High-resolution electron microscopy of interfaces and surfaces

Ultramicroscopy North-Holland,

22 (1987) 35-46 Amsterdam

35

HIGH-RESOLUTION J.M. GIBSON, AT&T

M.L. MCDONALD,

Bell Luboratories,

Received

ELECTRON

26 September

MICROSCOPY J.L. BATSTONE

OF INTERFACES AND

AND SURFACES

J.M. PHILLIPS

600 Mountain Avenue, Murray Hill, New Jersey 07974, USA 1986, presented

at Conference

April 1986

The enhanced resolution available in the latest generation of medium-voltage high-resolution electron microscopes can be utilized to study semiconductor interfaces in zone axes such as (lOO), (111) and (112), as well as the more familiar (110). This permits both “structural imaging” and three-dimensional reconstruction from two different projections. Preliminary results on semiconductor interfaces obtained with the JEOL 4000EX 400 kV instrument with point resolution better than 1.7 A are presented. In the discussion of interpretation of interface images the serious limitation of signal-to-noise ratio is raised. This is particularly poor in the case of ion-thinned samples. If signal-to-noise ratio could be improved to the theoretical shot-noise limit, it would permit much more extensive image interpretation and perhaps new classes of experiment such as point-defect imaging. We show that the high signal-to-noise ratio is attainable with in-situ specimen cleaning in a UHV electron microscope and report some results on Si surface science performed with our home-modified UHV high-resolution instrument.

1. Improved faces

resolution

and semiconductor

inter-

With the advent of the latest generation of medium-voltage High-Resolution Electron Microscopes (HREM’s) with point-to-point resolution better than 1.9 A (for example, the JEOL 400 kV 4000EX model) it has become possible to form useful images from semiconductors in zone axes other than (110). The implications of this to HREM imaging of semiconductors are significant. Fig. 1 is a stereographic projection for silicon which is appropriate for any cubic semiconductor with lattice parameter in the range 5-7 A. It shows the planes and zone axes which can be imaged with 3 A resolution (i.e. the {ill} planes and (110) zones)) as dashed lines and those which can be imaged with 1.9 A resolution as bold lines ((220) planes and (loo), (111) and (112) zone axes). Firstly, it should be noted that nothing would be gained for axial imaging of perfect silicon by an improvement of resolution from 3.0 to 2.0 A. Clearly, increased resolution beyond 1.9 A permits the imaging of many more zone axes than 3.0 A, and this is significant for several reasons. In the (110) projection 1.35 A resolution is required to image all the atom positions; to date this has 0304-3991/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

ice

oio

Fig. 1. A stereographic projection for the diamond cubic Si structure which is annotated to show planes which can be imaged with 3A resolution (dashed lines) and 1.9 A resolution (bold lines). Intersections of these planes represent zone axes which can be imaged with appropriate resolution. The diagram is valid for any cubic semiconductor with lattice parameter in the 5-7 A range.

B.V.

36

J.M. Gibson et al. / HREM

been impossible and all images show only atom pairs. However, in the (111) and (100) projections from cubic semiconductors all projected atom positions are visible with resolution of the (220) spacing. Thus images from these projections taken with an instrument with point resolution better than 1.9 A (such as the JEOL 4000EX) qualify as true structure images. Examples of such images, using one of these instruments, from Si were published by Ourmazd et al. [l], although this had previously been possible with higher-voltage instruments such as the Atomic Resolution Microscope in Berkeley [2,3]. At interfaces with cubic

of interfaces and surfaces

materials it should thus be possible to obtain structure images revealing all atomic positions in some cases. The ability to resolve other zone axes also relaxes constraints on the epitaxial relationships necessary at interfaces for HREM study. For example, the (100) projection should be useful in studying (100) interfaces, although in this regard (111) is of little use since the interface must be viewed edge-on. Finally, it is highly attractive to view an interface in two different projections so as to overcome the projection problem in HREM. For example a (100) interface could be viewed in both (100) and (110) directions. A (111) interface

Fig. 2. A (100) cross-section of a Si/SiO, interface on (100) Si formed by ion implantation of 0,. In this image all individual atomic columns in the Si structure can be seen and the point resolution, revealed by the inset optical diffraction pattern, is better than 1.7 A.

J.M. Gibson et al. / HREM

could

be viewed in both (110) and (112) direc[2]. It would be most beneficial to examine the same area by specimen tilting, and the 4000EX can be modified to achieve +25” specimen tilt angle which permits both these examples. An example of a (100) structure image from a Si/SiO, interface is shown in fig. 2, taken with a JEOL 4000EX near the Scherzer focus in an area less than 150 A thick. In this image all atoms can be seen in the Si crystal adjacent to the interface. This interface was formed by ion-implantation of oxygen and annealing [4], yet as can be seen it is very flat. The point-to-point resolution of the 4OOOEX, demonstrated from this image, is approximately 1.67 A. Another example of an image from the 4000EX is in fig. 3: this is an image of the CoSi,/Si interface taken in the (112) projection. The sample was grown by Molecular Beam Epitaxy. Simitions

Fig. 3. A (112) cross-section of a CoSi,/Si (111) interface from which the component of rigid lattice shift in the [llO] direction is determined to be close to zero.

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31

lar images taken with the ARM from Nisi, interfaces have been previously published [2]. This image allows measurement of the rigid shift between the CoSi, and Si lattices in a different plane (previous results were obtained only in the (110) plane [5]). In the [llO] direction this shift is zero, which is consistent with the models that employ tetrahedral coordination for Si atoms at the interface but does not distinguish the coordination of the Co atom there [5].

2. Quantification

of images: signal-to-noise

ratio

Measurement of rigid shifts at interfaces is one example of the quantitative analysis of high-resolution micrographs which has been discussed by several authors [6,7] Another obvious example is in the matching of simulated and experimental images, although this is still really an empirical process. A further method is the identification of the roughness and extent of an interface, which would be of great interest, for example, in cases such as fig. 2. The Fourier transform of the Si/SiO, interface has been obtained by inspection [8] and correlated with the mobility of electrons in fieldeffect transistors. Another method which appears to hold promise for such quantification and is less subjective is the scanning of a narrow elongated slit across the image and observing the apparent interface width as a function of slit size [9]. Of course, one must consider the effect of image artefacts, such as fresnel fringes, and the projection through the specimen thickness [8] in this sort of measurement Intensity measurements of the kind discussed here reveal a serious limitation to the interpretation of high-resolution images: limited signal-tonoise ratio. By noise we refer to any contribution to image intensity which is not essentially a part of the signal, e.g. lattice image. Major contributions to noise are’disordered surface layers, due to either contamination or specimen-thinning damage, and shot-noise in the electron beam or photographic plate. Signal-to-noise ratio is a limitation in high-resolution electron microscopy which is generally understated. In ion-thinned specimens it is particularly poor due to excessively

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J.M. Gibson et al. / HREM of interfaces and surfaces

thick damaged layers on the specimen surfaces. To see this we must examine the statistics of the intensities in the lattice image from thin specimens of perfect crystals which have been prepared in several different manners. We can do this by digitizing the intensities in an image and Fourier filtering. If, for example, we filter the Fourier transform of the image up to a spatial frequency just below that corresponding to the crystal lattice in the image of the boundary between a crystal and amorphous material such as in fig. 2, we see an image as in fig. 4. This reveals that there is a significant amorphous background “noise” superimposed on the crystal image. The standard deviation of this noise is 0.1 (all intensities normalized to unity main beam intensity), to be compared

with the standard deviation of the intensity in the amorphous SiO, layer of 0.17. Since we estimate the thickness of the $0, layer to be loo-150 A this implies a total of over 50 A of equivalent disordered material on the surfaces of the Si crystal. Clearly if the sample thickness was less than 70 A we would not reliably be able to identify the SiO, layer. (This should be taken into account by those who asign the character of amorphous to inclusions, etc., seen in HREM images.) The amplitude of the lattice modulation in this area is seen to be 0.4, approximately consistent with calculations for this crystal thickness. The statistics of the noise can be easily measured from the Fourier transform of the image. For example, the integral of the noise spectrum at and beyond the lattice frequency will give the probability distribution that adjacent points in the lattice image have different intensity. Another way to measure the distribution is by intensity measurement in real space. We expect that chemically thinned samples will have lower noise than ionthinned samples and that in-situ cleaned UHV samples will have the theoretically limited S/N given by shot noise. We should be aware that at high accelerating voltages some noise may arise from the creation of lattice defects in the crystal. To see the significance of this let us consider one of the classic problems in high-resolution electron microscopy: the detection of point defects [lo]. To simplify the discussion let us consider the vacancy, free of any strain field. In a sample which is thin enough for the weak-phase projection approximation to be valid, the contrast from such a defect is equivalent to the removal of a single atom from the thickness of one column. Within this simple approximation the minimum intensity (maximum excursion from the average) in the image from a column containing N atoms is Nf, where f is the image of a single atom in the column. Within the approximation f=

Fig. 4. A (100) Si/SiO, interface image as in fig. 1 from which the spatial frequencies at and beyond the 220 lattice frequencies have been filtered. It reveals the degree of disorder present presumably at the surfaces of the crystalline material.

iXCf(g)

e-ir(g)+Wg),

where y is the Scherzer aberration function and E(g) is a coherence-related envelope function. The sum is over all g vectors within the objective

J.M. Gibson et al. / HREM of interfaces and surfaces

aperture. For a single atom of Si in a (100) lattice net at 400 kV in an instrument with point resolution 1.7 A, f is typically 0.09. The question of detectability of a vacancy is a question of signal to noise, and since noise is always present to some degree, it becomes a question of minimum detectable concentration. Let us assume (reasonably) a “white” noise spectrum with a Gaussian probability distribution function, so that in a sample in which the mean intensity is Nf and noise standard deviation u, the probability that a column has intensity (N-1)f or less is

The maximum area that can be explored randomly finding one such column is

without

A = a2/P, where a is the lattice spacing. detectable gives the minimum tion as C,,

This immediately defect concentra-

= P/a2t,

where t is the specimen thickness. For a fixed concentration can be noise level the minimum detected in thicker samples With the measured noise level on our ion-thinned Si/SiO, specimen, P is 0.16, so that in a 100 A thick specimen the minimum detectable defect concentration is 4 x high level. On the 1021 cmm3, an impractically other hand if the noise level could be reduced from 0.1 to 0.05 the minimum detectable concentration drops by an order of magnitude. In in-situ cleaned, flat specimens where the noise level could easily reach shot-noise limited values of 0.02 or better, the minimum detectable point defect concentration becomes a very reasonable 1014 cmp3 or lower. The model used to obtain these numbers is very simple but it does imply some important results: not only could such defects be practically detected but perhaps single impurity atoms in normal concentration might be detectable. This analysis does not pretend to be exhaustive, for example it does not take into account defect strain fields, dynamical scattering effects and pos-

39

sible use of more sophisticated pattern recognition. However, it is illustrative of a limitation in HREM which is not often considered but which is a serious and untested limit to the potential applications.

3. Improved signal-to-noise men cleaning

ratios by in-situ speci-

The realization of improved signal-to-noise ratio by using in-situ cleaned samples is exciting. It opens the possibilities of examining single light atoms, either within or on the surface of samples and gives added sensitivity to phenomena on the single atomic level, both surface and bulk, which have hitherto been dismissed as impossible to detect by transmission electron microscopy. Of course, this requires an in-situ heating capability, which may destroy the structure of some specimens, and ultra-high vacuum environment. The use of such environments for surface transmission electron microscopy is distinctly a new frontier in the field. In our laboratory we have modified a JEOL 200CX to achieve such conditions while maintaining a point-to-point resolution of 2.5 A. A major justification for building this instrument was for in-situ studies of surface structure and molecularbeam epitaxy at high resolution. So far, we have only utilized the improved signal-to-noise ratios possible with this machine for the study of surface structure. The design of the instrument will be described in detail elsewhere. Its salient features are: base pressure in the lop9 Torr region with local cryopumping around the specimen; specimen heating by direct resistive dissipation to > 1400°C; thermal evaporation possible in the imaging position. The design employs complete differential pumping of the volume between the condenser and objective lenses, where the specimen is contained within the objective lens polepiece. Pumping is achieved with a 60 l/s triode ion pump (recently upgraded to 200 l/s) and an 800 l/s water-cooled Ti sublimation pump (recently upgraded to a liquid-nitrogen-cooled 1000 l/s pump). Roughing is provided by a 50 I/s turbomolecular pump. A

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J.M. Gibson et al. / HREM of interfaces and surfaces

4” pumping aperture above the objective lens polepiece is provided. In-situ specimen heating is achieved in a top-entry non-tilting stage where currents of up to 15 A can be directly passed through the specimen. In this way the heat load is minimized which not only permits higher specimen temperatures but also improves stability. This and the top-entry configuration are essential in maintaining the capabilities of high resolution at elevated specimen temperatures.

4. Surface microscopy

imaging with high-resolution

electron

There are two configurations in which such an instrument can study surfaces: plan view and profile. In the plan view geometry thin flat areas of specimen are observed with the electron beam parallel to the surface normal. In the profile geometry the edge of a thin specimen is examined with the electron beam parallel to a direction in the surface [ll]. In the latter case surfaces must be severely limited in dimension in at least one dimension: one is examining surface strips of typical width 100 A. The plan view geometry is the one which is most closely related to conventional surface science. With specimen thicknesses typically in excess of 100 A, and at reasonable distances (> 1 pm) from the specimen edge, it seems reasonable to suppose that each surface of such a sample is identical to that of a single surface of a bulk sampole. Although the scattered intensity from surface layers may be weak, the removal of the noise contribution from dirty and uneven surfaces allows the plan view geometry to be meaningfully utilised. The primary difficulty in this geometry is that both surfaces of the sample are superimposed on each other. This can be compensated for by including the behavior of interest on only one surface (e.g. by poisoning the other surface [12]). Theoretically it is easy to show that significant contrast could occur from surface reconstructions and monolayer adsorbates in the plan view geometry [13]. A practical difficulty which we have encountered in reproducing such theoretical results experimentally is in preparing suitably thin, clean

specimens. In the current design of our UHV surface instrument specimen cleaning is only possible by direct heating. At the temperatures necessary to fully clean thin specimens ( > 1200°C), the vapor pressure of Si is sufficiently high that sublimation of the thin areas occurs. Sublimation is in fact aggravated by the presence of the electron beam probably due to the effect of electron damage on the surface atoms whose binding energy has been effectively reduced at temperatures near the melting point. However, sublimation can be used for specimen thinning. Fig. 5 shows a low-magnification bright-field image of a thin area near a hole produced in an initially thick area of a specimen by sublimation. The image reveals a network of atomic steps on the surfaces of this clean sample. This demonstrates the greatly increased signalto-noise ratio obtainable with in-situ specimen cleaning. The height of these steps can be simply estimated by counting the number which correspond to an extinction distance, and they are typically monoatomic. Strong-beam dark-field images from the same area can reveal much greater strongly fluctuating contrast between steps. This we attribute to the 7 x 7 reconstruction which is seen in the diffraction pattern, and the presence of subsurface strain which is believed to exist in the structure due to the presence of a regular network of misfit dislocations [14,12]. The 7 X 7 reconstruction can only be very weakly imaged directly in this area because the specimen thickness is relatively large for high resolution imaging (> 500 A). This illustrates a problem in the sublimation method of specimen thinning in-situ. It is almost impossible to control the process precisely enough to obtain very thin areas (< 100 A). Calculations show [13] that the 7 X 7 structure could be strongly imaged in suitably thin specimen areas. Fig. 6 shows an example of such a calculation for the DAS [12] model performed with the multi-slice algorithm assuming reconstruction only on the top surface of a 27 A thick crystal. Clearly strong contrast is obtained. This contrast is also extraordinarily sensitive to thickness. (This is due to the rapid changes in the amplitude of the i (422) reflection with thickness.) This should not be a problem provided sufficiently flat surface areas could be formed and indicates the existence of a

J.M. Gibson et al. / HREM of interfaces and surfaces

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5. A bright-field diffraction contrast image from an area of a Si (111) specimen which was thinned to electron transparency

by

sublimation during in-situ heating. Monoatomic steps can be seen in this image, e.g. at A.

subsurface stacking fault. The presence of two reconstructed surfaces, which are not necessarily registered, does raise additional complications but it should be possible from a series of thicknesses to deduce structural details. Flat specimens with thicknesses of less than 100 A are not readily achieved by simple heating for specimen cleaning, due to the very high temperatures which are necessitated. If temperatures are kept to = lOOO”C, some thin although steeply inclined areas are obtained and an example is shown in fig. 7. This image is very interesting. It shows the 23 A period of the 7 x 7 reconstruction covering most of the area of the surfaces. However, large particles of cubic Sic are also seen. The surface has not been completely cleaned, yet the 7 X 7 reconstruction exists locally. It is important to note that it is very difficult to completely rid

the surface of Sic or defect it, which may have implications for MBE (Molecular Beam Epitaxy), since the areal coverage of Sic gets very small as the Sic particles form and grow. Clearly, the solution to the problem of cleaning a thin and flat Si specimen involves the use of lower-temperature processes due to the problem of sublimation. We have tried the modified RCA chemical cleaning procedure of Shiraki and coworkers [ 151 which is commonly employed in MBE as a cleaning procedure when combined with an 800” C in-situ anneal. Surprisingly, we did not notice much improvement using this technique. The oxide layer may sublimate at lower temperatures, but the carbon contamination problem does not seem to be much improved. In-situ sputtering followed by an 800°C anneal appears to be a more promising technique. There is one other

42 Pl

J. M. Gibson et al. / HREM of interfaces and surfaces Bulk

Sna=34Yns=

Layer Si i?th=

<7x7) . . <2/21>2/21,0> 26.7df= -650.r= .40dv= 1.57sa=. 938cn= . Sbt= .

skim=

1. ISbl-

.5dz=50.0vb=

.0nu= . 7&h=

.eecr~l.21-.025

2nc= 64hkps=.0.0.0.0.0.0 I ZIklc= .3Rig=

id=49@934706nb=71 rx=26.9er .9619

Fig. 6. The calculated image intensity distribution from a unit cell of the 7 x 7 unit cell from the ‘f’akayanagi model [12] on the top surface of a si crystal of thickness 27 A. Imaging conditions are otherwise appropriate to the JEOL 2OOCX. The contrast is 38% and the image asymmetry arises from the stacking fault beneath one half of the cell.

method which has been used to obtain thin specimen areas but is very irreproducible. It involves passing a very large current through the specimen instantaneously to deliberately melt parts of it and fracture the sample. Some fine, thin fingers of resolidified materials extend from the edges of the remaining solid parts which are extremely clean and can be relatively thin (< 500 A). Unfortunately this is the last heating operation which can be performed on the specimen. Naturally, the technique was not discovered deliberately. The sublimation of Si at high temperatures is, in contrast, an advantage in the profile study of surfaces. To effect this, (110) Si samples are chemically thinned so that the electron beam direction is close to the (110) zone axis needed for

high-resolution imaging at the 3 A level. The specimen is then heated to > 1200°C in vacuum and large amounts of material at the thin edges are sublimed. The resulting specimen geometry is shown in fig. 8. Around the edges of these long “fingers” which form, the surfaces are highly facetted, as might be expected. These facets represent low-index surface planes, many of which are perpendicular to the (110) electron beam direction and thus can be viewed in profile. Fig. 9 shows three examples of these: (a) a (100) surface; (b) a (111) surface and (c) a (113). The (100) surface exhibits an apparent 2 x 1 reconstruction as expected. (Actually one can only confirm the existence of a periodicity in one direction, i.e. 2 x n.) The (111) surface shows a modified region

J.M. Gibson et al. / HREM

ofinterfacesand

surfaces

43

;. 7. A bright-field image from the edge of a thin Si (111) specimen cleaned by heating to = 1000” C. Although Sic particles are seen to have formed in relatively high density, the surface exhibits a periodic 7 x 7 reconstruction in regions between these.

near the surface without obvious signs of a 7 X 7 periodicity. The (113) surface was found in many regions and shows a dramatic 1 X n “sawtooth” structure. In the profile view, although images appear graphically revealing, there are several difficulties in their interpretation. The major one is that the surfaces are really narrow strips so that edge interactions could be dominant. This may explain the lack of obvious structure in the “7 x 7” profile image or this may be due to the complexity of this structure in projection [16]. Equally serious is the difficulty of accurately locating structural detail in the direction perpendicular to the surface. Because of the absence of any periodicity in this direction images can only reasonably be interpreted to the level of the point resolution of the instrument [17],

that is, 2.5 A in our case. Images at edges are also very sensitive to specimen and instrumental parameters which are difficult to determine accurately [17]. Nonetheless, periodicities parallel to the surface, e.g. in figs. 9a and 9c, can be more reliability identified and the existence of at least one recognizable surface reconstruction, the (100) 2 X 1, suggests that these surface strips may be representative of flat surfaces in some cases. It is certainly clear that in the study of highly curved surfaces, such as catalytically active small particles, the results of profile imaging are unrivalled and highly relevant [ll]. The existence of large areas of (113) surface suggests that this has relatively low energy. Its structure is also easily modelled [18] and appears to fit a simple dimer model in which the dangling

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J.M. Gibson et al. / HREM of interfaces and surfaces

Fig. 8. The effect of > 12OO’C in-situ heating on a thin (110) Si specimen, which can then be used for profile imaging of a variety of facet surfaces formed on the edges of the “fingers”.

bond density is lower than either (100) or (111). Previous LEED studies of the (113) surface by Olshanetsky et. al. had shown it to be stable on annealing and apparently 3 x 1 reconstructed for Ge [19] and 3 x 2 reconstructed for Si [20]. Our results would be consistent with a 3 X 1 reconstruction, bearing in mind the loss of detail in the [llO] direction. However, LEED is more sensitive to very small atomic displacements which may break the symmetry. Chadi has considered this surface theoretically [21] and concludes that a model of the kind proposed here could have very low energy but that it was apparently not consistent with the LEED results. Bearing in mind our results the problem

may warrant more detailed investigation. It is also interesting to note that the model we propose [18] may be viewed as a dense packing of reconstructed single atomic steps on Si. Certainly if the (113) surface has low energy it may have important consequences for epitaxial growth, for example.

6. Conclusion In conclusion, we have discussed here the high-resolution electron microscopy of interfaces and surfaces involving semiconductors. The usefulness of improved resolution at the 1.4 A level

J. M. Gibson et al. / HREM of interfaces and surfaces

45

Fig. 9. Three examples of profile images from low-energy Si surfaces formed after in-situ cleaning of a Si (110) specimen: (a) (100); (b) (111) and (c) (113).

46

J.&f. Gibson et al. / HREM of interfaces and surfaces

has been demonstrated and the usually ignored limitations due to sample “noise” have been emphasized. One way of overcoming this limitation and approaching new frontiers in HREM is by in-situ specimen preparation and cleaning in a UHV HREM. Results from our own experiments with a home-modified UHV surface HREM are reported.

[5] [6] [7] [8] [9]

[lo]

Acknowledgements

We wish to acknowledge valuable discussions with Robert Hull and A.F.J. Levi and the technical assistance of Frank C. Unterwald and W.M. Augustyniak.

References [l] A. Ourmazd, K. Ahlbom, K. Ibeh and T. Honda, .Appl. Phys. Letters 47 (1985) 685. [2] J.M. Gibson, R.T. Tung, C.A. Pimentel and D.C. Joy, in: Microscopy of Semiconducting Materials 1985, Inst. Phys. Conf. Ser. 76, Eds. A.C. CuIIis and D.B. Holt (Inst. Phys., London-Bristol, 1985) p. 173. [3] J.M. Gibson, IEEE “Spectrum” (December 1985) 38. [4] A.E. White, K. Short, J.L. Batstone, D.C. Jacobson, J.M.

[ll] [12] [13] [14] [15]

[16]

[17] [18] [19] [20] [21]

Poate and K. West, in: Proc. Ion Beam Modification of Materials Conf., Catania, Italy, June 1986. J.M. Gibson, Appl. Phys. Letters 41 (1982) 818. J.M. Gibson, Ultramicroscopy 14 (1984) 1. W.O. Saxton and D.J. Smith, Ultramicroscopy 18 (1985) 39. Z. LiIIientaI, O.L. Krivanek, SM. Goodnick and C.W. Wihnsen, Mater. Res. Sot. Symp. Proc. 37 (1985) 193. R. Hull, J.C. Bean, J.M. Gibson, K.J. Marcantonio, A.T. Fiory and S. Nakahara, Mater. Res. Sot. Symp. Proc. 37 (1985) 261. W. Krakow, A.L.J. Chang and S.L. Sass, Phil Mag. 35 (1977) 575. L.D. Marks and D.J. Smith, Nature 303 (1983) 316. K. Takayanagi, Y. Tanashiro, S. Takahashi and M. Takahashi, Surface Sci. 164 (1985) 367. J.C.H. Spence, Ultramicroscopy 11 (1983) 117. P.M. Petroff and R.J. Wilson, Phys. Rev. Letters 51 (1983) 199. A. Ishizaka, K. Nakagawa and Y. Shiraki, in: Collected papers 2nd Intern. Symp. on MBE and Related Techniques, August 1982, p. 183. O.L. Krivanek and G.J. Wood, in: Proc. 43rd Annual EMSA Meeting, Louisville, KY, 1985, Ed. G.W. Bailey (San Francisco Press, 1985) p. 262. J.M. Gibson, Phys. Rev. Letters 53 (1984) 1859. J.M. Gibson, M.L. McDonald and F.C. UnterwaId, Phys. Rev. Letters 55 (1985) 1765. B.Z. Olshanetzky and V.I. Mashanov, Surface Sci. 111 (1981) 414. B.Z. Olshanetsky, V.I. Mashanov and AI. Nikiforov, Surface Sci. 111 (1981) 429. D.J. Chadi, Phys. Rev. B29 (1984) 785.