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Interpretation of Anomalous Scanning Tunneling Microscopy Images of Layered Materials† E. E. Mola,* C. A. Paola, and J. L. Vicente INIFTA, Division Quimica Teorica, Fac. Cs. Exactas, UNLP, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina Received September 1, 1994. In Final Form: August 11, 1995X We propose a method to correct drifts and aleatory noises of scanning tunneling microscopy images. The method is suitable to study atom chemisorption at the submonolayer level on extended layered materials. The method uses a linear transformation and statistical averages, based on the changes and distortions on a substrate of known symmetry.
I. Introduction The scanning tunneling microscopy (STM) is a powerful technique for determining electronic and structural properties of surfaces. This technique allows us to obtain atomic scale resolution. A detailed description about STM devices is presented by Binning and Rohrer,1-4 Feenstra,5 and Tersoff.6 A STM image is built as a bidimensional array of current measurement (constant height mode) or potential measurement (constant current or topography mode). Each measurement can be treated through the Bardeen theory7 or the approximations developed by Terssoff and Hamann8,9 and Baratoff.10 However, for an adequate interpretation of the images it is necessary to correct them from instrumental errors. In this work, we propose a method to correct two of those errors, drifts and aleatory noises, taking into account samples of known symmetry. The drift is mainly due to positional accumulative defects of the tip originated by the piezoelectric drivers. This error produces symmetry changes and distortions in the relative distance among the image points. Both defects can be eliminated by a linear transformation. The statistical method to diminish the random noise requires several measurements obtained under similar conditions. However, the above mentioned distortions due to the uncertainty of the tip to be placed at the original position, over the surface, when two or more images are sequentially generated provokes that the same scanning origin has two different reference systems, one of them related with the instrument and the other one (surface coordinates) with the sample. The accumulation of this effect provokes that there is only a 50% overlap between the first and the fourth images of a sequence, and this effect is greater when the scanning is slower. This is a † Presented at the symposium on Advances in the Measurement and Modeling of Surface Phenomena, San Luis, Argentina, August 24-30, 1994. X Abstract published in Advance ACS Abstracts, January 1, 1996.
(1) Binning, G.; Rohrer, H.; Gerber, Ch.; Weibel, E. Phys. Rev. Lett. 1982, 49, 57. (2) Binning, G.; Rohrer, H. Helv. Phys. Acta 1982, 55, 726. (3) Binning, G.; Rohrer, H. Surf. Sci. 1985, 152/153, 17. (4) Binning, G.; Rohrer, H. IBM J. Res. Develop. 1986, 30, 355. (5) Feenstra, R. M. Scanning Tunneling Microscopy and Related Methods; Behm, R. J., Garcia, N., Rohrer, H., Eds.; NATO ASI Series, Applied Sciences; Kluwer: Dordrecht, 1989; Vol. 184. (6) Tersoff, J. Scanning Tunneling Microscopy and Related Methods; Behm, R. J., Gracia, N., Rohrer, H., Eds.; NATO ASI Series, Applied Sciences; Kluwer: Dordrecht, 1989; Vol. 184. (7) Bardeen, J. Phys. Rev. Lett. 1961, 6, 57. (8) Tersoff, J.; Hamann, D. R. Phys. Rev. Lett. 1983, 50, 1998. (9) Tersoff, J.; Hamann, D. R. Phys. Rev. Lett. 1985, B31, 805. (10) Baratoff, A. Physica 1984, 127B, 143.
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great limitation on the possibility of improving an image by averaging a set of sequential “identical” images. Therefore, we correct the random noise making use of the image periodicity, applying the statistical concepts to a set of cells of the same image. The method presented in this paper allowed a successful analysis of experimental information such as those published in refs 11 and 12. In ref 11 we performed a straightforward interpretation of surface imaging with structures derived from theoretical models. Thus, STM imaging data of Ag electrodeposition on C(0001) under overpotential conditions have revealed that 3D Ag growth involves a Volmer-Weber mechanism through Ag submonolayer domains with an interatomic distance dAg-Ag ) 0.330 ( 0.16 nm, and an epitaxy angle with respect to the substrate θ ) 20 ( 10°.13 These domains can be considered as precursors of the 3D Ag crystal. From these structural data and further geometrical considerations, it was concluded in that paper that the surface structure on these domains could be assigned to a (x7/2 × x7/2)R19° lattice,13 coexisting with domains of the C(0001) and 3D Ag cristals. Likewise, the C(0001) reference structure allowed us to estimate, by using the method described in this paper, the image drift and, correspondingly, to determine the value of θ and its accuracy, which resulted in θ ) 15 ( 5°. In ref 12 we performed a careful analysis of STM images resulting from sulfur adsorption on C(0001), at the submonolayer level.14 These images showed a hexagonal underlaying lattice with a side distance dC-C = 0.14 nm. This C-C bond distance corresponds to the honeycomb lattice of C(0001) which can be observed under high resolution. In addition, bright spots related to sulfur atoms are observed. From these STM images, which are extensively described elsewhere,14 and by using the method described in this paper, it was clear that the location of sulfur atoms on the substrate does not coincide with hollow sites of the hexagons, but it was difficult to decide whether sulfur atom adsorption occurs at bridge or top positions. It should be noted that the adsorption of several gases such as argon and krypton on C(0001) also occurs at hollow sites of the substrate.15 The adsorption of sulfur atoms on the basal plane of graphite (11) Mola, E. E.; Appignanessi, A. G.; Vicente, J. L.; Vazquez, L.; Salvarezza, R. C.; Arvia, A. J. Surf. Rev. Lett. 1995, 2, 489. (12) Vicente, J. L.; Mola, E. E.; Appignanessi, A. G.; Zubimendi, J. L.; Vazquez, L.; Salvarezza, R. C.; Arvia, A. J. Langmuir, in press. (13) Vazquez, L.; Hernandez Creus, A.; Carro, P.; Ocon, P.; Herrasti, P.; Palacio, C.; Vara, J. M.; Salvarezza, R. C.; Arvia, A. J. J. Phys. Chem. 1992, 96, 10454. (14) Zubimendi, J. L.; Salvarezza, R. C.; Vazquez, L.; Arvia, A. J. Langmuir 1996, 12, 000.
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leads to a x3 × x3 lattice with a sulfur-sulfur distance dS-S ) 0.42 nm and hexagonal sulfur trimer adsorbates with dS-S ) 0.24 nm. II. Methods (A) Drift Correction. A STM image consists of a measurement array per form over N × N points of a square lattice (N being an instrumental property). Each measurement is denoted by Rij (i ) 1, ..., N; j ) 1, ..., N) (either in the mode of constant current or constant height). When scanning in the x direction, the tip yields the sequence Ri1 (i ) 1, ..., N). Then, it moves one step in the y direction and produces the sequence Ri2 (i ) 1, ..., N); this procedure goes on until the collection of measurements is completed. The distance between two arbitraty points, located over a line parallel to the x-axis, is determined better than the distance along lines parallel to the y-axis. This uncertainty causes an accumulative distortion known as drift. These distortions can be diminished by a linear transformation keeping the relative distances along the scanning direction (the x-axis). The transformation can be obtained by taking into account samples of known simmetry. In order to illustrate this method we analyze the graphite basal plane which presents a honeycomb structure. This structure has a triple-axis on the atomic positions. Although the drift distortion breaks the symmetry of the image, it is often possible to identify three characteristic directions and construct a triangle with their sides parallel to each direction (see Figure 1a). To recover the symmetry, we perform a linear transformation that carries the constructed triangle over an equilateral triangle (see Figure 1b). Note that in Figure 1b we have also done an additional rotation of the image. We propose to carry out the lineal bidimensional interpolation presented by Paola.16 Let (xi,yi) (i ) 1, 2, 3) be the positions of the distorted triangle vertices and (xi′,yi′) (i ) 1, 2, 3), be the corrected positions (the equilateral triangle vertices). After applying the linear transformation to the distorted vector, we obtain
xi′ ) xi + ay
(1)
Figure 2. Contour plot of STM images. A sequence of contour plot images by increasing the number M of averaged cells with (a) M ) 49, (b) M ) 86, (c) M ) 135, and (d) M ) 185.
(2)
Finally, the corrected image can be obtained. (B) Statistical Treatment of STM Corrected Images. In STM experiments, nonadjustable variables produce systematic errors (arising mainly from the particular shape of the tip) and random errors (aleatory noises originated in all electronic measurements). Since systematic errors are different in each image, it is impossible to correct random errors making a simple average of several measurements over the same sample. We propose an alternative method that makes use of the image periodicity in order to eliminate the aleatory noises, isolated details, and noncommensurable spectral components. We divide the image in M regular cells. Inside each cell we perform a fine mesh that includes m × m points. Finally, we superpose the cells and average them point by point to obtain the average image.16 This method gives a signal-noise ratio proportional to M1/2. In Figure 2, we show contour plots corresponding to the image presented in Figure 1b, where the averages were made over different values of M. It can be observed that there is an improvement in the regularity of the curves as M increases.
i ) 2, 3 yi′ ) byi where
a)
2 2 2 2 - x23 ) - (y21 + y23)(x21 - x31 ) (y31 + y21)(x21
2(y23 - y31) b)
x
(x3 + ay3)2 - (x2 + ay2)2
xij ) xj - xi,
(y22 - y23) yij ) yj - yi i,j ) 1, 2, 3
Figure 1. STM images of a C(0001) graphite plane: (A) graphite image taken at constant current mode over an square L × L region (L ) 4 nm) with N × N points (N ) 200); (B) corrected image employing the linear transformation, eqs 5 and 6, with a ) -0.09 and b ) 0.87. The triangle used is also shown.
(3)
(4)
(5)
The coefficients a and b can be interpreted as a shearing correction parallel to the x-axis and a contraction in the y-direction. (15) Adsorption on Metal Surfaces; Benard, J., Ed.; Elsevier: New York, 1983 and references therein. (16) Paola, C. A.; Pascua, G. D.; Busato, E. B.; Vicente, J. L.; Mola, E. E. To be submitted for publication.
STM Images of Layered Materials
(A)
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(B)
Figure 3. Two graphite STM standard images of C(0001) taken at constant current mode (L ) 4 nm) and the contour plots (inset). Although graphite STM image of Figure 3A is of lesser quality compared with the one shown in Figure 3B, in both cases the inset shows the characteristic symmetry of the surface.
(A)
(B)
Figure 5. Two graphite STM anomalous images of C(0001) taken at constant current mode (L ) 6 nm) and the contour plots (inset). The contour plots in parts A and B are different types of ellipses but the maxima are over a triangle lattice like those in Figure 4.
Figure 4. Symmetry of standard STM images of a C(0001) graphite plane: (a) Triple axes, showing the maximum (shaded) and minimum (white) zones. The positions of the triple axes are indicated by A, B, and C. (b) Atomic position of graphite basal plane (honeycomb structure). (c) Dots represent atomic positions of graphite basal plane (honeycomb structure). Circles represent atomic positions of the second layer.
III. Results and Discussion The method presented in section II has been used over 30 STM images of the graphite basal plane. The corrected images can be classified in two categories: standard and anomalous images. In Figure 3 we show two images, that we denote as standard, where we include the contour plots of their average cells. The symmetries observed in these images are sketched in Figure 4a where the points A, B, and C are triple-axes (note that the points A and C coincide with a maximum and minimum of the image, respectively). These symmetries do not agree with the symmetry of a honeycomb structure (Figure 4b), which presents two triple-axes and a sextuple-axis. One of the hypothesis used to explain this discrepancy assumed that each atom of the graphite surface is nonequivalent with the nearest neighbors; this hypothesis results when we consider the interaction with the second layer. In Figure 4c we sketch with fill and hollow circles the atomic positions of the first and second layers, respectively; this structure presents three triple-axes that can be identified with the standard image axes. However, STM images of graphite monolayers adsorbed over a platinum surface17 show similar features to standard images even though the interplanar interaction is different. We propose an alternative hyphotesis for the interpretation of STM images in terms of a combination between the symmetry of the tip and the sample. Thus, the standard images could originate from the combined effect of the axial symmetry of the tip, around a perpendicular axis to the surface, and the surface honeycomb structure. On the other hand, standard images, which present only a maximum in each cell, can be reproduced with an (17) Land, T. A.; Michely, T.; Behm, R. J.; Hemminger, J. C.; Comsa, G. Surf. Sci. 1992, 264, 261.
Figure 6. Symmetry of anomalous STM images of C(0001) graphite plane. Scheme of elliptic contour plot on the maximum zones showing the double axes indicated by D, E, F, and G.
harmonic expansion to the first order. This is due to the fact that the convolution among the wave functions involved in the tunneling process privilege low-frequency components of the image harmonic expansion. Since the obtained anomalous images are similar among themselves, we only show two images and the contour plots of their corresponding cells (Figure 5). In both cases it is possible to observe that the maximum are over a triangle lattice as in the case of standard images. However, symmetry elements are essentially different. In the maximum regions, the contour plots are elliptic and define a direction that eliminates the three tripleaxes presented in a standard image. In Figure 6 we indicate with D, E, F, and G the position of the double axes. Taking into account the same arguments used for the interpretation of standard images, we can describe anomalous cases as the composition of a honeycomb structure and a tip with a double axis. When a tip presents a double axis, it means that the active wave function has a double axis, for example, when a tip is constituted by two active atoms or when the tunneling effect involves nonspherical orbitals. This method is applicable to the following: (i) A bidimensional Bravais lattice of known general symmetry. (ii) If the general symmetry of the STM image is known in advance, the statistical treatment of STM corrected images, described in the previous section, will allow us to determine the additional symmetry properties of the experimentally averaged unit cell (Figures 2, 3, and 5).
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These additional symmetry porperties would be otherwise unseen by a naked-eye analysis or even by using standard filters. (iii) Eliminate random noise by giving a signal-noise ratio proportional to the square root of the averaged image area. One should be aware that the noise spectrum may partly overlap the desired spectrum of the experimental data, and therefore care has to be taken not to generate new artifacts.18-20 (iv) Eliminate those substrate details whose periods are not commensurables with the general symmetry lattice paramenter. Therefore, any kind of surface defects are also included. (v) Study the symmetry elements of each image cell and, thus, determine the characteristic directions of the tip electronic structure. As a consequence of points i to v the method is suitable to study atom chemisorption on extended layered materials.11,12 It is particularly powerful to study adsorption of atoms, at the submonolayer level, specially if the STM image shows domains where the underlaying lattice symmetry can be compared simultaneously with covered (18) Aguilar, M.; Garcia, A.; Pascual, P. J.; Presa, J.; Santiteban, A. Surf. Sci. 1987, 181, 15. (19) Becker, J. Surf. Sci. 1987, 181, 200. (20) Stoll, E.; Marti, O. Surf. Sci. 1987, 181, 222.
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substrate domains. Therefore, the locations of adatoms on the substrate will be facilitated with the present method. IV. Conclusions We found that distortions by drift can be corrected by a linear transformation. The statistical method we presented for the noise elimination exalts the dominant symmetries in the image unity cells. Nevertheless, the corrected images show anomalous symmetries in different contour plots. The observed distortions may be related with the complex symmetry of the electronic states of the tip. Work is in progress at La Plata to correct the latter distortion. Acknowledgment. This research project was financially supported by the Consejo Nacional de Investigaciones Cientificas y Tecnicas, Universidad Nacional de La Plata, and the Comision de Investigaciones Cientificas de la Provincia de Buenos Aires. The authors are also indebted to Fundacion Antorchas for a grant. The authors thank Mr. G. Pascua and Mrs. E. Busato. LA940693V
