Recent Highlights in Materials Reliability Division

Quantitative Nanomechanical Properties

hurley<at>boulder.nist.gov

(303)497-3081

New measurement solutions are required to address the rapidly burgeoning field of nanotechnology. In particular, information about mechanical properties on the nanoscale is needed. Knowledge of properties like elastic modulus and interfacial quality (defects, strain, adhesion, etc.) is critical to successful development of new films and nanoscale assemblies. Such information could also assess integrity or reliability in applications from microelectronics to biotechnology. Existing methods for mechanical-property measurements have drawbacks: they are destructive, limited to specialized test specimens, or not quantitative. Instrumented or “nano-” indentation (NI), a current industry workhorse, will have limited value as scales shrink well below 1 µm, and softer materials are more frequently used.

To meet this need, we are developing tools that exploit the spatial resolution of atomic force microscopy (AFM). Our approach, called atomic force acoustic microscopy (AFAM), involves the vibrational resonance of an AFM cantilever when its tip is in contact with a sample. By comparing the cantilever’s contact-resonance frequencies for an unknown material to those for a reference sample with known properties, the indentation modulus M of the unknown material can be determined. [For an isotropic material M = E/(1–ν2), where E is Young’s modulus and ν is Poisson’s ratio.] The small tip radius (~5–50 nm) means that we can obtain in-situ elastic stiffness images with nanoscale spatial resolution.

In FY04, we extended our quantitative AFAM techniques in a variety of ways. In one effort, the effect of film thickness on measurement accuracy was investigated. We measured M for three nickel (Ni) films approximately 50, 200 and 800 nm thick. The values of M ranged from 220 GPa to 223 GPa, significantly lower than that expected for bulk polycrystalline Ni. Scanning electron microscopy (SEM) revealed that the films were nanocrystalline (grain diameter < 30 nm). The observed reduction in M may be attributed to an increased volume fraction of grain boundaries in the nanocrystalline films. More importantly, the average values of M for all three films were the same within measurement uncertainty (~10 %). Thus the AFAM results were not influenced by the elastic properties of the silicon substrate, even for a 50 nm film. This behavior is due to the fact that the AFAM stress field extends less than 100 nm into the sample and decreases rapidly with depth due to the small applied static loads (0.3–3 µN) and small radius of contact (5–25 nm). Our result contrasts sharply with nanoindentation, in which substrate properties must be included to accurately measure submicrometer films.

The elastic properties of the 800 nm Ni film were also measured using NI, microtensile testing, and surface acoustic wave spectroscopy (SAWS). Both AFAM and NI measure the film’s out-of-plane indentation modulus. The results were in excellent agreement, validating AFAM as a quantitative method in spite of its relative newness. Microtensile testing values for the in-plane Young’s modulus of the film were not consistent with the AFAM and NI results if the film was assumed to be elastically isotropic. The apparently contradictory results were reconciled by use of a transversely anisotropic model for the film’s elastic properties. This model is consistent with the strong <111> film texture observed by x-ray diffraction. When analyzed with the same model, the SAWS results indicated that the film density was only slightly lower (< 5 %) than the bulk value. These results illustrate a relatively straightforward way to interpret mechanicalproperty measurements of thin films that is based on a more physically realistic model than the simple assumption of elastic isotropy.

Another effort investigated the effects of relative humidity (RH) on AFAM measurements. AFAM contact stiffness measurements may be affected by a variable water layer between the tip and sample, at least in some cases. By refining our data analysis methods to include the effects of such a layer, apparent correlations between the measured values of M and the ambient RH were eliminated. This year we also developed a RH-controlled AFM chamber in order to systematically study these effects. Samples for the experiments were provided by the Polymers Division and consisted of patterned self-assembled monolayers (SAM) of n-octyldimethylchloro-silane on Si substrates. Through controlled ultraviolet-ozone exposure, the relative hydrophobic/hydrophilic nature of the SAM was adjusted in different sample regions. Figure 1 shows an AFM topography image and an AFAM relative-stiffness image for a SAM/Si sample. The SAM stripes are virtually invisible in the topography image, even at very high resolution (10 nm full scale height). However, the AFAM image clearly reveals the hydrophobic SAM stripes. The regions covered by the SAM appear more compliant (lower contact stiffness) due to AFAM’s sensitivity to local variations in the tip-sample adhesion. We are currently performing further experiments on similar samples in order to quantify how humidity and adhesion effects can be distinguished from true mechanical-property variations.

Figure 1: a) AFM tapping-mode topography and b) AFAM relative-stiffness images of Si with n-octyldimethylchlorosilane SAM.

AFAM contact-resonance frequencies depend not only on elastic properties, but also on the value of the tip radius R. Thus knowledge of R and how it changes over time is essential for accurate measurements of elastic properties. To address this issue, we performed AFAM experiments with different AFM cantilevers on a sample with known elastic properties. The first measurements were done at relatively low static loads; the load was then successively increased up to several micronewtons to try to break and/or plastically deform the tip. High-magnification SEM images were obtained before and after each AFAM measurement. As can be seen in Figure 2, R increased with use, indicating tip wear. Values of R measured from the SEM images were compared to the values obtained from AFAM data using a Hertzian contact-mechanics model. The AFAM values of R were consistently smaller than the SEM values. Further data analysis and additional experiments are planned to clarify this issue. The knowledge gained in this way will help us to refine our understanding of AFAM contact mechanics, beyond the Hertz approximation, in order to improve measurement accuracy and repeatability.

Figure 2: SEM images of AFM cantilever tip a) before use and b) after repeated AFAM contact experiments. The circled regions indicate the tip wear that occurred through use.

In related work, we are performing finite-element studies of the AFM cantilever. The finite-element mesh is based on actual cantilever dimensions from SEM images and includes elastic anisotropy. The predicted free-space resonant frequencies are in excellent agreement with those observed experimentally. Work is underway to predict the vibrational behavior in contact. These results will allow us to refine our data analysis models and thus improve measurement accuracy.

The research described above involves either quantitative single-point measurements, or qualitative imaging of relative stiffness. In FY04, we worked to realize our ultimate goal of quantitative nanomechanical mapping. Critical to our success is a new frequency tracking circuit that can determine the contact-resonance frequencies at each image pixel. The circuit is based on digital signal processing architecture that enables rapid data acquisition (typically < 30 min. for a 256 × 256 image). We have begun to obtain resonance-frequency images for a variety of materials. Recent enhancements to our AFM mean that we can acquire images from not only the flexural modes, but also the torsional modes of the cantilever. By combining information from flexural and torsional images, it may be possible to determine simultaneously both Young’s modulus and Poisson’s ratio for an isotropic material. Work in upcoming months will focus on issues related to quantitative image interpretation such as calibration procedures, cantilever selection, tip wear, and choice of contact-mechanics model. Each of these elements plays a role in attaining our goal of truly quantitative nanomechanical imaging.

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