Observation of nanometer waves along fracture surface

Article abstract of DOI:10.1016/j.cplett.2004.05.012

The fracture in solid materials is ideally referred as a two-dimensional surface formed by a crack moving through a planar, straight-line path. In reality, the fracture has a complicated morphology. Recent studies have developed a dynamic model in which, a moving crack results in three-dimensional, elastic waves that generate morphology along the fracture surface. The waves are defined by their wavelengths of millimeters or higher scales. We present the observation of nanometer waves along the fracture surface of the silicon dioxide layers (thickness ～0.5-2 μm). These waves with the wavelengths of ～200 nm form a well-defined surface structure.

Full text of DOI:10.1016/j.cplett.2004.05.012

Chemical Physics Letters 391 (2004) 385–388
www.elsevier.com/locate/cplett
Observation of nanometer waves along fracture surface
*
Nguyen H. Tran , Robert N. Lamb
School of Chemistry, University of New South Wales, Sydney 2052, Australia
Received 22 March 2004; in final form 4 May 2004
Available online 1 June 2004
Abstract
The fracture in solid materials is ideally referred as a two-dimensional surface formed by a crack moving through a planar,
straight-line path. In reality, the fracture has a complicated morphology. Recent studies have developed a dynamic model in which,
a moving crack results in three-dimensional, elastic waves that generate morphology along the fracture surface. The waves are
defined by their wavelengths of millimeters or higher scales. We present the observation of nanometer waves along the fracture
surface of the silicon dioxide layers (thickness ꢀ0.5–2 lm). These waves with the wavelengths of ꢀ200 nm form a well-defined
surface structure.
Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction
energy. This is commonly referred to as a Hopf bifur-
cation [4–6].
Many recent studies have focused on the elastic waves
formed by a moving crack. These waves with intrinsi-
cally three-dimensional property do not exist in the
classical theories of crack propagation [1]. Their for-
mation provides an explanation of the complex fracture
morphology in nature (e.g. rock patterns) [2,3].
The average wavelengths of these waves are usually of
millimeters or higher scales, although the wavelengths of
several micrometers have recently been observed [2]. In
this Letter, nanometer scale waves are reported. These
nano-waves are uniformly distributed along the fracture
surface of the amorphous SiO2 thin film layers. They
generate a well-defined surface structure not observed
previously at nano-scale. Previous studies have sug-
gested that the fracture surface remains rough at this
scale [7]. The roughness is varied with varying the
cracking energy and crystallographic properties. In our
experiments, the formation of nano-waves is favoured as
the thermal stress in the films increases.
The mechanism of formation of waves in an ideal,
homogeneous material is related to the instability of the
propagation of a straight crack. Sharon et al. have
shown that when a crack propagates at a speed of ap-
proximately 0.4 the speed of sound across a free surface
(i.e. Rayleigh speed, ꢀ3.3 km sꢁ1), it becomes unstable
and will proceed via formation of micro-branches [2].
Branching leads to the increase of cracking energy and
triggers the formation of waves. Similarly in heteroge-
neous materials, interaction of the crack with material
inhomogenity leads to an energy fluctuation that also
generates the waves via formation of micro-branches [2].
The thermal stress in the material also influences the
formation of waves. In particular, a transition from
straight to wavy fracture occurs as the thermal stress
increases, due to the concomitant increase of cracking
2. Results and discussion
The nano-waves are created spontaneously following
cleaving the micrometer thick, amorphous films of sili-
con dioxide (Fig. 1). These waves form the mirror im-
ages on the opposing fracture plane. For the film with
thickness of ꢀ2 lm, the wavelengths are estimated as
200 nm. These SiO2 films are prepared by thermal
oxidation of Si wafers at 1000 °C (see Section 4).
By comparison, the films previously prepared via
* Corresponding author. Fax: +612-9385-6141.
E-mail address: n.tran@unsw.edu.au (N.H. Tran).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2004.05.012

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N.H. Tran, R.N. Lamb / Chemical Physics Letters 391 (2004) 385–388
In fact, the extreme condition for preparation of SiO2
film is related to the formation of nano-waves. It is well
known that these films are accompanied with a large
thermal stress, as a result of the significant volume ex-
pansion during oxidation of Si (oxidation at 1000 °C
should create a thermal stress in SiO2 of ꢀ3 ꢂ 108
N mꢁ2) [9]. Our results are in agreement with those from
Yuse and Sano [5] who showed that formation of mil-
limeter waves on the fracture surfaces were favoured as
the crack propagated through a large thermal stress
field. In their experiments, cracks were formed when a
glass plate was heated and transferred to a cold-water
bath. As the heating temperature and therefore thermal
stress was increased, the redistribution of stress gave rise
to a systematic transition from planar to sinusoidal and
other wavy fracture.
To test the influence of stress to the formation of
nano-waves, we examine the fracture morphology of
SiO2 films with lower thermal stress. The films are pre-
pared from oxidation of Si at temperature of 600 °C.
This should result in the thermal stress of ꢀ1.4 ꢂ 108
N mꢁ2 [9], i.e. decreased by a factor of two compared to
the above films. For this film, the fracture surface re-
mains virtually planar (Fig. 2). Although, the onset of
Fig. 1. Cross-section scanning electron microscopy of differently thick
SiO2 films. The films are prepared by thermal oxidation of Si(1 0 0)
wafers at 1000 °C between 1 and 14 days. (a) Formation of the nano-
waves along the fracture surface of the 2 lm thick film; (a0) enlarge-
ment of (a). The wavelengths are of ꢀ200 nm; (b)–(c) formation of
the nano-waves along the fracture surface of the films with thickness of
ꢀ1 and 0.5 lm, respectively. The fracture sections of the underlying
Si substrates remain virtually planar.
radio-frequency sputtering, chemical vapour deposition
and sol–gel resulted in a smooth or porous fracture [8].
Rapid thermal oxidation has been extensively used for
preparation of the ultra-thin SiO2 films (thickness of few
nanometers) that may be used as a dielectric layer in Si
integrated devices [9]. By contrast, a relatively extreme
condition is used in our experiments with the oxidation
time being substantially extended (see Section 4).
Fig. 2. Scanning electron microscopy showing the fracture morphology
of the 1 lm thick SiO2films prepared by thermal oxidation of Si(1 0 0)
at (a) 1000 °C and (b) 600 °C. (b)0 the enlargement of (b).

N.H. Tran, R.N. Lamb / Chemical Physics Letters 391 (2004) 385–388
387
tion of fracture morphology over a wide range of scales.
Further research into propagating speed is necessary in
order to understand whether the formation of nano-
waves involves dynamic crack (fast propagation) or
quasi-static crack (slow propagation). It would also be
of interest to carry out studies on whether the intrinsic
properties of SiO2 films such as short-range atomic
structures, interfacial stress or density have any influ-
ence on the formation of waves.
4. Methods
The amorphous films of SiO2 have been prepared
from thermal oxidation of Si with (1 0 0) crystallo-
graphic orientation. Our experimental conditions were
relatively extreme compared to the conventional thermal
oxidation process. In particular, we carried out oxida-
tion in air between 1and 14 days. This resulted in the
film thickness of maximum of 2 lm. The films were
cleaved using a diamond cleaver. Cleavage was per-
formed along the Si(1 0 0) direction and crack propa-
gated along the (1 0 0) plane. We did not observe the
formation of nano-waves at the beginning of the crack
tip. This section remained rough. The roughness was
probably related to the application of a large amount of
crack driving force [12]. With increasing length of crack,
the roughness decreased and the waves were grown
uniformly. Similar effects were also observed by Fine-
berg et al. [14].
Fig. 3. Transmission electron microscopy of the 1 lm thick SiO2film
prepared by thermal oxidation of Si(1 0 0) at 1000 °C. The film is not
columnar. For this experiment, due to the sample preparation proce-
dure, the fracture surface is heavily damaged and therefore the nano-
waves are not observed.
waves is evidenced via the formation of various thin
lines across the surface. This observation is similar to
that of the planar or sinusoidal wavy fracture in low-
stress material [5]. The combined results indicate that
the morphological transition in SiO2 fracture could also
be referred as a Hopf bifurcation [4–6].
In addition, there are possibilities that the nano-
structures of the films influence the formation of waves.
In particular, the columnar structures commonly ob-
served in ceramic films may also lead to formation of
wavy fractures [10]. For this, transmission electron mi-
croscopy shows that the films are not columnar and are
amorphous (Fig. 3). The amorphous nature is confirmed
from X-ray diffraction measurements. Previous studies
have also shown that the crack in crystalline Si propa-
gated along a crystallographic plane results in a planar
fracture [11–13]. This can be confirmed from our results,
where planar fractures of the underlying Si substrates
are clearly distinguishable with wavy fractures of the
films (Figs. 1 and 2). These combined results indicate
that formation of waves is not related to a specific nano-
structure of the films or substrates.
Acknowledgements
The authors acknowledge P. Munroe for TEM
support.
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3. Summary
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We report the observation of a fracture surface cre-
ated by the well-defined nanometer waves. The mecha-
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