- Email: [email protected]
The instability of vicinal electrode surfaces against step bunching I: Experiment
Surface Science 573 (2004) 17–23 www.elsevier.com/locate/susc
The instability of vicinal electrode surfaces against step bunching I: Experiment Sascha Baier b
a,1
, Harald Ibach a, Margret Giesen
b,*
a Institut fu¨r Schichten und Grenzfla¨chen ISG 3, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany Institut fu¨r Schichten und Grenzfla¨chen ISG 4, Forschungszentrum Ju¨lich, Leo-Brandt-Str, 52425 Ju¨lich, Germany
Received 7 August 2003; accepted for publication 17 March 2004 Available online 30 July 2004
Abstract Using electrochemical STM we have studied the stability of arrays of parallel, single atom height steps on vicinal Ag(1 1 1) electrodes in electrolyte. We find that the steps for Ag(1 1 1) electrodes are unstable and form first double-steps and later multiple steps, separated by wide, flat terraces. In this paper denoted as ‘‘I: Experiment’’ we deal with the experimental aspects whereas theoretical aspects are discussed in the following paper ‘‘II: Theory’’. 2004 Elsevier B.V. All rights reserved. Keywords: Vicinal single crystal surfaces; Surface thermodynamics (including phase transitions); Surface tension; Solid–liquid interfaces
1. Introduction Surfaces cut at a small angle to a low index plane are conventionally called vicinal surfaces. When prepared under ultra-high vacuum (UHV) conditions, vicinal surfaces tend to form regular arrays of terraces, separated by single atom height steps. This morphology is stabilized by an elastic
* Corresponding author. Tel.: +49 2461 614108; fax: +49 2461 613907. E-mail address: [email protected] (M. Giesen). 1 Present address: Infineon, Munich.
step-step repulsion which is inversely proportional to the square of the step-step distance (for reviews see [1,2]). The larger the elastic repulsive interaction, the narrower is the terrace width distribution. While these repulsive interactions stabilize the surface against an agglomeration of steps in certain areas of the surface (‘‘step-bunching’’), the stabilization against faceting is presumably due to the larger configurational and, more importantly, due to the vibrational entropy of the steps [3] compared to low-index surfaces. While regular step arrays are stable for most vicinal surfaces prepared in UHV an interaction with adsorbates may cause step-doubling [4] or step-bunching [5–8]. Step
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.03.075
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S. Baier et al. / Surface Science 573 (2004) 17–23
bunching in heteroepitaxial growth may result from a minimization of strain energy [9,10]. Step bunching also occurs on Si-surfaces as a result of electromigration [2]. Vicinal metal surfaces have also been studied in an electrochemical environment. Typically the surfaces were prepared by flame-annealing and/or by etching in an acidic solution and by immersing the electrode into the electrolyte while keeping the potential fixed with respect to a reference electrode. Scanning tunneling microscope (STM) images of such surfaces display a more or less regular array of monatomic height steps. However, unlike UHV-surfaces, the regular array is not stable when the surface is in contact with an electrolyte. In the course of thermal equilibrium fluctuations two steps merge to form a pair with a mean distance closer than the average distance on the surface and eventually the surface may separate into areas of large terraces and step bunches. Previous studies on stepped electrode surfaces have focused on the behavior of individual steps and in particular, spatial and time dependent step fluctuations. In such studies step pairing and the formation of bunches was an unwanted effect which eventually terminated the experiments. As a result, no quantitative studies on step bunching have been performed, to the best of our knowledge. The effect was noted though in Refs. [1,11] and attributed to an attractive step-step interaction of unknown nature.
In this experimental (and the following theoretical) paper we address the formation of steps of multiple height as a function of time and electrode potential by analyzing the results of STM investigations on Ag(19,19,17). The paper is organized as follows. The following section describes details of the experimental setup and the surface preparation. Experimental results on the development of the terrace width distribution with time are presented in Section 3 and discussed in Section 4.
2. Experimental For our studies we used a Topometrix TMX 2010 Discoverer STM modified for temperaturevariable measurements [12,13]. The tip and sample potential were independently controlled by a bipotentiostat. The tunneling tips were etched in a 6 M KCN + 2 M NaOH solution at 9 V AC (1000 Hz) and 4 V during the final etching process from Pt–Ir (80:20) wire. The tips were coated with an electrophoretic paint (BASF Glasophor ZQ 84– 3225) by means of galvanostatic deposition using a constant deposition current of 100 lA, leaving only the foremost part of the tip exposed to the electrolyte [14]. In all experiments, a tunneling current of 2 nA was used, i.e. no significant influence of the tip on the measurement is to be expected, as demonstrated previously [15].
Fig. 1. STM images (recorded in the x-t-mode) of Ag(19,19,17) in 1 mM CuSO4 + 0.05 H2SO4 at +50 mV and T = 34 C. The STM images were recorded (a) about 30 min, (b) 35 min and (c) 37 min after sample preparation. Fig. 1 demonstrates the dependence of the observed step configurations on the local area. The letters ‘‘M’’, ‘‘D’’, ‘‘T’’, and ‘‘F’’ indicate mono-, double-, triple- and four-layer steps. The scan width is 100 nm. How a local step configuration develops in time is shown in Fig. 2.
S. Baier et al. / Surface Science 573 (2004) 17–23
The electrolyte was 1 mM CuSO4 + 0.05H2SO4 made from suprapure (H2SO4) and p.a. (CuSO4) chemicals (Merck) and Milli-Q water (Millipore, 18.2 MX cm1). High purity copper and platinum wires (Goodfellow, 99.999%) served as reference and counter electrode, respectively. In this paper, all potentials are given with respect to the saturated calomel electrode (SCE). The measurements presented here were performed at electrode potentials +40, +50 and +60 mV. The Ag(19,19,17) samples were cut by spark erosion and oriented by diffractometry to an angle of 2.9 along the ½ 2 1 1-direction with respect to the (1 1 1) plane within 0.1. Hence, the sample surfaces revealed a step array of B-steps ((1 1 1)˚ wide microfacet) separated on average by 45.8 A (1 1 1)-terraces. Prior to the experiment, the Ag crystals were first chemically polished in a 0.42 M NaCN + 30% H2O2 (1:1) (NaCN: Merck p.A.; H2O2:Merck med. purity) solution for 5 s, then kept in air for 15 s and subsequently immersed in 0.76 M NaCN for another 5 s. The immersing cycle was repeated several times. Subsequent annealing of the crystal in an inert Ar gas flow for several minutes yielded well-oriented, clean Ag surfaces (Fig. 1).
3. Experimental results Fig. 1 displays STM images of the Ag(19, 19,17)-surface at +50 mV and T = 34 C. The potential of +50 mV is close to, yet still below, the potential of rapid Ag dissolution into the electrolyte. The images (a)–(c) are obtained from different areas of the sample at different times after sample preparation. In (a) 15 steps are visible, five monatomic steps (indicated by ‘‘M’’) and five double-layer high steps (indicated by ‘‘D’’). The frizziness of the step edges indicates a high atomic mobility at the step edges. It was previously shown [11–13] that the atomic mobility in this potential range is caused by atomic exchange between neighbor steps as well as between steps and the adjacent electrolyte solution. As can be seen from the STM image in (b), steps may also form double-, triple- (‘‘T’’) or even fourlayer (‘‘F’’) height step bunches. The STM images
19
in Fig. 1 are so-called ‘‘x-t’’- or ‘‘time’’-images where the axis perpendicular to the steps indicates a spatial direction while the axis along the steps is a time axis. Such time-images are produced by repetitively scanning the same line and displaying them in a pseudo-image. In the case of frizzy steps normal spatial STM images and x-t images are indistinguishable due to the finite scanning speed of the STM tip. If steps (such as for instance the ‘‘M’’-steps 6 and 7 from the left in Fig. 1(b)) are well separated in the upper part of the image merge to form double-steps in the lower part of the image, the merging process of the steps indeed occurs as a function of time and the local position of the scan line remains the same. Hence, the affiliation of the steps to a specific mono- or multilayer configuration may change with time. This is demonstrated in Fig. 2 in more detail. In Fig. 2, a series of STM images of the same area of the Ag(19,19,17) surface at different times is shown. Between t = 42 and 84 s, the two marked steps are well-separated and both steps are of monatomic height. Between t = 84 and 126 s, the steps start to merge and temporarily form a doublelayer step for a time span of about 20 s and the step edges can hardly be separated in the STM images. Eventually the steps separate again until in (c) between t = 218 and 260 s, the merging process continues and the steps seem to form a stable double-step configuration. If one observes the surface reconstruction for a long period of time, one sees that finally most of the steps tend to form stable double or multi-layer step configurations (apart from small time and spatial fluctuations [11]). Due to the formation of multi-layer step configurations the initial regular array of monatomic steps with a geometrically determined average terrace width is replaced by a distribution of very small and large terraces. Fig. 3 shows a frequency count of step-step distances as determined from a series of eight STM images of which four images are shown in Fig. 2. The histograms are obtained by averaging over the time span used to record an image (42 s). In order to analyze the general trend of the time evolution of a local step-step distance distribution this is a reasonable approximation. Between t = 0 and 42 s, (Fig. 3(a)) the step distance distribution is
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Fig. 2. Time images of Ag(19,19,17) in 1 mM CuSO4 + 0.05 H2SO4 at 50 mV and 32 C at constant position and different times. The indicated times denote the starting time of the image. Each image covers a total time span of 42 s from top to bottom (scan width 60 nm).
close to a Gaussian with a mean of 28.2a? (with a? the distance between densely packed atomic rows; a? = 0.25 nm for Ag(19,19, 17)). The mean square deviation from the mean terrace width of 28.2a? denoted as r is found to be r = 6.7a?. Between t = 294 and 336 s, the step-distance distribution has changed considerably. First, the mean of the distribution has shifted to a slightly smaller value 26a?. A total of 10% of steps in all recorded STM images and all available data (from which the images in Figs. 1 and 2 are merely representatives) have merged and can neither be separated by visual inspection nor by the computer software used to determine the step edges in the STM images. For these steps, the fre-
quency count is noted at Ls/a? = 0 in Fig. 3(b). The frequency count for small and large step distances has increased in the distribution in Fig. 3(b) whereas the count of intermediate distances close to the average terrace width has decreased. As a consequence, the distribution width has increased to r = 12.2a?. In order to follow the formation of multiple steps quantitatively, we have determined the relative distribution width r/hLsi (with hLsi the mean step-step distance as measured from the local step density in each STM image) vs. time for three different electrode potentials. The result is shown in Fig. 4. For all three data sets, the width increases with time and for U = +40 and +50 mV the increase is apparently
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Fig. 3. Histograms of the step distance distribution of the Ag(19,19,17) surface as displayed in Fig. 2 between (a) t = 0 and 42 s and (b) between t = 294 and 336 s. Since the histograms were obtained from the analysis of time images, each histogram represents the stepdistance distribution averaged over the time span of 42 s which is the recording time of an image.
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U= +40 mV, slope 0.84±0.21×10 s-1 -4 U= +50 mV, slope 6.95±0.53×10 s-1 -4 -1 U= +60 mV, slope 4.7±0.5×10 s
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4. Discussion
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tively. For U = +40 mV the slope is smallest, for U = +50 and +60 mV the slope is about the same, however slightly larger for U = +50 mV.
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linear. If all three data sets are fitted to a straight line the obtained slopes are (0.84 ± 0.21) · 104 s1, (6.95 ± 0.53) · 104 s1 and (4.7 ± 0.5) · 104 s1 for U = +40, +50 and +60 mV, respec-
Under UHV conditions, metal vicinal surfaces are known to be stabilized by repulsive forces between steps [1,2]. The experimental data show that Ag(19,19,17) vicinal surfaces with an initial regular step array are unstable under electrolytic conditions. The steps tend to form multilayer step bunches, starting with the formation of double-steps. Later triple- and four-layer steps are observed. The broadening of the step distance distribution as shown in Fig. 3 can be explained by the formation of local step bunches that requires the formation of larger terraces elsewhere. Hence, one would expect a double-peaked terrace width distribution to evolve at later times which is corroborated by the experimental finding that in Fig. 3 the frequency count for small and large terraces increase whereas the frequency count of intermediate terrace widths decreases with time. The mean of the terrace width distribution, however, should remain constant. This is not found in our analysis where we find a shift of the distribution mean to slightly
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smaller values with time. The reason for this is that our analysis focused primarily on local areas where multiple steps are observed and we did not perform a measurement of step-step distance distributions statistically averaged over the entire sample surface. We emphasize though that this is not necessary in order to study the kinetics of the time evolution of step bunch formation. The kinetics of multi-layer step formation becomes faster with increasing potential as is obvious from the data displayed in Fig. 4. The higher the electrode potential, the stronger is the increase in the distribution width as a function of time. Surprisingly no obvious difference in the measured apparent slopes is observed for the data obtained at +50 and +60 mV. The reason may be that in electrochemical STM cells the electrode potential is not as well defined as in large cells for classical electrochemical measurements such as cyclovoltammetry. Despite this possible inaccuracy, the general trend of the increase of the distribution width with time and with electrode potential is in accordance with previous observations of exponentially increasing equilibrium step fluctuations as a function of the electrode potential for Ag(19,19,17) in the same electrolyte [11,13]. In [11] it was demonstrated that the dominant mass transport underlying the step fluctuations is rapid surface mass transport between adjacent steps and desorption of adatoms from steps into the electrolyte and vice versa. Between +40 and +60 mV vs. SCE the step correlation value G(t0 = 1 s) [1] increases from 3a2? to 4a2? . The increase is a measure for the enhanced mass transport at higher electrode potentials which most probably is responsible for the stronger increase of the distribution width (as shown in Fig. 4) with time. Although a strong tendency toward multi-layer step formation is observed, no indication of crystallographic (1 1 1)-facet formation is found on Ag(19,19,17) in electrolyte. Even if steps are in close proximity for a while, so that they appear as a single step with twice the step height in the STM images, they do not form a facet. The evidence for this is twofold. Firstly, the steps continue to fluctuate in space and time just as single steps do. This is incompatible with the formation of a facet: Steps fluctuate because kinks in steps move
and the energy required to move a kink in a facet formed by two steps is much higher than for a normal kink in a step. Thirdly, steps which appear to be a single step with twice the height of a normal step in the STM-images may separate again after some time to become visibly two steps. Hence, even if a facet were formed locally it can not be a stable configuration. STM-images such as shown in Figs. 1 and 2 suggest that extended areas with bunches are formed via a pairing of two steps, with further steps associating the pair at later stages in time. This appears to be indicative of an attractive pair wise interaction between steps at intermediate distances. This observed interaction must be attributed to the presence of the electrolyte since clean vicinal surfaces in vacuum display regular arrays of steps. This regular array is also observed in electrolyte at early times after the Ag(19,19,17) surfaces had been prepared using the procedure described in Section 2. The longer the sample is kept in contact with the electrolyte under potential control, the higher the density of multi-layer steps becomes. At very short distances, on the other hand, steps on metal electrodes in electrolyte seem to undergo entropic and/or energetic repulsive interactions similar to metal surfaces in UHV [1,2]. This is corroborated by the observation that steps on Ag(19,19,17) in electrolyte in close proximity still undergo step fluctuations and no step facets are formed. The initial preference for step-pair-configurations prior to the formation of multi-layer steps may be caused by kinetic restrictions. Prior to mounting the samples in the STM cell and bringing the surface in contact with the electrolyte the surfaces are prepared by flame annealing in Ar atmosphere for which arrays of single steps are stable. The reconfiguration of the surface after contact with the electrolyte requires an immense mass transport across the surface which is kinetically hindered at temperatures around room temperature. Hence, in order to observe an advanced stage of step bunch formation in an experiment, measurements at higher temperatures would be useful. However, when using an aqueous electrolyte such as in the experiments reported here, temperatures higher than 40 C are difficult to achieve due to the high evaporation rate of the electrolyte.
S. Baier et al. / Surface Science 573 (2004) 17–23
5. Summary In summary we have shown that Ag(19,19,17) vicinal surfaces in contact with an electrolyte are unstable with respect to formation of step bunches. The initial regular step array, known from UHV investigations where such vicinal surfaces are stable, quickly changes into an arrangement of step pairs with steps in close proximity. Later on, multi-layer steps evolve. The formation of crystallographic (1 1 1)-facets is not observed. Acknowledgment Partial support by the Fond der Chemischen Industrie is gratefully acknowledged. References [1] M. Giesen, Prog. Surf. Sci. 68 (2001) 1. [2] H.-C. Jeong, E.D. Williams, Surf. Sci. Rep. 34 (1999) 171.
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[3] J.W.M. Frenken, P. Stoltze, Phys. Rev. Lett. 82 (1999) 3500. [4] B. Poelsema, G. Comsa, Scattering of thermal energy atoms from disordered surfaces, vol. 115, Springer, Berlin, 1989. [5] S. Fo¨lsch, G. Meyer, K.H. Rieder, M.H.-V. Hoegen, T. Schmidt, Surf. Sci. 394 (1997) 60. [6] O. Pierre-Louis, Surf. Sci. 529 (2003) 114. [7] S. Rousset, F. Pourmir, J.-M. Berroir, J. Klein, J. Lecoeur, P. Hecquet, B. Salanon, Surf. Sci. 422 (1999) 33. [8] V.B. Shenoy, S. Zhang, W.F. Saam, Surf. Sci. 467 (2000) 58. [9] J. Tersoff, Y.H. Phang, Z. Zhang, M.G. Lagally, Phys. Rev. Lett. 75 (1995) 2730. [10] J. Tersoff, Phys. Rev. Lett. 77 (1996) 2017. [11] M. Giesen, M. Dietterle, D. Stapel, H. Ibach, D.M. Kolb, Surf. Sci. 384 (1997) 168. [12] S. Baier, M. Giesen, Phys. Chem. Chem. Phys. 2 (2000) 3675. [13] M. Giesen, S. Baier, J. Phys. Condens. Mater. 13 (2001) 5009. [14] C.E. Bach, R.J. Nichols, W. Beckmann, H. Meyer, A. Schulte, J.O. Besenhard, P.D. Jannakoudakis, J. Electrochem. Soc. 140 (1993) 2181. [15] M. Giesen, R. Randler, S. Baier, H. Ibach, D.M. Kolb, Electrochim. Acta 45 (1999) 527.
The instability of vicinal electrode surfaces against step bunching I: Experiment Sascha Baier b
a,1
, Harald Ibach a, Margret Giesen
b,*
a Institut fu¨r Schichten und Grenzfla¨chen ISG 3, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany Institut fu¨r Schichten und Grenzfla¨chen ISG 4, Forschungszentrum Ju¨lich, Leo-Brandt-Str, 52425 Ju¨lich, Germany
Received 7 August 2003; accepted for publication 17 March 2004 Available online 30 July 2004
Abstract Using electrochemical STM we have studied the stability of arrays of parallel, single atom height steps on vicinal Ag(1 1 1) electrodes in electrolyte. We find that the steps for Ag(1 1 1) electrodes are unstable and form first double-steps and later multiple steps, separated by wide, flat terraces. In this paper denoted as ‘‘I: Experiment’’ we deal with the experimental aspects whereas theoretical aspects are discussed in the following paper ‘‘II: Theory’’. 2004 Elsevier B.V. All rights reserved. Keywords: Vicinal single crystal surfaces; Surface thermodynamics (including phase transitions); Surface tension; Solid–liquid interfaces
1. Introduction Surfaces cut at a small angle to a low index plane are conventionally called vicinal surfaces. When prepared under ultra-high vacuum (UHV) conditions, vicinal surfaces tend to form regular arrays of terraces, separated by single atom height steps. This morphology is stabilized by an elastic
* Corresponding author. Tel.: +49 2461 614108; fax: +49 2461 613907. E-mail address: [email protected] (M. Giesen). 1 Present address: Infineon, Munich.
step-step repulsion which is inversely proportional to the square of the step-step distance (for reviews see [1,2]). The larger the elastic repulsive interaction, the narrower is the terrace width distribution. While these repulsive interactions stabilize the surface against an agglomeration of steps in certain areas of the surface (‘‘step-bunching’’), the stabilization against faceting is presumably due to the larger configurational and, more importantly, due to the vibrational entropy of the steps [3] compared to low-index surfaces. While regular step arrays are stable for most vicinal surfaces prepared in UHV an interaction with adsorbates may cause step-doubling [4] or step-bunching [5–8]. Step
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.03.075
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S. Baier et al. / Surface Science 573 (2004) 17–23
bunching in heteroepitaxial growth may result from a minimization of strain energy [9,10]. Step bunching also occurs on Si-surfaces as a result of electromigration [2]. Vicinal metal surfaces have also been studied in an electrochemical environment. Typically the surfaces were prepared by flame-annealing and/or by etching in an acidic solution and by immersing the electrode into the electrolyte while keeping the potential fixed with respect to a reference electrode. Scanning tunneling microscope (STM) images of such surfaces display a more or less regular array of monatomic height steps. However, unlike UHV-surfaces, the regular array is not stable when the surface is in contact with an electrolyte. In the course of thermal equilibrium fluctuations two steps merge to form a pair with a mean distance closer than the average distance on the surface and eventually the surface may separate into areas of large terraces and step bunches. Previous studies on stepped electrode surfaces have focused on the behavior of individual steps and in particular, spatial and time dependent step fluctuations. In such studies step pairing and the formation of bunches was an unwanted effect which eventually terminated the experiments. As a result, no quantitative studies on step bunching have been performed, to the best of our knowledge. The effect was noted though in Refs. [1,11] and attributed to an attractive step-step interaction of unknown nature.
In this experimental (and the following theoretical) paper we address the formation of steps of multiple height as a function of time and electrode potential by analyzing the results of STM investigations on Ag(19,19,17). The paper is organized as follows. The following section describes details of the experimental setup and the surface preparation. Experimental results on the development of the terrace width distribution with time are presented in Section 3 and discussed in Section 4.
2. Experimental For our studies we used a Topometrix TMX 2010 Discoverer STM modified for temperaturevariable measurements [12,13]. The tip and sample potential were independently controlled by a bipotentiostat. The tunneling tips were etched in a 6 M KCN + 2 M NaOH solution at 9 V AC (1000 Hz) and 4 V during the final etching process from Pt–Ir (80:20) wire. The tips were coated with an electrophoretic paint (BASF Glasophor ZQ 84– 3225) by means of galvanostatic deposition using a constant deposition current of 100 lA, leaving only the foremost part of the tip exposed to the electrolyte [14]. In all experiments, a tunneling current of 2 nA was used, i.e. no significant influence of the tip on the measurement is to be expected, as demonstrated previously [15].
Fig. 1. STM images (recorded in the x-t-mode) of Ag(19,19,17) in 1 mM CuSO4 + 0.05 H2SO4 at +50 mV and T = 34 C. The STM images were recorded (a) about 30 min, (b) 35 min and (c) 37 min after sample preparation. Fig. 1 demonstrates the dependence of the observed step configurations on the local area. The letters ‘‘M’’, ‘‘D’’, ‘‘T’’, and ‘‘F’’ indicate mono-, double-, triple- and four-layer steps. The scan width is 100 nm. How a local step configuration develops in time is shown in Fig. 2.
S. Baier et al. / Surface Science 573 (2004) 17–23
The electrolyte was 1 mM CuSO4 + 0.05H2SO4 made from suprapure (H2SO4) and p.a. (CuSO4) chemicals (Merck) and Milli-Q water (Millipore, 18.2 MX cm1). High purity copper and platinum wires (Goodfellow, 99.999%) served as reference and counter electrode, respectively. In this paper, all potentials are given with respect to the saturated calomel electrode (SCE). The measurements presented here were performed at electrode potentials +40, +50 and +60 mV. The Ag(19,19,17) samples were cut by spark erosion and oriented by diffractometry to an angle of 2.9 along the ½ 2 1 1-direction with respect to the (1 1 1) plane within 0.1. Hence, the sample surfaces revealed a step array of B-steps ((1 1 1)˚ wide microfacet) separated on average by 45.8 A (1 1 1)-terraces. Prior to the experiment, the Ag crystals were first chemically polished in a 0.42 M NaCN + 30% H2O2 (1:1) (NaCN: Merck p.A.; H2O2:Merck med. purity) solution for 5 s, then kept in air for 15 s and subsequently immersed in 0.76 M NaCN for another 5 s. The immersing cycle was repeated several times. Subsequent annealing of the crystal in an inert Ar gas flow for several minutes yielded well-oriented, clean Ag surfaces (Fig. 1).
3. Experimental results Fig. 1 displays STM images of the Ag(19, 19,17)-surface at +50 mV and T = 34 C. The potential of +50 mV is close to, yet still below, the potential of rapid Ag dissolution into the electrolyte. The images (a)–(c) are obtained from different areas of the sample at different times after sample preparation. In (a) 15 steps are visible, five monatomic steps (indicated by ‘‘M’’) and five double-layer high steps (indicated by ‘‘D’’). The frizziness of the step edges indicates a high atomic mobility at the step edges. It was previously shown [11–13] that the atomic mobility in this potential range is caused by atomic exchange between neighbor steps as well as between steps and the adjacent electrolyte solution. As can be seen from the STM image in (b), steps may also form double-, triple- (‘‘T’’) or even fourlayer (‘‘F’’) height step bunches. The STM images
19
in Fig. 1 are so-called ‘‘x-t’’- or ‘‘time’’-images where the axis perpendicular to the steps indicates a spatial direction while the axis along the steps is a time axis. Such time-images are produced by repetitively scanning the same line and displaying them in a pseudo-image. In the case of frizzy steps normal spatial STM images and x-t images are indistinguishable due to the finite scanning speed of the STM tip. If steps (such as for instance the ‘‘M’’-steps 6 and 7 from the left in Fig. 1(b)) are well separated in the upper part of the image merge to form double-steps in the lower part of the image, the merging process of the steps indeed occurs as a function of time and the local position of the scan line remains the same. Hence, the affiliation of the steps to a specific mono- or multilayer configuration may change with time. This is demonstrated in Fig. 2 in more detail. In Fig. 2, a series of STM images of the same area of the Ag(19,19,17) surface at different times is shown. Between t = 42 and 84 s, the two marked steps are well-separated and both steps are of monatomic height. Between t = 84 and 126 s, the steps start to merge and temporarily form a doublelayer step for a time span of about 20 s and the step edges can hardly be separated in the STM images. Eventually the steps separate again until in (c) between t = 218 and 260 s, the merging process continues and the steps seem to form a stable double-step configuration. If one observes the surface reconstruction for a long period of time, one sees that finally most of the steps tend to form stable double or multi-layer step configurations (apart from small time and spatial fluctuations [11]). Due to the formation of multi-layer step configurations the initial regular array of monatomic steps with a geometrically determined average terrace width is replaced by a distribution of very small and large terraces. Fig. 3 shows a frequency count of step-step distances as determined from a series of eight STM images of which four images are shown in Fig. 2. The histograms are obtained by averaging over the time span used to record an image (42 s). In order to analyze the general trend of the time evolution of a local step-step distance distribution this is a reasonable approximation. Between t = 0 and 42 s, (Fig. 3(a)) the step distance distribution is
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S. Baier et al. / Surface Science 573 (2004) 17–23
Fig. 2. Time images of Ag(19,19,17) in 1 mM CuSO4 + 0.05 H2SO4 at 50 mV and 32 C at constant position and different times. The indicated times denote the starting time of the image. Each image covers a total time span of 42 s from top to bottom (scan width 60 nm).
close to a Gaussian with a mean of 28.2a? (with a? the distance between densely packed atomic rows; a? = 0.25 nm for Ag(19,19, 17)). The mean square deviation from the mean terrace width of 28.2a? denoted as r is found to be r = 6.7a?. Between t = 294 and 336 s, the step-distance distribution has changed considerably. First, the mean of the distribution has shifted to a slightly smaller value 26a?. A total of 10% of steps in all recorded STM images and all available data (from which the images in Figs. 1 and 2 are merely representatives) have merged and can neither be separated by visual inspection nor by the computer software used to determine the step edges in the STM images. For these steps, the fre-
quency count is noted at Ls/a? = 0 in Fig. 3(b). The frequency count for small and large step distances has increased in the distribution in Fig. 3(b) whereas the count of intermediate distances close to the average terrace width has decreased. As a consequence, the distribution width has increased to r = 12.2a?. In order to follow the formation of multiple steps quantitatively, we have determined the relative distribution width r/hLsi (with hLsi the mean step-step distance as measured from the local step density in each STM image) vs. time for three different electrode potentials. The result is shown in Fig. 4. For all three data sets, the width increases with time and for U = +40 and +50 mV the increase is apparently
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Distance between steps L s / a
Fig. 3. Histograms of the step distance distribution of the Ag(19,19,17) surface as displayed in Fig. 2 between (a) t = 0 and 42 s and (b) between t = 294 and 336 s. Since the histograms were obtained from the analysis of time images, each histogram represents the stepdistance distribution averaged over the time span of 42 s which is the recording time of an image.
1.5 -4
U= +40 mV, slope 0.84±0.21×10 s-1 -4 U= +50 mV, slope 6.95±0.53×10 s-1 -4 -1 U= +60 mV, slope 4.7±0.5×10 s
1.0
σ / Ls
4. Discussion
0.5
0.0
tively. For U = +40 mV the slope is smallest, for U = +50 and +60 mV the slope is about the same, however slightly larger for U = +50 mV.
0
2000
4000
6000
Time / s Fig. 4. Total width of the step distance distribution as a function of time for three different potentials +60 mV (d), +50 mV (m), +40 mV (j). The values for the width of the distributions was calculated as the mean square deviation of histogram values from the mean of the distribution divided by the number of individual data points in the histogram.
linear. If all three data sets are fitted to a straight line the obtained slopes are (0.84 ± 0.21) · 104 s1, (6.95 ± 0.53) · 104 s1 and (4.7 ± 0.5) · 104 s1 for U = +40, +50 and +60 mV, respec-
Under UHV conditions, metal vicinal surfaces are known to be stabilized by repulsive forces between steps [1,2]. The experimental data show that Ag(19,19,17) vicinal surfaces with an initial regular step array are unstable under electrolytic conditions. The steps tend to form multilayer step bunches, starting with the formation of double-steps. Later triple- and four-layer steps are observed. The broadening of the step distance distribution as shown in Fig. 3 can be explained by the formation of local step bunches that requires the formation of larger terraces elsewhere. Hence, one would expect a double-peaked terrace width distribution to evolve at later times which is corroborated by the experimental finding that in Fig. 3 the frequency count for small and large terraces increase whereas the frequency count of intermediate terrace widths decreases with time. The mean of the terrace width distribution, however, should remain constant. This is not found in our analysis where we find a shift of the distribution mean to slightly
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S. Baier et al. / Surface Science 573 (2004) 17–23
smaller values with time. The reason for this is that our analysis focused primarily on local areas where multiple steps are observed and we did not perform a measurement of step-step distance distributions statistically averaged over the entire sample surface. We emphasize though that this is not necessary in order to study the kinetics of the time evolution of step bunch formation. The kinetics of multi-layer step formation becomes faster with increasing potential as is obvious from the data displayed in Fig. 4. The higher the electrode potential, the stronger is the increase in the distribution width as a function of time. Surprisingly no obvious difference in the measured apparent slopes is observed for the data obtained at +50 and +60 mV. The reason may be that in electrochemical STM cells the electrode potential is not as well defined as in large cells for classical electrochemical measurements such as cyclovoltammetry. Despite this possible inaccuracy, the general trend of the increase of the distribution width with time and with electrode potential is in accordance with previous observations of exponentially increasing equilibrium step fluctuations as a function of the electrode potential for Ag(19,19,17) in the same electrolyte [11,13]. In [11] it was demonstrated that the dominant mass transport underlying the step fluctuations is rapid surface mass transport between adjacent steps and desorption of adatoms from steps into the electrolyte and vice versa. Between +40 and +60 mV vs. SCE the step correlation value G(t0 = 1 s) [1] increases from 3a2? to 4a2? . The increase is a measure for the enhanced mass transport at higher electrode potentials which most probably is responsible for the stronger increase of the distribution width (as shown in Fig. 4) with time. Although a strong tendency toward multi-layer step formation is observed, no indication of crystallographic (1 1 1)-facet formation is found on Ag(19,19,17) in electrolyte. Even if steps are in close proximity for a while, so that they appear as a single step with twice the step height in the STM images, they do not form a facet. The evidence for this is twofold. Firstly, the steps continue to fluctuate in space and time just as single steps do. This is incompatible with the formation of a facet: Steps fluctuate because kinks in steps move
and the energy required to move a kink in a facet formed by two steps is much higher than for a normal kink in a step. Thirdly, steps which appear to be a single step with twice the height of a normal step in the STM-images may separate again after some time to become visibly two steps. Hence, even if a facet were formed locally it can not be a stable configuration. STM-images such as shown in Figs. 1 and 2 suggest that extended areas with bunches are formed via a pairing of two steps, with further steps associating the pair at later stages in time. This appears to be indicative of an attractive pair wise interaction between steps at intermediate distances. This observed interaction must be attributed to the presence of the electrolyte since clean vicinal surfaces in vacuum display regular arrays of steps. This regular array is also observed in electrolyte at early times after the Ag(19,19,17) surfaces had been prepared using the procedure described in Section 2. The longer the sample is kept in contact with the electrolyte under potential control, the higher the density of multi-layer steps becomes. At very short distances, on the other hand, steps on metal electrodes in electrolyte seem to undergo entropic and/or energetic repulsive interactions similar to metal surfaces in UHV [1,2]. This is corroborated by the observation that steps on Ag(19,19,17) in electrolyte in close proximity still undergo step fluctuations and no step facets are formed. The initial preference for step-pair-configurations prior to the formation of multi-layer steps may be caused by kinetic restrictions. Prior to mounting the samples in the STM cell and bringing the surface in contact with the electrolyte the surfaces are prepared by flame annealing in Ar atmosphere for which arrays of single steps are stable. The reconfiguration of the surface after contact with the electrolyte requires an immense mass transport across the surface which is kinetically hindered at temperatures around room temperature. Hence, in order to observe an advanced stage of step bunch formation in an experiment, measurements at higher temperatures would be useful. However, when using an aqueous electrolyte such as in the experiments reported here, temperatures higher than 40 C are difficult to achieve due to the high evaporation rate of the electrolyte.
S. Baier et al. / Surface Science 573 (2004) 17–23
5. Summary In summary we have shown that Ag(19,19,17) vicinal surfaces in contact with an electrolyte are unstable with respect to formation of step bunches. The initial regular step array, known from UHV investigations where such vicinal surfaces are stable, quickly changes into an arrangement of step pairs with steps in close proximity. Later on, multi-layer steps evolve. The formation of crystallographic (1 1 1)-facets is not observed. Acknowledgment Partial support by the Fond der Chemischen Industrie is gratefully acknowledged. References [1] M. Giesen, Prog. Surf. Sci. 68 (2001) 1. [2] H.-C. Jeong, E.D. Williams, Surf. Sci. Rep. 34 (1999) 171.
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[3] J.W.M. Frenken, P. Stoltze, Phys. Rev. Lett. 82 (1999) 3500. [4] B. Poelsema, G. Comsa, Scattering of thermal energy atoms from disordered surfaces, vol. 115, Springer, Berlin, 1989. [5] S. Fo¨lsch, G. Meyer, K.H. Rieder, M.H.-V. Hoegen, T. Schmidt, Surf. Sci. 394 (1997) 60. [6] O. Pierre-Louis, Surf. Sci. 529 (2003) 114. [7] S. Rousset, F. Pourmir, J.-M. Berroir, J. Klein, J. Lecoeur, P. Hecquet, B. Salanon, Surf. Sci. 422 (1999) 33. [8] V.B. Shenoy, S. Zhang, W.F. Saam, Surf. Sci. 467 (2000) 58. [9] J. Tersoff, Y.H. Phang, Z. Zhang, M.G. Lagally, Phys. Rev. Lett. 75 (1995) 2730. [10] J. Tersoff, Phys. Rev. Lett. 77 (1996) 2017. [11] M. Giesen, M. Dietterle, D. Stapel, H. Ibach, D.M. Kolb, Surf. Sci. 384 (1997) 168. [12] S. Baier, M. Giesen, Phys. Chem. Chem. Phys. 2 (2000) 3675. [13] M. Giesen, S. Baier, J. Phys. Condens. Mater. 13 (2001) 5009. [14] C.E. Bach, R.J. Nichols, W. Beckmann, H. Meyer, A. Schulte, J.O. Besenhard, P.D. Jannakoudakis, J. Electrochem. Soc. 140 (1993) 2181. [15] M. Giesen, R. Randler, S. Baier, H. Ibach, D.M. Kolb, Electrochim. Acta 45 (1999) 527.