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Electron diffraction conditions and surface imaging in reflection electron microscopy
Ultramicroscopy 33 (1990) 237-254 North-Holland
ELECTRON DIFFRACTION CONDmONS ELECTRON MICROSCOPY
237
A N D S U R F A C E I M A G I N G IN R E F L E C T I O N
N a n Y A O and J.M. C O W L E Y Department of Physics, Arizona State University, Tempe, A Z 85287-1504, USA
Received 8 May 1990
Two resonance conditions responsible for enhancement of the specular reflected beam observed in the RHEED pattern have been characterized as Bragg-ehanneUing reflection and Bragg-Bragg reflection, respectively, in terms of different scattering mechanisms. Under the resonance condition, the tremendous increase of both elastic and inelastic electron scattering results in the intensity enhancement of the specular reflected beam. The total reflectivity does not change considerably with the variation of the diffraction condition. The improvement of the topographical contrast in surface imaging is not simply related to increase in the intensity of the specular reflected beam. The surface image obtained from the Bragg-Bragg reflection condition shows a better image contrast for the surface structure among the varieties of resonance conditions. The appearance of the abnormal double-contour contrast for a single-atom-height step is also closely associated with the Bragg-Braggreflection condition.
1. Introduction In the last decade, the use of transmission electron microscopy for surface imaging in the reflection mode has shown a considerable potential as a means for studying crystal surfaces. Many significant R E M (reflection electron microscopy) studies have been done, as reviewed recently by Cowley and Yagi [1-3]. In order to increase intensity and contrast in the image of a surface, the surface resonance condition has been widely used to enhance the Bragg reflection for image formation. The commonly cited geometries for attaining such surface resonance conditions require either that (i) a specular reflected Bragg spot falls on an intersection of a Kikuchi line parallel to the surface with a socalled surface resonance parabola [4-6], or (ii) a specular reflected Bragg spot coincides with an intersection of Kikuchi lines running parallel to, and oblique to, the crystal surface [7,8]. Both conditions have been considered to be associated with a simultaneously diffracted beam travelling in a direction parallel, or nearly parallel, to the
crystal surface. The electrons in this beam do not have a sufficient momentum perpendicular to the surface to allow them to escape over the potential barriers of the inner potential and hence are refleeted back and trapped in the surface region, travelling relatively large distances parallel to the surface. Consequently, the building-up of intensity of the re-diffracted surface wave back to the vacuum side results in the enhancement of all diffracted beams, especially of the specular beam which is related to the surface diffracted wave by a strong reflection condition. The enhancement of the reflected beam intensity has also been interpreted in terms of monolayer resonances. Under this assumption, it was predicated that the incident electrons are efficiently coupled to states in which the electrons channel along the paths parallel to the surface and are confined to the potential troughs of the topmost atom layer of the crystal
[9]. The resonance condition is so important in R E M imaging that, with its aid, the fine detail such as single-atom-height steps, surface domains with different chemical composition, and surface
0304-3991/90/$03.50 © 1990 - Elsevier Science Publisbers B.V. (North-Holland)
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
dynamic processes of areas of the single crystal surface many micrometers in diameter can be easily revealed [10-16]. Although the images suffer from severe foreshortening in the beam direction, the resolution obtained in the one direction in the surface perpendicular to the incident beam can be better than 1 nm, and several contrast-producing mechanisms can be involved, giving sensitivity to the micromorphology of the surface. Although the resonance condition has been widely recognized in reflection high energy electron diffraction ( R H E E D ) and used for R E M imaging, the detailed studies of how the above cited two geometrical resonance conditions relate with the imaging contrast have not been reported. The differences between these two conditions need to be investigated in the following three aspects: (i) the nature of electron scattering mechanism, (ii) the contributions to the enhancement of intensity of the specular reflected beam and the total reflectivity, and (iii), the imaging contrast in REM. This paper concentrates on the studies of these problems. Along with theoretical commentary, it includes the general properties of these two resonance conditions that have been distinguished experimentally.. The intensity of the specular refleeted beam responsible for the formation of the image, as well as the total reflectivity, is analyzed quantitatively. The appearance of doubling contrast for a single-atom-height step in REM imaging is closely related to the selection of the diffraction conditions. The material of the present paper is arranged as follows. Section 2 gives briefly the sample preparation process and experimental conditions. Section 3 deals with the experimental observations for both transmission and reflection diffractions and the identification of diffraction conditions. It consists of a schematic description of the formation of the parabola (section 3.1) and the surface potential effect on the reflection electron diffraction pattern (section 3.2) followed by a detailed study of the geometrical arrangement of the diffraction pattern with the variation of the incidence beam condition (section 3.3). Section 4 gives a parallel investigation on the electron energy distribution and the total reflectivity, and section 5 presents a series of reflection images aimed at the demonstration of the significant in-
fluence on surface image contrast by the selection of diffraction conditions. Section 6 provides a critical summary of the characterization of resonance conditions together with commentary on surface imaging contrast.
2. Experimental conditions The specimen used in the experiments is the spherical single crystal of platinum with some gold particles deposited on the surfaces. The platinum sphere was formed in the vacuum chamber by a method similar to that for preparing the single copper sphere with many low-indexed facets formed on its surface [17]. With this method, a well prepared surface can be obtained easily without the extra contamination left on the surfaces of single crystals formed during the recrystallization process after melting the thin metal wire in air. (The configuration of the system inside the vacuum chamber is illustrated schematically in fig. 1.) In order to have a relatively uniform evaporation coverage on a spherical sample, two evaporating sources were set equidistant between the molybdenum wire and the crystal sensor and between the upper and lower sides. A small piece Evaporating Au Source .-=~=..
Crystal Sensor
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Fig. 1. Schematic configuration of a specimen preparation arrangement inside the vacuum system.
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
of platinum wire (0.1 ram) is wrapped on a molybdenum wire of 0.2 mm in diameter. The melt-grown spherical platinum single crystal was formed by melting the platinum wire inside the chamber with a pressure of about 2 × 10-s Torr with a DC current fed through the molybdenum wire, which served both as electric heating element and a support. Gold particles were subsequently evaporated on the platinum sphere by shutting the shield on or off from each side, one after the other. The thickness of the coverage was controlled by the crystal sensor. The indium phosphide and gallium arsenide (110) faces were obtained by cleavage in air of single crystal wafers having extended (001) faces. Before the cleavage, the wafers were chemically treated [18] and mechanically polished and shaped in order to fit the specimen holder. The experiments were performed on a Philips 400T transmission electron microscope operated at 100 keV. The 200 keV JEM 2000FX and ISI-002B transmission electron microscopes were also used. Each of these instruments is equipped with a double-tilt holder. The vacuum condition around the specimen stage during the operation ranged from 10 -6 to 10 -7 Torr. The energy loss spectra were recorded at 200 keV, using the JEM 2000FX electron microscope, and a Gatan 666 parallel-detection electron energy loss spectrometer. This spectrometer was equipped with a 1024-channel photodiode array coupled to a YAG scintillator, capable of full spectrum acquisition in as short a time as 25 ms with an energy resolution of about 1.5 eV.
3. Geometry of the diffraction condition The Kikuchi lines appearing in the RHEED pattern are very important for characterization of the specimen 0dentation. If the examined crystal has certain symmetries about the horizontal and vertical axes, the RHEED pattern, especially with the large incident angle, will show exactly the same symmetry as observed in the corresponding transmission high energy electron diffraction (THEED) pattern with the bottom half missing, with certain modifications due to the breakdown in the three-dimensional structure. Therefore, gen-
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Fig. 2. A R H E E D pattern produced from a 200 keV convergent electron b e a m illuminating a P t ( l l l ) surface for a large incidence angle with zero aTimuth.
erally speaking, the Kikuchi pattern in RH E E D can also be used to characterize the crystal symmetry [19].
3.1. The origin of the parabola The first surface resonance condition used to form REM imaging is closely related to the appearance of a parabola in the RHEED pattern. It is essential to propose a clear picture about the formation of such a parabola in order to further understand the resonance condition. The RH E E D pattern shown in fig. 2 was obtained from a platinum (111) surface with (999) specular Bragg reflection condition fulfilled for a 200 keV incident electron beam along a direction close to [112] zone axis with zero azimuth. Detailed study indicates that a parabola appearing in the diffraction pattern has properties similar to the Kikuchi lines. Like the Kikuchi lines, the parabola appears permanently in the background and brightens considerably and becomes relatively diffuse when the resonance condition is fulfilled. The positions of
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
e-
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Fig. 3. Schematic diagram showing the diffraction pattern formation with the reflected electrons from a terraced surface.
the parabolas are, fixed relative to the K line s and d o n o t change with t h e variation o f the incident angle. T h e parabolas m a y b e t h o u g h t to a r i s e as
an extension of the effect of the split in the intersection of Kikuchi lines which has been c o m m o n l y interpreted as a non-systematic, m a n y - b e a m d y n a m i c effect [20]. In the n o r m a l R H E E D pattern from a relative large flat surface, only the u p p e r b r a n c h of the p a r a b o l a can be seen due to the blocking b y the bulk crystal. However, for the vicinal surface c o m p o s e d of a high density of terraces with an orientation inclined to a zone axis, a complete p a r a b o l a m a y be seen. Fig. 3 illustrates schematically the reflection f r o m a single c o p p e r crystal surface, which facets to (111) orientation plus a second misorientation which contains a high density of steps a n d inclined to a [211] zone axis. " N R " indicates the reflection area which can be observed in the n o r m a l reflection condition, and " A R " illustrates the extra reflection area which can be seen only for the surface c o m p o s e d of m a n y steps as shown here. The c o r r e s p o n d i n g
Fig. 4. A pair of RHEED patterns obtained from a melt-grown Cu(lll) facet, with the surface structure illustrated in fig. 3, for a 200 keY incident electron beam along a direction close to [211] zone axis with (a) a small and (b) a large incidence angle. The parabola with both a bright (excess) upper branch and a dark (defect) lower branch can be seen clearly in (b).
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
R H E E D patterns are shown in fig. 4 for an incident electron b e a m in a direction close to [211] zone, with a small incidence angle (fig. 4a) and a large (fig. 4b) incidence angle. The half parabola seen in fig. 4a becomes a complete parabola in fig. 4b, with upper branch bright (excess), and lower branch dark (defec0. These two branches are positioned one closer to and another further from the incident beam. In fig. 4b, it can be seen that the position of the shadow edge as indicated by an arrow shown in fig. 4a is now replaced by a
241
horizontal Kikuchi b a n d which corresponds to the main (111) reflection planes of the crystal. On the other hand, the gap between the parabola and the Kikuchi lines oblique to the crystal surface shown in fig. 4a can hardly be seen in fig. 4b. It has been also found that the width of such a gap increases with the increasing incident b e a m energy due to the relativistic effect [21]. These characteristics evidently indicate that the parabola does not simply belong to the Kikuchi envelop family described by Laue [22].
4
Fig. 5. Direct comparisons of reflection (a, c) and transmission (b, d) diffraction patterns with the variation of the incidence angle, where (660) and (10,10,0) specular Bragg resonance conditions are fulfilled in (a, b) and (c, d), respectively.
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
The properties presented so far, as well as the energy loss analysis given in the next section, contain sufficient information to develop a plausible picture of the origin of the parabola as follows. When an electron beam encounters the surface, it is incoherently scattered with loss of energy to phonon, plasmon or interband excitations. A certain amount of incoherently scattered electrons are trapped by the planar potential and travel along those planes of atoms (these planes are those major reflection planes belonging to the same zone axis, and are not necessary parallel to the crystal surface in the reflection case). After a certain distance of travelling, these electrons decay in terms of subsequent re-diffraction by other lattice planes by satisfying the Bragg condition and form the parabolas which are tangential to sequences of Kikuchi lines. Comparing the mechan i s m of the formation of the Kikuchi lines, which are due to the electrons which have suffered inelastic scattering followed by Bragg reflection in the course of their escape from the crystal, the formation of the parabola can be considered as being due to those electrons undergoing a threestep process, namely phonon scattering, planar channelling and Bragg reflection, before re-emergence in vacuum. This description would be appropriate for both transmission and reflection scattering, although the additional surface potential effect has to be taken into account for the latter case. The direct comparison of the behavior of the parabolas appearing in the transmission and reflection cases were carried out in a n experiment [23] in which both R H E E D and T H E E D are acquired with exactly the same diffraction condition. Fig, 5 shows the R H E E D and T H E E D patterns from GaAs single crystal with 100 keV incident electron beam close to [001] zone axis. Figs. 5a and 5c are R H E E D and T H E E D patterns taken in e q u i ~ t e n t orientations with the (6,6,0) reflection at the Bragg angle. Figs. 5b and 5d form a similar pair with excitation Of (10,10,0)Bragg reflection. Detailed i n s p e c t i o n suggests the R H E E D pattern and the t o p ~ f part of the T H E E D pattern shown in figs. 5b and 5d bear a much closer similarity than those observed in figs. 5a and 5c.
The most dominant difference between these two diffraction conditions lies in the appearances of the parabola with respect to the incident angle. For the higher incident angle, as shown in figs. 5b and 5d, the parabolas in both cases are very strong. For the lower incident angle, the parabolas are quite bright in the reflection case, but not in the transmission case. This can be interpreted by the effect caused by the existence of a surface potential barrier due to the breakdown of the three-dimensional crystal structure. In the reflection case, from the consideration of the conservation of energy between the incident and diffracted beam, the relationship between the incident angle outside crystal, 00, and the equivalent angle inside crystal, 0, can be approximately described by cos 00
=
(1
-
VolE) 1/2 COS O,
where E is the primary beam energy, the inner potential V0 is negative relative to the vacuum level. The refraction effect, therefore, makes the angle inside always greater than the angle outside. Although the variation is very small, it is significant enough at a low angle of incidence to highly increase the probability for the electrons channelling in the surface region. For those electrons which do not have a sufficient momentum perpendicular to the surface, the potential barriers of the inner potential force them to travel a relatively large distance parallel to the surface. Consequently, the building-up of intensity of re-diffracted surface wave back to the vacuum side forms the intense parabola. In the transmission case, without the refraction effect on both incident and diffracted electrons due to surface potential, the number of scattered electrons which undergo this three-step process is greatly reduced. Therefore, the parabola cannot be formed with any appreciable intensity. On the other hand, for a relatively large incidence angle, as shown in figs. 5b and 5d, the parabola together with the Kikuchi pattern is able to appear with appreciable intensity in both reflection and transmission cases. This is because, by having a large incidence angle with a major zone axis, the possibility of the electrons interacting with a large number of lattice planes and channelling along some favorable planes is highly increased due to
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging e m
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equally spaced as in the transmission case. The spacing decreases with the increase of the reflection order n and approaches the value of the interplanar spacing of the reflection plane, when n is sufficiently large. For the high order, such as the (11,11,11) Bragg reflection, the variation of this effect cannot be detected with any accuracy in R H E E D patterns as shown in fig. 2. This configuration of Kikuchi line patterns does not change with the incident beam angle. Apparently, the decrease in the refraction effect predicates the variation of the influence of surface effective potential on the reflected beam with the order of reflection. This variation may be understood by considering that refraction is caused not only by the constant term in the Fourier expansion of the crystal potential, but also by all the periodic terms which are usually ignored in the first-order approximation [24]. Some other possible reasons for the variation of the parallel Kikuchi line distribution were suggested to be the distortion of the lattice plane spacing near the surface, or the effect of the adsorbed layers [25,26]. The refraction effect will affect not only the reflected spots and the parallel Kikuchi lines, but all the electrons reflected back to the vacuum side regardless of the scattering process before the electrons emerge on the surface. Careful inspection shows that there is a distortion of the parabola in the lower-reflection-order region. The distance of a point on the segment from the focus is no longer equal to its distance from a fixed straight line (directrix), but reduced by a certain amount due to the effect caused by the surface potential in the direction perpendicular to the surface. Similar effects can also be found for the Kikuchi lines inclined to the crystal surface. Their angle with the parallel K lines has been increased by a certain amount compared to normal transmission condition. If the incident electron beam illumination is located in the area very close to the edge of the bulk crystal, both reflection and transmission electron diffraction patterns may be achieved in the diffraction plane simultaneously. Hence the effect of surface potential on the reflected beam together with normal transmitted beam can be seen. Fig. 7 is a diffraction pattern acquired under such a
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Fig. 6. Schematic diagram for the electron resonance scattering for (a) reflection and (b) transmission geometries. I, II and Ill illustrate three different scattering processes, namely phonon scattering, planar channelling and Bragg reflection, respectively.
the significant increasing of the penetration depth in the direction perpendicular to the zone axis. This allows a large number of electrons to fulfill the three-step scattering process before leaving the crystal. The accumulating of these electrons re-refleeted from the crystal produce the parabolas with a considerable resultant intensity. The resonance scattering mechanisms for reflection and transmission electron diffraction conditions with a small incidence angle with respect to a zone axis are illustrated schematically in figs. 6a and 6b.
3.2. Surface potential effect on R H E E D pattern The effect of refraction on both incident and reflected electrons due to the surface potential has been shown in the previous section to play a predominant role in the formation of the surface parabola. This effect is also very important for understanding the distortion of Kikuchi patterns in R H E E D , although it has been frequently negiected. As demonstrated in fig. 2, the horizontal Kikuchi lines parallel to the surface are no longer
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
condition. This special pattern was obtained from a bulk InP single crystal with a 100 keV electron beam incident in a direction close to [001] zone axis. It shows a superposition of the intensity distribution for both reflected and transmitted electrons from entrance and exit plane of the bulk crystal, with the entrance and exit planes parallel to the (110) and (001) lattice planes, respectively. The doubling of both the parabola and the oblique Kikuchi lines as indicated by arrows can be seen clearly. The appearance of the lower branch indicates that the reflected electrons have been moved away from those transmitted, corresponding to the upper lines of the doubling, due to the surface potential effect. Because the reflected spots are diffuse, it is difficult to perform a precise measurement of the refraction effect in terms of the spacing of these spots. For a certain order of Bragg reflection, the specular reflected spot falls on the parallel K line with the same order. Therefore, measuring the variation of the Kikuchi line spacing instead of the position of the reflected spots would give a much better accuracy for studying the refraction effect. Due to the refraction effect, all the reflected spots, Kikuchi lines with small emerging angle, are bent towards the surface, which makes the intersection of Kikuchi lines and parabola outside and inside the crystal no longer symmetrical about the
shadow edge of the crystal, as will be shown in next section. Therefore, the satisfaction of the resonance condition in reflection geometry becomes more critical. 3.3. Ewald sphere construction for the resonance conditions In order to interpret the observed enhancement we have studied the geometrical condition for various incident conditions. Fig. 8 is a series of R H E E D patterns from the same region of a P t ( l l l ) surface for a 200 keV incident electron beam in a direction close to the [112] zone axis, with a glancing incident angle about 26 mrad which corresponds to the (555) Bragg reflection condition inside the crystal. For the purpose of convenience in discussion, we name these four different diffraction conditions shown in figs. 8 a 8d as D 1 - D 4 . With D1, the specular reflected spot falls in an intersection of a parallel Kikuchi line with a parabola; with D2, the specular reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; with D3, that is pure specular Bragg reflection (the specular reflected spot crosses only the parallel Kikuchi line); and with D4, the specular reflected spot intersects only with a parabola.
Fig. 7. Diffraction pattern showing the supcrposition of intensity distribution for both reflected and transmitted electrons from entrance and exit surface, s of a bulk InP single crystal. The doubling of the parabola and the oblique Kikuchi lines as a result of refraction effect on the reflected electron can be seen clearly.
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
F o r e l e c t r o n d i f f r a c t i o n t a k e n in reflection m o d e , the p a t t e r n is, in general, l i m i t e d t o w a r d s the l o w e r angle b y the s h a d o w edge, b u t one c a n i m a g i n e t h a t the p a t t e r n w o u l d b e there if the c r y s t a l were t r a n s p a r e n t for electrons. Therefore, a clear p i c t u r e o f t h e c o m p l e t e d i f f r a c t i o n p a t t e r n c a n b e achieved b y a d d i n g the t r a n s m i s s i o n p a r t b e l o w the s h a d o w edge. T h e s i m u l a t e d d i f f r a c t i o n
245
p a t t e r n s for those d i f f r a c t i o n c o n d i t i o n s s h o w n in figs. 8 a - 8 d are d e m o n s t r a t e d in figs. 9 a - 9 d . Fig. 9e illustrates the d i f f r a c t i o n c o n d i t i o n D5, w h e r e the s p e c u l a r reflected s p o t falls o n l y o n the o b lique K i k u c h i lines w h e r e n o B r a g g reflection is satisfied. T h e s e p a t t e r n s p r o v i d e a g r e a t d e a l o f information on variations of diffraction geometries with the i n c i d e n t b e a m c o n d i t i o n . T h e u p p e r
....
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Fig. 8. A series of RHEED patterns produced from a Pt(lll) surface under four different diffraction conditions, with (a) condition D1, where the specular Bragg-reflected spot falls at an intersection of a parallel Kikuchi line with the parabola; (b) condition D2, where the specular Bragg-reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; (c) condition D3, where there is pure specular Bragg reflection (the specular reflected spot crosses only the parallel Kikuchi hne); and (d) condition IM, where the specular reflected spot intersects only with a parabola.
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
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Fig. 9. ( a - d ) A series of simulated diffraction patterns including both R H E E D and THEED, based on the conditions shown in figs. 8a-8d. For (e) the specular spot falls only on an oblique Kikuchi line
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
half of each diagram in fig. 9 is the R H E E D pattern based on a series of experimental results with the variation of refraction effect for the different reflection orders concerned, and the lower half is the transmission pattern based on the conventional transmission diffraction conditions [27]. The black and white spots represent the incident electron beam and the specular reflected electron beam, respectively. The circle illustrates the intersection of the Ewald sphere with the reciprocal lattice plane of the zero-order Laue zone, with upper and lower semicircles outside and inside the crystal, respectively. The variation of the incident angle is just a matter of changing the radius of the circle with a fixed center on a zone axis. As shown in the diagrams, the projection of the center of the Ewald sphere, the zone axis and the focus of the parabola are always coincident on the same point, as the origin of the X and Y axes, on the diffraction plane regardless of the variation of the incident angle. X and Y represent the directions of the [111] and [1-10] zone axes in reciprocal space, respectively. The shape of the parabola depends only on the configuration of the K line pattern, that is, the orientation of the crystal. In reflection electron diffraction, the standard Ewald construction provides a method of determining the geometrically allowed reflection for a given lattice, as a function of incident electron energy, diffraction angle and crystal orientation, although the refraction effect has to be taken into account in order to achieve certain accuracy. As shown in fig. 9a, that is the diffraction condition D1, where the Ewald sphere passes through only the incident beam (000) spot and specular Braggreflected (555) spot. These two spots are not exactly bisected by the Y axis due to the refraction effect on the reflected beam. Both parts of the Ewald sphere outside or inside the crystal are not tangential to any reciprocal lattice rod normal to the surface. N o elongated spots can be seen in the R H E E D pattern. This indicates that this geometrical configuration satisfies neither a beam threshold resonance condition in which the Ewald sphere is tangential to one of the reciprocal lattice rods perpendicular to the surface at a lattice point position, nor a trapped beam resonance condition where some non-specular Bragg-reflected beams at
247
a low angle to the surface are internally reflected and therefore cannot emerge due to the effect of surface potential. Therefore, for condition D1, it is inappropriate to interpret the intensity enhancement of the specular reflected beam as a result of the excitation of a Bragg diffracted wave inside the crystal propagating parallel or nearly parallel to the surface. In general, the condition under which the incident beam spot falls on a Kikuchi line is equivalent to the condition of the Bragg reflection of the incident beam by the corresponding lattice plane. For the diffraction condition D2, shown in figs. 8b and 9b, the incident beam spot lies on an intersection of three Kikuchi lines. The same is true for the specular Brag,g-reflected spot. The Ewald sphere inside the crystal touches the reciprocal lattice rod and touches two lattice spots with one elongated towards the shadow edge outside the crystal. Under this particular condition, the excitation of the simultaneous Bragg reflections leads to the enhancement of the specular reflection. Figs. 8c and 9c show a diffraction condition in which the specular reflected spot falls in a position between conditions D1 and D2, and only the Bragg reflection corresponding to the lattice plane parallel to the crystal surface is fulfilled. Although the Ewald sphere is nearly tangential to the lattice rod on the right side of the pattern, no elongated spot such as that observed
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ENERGY LOSS [eV] Fig. 10. A series of electron energy loss spectra acquired from the specular reflected beam for different diffraction conditions, D1-D4.
248
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
under condition D2 can be seen. It has been found that the absolute intensity of a reflected spot sitting on the Ewald sphere decreases with the increase of its corresponding wave vector to the specular spot in the reciprocal space. As shown in figs. 8c and 9c, the fact that the Ewald sphere touches the two lattice spots belonging to the same lattice rod perpendicular to the surface on the left side of the pattern apparently does not account for the enhanced specular b e a m intensity. This important phenomenon indicates that the Ewald sphere tangential to the reciprocal lattice rod cannot be considered as a full criterion for the resonance condition. The intensity of specular reflected b e a m is in general fairly weak in the angular ranges between two successive Bragg reflections even as it crosses the parabola, as shown in figs. 8d and 9d. This shows that the enhancement of the specular reflected b e a m occurs only with the satisfaction of the Bragg-reflection condition.
4. Electron energy distribution and reflectivity A series of specular reflected electron energy loss spectra collected from the same region of Pt(111) surface with the incident beam in a direction close to the [112] zone axis is shown in fig. 10, where the spectra 1 - 4 correspond to diffraction conditions D 1 - D 4 , respectively. All the spectra were acquired at 200 keV in diffraction mode, and each of the spectra was collected by 50 sweeps with 50 ms acquisition time at 0.5 eV/channel, and then normalized to the same number of counts in the specular b e a m zero-loss channel. Detailed inspection indicates the variation in the portion of inelastic scattered electrons within the total specular reflected b e a m intensity. It can be seen that the energy loss peaks at 5.8 eV, 11.6 eV, 23.2 eV and 34.6 eV dominate the spectra, where the second and the fourth peaks show as weak shoulders relative to the first and the third ones, respectively. It m a y be pointed out that only the first surface plasmon peak at 5.8 eV can be recognized in all the spectra and the second surface plasmon peak is superposed on the first bulk plasmon at 11.6 eV. This suggests that the energies of the
Table 1 Comparison of the experimental results of total reflectivity, the intensity of the specular reflected beam, and the ratio of inelastic-and-total scattered electrons within the specular beam acquired from different diffraction conditions Diffraction Total Specular conditions reflectivity reflected Ir/I o beam inten(+0.005) sit),/s D1 0.335 0.434 × 10s D2 0.314 0.382 × 10s D3 0.317 0.221 x 10a D4 0.353 0.721 × 10 7 D5 0.345 0.195 × 107
Ratio of inelastic/total scattered electrons linc/I s (+2%) 57% 63% 50% 64% 72%
surface and bulk plasmon loss cannot be simply related by v ~ [28] in this case. The total incident b e a m intensity was determined in diffraction m o d e by measuring the viewing-screen current density with the specimen moved away from the electron path. The total reflection intensity is obtained with only the R H E E D pattern showing in the view-screen, while the incident b e a m was completely blocked out by the bulk specimen. The count of the inelastic scattered electrons was obtained b y subtracting the zero-loss peak from the total spectrum, where the total count for the zero-loss peak is produced b y doubling the integration from - 6 eV to 0 eV for each spectrum. Table 1 summarizes the relationships among the total reflectivity, the intensity of the specular reflected b e a m and the ratio of inelastic-to-total scattered electrons within the specular reflected b e a m for the different diffraction conditions. I 0 and I r are total incident and reflected b e a m intensifies; I s represents the intensity for the specular reflected beam. Column 4 lists the values of the intensity ratio, I i ~ e / I s ( + 2 ~ ) , between inelastic and total scattering electrons within the specular reflected beam. It can be seen that the intensity of the specular beam changes greatly with the variation of the diffraction condition, while the total reflectivity changes only within the range of about 5%. This indicates that the enhancement of the specular reflected beam does not necessarily mean the increase of the total reflectivity, even though the Kikuchi pattern background brightens with
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
this condition. No certain relationship can be found at this stage between the increases of the specular reflected beam intensity and the total reflectivity. It has been found that under diffraction condition D1 or D2 the apparent enhancement of the total reflectivity in the range 10%-15% only occurs when the incident beam has a large azimuthal angle. This variation may be considered as a result of the intensity contribution due to the excitement of the diffractions from the reflection planes belonging to another low index zone axis. It was suggested that the RHEED pattern with the higher incidence angle is close to the THEED case [23], that is, the depth of electron penetration is critically limited by the variation of small glancing incident angle. The ratio of the surface and bulk plasmon in the electron energy loss spectrum would directly reflect the change of electron penetration depth beneath the crystal surface. If there is no other scattering process involved, the ratio of the plasmon loss peaks collected from the diffraction conditions D1 and D2 would be expected to be the same, because of the same glancing incidence. However, the analysis shows that there are two major differences: (i) the intensity of the specular reflected beam and the total reflectivity for condition D2 are decreased about 12% and 2%, respectively, and (ii) the portion of inelastic reflected electrons is increased about 6%, compared to those for diffraction condition D1. The least ratio of I i n J I s ( = 50%) is provided by the spectrum acquired from diffraction condition D3, where only specular Bragg reflection from the lattice planes parallel to the crystal surface is involved. Therefore, one cannot expect to obtain the pure elastic scattering alone in the reflection process, It has to be accompanied by the simultaneous inelastically scattered electrons. Due to the loss of the contributions from the surface channelled wave and the simultaneous Bragg reflections for the lattice planes oblique to the crystal surface, the intensities of the specular reflected beam have been reduced about 49% and 42%, respectively, under this condition D3, compared to those observed in conditions D1 and D2. The spectrum acquired from diffraction condition D4 does not show a significant increase in surface plasmon peak relative to the inelastic scattering
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ENERGYLOSS[eV] Fig. 11. Comparison of the energy loss spectra acquired from diffraction conditions 1)4 and D5. The relative ratio of elasticto-total scattered electrons in D5 is increased about 8% compared to that in D4.
background. This is consistent with the argument in section 3.3 that the channelled electrons are confined in a region involving several atomic layers beneath the surface rather than along the topmost layer of the crystal surface. Another comparison has been made for the spectra acquired from conditions D4 and D5 as shown in fig. 11, with the condition D5, i.e. the specular reflected spot, falling only on the Kikuchi lines oblique to the surface with no Bragg reflection, as illustrated in fig. 9e. It shows that the ratio I i , e / I s has increased about 8% for D5, although the intensity of the specular reflected beam has reduced more than three times that in D4. This indicates again that the parabola most likely originates from the surface region and an oblique Kikuchi line is produced by the electrons scattered in a larger depth beneath the surface. By comparison of the electron energy distribution in spectrum D5 with that in spectra D1 and D2 shown in fig. 10, it was found that under the resonance conditions, the intensity enhancement of the specular reflected beam is due to the tremendous increase of both elastically and inelastically scattered electrons. The spectra acquired from the specular reflected beam for both diffraction conditions D1 and D4, which are both related to the parabola, do not show a significant increase in surface
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
plasmon peak on the inelastic scattering background compared to the other diffraction conditions, and all the spectra from the different diffraction conditions show a relatively large portion of inelastic scattered electrons in the specular refleeted beams. Satisfying either of two diffraction conditions D1 and D2 with the same glancing incidence angle does not necessarily mean a tremendous reduction of penetration depth of incident electrons, because the Kikuchi lines and envelopes, which are closely associated with three-dimensional diffraction, are also enhanced at this condition. At least, this difference cannot be simply observed from the variation of the specular beam intensity and analyzed from energy distribution within the specular reflected beam. For some crystals, such as I I I - V materials InP and GaAs, etc., the gap between a parabola and an oblique Kikuchi line is almost invisible for certain geometric conditions, which implies the degeneracy of diffraction conditions D1 and D2. When the specular Bragg-reflected beam overlaps with such an intersection, both diffraction conditions are satisfied simultaneously. The probability of exciting either of these two conditions is extremely sensitive to the incident beam condition. Slightly adjusting the collection aperture or changing the incidence angle would make an apparent variation in the ratio between inelastic and total scattered electrons, owing to the switch between diffraction conditions D1 and D2. One example, illustrated in fig. 12, shows a comparison of the spectra produced from the GaAs(110) cleavage surface of a single crystal with the (660) specular Bragg reflection satisfied. A relatively large condenser aperture has been used in order to make the 200 keV incident electron beam impact the crystal surface with a large convergence. The~e two spectra were acquired from two different collecting positions corresponding to diffraction conditions D1 and D2 inside the same specular refleeted beam disk. Switching from condition D1 to D2 has made a change from 75% to 82% for the ratio of inelastic-to-total scattering. Both of these ratios are about 15% higher than that for the P t ( l l l ) surface with a similar incidence condition. It is worth mentioning the appearance of the
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ENERGY LOSS [eV] Fig. 12. Experimental energy loss spectra acquired from a G a A s single crystal (110) surface, with a 200 keV incident electron b e a m along a direction close to [001] zone axis. The spectra with solid and dashed lines were taken from the selected positions inside a (660) specular Brag,g-reflected beam disk, corresponding to diffraction conditions D1 and D2, respectively.
array of the thermal diffuse diffracted spots in a non-Bragg condition on the background of the diffraction patterns shown in fig. 2 and fig. 8. Although the intensity of these spots is very weak, the electron energy loss spectra acquired from these spots show an energy distribution similar to that for the specular Brag,g-reflected spot. The detailed studies will be discussed elsewhere.
5. I m a g e contrast with diffraction c o n d i t i o n s
Previous sections have examined the different diffraction conditions responsible for R E M imaging by means of geometries, intensity and energy distribution. It was found that the diffraction conditions D1 and D2 cannot be considered as identical diffraction conditions, although the specular reflected spots for both cases are commonly regarded as the (555) Bragg reflection in the R H E E D pattern obtained from P t ( l l l ) surface with the incident beam along a direction close to [211] zone axis. Characteristic surface step contrasts for the surface imaging obtained from the specular reflected beam for different diffraction conditions cited in section 3.3 are shown in the series of
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
R E M i m a g e s in fig. 13, w h e r e a - d c o r r e s p o n d to d i f f r a c t i o n c o n d i t i o n s D 1 - D 4 , respectively. T h e s m a l l b l a c k s p o t s a p p e a r i n g in the i m a g e s are s m a l l g o l d p a r t i c l e s e v a p o r a t e d o n the P t ( l l l ) surface. T h e s e p a r t i c l e s d o n o t have a p a r t i c u l a r e p i t a x i a l r e l a t i o n s h i p w i t h the substrate.
251
It has b e e n g e n e r a l l y c o n s i d e r e d t h a t the imp r o v e m e n t of the surface i m a g e q u a l i t y a l w a y s goes with the e n h a n c e m e n t o f the i n t e n s i t y o f the p a r t i c u l a r reflected s p o t u s e d to f o r m the image; t h a t is, the s t r o n g e r r e f l e c t e d b e a m i n t e n s i t y o n e c a n have, the b e t t e r c o n t r a s t o f the i m a g e m a y b e
o
.
.
.
.
.
.
Fig. 13. A series of surface images obtained from each diffraction condition shown in fig. 8, where (a-d) correspond to D1-D4, respectively. The topographical contrast for the surface imaging changes in a way different from the intensity. Although the strongest specular reflected beam intensity occurred for diffraction condition D1, the sharpest contrast and the dominant double-line contrast can be seen only in (b) corresponding diffraction condition D2. The gold panicles shown in (a-c) are almost invisible in (d), and some of them even appear as bright spots as indicated by arrows. (Scale bar = 100 nm.)
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
achieved. However, comparison of figs. 13a to 13d dearly indicates that the surface image contrast is determined not only by the absolute beam intensity, but also by the scattering mechanism underlying the excitation of the reflected electrons. The sharpness of the fine details in the near focusing region for the surface imaging decreases in the order of (b), (c), (a) and (d), differing from the order (a), (b), (c) and (d), for the decrease of the specular beam intensities. Comparing panels (a) and (b), one can see that a tremendous contrast improvement has been achieved for the surface topography in image (b), although the specular beam intensity for D2 is about 14% less than that for D1. For the diffraction condition D1, the specular Bragg-reflected electron beam is incoherently enhanced by the surface region channeled wave, which results in a strong increase in image intensity, but not quite in image contrast. For diffraction condition !:)2, the contrast of the surface image is significantly improved, although the enhancement of the specular Bragg-reflected beam due to the coherent coupling among the simultaneous Bragg reflections is not as strong as that in D1. The most significant phenomenon in fig. 13b is the appearance of the doubling line contrast for the single-atom-height steps on the crystal surface. This pronounced double line contrast can be observed with both dark and bright lines whenever the diffraction condition D2 is fulfilled; that is, the incoming beam impacts the surface with a critical angle, which makes the specular reflected beam fall in an intersection of K.ikuchi lines running parallel to and inclined to the crystal surface. It is found that the double-bright lines correspond to an up step, and the double-black contrast corresponds to a down step, as viewed in the incident beam direction. The center line of the double contour (bright for the double-black contrast and black for the double-bright contrast) moves in the same sense with the change of focus condition, and finally the double-contour contrast emerges as the simple dark-light contrast. T o expose these dramatic variations for the image contrast in more detail, the enlarged images for the left and right parts of fig. 13b are shown in figs. 14a and 14b, respectively. The up step which used to exhibit a
Fig. 14. The enlarged images for the left (a) and right (b) surface areas shown in fig. 13b. The double-bright, and darkline contrasts can be seen clearly for the up and down steps, respectively,with single-atom height. minimum contrast in the in-focus region shown at the left part in fig. 13a now gives a sharp doublebright contour. The further studies of the properties of these double-line contrasts with respect to the parameters of the instruments will be discussed in detail in a separate paper [29]. The image 13c produced from a pure Brag,g-reflection condition (D3) gives a slightly better contrast than image 13a, even though the specular reflected beam in D1 has an intensity about twice as great as that in D3. For the pure resonances condition shown in fig. 13d, the most significant phenomenon is that the small gold particles evaporated on the Pt(111 ) surface become almost invisible. Some gold particles can even be reco~niTod as bright spots, as indicated by arrows. Simihr phenomena for the variation of the surface image contrast with the diffraction conditions, as well as the appearance of the double-contour contrast for the single-atom-height step, have been also observed in the surface imaging with the incident beam along different zone axes, such as [110] and [123].
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
6. Discussion and conclusion In conclusion, the two diffraction conditions responsible for the enhancement of the specular reflected beam in RI-IEED can be understood in terms of different electron scattering mechanisms. The diffraction condition 1, i.e. the specular reflected spot, falls on an intersection of a parabola with a Kikuchi line parallel to the crystal surface, exciting both the Bragg reflection and the electron surface channelling wave. This surface-channelled wave does not necessarily mean that the wave has to travel parallel to the surface. This channeling wave normally travels between the lattice planes inclined to the crystal surface in the surface region before being re-reflected to the vacuum side. This condition gives the strongest intensity of the specular reflected beam and good surface contrast. The diffraction condition 2, i.e. the specular reflected spot crossing an intersection of Kikuchi lines running parallel to and oblique to the crystal surface, represents the excitement of simultaneous Bragg reflections closely associated with the properties of three-dimensional dynamical diffraction for a bulk crystal. Although this condition produces a specular reflected beam which contains a rather large portion of inelastically scattered electrons, and has an intensity not as bright as that in condition 1, it does provide a better resolution for surface imaging. These two conditions, therefore, can be recognized as Bragg-channelling resonance reflection and Bragg-Bragg resonance reflection. For the latter case, the coherent superposition of the simultaneous Bragg reflection contributes to the scattering amplitude, providing a better chance to have a high resolution surface image with sharp contrast. The abnormal double-contour contrast of a single-atom-height step observed in surface imaging is closely associated with the satisfaction of the Bragg-Bragg resonance condition. It is suggested that the intensity enhancement of the specular Bragg-reflected beam is due to the tremendous increase in both elastic and inelastic scattering. The ratio of these two kinds of scattering varies slowly relative to the variation of the beam intensity with respect to the diffraction glancing condition. It has long been considered that under the condition of intensity enhancement
253
of the specular reflected beam, the simultaneous enhancement of the whole reflection pattern occurs [30-32]. However, our experimental evidence shows that neither of these two resonance conditions can make a considerable increase of the total reflectivity with respect to other diffraction conditions. For the pure Bragg-reflection condition, in which the specular reflected spot falls only on a Kikuchi line parallel to the crystal surface, the specular reflected beam contains the least proportion of inelastically scattered electrons and provides the surface image with a slightly better contrast than that from the Bragg-channelling reflection condition. The so-called pure resonance condition, i.e. the specular reflected beam, intersects only with a parabola, producing a weak specular beam intensity and a relatively higher total reflectivity.
Acknowledgements This work was supported by N S F grant DMR88-10238 and made use of the resources of the ASU Facility for High Resolution Electron Microscopy which is supported by N S F grant DMR-8611609 and Arizona State University.
References [1] J.M. Cowley, in: Surface and Interface Characterization by Electron Optical Methods, Eds. A. Howie and U. Valdr~ (Plenum, New York, 1988) p. 127. [2] J.M. Cowley, in: Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces, Eds. P.K. Larsen and P.J. Dobson (Plenum, New York, 1988) p. 26. [3] K. Yagi, J. Appl. Cryst. 20 (1987) 147. [4] A. Ichimiya, K. Kambe and (3. Lehmpfuhl, J. Phys. Soc. Jpn. 49 (1980) 684. [5] G. Lehmpfuhl and W.C.T. Dowell, Acta Cryst. A 42 (1986) 569. [6] L.M. Peng and J.M. Cowley, J. Electron Microsc. Techn.
6 (1987) 43. [7] S. Miyake and K. Hayakawa, Aeta Cryst. A 26 (1970) 60. [8] K. Kohra, K. Moliere, S. Nakano and M. Ariyama, J. Phys. Soc. Jpn. Suppl. B-II, 17 (1962) 82. [9] H. Marten and (3. Meyer-Ehmsen, Surf. Sci. 151 (1985) 570. [10] T. Hsu and J.M. Cowley, Ultramicroscopy 11 (1983) 239.
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[11] T. Hsu, S. lijima and J.M. Cowley, Surf. Sci., 137 (1984) 551. [12] Y. Uehida and G. Lehmpfuhl, Ultramicroscopy 11 (1987) 53. [13] Nan Yao, Z.L. Wang and J.M. Cowley, Surf. Sci. 208 (1989) 533. [14] N. Osakabe, Y. Tanishiro, K. Yagi and G. Honjo, Surf. Sci. 102 (1981) 424. [15] N. Osakabe, Y. Tanishiro, K. Yagi and C. Honjo, Surf. Sci. 109 (1981) 353. [16] Y. Tanishiro and K. Takayanagi, Ultramieroscopy 31 (1989) 20. [17] Nan Yao, in: Proc. 47th Annu. EMSA Meeting, San Antonio, TX, 1989, Ed. G.W. Bailey (San Francisco Press, San Francisco, 1989) p. 540. [18] Nan Yao and J.M. Cowley, in: Proc. 46th Armu. EMSA Meeting, Milwaukee, WI, 1988, Ed. G.W. Bailey (San Francisco Press, San Francisco, 1988) p. 690. [19] J.A. Eades and M.D. Shannon, in: Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces, Eds. P.K. Larsen and P.J. Dobson (Plenum, New York, 1988) p. 237.
[20] J. Gjonnes and R. Hoier, Acta Cryst. A 27 (1971) 313. [21] Nan Yao and J.M. Cowley, in: Proc. 47th Annu. EMSA Meeting, San Antonio, TX, 1989, Ed. G.W. Bailey (San Francisco Press, San Francisco, 1989) p. 530. [22] M. yon Lane, Materiewellen und ihre Interferenzen (Akademische Verlagsgesellschaft, Leipzig, 1948) p. 343. [23] Nan Yao and J.M. Cowley, Ultramicroscopy 31 (1989) 149. [24] K. Kohra and K. Shinohara, J. Phys. Soc. Jpn. 4 (1949) 155. [25] T. Yamaguti, Proe. Phys.-Math. Soe. Jpn. 16 (1934) 95. [26] J.W. Harding, Phil. Mag. 23 (1937) 271. [27] P.B. Hirsch, A. Howie, R.B. Nieholson, P.W. Pashley and M.J. Whelan, Electron Microscopy of Thin Crystals (Butterworths, London, 1965) p. 119. [28] H. Raether, Surf. Sei. 8 (1967) 233. [29] Nan Yao and J.M. Cowley, J. Electron Mierosc. Techn., in press. [30] S. Miyake, J. Phys. Soc. Jpn. 17 (1962) 1642. [31] S. Takagi, J. Phys. Soc. Jpn. 13 (1958) 278, 287. [32] S. Miyake, K. Hayakawa and R. Miida, Acta Cryst. A 24 (1968) 182.
ELECTRON DIFFRACTION CONDmONS ELECTRON MICROSCOPY
237
A N D S U R F A C E I M A G I N G IN R E F L E C T I O N
N a n Y A O and J.M. C O W L E Y Department of Physics, Arizona State University, Tempe, A Z 85287-1504, USA
Received 8 May 1990
Two resonance conditions responsible for enhancement of the specular reflected beam observed in the RHEED pattern have been characterized as Bragg-ehanneUing reflection and Bragg-Bragg reflection, respectively, in terms of different scattering mechanisms. Under the resonance condition, the tremendous increase of both elastic and inelastic electron scattering results in the intensity enhancement of the specular reflected beam. The total reflectivity does not change considerably with the variation of the diffraction condition. The improvement of the topographical contrast in surface imaging is not simply related to increase in the intensity of the specular reflected beam. The surface image obtained from the Bragg-Bragg reflection condition shows a better image contrast for the surface structure among the varieties of resonance conditions. The appearance of the abnormal double-contour contrast for a single-atom-height step is also closely associated with the Bragg-Braggreflection condition.
1. Introduction In the last decade, the use of transmission electron microscopy for surface imaging in the reflection mode has shown a considerable potential as a means for studying crystal surfaces. Many significant R E M (reflection electron microscopy) studies have been done, as reviewed recently by Cowley and Yagi [1-3]. In order to increase intensity and contrast in the image of a surface, the surface resonance condition has been widely used to enhance the Bragg reflection for image formation. The commonly cited geometries for attaining such surface resonance conditions require either that (i) a specular reflected Bragg spot falls on an intersection of a Kikuchi line parallel to the surface with a socalled surface resonance parabola [4-6], or (ii) a specular reflected Bragg spot coincides with an intersection of Kikuchi lines running parallel to, and oblique to, the crystal surface [7,8]. Both conditions have been considered to be associated with a simultaneously diffracted beam travelling in a direction parallel, or nearly parallel, to the
crystal surface. The electrons in this beam do not have a sufficient momentum perpendicular to the surface to allow them to escape over the potential barriers of the inner potential and hence are refleeted back and trapped in the surface region, travelling relatively large distances parallel to the surface. Consequently, the building-up of intensity of the re-diffracted surface wave back to the vacuum side results in the enhancement of all diffracted beams, especially of the specular beam which is related to the surface diffracted wave by a strong reflection condition. The enhancement of the reflected beam intensity has also been interpreted in terms of monolayer resonances. Under this assumption, it was predicated that the incident electrons are efficiently coupled to states in which the electrons channel along the paths parallel to the surface and are confined to the potential troughs of the topmost atom layer of the crystal
[9]. The resonance condition is so important in R E M imaging that, with its aid, the fine detail such as single-atom-height steps, surface domains with different chemical composition, and surface
0304-3991/90/$03.50 © 1990 - Elsevier Science Publisbers B.V. (North-Holland)
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
dynamic processes of areas of the single crystal surface many micrometers in diameter can be easily revealed [10-16]. Although the images suffer from severe foreshortening in the beam direction, the resolution obtained in the one direction in the surface perpendicular to the incident beam can be better than 1 nm, and several contrast-producing mechanisms can be involved, giving sensitivity to the micromorphology of the surface. Although the resonance condition has been widely recognized in reflection high energy electron diffraction ( R H E E D ) and used for R E M imaging, the detailed studies of how the above cited two geometrical resonance conditions relate with the imaging contrast have not been reported. The differences between these two conditions need to be investigated in the following three aspects: (i) the nature of electron scattering mechanism, (ii) the contributions to the enhancement of intensity of the specular reflected beam and the total reflectivity, and (iii), the imaging contrast in REM. This paper concentrates on the studies of these problems. Along with theoretical commentary, it includes the general properties of these two resonance conditions that have been distinguished experimentally.. The intensity of the specular refleeted beam responsible for the formation of the image, as well as the total reflectivity, is analyzed quantitatively. The appearance of doubling contrast for a single-atom-height step in REM imaging is closely related to the selection of the diffraction conditions. The material of the present paper is arranged as follows. Section 2 gives briefly the sample preparation process and experimental conditions. Section 3 deals with the experimental observations for both transmission and reflection diffractions and the identification of diffraction conditions. It consists of a schematic description of the formation of the parabola (section 3.1) and the surface potential effect on the reflection electron diffraction pattern (section 3.2) followed by a detailed study of the geometrical arrangement of the diffraction pattern with the variation of the incidence beam condition (section 3.3). Section 4 gives a parallel investigation on the electron energy distribution and the total reflectivity, and section 5 presents a series of reflection images aimed at the demonstration of the significant in-
fluence on surface image contrast by the selection of diffraction conditions. Section 6 provides a critical summary of the characterization of resonance conditions together with commentary on surface imaging contrast.
2. Experimental conditions The specimen used in the experiments is the spherical single crystal of platinum with some gold particles deposited on the surfaces. The platinum sphere was formed in the vacuum chamber by a method similar to that for preparing the single copper sphere with many low-indexed facets formed on its surface [17]. With this method, a well prepared surface can be obtained easily without the extra contamination left on the surfaces of single crystals formed during the recrystallization process after melting the thin metal wire in air. (The configuration of the system inside the vacuum chamber is illustrated schematically in fig. 1.) In order to have a relatively uniform evaporation coverage on a spherical sample, two evaporating sources were set equidistant between the molybdenum wire and the crystal sensor and between the upper and lower sides. A small piece Evaporating Au Source .-=~=..
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
of platinum wire (0.1 ram) is wrapped on a molybdenum wire of 0.2 mm in diameter. The melt-grown spherical platinum single crystal was formed by melting the platinum wire inside the chamber with a pressure of about 2 × 10-s Torr with a DC current fed through the molybdenum wire, which served both as electric heating element and a support. Gold particles were subsequently evaporated on the platinum sphere by shutting the shield on or off from each side, one after the other. The thickness of the coverage was controlled by the crystal sensor. The indium phosphide and gallium arsenide (110) faces were obtained by cleavage in air of single crystal wafers having extended (001) faces. Before the cleavage, the wafers were chemically treated [18] and mechanically polished and shaped in order to fit the specimen holder. The experiments were performed on a Philips 400T transmission electron microscope operated at 100 keV. The 200 keV JEM 2000FX and ISI-002B transmission electron microscopes were also used. Each of these instruments is equipped with a double-tilt holder. The vacuum condition around the specimen stage during the operation ranged from 10 -6 to 10 -7 Torr. The energy loss spectra were recorded at 200 keV, using the JEM 2000FX electron microscope, and a Gatan 666 parallel-detection electron energy loss spectrometer. This spectrometer was equipped with a 1024-channel photodiode array coupled to a YAG scintillator, capable of full spectrum acquisition in as short a time as 25 ms with an energy resolution of about 1.5 eV.
3. Geometry of the diffraction condition The Kikuchi lines appearing in the RHEED pattern are very important for characterization of the specimen 0dentation. If the examined crystal has certain symmetries about the horizontal and vertical axes, the RHEED pattern, especially with the large incident angle, will show exactly the same symmetry as observed in the corresponding transmission high energy electron diffraction (THEED) pattern with the bottom half missing, with certain modifications due to the breakdown in the three-dimensional structure. Therefore, gen-
239
Fig. 2. A R H E E D pattern produced from a 200 keV convergent electron b e a m illuminating a P t ( l l l ) surface for a large incidence angle with zero aTimuth.
erally speaking, the Kikuchi pattern in RH E E D can also be used to characterize the crystal symmetry [19].
3.1. The origin of the parabola The first surface resonance condition used to form REM imaging is closely related to the appearance of a parabola in the RHEED pattern. It is essential to propose a clear picture about the formation of such a parabola in order to further understand the resonance condition. The RH E E D pattern shown in fig. 2 was obtained from a platinum (111) surface with (999) specular Bragg reflection condition fulfilled for a 200 keV incident electron beam along a direction close to [112] zone axis with zero azimuth. Detailed study indicates that a parabola appearing in the diffraction pattern has properties similar to the Kikuchi lines. Like the Kikuchi lines, the parabola appears permanently in the background and brightens considerably and becomes relatively diffuse when the resonance condition is fulfilled. The positions of
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
e-
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Fig. 3. Schematic diagram showing the diffraction pattern formation with the reflected electrons from a terraced surface.
the parabolas are, fixed relative to the K line s and d o n o t change with t h e variation o f the incident angle. T h e parabolas m a y b e t h o u g h t to a r i s e as
an extension of the effect of the split in the intersection of Kikuchi lines which has been c o m m o n l y interpreted as a non-systematic, m a n y - b e a m d y n a m i c effect [20]. In the n o r m a l R H E E D pattern from a relative large flat surface, only the u p p e r b r a n c h of the p a r a b o l a can be seen due to the blocking b y the bulk crystal. However, for the vicinal surface c o m p o s e d of a high density of terraces with an orientation inclined to a zone axis, a complete p a r a b o l a m a y be seen. Fig. 3 illustrates schematically the reflection f r o m a single c o p p e r crystal surface, which facets to (111) orientation plus a second misorientation which contains a high density of steps a n d inclined to a [211] zone axis. " N R " indicates the reflection area which can be observed in the n o r m a l reflection condition, and " A R " illustrates the extra reflection area which can be seen only for the surface c o m p o s e d of m a n y steps as shown here. The c o r r e s p o n d i n g
Fig. 4. A pair of RHEED patterns obtained from a melt-grown Cu(lll) facet, with the surface structure illustrated in fig. 3, for a 200 keY incident electron beam along a direction close to [211] zone axis with (a) a small and (b) a large incidence angle. The parabola with both a bright (excess) upper branch and a dark (defect) lower branch can be seen clearly in (b).
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
R H E E D patterns are shown in fig. 4 for an incident electron b e a m in a direction close to [211] zone, with a small incidence angle (fig. 4a) and a large (fig. 4b) incidence angle. The half parabola seen in fig. 4a becomes a complete parabola in fig. 4b, with upper branch bright (excess), and lower branch dark (defec0. These two branches are positioned one closer to and another further from the incident beam. In fig. 4b, it can be seen that the position of the shadow edge as indicated by an arrow shown in fig. 4a is now replaced by a
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horizontal Kikuchi b a n d which corresponds to the main (111) reflection planes of the crystal. On the other hand, the gap between the parabola and the Kikuchi lines oblique to the crystal surface shown in fig. 4a can hardly be seen in fig. 4b. It has been also found that the width of such a gap increases with the increasing incident b e a m energy due to the relativistic effect [21]. These characteristics evidently indicate that the parabola does not simply belong to the Kikuchi envelop family described by Laue [22].
4
Fig. 5. Direct comparisons of reflection (a, c) and transmission (b, d) diffraction patterns with the variation of the incidence angle, where (660) and (10,10,0) specular Bragg resonance conditions are fulfilled in (a, b) and (c, d), respectively.
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
The properties presented so far, as well as the energy loss analysis given in the next section, contain sufficient information to develop a plausible picture of the origin of the parabola as follows. When an electron beam encounters the surface, it is incoherently scattered with loss of energy to phonon, plasmon or interband excitations. A certain amount of incoherently scattered electrons are trapped by the planar potential and travel along those planes of atoms (these planes are those major reflection planes belonging to the same zone axis, and are not necessary parallel to the crystal surface in the reflection case). After a certain distance of travelling, these electrons decay in terms of subsequent re-diffraction by other lattice planes by satisfying the Bragg condition and form the parabolas which are tangential to sequences of Kikuchi lines. Comparing the mechan i s m of the formation of the Kikuchi lines, which are due to the electrons which have suffered inelastic scattering followed by Bragg reflection in the course of their escape from the crystal, the formation of the parabola can be considered as being due to those electrons undergoing a threestep process, namely phonon scattering, planar channelling and Bragg reflection, before re-emergence in vacuum. This description would be appropriate for both transmission and reflection scattering, although the additional surface potential effect has to be taken into account for the latter case. The direct comparison of the behavior of the parabolas appearing in the transmission and reflection cases were carried out in a n experiment [23] in which both R H E E D and T H E E D are acquired with exactly the same diffraction condition. Fig, 5 shows the R H E E D and T H E E D patterns from GaAs single crystal with 100 keV incident electron beam close to [001] zone axis. Figs. 5a and 5c are R H E E D and T H E E D patterns taken in e q u i ~ t e n t orientations with the (6,6,0) reflection at the Bragg angle. Figs. 5b and 5d form a similar pair with excitation Of (10,10,0)Bragg reflection. Detailed i n s p e c t i o n suggests the R H E E D pattern and the t o p ~ f part of the T H E E D pattern shown in figs. 5b and 5d bear a much closer similarity than those observed in figs. 5a and 5c.
The most dominant difference between these two diffraction conditions lies in the appearances of the parabola with respect to the incident angle. For the higher incident angle, as shown in figs. 5b and 5d, the parabolas in both cases are very strong. For the lower incident angle, the parabolas are quite bright in the reflection case, but not in the transmission case. This can be interpreted by the effect caused by the existence of a surface potential barrier due to the breakdown of the three-dimensional crystal structure. In the reflection case, from the consideration of the conservation of energy between the incident and diffracted beam, the relationship between the incident angle outside crystal, 00, and the equivalent angle inside crystal, 0, can be approximately described by cos 00
=
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where E is the primary beam energy, the inner potential V0 is negative relative to the vacuum level. The refraction effect, therefore, makes the angle inside always greater than the angle outside. Although the variation is very small, it is significant enough at a low angle of incidence to highly increase the probability for the electrons channelling in the surface region. For those electrons which do not have a sufficient momentum perpendicular to the surface, the potential barriers of the inner potential force them to travel a relatively large distance parallel to the surface. Consequently, the building-up of intensity of re-diffracted surface wave back to the vacuum side forms the intense parabola. In the transmission case, without the refraction effect on both incident and diffracted electrons due to surface potential, the number of scattered electrons which undergo this three-step process is greatly reduced. Therefore, the parabola cannot be formed with any appreciable intensity. On the other hand, for a relatively large incidence angle, as shown in figs. 5b and 5d, the parabola together with the Kikuchi pattern is able to appear with appreciable intensity in both reflection and transmission cases. This is because, by having a large incidence angle with a major zone axis, the possibility of the electrons interacting with a large number of lattice planes and channelling along some favorable planes is highly increased due to
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equally spaced as in the transmission case. The spacing decreases with the increase of the reflection order n and approaches the value of the interplanar spacing of the reflection plane, when n is sufficiently large. For the high order, such as the (11,11,11) Bragg reflection, the variation of this effect cannot be detected with any accuracy in R H E E D patterns as shown in fig. 2. This configuration of Kikuchi line patterns does not change with the incident beam angle. Apparently, the decrease in the refraction effect predicates the variation of the influence of surface effective potential on the reflected beam with the order of reflection. This variation may be understood by considering that refraction is caused not only by the constant term in the Fourier expansion of the crystal potential, but also by all the periodic terms which are usually ignored in the first-order approximation [24]. Some other possible reasons for the variation of the parallel Kikuchi line distribution were suggested to be the distortion of the lattice plane spacing near the surface, or the effect of the adsorbed layers [25,26]. The refraction effect will affect not only the reflected spots and the parallel Kikuchi lines, but all the electrons reflected back to the vacuum side regardless of the scattering process before the electrons emerge on the surface. Careful inspection shows that there is a distortion of the parabola in the lower-reflection-order region. The distance of a point on the segment from the focus is no longer equal to its distance from a fixed straight line (directrix), but reduced by a certain amount due to the effect caused by the surface potential in the direction perpendicular to the surface. Similar effects can also be found for the Kikuchi lines inclined to the crystal surface. Their angle with the parallel K lines has been increased by a certain amount compared to normal transmission condition. If the incident electron beam illumination is located in the area very close to the edge of the bulk crystal, both reflection and transmission electron diffraction patterns may be achieved in the diffraction plane simultaneously. Hence the effect of surface potential on the reflected beam together with normal transmitted beam can be seen. Fig. 7 is a diffraction pattern acquired under such a
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the significant increasing of the penetration depth in the direction perpendicular to the zone axis. This allows a large number of electrons to fulfill the three-step scattering process before leaving the crystal. The accumulating of these electrons re-refleeted from the crystal produce the parabolas with a considerable resultant intensity. The resonance scattering mechanisms for reflection and transmission electron diffraction conditions with a small incidence angle with respect to a zone axis are illustrated schematically in figs. 6a and 6b.
3.2. Surface potential effect on R H E E D pattern The effect of refraction on both incident and reflected electrons due to the surface potential has been shown in the previous section to play a predominant role in the formation of the surface parabola. This effect is also very important for understanding the distortion of Kikuchi patterns in R H E E D , although it has been frequently negiected. As demonstrated in fig. 2, the horizontal Kikuchi lines parallel to the surface are no longer
243
244
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
condition. This special pattern was obtained from a bulk InP single crystal with a 100 keV electron beam incident in a direction close to [001] zone axis. It shows a superposition of the intensity distribution for both reflected and transmitted electrons from entrance and exit plane of the bulk crystal, with the entrance and exit planes parallel to the (110) and (001) lattice planes, respectively. The doubling of both the parabola and the oblique Kikuchi lines as indicated by arrows can be seen clearly. The appearance of the lower branch indicates that the reflected electrons have been moved away from those transmitted, corresponding to the upper lines of the doubling, due to the surface potential effect. Because the reflected spots are diffuse, it is difficult to perform a precise measurement of the refraction effect in terms of the spacing of these spots. For a certain order of Bragg reflection, the specular reflected spot falls on the parallel K line with the same order. Therefore, measuring the variation of the Kikuchi line spacing instead of the position of the reflected spots would give a much better accuracy for studying the refraction effect. Due to the refraction effect, all the reflected spots, Kikuchi lines with small emerging angle, are bent towards the surface, which makes the intersection of Kikuchi lines and parabola outside and inside the crystal no longer symmetrical about the
shadow edge of the crystal, as will be shown in next section. Therefore, the satisfaction of the resonance condition in reflection geometry becomes more critical. 3.3. Ewald sphere construction for the resonance conditions In order to interpret the observed enhancement we have studied the geometrical condition for various incident conditions. Fig. 8 is a series of R H E E D patterns from the same region of a P t ( l l l ) surface for a 200 keV incident electron beam in a direction close to the [112] zone axis, with a glancing incident angle about 26 mrad which corresponds to the (555) Bragg reflection condition inside the crystal. For the purpose of convenience in discussion, we name these four different diffraction conditions shown in figs. 8 a 8d as D 1 - D 4 . With D1, the specular reflected spot falls in an intersection of a parallel Kikuchi line with a parabola; with D2, the specular reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; with D3, that is pure specular Bragg reflection (the specular reflected spot crosses only the parallel Kikuchi line); and with D4, the specular reflected spot intersects only with a parabola.
Fig. 7. Diffraction pattern showing the supcrposition of intensity distribution for both reflected and transmitted electrons from entrance and exit surface, s of a bulk InP single crystal. The doubling of the parabola and the oblique Kikuchi lines as a result of refraction effect on the reflected electron can be seen clearly.
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
F o r e l e c t r o n d i f f r a c t i o n t a k e n in reflection m o d e , the p a t t e r n is, in general, l i m i t e d t o w a r d s the l o w e r angle b y the s h a d o w edge, b u t one c a n i m a g i n e t h a t the p a t t e r n w o u l d b e there if the c r y s t a l were t r a n s p a r e n t for electrons. Therefore, a clear p i c t u r e o f t h e c o m p l e t e d i f f r a c t i o n p a t t e r n c a n b e achieved b y a d d i n g the t r a n s m i s s i o n p a r t b e l o w the s h a d o w edge. T h e s i m u l a t e d d i f f r a c t i o n
245
p a t t e r n s for those d i f f r a c t i o n c o n d i t i o n s s h o w n in figs. 8 a - 8 d are d e m o n s t r a t e d in figs. 9 a - 9 d . Fig. 9e illustrates the d i f f r a c t i o n c o n d i t i o n D5, w h e r e the s p e c u l a r reflected s p o t falls o n l y o n the o b lique K i k u c h i lines w h e r e n o B r a g g reflection is satisfied. T h e s e p a t t e r n s p r o v i d e a g r e a t d e a l o f information on variations of diffraction geometries with the i n c i d e n t b e a m c o n d i t i o n . T h e u p p e r
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246
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
half of each diagram in fig. 9 is the R H E E D pattern based on a series of experimental results with the variation of refraction effect for the different reflection orders concerned, and the lower half is the transmission pattern based on the conventional transmission diffraction conditions [27]. The black and white spots represent the incident electron beam and the specular reflected electron beam, respectively. The circle illustrates the intersection of the Ewald sphere with the reciprocal lattice plane of the zero-order Laue zone, with upper and lower semicircles outside and inside the crystal, respectively. The variation of the incident angle is just a matter of changing the radius of the circle with a fixed center on a zone axis. As shown in the diagrams, the projection of the center of the Ewald sphere, the zone axis and the focus of the parabola are always coincident on the same point, as the origin of the X and Y axes, on the diffraction plane regardless of the variation of the incident angle. X and Y represent the directions of the [111] and [1-10] zone axes in reciprocal space, respectively. The shape of the parabola depends only on the configuration of the K line pattern, that is, the orientation of the crystal. In reflection electron diffraction, the standard Ewald construction provides a method of determining the geometrically allowed reflection for a given lattice, as a function of incident electron energy, diffraction angle and crystal orientation, although the refraction effect has to be taken into account in order to achieve certain accuracy. As shown in fig. 9a, that is the diffraction condition D1, where the Ewald sphere passes through only the incident beam (000) spot and specular Braggreflected (555) spot. These two spots are not exactly bisected by the Y axis due to the refraction effect on the reflected beam. Both parts of the Ewald sphere outside or inside the crystal are not tangential to any reciprocal lattice rod normal to the surface. N o elongated spots can be seen in the R H E E D pattern. This indicates that this geometrical configuration satisfies neither a beam threshold resonance condition in which the Ewald sphere is tangential to one of the reciprocal lattice rods perpendicular to the surface at a lattice point position, nor a trapped beam resonance condition where some non-specular Bragg-reflected beams at
247
a low angle to the surface are internally reflected and therefore cannot emerge due to the effect of surface potential. Therefore, for condition D1, it is inappropriate to interpret the intensity enhancement of the specular reflected beam as a result of the excitation of a Bragg diffracted wave inside the crystal propagating parallel or nearly parallel to the surface. In general, the condition under which the incident beam spot falls on a Kikuchi line is equivalent to the condition of the Bragg reflection of the incident beam by the corresponding lattice plane. For the diffraction condition D2, shown in figs. 8b and 9b, the incident beam spot lies on an intersection of three Kikuchi lines. The same is true for the specular Brag,g-reflected spot. The Ewald sphere inside the crystal touches the reciprocal lattice rod and touches two lattice spots with one elongated towards the shadow edge outside the crystal. Under this particular condition, the excitation of the simultaneous Bragg reflections leads to the enhancement of the specular reflection. Figs. 8c and 9c show a diffraction condition in which the specular reflected spot falls in a position between conditions D1 and D2, and only the Bragg reflection corresponding to the lattice plane parallel to the crystal surface is fulfilled. Although the Ewald sphere is nearly tangential to the lattice rod on the right side of the pattern, no elongated spot such as that observed
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248
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
under condition D2 can be seen. It has been found that the absolute intensity of a reflected spot sitting on the Ewald sphere decreases with the increase of its corresponding wave vector to the specular spot in the reciprocal space. As shown in figs. 8c and 9c, the fact that the Ewald sphere touches the two lattice spots belonging to the same lattice rod perpendicular to the surface on the left side of the pattern apparently does not account for the enhanced specular b e a m intensity. This important phenomenon indicates that the Ewald sphere tangential to the reciprocal lattice rod cannot be considered as a full criterion for the resonance condition. The intensity of specular reflected b e a m is in general fairly weak in the angular ranges between two successive Bragg reflections even as it crosses the parabola, as shown in figs. 8d and 9d. This shows that the enhancement of the specular reflected b e a m occurs only with the satisfaction of the Bragg-reflection condition.
4. Electron energy distribution and reflectivity A series of specular reflected electron energy loss spectra collected from the same region of Pt(111) surface with the incident beam in a direction close to the [112] zone axis is shown in fig. 10, where the spectra 1 - 4 correspond to diffraction conditions D 1 - D 4 , respectively. All the spectra were acquired at 200 keV in diffraction mode, and each of the spectra was collected by 50 sweeps with 50 ms acquisition time at 0.5 eV/channel, and then normalized to the same number of counts in the specular b e a m zero-loss channel. Detailed inspection indicates the variation in the portion of inelastic scattered electrons within the total specular reflected b e a m intensity. It can be seen that the energy loss peaks at 5.8 eV, 11.6 eV, 23.2 eV and 34.6 eV dominate the spectra, where the second and the fourth peaks show as weak shoulders relative to the first and the third ones, respectively. It m a y be pointed out that only the first surface plasmon peak at 5.8 eV can be recognized in all the spectra and the second surface plasmon peak is superposed on the first bulk plasmon at 11.6 eV. This suggests that the energies of the
Table 1 Comparison of the experimental results of total reflectivity, the intensity of the specular reflected beam, and the ratio of inelastic-and-total scattered electrons within the specular beam acquired from different diffraction conditions Diffraction Total Specular conditions reflectivity reflected Ir/I o beam inten(+0.005) sit),/s D1 0.335 0.434 × 10s D2 0.314 0.382 × 10s D3 0.317 0.221 x 10a D4 0.353 0.721 × 10 7 D5 0.345 0.195 × 107
Ratio of inelastic/total scattered electrons linc/I s (+2%) 57% 63% 50% 64% 72%
surface and bulk plasmon loss cannot be simply related by v ~ [28] in this case. The total incident b e a m intensity was determined in diffraction m o d e by measuring the viewing-screen current density with the specimen moved away from the electron path. The total reflection intensity is obtained with only the R H E E D pattern showing in the view-screen, while the incident b e a m was completely blocked out by the bulk specimen. The count of the inelastic scattered electrons was obtained b y subtracting the zero-loss peak from the total spectrum, where the total count for the zero-loss peak is produced b y doubling the integration from - 6 eV to 0 eV for each spectrum. Table 1 summarizes the relationships among the total reflectivity, the intensity of the specular reflected b e a m and the ratio of inelastic-to-total scattered electrons within the specular reflected b e a m for the different diffraction conditions. I 0 and I r are total incident and reflected b e a m intensifies; I s represents the intensity for the specular reflected beam. Column 4 lists the values of the intensity ratio, I i ~ e / I s ( + 2 ~ ) , between inelastic and total scattering electrons within the specular reflected beam. It can be seen that the intensity of the specular beam changes greatly with the variation of the diffraction condition, while the total reflectivity changes only within the range of about 5%. This indicates that the enhancement of the specular reflected beam does not necessarily mean the increase of the total reflectivity, even though the Kikuchi pattern background brightens with
249
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
this condition. No certain relationship can be found at this stage between the increases of the specular reflected beam intensity and the total reflectivity. It has been found that under diffraction condition D1 or D2 the apparent enhancement of the total reflectivity in the range 10%-15% only occurs when the incident beam has a large azimuthal angle. This variation may be considered as a result of the intensity contribution due to the excitement of the diffractions from the reflection planes belonging to another low index zone axis. It was suggested that the RHEED pattern with the higher incidence angle is close to the THEED case [23], that is, the depth of electron penetration is critically limited by the variation of small glancing incident angle. The ratio of the surface and bulk plasmon in the electron energy loss spectrum would directly reflect the change of electron penetration depth beneath the crystal surface. If there is no other scattering process involved, the ratio of the plasmon loss peaks collected from the diffraction conditions D1 and D2 would be expected to be the same, because of the same glancing incidence. However, the analysis shows that there are two major differences: (i) the intensity of the specular reflected beam and the total reflectivity for condition D2 are decreased about 12% and 2%, respectively, and (ii) the portion of inelastic reflected electrons is increased about 6%, compared to those for diffraction condition D1. The least ratio of I i n J I s ( = 50%) is provided by the spectrum acquired from diffraction condition D3, where only specular Bragg reflection from the lattice planes parallel to the crystal surface is involved. Therefore, one cannot expect to obtain the pure elastic scattering alone in the reflection process, It has to be accompanied by the simultaneous inelastically scattered electrons. Due to the loss of the contributions from the surface channelled wave and the simultaneous Bragg reflections for the lattice planes oblique to the crystal surface, the intensities of the specular reflected beam have been reduced about 49% and 42%, respectively, under this condition D3, compared to those observed in conditions D1 and D2. The spectrum acquired from diffraction condition D4 does not show a significant increase in surface plasmon peak relative to the inelastic scattering
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background. This is consistent with the argument in section 3.3 that the channelled electrons are confined in a region involving several atomic layers beneath the surface rather than along the topmost layer of the crystal surface. Another comparison has been made for the spectra acquired from conditions D4 and D5 as shown in fig. 11, with the condition D5, i.e. the specular reflected spot, falling only on the Kikuchi lines oblique to the surface with no Bragg reflection, as illustrated in fig. 9e. It shows that the ratio I i , e / I s has increased about 8% for D5, although the intensity of the specular reflected beam has reduced more than three times that in D4. This indicates again that the parabola most likely originates from the surface region and an oblique Kikuchi line is produced by the electrons scattered in a larger depth beneath the surface. By comparison of the electron energy distribution in spectrum D5 with that in spectra D1 and D2 shown in fig. 10, it was found that under the resonance conditions, the intensity enhancement of the specular reflected beam is due to the tremendous increase of both elastically and inelastically scattered electrons. The spectra acquired from the specular reflected beam for both diffraction conditions D1 and D4, which are both related to the parabola, do not show a significant increase in surface
250
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
plasmon peak on the inelastic scattering background compared to the other diffraction conditions, and all the spectra from the different diffraction conditions show a relatively large portion of inelastic scattered electrons in the specular refleeted beams. Satisfying either of two diffraction conditions D1 and D2 with the same glancing incidence angle does not necessarily mean a tremendous reduction of penetration depth of incident electrons, because the Kikuchi lines and envelopes, which are closely associated with three-dimensional diffraction, are also enhanced at this condition. At least, this difference cannot be simply observed from the variation of the specular beam intensity and analyzed from energy distribution within the specular reflected beam. For some crystals, such as I I I - V materials InP and GaAs, etc., the gap between a parabola and an oblique Kikuchi line is almost invisible for certain geometric conditions, which implies the degeneracy of diffraction conditions D1 and D2. When the specular Bragg-reflected beam overlaps with such an intersection, both diffraction conditions are satisfied simultaneously. The probability of exciting either of these two conditions is extremely sensitive to the incident beam condition. Slightly adjusting the collection aperture or changing the incidence angle would make an apparent variation in the ratio between inelastic and total scattered electrons, owing to the switch between diffraction conditions D1 and D2. One example, illustrated in fig. 12, shows a comparison of the spectra produced from the GaAs(110) cleavage surface of a single crystal with the (660) specular Bragg reflection satisfied. A relatively large condenser aperture has been used in order to make the 200 keV incident electron beam impact the crystal surface with a large convergence. The~e two spectra were acquired from two different collecting positions corresponding to diffraction conditions D1 and D2 inside the same specular refleeted beam disk. Switching from condition D1 to D2 has made a change from 75% to 82% for the ratio of inelastic-to-total scattering. Both of these ratios are about 15% higher than that for the P t ( l l l ) surface with a similar incidence condition. It is worth mentioning the appearance of the
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array of the thermal diffuse diffracted spots in a non-Bragg condition on the background of the diffraction patterns shown in fig. 2 and fig. 8. Although the intensity of these spots is very weak, the electron energy loss spectra acquired from these spots show an energy distribution similar to that for the specular Brag,g-reflected spot. The detailed studies will be discussed elsewhere.
5. I m a g e contrast with diffraction c o n d i t i o n s
Previous sections have examined the different diffraction conditions responsible for R E M imaging by means of geometries, intensity and energy distribution. It was found that the diffraction conditions D1 and D2 cannot be considered as identical diffraction conditions, although the specular reflected spots for both cases are commonly regarded as the (555) Bragg reflection in the R H E E D pattern obtained from P t ( l l l ) surface with the incident beam along a direction close to [211] zone axis. Characteristic surface step contrasts for the surface imaging obtained from the specular reflected beam for different diffraction conditions cited in section 3.3 are shown in the series of
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
R E M i m a g e s in fig. 13, w h e r e a - d c o r r e s p o n d to d i f f r a c t i o n c o n d i t i o n s D 1 - D 4 , respectively. T h e s m a l l b l a c k s p o t s a p p e a r i n g in the i m a g e s are s m a l l g o l d p a r t i c l e s e v a p o r a t e d o n the P t ( l l l ) surface. T h e s e p a r t i c l e s d o n o t have a p a r t i c u l a r e p i t a x i a l r e l a t i o n s h i p w i t h the substrate.
251
It has b e e n g e n e r a l l y c o n s i d e r e d t h a t the imp r o v e m e n t of the surface i m a g e q u a l i t y a l w a y s goes with the e n h a n c e m e n t o f the i n t e n s i t y o f the p a r t i c u l a r reflected s p o t u s e d to f o r m the image; t h a t is, the s t r o n g e r r e f l e c t e d b e a m i n t e n s i t y o n e c a n have, the b e t t e r c o n t r a s t o f the i m a g e m a y b e
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Fig. 13. A series of surface images obtained from each diffraction condition shown in fig. 8, where (a-d) correspond to D1-D4, respectively. The topographical contrast for the surface imaging changes in a way different from the intensity. Although the strongest specular reflected beam intensity occurred for diffraction condition D1, the sharpest contrast and the dominant double-line contrast can be seen only in (b) corresponding diffraction condition D2. The gold panicles shown in (a-c) are almost invisible in (d), and some of them even appear as bright spots as indicated by arrows. (Scale bar = 100 nm.)
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
achieved. However, comparison of figs. 13a to 13d dearly indicates that the surface image contrast is determined not only by the absolute beam intensity, but also by the scattering mechanism underlying the excitation of the reflected electrons. The sharpness of the fine details in the near focusing region for the surface imaging decreases in the order of (b), (c), (a) and (d), differing from the order (a), (b), (c) and (d), for the decrease of the specular beam intensities. Comparing panels (a) and (b), one can see that a tremendous contrast improvement has been achieved for the surface topography in image (b), although the specular beam intensity for D2 is about 14% less than that for D1. For the diffraction condition D1, the specular Bragg-reflected electron beam is incoherently enhanced by the surface region channeled wave, which results in a strong increase in image intensity, but not quite in image contrast. For diffraction condition !:)2, the contrast of the surface image is significantly improved, although the enhancement of the specular Bragg-reflected beam due to the coherent coupling among the simultaneous Bragg reflections is not as strong as that in D1. The most significant phenomenon in fig. 13b is the appearance of the doubling line contrast for the single-atom-height steps on the crystal surface. This pronounced double line contrast can be observed with both dark and bright lines whenever the diffraction condition D2 is fulfilled; that is, the incoming beam impacts the surface with a critical angle, which makes the specular reflected beam fall in an intersection of K.ikuchi lines running parallel to and inclined to the crystal surface. It is found that the double-bright lines correspond to an up step, and the double-black contrast corresponds to a down step, as viewed in the incident beam direction. The center line of the double contour (bright for the double-black contrast and black for the double-bright contrast) moves in the same sense with the change of focus condition, and finally the double-contour contrast emerges as the simple dark-light contrast. T o expose these dramatic variations for the image contrast in more detail, the enlarged images for the left and right parts of fig. 13b are shown in figs. 14a and 14b, respectively. The up step which used to exhibit a
Fig. 14. The enlarged images for the left (a) and right (b) surface areas shown in fig. 13b. The double-bright, and darkline contrasts can be seen clearly for the up and down steps, respectively,with single-atom height. minimum contrast in the in-focus region shown at the left part in fig. 13a now gives a sharp doublebright contour. The further studies of the properties of these double-line contrasts with respect to the parameters of the instruments will be discussed in detail in a separate paper [29]. The image 13c produced from a pure Brag,g-reflection condition (D3) gives a slightly better contrast than image 13a, even though the specular reflected beam in D1 has an intensity about twice as great as that in D3. For the pure resonances condition shown in fig. 13d, the most significant phenomenon is that the small gold particles evaporated on the Pt(111 ) surface become almost invisible. Some gold particles can even be reco~niTod as bright spots, as indicated by arrows. Simihr phenomena for the variation of the surface image contrast with the diffraction conditions, as well as the appearance of the double-contour contrast for the single-atom-height step, have been also observed in the surface imaging with the incident beam along different zone axes, such as [110] and [123].
Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
6. Discussion and conclusion In conclusion, the two diffraction conditions responsible for the enhancement of the specular reflected beam in RI-IEED can be understood in terms of different electron scattering mechanisms. The diffraction condition 1, i.e. the specular reflected spot, falls on an intersection of a parabola with a Kikuchi line parallel to the crystal surface, exciting both the Bragg reflection and the electron surface channelling wave. This surface-channelled wave does not necessarily mean that the wave has to travel parallel to the surface. This channeling wave normally travels between the lattice planes inclined to the crystal surface in the surface region before being re-reflected to the vacuum side. This condition gives the strongest intensity of the specular reflected beam and good surface contrast. The diffraction condition 2, i.e. the specular reflected spot crossing an intersection of Kikuchi lines running parallel to and oblique to the crystal surface, represents the excitement of simultaneous Bragg reflections closely associated with the properties of three-dimensional dynamical diffraction for a bulk crystal. Although this condition produces a specular reflected beam which contains a rather large portion of inelastically scattered electrons, and has an intensity not as bright as that in condition 1, it does provide a better resolution for surface imaging. These two conditions, therefore, can be recognized as Bragg-channelling resonance reflection and Bragg-Bragg resonance reflection. For the latter case, the coherent superposition of the simultaneous Bragg reflection contributes to the scattering amplitude, providing a better chance to have a high resolution surface image with sharp contrast. The abnormal double-contour contrast of a single-atom-height step observed in surface imaging is closely associated with the satisfaction of the Bragg-Bragg resonance condition. It is suggested that the intensity enhancement of the specular Bragg-reflected beam is due to the tremendous increase in both elastic and inelastic scattering. The ratio of these two kinds of scattering varies slowly relative to the variation of the beam intensity with respect to the diffraction glancing condition. It has long been considered that under the condition of intensity enhancement
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of the specular reflected beam, the simultaneous enhancement of the whole reflection pattern occurs [30-32]. However, our experimental evidence shows that neither of these two resonance conditions can make a considerable increase of the total reflectivity with respect to other diffraction conditions. For the pure Bragg-reflection condition, in which the specular reflected spot falls only on a Kikuchi line parallel to the crystal surface, the specular reflected beam contains the least proportion of inelastically scattered electrons and provides the surface image with a slightly better contrast than that from the Bragg-channelling reflection condition. The so-called pure resonance condition, i.e. the specular reflected beam, intersects only with a parabola, producing a weak specular beam intensity and a relatively higher total reflectivity.
Acknowledgements This work was supported by N S F grant DMR88-10238 and made use of the resources of the ASU Facility for High Resolution Electron Microscopy which is supported by N S F grant DMR-8611609 and Arizona State University.
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Nan Yao, J.M. Cowley / Electron diffraction conditions and surface imaging
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