The surface morphology of a growing crys

1062

Surface Science 189/190 (1987) 1062-1068
North-Holland, Amsterdam

THE SURFACE MORPHOLOGY OF A GROWING CRYSTAL STUDIED
BY T H E R M A L E N E R G Y A T O M S C A T I ' E R I N G ( T E A S )
J.J. DE M I G U E L , A. S , ~ N C H E Z , A. C E B O L L A D A , J.M. G A L L E G O ,
J. F E R R O N and S. F , E R R E R
Departamento de Fisica de la Materia Condensada, C-Ill, Facultad de Ciencias,
Unwersidad Autbnoma de Madrid, Cantoblanco, 28049-Madrid, Spain

Received 31 March 1987; accepted for publication 16 April 1987

The growth of a Cu(100) surface from its vapour has been investigated by TEAS-for different
surface temperatures. The specularly reflected intensity of the growing surface shows temporal
oscillations for in-phase and out-of-phase scattering conditions. In-phase data have been analyzed
in terms of the diffuse scattering from the surface steps whereas out-of-phase oscillations in terms
of a kinematical and purely elastic description of the scattering from a random distribution of
terraces. In both cases the temporal evolution of the step concentration of the growing crystal was
obtained. Also, the surface diffusion coefficient of Cu adatoms was directly estimated from the

experiments resulting in a preexponential of l a x 10 -4 cm2 s -1 and an activation energy of 0.40
eV.

1. Introduction
The characterization of the m o r p h o l o g y of thin films grown by v a p o u r
deposition is one of the major areas bridging basic surface science with
technological necessities in s e m i c o n d u c t o r i n d u s t r y or materials research. The
quality of epitaxial films and of their interfaces with different materials is a
crucial p a r a m e t e r for d e t e r m i n i n g the characteristics of electronic devices or
superlattices.
In principle several surface science, d i f f r a c t i o n - b a s e d techniques are adequate for studying a growing film since they p r o v i d e average i n f o r m a t i o n over
large areas of the surface which is c o m m o n l y w h a t is desired. A l t h o u g h L E E D
is by far the most p o p u l a r one, multiple diffraction effects a n d geometrical
constraints usually complicate the characterization of a film surface while it is
growing. As the geometry is m o r e suitable in R H E E D , this technique is
nowadays widely used in M B E studies of growing films since the early works
[1,2] which revealed t e m p o r a l intensity oscillations in the features of the
R H E E D p a t t e r n from a growing G a A s surface. However, as discussed in
detail in the literature [3] a simple i n t e r p r e t a t i o n of the intensities on the basis
of a kinematical a p p r o x i m a t i o n , often reveals to be inadequate. D u e to that

0039-6028/87/$03.50 9 Elsevier Science Publishers B.V.
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J.J. de Miguel et al. / Surface morphology of a growing crystal

1063

obtaining morphological parameters such as the density of surface steps as a
function of growing time is, in many cases, impossible. TEAS is also a
diffraction technique and has the advantage that it is purely kinematical
allowing a relatively straightforward interpretation of the data. A previous
study in our laboratory revealed that, as in RHEED, layer-by-layer type of
growth of a crystal surface from its own vapour causes temporal oscillations in
the specularly reflected intensity [4]. In the present paper, a more detailed
analysis of the intensity oscillations on a Cu(100) surface while it is growing
from its own vapour is reported. Two similar but conceptually different
experiments allowed to independently determine the surface concentration of
steps during growth, obtaining agreement within the limitations of the data.
Also the surface diffusion coefficient (preexponential and activation energy)
was directly obtained from the experiments.

2. Experiment
The experimental set-up has been previously described in detail [5]. A
mono-energetic helium beam (k = 11 A-1) collides with the crystal surface at
a variable incidence angle and the specularly reflected intensity is detected
with a movable quadrupole. A home-made Cu evaporator is mounted inside
the chamber and directed towards the surface after collimation. The basic
experiment consisted in monitoring the specularly scattered He beam intensity
as a function of time while Cu was being deposited on the surface. This was
performed for a variety of incidence angles and surface temperatures.

3. Results
The clean and well ordered Cu(100) surface consisted initially in a distribution of terraces limited by steps of monoatomic height as revealed by the
analysis of the rocking curve [4,6] (specular intensity versus incidence angle).
From the maxima and minima of the rocking curve, scattering conditions
satisfying constructive or destructive interference along the surface normal
could be chosen.

3.1. Constructive interference
For an incidence angle 0i = 61.6 o from the surface normal, the scattering

intensities from terraces at different surface levels interfere constructively,
therefore the scattered intensity is unsensitive to the surface terrace distribution except for the diffuse scattering from the step edges. In previous experiments [7] we measured a value o f 13 ~, per unit step length for the cross

1064

J.J. de Migue[ et al. / Surface morphology of a growing crystal

DESIRUCT'[VEINTERFERENCE

CONSTRUCTP,
EJNTERFERENCE

T =367K

1,01

::330 K

I-0

J~ /~ ,I ~
T:367K

s

\

T:3~BK

T=330K
0.5
0 . 5 ~
i

l

I

t

I

t

T--318K

l

E'vAPO~ATION T: ME ira:n:

EVAPORATIONTIME { rain,]

Fig. 1. Temporal evolution of the specularly reflected He intensity (normalized to the intensity
before deposition) as a function of deposition time for different surface temperatures. The
scattering conditions were chosen to be in-phase (left-hand side) and out-of-phase (fight-hand
side).

section for diffuse scattering of steps in the Cu(100) surface, in good agreement with ref. [8]. This value means the distance normal to the step edge over
which the surface is not reflective for scattering of He atoms. The evolution of
the specular intensity versus deposition time at temperatures in the range

300-420 K displayed damped oscillations as may be seen in the left-hand side
of fig. 1. The oscillating behaviour indicates growth by nucleation of Cu
islands on top of the substrate terraces. These islands are of mono-atomic
height [4] and the atoms at their edges may be viewed as step atoms [6]. The
minima in the relative intensity (i.e. maxima in the diffuse scattering) correspond to maximum perimeter of the growing islands. These have been found
to occur approximately at coverages equal to 1 / 2 , 3 / 2 , 5 / 2 . . . . deposited
monolayers. The maxima in the I / I o curves occur at completion of successive
m0nolayers.
If 2~ denotes the scattering cross section per unit length (13 ,~) and d the
nearest neighbour distance for surface atoms (2.55 ,~) then
t / l o = (1 2,
(1).
where 8st is the fraction of surface atoms in step sites (/9~t does not include the
steps already present at t = 0 since the intensity is normalized to Io). Eq. (1)

J.J. de Miguel et al. / Surface morphology of a growing crystal

1065

Table 1

Constructive interference (~st X 100)
T (K)

318
330
367
403
415

0 (ML)

Stationary

0.5

1.0

1.5

2.0

1.9
1.4
1.3
0.4
0.2

1.1
0.8
0.6
0.2
0.0

1.9
1.3
1.3
0.3
0.2

1.3

0.9
0.7
0.1
0.1

2.0
-2.0
1.2
0.1
0.0

and the experimental data displayed in the left-hand side of fig. 1 allow to
determine the temporal evolution of the step concentration at the surface
while the crystal is growing. Table 1 illustrates some of the results at different
temperatures. As may be seen the step concentration at a given deposited
coverage decreases for increasing temperatures indicating larger islands. At
temperatures of 420 K or above, no oscillations appear in 1/10 meaning that
the growth does not occur through island nucleation but that the adatoms
diffuse to the surface steps, that act as sinks. In these cases the crystal grows
by lateral displacement of the already existing steps and the step concentration

remains stationary. At lower temperatures where nucleation takes place, the
oscillations are damped and 1/10 practically levels off after a number of
layers have been completed. At this moment the surface may be visioned as a
mosaic of terraces bounded by steps whose separation is small enough so that
adatoms can reach them. Then again the growth occurs via step propagation.
In the last column of table 1, the step concentration for this (almost)
stationary situation is shown. It diminishes for increasing temperatures indicating that the terraces are larger.

3.2. Destructiue interference
In this case He atoms specularly reflected from two adjacent terraces at two
different levels separated by one atom height have a phase difference of an
odd multiple of ~r. If one assumes that the non-reflective area around a step is
evenly distributed at both sides of the step edge (6.5 ~, each side in our case)
then it may be easily seen that the specularly reflected intensity from a
distribution of terraces at different levels only depends on the balance between
the sizes of the terraces at different heights and it is unaffected by the diffuse
scattering from the steps. Due to that one may ignore the diffuse scattering
and analyze the intensity variations in terms of an elastic description of the
scattering process. A previous paper by Lapujoulade [9] studies in detail the
elastic scattering of He atoms from. randomly stepped surfaces and we have
utilized it as a basis for analyzing our data of the growth process. The

1066

J.J. de Miguel et al. / Surface morphology of a growing crystal

Table 2
Destructive interference (0~t x 100)
T (K)

318
330
367
379
415

Stationary

0 (ML)
0.5

1.0

1.5

2.0

2.5
2.1
1.8
1.4
0.8

1.4
1.2
1.0
0.9
0.7

2.3
2.0
1.9
1.4
0.9

1.8
1.3
1.2
1.0
0.8

2.3
1.8
1.6
1.3
0.9

right-hand side of fig. 1 shows the intensity oscillations for destructive
interference scattering conditions (0 i = 66.6~ The qualitative behaviour of
the oscillations is similar to that observed for in-phase conditions. The
amplitudes are noticeably larger in this case. In order to extract from these
data the step concentration as a function of deposition time by using the
formalism of Lapujoulade without any adjustable parameter, the step concentration at t = 0 was independently measured in a direct way by decorating
the steps with foreign atoms as previously described [10]. Representative
results are shown in table 2. As may be seen, at a fixed deposited coverage, the
step concentration decreases with increasing temperature indicating larger
islands. By comparing with table 1 one may note that the agreement between
both sets of results is good within a factor of two for all temperatures except
415 K. The discrepancy at this temperature is probably due to the poor quality
of the experimental data under constructive interference conditions. Note that
both sets of experiments are conceptually different and lead to basically the
same result in terms of step concentration. To our knowledge these constitute
the first quantitative evaluations of the morphology of a growing crystal.

3.3. Surface diffusion coefficient
The surface diffusion coefficient of deposited Cu adatoms may be estimated as will be illustrated in what follows. Let us consider the stationary
situation of growth where no island nucleation occurs. This implies that
deposited adatoms reach the step edges causing step propagation. In this
situation the diffusive displacement of an adatom must be of the order of the
size of the terrace where it is lying. If A denotes the mean terrace size, then
is the
from the Einstein relation A = (D~) 1/2 where D = D O e x p ( - E a / k T )
diffusion coefficient and T is the time interval for the random walk of the
adatom. As discussed in detail by Madhukar [11], ~" is the average time
interval between the arrival of two consecutive atoms to the terrace under
consideration. Therefore z = (FA2) -1 where F denotes the incident flux. By
eliminating z one gets D = FA 4. This expression allows to determine D

J.J. de Miguel et a L / Surface morphology of a growing crystal

/,50
10-81

TEMPERATURE [K]
350
300

400
I

tn

1067

1

I

o\

r~E 10- 9

Z
w

o

u_

o

3 10-10
Z
0

Lt_
t~
C3

10-11

I
2,5

I
3.0
1/T

I
3.5
110-3.K -1 ]

Fig. 2. Arrhenius plot of the surface diffusion coefficient for Cu adatoms on Cu(100).

provided F and A are known. As discussed in ref. [9], in a mean field
approach, one has A = d/Ost. By substituting the values of 0st of the right-hand
column in table 2 one may thus obtain A and D. In our experiments
F = 4.4 X 1013 atoms cm -2 s -1 (this corresponds to one atomic layer being
deposited every 35 s). Fig. 2 shows an Arrhenius plot of D versus 1/T. F r o m
the slope one obtains E a = 0.40 eV and from the ordinate at the origin
D O = 1.4 x 10 -4 cm 2 s -1. A similar analysis to obtain the surface diffusion
coefficient has been previously performed by Neave et al. [12] and later by
Van Hove and Cohen [13] by studying R H E E D oscillations and profiles of the
specular beam in GaAs growth with MBE. Both groups reported values for the
diffusion coefficient of G a a d a t o m s obtaining at T = 877 K, D = 3 X 10 -13
cm 2 s -1. F r o m our data we obtain for Cu on Cu(100) D = 4 x 1 0 - 7 c m 2 s -1 at
T = 877 K, which looks reasonable [14]. Although both surfaces (GaAs and
Cu) are very different in nature, a difference of six orders of magnitude in D

1068

J.J. de Miguel et al. / Surface morphology of a growing crystal

seems to be too high. We think that the analysis of the above mentioned
groups is incorrect since they suppose that r is the time required to deposit
one monolayer of Ga atoms, which is typically a few seconds. In our case, for
terrace sizes of several hundred hngstr~Sms, we obtain r values in the range
10-2-10 -3 s, meaning that the reported diffusion coefficients in refs. [13,14]
should be decreased by two or three orders of magnitude.
Finally, preliminary results of a Monte Carlo study of the growing crystal
show that the experimental I / I o versus time data may be reproduced by only
assuming that the critical island size is a trimer in the range of temperatures
investigated.

Acknowledgments
Thanks to Dr. J.M. Soler for discussion. This work has been supported by
the CAICyT under Grant No. 387/84 and by the Spain-US Joint Committee
for Scientific Research under Grant CCA-8411063. One of us (J.F.) acknowledges a Fellowship of the Consejo Nacional de Investigaciones Cientificas y
Trcnicas of Argentina.

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[4] L.J. Grmez, S. Bourgeal, J. I b ~ e z and M. Salmerrn, Phys. Rev. B31 (1985) 2551.
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