PHYSICAL REVIEW B
VOLUME 54, NUMBER 12
15 SEPTEMBER 1996-II
Surface structure of the „331… and „332… reconstructions of Ge„113… Zheng Gai, Hang Ji, Bo Gao, R. G. Zhao, and W. S. Yang* Mesoscopic Physics Laboratory and Department of Physics, Peking University, Beijing 100871, China ~Received 23 April 1996! We have studied the clean and well-annealed Ge~113! surface with scanning tunneling microscopy ~STM! and low-energy electron diffraction. The surface consists of very large 331-reconstructed domains with many small 332 antiphase domains scattered in them. STM has disclosed that neither the 331 nor 332 reconstruction of the surface has a mirror plane. This fact rules out all models proposed so far for the Si~113! surface as candidates for the Ge~113! surface. For further investigations, a model without a mirror plane has been proposed for the 331 reconstruction. The model contains a rebonded atom and an adatom as well as five dangling bonds in each unit cell. For the 332 reconstruction a model has also been proposed, which is different from but similar to the interstitialcy model recently proposed for the Si~113!332 surface. A unit cell of the present 332 model consists of two unit cells of the present 331 model, and a subsurface interstitial in one of the 331 unit cells. Both the proposed models are compatible with the experimental STM images. @S0163-1829~96!01436-1#
INTRODUCTION
The first study on the Si~113! surface was reported a long time ago,1 and the interest in it since then has been gradually increasing, as the surface has quite a low surface energy and is hence stable,2 and since annealing of low-index Si surfaces frequently results in $ 113% facets.3 It also has great potential as a substrate of heteroepitaxial growth,4 and the interesting phenomenon of chiral melting has been observed on it.5 Although the unreconstructed Si~113! surface does not have a low surface energy,6 many plausible models have been proposed for its (331) and (332) reconstructions,7 and these have been tested with different techniques8–14 including scanning tunneling microscopy ~STM! ~Refs. 9, 11, 12, and 14! and first-principles calculations.10,11,14 Very recently, an interesting structural model of the (332) reconstruction was proposed by Dabrovski, Mu¨ssig, and Wolff, which is supported by their STM observation and ab initio calculations.14 Ge~113!, however, has received less attention than its silicon counterpart, just as in the case of low-index germanium surfaces, only because of their lesser importance in applications.15,16 From the basic scientific point of view investigations on germanium surfaces should not be neglected, since if we could compare germanium surfaces with their silicon counterpart our knowledge in this regrad would become more systematic.16,17 This has been the motivation for the present work. EXPERIMENT
The experiment was performed with an UHV-STM system that has been described previously.18 The system consists of a main chamber and a sample preparation chamber. Both of them have a base pressure of low 10210 torr. In the former a homemade STM along with low-energy electron diffraction ~LEED! and Auger electron spectroscopy ~AES!, is installed while in the latter ion bombardment and annealing is carried out. The STM is able routinely to achieve atomic resolutions on surfaces of semiconductors as well as 0163-1829/96/54~12!/8593~7!/$10.00
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metals.18 The bias is applied to the sample, and the tip is grounded. The constant-current mode of the STM was used throughout the work, and the scanning rate was from 200 to 2000 Å/s. The tip was made out of W wire with electrochemical etching. The Ge sample with a dimension of 73730.5 mm 3 was cut from a Ge~113! wafer ~40–50 V cm!. After Ar 1 bombardment (531025 torr, 600 V 31 m A34 h! and annealing at 800 ° for some 10 min, a clean and well-ordered surface was always obtained, as indicated by LEED and AES. RESULTS AND DISCUSSIONS
The clean and well-ordered Ge~113! surface exhibits bright and sharp 331 LEED patterns, in agreement with previous works,15,16 and hence we call the surface Ge~113! 331 or simply Ge~113!. Two such patterns are shown in Fig. 1, on which a mirror plane along @ 3 32 # direction ~nearly vertical! can be seen. In our case, however, a couple of very dim 332 fractional-order beams were occasionally visible at some beam energies. The STM images show, surprisingly, only small patches of both 331 and 332 reconstructions, as shown in Fig. 2, rather than pure large 331 domains, as one would expect from the LEED patterns. However, a careful inspection of the images tells us that in most area in the 33 direction the surface order extends to thousands of Å without a break. This fact conciliates the ‘‘contradiction’’ between the STM images and the LEED patterns: The 332 reconstruction consists of small antiphase domains, thus resulting in fractional-order beams with almost zero intensities; while the 331 domains are much larger than the coherent length of the LEED incident beam, although they look like small patches in STM images as they are split into small patches by small 332 domains, a fact that is not reflected in LEED patterns. Another eye-catching feature of all the STM images that we obtained from the surface, with many very different effective tips, is that neither the 331 nor the 332 reconstruction 8593
© 1996 The American Physical Society
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ZHENG GAI, HANG JI, BO GAO, R. G. ZHAO, AND W. S. YANG
FIG. 1. LEED patterns of the Ge~113!331 surface. Note the vertical mirror plane at the center. ~a! 42 eV. ~b! 100 eV.
has a mirror plane, thereby indicating that the reconstructed surface does not have the mirror plane that the truncated surface has ~see Figs. 2 and 3!. The mirror plane seen in the LEED patterns thus is intrinsic to neither of the reconstructions, but a result of superposition of the contributions from different domains in mirror-reflection relationship to each other. On the basis of this fact alone, all the models that have been proposed for the Si~113!331 or 332 reconstructions should be ruled out for the Ge~113! surface, since they all have a mirror plane along the @ ¯ 3¯ 32 # direction.7,8,14 It has been known since the very beginning of STM that care has to be taken if one wants to correlate STM features with the atomic structure of semiconductor surfaces, as it is the local density of states, instead of the surface topology,
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that directly determines the STM features.19 The theoretical methods for calculations of STM images have been well developed;19,20 the concrete calculations, however, are still quite time consuming. This situation is clearly reflected in the fact that, on one hand, STM images with an atomic resolution can be obtained routinely from semiconductor surfaces and there are a great deal of important surface structures remaining unknown, and, on the other hand, only a small percentage of the published STM papers interpret their STM images by means of image calculations. In order to be able to extract as much surface topological information as possible from the STM images, while also avoiding tedious image calculations, we propose to take the average of a pair of occupied- and empty-state images collected simultaneously from a surface as an approximation of the surface topology ~or atomic geometry!. The intuitive thought behind this idea was that both the topology and the electronic charge of a surface may make some contribution to its STM images, and that the topological contributions in the occupied and emptystate images are similar, while the electronic parts are different, thereby the ‘‘topology-to-charge ratio’’ may be increased by averaging. Furthermore, we may subtract the topological contribution from the occupied-state ~emptystate! image to obtain the image of the occupied states ~empty states!. This idea finds support from the results of an early paper by Tersoff and Hamann,19 as well as many recent papers,9,11,14,20–22 as ~i! it is only the top most surface atoms that may contribute to STM images; ~ii! these atoms in most cases can be imaged either in occupied- or empty-state images or sometimes in both; ~iii! the valence electrons may deviate from, but never far from the relevant atoms; and ~iv! in the occupied- and empty-state images the deviations very often are in different directions. It should be emphasized that the averaged image of a pair of dual-bias images is only an approximation of the topology or atomic geometry of a surface, but it could serve as a very good starting point for further investigations, especially when it is compatible with the results of other papers or the established principles governing surface reconstructions. Shown in Fig. 3 is a pair of empty- and occupied-state STM images collected simultaneously from the Ge~113! surface. According to the above discussion, the atomic image, i.e., the average of the normalized empty- and occupied-state images, as well as the image of the empty states obtained by subtracting 50% corrugation of the atomic image from the normalized empty-state image, are made and also shown in
FIG. 2. STM images (1803180 Å 2 ) of the Ge~113! surface, showing a large 331 domain with many small antiphase 332 domains scattered in it. To check this, one only needs to raise the bottom side of the images and look at them from the bottom; then one can see clearly the 33 chains running through the images from bottom to top. ~a! 2.5 V, 0.5 nA. The mirror plane ~in the @ ¯ 3¯ 32 # direction! of the bulk and also of the truncated surface is also shown with a thin line. ~b! From a different area, 22.0 V, 0.5 nA.
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SURFACE STRUCTURE OF THE (331) and (332) . . .
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FIG. 3. STM images (30330 Å 2 ) obtained from a 331 area of the Ge~113! surface. ~a! Empty-state image, 1.5 V, 0.5 nA. The mirror plane ~in the @ ¯ 3¯ 32 # direction! of the bulk and also of the truncated surface is also shown with a thin line. ~b! Occupied-state image, 21.5 V, 0.5 nA. ~c! Atomic image obtained from ~a! and ~b! ~see text!. ~d! Image of the empty states obtained from ~a! and ~c! ~see text!.
Fig. 3. The image of the occupied states can be obtained similarly and, by its definition, is merely the negative of the image of the empty states, and therefore is not shown here. On the basis of the atomic image @Fig. 3~c!#, we propose the model shown in Fig. 4~a! for the 331 reconstruction of the Ge~113! surface. To prove the correctness of the model, we superimpose the model onto the atomic image and the image of the empty states, obtaining Figs. 5~a! and 5~b!, respectively. We see that in Fig. 5~a!, i.e., the atomic image, almost all surface atoms appear as a protrusion, while in Fig. 5~b!, i.e., the image of the empty states, only those with an empty or partly empty dangling bond appear as a protrusion. This means that the model reproduces the major features in these images nicely. To understand why the surface favors the reconstruction described by the model, we recall that it is the
balance between the energy gain due to the reduction of dangling bonds and the energy cost due to induced strain that determines the nature of the surface reconstruction.17 In this model rebonding of atom d to atom c and formation of adatom a, which is bonded to atoms b, c, and g, reduce the number of dangling bonds in a 331 unit cell from 9 to 5. In addition, the surface atoms can relax and redistribute their dangling-bond charge density to further reduce the energy. Specifically, atoms e and f relax downward ~inward!, and their dangling bonds accordingly become p like and empty, while atom a relaxes upward ~outward! and its dangling bond becomes s like and occupied. Since there is some intensity between atoms d of one unit and b and f of the neighboring units in the image of the empty states @see Fig. 5~b!#, the dangling bond of atoms b and d must be at least
FIG. 4. ~a! Model proposed for the 331 reconstruction of the Ge~113! surface, with large and small circles representing first- and second-layer atoms, respectively, and the open, filled, and shaded oblongs the empty, occupied, and partly occupied dangling bonds, respectively. A 331 unit cell is also shown in the figure. ~b! The 331 model proposed by Ranke ~Ref. 7! for the Si~113!331 surface, with large and small circles representing first- and second-layer atoms, respectively. ~c! A schematic drawing of the truncated Ge~113! surface, with the triangles representing the dangling bonds. 131 and 331 unit cells are outlined.
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FIG. 5. ~a! Superposition of Fig. 4~a! with Fig. 3~c!. ~b! Superposition of Fig. 4~a! with Fig. 3~d!. For clarity, in ~a! the model is black, while in ~b! it is gray.
partly empty, and thereby these atoms, especially d, may have some downward ~inward! relaxation. However, if only the number of dangling bonds is concerned, this model is similar to the 331 model proposed by Ranke,7 which also consists of adatoms and rebonded atoms ~dimers! and has five dangling bonds in each unit cell @see Fig. 4~b!#. So there must be some other reason responsible for the preference to the present model. Actually, there are two big differences between the two models. First, in the former ~the present model! the adatom ~atom a) is added on top of atoms c, d, and g, while in the latter the adatom ~atom g) is formed by removing atom d and letting g bond directly to the atom below d @see Fig. 4~c!#. This means that the adatom in the former model is at a higher level than that in the latter. Second, different from the former model, the latter, as well as all other models proposed so far for Si~113!, has a mirror plane along @ ¯ 3¯ 32 # , and is thus incompatible with the STM images
obtained from the Ge~113! surface. Obviously, because of the two interconnected features, which are interrelated to one another, the present model has more flexibility to reduce the tensile stress induced by reconstruction, and thus costs less energy to form. At this point it is natural and interesting to consider why, on the Si~113!332 surface, the adatoms are at the lower rather than the higher level.14 To answer this subtle question with certainty, careful theoretical calculations are necessary. Qualitatively, however, the answer to this question might be the same as that to the question of why the Ge~111! reconstructs to c(238) while the Si~111! surface reconstructs to 737: The strain-energy cost associated with defect formation for the Si~111! surface is less than the energy gain associated with the reduction in the number of dangling bonds,23 while the opposite is true for the Ge~111! surface; hence the existence of different surface reconstructions.17 More generally, multilayer relaxations are
FIG. 6. STM images (60360 Å 2 ) obtained from an area where both 331 ~upper portion! and 332 ~lower portion! reconstructions are seen. ~a! Empty-state image, 1.5 V, 0.5 nA. ~b! Occupied-state image, 21.5 V, 0.5 nA. ~c! Atomic image obtained from ~a! and ~b! ~see text!. ~d! Image of the empty states obtained from ~a! and ~c! ~see text!.
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SURFACE STRUCTURE OF THE (331) and (332) . . .
FIG. 7. ~a! Line scans along the A-A and B-B lines marked in Fig. 6~c!, respectively. ~b! Line scans along the A-A and B-B lines marked in Fig. 6~d!, respectively. The A-A and B-B lines in both Figs. 6~c! and 6~d! are also marked in Figs. 4~a! and 8~a!, respectively, with the thin line running from the upper left to the lower right.
likely energetically more expensive in the case of germanium surfaces than silicon. This might be also responsible for the fact that group-III metals induce the A33 A3 reconstruction on Si~111!, which requires a deep multilayer relaxation for stress relief,17 but not on Ge~111!.24 As mentioned earlier, STM has revealed the existence of many 332-reconstructed patches on the Ge~113! surface, although LEED exhibits almost pure 331 patterns. Now we turn to these 332-reconstructed patches. To disclose the atomic structure of the 332 reconstruction, we constructed an atomic image @Fig. 6~c!#, and an image of the empty states @Fig. 6~d!# from a pair of empty-state and occupied-state images, which were collected simultaneously @Figs. 6~a! and 6~b!# from an area where the 332 reconstruction coexisted with the 331. We see immediately that the two reconstructions consist of similar building blocks, but also exhibit significant differences. To make further comparisons easier, in addition to showing the images we show also some line scans in Fig. 7. Obviously, as far as only the peak positions are concerned, the line scans from the 332 areas are quite similar to their counterpart from the 331 areas. The relative peak heights, however, have significant differences. In particular, peak a 2 on curve B-B of Fig. 7~a! and peak e 2 on curve B-B of Fig. 7~b! are reduced greatly. These differences cannot be explained by assuming that a 332 unit cell consists of two 331 unit cells, and that there is some charge transfer between the two. In view of the fact that the Ge~100! and ~111! surfaces all have some ingredients similar to their
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FIG. 8. ~a! Top view of the model proposed for the 332 reconstruction of the Ge~113! surface, with the large solid, small solid, shaded, and thick open circles representing the first layer, second layer, raised second layer, and interstitialcy atoms, respectively, and the filled and shaded oblongs the occupied and partly occupied dangling bonds, respectively. Atoms surrounded by a dashed circle are expected to be visible in empty-state images, according to calculations of Ref. 14. ~b! Side view of the same model. Note that the interstitial ~thick open circle! is bonded to atoms a 1 , b 1 , e 1 , and f 1 , the raised second-layer atom ~shaded circle!, and the atom directly below itself, thus being sixfold coordinated. Note also that without the interstitial the raised second-layer atom would be at the position of the dotted circle and would have a bond ~the dotted line, in the ^ 111& direction! bonding to the atom directly below it. The interstitial splits this bond, and thus is called a split interstitial ~or more precisely a ^ 111& -split interstitial! ~Refs. 25 and 14!.
silicon counterpart, we believe that some similarity might also exist between the ~113! surfaces of germanium and silicon. It has been shown very recently that a Si~113!332 unit cell consists of two 331 unit cells schematically shown in Fig. 4~b! along with a subsurface interstitial.14 Borrowing the idea of subsurface interstitial, we propose the model shown in Fig. 8 for the Ge~113! surface. The justifications for this model are the following. ~i! The interstitials are ^ 111& split and sixfold coordinated, the same as those in the Si~113! 332 surface.14 ~ii! In bulks, the split interstitials compared with the tetrahedral and hexagonal interstitials have a much lower total energy,25 and in the case of Si~113!332 the subsurface interstitialcy model compared with the other models is also energetically favorable.14 ~iii! The compressive stress caused by the interstitials makes a reduction of the tensile stress induced by the adatoms easier.14 ~iv! Since the interstitials are sixfold coordinated while the atoms bonded to it are all fourfold coordinated, there are two electrons unused in this group ~group 1!.14 These two electrons may be accommodated into the group of the same unit cell that does
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FIG. 9. Examples of the STM images (1103110 Å 2 ) obtained from the Ge~113! surface with ‘‘bad’’ tips. ~a! 1.5 V, 0.5 nA. ~b! 1.5 V, 0.5 nA. ~c! 2.0 V, 3.0 nA.
not have an interstitial ~group 2!, to further reduce the total energy. Now we discuss how the model can reproduce the features seen from the experimental STM images ~Fig. 6! and line scans ~Fig. 7!. To accommodate the seven electrons ~two electrons transferred from group 1 plus the five native dangling-bond electrons! into the five dangling bonds of group 2, atoms e 2 and f 2 @see Fig. 8~a!# relax upward @see the lower curve of Fig. 7~a!#, making their dangling bonds s like and occupied by four electrons, instead of p like and empty in the case of 331. This explains why peak e 2 ~and also f 2 not shown! on the line scan of the empty states @curve B-B of Fig. 7~b!# is very low, while in 331 very high @curve A-A of Fig. 7~b!#. As a result of the upward relaxations of atoms e 2 and f 2 , atom a 2 must relax downward, causing the very low height of peak a 2 on curve B-B of Fig. 7~a!. This downward relaxation changes its dangling bond from s like and fully occupied towards p like and less occupied, thus slightly increasing the peak a 2 on the line scan of the empty states @curve B-B of Fig. 7~b!#. Also, as a result of the upward relaxations of atoms e 2 and f 2 , atoms b 2 and c 2 and probably also d 2 need to relax a bit. Since the dangling bonds of atoms b 2 , d 2 , and d 1 are essentially parallel to the surface, their changes cannot be reflected sensitively in STM images. According to the calculations made for the interstitialcy model of the Si~113!332 surface,14 in empty-state images group 2 should be more visible than group 1, and this is indeed so in our experiment @see the 332 portion of Fig. 6~a!#. Very often, STM images very different from those shown above were obtained. Several of them are shown in Fig. 9, as examples. Actually, it is well known that STM images are
always the convolution of tip and surface.26 Therefore, one should not be surprised to see STM images varying more or less with the varying tip, from time to time. What we want to emphasize here is that as a result of the very low symmetry of the Ge~113! surface the variations of its STM images are much more frequent and dramatic than what is ever observed from other highly symmetric surfaces, and probably are also beyond what one would expect to see. To avoid being cheated by the wrong images, it is of crucial importance to adopt only those images that can be obtained reproducibly after many tip changes, rather than to choose others simply because of their nice resolutions.
SUMMARY
We have studied the clean and well-annealed Ge~113! surface with STM and LEED. The surface consists of very large 331 domains with many small 332 antiphase domains scattered in, thus giving rise to nice 331 LEED patterns but not very lovely STM images. STM has disclosed that neither the 331 nor the 332 reconstruction of the surface has a mirror plane, although its LEED patterns as well as its truncated surface do have one. This fact rules out all models proposed so far for the Si~113! surface as candidates for the Ge~113! surface. For further investigations, a model without a mirror plane has been proposed for the 331 reconstruction. The model contains a rebonded atom and an adatom as well as five dangling bonds in each unit cell, and is compatible with the experimental STM images. For the 332 reconstruction a
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SURFACE STRUCTURE OF THE (331) and (332) . . .
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model has also been proposed, which is different from but similar to the interstitialcy model recently proposed for the Si~113!332 surface.14 A unit cell of the present 332 model consists of two unit cells of the present 331 model, and a subsurface interstitial in one of the two 331 unit cells. The model is compatible with experimental STM images. A method is proposed and used in the present work to extract
as much as possible topological information about semiconductor surfaces from their dual-bias STM images.
*Author to whom correspondence should be addressed. Electronic
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address:
[email protected] 1 H. E. Farnsworth, R. E. Schlier, and J. A. Dillon, J. Phys. Chem. Solids 8, 116 ~1959!. 2 D. J. Eaglesham, A. E. White, L. C. Feldman, N. Moriya, and D. C. Jacobson, Phys. Rev. Lett. 70, 1643 ~1993!. 3 J. M. Gibson, M. L. McDonald, and F. C. Unterwald, Phys. Rev. Lett. 55, 1765 ~1985!. 4 U. J. Knall and J. B. Pethica, Surf. Sci. 265, 156 ~1992!. 5 Y.-N. Yang, E. D. Williams, R. L. Park, N. C. Bartelt, and T. L. Einstein, Phys. Rev. Lett. 64, 2410 ~1990!; D. L. Abernathy, R. J. Birgeneau, K. I. Blum, and S. G. Mochrie, ibid. 71, 750 ~1993!. 6 D. J. Chadi, Phys. Rev. B 29, 785 ~1984!. 7 W. Ranke, Phys. Rev. B 41, 5243 ~1990!. 8 U. Myler, P. Althainz, and K. Jacobi, Surf. Sci. 251/252, 607 ~1991!. 9 U. J. Knall, J. B. Pethica, J. D. Todd, and J. H. Wilson, Phys. Rev. Lett. 66, 1733 ~1991!. 10 D. M. Bird, L. J. Clark, R. D. King-Smith, M. C. Payne, I. Stich, and A. P. Sutton, Phys. Rev. Lett. 69, 3785 ~1992!. 11 J. H. Wilson, D. A. McInnes, J. Knall, A. P. Sutton, and J. B. Pethica, Ultramicroscopy 42-44, 801 ~1992!. 12 M. J. Hadley, S. P. Tear, B. Ro¨ttger, and H. Neddermeyer, Surf. Sci. 280, 258 ~1993!. 13 K. Jacobi and U. Myler, Surf. Sci. 284, 223 ~1993!.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China, and the Doctoral Program Foundation of the Education Ministry of China.
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