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Charging effect on the HRTEM imaging of small MgO crystals
Ultramicroscopy 27 (1989) 223-232 North-Holland, Amsterdam
223
CHARGING EFFECT ON THE HRTEM IMAGING OF SMALL MgO CRYSTALS Takayoshi T A N J I , Hideki M A S A O K A *, Jhota I T O and Keiji Y A D A Research Institute for Scientific Measurements, Tokohu University, Sendai 980, Japan and
John M. C O W L E Y Department of Physics, Arizona State Unioersity, Tempe, Arizona 85287, USA
Received 21 September 1988; in final form 2 January 1989
It is reported that lattice fringes appearing in the profile image of the (100) surface of a small MgO crystal observed from the [001]or [011] direction by a high-resolution conventional transmission electron microscope show strange bending at the comers of the crystal. In order to interpret this bending of fringes on the surface, a charging effect is introduced into the contrast simulation with the multi-slice method. Contrasts simulated on the assumption of three types of charge distribution are compared with actual micrographs. It is found that the bending of fringes can be explained by the charging effect, that is, lattice fringes are observed as being bent even if the atomic arrangement is not distorted. The seriousness of the effect of charging on imaging does not depend on the density of charge, but on the total amount of additive charges in the whole of the crystal. The calculated images that include the effects of defocus and aberrations of the electron lenses are much more sensitive to the charging effects than the calculated intensity distributions at the exit surface of the crystal.
1. Introduction
The profile image method, the lateral observation of surfaces b y electron microscopy, allows the high resolution microscopy of flat surfaces of small crystals and thin films. Although the information obtained by this method is the projection of those surfaces, it has the great advantage of allowing the study of surfaces in real space, especially for the dynamical observations of the surface reconstruction, relaxation, reactions with gases and so on. Tanji and Cowley [1] have shown that strange bending of lattice and contour fringes is recognized at the comers of the (100) surfaces of MgO smoke crystallites observed from the [001] direction by a 200 kV transmission electron microscope (fig. 1). The fringes give the impression that there is a large surface relaxation on a gold thin film as reported by Marks and Smith [2] with a 600 kV * Present address: JEOL Ltd., Akishima, Tokyo 196, Japan.
electron microscope. MgO is an insulator which has a high secondary-electron yield. As almost all the high energy primary electrons pass through the small MgO particle prepared by the burning method, it is reasonable to guess that the excess of secondary-electron emission causes the specimen to be charged positively. It has been pointed out by several persons that the charging effect would play an appreciable role in the observation of small particles. Howie and Milne [3] reported that their electron energy loss spectrum from a small MgO particle could be understood by using the positive charging effect and also that the b e a m deflection observed b y Cowley [4] was explainable by this effect. Iijima and Ichihashi [5] showed that gold atoms move on the surface during the observation of very small gold particles in a transmission electron microscope. Ichihashi and Iijima [6] suggested that the charging effect plays a more important role for that motion of atoms than the thermal energy supplied by the electron irradia-
0304-3991/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
224
T. Tanji et aL / Charging effect on HRTEM imaging of small MgO crystals
Fig. 1. Bending fringes on the (100) surface of MgO, 200 nm cube, projected on the (001) plane at the accelerating voltage of The behavior of the bending changes from (a) to (b) with the defocus value of the electron microscope[1].
tion. The present authors have reported that the positive charging m a y distort high resolution profile images [7]. It is the purpose of this paper to show that the bending of the fringes at a c o m e r can be explained by the charging effect without any deviation of the atom positions at the surface from the lattice points of the bulk crystal. 2. Experiment
Both the preparation of specimen and the procedure for obtaining the image of the surface of a small crystal at an exact orientation have been reported in the previous paper [1]. Images of (100) surfaces of MgO smoke crystals shown in figs. 1 and 2 were obtained by using a conventional transmission electron microscope with an accelerating voltage of 200 kV from the [001] direction. Fig. 1 shows a pair of images of a cubic crystal with edges of 200 nm taken with different defocus values, where contour fringes like the Fresnel •fringes (see ref. [1] for details) on the two sides of the crystal are bent near the c o m e r of the crystal, as are the lattice fringes. The bending behavior of
Fig. 2. Profile images of a surface step ( - 3 nm × 3 nm on the same (100) surface shown in fig. 1 [1].
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
225
the fringes varies with the defocus value. The side view of small steps on the (100) surface shown in fig. 2 also shows distorted fringes. If a higher accelerating voltage is used, the bending behavior is observed more clearly, as seen i n fig. 3 which is the image of a 100 n m cube taken by a 400 kV electron microscope. When the (100) surfaces are observed from the [011] direction with an accelerating voltage of 200 kV, weak bending of the fringes is noted, as shown in fig. 4.
3. Numerical approach
Fig. 3. Bending of lattice fringes projected on the (001) plane at the accelerating voltage of 400 kV. The crystal is a 100 nm cube.
In order to simulate the contrast of the surface profile image, the unit cell in the multi-slice calculation should be extended. Considering that the charging-up of the specimen causes a long-range force, the virtual unit cell used has dimensions 5.04 n m (12a0) x 5.04 n m (12a0) x 0.42 nm (a0), one: fourth of which is occupied by=the real crystal of 2.52 n m (6a0) x 2.52 n m (6a0) x 0.42 nm (a0) (a0: lattice parameter of MgO) in the centre and elsewhere by a vacuum,-as shown in fig. 5. The instrumental parameters used in the calculation were as follows: the spherical aberration coefficient, Cs, is 1.2 m m at 200 kV and 1.0 m m at 400 kV, the half-angle of the incident b e a m convergence, a¢, is 1.5 mrad, and the half-width of the focal spread, 8, is 15 nnL The number of pixels used in the multi-slice calculation was 512 x 512. The transmission cross-coefficients [8] between diffracted waves were taken into consideration, because they play a very important role in a contrast transfer function for images of thick crystals as considered here. In the simulation of real images including the effects of aberrations,
T
q 2.52 nm, (6d ~oo)
-~
[..cr yst..1
o ui
•I Fig. 4. Bending of the surface fringe appearing on the (001) surface projected on the (011) plane,
vacuum
Fig. 5. Extended unit cell for the simulation of charged partides.
226
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
Fig. 6. Simulated wave fields (a,c,e) and images at Cs ffi 1.2 m m , d f ffi 50 n ~ (b,d,f) of M g O particles charged as p ffi 0 (a,b), e / a t o m (c,d) a n d O ffi C [ r] 2, p = 1 / 8 e / a t o m at m a x i m u m (e,f). The crystal thickness is 200 n m and the accelerating volta~
T. Tanji et al. / Charging effect on HRTEM imaging of small MgO crystals
a
227
b
Fig. 7. Simulated wave fields (a,c,e) and images at C s =1.0 nun, d / = 30 n m (b,d,f) of M g O particles charged as p = 0 (a,b), p = 1 / 1 6 e / a t o m (c,d) and O = Clrl 2, p = 1 / 4 e / a t o m at m a x i m u m (e,f). The crystal is 100 n m thick projected on the (001) plane and the accelerating voltage 400 kV.
228
T. Tanjiet al. / Chargingeffect on HRTEM imagingof small MgO crystals
waves up to the 220 reflections were m a d e to contribute to imaging through an objective aperture. T h e structure factors for the extended virtual unit cell are given b y
Fc(k) = Fo(k ) + E L ( k )
Fo( k ) = E f 2 : ( k ) e x p ( - 2 ~ ' i k ,
f , ( k ) = moe2p( r,) /(2rrh2¢o I k [2),
r~)
+ Y~fo2-(k) e x p ( - Z ~ r i k . r j ) ,
(1)
where f 2 ~ and f 2 - are the atomic scattering amplitudes of M g 2+ [9] and 0 2- [1] respectively, k is the wave vector, r~ the position of the i th M g ion and ~ the position of the j t h 0 ion. T h e effect of charging on the structure factor was introduced
Fig. 8.
b y adding a charge p(r.) at the position pixel, where r. is the vector f r o m the cente extended unit cell; thus exp(-2~rik,
r,)
where m0, e, h a n d c o have their usual m and the density of positive charge at a poi assumed to be
p(r.)=Clr, l', where C and 1 are constant.
Variation of the simulated image contrast with the defocus values of - 50 n m (a), 0 (b), 50 n m (c) and 100 nm (d) un, T h e crystal thickness is 100 nm, p = 1/16 e/atom, the accelerating voltage is 400 kV and Cs = 1.0 mm.
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
4. Results of simulation
Fig. 6 shows the calculated contrast of images at the comer of a MgO crystal of 200 nm thickness for the accelerating voltage of 200 kV. In the case of p = 0 (figs. 6a and 6b), i.e. without charging effect, bending of the fringes is not observed under any focusing condition. In the cases of a
229
constant p (i.e. l ffi0; figs. 6c and 6d) and a parabolic p (i.e. 1 ffi 2; figs. 6e and 50, the bending of fringes can be seen both in the wave-fields and in the images including aberration effects. Especially the image contrast with the constant p (fig. 6d) is similar to the electron microscopic image shown in fig. 1. The charges put on each pixel were 4.5 e / n m 3, which corresponds to 1/24
Fig. 9. Simulated wave fields (a,d,g), and images at Cs ffi 1.2 m m , d / = 30 n m undvrfocus (b,e,h) a n d images at Cs ffi 1.2 m m , d/ffi 100 n m underfocus (c,f,i) of M g O small particles charged as p ffi 0 (a,b,c), p • 1 / 1 6 e / a t o m (d,e,f) a n d p • 1 / 4 e / a t o m (g,h,i). The crystal is 5 n m thick projected on the (001) plane a n d the accelerating voltage is 200 kV.
230
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
e / a t o m for figs. 6c and 6d. The charged varied from 0 at the center to 13.5 e / n m 3 ( 1 / 8 e / a t o m ) at the comer for figs. 6e and 6f. Results for the accelerating voltage of 400 kV are shown in fig. 7. In contrast to images of p = 0 (figs. 7a and 7b), both the wave-field and the image distorted by aberrations clearly show bending of lattice fringes when p is either constant (i.e. l = 0; figs. 7c and 7d) or parabolic (i.e. l = 2; figs. 7e and 7f). The positive charges were 6.7 e / n m 3, which corresponds to 1 / 1 6 e / a t o m , for figs. 7c and 7d, and varied from 0 at the center to 27.0 e / n m 3 ( 1 / 4 e / a t o m ) at the comer for figs. 7e and 7f. Fig. 8 shows examples where the bending of the lattice fringe appears and disappears according to the focussing, while other conditions are the same as figs. 7c and 7d. For a very small crystal, the bending is not caused unless the amount of additive charges is very large. In fig. 9 the amount of positive charge is increased up to 27.0 e / n m 3 ( 1 / 4 e / a t o m ) for the case of the crystal 5 nm cube at the accelerating voltage of 200 kV. The slight bending of fringes is seen in figs. 9h and 9i, although the corresponding wave field on the exit surface of the specimen shows nearly the same contrast as that without any additive charge (fig. 9a). The defocus values used are 30 and 100 nm underfocus.
5. Discussion and conclusions In order to interpret high resolution electron microscopic images of small MgO crystals, the positive charging effect was introduced into the contrast simulation with the multi-slice method. It depends on the accelerating voltage and the thickness of specimens whether the charging is positive or negative. Moreover, the result shown in fig. 10, where the negative charging was assumed, supports that the positive charging is more plausible in the case considered here. Since the distribution of positive charges p has not been measured experimentally on these small particles, some kinds of the distribution of additive charges were assumed in the calculation. The homogeneous distribution, that is, the constant p, seems to present
contrast most similar to the actual image fringe bending outward may be explained lows. The uniform charging will cause the gl of the average inner potential near the edl the comer of the crystal, because the poter each additive charge is not screened and e to a very long range. When the charging i; tive, the potential near the comer is sh~ than that at the inner area, and may act incident electrons as if it were repulsive seems to be the reason the fringes bend ou at comers. Present electron microscopes, hc have not enough spatial resolving power termine clearly this charge distribution. T~ ousness of the effect of charging on imagi pends strongly upon the total amount of a~ charges over the whole crystal. The area crystal in the virtual unit cell shown in fig. 5 be too small to simulate the charging eft actual images very accurately. Therefore the of charging used in figs. 6 and 7 is not a pl~ one. However, the amount of additive charg balanced state will be estimated if we can t extended unit cell so that the area occup real atoms in fig. 5 is as large as the specimen. A matter of importance is th bending of fringes at the comer can be sirr by the positive charging of the specimen, q the atomic arrangement is not distorted th~ shown in fig. 9, the charging to a very particle has no effect for the wave field, bu so, the aberrations of the imaging syste: cause the bending of fringes when cryst,' heavily charged. Although we may obser atomic arrangement at the surface of a under 5 n m in diameter, it should be rer that in the case of the surface step shown il or the thin edge in fig. 4, the effect of c stored in the mother crystal or in the particl cannot be ignored in the interpretation surface profile images. Because of the lonl~ of the Coulomb force, the effect of the char mostly a deflection of the electron beam, a effects on the images are expected to increa~ defocus. Thus the effect on the in-focus zer~ ration image is very small, but the effect is I for the out-of-focus conditions usually em I The inhomogeneity of the Coulomb force t
T. Tanji et al. / Charging effect on HRTEM imaging of small MgO crystals
¢
231
d
Fig. 10. Effects of the negative charging on wave fields (a,c) and images at Cs = 1.2 mm, d f = 50 nm underfocus (b,e) Of a MgO particle. The crystal thickness is 200 nm, p = - 1/24 e / a t o m (a,b) and p = C I r 12, O = _ 1 / 8 e / a t o m at maximum (c,d), and the accelerating voltage is 200 kV.
the comers of the crystal can be considered as the origin of the bending of the fringes.
Acknowledgements This work was partly supported by the National Science Foundation Grant DMR792640 and utilized resources of the Facility for High Resolution Electron Microscopy at Arizona State University supported by the NSF Grant DMR8306501.
References [1] T. Tanji and J.M. Cowley, Ultramicroscopy 17 (1985) 287.
[2] L.D. Marks and D.J. Smith, Surface Sci. 143 (1984) 495. [3] A. Howie and R.H. Milne, Ultramicroscopy 18 (1985) 427. [4] J.M. Cowley, Ultramicroscopy 7 (1981); Surface Sci. 114 (1982) 587. [5] S. Iijima and T. Ichihashi, Japan. J. Appl. Phys. 24 (1985) L125. [6] T. Ichihashi and S. Iijima, in: Proc. 41st Annual Meeting of Physical Society of Japan, Tokyo, 1986, p. 373 (in Japanese). [7] T. Tanji, H. Masaoka, K. Yada and J.M. Cowley, in: Proc. 11th Intern. Congr. on Electron Microscopy, Kyoto, 1986, Vol. 1, Eds. T. Imura, S. Maruse and T. Suzuki (Japan. Soc. of Electron Microscopy, Tokyo, 1986) p. 1353. [8] K. Ishizuka, Ultramicroscopy 5 (1980) 178. [9] International Tables for X-Ray Crystallography, Vol. 4, Eds. J. Ibers and W. Hamilton (Kynoch, Birmingham, 1974) p. 152.
223
CHARGING EFFECT ON THE HRTEM IMAGING OF SMALL MgO CRYSTALS Takayoshi T A N J I , Hideki M A S A O K A *, Jhota I T O and Keiji Y A D A Research Institute for Scientific Measurements, Tokohu University, Sendai 980, Japan and
John M. C O W L E Y Department of Physics, Arizona State Unioersity, Tempe, Arizona 85287, USA
Received 21 September 1988; in final form 2 January 1989
It is reported that lattice fringes appearing in the profile image of the (100) surface of a small MgO crystal observed from the [001]or [011] direction by a high-resolution conventional transmission electron microscope show strange bending at the comers of the crystal. In order to interpret this bending of fringes on the surface, a charging effect is introduced into the contrast simulation with the multi-slice method. Contrasts simulated on the assumption of three types of charge distribution are compared with actual micrographs. It is found that the bending of fringes can be explained by the charging effect, that is, lattice fringes are observed as being bent even if the atomic arrangement is not distorted. The seriousness of the effect of charging on imaging does not depend on the density of charge, but on the total amount of additive charges in the whole of the crystal. The calculated images that include the effects of defocus and aberrations of the electron lenses are much more sensitive to the charging effects than the calculated intensity distributions at the exit surface of the crystal.
1. Introduction
The profile image method, the lateral observation of surfaces b y electron microscopy, allows the high resolution microscopy of flat surfaces of small crystals and thin films. Although the information obtained by this method is the projection of those surfaces, it has the great advantage of allowing the study of surfaces in real space, especially for the dynamical observations of the surface reconstruction, relaxation, reactions with gases and so on. Tanji and Cowley [1] have shown that strange bending of lattice and contour fringes is recognized at the comers of the (100) surfaces of MgO smoke crystallites observed from the [001] direction by a 200 kV transmission electron microscope (fig. 1). The fringes give the impression that there is a large surface relaxation on a gold thin film as reported by Marks and Smith [2] with a 600 kV * Present address: JEOL Ltd., Akishima, Tokyo 196, Japan.
electron microscope. MgO is an insulator which has a high secondary-electron yield. As almost all the high energy primary electrons pass through the small MgO particle prepared by the burning method, it is reasonable to guess that the excess of secondary-electron emission causes the specimen to be charged positively. It has been pointed out by several persons that the charging effect would play an appreciable role in the observation of small particles. Howie and Milne [3] reported that their electron energy loss spectrum from a small MgO particle could be understood by using the positive charging effect and also that the b e a m deflection observed b y Cowley [4] was explainable by this effect. Iijima and Ichihashi [5] showed that gold atoms move on the surface during the observation of very small gold particles in a transmission electron microscope. Ichihashi and Iijima [6] suggested that the charging effect plays a more important role for that motion of atoms than the thermal energy supplied by the electron irradia-
0304-3991/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
224
T. Tanji et aL / Charging effect on HRTEM imaging of small MgO crystals
Fig. 1. Bending fringes on the (100) surface of MgO, 200 nm cube, projected on the (001) plane at the accelerating voltage of The behavior of the bending changes from (a) to (b) with the defocus value of the electron microscope[1].
tion. The present authors have reported that the positive charging m a y distort high resolution profile images [7]. It is the purpose of this paper to show that the bending of the fringes at a c o m e r can be explained by the charging effect without any deviation of the atom positions at the surface from the lattice points of the bulk crystal. 2. Experiment
Both the preparation of specimen and the procedure for obtaining the image of the surface of a small crystal at an exact orientation have been reported in the previous paper [1]. Images of (100) surfaces of MgO smoke crystals shown in figs. 1 and 2 were obtained by using a conventional transmission electron microscope with an accelerating voltage of 200 kV from the [001] direction. Fig. 1 shows a pair of images of a cubic crystal with edges of 200 nm taken with different defocus values, where contour fringes like the Fresnel •fringes (see ref. [1] for details) on the two sides of the crystal are bent near the c o m e r of the crystal, as are the lattice fringes. The bending behavior of
Fig. 2. Profile images of a surface step ( - 3 nm × 3 nm on the same (100) surface shown in fig. 1 [1].
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
225
the fringes varies with the defocus value. The side view of small steps on the (100) surface shown in fig. 2 also shows distorted fringes. If a higher accelerating voltage is used, the bending behavior is observed more clearly, as seen i n fig. 3 which is the image of a 100 n m cube taken by a 400 kV electron microscope. When the (100) surfaces are observed from the [011] direction with an accelerating voltage of 200 kV, weak bending of the fringes is noted, as shown in fig. 4.
3. Numerical approach
Fig. 3. Bending of lattice fringes projected on the (001) plane at the accelerating voltage of 400 kV. The crystal is a 100 nm cube.
In order to simulate the contrast of the surface profile image, the unit cell in the multi-slice calculation should be extended. Considering that the charging-up of the specimen causes a long-range force, the virtual unit cell used has dimensions 5.04 n m (12a0) x 5.04 n m (12a0) x 0.42 nm (a0), one: fourth of which is occupied by=the real crystal of 2.52 n m (6a0) x 2.52 n m (6a0) x 0.42 nm (a0) (a0: lattice parameter of MgO) in the centre and elsewhere by a vacuum,-as shown in fig. 5. The instrumental parameters used in the calculation were as follows: the spherical aberration coefficient, Cs, is 1.2 m m at 200 kV and 1.0 m m at 400 kV, the half-angle of the incident b e a m convergence, a¢, is 1.5 mrad, and the half-width of the focal spread, 8, is 15 nnL The number of pixels used in the multi-slice calculation was 512 x 512. The transmission cross-coefficients [8] between diffracted waves were taken into consideration, because they play a very important role in a contrast transfer function for images of thick crystals as considered here. In the simulation of real images including the effects of aberrations,
T
q 2.52 nm, (6d ~oo)
-~
[..cr yst..1
o ui
•I Fig. 4. Bending of the surface fringe appearing on the (001) surface projected on the (011) plane,
vacuum
Fig. 5. Extended unit cell for the simulation of charged partides.
226
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
Fig. 6. Simulated wave fields (a,c,e) and images at Cs ffi 1.2 m m , d f ffi 50 n ~ (b,d,f) of M g O particles charged as p ffi 0 (a,b), e / a t o m (c,d) a n d O ffi C [ r] 2, p = 1 / 8 e / a t o m at m a x i m u m (e,f). The crystal thickness is 200 n m and the accelerating volta~
T. Tanji et al. / Charging effect on HRTEM imaging of small MgO crystals
a
227
b
Fig. 7. Simulated wave fields (a,c,e) and images at C s =1.0 nun, d / = 30 n m (b,d,f) of M g O particles charged as p = 0 (a,b), p = 1 / 1 6 e / a t o m (c,d) and O = Clrl 2, p = 1 / 4 e / a t o m at m a x i m u m (e,f). The crystal is 100 n m thick projected on the (001) plane and the accelerating voltage 400 kV.
228
T. Tanjiet al. / Chargingeffect on HRTEM imagingof small MgO crystals
waves up to the 220 reflections were m a d e to contribute to imaging through an objective aperture. T h e structure factors for the extended virtual unit cell are given b y
Fc(k) = Fo(k ) + E L ( k )
Fo( k ) = E f 2 : ( k ) e x p ( - 2 ~ ' i k ,
f , ( k ) = moe2p( r,) /(2rrh2¢o I k [2),
r~)
+ Y~fo2-(k) e x p ( - Z ~ r i k . r j ) ,
(1)
where f 2 ~ and f 2 - are the atomic scattering amplitudes of M g 2+ [9] and 0 2- [1] respectively, k is the wave vector, r~ the position of the i th M g ion and ~ the position of the j t h 0 ion. T h e effect of charging on the structure factor was introduced
Fig. 8.
b y adding a charge p(r.) at the position pixel, where r. is the vector f r o m the cente extended unit cell; thus exp(-2~rik,
r,)
where m0, e, h a n d c o have their usual m and the density of positive charge at a poi assumed to be
p(r.)=Clr, l', where C and 1 are constant.
Variation of the simulated image contrast with the defocus values of - 50 n m (a), 0 (b), 50 n m (c) and 100 nm (d) un, T h e crystal thickness is 100 nm, p = 1/16 e/atom, the accelerating voltage is 400 kV and Cs = 1.0 mm.
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
4. Results of simulation
Fig. 6 shows the calculated contrast of images at the comer of a MgO crystal of 200 nm thickness for the accelerating voltage of 200 kV. In the case of p = 0 (figs. 6a and 6b), i.e. without charging effect, bending of the fringes is not observed under any focusing condition. In the cases of a
229
constant p (i.e. l ffi0; figs. 6c and 6d) and a parabolic p (i.e. 1 ffi 2; figs. 6e and 50, the bending of fringes can be seen both in the wave-fields and in the images including aberration effects. Especially the image contrast with the constant p (fig. 6d) is similar to the electron microscopic image shown in fig. 1. The charges put on each pixel were 4.5 e / n m 3, which corresponds to 1/24
Fig. 9. Simulated wave fields (a,d,g), and images at Cs ffi 1.2 m m , d / = 30 n m undvrfocus (b,e,h) a n d images at Cs ffi 1.2 m m , d/ffi 100 n m underfocus (c,f,i) of M g O small particles charged as p ffi 0 (a,b,c), p • 1 / 1 6 e / a t o m (d,e,f) a n d p • 1 / 4 e / a t o m (g,h,i). The crystal is 5 n m thick projected on the (001) plane a n d the accelerating voltage is 200 kV.
230
T. Tanji et al. / Charging effect on H R T E M imaging of small MgO crystals
e / a t o m for figs. 6c and 6d. The charged varied from 0 at the center to 13.5 e / n m 3 ( 1 / 8 e / a t o m ) at the comer for figs. 6e and 6f. Results for the accelerating voltage of 400 kV are shown in fig. 7. In contrast to images of p = 0 (figs. 7a and 7b), both the wave-field and the image distorted by aberrations clearly show bending of lattice fringes when p is either constant (i.e. l = 0; figs. 7c and 7d) or parabolic (i.e. l = 2; figs. 7e and 7f). The positive charges were 6.7 e / n m 3, which corresponds to 1 / 1 6 e / a t o m , for figs. 7c and 7d, and varied from 0 at the center to 27.0 e / n m 3 ( 1 / 4 e / a t o m ) at the comer for figs. 7e and 7f. Fig. 8 shows examples where the bending of the lattice fringe appears and disappears according to the focussing, while other conditions are the same as figs. 7c and 7d. For a very small crystal, the bending is not caused unless the amount of additive charges is very large. In fig. 9 the amount of positive charge is increased up to 27.0 e / n m 3 ( 1 / 4 e / a t o m ) for the case of the crystal 5 nm cube at the accelerating voltage of 200 kV. The slight bending of fringes is seen in figs. 9h and 9i, although the corresponding wave field on the exit surface of the specimen shows nearly the same contrast as that without any additive charge (fig. 9a). The defocus values used are 30 and 100 nm underfocus.
5. Discussion and conclusions In order to interpret high resolution electron microscopic images of small MgO crystals, the positive charging effect was introduced into the contrast simulation with the multi-slice method. It depends on the accelerating voltage and the thickness of specimens whether the charging is positive or negative. Moreover, the result shown in fig. 10, where the negative charging was assumed, supports that the positive charging is more plausible in the case considered here. Since the distribution of positive charges p has not been measured experimentally on these small particles, some kinds of the distribution of additive charges were assumed in the calculation. The homogeneous distribution, that is, the constant p, seems to present
contrast most similar to the actual image fringe bending outward may be explained lows. The uniform charging will cause the gl of the average inner potential near the edl the comer of the crystal, because the poter each additive charge is not screened and e to a very long range. When the charging i; tive, the potential near the comer is sh~ than that at the inner area, and may act incident electrons as if it were repulsive seems to be the reason the fringes bend ou at comers. Present electron microscopes, hc have not enough spatial resolving power termine clearly this charge distribution. T~ ousness of the effect of charging on imagi pends strongly upon the total amount of a~ charges over the whole crystal. The area crystal in the virtual unit cell shown in fig. 5 be too small to simulate the charging eft actual images very accurately. Therefore the of charging used in figs. 6 and 7 is not a pl~ one. However, the amount of additive charg balanced state will be estimated if we can t extended unit cell so that the area occup real atoms in fig. 5 is as large as the specimen. A matter of importance is th bending of fringes at the comer can be sirr by the positive charging of the specimen, q the atomic arrangement is not distorted th~ shown in fig. 9, the charging to a very particle has no effect for the wave field, bu so, the aberrations of the imaging syste: cause the bending of fringes when cryst,' heavily charged. Although we may obser atomic arrangement at the surface of a under 5 n m in diameter, it should be rer that in the case of the surface step shown il or the thin edge in fig. 4, the effect of c stored in the mother crystal or in the particl cannot be ignored in the interpretation surface profile images. Because of the lonl~ of the Coulomb force, the effect of the char mostly a deflection of the electron beam, a effects on the images are expected to increa~ defocus. Thus the effect on the in-focus zer~ ration image is very small, but the effect is I for the out-of-focus conditions usually em I The inhomogeneity of the Coulomb force t
T. Tanji et al. / Charging effect on HRTEM imaging of small MgO crystals
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d
Fig. 10. Effects of the negative charging on wave fields (a,c) and images at Cs = 1.2 mm, d f = 50 nm underfocus (b,e) Of a MgO particle. The crystal thickness is 200 nm, p = - 1/24 e / a t o m (a,b) and p = C I r 12, O = _ 1 / 8 e / a t o m at maximum (c,d), and the accelerating voltage is 200 kV.
the comers of the crystal can be considered as the origin of the bending of the fringes.
Acknowledgements This work was partly supported by the National Science Foundation Grant DMR792640 and utilized resources of the Facility for High Resolution Electron Microscopy at Arizona State University supported by the NSF Grant DMR8306501.
References [1] T. Tanji and J.M. Cowley, Ultramicroscopy 17 (1985) 287.
[2] L.D. Marks and D.J. Smith, Surface Sci. 143 (1984) 495. [3] A. Howie and R.H. Milne, Ultramicroscopy 18 (1985) 427. [4] J.M. Cowley, Ultramicroscopy 7 (1981); Surface Sci. 114 (1982) 587. [5] S. Iijima and T. Ichihashi, Japan. J. Appl. Phys. 24 (1985) L125. [6] T. Ichihashi and S. Iijima, in: Proc. 41st Annual Meeting of Physical Society of Japan, Tokyo, 1986, p. 373 (in Japanese). [7] T. Tanji, H. Masaoka, K. Yada and J.M. Cowley, in: Proc. 11th Intern. Congr. on Electron Microscopy, Kyoto, 1986, Vol. 1, Eds. T. Imura, S. Maruse and T. Suzuki (Japan. Soc. of Electron Microscopy, Tokyo, 1986) p. 1353. [8] K. Ishizuka, Ultramicroscopy 5 (1980) 178. [9] International Tables for X-Ray Crystallography, Vol. 4, Eds. J. Ibers and W. Hamilton (Kynoch, Birmingham, 1974) p. 152.