structural characterisation and homoepitaxial growth on cu(111)

Surface Science 459 (2000) 191–205www.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,J. Alvarez a,3, S. Ferrer b

a Departmento de Fısica de la Materia Condensada and Instituto de Ciencia de Materiales ‘Nicolas Cabrera’,

Universidad Autonoma 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 is the basis of our current understanding of epitax-ial growth phenomena. Thus, the fundamentalaspects of this problem seem to be well understood.Crystal growth has been an active field ofRecently, however, the great surge of research onresearch for a long time. Its thermodynamic foun-low-dimensional and nanostructured materials hasdations were laid as early as the 19th century withawakened renewed interest to identify and gainthe work by Gibbs [1]. Atomistic formulationscontrol over the finest details involved in theappeared later [2,3] opening a way that culminatedgrowth process, which strongly influence the mor-with the formulation of the BCF theory [4], whichphology of the grown materials, and hence theirresulting electronic and magnetic properties. Fcc

* Corresponding author. Fax:+34 91 3973961. metals are a good example of the subtletiesE-mail address: [email protected] (J.J. de Miguel ) involved in epitaxy. On (100) faces, growth usually1 Present address: Laboratoire Louis Neel-CNRS, 38042 takes place in a layer-by-layer mode, with high

Grenoble Cedex, France.structural quality at relatively low temperature and

2 Present address: Sandia National Laboratories, Livermore,for typical deposition rates of the order ofCA, USA.1 ML min−1. In contrast, films grown with (111)3 Present address: Dpto. Fısica de la Materia Condensada,

Univ. Autonoma, Cantoblanco, 28049-Madrid, Spain. orientation on the same materials and under sim-

0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S0039-6028 ( 00 ) 00463-5

192 J. Camarero et al. / Surface Science 459 (2000) 191–205

ilar conditions show a tendency to roughen during 2. Experimental

deposition up to considerably higher temperatures.

In this paper we will demonstrate that such a The same Cu(111) crystal was used for all the

experiments: it has a miscut angle of ~1° and hasdifferent behaviour is caused by two intrinsic char-

acteristics of the (111) faces: first, the existence of been used in UHV for several years. It was rou-

tinely cleaned by cycles of Ar+ bombardmenttwo very similar, threefold adsorption sites, which

leads to the formation of stacking faults during (500 eV, 5 mA cm−2) and annealing at 500°C. The

sample temperature was determined by a chromel–growth; and second, the poor interlayer diffusion

due to the presence of the so-called Ehrlich– alumel thermocouple pressed against the crystal

edge.Schwoebel (ES) barrier at atomic steps. This mag-

nitude describes the energy cost that a diffusing Cu was evaporated from a water-cooled

Knudsen cell. The crucible temperature was mea-adatom has to overcome in order to cross a

descending step and fall to the lower terrace. It is sured by a thermocouple attached to it; this reading

was fed to a temperature controller which regu-usually explained in terms of the low coordination

felt by the adatom at the transition stage, although lated the output of the power supply. The depos-

ition rates have been calibrated from the layer-by-it should be regarded as an effective parameter

which takes into account all the factors that can layer intensity oscillations observed in other experi-

ments employing Pb as surfactant [13].potentially differentiate diffusion across the steps

(such as vibrational frequencies, correlated dis- TEAS experiments were conducted at the He

diffractometer available at the Universityplacements for atomic exchange, etc.) from that

on terraces [5,6 ]. The existence of this barrier was Autonoma. The He source, of the Campargue

type, provides a beam of momentum ki=11 A−1experimentally demonstrated by FIM experiments

[7] and it led to a generalization of the BCF model (l=0.57 A) highly monochromatic (Dki/ki=0.01),

with 1.0 mm diameter at the surface. It is modu-[8]. In Cu(111), recent experiments have measured

a value EES#22 meV [9], comparable with the lated by a piezo-driven chopper vibrating at

~240 Hz, and detected by a quadrupole massactivation energy for surface diffusion, which is

estimated to be Es#40 meV [10–12]. Therefore, analyzer equipped with a channeltron multiplier

whose analog output is processed by a lock–inwhen an adatom reaches the upper edge of a step

it finds it easier to move away from it and back amplifier. The detector can be moved inside the

vacuum chamber to change the incidence angleinto the terrace than to cross it, which effectively

suppresses interlayer diffusion and favours multi- and select the desired interference conditions. The

instrumental response function has a gaussianlayer growth. On more open faces such as the fcc-

(100), in contrast, in-plane diffusion is slower and shape, with an angular resolution of 0.65°. The

system’s base pressure is in the 10−10 Torr range,the effect of the ES barrier is less noticeable. In

this work we intend to perform an in-depth study and it is further furnished with LEED and AES

facilities.of the influence of these two basic features on the

morphology and structure of homoepitaxial films Surface X-ray diffraction (S-XRD) measure-

ments were performed at beamline ID3 of thegrown on Cu(111) by MBE. The knowledge

obtained in this way should be applicable to more European Synchrotron Radiation Facility (ESRF)

in Grenoble. This experimental system has beencomplex systems as well.

This paper is organized as follows: Section 2 described in detail elsewhere [14]; its most relevant

feature for our research is the possibility to evapo-briefly describes the experimental details and tech-

niques employed; in Section 3, we characterize the rate in situ during the measurements. Together

with the high photon flux available at the ESRF,clean Cu(111) surface. Section 4 describes the evo-

lution of surface roughness during growth, which this allows growth to be studied in real time. In

these experiments we have used the typical surfaceis analyzed with the help of a kinetic growth model.

Finally, in Section 5 we focus on the crystalline notation in reciprocal space, with vectors b1, b2

contained in the surface plane, while b3

pointsstructure of the homoepitaxial Cu films.

193J. Camarero et al. / Surface Science 459 (2000) 191–205

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 tem-

plates for producing nanostructures. This section

presents a characterization of the crystallographicFig. 1. S-XRD scans along the {1,0} and {0,1} CTRs on clean

structure and surface morphology of the clean Cu(111). The solid line is a fit to the data (full circles), includingCu(111) face. a 2% compression of the uppermost atomic layer.

3.1. Surface relaxation

yielding a reliability factor x2=0.90±0.02. The

intense peaks at l=1 and 4 ({1,0} CTR) and l=2Surface relaxations, reconstructions and, in

general, any effects associated with elastic strain and 5 ({0,1} CTR) are bulk Bragg reflections; the

asymmetric rod profile between them signals thecan play an important role in heteroepitaxial

growth, influencing the interface quality or the different interlayer spacing at the surface.

adjustment between the crystal lattices of the two

materials in contact. 3.2. Step bunching during sublimation

We have used S-XRD to investigate the struc-

ture of clean Cu(111). This surface does not show The most interesting feature of the clean

Cu(111) surface is the formation of step bunches.any reconstruction, but we have found a −2

(±0.4)% relaxation (compression) of the last This is a well-known kinetic phenomenon, derived

from the existence of a high ES barrier. In suchatomic layer with respect to the bulk spacing. This

value is in very good agreement with predictions cases, interlayer diffusion is strongly reduced and

the rates of adatom incorporation from both sidesobtained from calculations using empirical poten-

tials [16 ], which range between −1.6% and of a step become strongly asymmetric. Steps then

move across the surface with different velocities;−1.9%. First-principles calculations [17], in con-

trast, yield a smaller value (1.15%). Finally, previ- in particular, during sublimation atoms are first

released from each step to its lower terrace andous LEED experiments have reported still lower

contractions, of −0.8% [18] and −0.7% [19,20]; then evaporate into the vacuum. In thermal equi-

librium, wide terraces can accommodate more freethese values are close to the experimental error

limit. In any case, these differences are not very adatoms and therefore their ascending steps recede

faster. Thus, any fluctuations in the terrace widthsignificant and there is general agreement with

respect to the sign of the relaxation. are amplified: wide terraces grow while narrow

ones shrink. After some time, the fast steps catchFig. 1 shows two rod scans along the {1,0} and

{0,1} CTRs: the circles are the experimental data, up with the slow ones, forming groups of them or

‘bunches’, separated by flat terraces much widerand the solid line is the kinematic fit to them,


than the nominal size corresponding to the surface races separated by atomic steps. Our data, in

contrast, vary smoothly within the angular rangemiscut [21,22]. This effect can easily appear as a

result of sample preparation in UHV, which is probed. At low angle (corresponding to more

perpendicular incidence, following the usual con-usually performed by cycles of ion bombardment

and high-temperature annealing. After such a vention for He scattering experiments), the reflec-

tivity decreases due to the enhanced effect oftreatment, the freshly prepared surface frequently

contains two types of domains, characterized by thermal scattering, accounted for by means of the

surface Debye–Waller factor. At grazing incidence,their very different terrace width. This initial sur-

face configuration has a strong influence on diffu- on the other hand, the reduction of the specular

intensity is caused by the finite size of the sample,sion and nucleation processes, as we will

demonstrate in Section 4. since its surface does not intercept completely the

incident beam. The maxima and minima of theUsing TEAS, we have detected the formation

of step bunches in Cu(111). Fig. 2a shows a h–2h interference cannot be observed because the wider

terraces in the surface are much larger than thescan obtained on a clean surface prepared by

Ar+ sputtering and annealing cycles. In this experi- transfer width of our He diffractometer (~150 A),

whereas the narrow ones are of the order of, orment, the sample reflectivity is measured as a

function of the incidence angle of the He beam. smaller than, the cross section for diffuse scattering

from atomic steps (approximately 12 A for CuUsually, one expects to observe oscillations in the

specular intensity corresponding to the different [23]). The latter then barely contribute to the

measured intensity, while the former behave as ainterference conditions between consecutive ter-

nearly perfect mirror. A rough estimate of the

average width of the large flat areas yields

~1500 A [24].

The mean distance between step bunches can

be independently obtained from S-XRD measure-

ments. Fig. 2b shows an angular scan across the

{0,1} CTR at very grazing incidence and an out-

of-phase condition (l=0.5, i.e., k)=0.502 A−1),

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

(5.61×10−3 A−1) we calculate an average terrace

size of ~1120 A, consistent with the TEAS

estimate.

3.3. Step de-bunching upon growth

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 substrateFig. 2. (a) He diffraction (TEAS) h–2h scan on a clean Cu(111)

surface. The absence of maxima and minima of interference

4 The peak broadening due to the convolution of theindicates step bunching. (b) S-XRD beam profile at the out-of-

phase condition of the {0,1} CTR. The solid line is a Lorentzian diffracted beam with the instrument response function is negligi-

ble: see e.g., Ref. [25].fit to the data (filled circles).


we deposit material on it under step-flow condi-tions, the lowest step in each bunch will receive allthe atoms landed on the adjacent wide terrace andadvance faster than the others. This step thusleaves the bunch; its displacement reduces the sizeof the lower terrace and expands the upper one.During random deposition, the number of atomsarriving at each terrace is proportional to its size;therefore, the fast steps progressively slow down,as their movement reduces their own supply ofadatoms at the same time that it contributes toaccelerating the next step in the bunch. This kindof negative feedback leads to an equilibrium situa-tion, in which all terraces recover their nominalwidth and the equidistant steps advance with thesame velocity.

The miscut angle of our sample is ~1°, corre-sponding to terraces of ca. 120 A. This magnitudeis comparable with the transfer width of our TEASdiffractometer, so that a surface with regularlyspaced monoatomic steps must produce noticeableinterference effects. The h–2h scan depicted inFig. 3a was measured after depositing 5 ML of Cu

Fig. 3. (a) TEAS h–2h scan obtained after growing 5 ML of Cuon the Cu(111) surface at 450 K. The deposition

in the step-flow mode. The step bunches have dissolved and therate was 1.5 ML min−1; under such experimental different interference conditions can now be clearly distin-conditions, step-flow growth takes place, as will guished. (b) Applying Bragg’s law to the angular positions of

the maxima and minima of interference, a monoatomic stepbe shown in detail in Section 4.1. The Braggheight of (2.08±0.02) A is determined.maxima and minima are now clearly visible: they

have been labelled according to their interferenceof steps grouped in the bunches. In the next sectionorder n. From their angular positions, and bywe present a detailed study of homoepitaxialapplying Bragg’s law,growth on Cu(111), discussing also the influence

of the sample preparation on the growth mode.2hCu

cos hi=nA

l

2 B, (1)

it is possible to determine the step height. The4. Homoepitaxial growth on Cu(111)

slope of the straight line in Fig. 3b giveshCu=(2.08±0.02) A, in excellent agreement with

4.1. Multilayer growththe bulk interlayer spacing along the [111] direc-tion. This measurement thus confirms the disap-

One of the great advantages of TEAS is thepearance of the bunches and their break-up intokinematic nature of the scattering process betweenseparated steps of single atomic height.the incoming He atoms and the surface. TakingTo summarize this section, we have demon-advantage of this fact, we have developed a generalstrated that the existence of high ES barriersprocedure to study the growth of thin epitaxialhindering interlayer diffusion on Cu(111) canfilms. From the experimental point of view, ourcause kinetic step bunching due to sublimationmethod involves measuring mainly timescans, i.e.,during the usual preparation procedure. A regularcurves showing the variation of the specular peakarray of equally spaced steps can be recovered byintensity in real time during evaporation. Thedepositing, under step-flow conditions, a number

of Cu monolayers roughly similar to the number deposition of Cu on Cu(111) at room temperature


where R is the deposition rate and hi

gives the

coverage (expressed in monolayers) of each atomic

level. Random deposition is simulated by pro-

gressively 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 ai:

ai=A

di(hi)

di(hi)+di+1

(hi+1

). (3)

Fig. 4. Schematic representation of the fundamental atomic pro-

There, di(hi) has been defined ascesses included in our kinetic growth model: parameter A con-

trols the efficiency of interlayer diffusion, while WDZ

is the widthdi(hi)=[h

i(1−h

i)]1/2 , (4)of the denuded zones near the steps, where no islands are nucle-

ated; its magnitude is related to the diffusive mean free path ofso that it measures the total island perimeter onthe adatoms.

level i. In this way, the definition of ai

given by

Eq. (3) contains information on the average dis-(RT) typically shows a monotonic decrease of the tance between steps on the surface. Moreover, thediffracted intensity, signalling a steady accumula- efficiency of interlayer mass transport is describedtion of defects, as opposed to the periodic variation by a single adjustable parameter A. When A=0,expected for layer-by-layer growth. The origin and step crossings are forbidden; on the other hand, ifbehaviour of this roughness will be dealt with in A=1.0, perfect layer-by-layer growth takes placefollowing sections. and no atomic level starts to grow before the lower

Our experimental data have been analyzed with one is completely filled. After solving the kineticthe help of a kinetic growth model that takes into equations, all layer occupations are known, and itaccount the most relevant features of the real is easy to calculate the corresponding TEASCu(111) surface, namely the lack of interlayer diffracted amplitude, simply adding the fractionstransport and the existence of terraces of finite of exposed area with the appropriate phases.size, bounded by atomic steps. These two phen- The second crucial feature that must be consid-omena, and the parameters A and W

DZthat we ered is the existence of steps on the surface, due

use to describe them, are schematically shown in to the crystal miscut. These steps act as sinks forFig. 4. Our model closely follows that proposed the atoms arriving at them from the lower terrace.by Cohen et al. [26 ]. We write a set of coupled The concentration of monomers in their vicinity isdifferential equations describing the time evolution thus depleted, and consequently the nucleationof the occupation of each atomic level in terms of probability decreases. An area devoid of islands isdifferent elementary processes. formed near the steps which is called ‘denuded’ or

These equations have the following form: ‘capture zone’. When the size of the denuded zone

equals that of the terraces, no islands are formeddhi

dt=R[(h

i−1−hi)+ai(hi−hi+1

) and growth proceeds in the step-flow mode. This

effect must necessarily be included in the model in

order to reproduce the experimentally observed−ai−1

(hi−1−hi)], (2)


transition to step flow with increasing substrate The fitting routine is graphically illustrated in

Fig. 5 and proceeds in the following way: giventemperature. Diffraction measurements taken in

the out-of-phase condition are mostly sensitive to two values of these parameters, we solve the kinetic

equations for the layer occupations hi(t) (panel a).the balance of exposed areas at different heights.

As a first approximation, one can consider that Once these occupations have been determined for

the whole range of film thicknesses desired, we usewithin the denuded zone the surface morphology

does not change, and therefore the diffracted inten- kinematic diffraction theory to calculate a set of

h–2h curves for a number of increasing film cover-sity is not affected (this simplification will be

refined later). To take this effect into account in a ages, including all the experimental factors

described in Section 3.2. The results are shown insimple way, we define a second adjustable parame-

ter, WDZ

, representing the fraction of surface cov- Fig. 5b. Following this, the theoretical curves are

convolved with the instrument response function,ered by the denuded zones. This area contributes

to the measurement with a constant intensity, which partially washes out the features due the

different interference conditions, resulting in thewhereas the result of the kinetic growth model

applies only to the rest of the sample surface. This smoother curves depicted in Fig. 5c: They give us

the predicted evolution of the diffracted intensityis a rough approximation, but it is justified because

the denuded zones are separated by distances for all incidence angles accessible experimentally.

It then suffices to choose the desired incidencesimilar to the transfer width of our instrument

(~150 A). In fact, our treatment is equivalent to angle and to take from the curves the correspond-

ing values of the diffracted intensity for each filmincoherently adding the intensities diffracted from

the different surface patches. thickness. After comparing the theoretical times-

can constructed in this way (Fig. 5d) with theIn this way, the whole growth model is specified

with just two variable parameters, A and WDZ

. 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.


ters can be modified and the whole calculation only WDZ

as shown in the figure. In principle, one

could expect to observe some variations in A as aprocedure repeated until a satisfactory agreement

between the model and the data is reached. function of substrate temperature. Neglecting

other aspects that can influence the probability ofWe have used this method to characterize the

homepitaxy on Cu(111) under different experi- step crossing, such as the different island sizes or

step morphologies, A should behave as a thermallymental conditions. It turns out that the fine details

of the growth process depend very sensitively on activated process. The fact that we fail to observe

such a temperature dependence in the data ana-the initial surface morphology. As a first example,

we have analyzed the data published by Wulfhekel lyzed indicates that the corresponding activation

energy must be considerably higher than, foret al. [27]. The main characteristic of these experi-

ments is that they were performed on a very low instance, the energy for surface diffusion, which

must be responsible for the observed dependencemiscut sample (≤0.1°), with large terraces of at

least ~1200 A and presumably a small degree of of WDZ

on the substrate temperature. The denuded

zone near the steps is an area where the supersat-step bunching. The deposition rate used was

0.375 ML min−1. Under such conditions, island uration is not high enough to produce island

nucleation; provided that the critical nucleus sizenucleation and growth is expected to dominate the

growth process. The data points and the results of remains constant, the changes in the width of this

area with increasing temperature must reflect theour fits (displayed as circles and solid lines, respec-

tively) are presented in Fig. 6a. The experiments enhancement of in-plane diffusion [28]. We have

plotted the values of WDZ

resulting from the fitsare very well described by our growth model,

keeping fixed the value of parameter A=0.0 (which in the Arrhenius form, as shown in Fig. 6b. In the

higher temperature range, the denuded zone widthmeans negligible interlayer diffusion) and varying

clearly shows an exponential dependence on the

substrate temperature, with an activation energy

EDZ=(17±3) meV. Such a low value is of the

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 temper-

ature 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 labora-

tory. 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, whereasFig. 6. (a) Fits to the TEAS data of Ref. [27] with our kinetic beyond this point the experimental curves deviategrowth model. For all curves, A=0.0, indicating that the likeli- from the model (shown with solid lines) and con-hood of step crossings is negligible. W

DZincreases with temper-

tinue to fall at a much slower rate. In order toature reflecting the enhanced atomic mobility. (b) Arrhenius

understand these observations, it is important toplot of WDZ

. An activation energy EDZ=(17±3) meV can be

obtained from the slope of the data at higher temperature. notice that our Cu(111) crystal has a higher miscut


of 82% at 280 K, the lowest temperature used in

our experiments. Again in this case we find that

the values of WDZ

display an Arrhenius behaviour,

with an activation energy EDZ=(11±6) meV, in

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

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-flowFig. 7. (a) Fits to our own TEAS data, during growth on a

growth (which is quite important in our case,surface containing step bunches. Only in the low coverage

judging from the high values of WDZ

) the bunchesregion is the evolution of the specular intensity controlled by

the nucleation and growth of islands on the largest terraces, dissolve as described in Section 3.3, and the equilib-and can be fitted with our growth model. (b) During the initial rium terrace size is recovered. The maximum dis-stage, the variation of the denuded zone width follows a ther-

tance between steps is strongly reduced, and islandmally activated behaviour with an energy E

DZ=(11±6) meV,

nucleation stops. During their advance across thecompatible with the value obtained previously from Ref. [27].

surface, the steps coming from the bunches run

over the previously formed islands, which are thus

incorporated into the terraces. Finally, conditionsangle (~1°). As a result of this, the equilibrium

width of our terraces is smaller (~120 A), and the are reached where the balance of exposed areas

probed by the He beam does not change any more.step bunching effect caused by the cleaning pro-

cedure is much more noticeable than in the former This overall picture is illustrated by the Monte

Carlo snapshots presented in Fig. 8. We start ourcase. In fact, the surface morphology of our sample

at the beginning of these Cu depositions was simulation (first panel ) with a surface containing

a group of narrow terraces separated by straightequivalent to that described in Section 3.2, con-

sisting of flat terraces of more than 1100 A sepa- steps, plus a single, wide terrace on the lower side

of the bunch. Each atomic height is coded with arated by bunches of single-atomic-height steps. We

will therefore restrict ourselves here to analyze the different level of grey in the figure, with darker

tones representing lower layers, and the field oflow coverage region. The shorter average distance

between steps is reflected in the larger fraction of view of the images advanced together with the

propagating steps, as revealed by the shifting posi-surface covered by the denuded zone: a minimum


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 so-called ‘Bales–Zangwill instability’ [30] can take

place: statistical fluctuations during growth resultdeposition, an island is nucleated on the wide

terrace. This island soon acquires a pyramidal in the appearance of protrusions along the steps.

Since most of the incoming atoms arrive from theshape, owing to the almost negligible interlayer

diffusion (second panel, for a total deposited cover- lower terrace, they are more likely to stick to the

tips of these protrusions than to fill the cavitiesage of 2.0 ML). Meanwhile, the rest of the depos-

ited material sticks to the lower steps in the bunch, between them. The step meandering progressively

evolves to the formation of dendrites. For thisthat advance across the terrace and run over the

island. This is more clearly seen in the third panel behaviour to appear, only two requirements must

be fulfilled. First, the currents of adatoms reaching(3.5 ML coverage). For 5.0 ML total thickness

(fourth panel ) we see at the top of the image the a step from both sides must be asymmetric; as we

have seen, Cu(111) – as many other compactremainder of the island, plus a new, smaller one

formed at the bottom; however, the average dis- crystal faces – meets this condition. The second is

that diffusion along the steps be slower than ontance between steps is progressively increasing.

Finally (8.0 ML), the equilibrium terrace size is the terraces [31–34]. This is also a common feature

of fcc-(111) faces, owing to their threefold symme-recovered. This simple kinetic simulation includes

the most relevant characteristics of this system, try [10,35,36 ]. This phenomenon can easily be

detected with TEAS. Near a step edge, the surfacenamely a large ES barrier hindering interlayer

diffusion and an initial surface containing step electronic density is distorted and therefore the He

beam is scattered away from the specular directionbunches; its success to reproduce the main features

of the experiment without any special assumptions [24]. Consequently, the diffracted intensity

decreases even at the out-of-phase condition andprovides additional support.

The question then is how to explain the con- with no variation of the relative occupation of

adjacent terraces. The cross section for diffusetinuous decrease of the specular beam intensity

observed in the second stage of our experiments. scattering from Cu steps, defined as the width of

the distorted area per unit step length, isConventionally, one expects a constant diffracted

intensity during step flow, since this growth mode SCu#12 A [23]. With these data in hand, it is easy

to calculate the total length of steps on the surfaceis assumed to maintain unchanged the surface

morphology. Nevertheless, this is not always the [37] at any time; in this way, one can monitor in

real time during deposition the evolution of stepcase. It is well known that systems with poor

interlayer diffusion (i.e., with large ES barriers) roughness.

Kinetic roughening has been widely studieddevelop increasing roughness due to kinetic restric-

tions [29]. During step flow, in particular, the from the theoretical point of view; several excellent


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 pre-

sented 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 Fig. 9. (a) Evolution of the total length of steps on the surface,

once the growth mode has switched to rough step flow. (b)the behaviour expected from Eq. (5). The valuesTemperature dependence of the roughness exponent b; its varia-of the b exponent, obtained from the slopes oftion reveal the existence of different regimes of adatom diffusion

these fits, are depicted in Fig. 9b. From the evolu-along the steps (see text). The solid line is a guide to the eye.

tion of b with substrate temperature, a consider-

able amount of information on the atomic

mechanisms of edge diffusion can be gathered. A behaviour near 500 K. Lowering the substrate

temperature and restricting diffusion further, thevalue b=0 is expected at high temperature, with

unlimited atomic diffusion along the steps, so that experimentally determined b increases and reaches

a plateau around 3/8, extending between approxi-all roughness derived from kinetic limitations is

suppressed. Extrapolation from our data indicates mately 300 and 400 K. This value corresponds to

the Mullins–Herring (MH) universality class; athat this regime could be reached at temperatures

close to 700 K. In contrast, b=1/4 is predicted for very similar result (0.37) has also been found in

atomistic simulations of growth [40,41] in whichthe Edwards–Wilkinson (EW ) universality class

in (1+1) dimensions, allowing only for a limited atoms are allowed limited displacements along

straight segments of the steps, but cannot turnamount of diffusion between different levels (i.e.,

crossing corners along the rough step line and corners. Below RT, diffusion parallel to the steps

is reduced still further and b approaches 0.5,sticking to the kink site). We observe this kind of


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 sur-

face 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 Fig. 10. S-XRD rod scans along the {1,0} CTR for Cu filmsS-XRD. With this technique, the information grown at different temperatures. The peak developing at l=2

is a Bragg reflection of the twinned structure. The curves haveabout the stacking sequence probed by the X-raybeen shifted vertically for clarity, and the reliability factors x2beam is contained in the so-called crystal trunca-of the corresponding fits are shown near each of them.

tion rods (CTRs) [42]: these are the profiles of

diffracted intensity along a particular direction inThe very intense peaks at l=1, l=4 are bulkreciprocal space, as a function of perpendicular

Bragg reflections of the fcc substrate, while themomentum transfer.peak developing at l=2 signals the appearance ofAs mentioned in Section 1, the main source oftwinned domains. Visual inspection of the experi-structural defects in this system is the existence ofmental data shows that the fraction of twinstwo different, but nearly equivalent, threefoldformed during growth decreases with increasingadsorption sites on the Cu(111) surface. One oftemperature. This fact does not necessarily implythem corresponds to the correct fcc sequence, asthat the probability p

SFalso decreases; to under-dictated by the substrate. Islands nucleated on the

stand these results correctly, one has to keep inother position form stacking faults (SFs) uponmind the transition to step-flow growth takingwhich twin crystallites develop. Twin fcc stackingplace in this temperature range, because all atomssequences are specular reflections from each other;sticking to the substrate steps are forced to followin reciprocal space this results in interchanging thethe same fcc stacking sequence of the Cu crystal.characteristics of the {10} and {01} CTRs. TheApplying our model only to the islands nucleated{00} and its equivalent with zero parallel momen-on the terraces, we find that p

SFactually increasestum transfer are insensitive to these type of defects.

with temperature.Fig. 10 shows a set of rod scans measured onFurther support for our structural descriptionthe {10} CTR after having grown Cu films at

comes from the data obtained in real time duringdifferent substrate temperatures. The full circlesCu deposition, which are depicted in Fig. 11. Hereare the experimental data, and the solid lines arewe show the continuous evolution of the diffractedkinematic fits to them. The latter are based onintensity at point (1,0,1.95)5. In reciprocal space,theoretical structural models constructed using ourwith increasing Cu thickness. The solid lines arekinetic growth equations to determine level occu-

pations, as described in Section 4. Additionally,5 (1,0,2) is the exact Bragg condition for fcc twins.we now consider a probability p

SFto form an SF

Nevertheless, the measurements were not performed at thisat random positions on each atomic level. As is

point in order to avoid the spurious signal due to photons ofcustomary, the fit accuracy is determined from the energy corresponding to the third harmonic of the Si(111) mon-

ochromator crystal.values of the x2 parameter, also listed in the figure.


Fig. 12. Arrhenius plot of the probabilities to form stacking

faults ( pSF

) determined from the fits to the timescans taken inFig. 11. S-XRD timescans showing the evolution with Cu thick-

real time during Cu deposition and listed in Table 1. From theness of the X-ray intensity at point (1,0,1.95) in reciprocal

slope of this line we calculate that the stacking fault energy inspace, which is sensitive to twin formation. The solid lines are

Cu(111) is n1ESF=(21±3) meV, where n1 is the number of

fits obtained describing the growth process with our kineticatoms in the critical nucleus.

model discussed above, and including a probability to nucleate

at random a fraction of islands at hcp positions. The fit parame-

ters are listed in Table 1.

temperature must be given by the Boltzmann factorsimulations obtained using our growth model with

of its adsorption energy. The probability of anthe same parameters A, W

DZdescribed previously,

island nucleating at hcp sites and forming a SF isplus p

SF. The excellent agreement with the data

then:indicates that our model captures the essential

physics of the growth process. The results of thesepSF=expC−

n1(Ehcp−Efcc

)

kB

T D, (7)fits are summarized in Table 1. A was held at 0.0

for all cases.where n1 is the number of atoms in the criticalIt is remarkable that in these fits to a new setnucleus. The experimentally determined values ofof data measured with a different technique wepSF

are displayed in an Arrhenius plot in Fig. 12.obtain the same values of A and WDZ

as in ourFrom the slope of this plot we findTEAS experiments. This lends additional supportn1(Ehcp−Efcc

)=(21±3) meV. Again in this case,to our growth model. Besides, the large values ofwe cannot be more precise because we do notW

DZin this temperature range indicate that the

know the size of the critical nucleus. However, inCu atoms are highly mobile on the surface. Thisthis temperature range one can safely assume thatin turn implies that they probe a large number ofn1 must be 2 or 3. Our estimate for the stacking-sites, both fcc and hcp, before nucleating; thefault energy is then 7–10 meV per atom, in excel-probability of each site being occupied at any finitelent agreement with the value of 10 meV obtained

recently by means of ab initio calculations [43].Table 1

Parameters used in the kinetic growth model to fit the S-XRD Similar values have been reported previously,timescans of Fig. 11. A=0.0 in all cases; W

DZalso agrees well resulting either from calculations [44] or from

with the values found in Section 4estimates based on the value of the activation

energy for self-diffusion [10–12].6T ( K) WDZ

pSF

215 0.60 0.156 Assuming that diffusion on Cu(111) takes place by hop-295 0.85 0.20

ping, then the difference Ehcp−Efcc

must be a fraction of the360 0.92 0.24activation energy for surface diffusion; for experimental results,400 0.96 0.28see Refs. [45,46 ].


[7] G. Ehrlich, F.G. Hudda, J. Chem. Phys. 44 (1966) 1039.6. Summary[8] R.L. Schwoebel, E.J. Shipsey, J. Appl. Phys. 37 (1966)

3682.We have performed a complete, fully detailed

[9] M. Giesen, H. Ibach, Surf. Sci. 431 (1999) 109.study of the morphology and crystalline structure [10] M. Karimi, T. Tomkowski, G. Vidali, O. Biham, Phys.of Cu(111) surfaces and homoepitaxial films. Our Rev. B 52 (1995) 5364.

[11] Y. Li, A.E. DePristo, Surf. Sci. 351 (1996) 189.findings are of fundamental importance, because[12] C.L. Liu, J.M. Cohen, J.B. Adams, A.F. Voter, Surf. Sci.they allow us to identify the elementary atomic

253 (1991) 334.processes such as surface versus step diffusion that[13] J. Camarero, J. Ferron, V. Cros, L. Gomez, A.L. Vazquez

control the accumulation of roughness. In addi-de Parga, J.M. Gallego, J.E. Prieto, J.J. de Miguel, R.

tion, the applicability of these results to other Miranda, Phys. Rev. Lett. 81 (1998) 850.systems must be wide ranging, because they ulti- [14] S. Ferrer, F. Comin, Rev. Sci. Instrum. 66 (1995) 1674.

[15] H.A. van der Vegt, M. Breeman, S. Ferrer, V.H. Etgens,mately derive from very general characteristics ofX. Torrelles, P. Fajardo, E. Vlieg, Phys. Rev. B 51the substrate surface, such as the existence of high(1995) 14 806.ES barriers or two similar adsorption sites. In

[16 ] J. Uppenbrink, R.L. Johnson, J.N. Murrell, Surf. Sci. 304particular, these factors have been known to

(1994) 223.hamper the preparation of high-quality heteroepi- [17] N.C. Bartelt, personal communication.taxial films, with potential applications in nano- [18] J.E. Prieto, Ch. Rath, S. Muller, R. Miranda, K. Heinz,

Surf. Sci. 401 (1998) 248.technology [47]. In order to solve these difficulties[19] F. Jona, P.M. Marcus, in: J.F. van der Veen, M.A. vanit is necessary to use more efficient growth methods

Hove (Eds.), The Structure of Surfaces II, Springer,such as surfactants. The modifications of Cu(111)Berlin, 1987.

homoepitaxy provoked by a surfactant layer of Pb[20] M.A. van Hove, S.W. Wang, D.F. Ogletree, G.A. Somor-

will be the subject of a forthcoming publication jai, Adv. Quantum Chem. 20 (1989) 1.[48]. [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.Acknowledgements [23] A. Sanchez, S. Ferrer, Surf. Sci. 187 (1987) L587.

[24] B. Poelsema, G. Comsa, Scattering of Thermal Energy

Atoms, Springer Tracts in Modern Physics, Vol. 115,We are grateful to the staff of the ESRF forSpringer, Berlin, 1989.their help during the realization of our experiments

[25] X. Torrelles, H.A. van der Vegt, V.H. Etgens, P. Fajardo,there, and to Prof. I. Markov and Drs. M.C.J. Alvarez, S. Ferrer, Surf. Sci. 364 (1996) 242.

Bartelt and N.C. Bartelt for their critical reading[26 ] P.I. Cohen, G.S. Petrich, P.R. Pukite, G.J. Whaley, Surf.

of the manuscript and their valuable comments. Sci. 216 (1989) 222.Work by the Spanish group has been supported [27] W. Wulfhekel, N.N. Lipkin, J. Kliewer, G. Rosenfeld, L.C.

Jorritsma, B. Poelsema, G. Comsa, Surf. Sci. 348 (1996)by the CICyT under Grant MAT98-0965-C04-02.227.

[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.), Morpho-References logical Organization in Epitaxial Growth and Removal-

Series on Directions on Condensed Matter Physics Vol. 14,

World Scientific, Singapore, 1998, p. 94.[1] J.W. Gibbs, Trans. Conn. Acad. 3 (1878) 343.[30] G.S. Bales, A. Zangwill, Phys. Rev. B 41 (1990) 5500.[2] W. Kossel, Nachr. Ges. Wiss. Gottingen Math. Phys. K1.[31] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34 (1963) 323.135 (1927).[32] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1963) 444.[3] I.N. Stranski, Z. Phys. Chem. 36 (1928) 259.[33] R.Q. Hwang, J. Schroder, C. Gunther, R.J. Behm, Phys.[4] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. R.

Rev. Lett. 67 (1991) 3279.Soc. London 243 (1951) 299.[34] M.C. Bartelt, J.W. Evans, Surf. Sci. 314 (1994) L829.[5] A. Golzhauser, G. Ehrlich, Phys. Rev. Lett. 77 (1996)

[35] Z. Zhang, X. Chen, M.G. Lagally, Phys. Rev. Lett. 731334.

[6 ] K.R. Roos, M.C. Tringides, Surf. Rev. Lett. 5 (1998) 833. (1994) 1829.


[36 ] C.L. Liu, J.B. Adams, Surf. Sci. 265 (1992) 262. [43] P.J. Feilbelman, personal communication.

[44] S. Crampin, K. Hampel, D.D. Vvedensky, J. MacLaren,[37] J.J. de Miguel, A. Cebollada, J.M. Gallego, J. Ferron, S.

Ferrer, J. Cryst. Growth 88 (1988) 442. J. Mater. Res. 5 (1990) 2107.

[45] G. Ehrlich, MRS Symposia Proceedings, No. 57, Materials[38] J. Krug, Adv. Phys. 46 (1997) 139.

[39] A.-L. Barbasi, H.E. Stanley, Fractal Concepts in Surface Research Society, Pittsburgh, PA, 1987.

[46 ] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley Inter-Growth, Cambridge University Press, Cambridge, 1995.

[40] S. Das Sarma, P.I. Tamborenea, Phys. Rev. Lett. 66 science, New York, 1982.

[47] J. Camarero, L. Spendeler, G. Schmidt, K. Heinz, J.J. de(1991) 325.

[41] P.I. Tamborenea, Z.-W. Lai, S. Das Sarma, Surf. Sci. 267 Miguel, R. Miranda, Phys. Rev. Lett. 73 (1984) 2448.

[48] J. Camarero, J. de la Figuera, J. Alvarez, M.A. Nino, S.(1992) 1.

[42] I.K. Robinson, Phys. Rev. B 33 (1986) 3830. Ferrer, J.J. de Miguel, R. Miranda, in preparation.

structural characterisation and homoepitaxial growth on cu(111)

Documents