By Agilent Technologies
Results and Discussion
Correlation of Results
About Agilent Technologies
The processing that is required to lower the dielectric constant in a low-k film has the adverse effect of degrading the
mechanical properties of the film. Low-k films are subjected to many processes that test the strength of these films and
their adhesion to the substrate, such as chemical and mechanical polishing (CMP) and wire bonding. It is important for these
materials to resist plastic deformation during these processes and remain intact without blistering up from the substrate.
Ideally, a dielectric material will have a high hardness and elastic modulus because, traditionally, these two parameters
help to define how the material will react when subjected to manufacturing processes.
Here, scratch tests are performed on several low-k samples using a ramp-load scratch test. The results from scratch
testing and nanoindentation are examined through correlation analysis to better understand the interconnectedness of scratch
Ten low-k samples were provided for scratch testing by SBA Materials, Inc. The films were deposited on silicon substrates
by spin coating; thicknesses varied between the samples, ranging from 375 to 743 nm. The samples were supplied with the
elastic modulus and hardness measurements of the films. Mechanical properties data were collected using an Agilent Nano Indenter G200 with a special test method for
measuring the substrate-independent properties of low-k dielectric films. This test method is described elsewhere . A
summary of the sample thicknesses and mechanical properties is given in Table 1.
Table 1. Film thicknesses and mechanical properties of the low-k film samples.
|Sample A ||500.7 ||6.61 ||1.08
|Sample B ||617 ||8.1 ||1.25
|Sample C ||743 ||8.05 ||1.28
|Sample D ||470 ||8.25 ||1.25
|Sample E ||526 ||8.66 ||1.26
|Sample F ||641.6 ||6.9 ||1.11
|Sample G ||488.9 ||7.13 ||1.14
|Sample H ||375 ||8.66 ||1.26
|Sample I ||423 ||*** ||***
|Sample J ||650 ||8.15 ||1.28
All of the scratch tests were performed on an Agilent Nano Indenter G200. The Nano
Indenter G200 is powered by electromagnetic actuation to achieve unparalleled dynamic range in force and displacement.
The instrument’s unique design avoids lateral displacement artifacts during the scratch process. Using the G200, researchers can measure Young’s modulus and
hardness in compliance with ISO 14577, as well as scratch and wear properties. Deformation can be measured over six orders of
magnitude (from nanometers to millimeters).
A ramp-load scratch test was used to conduct three tests on each wafer in three locations - this totaled nine tests for
each sample. In a ramp-load scratch test, a tip is brought into contact with the sample; then the tip is loaded at a constant
loading rate while simultaneously translating the sample. Prior to and following the scratch test, a single-line scan of the
surface topography is completed for comparing the original surface to the deformation caused by the scratch test.
Therefore, each scratch test consists of three steps: a single-line pre-scan of the area to be scratched, the ramp-load
scratch test, and a final scan to evaluate the residual deformation. Before and after each step, a pre-scan and a post-scan,
usually equal to 20% of the scratch length, is performed so that the software can automatically align the data in the three
steps. The original and residual single-line scans allow the evaluation of deformation mechanisms and the quantification of
deformation. The scratch process is diagrammed in Figure 1.
Figure 1. Diagram of the three-step ramp-load scratch test. Red lines show the areas of pre- and post
-profile scans used to perform leveling of the three steps.
When performing scratch testing on any sample set, it is critical that all test parameters and tip geometries remain
consistent for all samples being compared. This ensures that qualitative comparisons can be made using the resultant data.
The test parameters used for testing the low-k materials are listed in Table 2.
Table 2. Parameters used for the ramp-load scratch test.
|Scratch Length ||300µm
|Scratch Velocity ||30µm
|Maximum Scratch Load ||3mN
|Scratch Direction ||Face-Forward
The tip chosen for conducting the scratch tests was a cube-corner tip with a tip radius that was, nominally, less than 20
nm. A cube-corner tip creates a triangular projected contact with the sample; this tip geometry creates high levels of stress
in the material during the scratch. Scratches can be performed either face-forward or edge-forward when using a pyramid-
Scratching face-forward with the cube-corner tip acts like a snow plow and pushes the material out of the way, while edge
-forward cuts the material like a knife. A diagram of a cube-corner tip is shown in Figure 2. The low-k samples were tested
using the cube-corner tip positioned so that it scratched face-forward.
Figure 2. Diagram of a cube-corner tip.
Results and Discussion
All of the low-k films failed in a similar manner; the films exhibited plastic deformation up to a critical point where
blistering of the film occurred. Following blistering, complete failure of the film occurred and the substrate was scratched
for the remainder of the test. To gain a comprehensive understanding of the mode of failure exhibited during the scratch
tests on the low-k samples, a typical scratch test was analyzed using scanning probe microscopy (SPM), which was available on
the Nano Indenter G200 via the Agilent NanoVision
Figure 3.The Displacement into Surface versus Scratch Distance data for the scratch that was used for imaging to further examine failure; the blue trace is the Original Surface Topography, the green trace is the Scratch Curve, and the orange trace is the Residual Deformation. The locations of blistering and total film failure are labeled.
Figure 3. The Displacement into Surface versus Scratch Distance data for the scratch that was used for imaging to further examine failure; the blue trace is the Original Surface Topography, the green trace is the Scratch Curve, and the orange trace is the Residual Deformation. The locations of blistering and total film failure are labeled.
The NanoVision option allows imaging through the use of a high-precision piezo translation stage; lateral resolution and
flatness of travel are better than 2 nm. This microscopy module allows quantitative imaging and high-precision targeting for
the investigation of material properties. Figure 3 shows the top and side views of the scratch test, whereas Figure 4 shows
the scan of the scratch test at the start of blistering.
Figure 5. Typical blistering and failure in the low-k films. Imaging of the scratch was performed
using the Agilent NanoVision option on the Agilent Nano Indenter G200. Notice that the film has blistered up approximately
400 nm from the surface.
Figure 6. Typical scratch tests on the low-k films showing the start of blistering. Notice that the
residual scratch depth increases until blistering occurs. Following the start of blistering, the residual deformation in the
film has been lifted upwards.
A summary of the scratch results for all ten samples is provided in Table 3. The sixth column of this table provides the
amount of elastic deformation that occurred during the scratch up to the point of film failure. Elastic and plastic
deformation during the scratch test are determined by measuring the areas between the Scratch Curve and the Original Surface
Topography and between the Residual Deformation Scan and the Original Surface Topography.
Table 3. Summary of scratch results.
|Sample A ||0.97±0.029 ||197±17 ||10.6±1.0 ||59.5±5.1 ||74.5±0.7
|Sample B ||1.306±0.083 ||261±23 ||18.9±2.0 ||73.9±6.5 ||75.4±3.3
|Sample C ||1.22±0.022 ||257±9 ||17.4±0.8 ||73.6±2.6 ||77.4±2.2
|Sample D ||1.045±0.055 ||204±16 ||11.4±1.1 ||51.2±4.0 ||66.3±3.6
|Sample E ||1.157±0.052 ||233±12 ||15.1±1.3 ||75.9±3.9 ||72.8±2.1
|Sample F ||1.067±0.019 ||225±6 ||13.1±0.6 ||55.8±1.5 ||78.5±1.2
|Sample G ||1.025±0.063 ||212±21 ||11.6±1.4 ||54.0±5.3 ||74.7±1.9
|Sample H ||0.811±0.063 ||162±8 ||7.3±0.4 ||44.2±2.2 ||72.1±4
|Sample I ||0.927±0.048 ||168±5 ||7.4±0.6 ||45.4±1.4||72.4±1.5
|Sample J ||1.345±0.041 ||278±12 ||20.5±1.2 ||76.1±3.3 ||74.3±3.2
This new parameter, Percent Elastic Deformation up to Critical Load, provides a measure of the film’s resistance to
permanent deformation and offers a more complete evaluation of the film’s performance by quantifying not only the load at
which film failure occurs, but also the type of deformation occurring up to film failure. The areas of elastic and plastic
deformation are shaded on the scratch curves of Figure 5.
Figure 7. Elastic and plastic deformation of a scratch test performed on Sample J; the elastic
deformation is shaded in blue and the plastic deformation is shaded in yellow. The film thickness for Sample J is 650 nm.
Figures 6 and 7 graphically display the results of Critical Load and Total Deformation, as well as the Percent
Penetration/Elastic Deformation and Elastic Modulus, for the four top performing samples based on the results of Critical
Load - B, C, E, and J. There are subtle differences between the top performers. Samples B and J, which had the highest
critical loads of all the samples, show no significant statistical difference in the result for Critical Load; however, the
Sample J results possessed a much smaller standard deviation, suggesting better repeatability and predictability.
Figure 8. Critical Load and Total Deformation for the four top performing samples (based on Critical
Load). Ideally, the results for Critical Load will be high and the Total Deformation will below.
Figure 9. Percent Penetration/Elastic Deformation and Elastic Modulus for the four top performing
samples (based on Critical Load).
Correlation of Results
It is easy to look at a sprawling matrix of test results, focus on large numerical differences in single columns, and
overlook significant independent results. By examining the correlation of results, patterns can be recognized, thus ensuring
that the sample results are analyzed based on independent results instead of on groups of results that have strong
correlations to a single parameter.
A good example of a strong linear correlation is in Figure 6 where there is obviously a strong correlation between the
Critical Load and the Total Deformation; if a researcher decided to neglect other information and only focus on these two
parameters as a basis for analyzing the performance of these films, both of these results would point to the same
Many times, a correlation is not as obvious as the one demonstrated in Figure 6, which is easily recognized because there
happens to be a 97% linear correlation between these two results. It is when the correlation drops below 60% that it becomes
hard to recognize. For analyzing the correlation of the results in these scratch tests, normal correlation analysis was
conducted and is described elsewhere . In order to rate the levels of correlation between results, four levels were
defined: very weak correlation (40 to 50%), weak correlation (50 to 60%), moderate correlation (60 to 75%), and strong
correlation (>75%). Table 4 lists the correlation levels between different results provided for the low-k samples.
Table 4. Correlation table of results.
|% Penetration||59 %||5%||17%||82%||86%||
|% Elastic Deformation||43%||21%||10%||11%||15%||15%
It is apparent from the correlation analysis that all of the results - save hardness and elastic modulus, which were
measured using a test method specifically developed for measuring substrate-independent properties - are at least weakly
dependent on film thickness. The variation in Critical Load, for example, can be accounted for by a linear relationship with
Film Thickness approximately 67% of the time. These results, however, should not simply be neglected based on this moderate
correlation. Sample E, which was one of the thinnest samples but also had one of the highest critical loads, provides an
Some of the correlations shown in the table are of no surprise, such as Percent Penetration and Total Deformation coming
in with a correlation of 86%; higher penetration at film failure would logically yield higher Total Deformation. In fact, if
the Total Deformation is correlated to Penetration Depth at Critical Load, as opposed to Percent Penetration (which is
normalized by the film thickness), the correlation factor jumps to more than 98%.
Among the more surprising results is the almost complete absence of correlations to results of hardness, elastic modulus,
and Percent Elastic Deformation. It is speculated that a correlation to hardness is absent because the interface between the
film and substrate failed prior to the failure of the film itself.
Ramp-load scratch testing, a standard test method on the Agilent Nano Indenter platform, was utilized to evaluate the
scratch response of low-k films on silicon substrates. All of the low-k samples that were tested experienced blistering of
the film well before complete film failure occurred; imaging was completed using the Agilent NanoVision option to confirm the
mode of failure.
In addition to revealing significant statistical differences between the results of the scratch tests, the scratch results
themselves were analyzed using correlation analysis. All of the scratch results were found to have at least a very weak
correlation to film thickness. This weak dependence on film thickness makes sense given the fact that in usual scratch tests
the film does not fail until the probe has significantly penetrated the film. Hence, the stresses from the scratch test
propagate well into the substrate.
There were also some surprising results of complete absence of correlation. Neither hardness nor elastic modulus
correlated to any of the scratch parameters. The Percent of Elastic Deformation up to the Critical Load did not correlate to
any result other than Film Thickness - and this was only a very weak correlation.
Sample J was determined to be the best performing sample due to its excellent ability to resist deformation, withstand a
high percentage of penetration, and support the highest load before failure. Even though the results for Sample J were very
similar to those for Sample B, Sample J was selected because its test results had a lower standard deviation, thus proving
better repeatability and predictability.
Agilent Technologies would like to thank SBA Materials for supplying the samples and some of the results for this
 J. Hay, "Measuring substrate-independent modulus of dielectric films by instrumented indentation," J. Mater. Res.,
Vol. 24, pp. 667-677, March 2009.
 J.E. Freund, Mathematical Statistics, 5th Edition, New York: Prentice Hall, 1992.
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