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Estimation of suitable condition for observing copper–phthalocyanine crystalline film by transmission electron microscopy
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 248 (2006) 273–278 www.elsevier.com/locate/nimb
Estimation of suitable condition for observing copper–phthalocyanine crystalline film by transmission electron microscopy Misa Hayashida *, Tadahiro Kawasaki, Yoshihide Kimura, Yoshizo Takai Department of Material and Life Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan Received 25 March 2006; received in revised form 13 April 2006 Available online 22 June 2006
Abstract The decay of the electron diffraction intensity of a copper–phthalocyanine crystalline film was quantitatively measured at room temperature by transmission electron microscopy (TEM) as a function of current density and beam diameter. The measurements revealed that the critical dose increases with decreasing current density, decreasing beam diameter and increasing acceleration voltage. Generally, the damage process only depends on the electron dose. However, the temperature rise of the copper–phthalocyanine enhances the damage process. The relationship between damage and acceleration voltage has been measured, and the result shows that an increase in acceleration voltage decreases the damage. The relationship between image contrast and acceleration voltage was also measured using a single-wall carbon nanotube (SWNT) as a radiation-insensitive substitute for the copper–phthalocyanine in order to obtain atomic-level images. The results revealed that image contrast increases with decreasing acceleration voltage. Using these oppositely behaving results, the most suitable voltage for observing copper–phthalocyanine crystalline films was estimated. The results show that low acceleration voltages should be used for imaging to achieve the minimum specimen resolution limit. Ó 2006 Elsevier B.V. All rights reserved. PACS: 42.25.Fx Keywords: Critical dose; Radiation damage; Transmission electron microscopy
1. Introduction The clarity of an observed image is generally determined by the relationship between the object contrast and the signal to noise ratio (S/N). The image becomes blurry when the S/N of the image is low and the object contrast is weak. The image sharpens when the S/N and object contrast increase. The clearness of the image depends on the balance between the object contrast and the S/N. In transmission electron microscopy (TEM), the object contrast of a specimen is changed by acceleration voltage. On the other hand, the S/N is determined by the statistical fluctuation *
Corresponding author. Tel.: +81 6 6879 4581; fax: +81 6 6879 7843. E-mail address: [email protected] (M. Hayashida). 0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.04.168
of the detection pixel, which is proportional to the electron dose used for the observation. For observing radiation-sensitive materials, such as organic or biological samples, only very low electron doses are permitted. Otherwise the structure of the specimen will be destroyed. As a result, the S/N of the observed image becomes low. Furthermore, since such biological specimens consist of light atoms, the object contrast is very low. These situations lead to the most crucial problem of achieving high-resolution images of radiation-sensitive materials. Electron-beam-induced damage in TEM samples has been evaluated by many researchers [1–5], measuring the fading rate of electron diffraction spot intensities of crystalline objects under electron beam irradiation. In these measurements, the critical dose (Dc) was defined as the dose at which the diffraction spot intensity decreases to 1/e of the
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M. Hayashida et al. / Nucl. Instr. and Meth. in Phys. Res. B 248 (2006) 273–278
initial value. The critical dose serves as a measure for the tolerance of the object with respect to the electron beam irradiation. If Dc becomes M times larger, the radiation damage reduces to 1/M. Hence, the M times larger electron dose can be used for the observation. Aspaffiffiffiffiffiresult, the S/N of the observed image will be improved M times because the noise is defined as the statistical fluctuation of the number of irradiated electrons. In general, the magnitude of the irradiation damage depends on the accumulated total electron dose. However, Sali and Cosslett [3] and Fujiyoshi [4] reported that Dc decreases with increasing temperature of the specimen induced by the electron beam. Therefore, the magnitude of the radiation damage depends on the radiation conditions in terms of parameters such as current density and beam size. We must resolve the problem whether the magnitude of the radiation damage depends on the radiation conditions. Kobayashi et al. [1] reported that the magnitude of the radiation damage decreases as acceleration voltage increases, because the inelastic scattering cross section of the atoms becomes smaller as the acceleration voltage increases, leading to an increase in Dc at a high acceleration voltage. However, the image contrast becomes weak as the acceleration voltage increases because the elastic scattering cross section decreases in inverse proportion to the square of electron velocity. Therefore, we must also resolve the problem if it is better to take an image at a high accelerating voltage and a high electron dose by improving S/N or at a relatively low voltage and low dose by improving the object contrast. In the present paper, we used a copper–phthalocyanine crystalline film as an example for a radiation sensitive sample to estimate the most suitable TEM conditions. We measured the decay of the electron diffraction intensity from a copper–phthalocyanine crystalline film as function of current density, beam diameter and acceleration voltage. For measuring the image contrast, we used a single-wall carbon nanotube (SWNT), because it is difficult to obtain atomiclevel-resolution images of radiation-sensitive samples such as copper–phthalocyanine. Since carbon atoms are the main element of copper–phthalocyanine, the SWNT was used as a substitute. We estimated the so-called specimen resolution limit by using it as a criterion of the minimum observable object size. Our experimental results demonstrated that images of copper–phthalocyanine crystalline film should be obtained at small illuminating beam diameters, low current densities and low acceleration voltages.
ferred onto a TEM microgrid [6]. Electron diffraction was observed by TEM (Hitachi H-7500). To determine the current density on the sample, we measured the spot size of the electron beam on a screen and the current intensity with a pico-ammeter and took into account the magnification value of the TEM apparatus. Fig. 1 shows an example of the decay sequence of the electron diffraction patterns of copper–phthalocyanine. The patterns were recorded with an imaging plate at a fixed ˚ 2 s at 60 kV. Each image current density of 0.03 electrons/A of Fig. 1 was recorded for 30 s and the total dose is indicated in each frame. To reduce the effect of specimen drift and the fluctuation of the beam current during observation, we used a slow-scan CCD camera to reduce the total recording time. To avoid saturation of the CCD camera, we only selected the part of the diffraction pattern which did not contain the bright central spot. The dependence of the fading of the diffraction spot intensity was measured at a 60 kV acceleration voltage by changing current density and beam diameter in two ways: (a) by changing the brightness at a constant beam current and (b) by changing the beam current at a fixed beam diameter. The dependence on acceleration voltage was also measured in the range between 40 and 100 kV with a fixed current density and a fixed beam diameter. In addition, we measured the change in contrast as a function of acceleration voltage from the SWNT images, which were recorded with imaging plates at a constant current density. These images were recorded without an aperture at an almost constant defocus.
2. Experimental ˚ -thick copFor our experiments, we prepared a 100-A per–phthalocyanine crystalline film by vacuum evaporation on a freshly cleaved mica surface whose temperature was kept at 250 °C. After removing the evaporated film from the mica substrate on the water surface, the film was trans-
Fig. 1. Decay sequence of electron diffraction pattern of copper– phthalocyanine crystalline film for different doses obtained at 60 kV.
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3. Results The structure of the electron diffraction patterns decays with increasing dose, as shown in Fig. 1 for copper–phthalocyanine. As an example, we chose the decrease in the ˚) intensity of the (0 0 2) diffraction spot (half of 13 A depicted in Fig. 2(a) and measured the line profile in the rectangular area shown by a white broken line. The line profile is shown in Fig. 2(b). The ratio of the spot intensity to background intensity, A/B, in Fig. 2(b) is plotted in Fig. 2(c) as a function of the total electron dose using the patterns shown in Fig. 1. In this case, Dc is 17 electrons/ ˚ 2. Then we measured the critical dose Dc as a function A of current density (Figs. 3 and 4) obtained by maintaining (a) the beam current at approximately 0.07 nA (Fig. 3) and (b) the beam diameter at approximately 2.2 lm (Fig. 4). The curves clearly indicate that Dc decreases as current density increases. Hence, the radiation damage increases with current density.
Fig. 4. Critical dose as function of current density. The measurements were performed by maintaining the beam diameter (approximately 2.2 lm) constant.
Fig. 5. Critical dose as function of acceleration voltage.
Fig. 2. (a) Electron diffraction pattern. (b) Line profile along square in (a). (c) Spot intensity as function of electron dose.
Critical dose is plotted in Fig. 5 as a function of the acceleration voltage U for a constant beam diameter (approximately 1.3 lm) and a constant beam current (approximately 0.012 nA). The result shows that Dc decreases with decreasing acceleration voltage, approximately proportional to U2.3. The recorded images of SWNT shown in Fig. 6 demonstrate that the contrast (Ia Ib)/Ib increases with decreasing voltage, where Ia and Ib are the intensities of the SWNT and vacuum area, respectively. The contrast was plotted as a function of acceleration voltage as shown in Fig. 7. It is roughly proportional to 1/U1.6 in the range of 40 kV 6 U 6 120 kV. We can understand this dependence if we consider that the total contrast is composed of the phase contrast and the scattering absorption contrast. The former is proportional to 1/U, while the latter is proportional to 1/U2 becoming predominant at low voltages. 4. Discussion
Fig. 3. Critical dose as function of current density. The measurements were performed for a fixed beam current (approximately 0.07 nA).
The two curves shown in Figs. 3 and 4 intersect each other at a current density of approximately 1.15 elec˚ 2 s. As a result, the beam diameter in Fig. 4 is trons/A smaller than that in Fig. 3 at current densities lower than ˚ 2 s. Moreover, Dc increases not only with 1.15 electrons/A decreasing current density but also with decreasing beam
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Fig. 7. Contrast as function of acceleration voltage.
Here, E is the energy loss, e is the charge of the electron, q is the mean density, NA is Avogadro’s number, Z is the average atomic number and hAi is the average atomic weight of the material. For hAi < 11, the mean excitation energy is J = 11.5Z eV, for hAi P 11, J = (9.76Z + 58.5Z0.19) eV [8]. In the case of thin specimens, we can obtain the average energy loss per depth length using the relation dE/dz DE/Dz, where DE is the energy loss averaged over all electrons and Dz is the specimen thickness. Under steady-state conditions, the heat generated by the transmitted beam is equal to the energy loss DE. Assuming that the heat dissipates from the radiated area (radius r) to the grid bars located at a distance R = 100 lm r from the center of the area, we find the temperature Tm at the center from the following formula [9]. T m ¼ T 0 þ ðI 0 r2 DE=4jDzÞ½c þ lnðR=rÞ2 :
Fig. 6. SWNT images taken with imaging plates at acceleration voltages of 40, 60, 100 and 120 kV, respectively.
diameter at a fixed current density. Hence, it is advantageous to observe radiation-sensitive samples using a low current density and a small illuminated object area. The energy loss of inelastic scattering per depth of a specimen is given by the Bethe energy-loss formula [7]. dE 2pe4 qN A Z 2E ¼ ln : ð1Þ dz E hAi J
ð2Þ
Here, I0 is the current density and T0 is the temperature of the grid; Dz and c denote the thickness of the sample (10 nm) and the Euler constant, respectively. Employing Eqs. (1) and (2), we calculated the temperature rise DT = Tm T0 for each radiation condition. Using Eqs. (1) and (2), we represent the critical dose shown in Figs. 3 and 4 as a function of the product of temperature rise and thermal conductivity. The result is shown in Fig. 8. We substitute the thermal conductivity of a polycarbonate, j = 0.19 [10], for the unknown thermal conductivity of copper–phthalocyanine, although this substitution overestimates the thermal conductivity of copper–phthalocya˚ 2 and j = 0.19 W/ nine. Choosing Dc 25 electrons/A m K, we obtain DT 0.3 K. Since this increase is unreasonably small, we conclude that the thermal conductivity of copper–phthalocyanine might be much lower than that of a polycarbonate. Our conclusion is based on the fact that the thermal conductivity decreases with decreasing sample thickness [11]. For a thickness of approximately 10 nm, the thermal conductivity is approximately three times smaller than that of the bulk. Moreover, thermal conductivity is related to crystal orientation. The shape of the copper–phthalocyanine molecule is that of a disk. These disks forming the film stand up vertically on the mica plane. Therefore, the stacking direction is parallel to the mica plane. This direction coincides with the heat flow. It
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Fig. 9. Specimen resolution as function of acceleration voltage. Fig. 8. Critical dose as function of product of temperature rise and thermal conductivity.
is known that graphite also has such a layer structure. The thermal conductivity in the direction perpendicular to the layer is approximately 40 times lower than that in the direction parallel to the layer. Therefore, we assume the same properties for copper–phthalocyanine. We used for this specimen the thermal conductivity of copper–phthalocyanine, which is 120 times lower than 0.19 W/m K. Choosing Dc 25, we obtain DT 50 K for j = 0.00158 W/m K. Fig. 8 shows that the critical dose increases with decreasing temperature rise. This representation shows that the critical dose of copper–phthalocyanine only depends on temperature rise, because the curves of Figs. 3 and 4 can be fitted by a common line. If the electron dose is limited by the critical dose Dc, the maximum number of electrons n, which we can use for one pixel, whose area is the square of the pixel size ds, is given by n ¼ d 2s Dc :
ð3Þ
Moreover, the noise induced in the pixel is equal to the statistical fluctuation of n, and the signal intensity is equal to the product of the object contrast C and n. Consequently, S/N is given as n S=N ¼ C pffiffiffi : ð4Þ n Employing Eq. (3), the ratio of S/N to ds depends on C and Dc as pffiffiffiffiffiffi S=N ð5Þ ¼ C Dc : ds If we want to observe a sample with a high-resolution, the pixel size must be small. Therefore, we can replace in Eq. (5) the pixel size ds to the specimen resolution limit [12]. If ds is large, S/N becomes high, but resolution becomes low. Inversely, if the specimen resolution limit ds is small, S/N becomes low. Using the contrast and critical dose shown in Figs. 5 and 7, respectively, we have calculated the product of C and pffiffiffiffiffi ffi Dc for copper–phthalocyanine as a function of acceleration voltage, which is shown as a plot in Fig. 9. This product served as a measure for image quality. Fig. 9 demonstrates that the specimen resolution improves by a factor
of 1.5 if we decrease the voltage from approximately 100 kV to approximately 40 kV. Assuming S/N = 4, we ˚ at 40 kV, whereas we obtain ds = 8 A ˚ at obtain ds = 5.3 A 100 kV. In conclusion, our studies demonstrate that images of copper–phthalocyanine should be taken with a small illuminated objective area and at low acceleration voltages to obtain maximum specimen resolution. Moreover, our results may be applied to carbonaceous samples whose radiation damage mechanisms are similar to those of copper–phthalocyanine. 5. Conclusions Our experimental results showed that the critical dose for extinction of the diffraction pattern from the copper– phthalocyanine crystalline film increased with decreasing current density, decreasing beam diameter and increasing acceleration voltage. However, the result for the SWNT demonstrated that the image contrast of the thin sample composed of light atoms increased with decreasing acceleration voltage. By detailed discussions, it was demonstrated that images of copper–phthalocyanine should be taken at low acceleration voltages to achieve the minimum specimen resolution limit at voltages of 40 kV 6 U 6 100 kV. Our result should be useful, in observing samples whose radiation damage mechanisms and composing atoms are similar to those of copper–phthalocyanine. Acknowledgements We are very grateful to Professor H. Rose of Darmstadt University of Technology, Germany for critical reading, stimulating discussion and important suggestions. Thanks are also due to Professor R. Shimizu of Osaka Institute of Technology, Japan for encouragement and critical discussion. References [1] K. Kobayashi, K. Sakaoku, Bull. Inst. Chem. Res. Kyoto Univ. 42 (1964) 473. [2] R.M. Glaeser, Physical Aspects of Electron Microscopy and Microbeam Analysis, Wiley, New York, 1975, p. 205. [3] S.M. Salih, V.E. Cosslett, J. Microsc. 105 (1975) 269.
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[4] Y. Fujiyoshi, Advances in Biophysics, vol. 35, Japan Sciences Societies Press, Tokyo, 1998, p. 25. [5] T. Ohno, M. Sengoku, T. Arii, Micron 33 (2002) 403. [6] A. Fukami, K. Adachi, J. Microsc. 14 (2) (1965) 112. [7] H. Bethe, Ann. Physik. 5 (1930) 325. [8] R. Wilson, Phys. Rev. 60 (1941) 749.
[9] S.B. Fisher, Radiat. Eff. 5 (1970) 239. [10] J.F. Shackelford, W. Alexander, J.S. Park (Eds.), CRC Material Science and Engineering Handbook, CRC Press, Boca Raton, 1994, p. 296. [11] H. Hieber, L. Lassak, Thin Solid Films 20 (1974) 63. [12] H. Rose, J. Fertig, Ultramicroscopy 2 (1976) 77.
Nuclear Instruments and Methods in Physics Research B 248 (2006) 273–278 www.elsevier.com/locate/nimb
Estimation of suitable condition for observing copper–phthalocyanine crystalline film by transmission electron microscopy Misa Hayashida *, Tadahiro Kawasaki, Yoshihide Kimura, Yoshizo Takai Department of Material and Life Science, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan Received 25 March 2006; received in revised form 13 April 2006 Available online 22 June 2006
Abstract The decay of the electron diffraction intensity of a copper–phthalocyanine crystalline film was quantitatively measured at room temperature by transmission electron microscopy (TEM) as a function of current density and beam diameter. The measurements revealed that the critical dose increases with decreasing current density, decreasing beam diameter and increasing acceleration voltage. Generally, the damage process only depends on the electron dose. However, the temperature rise of the copper–phthalocyanine enhances the damage process. The relationship between damage and acceleration voltage has been measured, and the result shows that an increase in acceleration voltage decreases the damage. The relationship between image contrast and acceleration voltage was also measured using a single-wall carbon nanotube (SWNT) as a radiation-insensitive substitute for the copper–phthalocyanine in order to obtain atomic-level images. The results revealed that image contrast increases with decreasing acceleration voltage. Using these oppositely behaving results, the most suitable voltage for observing copper–phthalocyanine crystalline films was estimated. The results show that low acceleration voltages should be used for imaging to achieve the minimum specimen resolution limit. Ó 2006 Elsevier B.V. All rights reserved. PACS: 42.25.Fx Keywords: Critical dose; Radiation damage; Transmission electron microscopy
1. Introduction The clarity of an observed image is generally determined by the relationship between the object contrast and the signal to noise ratio (S/N). The image becomes blurry when the S/N of the image is low and the object contrast is weak. The image sharpens when the S/N and object contrast increase. The clearness of the image depends on the balance between the object contrast and the S/N. In transmission electron microscopy (TEM), the object contrast of a specimen is changed by acceleration voltage. On the other hand, the S/N is determined by the statistical fluctuation *
Corresponding author. Tel.: +81 6 6879 4581; fax: +81 6 6879 7843. E-mail address: [email protected] (M. Hayashida). 0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.04.168
of the detection pixel, which is proportional to the electron dose used for the observation. For observing radiation-sensitive materials, such as organic or biological samples, only very low electron doses are permitted. Otherwise the structure of the specimen will be destroyed. As a result, the S/N of the observed image becomes low. Furthermore, since such biological specimens consist of light atoms, the object contrast is very low. These situations lead to the most crucial problem of achieving high-resolution images of radiation-sensitive materials. Electron-beam-induced damage in TEM samples has been evaluated by many researchers [1–5], measuring the fading rate of electron diffraction spot intensities of crystalline objects under electron beam irradiation. In these measurements, the critical dose (Dc) was defined as the dose at which the diffraction spot intensity decreases to 1/e of the
274
M. Hayashida et al. / Nucl. Instr. and Meth. in Phys. Res. B 248 (2006) 273–278
initial value. The critical dose serves as a measure for the tolerance of the object with respect to the electron beam irradiation. If Dc becomes M times larger, the radiation damage reduces to 1/M. Hence, the M times larger electron dose can be used for the observation. Aspaffiffiffiffiffiresult, the S/N of the observed image will be improved M times because the noise is defined as the statistical fluctuation of the number of irradiated electrons. In general, the magnitude of the irradiation damage depends on the accumulated total electron dose. However, Sali and Cosslett [3] and Fujiyoshi [4] reported that Dc decreases with increasing temperature of the specimen induced by the electron beam. Therefore, the magnitude of the radiation damage depends on the radiation conditions in terms of parameters such as current density and beam size. We must resolve the problem whether the magnitude of the radiation damage depends on the radiation conditions. Kobayashi et al. [1] reported that the magnitude of the radiation damage decreases as acceleration voltage increases, because the inelastic scattering cross section of the atoms becomes smaller as the acceleration voltage increases, leading to an increase in Dc at a high acceleration voltage. However, the image contrast becomes weak as the acceleration voltage increases because the elastic scattering cross section decreases in inverse proportion to the square of electron velocity. Therefore, we must also resolve the problem if it is better to take an image at a high accelerating voltage and a high electron dose by improving S/N or at a relatively low voltage and low dose by improving the object contrast. In the present paper, we used a copper–phthalocyanine crystalline film as an example for a radiation sensitive sample to estimate the most suitable TEM conditions. We measured the decay of the electron diffraction intensity from a copper–phthalocyanine crystalline film as function of current density, beam diameter and acceleration voltage. For measuring the image contrast, we used a single-wall carbon nanotube (SWNT), because it is difficult to obtain atomiclevel-resolution images of radiation-sensitive samples such as copper–phthalocyanine. Since carbon atoms are the main element of copper–phthalocyanine, the SWNT was used as a substitute. We estimated the so-called specimen resolution limit by using it as a criterion of the minimum observable object size. Our experimental results demonstrated that images of copper–phthalocyanine crystalline film should be obtained at small illuminating beam diameters, low current densities and low acceleration voltages.
ferred onto a TEM microgrid [6]. Electron diffraction was observed by TEM (Hitachi H-7500). To determine the current density on the sample, we measured the spot size of the electron beam on a screen and the current intensity with a pico-ammeter and took into account the magnification value of the TEM apparatus. Fig. 1 shows an example of the decay sequence of the electron diffraction patterns of copper–phthalocyanine. The patterns were recorded with an imaging plate at a fixed ˚ 2 s at 60 kV. Each image current density of 0.03 electrons/A of Fig. 1 was recorded for 30 s and the total dose is indicated in each frame. To reduce the effect of specimen drift and the fluctuation of the beam current during observation, we used a slow-scan CCD camera to reduce the total recording time. To avoid saturation of the CCD camera, we only selected the part of the diffraction pattern which did not contain the bright central spot. The dependence of the fading of the diffraction spot intensity was measured at a 60 kV acceleration voltage by changing current density and beam diameter in two ways: (a) by changing the brightness at a constant beam current and (b) by changing the beam current at a fixed beam diameter. The dependence on acceleration voltage was also measured in the range between 40 and 100 kV with a fixed current density and a fixed beam diameter. In addition, we measured the change in contrast as a function of acceleration voltage from the SWNT images, which were recorded with imaging plates at a constant current density. These images were recorded without an aperture at an almost constant defocus.
2. Experimental ˚ -thick copFor our experiments, we prepared a 100-A per–phthalocyanine crystalline film by vacuum evaporation on a freshly cleaved mica surface whose temperature was kept at 250 °C. After removing the evaporated film from the mica substrate on the water surface, the film was trans-
Fig. 1. Decay sequence of electron diffraction pattern of copper– phthalocyanine crystalline film for different doses obtained at 60 kV.
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3. Results The structure of the electron diffraction patterns decays with increasing dose, as shown in Fig. 1 for copper–phthalocyanine. As an example, we chose the decrease in the ˚) intensity of the (0 0 2) diffraction spot (half of 13 A depicted in Fig. 2(a) and measured the line profile in the rectangular area shown by a white broken line. The line profile is shown in Fig. 2(b). The ratio of the spot intensity to background intensity, A/B, in Fig. 2(b) is plotted in Fig. 2(c) as a function of the total electron dose using the patterns shown in Fig. 1. In this case, Dc is 17 electrons/ ˚ 2. Then we measured the critical dose Dc as a function A of current density (Figs. 3 and 4) obtained by maintaining (a) the beam current at approximately 0.07 nA (Fig. 3) and (b) the beam diameter at approximately 2.2 lm (Fig. 4). The curves clearly indicate that Dc decreases as current density increases. Hence, the radiation damage increases with current density.
Fig. 4. Critical dose as function of current density. The measurements were performed by maintaining the beam diameter (approximately 2.2 lm) constant.
Fig. 5. Critical dose as function of acceleration voltage.
Fig. 2. (a) Electron diffraction pattern. (b) Line profile along square in (a). (c) Spot intensity as function of electron dose.
Critical dose is plotted in Fig. 5 as a function of the acceleration voltage U for a constant beam diameter (approximately 1.3 lm) and a constant beam current (approximately 0.012 nA). The result shows that Dc decreases with decreasing acceleration voltage, approximately proportional to U2.3. The recorded images of SWNT shown in Fig. 6 demonstrate that the contrast (Ia Ib)/Ib increases with decreasing voltage, where Ia and Ib are the intensities of the SWNT and vacuum area, respectively. The contrast was plotted as a function of acceleration voltage as shown in Fig. 7. It is roughly proportional to 1/U1.6 in the range of 40 kV 6 U 6 120 kV. We can understand this dependence if we consider that the total contrast is composed of the phase contrast and the scattering absorption contrast. The former is proportional to 1/U, while the latter is proportional to 1/U2 becoming predominant at low voltages. 4. Discussion
Fig. 3. Critical dose as function of current density. The measurements were performed for a fixed beam current (approximately 0.07 nA).
The two curves shown in Figs. 3 and 4 intersect each other at a current density of approximately 1.15 elec˚ 2 s. As a result, the beam diameter in Fig. 4 is trons/A smaller than that in Fig. 3 at current densities lower than ˚ 2 s. Moreover, Dc increases not only with 1.15 electrons/A decreasing current density but also with decreasing beam
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Fig. 7. Contrast as function of acceleration voltage.
Here, E is the energy loss, e is the charge of the electron, q is the mean density, NA is Avogadro’s number, Z is the average atomic number and hAi is the average atomic weight of the material. For hAi < 11, the mean excitation energy is J = 11.5Z eV, for hAi P 11, J = (9.76Z + 58.5Z0.19) eV [8]. In the case of thin specimens, we can obtain the average energy loss per depth length using the relation dE/dz DE/Dz, where DE is the energy loss averaged over all electrons and Dz is the specimen thickness. Under steady-state conditions, the heat generated by the transmitted beam is equal to the energy loss DE. Assuming that the heat dissipates from the radiated area (radius r) to the grid bars located at a distance R = 100 lm r from the center of the area, we find the temperature Tm at the center from the following formula [9]. T m ¼ T 0 þ ðI 0 r2 DE=4jDzÞ½c þ lnðR=rÞ2 :
Fig. 6. SWNT images taken with imaging plates at acceleration voltages of 40, 60, 100 and 120 kV, respectively.
diameter at a fixed current density. Hence, it is advantageous to observe radiation-sensitive samples using a low current density and a small illuminated object area. The energy loss of inelastic scattering per depth of a specimen is given by the Bethe energy-loss formula [7]. dE 2pe4 qN A Z 2E ¼ ln : ð1Þ dz E hAi J
ð2Þ
Here, I0 is the current density and T0 is the temperature of the grid; Dz and c denote the thickness of the sample (10 nm) and the Euler constant, respectively. Employing Eqs. (1) and (2), we calculated the temperature rise DT = Tm T0 for each radiation condition. Using Eqs. (1) and (2), we represent the critical dose shown in Figs. 3 and 4 as a function of the product of temperature rise and thermal conductivity. The result is shown in Fig. 8. We substitute the thermal conductivity of a polycarbonate, j = 0.19 [10], for the unknown thermal conductivity of copper–phthalocyanine, although this substitution overestimates the thermal conductivity of copper–phthalocya˚ 2 and j = 0.19 W/ nine. Choosing Dc 25 electrons/A m K, we obtain DT 0.3 K. Since this increase is unreasonably small, we conclude that the thermal conductivity of copper–phthalocyanine might be much lower than that of a polycarbonate. Our conclusion is based on the fact that the thermal conductivity decreases with decreasing sample thickness [11]. For a thickness of approximately 10 nm, the thermal conductivity is approximately three times smaller than that of the bulk. Moreover, thermal conductivity is related to crystal orientation. The shape of the copper–phthalocyanine molecule is that of a disk. These disks forming the film stand up vertically on the mica plane. Therefore, the stacking direction is parallel to the mica plane. This direction coincides with the heat flow. It
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Fig. 9. Specimen resolution as function of acceleration voltage. Fig. 8. Critical dose as function of product of temperature rise and thermal conductivity.
is known that graphite also has such a layer structure. The thermal conductivity in the direction perpendicular to the layer is approximately 40 times lower than that in the direction parallel to the layer. Therefore, we assume the same properties for copper–phthalocyanine. We used for this specimen the thermal conductivity of copper–phthalocyanine, which is 120 times lower than 0.19 W/m K. Choosing Dc 25, we obtain DT 50 K for j = 0.00158 W/m K. Fig. 8 shows that the critical dose increases with decreasing temperature rise. This representation shows that the critical dose of copper–phthalocyanine only depends on temperature rise, because the curves of Figs. 3 and 4 can be fitted by a common line. If the electron dose is limited by the critical dose Dc, the maximum number of electrons n, which we can use for one pixel, whose area is the square of the pixel size ds, is given by n ¼ d 2s Dc :
ð3Þ
Moreover, the noise induced in the pixel is equal to the statistical fluctuation of n, and the signal intensity is equal to the product of the object contrast C and n. Consequently, S/N is given as n S=N ¼ C pffiffiffi : ð4Þ n Employing Eq. (3), the ratio of S/N to ds depends on C and Dc as pffiffiffiffiffiffi S=N ð5Þ ¼ C Dc : ds If we want to observe a sample with a high-resolution, the pixel size must be small. Therefore, we can replace in Eq. (5) the pixel size ds to the specimen resolution limit [12]. If ds is large, S/N becomes high, but resolution becomes low. Inversely, if the specimen resolution limit ds is small, S/N becomes low. Using the contrast and critical dose shown in Figs. 5 and 7, respectively, we have calculated the product of C and pffiffiffiffiffi ffi Dc for copper–phthalocyanine as a function of acceleration voltage, which is shown as a plot in Fig. 9. This product served as a measure for image quality. Fig. 9 demonstrates that the specimen resolution improves by a factor
of 1.5 if we decrease the voltage from approximately 100 kV to approximately 40 kV. Assuming S/N = 4, we ˚ at 40 kV, whereas we obtain ds = 8 A ˚ at obtain ds = 5.3 A 100 kV. In conclusion, our studies demonstrate that images of copper–phthalocyanine should be taken with a small illuminated objective area and at low acceleration voltages to obtain maximum specimen resolution. Moreover, our results may be applied to carbonaceous samples whose radiation damage mechanisms are similar to those of copper–phthalocyanine. 5. Conclusions Our experimental results showed that the critical dose for extinction of the diffraction pattern from the copper– phthalocyanine crystalline film increased with decreasing current density, decreasing beam diameter and increasing acceleration voltage. However, the result for the SWNT demonstrated that the image contrast of the thin sample composed of light atoms increased with decreasing acceleration voltage. By detailed discussions, it was demonstrated that images of copper–phthalocyanine should be taken at low acceleration voltages to achieve the minimum specimen resolution limit at voltages of 40 kV 6 U 6 100 kV. Our result should be useful, in observing samples whose radiation damage mechanisms and composing atoms are similar to those of copper–phthalocyanine. Acknowledgements We are very grateful to Professor H. Rose of Darmstadt University of Technology, Germany for critical reading, stimulating discussion and important suggestions. Thanks are also due to Professor R. Shimizu of Osaka Institute of Technology, Japan for encouragement and critical discussion. References [1] K. Kobayashi, K. Sakaoku, Bull. Inst. Chem. Res. Kyoto Univ. 42 (1964) 473. [2] R.M. Glaeser, Physical Aspects of Electron Microscopy and Microbeam Analysis, Wiley, New York, 1975, p. 205. [3] S.M. Salih, V.E. Cosslett, J. Microsc. 105 (1975) 269.
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[4] Y. Fujiyoshi, Advances in Biophysics, vol. 35, Japan Sciences Societies Press, Tokyo, 1998, p. 25. [5] T. Ohno, M. Sengoku, T. Arii, Micron 33 (2002) 403. [6] A. Fukami, K. Adachi, J. Microsc. 14 (2) (1965) 112. [7] H. Bethe, Ann. Physik. 5 (1930) 325. [8] R. Wilson, Phys. Rev. 60 (1941) 749.
[9] S.B. Fisher, Radiat. Eff. 5 (1970) 239. [10] J.F. Shackelford, W. Alexander, J.S. Park (Eds.), CRC Material Science and Engineering Handbook, CRC Press, Boca Raton, 1994, p. 296. [11] H. Hieber, L. Lassak, Thin Solid Films 20 (1974) 63. [12] H. Rose, J. Fertig, Ultramicroscopy 2 (1976) 77.