Research Express@NCKU Volume 6 Issue 4 - October 31, 2008
[ http://research.ncku.edu.tw/re/articles/e/20081031/1.html ]
Nano-Indentation Tests Applied to
Measurement of the Mechanical Properties
for the C/a-Si Composite Film
Chang-Fu Han
1, Bo-Hsiung Wu
2, Jen-Fin Lin
1,2,*, Chen-Kuei Chung
1,21Department of Mechanical Engineering, National Cheng Kung University
2Center for Micro/Nano Science and Technology, National Cheng Kung University [email protected]
Nanotechnology 19, 325710 (13 pp) (2008)
I
ndentation load–depth curves can be measured with a depth-sensing indenter instrument and used to determine the mechanical properties of materials. The hardness of a film-substrate sample is thecomposite hardness, which is affected by the film, the substrate, and the interface properties. The composite hardness is believed to approach the film hardness when the indentation depth is extremely small and the substrate hardness when the depth is very large. The transition behavior of composite hardness is complicated and it is difficult to observe the film hardness directly when the thickness of the film is very small. A general mechanical model in Fig. 1, which is composed of the mechanical models employed to describe the contact behaviors and deformations arising at all layers (including the substrate), is successfully developed in the present study for multilayer specimens in order to evaluate the contact projected area by a theoretical model, and thus the hardness and reduced modulus, using nano-indentation tests [1-3].
Fig.1 The mechanical model of the indentation instrument.
Fig. 2 The FIB image of the cross-section on the C(200 nm)/a-Si(50 nm) specimen after indentation test.
The indentation tests were carried out on a TriboScope (Hysitron, USA) tester. All experiments were carried out using the Berkovich indenter, which was made of diamond (Young’s modulus E=1140 GPa, Poisson’s ratio ν=0.07). The indentation tests were carried out at an ambient temperature of 25°C and at a relative humidity of 45 %. The indentation tests using a Berkovich indenter (equivalent cone angle 70.3 ˚) with a round tip of a radius of about 50 nm (provided by the commercial resource of Hysitron, USA.) Figure 2 shows the FIB (Focus Ion Beam) image for the cross-section of the C(200 nm)/a-Si(50 nm) specimen. The C/a-Si composite films demonstrated the sink-in behavior in the indentation tests. Because no pile-up was exhibited on the undeformed top surface, the sink-in evidence was exhibited.
Fig.3 The load-depth curves obtained from experiments. (a) A comparison of the load-depth curves obtained from experiments with C(50 nm)/a-Si(50 nm) and C(100 nm)/a-Si(50 nm) specimen. (b) A comparison of the load-depth curves obtained from experiments with C(100 nm)/a-Si(50 nm) and C (200 nm)/a-Si(50 nm) specimen.
The two plots shown in Fig. 3 show the load-depth profiles for the three specimens, C(50 nm)/a-Si(50
nm), C(100 nm)/a-Si(50 nm), and C(200 nm)/a-Si(50 nm). When the indentation depth is close to the
interface of the C film and a-Si film, the depth-transition occurred at an indentation depth in the loading process, but still within the C film. The differences of these two mechanical properties cause the
noticeable changes in their profile slopes. Nevertheless, the profiles are still continuous at this point. The pop-in behavior only occurred before the indentation depth reached the interface of the a-Si layer and the Si substrate. The characteristic exhibited in the pop-in behavior is a discontinuity in the load-depth profile. The formation of a pop-in is related to the phase change in the Si substrate or/and the growth of microcracks in the a-Si/Si interface [4]. The gap in the load-depth profile substantially influences evaluations of hardness and elastic modulus, which also have a gap at pop-in.
Since the contact area of the indenter (Ac) is obtained by the present model in Fig. 1, the material hardness can be obtained as:
. (1)
Hainsworth et al. [5] showed that the P/h2 can be expressed as a function of the hardness (H) and the reduced modulus (Er):
, (2)
respectively. In each of these figures, the solid curve symbolized by ″Δ″ is the hardness profile of the composite specimen; whereas the curve symbolized by ″□″ is the hardness profile of a pure Si substrate. The solid curve in this figure is asymptotic to a constant value if the indentation depth can be increased to be sufficiently large. This constant hardness is still slightly higher than that of a pure Si substrate although it was actually dominated by the Si substrate at sufficiently large depths. The three solid curves shown in Fig.4(a) to Fig.4(c) are grouped and shown in Fig.4(d). A comparison of these three curves reveals that the appearance of pop-in can influence the hardness evaluations. Nevertheless, the hardness results predicted by the present model allow us to investigate the influence of the buffer layer (the a-Si film) and the Si substrate on the hardness of the C film with various thickness. The reduced modulus (Er) results corresponding to the specimens and operating conditions shown in Fig.4(a) to Fig.4(c) are shown in Fig.5(a) to Fig.5(c), respectively. Figure 5(d) shows the collections of the three solid curves shown in Fig.5(a) to Fig.5(c). The behavior demonstrated in the reduced modulus due to the changes in the indentation depth and the thickness of the C film is quite similar to that demonstrated in the specimen hardness (H). In general, the real contact projected area occurring in the nano-indentation tests of the specimens with multilayer coating films is quite hard to obtain. This problem is caused due to the difficulty of evaluating the substrate effect on the hardness and reduced modulus of the composite specimen at various indentation depths. A general mechanical model was successfully developed in the present study for multilayer specimens in order to evaluate the real contact projected area, and thus the hardness and reduced modulus at various indentation depths, and the effects of the multilayer
Fig.4 The relationship of the hardness obtained by the present model. (a) The variations of hardness with the indentation depth for the C(50 nm)/a-Si(50 nm) specimen. (b) The variations of hardness with the indentation depth for the C(100 nm)/a-Si(50 nm) specimen. (c) The variations of hardness with the indentation depth for the C(200 nm)/a-Si(50 nm) specimen.(d) A comparison of the hardness obtained using the present model.
Fig. 5 The relationship of the reduced modulus obtained by the present model. (a) The variations of reduced modulus with the indentation depth for the C(50 nm)/a-Si(50 nm) specimen. (b) The variations of reduced modulus with the indentation depth for the C(100 nm)/a-Si(50 nm) specimen. (c) The variations of reduced modulus with the indentation depth for the C(200 nm)/a-Si(50 nm) specimen. (d) A comparison of the reduced modulus obtained using the present model.
[4] Haq A J, Munroe P R, Hoffman M, Martin P J and Bendavid A 2007 Thin Solid Films 516 267-271. [5] Hainsworth S V, Chandler H W and Page T F 1996 J. Mater. Res. 11 1987-1995.
