Structural characterisation and homoepitaxial growth on Cu(111)

Surface Science 459 (2000) 191–205 www.elsevier.nl/locate/susc

Structural characterisation and homoepitaxial growth on Cu(111) J. Camarero a,1, J. de la Figuera a,2, J.J. de Miguel a, *, R. Miranda a, ´ lvarez a,3, S. Ferrer b J. A a Departmento de Fı´sica de la Materia Condensada and Instituto de Ciencia de Materiales ‘Nicola´s Cabrera’, Universidad Auto´noma de Madrid, Cantoblanco, 28049-Madrid, Spain b European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France Received 7 January 2000; accepted for publication 30 March 2000

Abstract A comprehensive study of the homoepitaxial MBE growth of Cu on Cu(111) is presented. This system displays a wealth of features and a large accumulation of morphological and structural defects. It is demonstrated that all of them can be ascribed to two basic characteristics of fcc-(111) faces: the presence of two threefold adsorption sites at the surface, which allows the formation of stacking faults, and the existence of high Ehrlich–Schwoebel barriers at steps, hindering interlayer diffusion. This behaviour, therefore, must be common during growth on compact metallic faces, and could have important implications for the preparation of low-dimensional heterostructures. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Atom–solid scattering and diffraction – elastic; Copper; Diffusion and migration; Molecular beam epitaxy; Surface defects; Surface structure, morphology, roughness, and topography; X-ray scattering, diffraction, and reflection

1. Introduction Crystal growth has been an active field of research for a long time. Its thermodynamic foundations were laid as early as the 19th century with the work by Gibbs [1]. Atomistic formulations appeared later [2,3] opening a way that culminated with the formulation of the BCF theory [4], which * Corresponding author. Fax: +34 91 3973961. E-mail address: [email protected] (J.J. de Miguel ) 1 Present address: Laboratoire Louis Ne´el-CNRS, 38042 Grenoble Cedex, France. 2 Present address: Sandia National Laboratories, Livermore, CA, USA. 3 Present address: Dpto. Fı´sica de la Materia Condensada, Univ. Auto´noma, Cantoblanco, 28049-Madrid, Spain.

is the basis of our current understanding of epitaxial growth phenomena. Thus, the fundamental aspects of this problem seem to be well understood. Recently, however, the great surge of research on low-dimensional and nanostructured materials has awakened renewed interest to identify and gain control over the finest details involved in the growth process, which strongly influence the morphology of the grown materials, and hence their resulting electronic and magnetic properties. Fcc metals are a good example of the subtleties involved in epitaxy. On (100) faces, growth usually takes place in a layer-by-layer mode, with high structural quality at relatively low temperature and for typical deposition rates of the order of 1 ML min−1. In contrast, films grown with (111) orientation on the same materials and under sim-

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ilar conditions show a tendency to roughen during deposition up to considerably higher temperatures. In this paper we will demonstrate that such a different behaviour is caused by two intrinsic characteristics of the (111) faces: first, the existence of two very similar, threefold adsorption sites, which leads to the formation of stacking faults during growth; and second, the poor interlayer diffusion due to the presence of the so-called Ehrlich– Schwoebel ( ES ) barrier at atomic steps. This magnitude describes the energy cost that a diffusing adatom has to overcome in order to cross a descending step and fall to the lower terrace. It is usually explained in terms of the low coordination felt by the adatom at the transition stage, although it should be regarded as an effective parameter which takes into account all the factors that can potentially differentiate diffusion across the steps (such as vibrational frequencies, correlated displacements for atomic exchange, etc.) from that on terraces [5,6 ]. The existence of this barrier was experimentally demonstrated by FIM experiments [7] and it led to a generalization of the BCF model [8]. In Cu(111), recent experiments have measured a value E #22 meV [9], comparable with the ES activation energy for surface diffusion, which is estimated to be E #40 meV [10–12]. Therefore, s when an adatom reaches the upper edge of a step it finds it easier to move away from it and back into the terrace than to cross it, which effectively suppresses interlayer diffusion and favours multilayer growth. On more open faces such as the fcc(100), in contrast, in-plane diffusion is slower and the effect of the ES barrier is less noticeable. In this work we intend to perform an in-depth study of the influence of these two basic features on the morphology and structure of homoepitaxial films grown on Cu(111) by MBE. The knowledge obtained in this way should be applicable to more complex systems as well. This paper is organized as follows: Section 2 briefly describes the experimental details and techniques employed; in Section 3, we characterize the clean Cu(111) surface. Section 4 describes the evolution of surface roughness during growth, which is analyzed with the help of a kinetic growth model. Finally, in Section 5 we focus on the crystalline structure of the homoepitaxial Cu films.

2. Experimental The same Cu(111) crystal was used for all the experiments: it has a miscut angle of ~1° and has been used in UHV for several years. It was routinely cleaned by cycles of Ar+ bombardment (500 eV, 5 mA cm−2) and annealing at 500°C. The sample temperature was determined by a chromel– alumel thermocouple pressed against the crystal edge. Cu was evaporated from a water-cooled Knudsen cell. The crucible temperature was measured by a thermocouple attached to it; this reading was fed to a temperature controller which regulated the output of the power supply. The deposition rates have been calibrated from the layer-bylayer intensity oscillations observed in other experiments employing Pb as surfactant [13]. TEAS experiments were conducted at the He diffractometer available at the University Auto´noma. The He source, of the Campargue ˚ −1 type, provides a beam of momentum k =11 A i ˚ ) highly monochromatic (Dk /k (l=0.57 A =0.01), i i with 1.0 mm diameter at the surface. It is modulated by a piezo-driven chopper vibrating at ~240 Hz, and detected by a quadrupole mass analyzer equipped with a channeltron multiplier whose analog output is processed by a lock–in amplifier. The detector can be moved inside the vacuum chamber to change the incidence angle and select the desired interference conditions. The instrumental response function has a gaussian shape, with an angular resolution of 0.65°. The system’s base pressure is in the 10−10 Torr range, and it is further furnished with LEED and AES facilities. Surface X-ray diffraction (S-XRD) measurements were performed at beamline ID3 of the European Synchrotron Radiation Facility ( ESRF ) in Grenoble. This experimental system has been described in detail elsewhere [14]; its most relevant feature for our research is the possibility to evaporate in situ during the measurements. Together with the high photon flux available at the ESRF, this allows growth to be studied in real time. In these experiments we have used the typical surface notation in reciprocal space, with vectors b , b 1 2 contained in the surface plane, while b points 3

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along the [111] direction [15]. In this way, the crystal truncation rods (CTRs) normal to the surface are designated by their {h, k} Miller indices, while l measures perpendicular momentum transfer. The bulk unit cell contains three atomic layers, with one atom in each.

3. The clean Cu(111) surface The initial surface morphology deserves being carefully studied, not only because of its strong influence on the subsequent growth, but also in its own right because this knowledge can be fruitfully applied, for instance, to prepare well-ordered, atomic-scale patterns that may be used as templates for producing nanostructures. This section presents a characterization of the crystallographic structure and surface morphology of the clean Cu(111) face.

Fig. 1. S-XRD scans along the {1,0} and {0,1} CTRs on clean Cu(111). The solid line is a fit to the data (full circles), including a 2% compression of the uppermost atomic layer.

3.1. Surface relaxation Surface relaxations, reconstructions and, in general, any effects associated with elastic strain can play an important role in heteroepitaxial growth, influencing the interface quality or the adjustment between the crystal lattices of the two materials in contact. We have used S-XRD to investigate the structure of clean Cu(111). This surface does not show any reconstruction, but we have found a −2 (±0.4)% relaxation (compression) of the last atomic layer with respect to the bulk spacing. This value is in very good agreement with predictions obtained from calculations using empirical potentials [16 ], which range between −1.6% and −1.9%. First-principles calculations [17], in contrast, yield a smaller value (1.15%). Finally, previous LEED experiments have reported still lower contractions, of −0.8% [18] and −0.7% [19,20]; these values are close to the experimental error limit. In any case, these differences are not very significant and there is general agreement with respect to the sign of the relaxation. Fig. 1 shows two rod scans along the {1,0} and {0,1} CTRs: the circles are the experimental data, and the solid line is the kinematic fit to them,

yielding a reliability factor x2=0.90±0.02. The intense peaks at l=1 and 4 ({1,0} CTR) and l=2 and 5 ({0,1} CTR) are bulk Bragg reflections; the asymmetric rod profile between them signals the different interlayer spacing at the surface. 3.2. Step bunching during sublimation The most interesting feature of the clean Cu(111) surface is the formation of step bunches. This is a well-known kinetic phenomenon, derived from the existence of a high ES barrier. In such cases, interlayer diffusion is strongly reduced and the rates of adatom incorporation from both sides of a step become strongly asymmetric. Steps then move across the surface with different velocities; in particular, during sublimation atoms are first released from each step to its lower terrace and then evaporate into the vacuum. In thermal equilibrium, wide terraces can accommodate more free adatoms and therefore their ascending steps recede faster. Thus, any fluctuations in the terrace width are amplified: wide terraces grow while narrow ones shrink. After some time, the fast steps catch up with the slow ones, forming groups of them or ‘bunches’, separated by flat terraces much wider

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than the nominal size corresponding to the surface miscut [21,22]. This effect can easily appear as a result of sample preparation in UHV, which is usually performed by cycles of ion bombardment and high-temperature annealing. After such a treatment, the freshly prepared surface frequently contains two types of domains, characterized by their very different terrace width. This initial surface configuration has a strong influence on diffusion and nucleation processes, as we will demonstrate in Section 4. Using TEAS, we have detected the formation of step bunches in Cu(111). Fig. 2a shows a h–2h scan obtained on a clean surface prepared by Ar+ sputtering and annealing cycles. In this experiment, the sample reflectivity is measured as a function of the incidence angle of the He beam. Usually, one expects to observe oscillations in the specular intensity corresponding to the different interference conditions between consecutive ter-

races separated by atomic steps. Our data, in contrast, vary smoothly within the angular range probed. At low angle (corresponding to more perpendicular incidence, following the usual convention for He scattering experiments), the reflectivity decreases due to the enhanced effect of thermal scattering, accounted for by means of the surface Debye–Waller factor. At grazing incidence, on the other hand, the reduction of the specular intensity is caused by the finite size of the sample, since its surface does not intercept completely the incident beam. The maxima and minima of the interference cannot be observed because the wider terraces in the surface are much larger than the ˚ ), transfer width of our He diffractometer (~150 A whereas the narrow ones are of the order of, or smaller than, the cross section for diffuse scattering ˚ for Cu from atomic steps (approximately 12 A [23]). The latter then barely contribute to the measured intensity, while the former behave as a nearly perfect mirror. A rough estimate of the average width of the large flat areas yields ˚ [24]. ~1500 A The mean distance between step bunches can be independently obtained from S-XRD measurements. Fig. 2b shows an angular scan across the {0,1} CTR at very grazing incidence and an out˚ −1), of-phase condition (l=0.5, i.e., k =0.502 A ) with the sample prepared by a similar treatment. Under such conditions, the experiment is especially sensitive to correlations between defects on the surface. The width of the diffracted beam is then inversely proportional to the mean distance between steps.4 From the FWHM of this profile ˚ −1) we calculate an average terrace (5.61×10−3 A ˚ , consistent with the TEAS size of ~1120 A estimate. 3.3. Step de-bunching upon growth

Fig. 2. (a) He diffraction (TEAS ) h–2h scan on a clean Cu(111) surface. The absence of maxima and minima of interference indicates step bunching. (b) S-XRD beam profile at the out-ofphase condition of the {0,1} CTR. The solid line is a Lorentzian fit to the data (filled circles).

As we have seen, step bunching due to poor interlayer diffusion is a kinetic phenomenon and therefore it can be reversed by inverting the adatom flux. If instead of evaporating from the substrate 4 The peak broadening due to the convolution of the diffracted beam with the instrument response function is negligible: see e.g., Ref. [25].

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we deposit material on it under step-flow conditions, the lowest step in each bunch will receive all the atoms landed on the adjacent wide terrace and advance faster than the others. This step thus leaves the bunch; its displacement reduces the size of the lower terrace and expands the upper one. During random deposition, the number of atoms arriving at each terrace is proportional to its size; therefore, the fast steps progressively slow down, as their movement reduces their own supply of adatoms at the same time that it contributes to accelerating the next step in the bunch. This kind of negative feedback leads to an equilibrium situation, in which all terraces recover their nominal width and the equidistant steps advance with the same velocity. The miscut angle of our sample is ~1°, corre˚ . This magnitude sponding to terraces of ca. 120 A is comparable with the transfer width of our TEAS diffractometer, so that a surface with regularly spaced monoatomic steps must produce noticeable interference effects. The h–2h scan depicted in Fig. 3a was measured after depositing 5 ML of Cu on the Cu(111) surface at 450 K. The deposition rate was 1.5 ML min−1; under such experimental conditions, step-flow growth takes place, as will be shown in detail in Section 4.1. The Bragg maxima and minima are now clearly visible: they have been labelled according to their interference order n. From their angular positions, and by applying Bragg’s law, 2h

AB

l cos h =n , Cu i 2

(1)

it is possible to determine the step height. The slope of the straight line in Fig. 3b gives ˚ , in excellent agreement with h =(2.08±0.02) A Cu the bulk interlayer spacing along the [111] direction. This measurement thus confirms the disappearance of the bunches and their break-up into separated steps of single atomic height. To summarize this section, we have demonstrated that the existence of high ES barriers hindering interlayer diffusion on Cu(111) can cause kinetic step bunching due to sublimation during the usual preparation procedure. A regular array of equally spaced steps can be recovered by depositing, under step-flow conditions, a number of Cu monolayers roughly similar to the number

195

Fig. 3. (a) TEAS h–2h scan obtained after growing 5 ML of Cu in the step-flow mode. The step bunches have dissolved and the different interference conditions can now be clearly distinguished. (b) Applying Bragg’s law to the angular positions of the maxima and minima of interference, a monoatomic step ˚ is determined. height of (2.08±0.02) A

of steps grouped in the bunches. In the next section we present a detailed study of homoepitaxial growth on Cu(111), discussing also the influence of the sample preparation on the growth mode.

4. Homoepitaxial growth on Cu(111) 4.1. Multilayer growth One of the great advantages of TEAS is the kinematic nature of the scattering process between the incoming He atoms and the surface. Taking advantage of this fact, we have developed a general procedure to study the growth of thin epitaxial films. From the experimental point of view, our method involves measuring mainly timescans, i.e., curves showing the variation of the specular peak intensity in real time during evaporation. The deposition of Cu on Cu(111) at room temperature

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Fig. 4. Schematic representation of the fundamental atomic processes included in our kinetic growth model: parameter A controls the efficiency of interlayer diffusion, while W is the width DZ of the denuded zones near the steps, where no islands are nucleated; its magnitude is related to the diffusive mean free path of the adatoms.

(RT ) typically shows a monotonic decrease of the diffracted intensity, signalling a steady accumulation of defects, as opposed to the periodic variation expected for layer-by-layer growth. The origin and behaviour of this roughness will be dealt with in following sections. Our experimental data have been analyzed with the help of a kinetic growth model that takes into account the most relevant features of the real Cu(111) surface, namely the lack of interlayer transport and the existence of terraces of finite size, bounded by atomic steps. These two phenomena, and the parameters A and W that we DZ use to describe them, are schematically shown in Fig. 4. Our model closely follows that proposed by Cohen et al. [26 ]. We write a set of coupled differential equations describing the time evolution of the occupation of each atomic level in terms of different elementary processes. These equations have the following form: dh i =R[(h −h )+a (h −h ) i−1 i i i i+1 dt −a

(h −h )], i−1 i−1 i

(2)

where R is the deposition rate and h gives the i coverage (expressed in monolayers) of each atomic level. Random deposition is simulated by progressively incrementing the occupation of each level by amounts proportional to the exposed area of the one immediately below. This is described by the first term in the right-hand side of Eq. (2). The second and third terms account for interlayer diffusion, giving respectively the number of atoms that arrive at level i coming from i+1, and those which leave level i falling to i−1. Desorption into the vacuum has been neglected. The likelihood of step crossing at each level is controlled by the parameter a : i d (h ) i i a =A . (3) i d (h )+d (h ) i i i+1 i+1 There, d (h ) has been defined as i i d (h )=[h (1−h )]1/2, (4) i i i i so that it measures the total island perimeter on level i. In this way, the definition of a given by i Eq. (3) contains information on the average distance between steps on the surface. Moreover, the efficiency of interlayer mass transport is described by a single adjustable parameter A. When A=0, step crossings are forbidden; on the other hand, if A=1.0, perfect layer-by-layer growth takes place and no atomic level starts to grow before the lower one is completely filled. After solving the kinetic equations, all layer occupations are known, and it is easy to calculate the corresponding TEAS diffracted amplitude, simply adding the fractions of exposed area with the appropriate phases. The second crucial feature that must be considered is the existence of steps on the surface, due to the crystal miscut. These steps act as sinks for the atoms arriving at them from the lower terrace. The concentration of monomers in their vicinity is thus depleted, and consequently the nucleation probability decreases. An area devoid of islands is formed near the steps which is called ‘denuded’ or ‘capture zone’. When the size of the denuded zone equals that of the terraces, no islands are formed and growth proceeds in the step-flow mode. This effect must necessarily be included in the model in order to reproduce the experimentally observed

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transition to step flow with increasing substrate temperature. Diffraction measurements taken in the out-of-phase condition are mostly sensitive to the balance of exposed areas at different heights. As a first approximation, one can consider that within the denuded zone the surface morphology does not change, and therefore the diffracted intensity is not affected (this simplification will be refined later). To take this effect into account in a simple way, we define a second adjustable parameter, W , representing the fraction of surface covDZ ered by the denuded zones. This area contributes to the measurement with a constant intensity, whereas the result of the kinetic growth model applies only to the rest of the sample surface. This is a rough approximation, but it is justified because the denuded zones are separated by distances similar to the transfer width of our instrument ˚ ). In fact, our treatment is equivalent to (~150 A incoherently adding the intensities diffracted from the different surface patches. In this way, the whole growth model is specified with just two variable parameters, A and W . DZ

197

The fitting routine is graphically illustrated in Fig. 5 and proceeds in the following way: given two values of these parameters, we solve the kinetic equations for the layer occupations h (t) (panel a). i Once these occupations have been determined for the whole range of film thicknesses desired, we use kinematic diffraction theory to calculate a set of h–2h curves for a number of increasing film coverages, including all the experimental factors described in Section 3.2. The results are shown in Fig. 5b. Following this, the theoretical curves are convolved with the instrument response function, which partially washes out the features due the different interference conditions, resulting in the smoother curves depicted in Fig. 5c: They give us the predicted evolution of the diffracted intensity for all incidence angles accessible experimentally. It then suffices to choose the desired incidence angle and to take from the curves the corresponding values of the diffracted intensity for each film thickness. After comparing the theoretical timescan constructed in this way ( Fig. 5d ) with the experimental data, the values of the fitting parame-

Fig. 5. Sequence of steps in our procedure to fit the TEAS growth data: (a) trial calculation of layer occupations; (b) obtention of ‘ideal’ h–2h scans for different film thicknesses; (c) convolution with the instrument response function and (d) extraction of a theoretical timescan from the calculated curves. After comparing the latter with the data, the growth parameters are modified and the process reiterated until a satisfactory agreement is reached.

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ters can be modified and the whole calculation procedure repeated until a satisfactory agreement between the model and the data is reached. We have used this method to characterize the homepitaxy on Cu(111) under different experimental conditions. It turns out that the fine details of the growth process depend very sensitively on the initial surface morphology. As a first example, we have analyzed the data published by Wulfhekel et al. [27]. The main characteristic of these experiments is that they were performed on a very low miscut sample (≤0.1°), with large terraces of at ˚ and presumably a small degree of least ~1200 A step bunching. The deposition rate used was 0.375 ML min−1. Under such conditions, island nucleation and growth is expected to dominate the growth process. The data points and the results of our fits (displayed as circles and solid lines, respectively) are presented in Fig. 6a. The experiments are very well described by our growth model, keeping fixed the value of parameter A=0.0 (which means negligible interlayer diffusion) and varying

Fig. 6. (a) Fits to the TEAS data of Ref. [27] with our kinetic growth model. For all curves, A=0.0, indicating that the likelihood of step crossings is negligible. W increases with temperDZ ature reflecting the enhanced atomic mobility. (b) Arrhenius plot of W . An activation energy E =(17±3) meV can be DZ DZ obtained from the slope of the data at higher temperature.

only W as shown in the figure. In principle, one DZ could expect to observe some variations in A as a function of substrate temperature. Neglecting other aspects that can influence the probability of step crossing, such as the different island sizes or step morphologies, A should behave as a thermally activated process. The fact that we fail to observe such a temperature dependence in the data analyzed indicates that the corresponding activation energy must be considerably higher than, for instance, the energy for surface diffusion, which must be responsible for the observed dependence of W on the substrate temperature. The denuded DZ zone near the steps is an area where the supersaturation is not high enough to produce island nucleation; provided that the critical nucleus size remains constant, the changes in the width of this area with increasing temperature must reflect the enhancement of in-plane diffusion [28]. We have plotted the values of W resulting from the fits DZ in the Arrhenius form, as shown in Fig. 6b. In the higher temperature range, the denuded zone width clearly shows an exponential dependence on the substrate temperature, with an activation energy E =(17±3) meV. Such a low value is of the DZ same order of the surface diffusion energy, although it is difficult to relate them directly because we do not know the critical nucleus size. The deviation of the data points in the low temperature region could be due to a change in this size, but we do not have enough information to solve this question. Next, we will present a detailed analysis of a different set of data, obtained in our own laboratory. These experiments are depicted with circles in Fig. 7; the deposition rate R in this case was 1.5 ML min−1. Qualitatively, the curves show a monotonic decrease of the TEAS specular intensity analogous to the previous case. Nevertheless, upon careful inspection of the data two different regimes of intensity decay can be distinguished; the kinetic growth model described above only allows us to fit the low coverage stage up to ~1 ML, whereas beyond this point the experimental curves deviate from the model (shown with solid lines) and continue to fall at a much slower rate. In order to understand these observations, it is important to notice that our Cu(111) crystal has a higher miscut

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of 82% at 280 K, the lowest temperature used in our experiments. Again in this case we find that the values of W display an Arrhenius behaviour, DZ with an activation energy E =(11±6) meV, in DZ good agreement within the error bars with the value obtained from the previously discussed set of experiments. We conclude then that this initial stage of growth proceeds in the same way in our experiments and in those of Wulfhekel et al. [27]. We will now move on to discuss the second regime observed at higher thicknesses. 4.2. Kinetic roughening during step flow

Fig. 7. (a) Fits to our own TEAS data, during growth on a surface containing step bunches. Only in the low coverage region is the evolution of the specular intensity controlled by the nucleation and growth of islands on the largest terraces, and can be fitted with our growth model. (b) During the initial stage, the variation of the denuded zone width follows a thermally activated behaviour with an energy E =(11±6) meV, DZ compatible with the value obtained previously from Ref. [27].

angle (~1°). As a result of this, the equilibrium ˚ ), and the width of our terraces is smaller (~120 A step bunching effect caused by the cleaning procedure is much more noticeable than in the former case. In fact, the surface morphology of our sample at the beginning of these Cu depositions was equivalent to that described in Section 3.2, con˚ sepasisting of flat terraces of more than 1100 A rated by bunches of single-atomic-height steps. We will therefore restrict ourselves here to analyze the low coverage region. The shorter average distance between steps is reflected in the larger fraction of surface covered by the denuded zone: a minimum

It turns out that this phenomenon results from growing on an initial surface with an unstable distribution of steps and terraces. When deposition starts, and due to the high mobility of the Cu atoms, island nucleation takes place only at the large flat areas, while the steps forming the bunches propagate in the step flow mode. Our TEAS measurements are performed in the out-of-phase condition for monoatomic steps, so they are mostly sensitive to the growth of pyramidal islands. This corresponds to the first stage, whose experimental data can be well described by our kinetic growth model. However, with the progress of step-flow growth (which is quite important in our case, judging from the high values of W ) the bunches DZ dissolve as described in Section 3.3, and the equilibrium terrace size is recovered. The maximum distance between steps is strongly reduced, and island nucleation stops. During their advance across the surface, the steps coming from the bunches run over the previously formed islands, which are thus incorporated into the terraces. Finally, conditions are reached where the balance of exposed areas probed by the He beam does not change any more. This overall picture is illustrated by the Monte Carlo snapshots presented in Fig. 8. We start our simulation (first panel ) with a surface containing a group of narrow terraces separated by straight steps, plus a single, wide terrace on the lower side of the bunch. Each atomic height is coded with a different level of grey in the figure, with darker tones representing lower layers, and the field of view of the images advanced together with the propagating steps, as revealed by the shifting posi-

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Fig. 8. Kinetic Monte Carlo simulation showing growth on a surface with step bunches; atomic terraces are represented with different grey levels, with brighter tones indicating higher levels. Initially, islands are nucleated only at the large terraces, while the narrow ones grow in the step-flow mode. After some time, the advancing steps reach the island and absorb them. Finally, the bunches dissolve and the whole surface grows by step flow.

tion of the islands between frames. After initiating deposition, an island is nucleated on the wide terrace. This island soon acquires a pyramidal shape, owing to the almost negligible interlayer diffusion (second panel, for a total deposited coverage of 2.0 ML). Meanwhile, the rest of the deposited material sticks to the lower steps in the bunch, that advance across the terrace and run over the island. This is more clearly seen in the third panel (3.5 ML coverage). For 5.0 ML total thickness (fourth panel ) we see at the top of the image the remainder of the island, plus a new, smaller one formed at the bottom; however, the average distance between steps is progressively increasing. Finally (8.0 ML), the equilibrium terrace size is recovered. This simple kinetic simulation includes the most relevant characteristics of this system, namely a large ES barrier hindering interlayer diffusion and an initial surface containing step bunches; its success to reproduce the main features of the experiment without any special assumptions provides additional support. The question then is how to explain the continuous decrease of the specular beam intensity observed in the second stage of our experiments. Conventionally, one expects a constant diffracted intensity during step flow, since this growth mode is assumed to maintain unchanged the surface morphology. Nevertheless, this is not always the case. It is well known that systems with poor interlayer diffusion (i.e., with large ES barriers) develop increasing roughness due to kinetic restrictions [29]. During step flow, in particular, the

so-called ‘Bales–Zangwill instability’ [30] can take place: statistical fluctuations during growth result in the appearance of protrusions along the steps. Since most of the incoming atoms arrive from the lower terrace, they are more likely to stick to the tips of these protrusions than to fill the cavities between them. The step meandering progressively evolves to the formation of dendrites. For this behaviour to appear, only two requirements must be fulfilled. First, the currents of adatoms reaching a step from both sides must be asymmetric; as we have seen, Cu(111) – as many other compact crystal faces – meets this condition. The second is that diffusion along the steps be slower than on the terraces [31–34]. This is also a common feature of fcc-(111) faces, owing to their threefold symmetry [10,35,36 ]. This phenomenon can easily be detected with TEAS. Near a step edge, the surface electronic density is distorted and therefore the He beam is scattered away from the specular direction [24]. Consequently, the diffracted intensity decreases even at the out-of-phase condition and with no variation of the relative occupation of adjacent terraces. The cross section for diffuse scattering from Cu steps, defined as the width of the distorted area per unit step length, is ˚ [23]. With these data in hand, it is easy S #12 A Cu to calculate the total length of steps on the surface [37] at any time; in this way, one can monitor in real time during deposition the evolution of step roughness. Kinetic roughening has been widely studied from the theoretical point of view; several excellent

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reviews can be found in the literature [29,38,39]. Different model situations have been considered, both in (2+1) dimensions – describing the changes in surface morphology as a function of time – as in (1+1) – which corresponds to steps. Without going into many details, let us only point out that this phenomenon obeys dynamical scaling laws with characteristic exponents. The interface width W is defined as the root mean square deviation from the ideal shape, and it is a function of both growth time t and system size L. W(L, t) shows the following asymptotic behaviour: W(L, t)~tb

for t%Lz,

(5)

W(L, t)~La

for t2,

(6)

where b is the growth exponent, and a is known as the roughness exponent. These equations predict a power-law increase of the roughness with film thickness during the early stage of deposition, until a saturation value is reached that depends on the system size. In our case, the step roughness must be directly proportional to the amplitude of the dendrites, and therefore to the total step length, which is the magnitude that we can determine from the TEAS experiments. Our data are presented in a log–log plot in Fig. 9a. The solid lines are power-law fits to the data, excluding the points in the low-coverage region. For film thicknesses above 2 ML, (i.e., in the range where our fits based on the hypothesis of 2D growth failed) they follow the behaviour expected from Eq. (5). The values of the b exponent, obtained from the slopes of these fits, are depicted in Fig. 9b. From the evolution of b with substrate temperature, a considerable amount of information on the atomic mechanisms of edge diffusion can be gathered. A value b=0 is expected at high temperature, with unlimited atomic diffusion along the steps, so that all roughness derived from kinetic limitations is suppressed. Extrapolation from our data indicates that this regime could be reached at temperatures close to 700 K. In contrast, b=1/4 is predicted for the Edwards–Wilkinson ( EW ) universality class in (1+1) dimensions, allowing only for a limited amount of diffusion between different levels (i.e., crossing corners along the rough step line and sticking to the kink site). We observe this kind of

Fig. 9. (a) Evolution of the total length of steps on the surface, once the growth mode has switched to rough step flow. (b) Temperature dependence of the roughness exponent b; its variation reveal the existence of different regimes of adatom diffusion along the steps (see text). The solid line is a guide to the eye.

behaviour near 500 K. Lowering the substrate temperature and restricting diffusion further, the experimentally determined b increases and reaches a plateau around 3/8, extending between approximately 300 and 400 K. This value corresponds to the Mullins–Herring (MH ) universality class; a very similar result (0.37) has also been found in atomistic simulations of growth [40,41] in which atoms are allowed limited displacements along straight segments of the steps, but cannot turn corners. Below RT, diffusion parallel to the steps is reduced still further and b approaches 0.5,

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characteristic for conditions of random adsorption with no rearrangement. The information contained in Fig. 9b thus allows us to follow the temperature evolution of diffusion parallel to the atomic steps existing on the surface.

5. Crystalline structure of Cu films Having already described the evolution of surface morphology during growth, in this section we will concentrate on the structural characterization of the homoepitaxial Cu films. For this task, a probe is needed that can penetrate below the surface layer and detect the atomic positions within the crystal unit cell. Therefore we have resorted to S-XRD. With this technique, the information about the stacking sequence probed by the X-ray beam is contained in the so-called crystal truncation rods (CTRs) [42]: these are the profiles of diffracted intensity along a particular direction in reciprocal space, as a function of perpendicular momentum transfer. As mentioned in Section 1, the main source of structural defects in this system is the existence of two different, but nearly equivalent, threefold adsorption sites on the Cu(111) surface. One of them corresponds to the correct fcc sequence, as dictated by the substrate. Islands nucleated on the other position form stacking faults (SFs) upon which twin crystallites develop. Twin fcc stacking sequences are specular reflections from each other; in reciprocal space this results in interchanging the characteristics of the {10} and {01} CTRs. The {00} and its equivalent with zero parallel momentum transfer are insensitive to these type of defects. Fig. 10 shows a set of rod scans measured on the {10} CTR after having grown Cu films at different substrate temperatures. The full circles are the experimental data, and the solid lines are kinematic fits to them. The latter are based on theoretical structural models constructed using our kinetic growth equations to determine level occupations, as described in Section 4. Additionally, we now consider a probability p to form an SF SF at random positions on each atomic level. As is customary, the fit accuracy is determined from the values of the x2 parameter, also listed in the figure.

Fig. 10. S-XRD rod scans along the {1,0} CTR for Cu films grown at different temperatures. The peak developing at l=2 is a Bragg reflection of the twinned structure. The curves have been shifted vertically for clarity, and the reliability factors x2 of the corresponding fits are shown near each of them.

The very intense peaks at l=1, l=4 are bulk Bragg reflections of the fcc substrate, while the peak developing at l=2 signals the appearance of twinned domains. Visual inspection of the experimental data shows that the fraction of twins formed during growth decreases with increasing temperature. This fact does not necessarily imply that the probability p also decreases; to underSF stand these results correctly, one has to keep in mind the transition to step-flow growth taking place in this temperature range, because all atoms sticking to the substrate steps are forced to follow the same fcc stacking sequence of the Cu crystal. Applying our model only to the islands nucleated on the terraces, we find that p actually increases SF with temperature. Further support for our structural description comes from the data obtained in real time during Cu deposition, which are depicted in Fig. 11. Here we show the continuous evolution of the diffracted intensity at point (1,0,1.95)5. In reciprocal space, with increasing Cu thickness. The solid lines are 5 (1,0,2) is the exact Bragg condition for fcc twins. Nevertheless, the measurements were not performed at this point in order to avoid the spurious signal due to photons of energy corresponding to the third harmonic of the Si(111) monochromator crystal.

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Fig. 11. S-XRD timescans showing the evolution with Cu thickness of the X-ray intensity at point (1,0,1.95) in reciprocal space, which is sensitive to twin formation. The solid lines are fits obtained describing the growth process with our kinetic model discussed above, and including a probability to nucleate at random a fraction of islands at hcp positions. The fit parameters are listed in Table 1.

simulations obtained using our growth model with the same parameters A, W described previously, DZ plus p . The excellent agreement with the data SF indicates that our model captures the essential physics of the growth process. The results of these fits are summarized in Table 1. A was held at 0.0 for all cases. It is remarkable that in these fits to a new set of data measured with a different technique we obtain the same values of A and W as in our DZ TEAS experiments. This lends additional support to our growth model. Besides, the large values of W in this temperature range indicate that the DZ Cu atoms are highly mobile on the surface. This in turn implies that they probe a large number of sites, both fcc and hcp, before nucleating; the probability of each site being occupied at any finite Table 1 Parameters used in the kinetic growth model to fit the S-XRD timescans of Fig. 11. A=0.0 in all cases; W also agrees well DZ with the values found in Section 4 T (K)

W

215 295 360 400

0.60 0.85 0.92 0.96

DZ

p SF 0.15 0.20 0.24 0.28

Fig. 12. Arrhenius plot of the probabilities to form stacking faults ( p ) determined from the fits to the timescans taken in SF real time during Cu deposition and listed in Table 1. From the slope of this line we calculate that the stacking fault energy in Cu(111) is n1E =(21±3) meV, where n1 is the number of SF atoms in the critical nucleus.

temperature must be given by the Boltzmann factor of its adsorption energy. The probability of an island nucleating at hcp sites and forming a SF is then:

C

D

n1(E −E ) hcp fcc , (7) k T B where n1 is the number of atoms in the critical nucleus. The experimentally determined values of p are displayed in an Arrhenius plot in Fig. 12. SF From the slope of this plot we find n1(E −E )=(21±3) meV. Again in this case, hcp fcc we cannot be more precise because we do not know the size of the critical nucleus. However, in this temperature range one can safely assume that n1 must be 2 or 3. Our estimate for the stackingfault energy is then 7–10 meV per atom, in excellent agreement with the value of 10 meV obtained recently by means of ab initio calculations [43]. Similar values have been reported previously, resulting either from calculations [44] or from estimates based on the value of the activation energy for self-diffusion [10–12].6

p =exp − SF

6 Assuming that diffusion on Cu(111) takes place by hopping, then the difference E −E must be a fraction of the hcp fcc activation energy for surface diffusion; for experimental results, see Refs. [45,46 ].

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6. Summary We have performed a complete, fully detailed study of the morphology and crystalline structure of Cu(111) surfaces and homoepitaxial films. Our findings are of fundamental importance, because they allow us to identify the elementary atomic processes such as surface versus step diffusion that control the accumulation of roughness. In addition, the applicability of these results to other systems must be wide ranging, because they ultimately derive from very general characteristics of the substrate surface, such as the existence of high ES barriers or two similar adsorption sites. In particular, these factors have been known to hamper the preparation of high-quality heteroepitaxial films, with potential applications in nanotechnology [47]. In order to solve these difficulties it is necessary to use more efficient growth methods such as surfactants. The modifications of Cu(111) homoepitaxy provoked by a surfactant layer of Pb will be the subject of a forthcoming publication [48].

Acknowledgements We are grateful to the staff of the ESRF for their help during the realization of our experiments there, and to Prof. I. Markov and Drs. M.C. Bartelt and N.C. Bartelt for their critical reading of the manuscript and their valuable comments. Work by the Spanish group has been supported by the CICyT under Grant MAT98-0965-C04-02.

References [1] J.W. Gibbs, Trans. Conn. Acad. 3 (1878) 343. [2] W. Kossel, Nachr. Ges. Wiss. Go¨ttingen Math. Phys. K1. 135 (1927). [3] I.N. Stranski, Z. Phys. Chem. 36 (1928) 259. [4] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. R. Soc. London 243 (1951) 299. [5] A. Go¨lzha¨user, G. Ehrlich, Phys. Rev. Lett. 77 (1996) 1334. [6 ] K.R. Roos, M.C. Tringides, Surf. Rev. Lett. 5 (1998) 833.

[7] G. Ehrlich, F.G. Hudda, J. Chem. Phys. 44 (1966) 1039. [8] R.L. Schwoebel, E.J. Shipsey, J. Appl. Phys. 37 (1966) 3682. [9] M. Giesen, H. Ibach, Surf. Sci. 431 (1999) 109. [10] M. Karimi, T. Tomkowski, G. Vidali, O. Biham, Phys. Rev. B 52 (1995) 5364. [11] Y. Li, A.E. DePristo, Surf. Sci. 351 (1996) 189. [12] C.L. Liu, J.M. Cohen, J.B. Adams, A.F. Voter, Surf. Sci. 253 (1991) 334. [13] J. Camarero, J. Ferro´n, V. Cros, L. Go´mez, A.L. Va´zquez de Parga, J.M. Gallego, J.E. Prieto, J.J. de Miguel, R. Miranda, Phys. Rev. Lett. 81 (1998) 850. [14] S. Ferrer, F. Comin, Rev. Sci. Instrum. 66 (1995) 1674. [15] H.A. van der Vegt, M. Breeman, S. Ferrer, V.H. Etgens, X. Torrelles, P. Fajardo, E. Vlieg, Phys. Rev. B 51 (1995) 14 806. [16 ] J. Uppenbrink, R.L. Johnson, J.N. Murrell, Surf. Sci. 304 (1994) 223. [17] N.C. Bartelt, personal communication. [18] J.E. Prieto, Ch. Rath, S. Mu¨ller, R. Miranda, K. Heinz, Surf. Sci. 401 (1998) 248. [19] F. Jona, P.M. Marcus, in: J.F. van der Veen, M.A. van Hove ( Eds.), The Structure of Surfaces II, Springer, Berlin, 1987. [20] M.A. van Hove, S.W. Wang, D.F. Ogletree, G.A. Somorjai, Adv. Quantum Chem. 20 (1989) 1. [21] P. Bennema, G.H. Gilmer, in: P. Hartman (Ed.), Crystal Growth: An Introduction, North-Holland, Amsterdam, 1973, p. 317. Chapter 10. [22] C. van Leeuwen, R. van Rosmalen, P. Bennema, Surf. Sci. 44 (1974) 213. [23] A. Sa´nchez, S. Ferrer, Surf. Sci. 187 (1987) L587. [24] B. Poelsema, G. Comsa, Scattering of Thermal Energy Atoms, Springer Tracts in Modern Physics, Vol. 115, Springer, Berlin, 1989. [25] X. Torrelles, H.A. van der Vegt, V.H. Etgens, P. Fajardo, ´ lvarez, S. Ferrer, Surf. Sci. 364 (1996) 242. J. A [26 ] P.I. Cohen, G.S. Petrich, P.R. Pukite, G.J. Whaley, Surf. Sci. 216 (1989) 222. [27] W. Wulfhekel, N.N. Lipkin, J. Kliewer, G. Rosenfeld, L.C. Jorritsma, B. Poelsema, G. Comsa, Surf. Sci. 348 (1996) 227. [28] Y.-W. Mo, J. Kleiner, M.B. Webb, M.G. Lagally, Surf. Sci. 268 (1992) 275. [29] S. Das Sarma, in: Z. Zhang, M.G. Lagally ( Eds.), Morphological Organization in Epitaxial Growth and RemovalSeries on Directions on Condensed Matter Physics Vol. 14, World Scientific, Singapore, 1998, p. 94. [30] G.S. Bales, A. Zangwill, Phys. Rev. B 41 (1990) 5500. [31] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34 (1963) 323. [32] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1963) 444. [33] R.Q. Hwang, J. Schroder, C. Gu¨nther, R.J. Behm, Phys. Rev. Lett. 67 (1991) 3279. [34] M.C. Bartelt, J.W. Evans, Surf. Sci. 314 (1994) L829. [35] Z. Zhang, X. Chen, M.G. Lagally, Phys. Rev. Lett. 73 (1994) 1829.

J. Camarero et al. / Surface Science 459 (2000) 191–205 [36 ] C.L. Liu, J.B. Adams, Surf. Sci. 265 (1992) 262. [37] J.J. de Miguel, A. Cebollada, J.M. Gallego, J. Ferro´n, S. Ferrer, J. Cryst. Growth 88 (1988) 442. [38] J. Krug, Adv. Phys. 46 (1997) 139. [39] A.-L. Barba´si, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995. [40] S. Das Sarma, P.I. Tamborenea, Phys. Rev. Lett. 66 (1991) 325. [41] P.I. Tamborenea, Z.-W. Lai, S. Das Sarma, Surf. Sci. 267 (1992) 1. [42] I.K. Robinson, Phys. Rev. B 33 (1986) 3830.

205

[43] P.J. Feilbelman, personal communication. [44] S. Crampin, K. Hampel, D.D. Vvedensky, J. MacLaren, J. Mater. Res. 5 (1990) 2107. [45] G. Ehrlich, MRS Symposia Proceedings, No. 57, Materials Research Society, Pittsburgh, PA, 1987. [46 ] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley Interscience, New York, 1982. [47] J. Camarero, L. Spendeler, G. Schmidt, K. Heinz, J.J. de Miguel, R. Miranda, Phys. Rev. Lett. 73 (1984) 2448. ´ lvarez, M.A. Nin˜o, S. [48] J. Camarero, J. de la Figuera, J. A Ferrer, J.J. de Miguel, R. Miranda, in preparation.