Effect of Pore Structure of Nanometer Scale Porous Films on the
Measured Elastic Modulus
Kris Vanstreels,*
,†
Chen Wu,
†,‡
Mario Gonzalez,
†
Dieter Schneider,
§
David Gidley,
∥
Patrick Verdonck,
†
and Mikhail R. Baklanov
†
†
imec, Kapeldreef 75, 3001 Leuven, Belgium
‡
Katholieke Universiteit Leuven, 3000 Leuven, Belgium
§
Fraunhofer Institute for Materials and Beam Technology, Winterbergstraße 28, 01277 Dresden, Germany
∥
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, United States
ABSTRACT: The impact of pore structure of nanoporous films on
the measured elastic modulus is demonstrated for silica-based
nanoporous low-k films that are fabricated using an alternative
manufacturing sequence which allows a separate control of porosity
and matrix properties. For this purpose, different experimental
techniques for measuring the elastic properties were compared,
including nanoindentation, laser-induced surface acoustic wave
spectroscopy (LAwave), and ellipsometric porosimetry (EP). The
link between the elastic response of these nanoporous materials and
their internal pore structure was investigated using positronium
annihilation lifetime spectroscopy (PALS), EP, and diffusion
experiments. It is shown that the absolute value of the Berkovich
indentation modulus is very sensitive to the local pore structure and
stiffness of the substrate and can be influenced by densification and/or anisotropic elasticity upon indentation, while on the other
hand spherical indentation results are less sensitive to the local pore structure. The comparison of Berkovich and spherical
indentation results combined with finite element simulations can potentially reveal changes in the internal structure of the film.
For nanoporous films with porosity above the percolation threshold, the elastic modulus results obtained with LAwave and EP
agree very well with spherical indentation results. On the other hand, below the percolation threshold, the elastic modulus values
determined by these techniques deviate from the spherical indentation results. This was explained in terms of specific technique
related effects that appear to be sensitive to the specific arrangement and morphology of the pores.
1. INTRODUCTION
Porous materials are commonly found in nature, both in
biological systems and in natural minerals (bone, zeolites,
sponges, and rocks, among others) and as industrial materials
(ceramics, membranes, foams, cements, semiconductors, and
dielectrics, among others) for a multitude of purposes,
including liquid filtration, catalysis, microelectronics, tissue
engineering, and medical diagnosis, among others. These
materials consist of an organic or inorganic framework that
supports a porous structure. The size of the pores (voids) can
range from the macro-scale (>50 nm) down to the nano-scale
(<2 nm) depending on the application. The present tendency is
to develop and use thin porous films with small pore size below
10 nm. Such materials are necessary for sensors, catalysis,
microelectronics, and biotechnology. In order to successfully
implement these materials in specific applications, it is
important to understand how their mechanical properties
vary with porosity and their pore microstructure. Although
much advancement has been made in this field over the past 4
decades for a wide range of materials, there is relatively little
fundamental understanding of the effects of pore morphology
on mechanical properties. Ideally, to isolate the effects of
porosity alone, the different films should exhibit the same
matrix properties. In reality, this is seldom the case for
nanoporous films, and studying the effect of porosity on the
mechanical properties of nanoporous films is often complicated
by the difficulty to control the porosity and matrix properties
separately during fabrication.
1,2
On the other hand, it is not
trivial to accurately measure the elastic modulus of nanometer
scale porous thin films.
3−6
The measured elastic modulus of a
porous film is actually an effective modulus, which evolves
toward the elastic modulus of the matrix material near zero
porosity. An important challenge is that the actual techniques
used for characterizing bulk materials are hardly applicable in
the case of nanoporous thin films because of the small volume
size of the material under investigation. For this reason, several
advanced destructive and nondestructive techniques have been
developed to characterize the elastic properties of thin films on
Received: June 25, 2013
Revised: August 29, 2013
Published: September 2, 2013
Article
pubs.acs.org/Langmuir
© 2013 American Chemical Society 12025 dx.doi.org/10.1021/la402383g | Langmuir 2013, 29, 12025−12035