Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)
ABSTRACT We consider the influence of realistic island diffusion rates to homoepitaxial growth on metallic surfaces using a recently developed rate equation model which describes growth in the submonolayer regime with hyperthermal deposition. To this end, we incorporate realistic size and temperature-dependent island diffusion coefficients for the case of homoepitaxial growth on Cu(1 0 0) and Cu(1 1 1) surfaces. We demonstrate that the generic features of growth remain unaffected by the details of island diffusion, thus validating the generic scenario of high density of small islands found experimentally and theoretically for large detachment rates. However, the details of the morphological transition and scaling of the mean island size are strongly influenced by the size dependence of island diffusion. This is reflected in the scaling exponent of the mean island size, which depends on both temperature and the surface geometry.
Article: Jump processes in surface diffusion[show abstract] [hide abstract]
ABSTRACT: The traditional view of the surface diffusion of metal atoms on metal surfaces was that atoms carry on a random walk between nearest-neighbor surface sites. Through field ion microscopic observations and molecular dynamics simulations this picture has been changed completely. Diffusion by an adatom exchanging with an atom of the substrate has been identified on fcc(110), and subsequently also on fcc(100) planes. At elevated temperatures, multiple events have been found by simulations in which an atom enters the lattice, and a lattice atom at some distance from the entry point pops out. Much at the same time the contribution of long jumps, spanning more than a nearest-neighbour distance, has been examined; their rates have been measured, and such transitions have been found to contribute significantly, at least on tungsten surfaces. As higher diffusion temperatures become accessible, additional jump processes can be expected to be revealed.Surface Science Reports - SURF SCI REP. 01/2007; 62(2):39-61.
- [show abstract] [hide abstract]
ABSTRACT: The miniaturization of electronics in the past decades has lead to a situation where the size of current state-of-the-art microelectronic devices is approaching the nanometer length scale. The current methods of microelectronics, which can be used to control the fabrication of the manufacturing on atomic level, can be used only in limited conditions, and new methods are needed. This is especially acute as the recent advances in nanotechnology have given new tools for further development in microelectronics. Molecular Beam Epitaxy (MBE) is currently perhaps the most important atomic scale method for fabricating epitaxial thin films. The quality of films is very high and control over the growth of them is possible on the atomic scale. However, the MBE method works only under quite restricted growth conditions. At low temperatures it often leads to rough surfaces and three dimensional structures instead of smooth epitaxial films. The same happens when the deposition flux is increased. The limiting factor is the rate of surface diffusion, which should be high compared to the deposition rate, in which case the deposited atoms have enough time to diffuse on the surface and form clusters. In this Thesis submonolayer growth has been studied using Rate Equation formulation. Rate equations provide a flexible and computationally effective tool to model complex island growth phenomena and are particularly suitable in ion beam assisted deposition (IBAD) and low energy ion deposition (LEID) type of growth conditions. In IBAD and LEID the surface is under constant ion bombardment and growth is thus explicitly a nonequilibrium phenomenon. The advantage of such Hyperthermal Deposition (HTD) methods over the MBE is a higher deposition rate during the growth process. Also, control over the quality of the atomic layers is better. The results presented in this Thesis suggest that there is possible improvement to be gained from experimental studies of submonolayer island growth. A more detailed knowledge of diffusion of islands on different surfaces and the detailed measurements of island break-up probabilities under various growth conditions could lead to more quantitative descriptions of growth in computationally inexpensive and flexible models, which could be used to find the optimal growth conditions and extend the limits of the current thin film manufacturing methods. TKK dissertations, ISSN 1795-4584; 99978-951-22-9113-7.
arXiv:cond-mat/0507426v1 [cond-mat.mtrl-sci] 18 Jul 2005
Diffusion and submonolayer island growth
during hyperthermal deposition on Cu(100)
M.O. Jahmaa,b, M. Rusanena,∗, A. Karimd, I.T. Koponenb,
T. Ala-Nissilaa,c, and T.S. Rahmand
aLaboratory of Physics, P.O. Box 1100, Helsinki University of Technology,
FI-02015 TKK, Espoo, Finland
bDepartment of Physical Sciences, P.O. Box 64, FI-00014 University of Helsinki,
cDepartment of Physics, Box 1843, Brown University, Providence, RI 02912–1843
dDepartment of Physics, Cardwell Hall, Kansas State University, Manhattan, KS
We consider the influence of realistic island diffusion rates to homoepitaxial
growth on metallic surfaces using a recently developed rate equation model which
describes growth in the submonolayer regime with hyperthermal deposition. To this
end, we incorporate realistic size and temperature-dependent island diffusion coef-
ficients for the case of homoepitaxial growth on Cu(100) and Cu(111) surfaces. We
demonstrate that the generic features of growth remain unaffected by the details
of island diffusion, thus validating the generic scenario of high density of small is-
lands found experimentally and theoretically for large detachment rates. However,
the details of the morphological transition and scaling of the mean island size are
Preprint submitted to Surface Science2 February 2008
strongly influenced by the size dependence of island diffusion. This is reflected in
the scaling exponent of the mean island size, which depends on both temperature
and the surface geometry.
Key words: submonolayer island growth, hyperthermal deposition, diffusion,
Hyperthermal deposition (HTD) techniques, such as ion-beam assisted depo-
sition (IBAD) and low-energy ion deposition (LEID)  have recently been
shown to have great potential in controlling and improving the properties of
thin films as grown by molecular beam epitaxy. In HTD the island density
is larger, the average island size is smaller [2,3], and island size distributions
are considerably broader [1,3] than in ordinary thermal deposition. Possible
atomistic processes responsible for these effects include ion enhanced mobili-
ties, cluster dissociation , and defect creation during deposition [2,4].
A particularly striking observation made in the LEID experiments is that with
different deposition energies an anomalously high density of small islands is
observed, with the scaled distribution function behaving as f(x) ∼ 1/x for
x < 1 . We have recently shown using the rate equation (RE) approach
[5,6] that this anomalously high density of small islands is due to a unique
balance between island–island aggregation and enhanced adatom detachment.
These studies were aimed at describing the generic features of HTD, and thus
Email address: Marko.Rusanen@tkk.fi (M. Rusanen).
relatively idealized approximations for the terms in the rate equations were
used to obtain analytical estimates for the relevant growth exponents and
the scaling function. One of the most important questions that still remains
open is the role of island diffusion, since for mobile islands the aggregation
rates in the RE approach depend explicitly on the diffusion coefficients Ds
of islands of different sizes s. Island diffusion on surfaces has been studied
both theoretically [7,8,9] and experimentally [10,11,12,13,14,15,16]. While in
the large island limit the size dependence of the island diffusion coefficients
can be classified based on simple basic processes , for smaller islands Ds
depends on the geometric and energetic details of the underlying surface, and
can be a complicated, non-monotonic function of s [18,19].
In this work, our aim is to explore in detail the influence of realistic island
diffusion coefficients to submonolayer growth with HTD. To this end, we em-
ploy the RE model of Ref.  and replace the usually assumed idealized power
law forms of Dswith realistic, temperature and size–dependent diffusion co-
efficients Ds(T) for Cu on Cu(100) and Cu(111) surfaces. These two systems
highlight the large differences which occur for surfaces with different geome-
try and energetics. We demonstrate that while the scaling function of the size
distribution is largely unaffected by the details of the diffusion coefficients, the
quantitative values of the growth exponents are sensitive to island diffusion.
These predictions can be easily tested by HTD experiments on different Cu
In HTD the reversibility of growth is manifested through enhanced adatom
detachment from islands [1,4]. Detachment and island mobility allow us to ne-
glect spatial correlations between islands [20,21,22,23], which justifies the rate
equation description of the problem. Thus, growth is driven by the interplay
between aggregation and detachment, and can be schematically expressed to
be composed of reversible events Ai+ Aj→ Ai+j; Aj→ A1+ Aj−1between
islands of sizes i and j with the rates of aggregation and detachment specified
by reaction rates K(i,j) and F(i,j), respectively. The corresponding REs for
the areal density nsof islands of size s ≥ 1 read as [23,24]
[K(s,j)nsnj− F(s,j)ns+j] + Φδ1s, (1)
where Φ is the deposition flux of adatoms in monolayers per second (ML/s).
The aggregation rate K(i,j) for islands of sizes i and j with diffusivities Di
and Djis given by the Smoluchowski formula K(i,j) ∝ (Di+Dj), which is also
consistent with the point island approximation used here [20,24]. Previously
 we used a power-law form for the diffusion coefficients Di ∼ i−µwith
1 ≤ µ ≤ 2 appropriate for island diffusion on metal surfaces. In order to
study the effects of details of the aggregation rates in observable quantities
we replace the idealized power-law form by realistic size and temperature
dependent diffusion coefficients, as discussed below in more detail.
The detachment rate of adatoms from islands of size i + j = s depends on
the island size, but only detachment of single adatoms is allowed. Thus the
detachment rate is given by F(i,j) = F0(i+j)α(δ1i+δ1j), where the exponent
α is in principle a parameter, but is chosen to be α = 1/2 in the present study.
In LEID this form for the detachment rate is physically a well justified choice,
because in the regime of bombarding energies from 10 eV to 100 eV adatom
detachment dominates and island breakup into larger pieces is not expected
to occur [4,25]. Moreover, since every deposition event at the vicinity of an
island boundary can be assumed to detach adatoms at least with a probability
proportional to the island perimeter (i.e. s1/2), α = 1/2 is a reasonable lower
limit. This has been also confirmed by recent Molecular Dynamics simulations
on ion bombardment enhanced detachment in island size region up to 25 atoms
where values of 0.4 < α < 0.6 were found .
We solve the rate equations using the particle coalescence method (PCM)
[22,20,24]. PCM employs a point-island approximation, which is valid at low
coverages or large island separations. In PCM aggregation and detachment
events occur with probabilities specified by the corresponding reaction ker-
nels, and the deposition with the rate proportional to the given adatom flux.
An event is then randomly chosen with a probability weighted by the corre-
sponding rate. Since REs describe the system in the mean-field limit, there is
no information on spatial correlations in the system. Therefore, in the simula-
tions it is sufficient to construct a list of islands, which does not correspond to
a physical lattice. To conduct an aggregation event, for example, two islands
are randomly chosen from the list, and an attempt to aggregate them is made.
The complete mixing of the islands required by the mean-field approximation
 is thus implemented much faster than including island jumps into empty
lattice sites .