 (a) Simulation model. (b) Electric potential map obtained in the xy plane. (c) Simulation results showing the equipotential lines
around a biased FEG-emitter where the applied voltage is 60 V.
due to the electric fields in the upper-left region of the anode.
Here, it should be noted that with an increase in the applied
voltage, the positions of the sidebands indicated by white
arrows do not vary, while the distance between the sidebands
indicated by yellow arrows and the origin (corresponding to
autocorrelation1)) increases. These results indicate that
although the electric field between the FEG-emitter and the
anode increased, the electric field in the upper-left region of
the anode maintains to be almost zero field. Therefore, it is
reasonable to consider that the reference wave is not
modulated under the biased conditions. In Figs. 4(d)–(f),
due to the applied voltage, the distances between the
equipotential lines decreases and their gradients are concen-
trated at the edge of the FEG-emitter, which are identical to
the results shown in Fig. 3(d)–(f). However, some differences are observed in the shape and distribution of the
equipotential lines around the FEG-emitter: when compared
with the results of Fig. 4, the equipotential lines appear to
exhibit round shapes in Fig. 3.
Here, in order to verify the results of Fig. 4—obtained
under the condition that the reference wave is unperturbed—
we carry out the simulations using the three-dimensional
finite element method to take into account the three-dimensional configurations and shapes of the FEG-emitter and the
anode as well as the applied voltage. The simulation results
are presented in Fig. 5. The mesh partition of the calculation
Quantitative Electron Holographic Analysis of Electric Potential Distribution around FEG-Emitters
model is shown in Fig. 5(a). In this figure, the meshes of air
part are omitted. An FEG-emitter and anode pair is placed on
the direction parallel to the xy plane, and the incident electron
beam direction within a TEM is considered to be along the z
direction. Furthermore, the applied voltage is set to be 60 V
and the dimensions of each feature are the same as those of
the experimental conditions shown in Fig. 4(b). The electric
potential map obtained in the xy plane is shown in Fig. 5(b).
Here, we can confirm that the gradient of electric potential is
concentrated at the edge of the FEG-emitter. Further, in the
upper-left region of the anode, it is found that the electric
potential is maintained at a constant level, i.e., approximately
0 V. Figure 5(c) shows the simulation result that exhibits the
equipotential lines reflecting the electric potential distribution integrated along the z direction around the FEG-emitter
and anode. This simulation result is obtained on the basis of
the electric potential values calculated using the model
shown in Fig. 5(a) by the finite element method. Here, it is
found that there are the comparable agreements between the
experimental result of Fig. 4(e) and the simulation; the shape
and distribution of equipotential lines appears with almost the
same pattern as that of the experimental result; in particular,
the electric potential variation in the upper-left region of the
anode is negligible. Further, it is found that from the
simulation and the experimental results, the maximum
electric field at edge of the FEG-emitter is evaluated to be
1.4 V/nm when the applied voltage is 60 V. Therefore, it is
reasonable to consider that these results reveal that the
quantitative electron holographic analyses can be achieved
for a biased FEG-emitter.
On the other hand, in this study, the distance between the
FEG-emitter and the anode was controlled to be approximately 100 nm in order to achieve the experimental
condition that the reference wave was not modulated by the
long-range field due to a biased FEG-emitter. Thus, the
distance between the FEG-emitter and the anode was
different from that of the real application. However, through
controlling the applied voltage, we can obtain the various
electric field conditions including the same condition with the
real application. Therefore, we believe that the experimental
technique presented in this study is a quite useful for
evaluating the FEG-emitter.
4.
2635
Conclusions
An experimental technique for quantitatively evaluating
the electric potential distribution around a cold-type FEGemitter was proposed. By controlling the anode positions
within a transmission electron microscope, the electric field
due to the biased FEG-emitter can be shielded. Eventually,
the experimental condition for quantitative electron holography in which the reference wave is unperturbed by a long
range field can be achieved. Further, through the simulations
taking into account the three-dimensional configurations of
the FEG-emitter and the anode, it is found that the electron
holography results obtained by these experimental conditions
can be applied to the evaluation of a biased FEG-emitter.
Acknowledgments
This work was partly supported by a Grant-in-Aid for
Scientific Research (S) from the Japan Society for the
Promotion of Science and a grant (code #: 05K1501–01210)
from ‘‘Center for Nanostructured Materials Technology’’
under ‘‘21st Century Frontier R & D Programs’’ of the
Ministry of Science and Technology, Korea.
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