Surface diffusion dewetting of thin solid films: Numerical method and application to Si/ SiO
2
E. Dornel,* J-C. Barbé, F. de Crécy, and G. Lacolle
CEA-DRT-LETI - CEA/GRE- 17, rue des Martyrs, 38054 Grenoble cedex 9, France
J. Eymery
Équipe mixte CEA-CNRS-UJF, Nanophysique et Semiconducteurs, CEA/DRFMC/SP2M, 17, rue des Martyrs,
38054 Grenoble cedex 9, France
Received 18 October 2005; revised manuscript received 30 January 2006; published 27 March 2006
A method has been developed to calculate and use a surface chemical potential which is valid in the large
curvature regime for any surface energy function. It is applied to the solid-phase dewetting of a finite film with
an initial rectangular profile and considers the surface diffusion mechanism. For an isotropic surface energy,
the film aspect ratio and the adhesion energy between the film and the substrate are shown to be the main
parameters that quantify the retraction, the breaking time, and the number of agglomerates. Moreover, it is
found that mild surface energy anisotropy with an energy minimum in the horizontal plane postpones the mass
detachment. Simple models of the -plots for the surface energy illustrate the influence of cusp points on the
retraction profiles. Finally, the smooth and facetted experimental surfaces, that are observed in the Si/ SiO
2
system after 900 ° C annealing under H
2
, are explained by a quite small anisotropy of the -plot.
DOI: 10.1103/PhysRevB.73.115427 PACS numbers: 68.35.p, 68.55.Jk, 68.37.d, 81.16.Rf
I. INTRODUCTION
Thin solid films are basic building blocks in microelec-
tronics and optoelectronics. However, due to the shrinking of
the layer thickness imposed by technology requirements, the
surface to volume ratio is drastically increased and this leads
to capillarity instabilities. To ensure device reliability, these
morphological instabilities of stacked layers must be con-
trolled during the elaboration process to avoid an agglomera-
tion phenomenon that occurs well below the melting tem-
perature. For example, it has been observed that during a
classical thermal annealing at 850 ° C 2/3 of the Si melt-
ing temperature, a 10.5 nm silicon on insulator SOI film
can be fully agglomerated in a few minutes.
1
It has been
reported that the thinner the Si film is, the quicker the ag-
glomeration occurs.
1
More generally, the thermal stability of
silicon
1–10
and metals
11–13
on amorphous substrates has been
intensively studied.
In order to prevent the morphological evolution of the
thin films, the influence of the main physical ingredients
must be identified. It is well known that an unstrained nearly
plane infinite solid surface flattens due to capillarity effects,
14
whereas the boundaries of thin patterns must be considered
as destabilizing zones because they do not usually minimize
the surface energy.
15
At a temperature between half and two
thirds of the melting temperature of a crystalline material, it
is generally assumed that surface diffusion dominates the
other transport processes of matter, namely viscous flow,
evaporation/condensation, and volume diffusion.
14,16,17
Wong has studied the surface morphology evolution driven
by surface diffusion in the case of semi-infinite, isotropic,
and unstrained film using a numerical approach.
15,18
For typical annealing temperatures in the 650 ° C – 900 ° C
range, it has been shown that specific directions are favored
during the retraction of a Si film from a SiO
2
substrate.
3–6
This indicates that the anisotropy of surface energy and/or
diffusion needs to be taken into account. The surface diffu-
sion anisotropy has not been seen to be sensitive in two
dimensions this paper’s framework, contrary to the surface
energy anisotropy see hereafter. Moreover, a 1 nm Si film
not voluntarily strained on SiO
2
has a residual biaxial stress
of less than 100 MPa grazing incidence x-ray diffraction
GIXRD measurements have been performed to confirm this
point. Considering the Grinfeld-Azaro-Tiller instability, this
stress state is not destabilizing for continuous films thinner
than 15 nm.
19
In consequence, this paper focuses on the ef-
fect of the anisotropy of the surface energy neglecting the
strain energy. This paper will address the general problem of
the two-dimensional 2D retraction of a finite anisotropic
film from a rigid substrate. An interesting case to study is an
initial sharp step profile as shown in Fig. 1a. This profile,
representing for example a patterned SOI substrate, exhibits
two singular points: the upper corner and the contact point
with the substrate. It is generally calculated
15,18
and con-
firmed by our experiments see hereafter Fig. 11 that the
film retracts with a thickened edge followed by a valley as
shown in Fig. 1b. The film may pinch off after a breakup
time called t
c
. Phenomenology and dynamics differ with re-
gard to the aspect ratio of the initial patterned film and the
contact angle. In this paper, a discrete calculation of the sur-
face chemical potential is developed to take large curvature
morphologies and mass conservation into account. This will
be applied to the solid-state dewetting phenomenon to under-
stand the influences of the contact angle and aspect ratio.
This approach can also be used to simulate other physical
problems such as hole growth or thermal grooving. It allows
taking the anisotropy of the physical properties that signifi-
cantly alter the dynamics of the shape evolution
20
into ac-
count, as well as the final equilibrium shape known as the
Wulff’s construction.
21
The following section presents the physical basis of the
problem. The numerical method used to solve the evolution
equations is described in Sec. III, applied to the dewetting of
a finite solid film with different aspect ratios and compared
PHYSICAL REVIEW B 73, 115427 2006
1098-0121/2006/7311/11542710/$23.00 ©2006 The American Physical Society 115427-1