New Insight into Pile-up in Thin Film Indentation (MEMS and Nanotechnology)

ABSTRACT

A new method of accurately and reliably extract the actual Young’s modulus of a thin film on a substrate has been developed. The method is referred to as the discontinuous elastic interface transfer model. The method has been shown to work exceptionally well with films and substrates encompassing a wide range of elastic moduli and Poisson ratios. The advantage of the method is that it does not require a continuous stiffness method and can use the standard Oliver and Pharr analysis and the use of a predictive formula for determining the modulus of the film as long as the film thickness, substrate modulus and bulk Poisson ratio of the film are known. However, when there is much pile-up during the indentation process in a softer film, the experimental data does not follow the predictive formula but instead follows a similar model with a single Poisson ratio between the film and the substrate.

 (a) Schematic illustrating the concept of continuous transfer of strain between the film and substrate, (b) numerical simulation indicating that strain is likely discontinuously transferred between the film and substrate, and (c) schematic showing how the film and substrate components are decoupled in the discontinuous elastic interface transfer model


Figure 1 (a) Schematic illustrating the concept of continuous transfer of strain between the film and substrate, (b) numerical simulation indicating that strain is likely discontinuously transferred between the film and substrate, and (c) schematic showing how the film and substrate components are decoupled in the discontinuous elastic interface transfer model

INTRODCUTION

In the scientific and engineering communities, there has been much effort to accurately determine the properties of thin film coatings by means of discretely intrusive indents using nanoindentation techniques. However, the task in determining the properties is not trivial a trivial one. The problem with the measurement methods stems from deformation fields originating from the indent propagating in both the film and the substrate; therefore any properties measured in the experiment are that of a composite value. It has been challenging for scientists and engineers to obtain a theoretical method of investigating a complete description of the discontinuous properties of thin film coatings. Recently, a new model has been proposed for a new model referred to as the elastic interface transfer model. The new model accounts for a discontinuity in elastic strain transfer between the film and the substrate. A schematic of the theory underlying the elastic interface transfer model is shown in figure 1. The figure shows, based upon the theory, that between the boundaries of the film and substrate, there is not a continuous transfer of strain. Figure 1: (a) is representative of what Doerner and Nix [2] and Gao [3] have presented in their works as a spherically symmetric strain field emanating from the indent across the film/substrate interface. According to Doerner and Nix, the values of strain on either side of the film/substrate interface are equal to one another, suggesting that there is a continuous transfer of strain. However, numerical simulations have found that there should be a discontinuous transfer of the elastic strain field at the film/substrate boundary, Fig 1(b) and (c). Figure 1:(c) indicates that there is actually a film component as well as a substrate component describing the discontinuous strain field.

In the previous models, a single weight factor was used to describe the strain transfer, having the following form:

tmp16-47_thumb

Here, E’ is the composite modulus, Ef is the filmtmp16-48_thumbis the substratetmp16-49_thumbis a weighting factor which accounts for the continuously changing contribution of the film and substrate made by the indenter, which is given as,

tmp16-52_thumb

where, t is the film thickness, h is the indent depth and " is an empirically defined constant, usually around 0.25 according to Doerner and Nix. Different weighting factors have been applied to the previous model in order to describe the discontinuity in the elastic strain field in the following form:

tmp16-53_thumb

where,

tmp16-54_thumb

Here, # f and # s are the weighting factors to account for the effects of the film on the substrate and substrate on the film respectively and ‘f and "s are the constants.

In previous works, the discontinuous elastic transfer model has been compared to experimental data from various combinations of thin film materials on different substrates and was found to match experimental curves accurately. Through investigation of the theoretical curves, it was found that the constants, ‘f and "s, in each weighting factor were essentially equivalent to the bulk scale Poisson’s ratios for the film and substrate respectively.

EXPERIMENTAL PROCEDURE

In this work was AlOx deposited on five different substrates with a variable range of elastic moduli and Poisson ratios to investigate the discontinuous elastic interface transfer model. The substrates included <0001> sapphire (Al2O3), <100> magnesium oxide (MgO), <100> N-type undoped germanium (Ge), amorphous silicon (a-Si) and silicon dioxide (SiO2). All substrates were previously polished to ensure a uniform contact at the film/substrate interface. Gold films were deposited onto the substrates using a Denton sputtering system with RF and DC power and the parameters used during the process were determined by previous experiments. The substrate platform was rotated at 50 RPM to ensure uniform deposition during the sputtering process. Secondly, gold (Au) was sputtered on Quartz using the same procedure previously stated. An adhesion layer of titanium (Ti) was sputtered first on the substrate before sputtering the Au thin film. The final thickness of the Au film on the substrate was approximately 480 nm. Material properties of each material are shown in table 1. For Au, the elastic modulus is 72 GPa and the Poisson ratio value for the bulk scale is 0.44.

Table 1 Material properties for the substrates used

Substrate

Modulus (GPa)

Poisson’s Ratio [ref]

SiO2

70 ± 4

0.17 (quartz)

[39]

Ge

144 ± 7

0.27

[40]

Si

173 ± 9

0.28

[41]

MgO

249 ± 17

0.23

[42]

AI2O3

460 ± 28

0.21~0.27

[43]

Indentation tests on each sample were performed using an MTS Nanoindenter XP with a Berkovich diamond tip. Young’s modulus vs. displacement of the indenter into the sample was obtained using a continuous stiffness method (CSM) with a minimum thermal drift rate of 0.05 nm/s and a harmonic displacement target set to 2 nm. The depths of the indents were set to 500 nm. The Poisson’s ratio used in the CSM tests was that of the bulk value for gold. For each indentation test, 25 indents were made, each having the same parameters and indent depths, and averaged together for the final Young’s modulus vs. displacement data.

RESULTS AND DISCUSSIONS

In the work, raw indentation data of aluminum oxide (AlOx) on 5 different substrates were calibrated and compared to the discontinuous elastic interface transfer model. Figure 2 illustrates the measured Young’s modulus vs. displacement into the surface on each of the five substrates. The data was shown to fit the curves accurately in all substrates. The quality of the fit for all five substrates is shown in Figure 3, which exhibits a flat region that can be considered to represent the Young’s modulus of the film. The change in the value of Efiat for AlOx suggests that it is strongly dependent on the substrate modulus, increasing as the substrate’s modulus increases.

 Plot comparing the measured Young's modulus as a function of displacement for the AlOx films on different substrates

Figure 2 Plot comparing the measured Young’s modulus as a function of displacement for the AlOx films on different substrates

Plot illustrating the quality fit of the discontinuous elastic interface transfer model for the AlOx films and estimation of elastic homogeneity of the film/substrate composite (dashed line)

Figure 3 Plot illustrating the quality fit of the discontinuous elastic interface transfer model for the AlOx films and estimation of elastic homogeneity of the film/substrate composite (dashed line)

Plot comparing the measured Young's modulus of Au on a quartz substrate to the discontinuous elastic interface transfer model as well as the Doerner and Nix model

Figure 4 Plot comparing the measured Young’s modulus of Au on a quartz substrate to the discontinuous elastic interface transfer model as well as the Doerner and Nix model

However, when choosing a film substrate combination with elastic moduli values close to each other, the experimental data did not match the theoretical data of the discontinuous elastic interface transfer model as well. The experimental data of Au on Quartz is shown in figure 4. According to the model, the experimental data should have rapidly increased as the indenter penetrated the film and slowly decreased upon further depth. The trend predicted by the model is a result of the difference in Poisson ratio’s between the film and the substrate. However, the experimental data followed the Doerner and Nix model, in which there is but one weighting factor.

Because Au is a softer film, perhaps the behavior shown is due to pile-up of the film during the indentation process. Figures 5 and 6 show SEM micrographs of a single indent in the Au film on a quartz substrate. In the image, it is clear that there is significant pile-up of gold around the perimeter of the indent. In other words, the effect of the differences in the Poisson ratio’s of the Au film and Quartz substrate did not make a difference in the experimental data as predicted by the model.

SEM micrograph of indent on Au film at 18,000X

Fig 5 SEM micrograph of indent on Au film at 18,000X

 SEM micrograph of same indention at 30,000X

Fig 6 SEM micrograph of same indention at 30,000X

CONCLUSIONS

Indentation tests were conducted on various film and substrate combinations. It was found that the difference in material properties between the film and substrates had a large effect on the mechanical behavior of the film, as shown in the experimental data. The experimental data for AlOx films fit the discontinuous elastic interface transfer model accurately. However, when performing an indent on a soft film such as gold on a soft substrate such as quartz, the experimental data did not match the theoretical model but instead followed the model presented by Doerner and Nix. Because the data followed the D-N model, there is a single weight factor in effect which is related a single Poisson ratio. There was an indication of pile-up in the film around the indent of the Au film suggesting that the load of the indenter is directly transferred into the substrate as the depth of the indent increases.

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