Novel technique for measuring the mechanical properties of porous materials by nanoindentation
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Yong Xiang and Joost J. Vlassak Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138-2901 (Received 4 August 2005; accepted 8 December 2005)
A new technique for measuring the elastic-plastic properties of porous thin films by means of nanoindentation is proposed. The effects of porosity on indentation hardness and modulus are investigated through finite element analyses based on the Gurson model for plastic deformation of ductile porous materials. Intrinsic mechanical properties of the thin film are obtained by eliminating both substrate and densification effects. The technique is applied to the special case of a porous, low-permittivity dielectric thin film. The results are in good agreement with those obtained independently using the plane-strain bulge test.
I. INTRODUCTION
sintered materials, thermal-barrier coatings, or biological materials such as bone.
A. Motivation
The mechanical response of thin films can be measured using many different techniques, including microtensile or bulge testing of free-standing thin films,1–3 nanoindentation, the micro-beam cantilever deflection technique,4,5 and the substrate curvature technique.6,7 Compared to other methods, nanoindentation measurements can be made without having to remove the film from its substrate; moreover, nanoindentation is an isothermal technique that does not require thermal cycling. It is perhaps the quickest and easiest method for probing the mechanical properties of thin films. Special care is required, however, when nanoindentation is performed on porous materials. Because of their porous microstructure, the response of these materials during a nanoindentation experiment is very different from that of a dense bulk material. In this paper, we investigate the mechanics of nanoindentation of porous materials and develop a new technique to correlate the experimental data with the inherent microstructure and mechanical properties of these materials. The approach advanced in this paper is applied to the special case of a porous polymeric thin film used as a low-k dielectric in the microelectronics industry, but it is readily extended to other porous materials with relatively low pore density ( 30.12,14 If the material work hardens, the yield stress is taken at a representative strain,16 which is approximately 7% for a Berkovich indenter. As the indenter penetrates the specimen, the material exhibits both elastic sink-in and plastic pile-up at the edge of the indentation. The elastic effect is more pronounced when the yield strain of the material y/E is large; plastic pileup is important for materials with a small yield strain.14 The amount of pileup/sink-in is denoted as ␦p [Fig. 1(a)]. For the axisymmetric Berkovich indenter, the projected contact area A is given by: A = a2 = 共tan ␣兲2␦c2 = 24.5␦c2
,
(5)
where the contact depth, ␦c = ␦ + ␦p
(6)
.
Equation (6) contains contributions of both plastic pileup around the indenter and elastic sink-in, which is counted negative. It is obvious from Eqs. (1)
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