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: [email protected] 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. REFERENCES 1) D. Shindo and T. 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