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Study of the surface morphology of the (100) cleavage planes of MgO single crystals by atomic force microscopy
Surface Science 424 (1999) 139–144
Study of the surface morphology of the (100) cleavage planes of MgO single crystals by atomic force microscopy K. Sangwal a, *, F. Sanz b, P. Gorostiza b a Institute of Physics, Technical University of Lublin, ul. Nadbystrzycka 38, 20-618 Lublin, Poland b Departament de Quimica Fisica, Universitat de Barcelona, Marti I Franques 1, 08028 Barcelona, Spain Received 23 April 1998; accepted for publication 23 December 1998
Abstract Some experimental observations made on the nature and distribution of nearly circular and polygonal closed steps, and arrays of semicircular steps arranged between two multilayer steps on the (100) cleavage planes of MgO single crystals by atomic force microscopy are described. The results show that: (1) the formation of disc-shaped elevations and depressions, and series of semicircular steps takes place by a mechanism similar to the Frank–Read source [Phys. Rev. 79 (1950) 722]; (2) the diameters of disc-shaped structures are related with shear stresses of the order of the yield stress of the crystal; and (3) with an increase in the size of closed steps, their rounded shape changes to polygonal due to a lower edge free energy of the 010 and 011 steps compared to that of steps of other orientations. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Low-index single-crystal surfaces; Magnesium oxide; Morphology; Roughness; Single crystal surfaces; Surface stress; Surface structure, morphology, roughness, and topology
1. Introduction The investigation of the morphology of surfaces of crystalline solids is of practical and general interest because many processes such as the growth of epitaxial films, catalytic reactions and nanomanipulations are intimately connected with surfaces. In many cases cleavage faces are better than surfaces prepared by cutting, abrasion and polishing because the latter techniques introduce defects and impurities in the surface layer. A brief introduction to the surface morphology and commonly used terminology of cleaved faces may be found in Ref. [1]. During recent years an increasing interest has * Corresponding author. Fax: +48 81 5259385; e-mail: [email protected].
emerged in the investigation of the surface morphology of cleavages of a variety of ionic single crystals [2–6 ], using sophisticated techniques such as atomic force microscopy (AFM ) and scanning tunnelling microscopy. Most of these studies deal with the observation of mono- and bilayer steps [3–6 ], and step–terrace structures on the as-cleaved crystal faces [5]. In the case of MgO single crystals, which are widely used as a substrate material for the growth of epitaxial thin films and superlattices for a variety of applications [7–9], AFM studies of the cleavages of MgO crystals reveal mono-, bi- and trilayer steps [5–7] as well as multilayer steps up to 4–50 nm in height [7,10]. Until now except for the study of the nature of multilayer steps on the (100) face of MgO crystals [10], no other systematic investigation of the cleavage morphology of ionic crystals has been carried
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K. Sangwal et al. / Surface Science 424 (1999) 139–144
out. However, examination of relatively smooth regions of cleaved surfaces of MgO reveals a rich surface morphology composed of disc-shaped elevations and depressions and series of isolated monolayer semicircular steps originating from disc-like sources on the surface. To the authors’ knowledge such step patterns have not been reported so far. Therefore, the present paper is dedicated to such cleavage step patterns.
2. Experimental The specimens of the MgO single crystals were prepared by cleavage along the (100) planes from a batch of crystals (AERE, Harwell, UK ). Both freshly cleaved specimens and specimens cleaved several hours prior to the observations were examined. AFM was carried out with a Nanoscope III manufactured by Digital Instruments (Santa Barbara, CA). For the AFM images, the cleaved samples were mounted in the nanoscope head in such a manner that their 010 edges were used as reference for the determination of the direction of steps. The AFM images were recorded in ambient atmosphere at room temperature both in contact and tapping modes. The reliability of these imaging modes and conditions was ensured as follows. During the successive scanning of a particular region of the (100) cleaved faces of MgO in the contact mode it was found that with inappropriate force setpoint the configuration of monolayer steps (i.e. layers of height equal to the lattice parameter a=0.21 nm) can undergo modification. Therefore, prior to scanning a particular region of the cleavage in the contact mode, the force setpoint was adjusted in such a way that the configuration of monolayer steps remained practically unaltered. Although hard samples experience forces up to 10−6 N in the case of the tapping mode operation [11], it was found that the imaging mode does not change the arrangement of the monolayer steps during repetitive scanning of a particular region of the MgO cleavage. It is also known [12,13] that humidity strongly affects the monolayer step configuration on the (100) cleavage faces of NaCl and leads to their motion. However, in the case of
MgO, such an effect was not observed in the case of both monolayer as well as multilayer steps. The AFM images were scanned at different magnifications where images of disc-shaped structures and semicircular steps had mainly areas between 3 mm×3 mm and 5 mm×5 mm. The heights of steps and the mutual distances between them were determined using the standard software supplied by the manufacturer. The errors involved in the measurement of these quantities have been discussed earlier [10]. According to our estimates, for the sizes of images used in the measurement of diameters of disc-shaped structures the measurement error was less than ±5%.
3. Results 3.1. Stripes and cleavage steps As reported earlier [10], the (100) cleavages of MgO consist of clearly visible sharp multilayer steps, diffuse steps, V-shaped patterns and ‘‘river patterns’’ formed by the merging of monolayer steps into multilayer steps of different heights. Multilayer steps may be parallel to the 010 direction close to the edges of the cleavages but frequently also are found to be parallel to the
011 direction in the interior regions of the cleavage. However, diffuse multilayer steps are usually parallel to the 011 direction. For the AFM investigations, relatively flat regions between steps oriented along different directions and between steps of the river patterns were scanned. Typical examples of the morphology of cleavage surfaces are illustrates in Fig. 1. Fig. 1a shows several thick multilayer steps roughly oriented along the [017] direction, forming more or less parallel stripes on the (100) cleavage face. These cleavage stripes are at various levels but they do not remain at the same level in the entire region of the cleavage. Generally, a stripe at a higher level (i.e. an elevated stripe) has neighbouring stripes at lower levels (depressed stripes) and vice versa. However, in the case of a relatively wide depressed stripe confined between two very thick multilayer steps, the depressed stripe can be formed of two stripes at different levels (see stripes L2 and
K. Sangwal et al. / Surface Science 424 (1999) 139–144
Fig. 1. Typical examples of the morphology of cleavage surfaces: (a) several parallel stripes of the (100) cleavage face roughly oriented along the [017] direction and (b) several discshaped elevations. In (a) the stripes at relatively high and low levels relative to the average level are denoted by H and L, respectively. The edges of the images correspond to the [010] and [001] directions.
H5 between H2 and H3; L and H denote lower and higher levels, respectively). The difference in the levels of all neighbouring stripes decreases in the same direction a result of reduction in the thickness of multilayer steps. This process is accompanied by a change in the arrangement of monolayer steps within a stripe and in the multilayer step separating two stripes (for examples, see stripes L2, H5 and H3). Cleavage stripes also have different widths and even the width of the same cleavage stripe does not remain the same along its
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length. The width of elevated stripes lies between ca 200 and 1250 nm while that of depressed stripes varies between 1200 and 2200 nm. It is interesting to note from Fig. 1 that, in the case of depressed stripes L1, L2 and L3, arrays of semicircular monolayer steps appear to originate from localized sources generating rounded monolayer steps. The arrays of monolayer steps are confined by multilayer steps forming the stripes. When the difference between the levels of two neighbouring stripes is relatively small (ca 3– 4 monolayer steps), the multilayer step separating them disintegrates into isolated monolayer steps in the direction of decreasing difference in the levels of neighbouring stripes and the monolayer steps from the stripe at a higher level also cover the stripe at a lower level (see stripes L2 and H5). Moreover, the distance between successive monolayer steps in the array of semicircular steps decreases. Independent sources of monolayer steps on a stripe appear only when there exist multilayer steps bounding it and the stripe has a certain width. It is easy to see that the round monolayer step in the depressed stripe L3 of Fig. 1a is an elevation. However, in addition to the disc-shaped elevations in depressed stripes bounded by macrosteps we observed rounded closed steps in the elongated parts of elevated stripes found in between the split steps of river patterns. An example of this type of discs is presented in Fig. 1b. In Fig. 1a there is only one clearly distinguished disc-shaped elevation while several disc-shaped elevations are found in Fig. 1b. 3.2. Geometrical elevations and depressions Fig. 2a illustrates two sources of disc-shaped elevations and monolayer step patterns emanating from them. This figure illustrates a magnified region of Fig. 1b. It is interesting to note that the topmost discs are of different diameters. Moreover, the discs are slightly elongated in the direction of motion of semicircular monolayer steps emanating from them. Usually, we observed disc-shaped elevations in depressed stripes bounded by macrosteps and in the branching regions of elevated stripes. However, one case of rounded depressions spreading between two stripes and oriented in the
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tion, while the remaining sides are oriented in some arbitrary directions in between 010 and
011. To obtain information about the size of stable disc-shaped elevations and depressions, the ratio of their diameters D and D , parallel and perpen) || of propagation dicular to the direction of semicircular monolayer steps, was analysed for the elevations at the top and next to them and for the depressions at the bottom and next to them. Fig. 3 illustrates the dependence of this ratio of diameters, F=D /D (called here the anisotropy factor || ) F ), on the average diameter D=(D +D )/2 of the || ) discs. The figure shows data for seven elevations and one depression. The data for the elevations show that F increases linearly with D, with the intercept F #1 and the slope k=2.1×105 (±27%). 0 The value of unit for the intercept F is indeed 0 expected because this situation corresponds to a disc with D=0 nm. Obviously, deviations in the values F from the best-fit curve for elevations, as indicated by the error bars, are relatively large. For depressions we plausibly assumed bars of a size similar to that for elevation data. With such deviations it is difficult to say conclusively whether the value of the slope k of the plots of F against D is the same for both disc-shaped depressions
Fig. 2. Examples of elevations and depression steps on cleaved faces: (a) two sources of disc-shaped elevations and monolayer step patterns emanaging from them; (b) rounded depressions spreading between two stripes; and (c) polygonal elevation.
011 direction was also recorded (Fig. 2b). As in the case of discs of Fig. 2a, these discs are also elongated in the direction of the macrosteps. A rare of example of the observation of a polygonal elevation on an elevated stripe is illustrated in Fig. 2c. The left side, a part of the right side and the central part of the upper side of this elevation are parallel to the 010 direction, some others are roughly oriented in 011 direc-
Fig. 3. Dependence of the anisotropy factor F on the average diameter D of the elevation and depression discs. The linear fit was drawn using data for both first and second elevation discs. Deviations of the data from the best-fit curve were calculated for elevations. Error bars for the depression data were calculated on the assumption that they are similar to those for elevations. %, F values expected for observed depression diameters from the slope k=2.1×105 m−1 for the elevation data.
K. Sangwal et al. / Surface Science 424 (1999) 139–144
and elevations. Nevertheless, the values of F shown by open squares in Fig. 3, expected from the slope k=2.1×105 m−1 from the data on elevations, corresponding to the average diameters D of the first and second discs of the depression differ greatly from those observed for the depression. This suggests that the slope k of the F(D) plot for depressions is lower than that in the case of elevations. Fig. 3 shows that the first top elevations appear with average diameters between 360 and 720 nm while the second top elevations have diameters between 620 and 875 nm. However, the diameters of depressions are much greater (by a factor of 3– 4) than the diameters of elevations (see Fig. 3). Moreover, in contrast to the rounded elevations and depressions, the octagon-like elevation is >2 mm wide.
4. Discussion The observations of disc-shaped elevations and depressions, and series of semicircular steps described here are the first of its kind on the cleavage surfaces of crystals. The formation of closed steps and trains of semicircular steps may be explained by a mechanism similar to that of multiplication of dislocations, proposed by Frank and Read [14,15]. In analogy with the Frank–Read mechanism of dislocation multiplication, we propose that the formation of closed monolayer steps involves the following sequence: 1. Two points of dislocation line of length L are immobile. 2. Under the influence of a suitable applied shear stress the dislocation line between the immobile points undergoes bending along the slip plane such that finally the bending dislocation line breaks into a straight part, similar to the initial one, of the dislocation line and a close dislocation loop around it. 3. Repetition of step (2) in succeeding planes producing a series of loops. 4. Expansion of the dislocation loops, yielding closed disc-shaped and semicircular steps bound by the sides of stripe along the direction of the cleavage.
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According to the above mechanism, the dislocation line in between the immobile points is of edge type while the immobile points act as dislocation segments with screw components. This implies that the slip plane is {100} and the Burgers vector of the dislocation is perpendicular to the line and is equal to the lattice parameter a. In other words, the slip system involved in this process is {100} 010, which is the secondary slip system of MgO. It is also obvious that the height of the cleavage step in this case is equal to a, that is, equal to the Burgers vector of the dislocation involved in the process of generation of series of dislocation loops on either side of the source of dislocation lines of length L. Since in the Frank–Read mechanism a dislocation gliding in the slip plane of crystal undergoes bending under the application of stress, there is a shear stress t necessary to maintain a radius r of 0 curvature of the dislocation line, expressed by the relation [15]: aGb , t = 0 r
(1)
where G is the shear modulus of the crystal and the parameter a#1.3 for an edge dislocation involved in the Frank–Read mechanism (cf Ref. [15]). For MgO taking G=2.86×1011 N m−2 [16 ] and b=a (where the lattice parameter a=2.1×10−10 m) and t =t = 8×107 N m−2 0 y (where t is the yield stress) [17], from Eq. (1) one y obtains D=2r=1950 nm. The calculated value of the dislocation loop diameter D is in agreement with the experimental diameter D of ~2 mm when a transition in the geometry of closed rounded steps to polygonal ones takes place. The change in the geometry of closed rounded steps to polygonal ones taking place with increasing size may be attributed to a lower edge free energy of 010 and 011 steps than that of steps of other orientations [18]. It should be noted that the width of cleavage stripes is intimately connected with the diameters of rounded elevations and depressions. Both the minimum and the transition values of the average diameters of disc-shaped depressions are much higher than those for the elevations
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(Fig. 3). The exact cause of this difference is not understood at present. One possible explanation of this behaviour is associated with the difference in the mutual interaction between neighbouring disc-shaped steps in elevations and depressions. The difference in the interaction between steps is expected to be reflected by the difference in the slope k of the plots of anisotropy factor F against average disc diameter D for elevations and depressions. However, the sparse experimental data for depressions available in this study are insufficient to substantiate this explanation.
Acknowledgements The authors are indebted to one of the anonymous referees for his constructive comments and suggestions, which have greatly improved the contents of the paper. They also express their gratitude to Mr J. Servat for his technical assistance and to the ‘Serveis Cientifico-Tecnics’ of the Universitat de Barcelona for technical facilities. The experimental part of the work was carried out during the academic year 1995–1996 when one of the authors ( K.S.) worked in the Universitat de Barcelona as a visiting professor with a maintenance grant from Generalitat de Catalunya y Technologia under Research Project MAT94-1938,
and by the Comissarat de Generalitat de Catalunya under Research Project SGR344, 1995.
References [1] K. Sangwal, R. Rodriques-Clemente, Surface Morphology of Crystalline Solids, Trans Tech, Zurich, 1991, Chap. 8. [2] S.C. Langford, S. Zhenyi, L.C. Jensen, J.T. Dickinson, J. Vac. Soc. Technol. A 8 (1990) 3470. [3] R.M. Overney, H. Haefke, E. Meyer, H.-J. Gu¨ntherodt, Surf. Sci. 277 (1992) L29. [4] A. Seo, H. Shindo, Appl. Surf. Sci. 82/83 (1994) 475. [5] E. Perrot, M. Dayez, A. Humbert, O. Marti, C. Chapon, C.R. Henry, Europhys. Lett. 26 (1994) 659. [6 ] N. Ikemiya, A. Kitamura, S. Hara, J. Crystal Growth 160 (1996) 104. [7] S. Kim, S. Baik, J. Vac. Sci. Technol. A 13 (1995) 95. [8] M. Inayoshi, M. Hiramatsu, Y. Sugiura, H. Kawamura, M. Nawata, J. Vac. Sci. Technol. A 13 (1995) 255. [9] J.E. Mattson, E.E. Fullerton, C.H. Sowers, S.D. Bader, J. Vac. Sci. Technol. A 13 (1995) 276. [10] K. Sangwal, F. Sanz, J. Servat, P. Gorostiza, Surf. Sci. 383 (1997) 78. [11] J.P. Spatz, S. Sheiko, M. Mu¨ller, R.G. Winkler, O. Marti, Nanotechnology 6 (1995) 40. [12] H. Shindo, M. Ohashi, K. Baba, A. Seo, Surf. Sci. 357/ 358 (1996) 111. [13] A. Folch, P. Gorostiza, J. Servat, J. Tejada, F. Sanz, Surf. Sci. 380 (1997) 427. [14] F.C. Frank, W.T. Read, Phys. Rev. 79 (1950) 722. [15] D. Hull, Introduction to Dislocations, 2nd ed., Pergamon, Oxford, 1975. [16 ] C. Kittel, Introduction to Solid State Physics, 3rd ed., Wiley, New York, 1966. [17] P.F. Stablein, J. Appl. Phys. 34 (1963) 1867. [18] S. Toschev, in: P. Hartman (Ed.), Crystal Growth – An Introduction, North-Holland, Amsterdam, 1973, p. 328.
Study of the surface morphology of the (100) cleavage planes of MgO single crystals by atomic force microscopy K. Sangwal a, *, F. Sanz b, P. Gorostiza b a Institute of Physics, Technical University of Lublin, ul. Nadbystrzycka 38, 20-618 Lublin, Poland b Departament de Quimica Fisica, Universitat de Barcelona, Marti I Franques 1, 08028 Barcelona, Spain Received 23 April 1998; accepted for publication 23 December 1998
Abstract Some experimental observations made on the nature and distribution of nearly circular and polygonal closed steps, and arrays of semicircular steps arranged between two multilayer steps on the (100) cleavage planes of MgO single crystals by atomic force microscopy are described. The results show that: (1) the formation of disc-shaped elevations and depressions, and series of semicircular steps takes place by a mechanism similar to the Frank–Read source [Phys. Rev. 79 (1950) 722]; (2) the diameters of disc-shaped structures are related with shear stresses of the order of the yield stress of the crystal; and (3) with an increase in the size of closed steps, their rounded shape changes to polygonal due to a lower edge free energy of the 010 and 011 steps compared to that of steps of other orientations. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Low-index single-crystal surfaces; Magnesium oxide; Morphology; Roughness; Single crystal surfaces; Surface stress; Surface structure, morphology, roughness, and topology
1. Introduction The investigation of the morphology of surfaces of crystalline solids is of practical and general interest because many processes such as the growth of epitaxial films, catalytic reactions and nanomanipulations are intimately connected with surfaces. In many cases cleavage faces are better than surfaces prepared by cutting, abrasion and polishing because the latter techniques introduce defects and impurities in the surface layer. A brief introduction to the surface morphology and commonly used terminology of cleaved faces may be found in Ref. [1]. During recent years an increasing interest has * Corresponding author. Fax: +48 81 5259385; e-mail: [email protected].
emerged in the investigation of the surface morphology of cleavages of a variety of ionic single crystals [2–6 ], using sophisticated techniques such as atomic force microscopy (AFM ) and scanning tunnelling microscopy. Most of these studies deal with the observation of mono- and bilayer steps [3–6 ], and step–terrace structures on the as-cleaved crystal faces [5]. In the case of MgO single crystals, which are widely used as a substrate material for the growth of epitaxial thin films and superlattices for a variety of applications [7–9], AFM studies of the cleavages of MgO crystals reveal mono-, bi- and trilayer steps [5–7] as well as multilayer steps up to 4–50 nm in height [7,10]. Until now except for the study of the nature of multilayer steps on the (100) face of MgO crystals [10], no other systematic investigation of the cleavage morphology of ionic crystals has been carried
0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 00 2 3 -0
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K. Sangwal et al. / Surface Science 424 (1999) 139–144
out. However, examination of relatively smooth regions of cleaved surfaces of MgO reveals a rich surface morphology composed of disc-shaped elevations and depressions and series of isolated monolayer semicircular steps originating from disc-like sources on the surface. To the authors’ knowledge such step patterns have not been reported so far. Therefore, the present paper is dedicated to such cleavage step patterns.
2. Experimental The specimens of the MgO single crystals were prepared by cleavage along the (100) planes from a batch of crystals (AERE, Harwell, UK ). Both freshly cleaved specimens and specimens cleaved several hours prior to the observations were examined. AFM was carried out with a Nanoscope III manufactured by Digital Instruments (Santa Barbara, CA). For the AFM images, the cleaved samples were mounted in the nanoscope head in such a manner that their 010 edges were used as reference for the determination of the direction of steps. The AFM images were recorded in ambient atmosphere at room temperature both in contact and tapping modes. The reliability of these imaging modes and conditions was ensured as follows. During the successive scanning of a particular region of the (100) cleaved faces of MgO in the contact mode it was found that with inappropriate force setpoint the configuration of monolayer steps (i.e. layers of height equal to the lattice parameter a=0.21 nm) can undergo modification. Therefore, prior to scanning a particular region of the cleavage in the contact mode, the force setpoint was adjusted in such a way that the configuration of monolayer steps remained practically unaltered. Although hard samples experience forces up to 10−6 N in the case of the tapping mode operation [11], it was found that the imaging mode does not change the arrangement of the monolayer steps during repetitive scanning of a particular region of the MgO cleavage. It is also known [12,13] that humidity strongly affects the monolayer step configuration on the (100) cleavage faces of NaCl and leads to their motion. However, in the case of
MgO, such an effect was not observed in the case of both monolayer as well as multilayer steps. The AFM images were scanned at different magnifications where images of disc-shaped structures and semicircular steps had mainly areas between 3 mm×3 mm and 5 mm×5 mm. The heights of steps and the mutual distances between them were determined using the standard software supplied by the manufacturer. The errors involved in the measurement of these quantities have been discussed earlier [10]. According to our estimates, for the sizes of images used in the measurement of diameters of disc-shaped structures the measurement error was less than ±5%.
3. Results 3.1. Stripes and cleavage steps As reported earlier [10], the (100) cleavages of MgO consist of clearly visible sharp multilayer steps, diffuse steps, V-shaped patterns and ‘‘river patterns’’ formed by the merging of monolayer steps into multilayer steps of different heights. Multilayer steps may be parallel to the 010 direction close to the edges of the cleavages but frequently also are found to be parallel to the
011 direction in the interior regions of the cleavage. However, diffuse multilayer steps are usually parallel to the 011 direction. For the AFM investigations, relatively flat regions between steps oriented along different directions and between steps of the river patterns were scanned. Typical examples of the morphology of cleavage surfaces are illustrates in Fig. 1. Fig. 1a shows several thick multilayer steps roughly oriented along the [017] direction, forming more or less parallel stripes on the (100) cleavage face. These cleavage stripes are at various levels but they do not remain at the same level in the entire region of the cleavage. Generally, a stripe at a higher level (i.e. an elevated stripe) has neighbouring stripes at lower levels (depressed stripes) and vice versa. However, in the case of a relatively wide depressed stripe confined between two very thick multilayer steps, the depressed stripe can be formed of two stripes at different levels (see stripes L2 and
K. Sangwal et al. / Surface Science 424 (1999) 139–144
Fig. 1. Typical examples of the morphology of cleavage surfaces: (a) several parallel stripes of the (100) cleavage face roughly oriented along the [017] direction and (b) several discshaped elevations. In (a) the stripes at relatively high and low levels relative to the average level are denoted by H and L, respectively. The edges of the images correspond to the [010] and [001] directions.
H5 between H2 and H3; L and H denote lower and higher levels, respectively). The difference in the levels of all neighbouring stripes decreases in the same direction a result of reduction in the thickness of multilayer steps. This process is accompanied by a change in the arrangement of monolayer steps within a stripe and in the multilayer step separating two stripes (for examples, see stripes L2, H5 and H3). Cleavage stripes also have different widths and even the width of the same cleavage stripe does not remain the same along its
141
length. The width of elevated stripes lies between ca 200 and 1250 nm while that of depressed stripes varies between 1200 and 2200 nm. It is interesting to note from Fig. 1 that, in the case of depressed stripes L1, L2 and L3, arrays of semicircular monolayer steps appear to originate from localized sources generating rounded monolayer steps. The arrays of monolayer steps are confined by multilayer steps forming the stripes. When the difference between the levels of two neighbouring stripes is relatively small (ca 3– 4 monolayer steps), the multilayer step separating them disintegrates into isolated monolayer steps in the direction of decreasing difference in the levels of neighbouring stripes and the monolayer steps from the stripe at a higher level also cover the stripe at a lower level (see stripes L2 and H5). Moreover, the distance between successive monolayer steps in the array of semicircular steps decreases. Independent sources of monolayer steps on a stripe appear only when there exist multilayer steps bounding it and the stripe has a certain width. It is easy to see that the round monolayer step in the depressed stripe L3 of Fig. 1a is an elevation. However, in addition to the disc-shaped elevations in depressed stripes bounded by macrosteps we observed rounded closed steps in the elongated parts of elevated stripes found in between the split steps of river patterns. An example of this type of discs is presented in Fig. 1b. In Fig. 1a there is only one clearly distinguished disc-shaped elevation while several disc-shaped elevations are found in Fig. 1b. 3.2. Geometrical elevations and depressions Fig. 2a illustrates two sources of disc-shaped elevations and monolayer step patterns emanating from them. This figure illustrates a magnified region of Fig. 1b. It is interesting to note that the topmost discs are of different diameters. Moreover, the discs are slightly elongated in the direction of motion of semicircular monolayer steps emanating from them. Usually, we observed disc-shaped elevations in depressed stripes bounded by macrosteps and in the branching regions of elevated stripes. However, one case of rounded depressions spreading between two stripes and oriented in the
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K. Sangwal et al. / Surface Science 424 (1999) 139–144
tion, while the remaining sides are oriented in some arbitrary directions in between 010 and
011. To obtain information about the size of stable disc-shaped elevations and depressions, the ratio of their diameters D and D , parallel and perpen) || of propagation dicular to the direction of semicircular monolayer steps, was analysed for the elevations at the top and next to them and for the depressions at the bottom and next to them. Fig. 3 illustrates the dependence of this ratio of diameters, F=D /D (called here the anisotropy factor || ) F ), on the average diameter D=(D +D )/2 of the || ) discs. The figure shows data for seven elevations and one depression. The data for the elevations show that F increases linearly with D, with the intercept F #1 and the slope k=2.1×105 (±27%). 0 The value of unit for the intercept F is indeed 0 expected because this situation corresponds to a disc with D=0 nm. Obviously, deviations in the values F from the best-fit curve for elevations, as indicated by the error bars, are relatively large. For depressions we plausibly assumed bars of a size similar to that for elevation data. With such deviations it is difficult to say conclusively whether the value of the slope k of the plots of F against D is the same for both disc-shaped depressions
Fig. 2. Examples of elevations and depression steps on cleaved faces: (a) two sources of disc-shaped elevations and monolayer step patterns emanaging from them; (b) rounded depressions spreading between two stripes; and (c) polygonal elevation.
011 direction was also recorded (Fig. 2b). As in the case of discs of Fig. 2a, these discs are also elongated in the direction of the macrosteps. A rare of example of the observation of a polygonal elevation on an elevated stripe is illustrated in Fig. 2c. The left side, a part of the right side and the central part of the upper side of this elevation are parallel to the 010 direction, some others are roughly oriented in 011 direc-
Fig. 3. Dependence of the anisotropy factor F on the average diameter D of the elevation and depression discs. The linear fit was drawn using data for both first and second elevation discs. Deviations of the data from the best-fit curve were calculated for elevations. Error bars for the depression data were calculated on the assumption that they are similar to those for elevations. %, F values expected for observed depression diameters from the slope k=2.1×105 m−1 for the elevation data.
K. Sangwal et al. / Surface Science 424 (1999) 139–144
and elevations. Nevertheless, the values of F shown by open squares in Fig. 3, expected from the slope k=2.1×105 m−1 from the data on elevations, corresponding to the average diameters D of the first and second discs of the depression differ greatly from those observed for the depression. This suggests that the slope k of the F(D) plot for depressions is lower than that in the case of elevations. Fig. 3 shows that the first top elevations appear with average diameters between 360 and 720 nm while the second top elevations have diameters between 620 and 875 nm. However, the diameters of depressions are much greater (by a factor of 3– 4) than the diameters of elevations (see Fig. 3). Moreover, in contrast to the rounded elevations and depressions, the octagon-like elevation is >2 mm wide.
4. Discussion The observations of disc-shaped elevations and depressions, and series of semicircular steps described here are the first of its kind on the cleavage surfaces of crystals. The formation of closed steps and trains of semicircular steps may be explained by a mechanism similar to that of multiplication of dislocations, proposed by Frank and Read [14,15]. In analogy with the Frank–Read mechanism of dislocation multiplication, we propose that the formation of closed monolayer steps involves the following sequence: 1. Two points of dislocation line of length L are immobile. 2. Under the influence of a suitable applied shear stress the dislocation line between the immobile points undergoes bending along the slip plane such that finally the bending dislocation line breaks into a straight part, similar to the initial one, of the dislocation line and a close dislocation loop around it. 3. Repetition of step (2) in succeeding planes producing a series of loops. 4. Expansion of the dislocation loops, yielding closed disc-shaped and semicircular steps bound by the sides of stripe along the direction of the cleavage.
143
According to the above mechanism, the dislocation line in between the immobile points is of edge type while the immobile points act as dislocation segments with screw components. This implies that the slip plane is {100} and the Burgers vector of the dislocation is perpendicular to the line and is equal to the lattice parameter a. In other words, the slip system involved in this process is {100} 010, which is the secondary slip system of MgO. It is also obvious that the height of the cleavage step in this case is equal to a, that is, equal to the Burgers vector of the dislocation involved in the process of generation of series of dislocation loops on either side of the source of dislocation lines of length L. Since in the Frank–Read mechanism a dislocation gliding in the slip plane of crystal undergoes bending under the application of stress, there is a shear stress t necessary to maintain a radius r of 0 curvature of the dislocation line, expressed by the relation [15]: aGb , t = 0 r
(1)
where G is the shear modulus of the crystal and the parameter a#1.3 for an edge dislocation involved in the Frank–Read mechanism (cf Ref. [15]). For MgO taking G=2.86×1011 N m−2 [16 ] and b=a (where the lattice parameter a=2.1×10−10 m) and t =t = 8×107 N m−2 0 y (where t is the yield stress) [17], from Eq. (1) one y obtains D=2r=1950 nm. The calculated value of the dislocation loop diameter D is in agreement with the experimental diameter D of ~2 mm when a transition in the geometry of closed rounded steps to polygonal ones takes place. The change in the geometry of closed rounded steps to polygonal ones taking place with increasing size may be attributed to a lower edge free energy of 010 and 011 steps than that of steps of other orientations [18]. It should be noted that the width of cleavage stripes is intimately connected with the diameters of rounded elevations and depressions. Both the minimum and the transition values of the average diameters of disc-shaped depressions are much higher than those for the elevations
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(Fig. 3). The exact cause of this difference is not understood at present. One possible explanation of this behaviour is associated with the difference in the mutual interaction between neighbouring disc-shaped steps in elevations and depressions. The difference in the interaction between steps is expected to be reflected by the difference in the slope k of the plots of anisotropy factor F against average disc diameter D for elevations and depressions. However, the sparse experimental data for depressions available in this study are insufficient to substantiate this explanation.
Acknowledgements The authors are indebted to one of the anonymous referees for his constructive comments and suggestions, which have greatly improved the contents of the paper. They also express their gratitude to Mr J. Servat for his technical assistance and to the ‘Serveis Cientifico-Tecnics’ of the Universitat de Barcelona for technical facilities. The experimental part of the work was carried out during the academic year 1995–1996 when one of the authors ( K.S.) worked in the Universitat de Barcelona as a visiting professor with a maintenance grant from Generalitat de Catalunya y Technologia under Research Project MAT94-1938,
and by the Comissarat de Generalitat de Catalunya under Research Project SGR344, 1995.
References [1] K. Sangwal, R. Rodriques-Clemente, Surface Morphology of Crystalline Solids, Trans Tech, Zurich, 1991, Chap. 8. [2] S.C. Langford, S. Zhenyi, L.C. Jensen, J.T. Dickinson, J. Vac. Soc. Technol. A 8 (1990) 3470. [3] R.M. Overney, H. Haefke, E. Meyer, H.-J. Gu¨ntherodt, Surf. Sci. 277 (1992) L29. [4] A. Seo, H. Shindo, Appl. Surf. Sci. 82/83 (1994) 475. [5] E. Perrot, M. Dayez, A. Humbert, O. Marti, C. Chapon, C.R. Henry, Europhys. Lett. 26 (1994) 659. [6 ] N. Ikemiya, A. Kitamura, S. Hara, J. Crystal Growth 160 (1996) 104. [7] S. Kim, S. Baik, J. Vac. Sci. Technol. A 13 (1995) 95. [8] M. Inayoshi, M. Hiramatsu, Y. Sugiura, H. Kawamura, M. Nawata, J. Vac. Sci. Technol. A 13 (1995) 255. [9] J.E. Mattson, E.E. Fullerton, C.H. Sowers, S.D. Bader, J. Vac. Sci. Technol. A 13 (1995) 276. [10] K. Sangwal, F. Sanz, J. Servat, P. Gorostiza, Surf. Sci. 383 (1997) 78. [11] J.P. Spatz, S. Sheiko, M. Mu¨ller, R.G. Winkler, O. Marti, Nanotechnology 6 (1995) 40. [12] H. Shindo, M. Ohashi, K. Baba, A. Seo, Surf. Sci. 357/ 358 (1996) 111. [13] A. Folch, P. Gorostiza, J. Servat, J. Tejada, F. Sanz, Surf. Sci. 380 (1997) 427. [14] F.C. Frank, W.T. Read, Phys. Rev. 79 (1950) 722. [15] D. Hull, Introduction to Dislocations, 2nd ed., Pergamon, Oxford, 1975. [16 ] C. Kittel, Introduction to Solid State Physics, 3rd ed., Wiley, New York, 1966. [17] P.F. Stablein, J. Appl. Phys. 34 (1963) 1867. [18] S. Toschev, in: P. Hartman (Ed.), Crystal Growth – An Introduction, North-Holland, Amsterdam, 1973, p. 328.