Work on coated systems with the Nanohardness Tester (NHT) from CSM Instruments and integrated Scanning Force Microscope (SFM) objective has shown that the effects of pile-up have important consequences for the measurement of mechanical properties from nanoindentation load-displacement curves. This is because the calculated contact area between indenter and sample does not take into account any variation due to pile-up or sink-in of material around the indentation site.
This article focuses on a titanium thin film of thickness 200nm deposited onto a Si  substrate. Indentations have been performed using a Berkovich (three-sided) pyramidal indenter at depths from 25 nm up to 1225 nm, this being the total measurement range of the NHT instrument for this particular sample.
The plasma deposited titanium is in fact harder than the Si substrate, due to the high internal stresses produced as a result of deposition and the oxide film (usually TiO2) which forms immediately on removal of the sample from the reactor. The SFM images (Fig. 1) clearly show the surface morphology and grain structure of the deposited coating.
For the imaged indentation made with hmax = 50 nm, the residual imprint is barely visible and is of a similar magnitude as the surface roughness (~ 20 nm). As hmax is increased, no apparent pile-up effects are noticeable until the substrate is reached, suggesting that plastic flow is far more restricted than that of softer coatings (such as aluminium or gold). For depths where hmax > 200 nm (the film thickness), the amount of pile-up increases gradually but it can be observed that the surface morphology of the piled-up material remains the same as that surrounding it. This would suggest that, contrary to softer coatings where material is obviously pushed to the sides of the indenter, the material has undergone uplift due to substrate relaxation on unloading.
This is further confirmed by the concave edges of the imprints.
Figure 1. SFM images of residual imprints for maximum depths (hmax) of (a) 50 nm, (b) 175 nm, (c) 400 nm, and (d) 1225 nm. The sample is a titanium film (thickness = 200 nm) sputtered onto a Si  substrate.
Depths Much Greater Than Film Thickness
For depths much greater than the film thickness (e.g., Fig. 1 (d)), the relative amount of pile-up is significantly smaller because a greater portion of the deformed volume is in the Si substrate. The evolution of pile-up with penetration depth is represented in Fig. 2, by plotting a selection of cross-sectional profiles through imaged imprints. At depths greater than the film thickness, the transition between the coating and substrate is clearly visible, as is the elastic relaxation of the Si substrate which gives a bulge in the profile at the interface.
Figure 2. A selection of cross-sectional profiles through imaged indentations for depths (hmax) from 50 up to 1225 nm. Note the increasing influence of the Si substrate for depths exceeding the Ti film thickness (200nm).
Variations Of Hardness And Modulus
The variations of hardness and modulus are plotted in Fig. 3 as a function of the maximum penetration depth, hmax, normalised with respect to the film thickness, tf. For the hardness plot, a steep decrease is observed from a value approaching 16 GPa at shallow depths to approximately 11 GPa at the coating-substrate interface. For values of hmax/tf > 1, the hardness decreases more gradually down to a value of 9 GPa, this being the hardness of the substrate. The greater dispersion of experimental points at shallow depths can be attributed to surface roughness effects and the varying influence of the surface oxide layer, which, for such a thin film, may well extend a significant distance into the coating. The variation in elastic modulus, shown in Fig. 3 (b), descends from 270 GPa to 140 GPa, with no apparent discontinuity as a result of the coating-substrate interface. Such results confirm the applicability of the NHT to measuring mechanical properties as a function of depth in a precise and logical manner.
Figure 3. The variation of hardness (a) and elastic modulus (b) are plotted as a function of normalised depth (hmax/tf) for a titanium film sputtered onto a Si  substrate.
Figure 4. Three-dimensional representation of the image shown in Fig. 1 (d). Note the extent of pile-up and the morphology of the Si substrate.
Regarding common coated systems, the NHT has proved that load displacement information alone is not always able to determine the true deformation mechanisms occurring at the tip-sample interface, and that SFM imaging of the residual imprints at various depths is an invaluable means of characterising coating-substrate deformation behaviour.
In addition, the NHT/SFM is capable of providing load-displacement data together with topographical information (i.e., surface roughness, extent of pile-up/sink-in effects, true area of contact, volume of material displaced, indenter tip shape, etc.) in a fast and efficient manner.