Nanomechanical Measurements and Tools

Nanotechnology provides great opportunities for the development of advanced devices with enormous quality-of-life and economic benefits, with applications ranging from biomedical implantable actuators to environmental toxin detectors to infrastructural remote sensors. Enabling these applications is the fact that nano-scale mechanical properties of materials are often radically different from those of their bulk or macro-scale counterparts.

Hence, a critical requirement for the commercial innovation and manufacturing of these devices is the parallel development of nanomechanical measurements to determine the elastic, plastic, viscous, and fracture properties of materials,¹ and local states of deformation and stress,² in quantitative detail and with nanometer spatial resolution. Nanomechanical measurements research is an exciting multi-disciplinary field at the intersection of mechanics, physics, and chemistry: New nanomechanical measurements not only reveal fundamental phenomena at the nano-scale but also have direct application in nanotechnology.

Many nanomechanical measurements focus on mechanical properties of materials or structures that have macroscopic analogs (e.g., the measurement of elastic modulus, yield stress, or fracture toughness). At issue here is performing measurements at small length scales. Intriguing new phenomena are observed in such measurements, such as increased elastic moduli of small-radii nanowires,^3,4 but perhaps the most interesting nanomechanical measurements are those focused on mechanical behavior intrinsic to the nano-scale: Forces associated with interactions between surfaces become comparable to those associated with bulk deformation at small scales⁵ and such forces become quantized as intrinsic material and system length scales are approached. At issue here is performing measurements of small-scale phenomena.

The Nanomechanical Properties Group at the National Institute of Standards and Technology, under the leadership of Dr. Robert F. Cook, develops measurement techniques and standards to enable the use of materials in nanomechanical applications. Many of the nanomechanical measurement tools developed are contact-probe based: Atomic force microscope (AFM) or instrumented indentation testing (IIT, or "nanoindentation") platforms are used to manipulate such probes and measure mechanical properties of material surfaces with nano-scale precision (see Figure 1). Non-contact beam-based tools include confocal Raman microscopy (CRM) and electron backscatter diffraction (EBSD), used for nano-scale stress mapping.

Figure 1. Map illustrating the dominant indentation contact modes with variations in material properties and measurement configurations: Increasing material yield resistance or test measurement time leads to plastic-dominated responses; increasing viscous flow resistance or probe indenter acuity ("sharpness") leads to viscous-dominated responses. The nano-scale contact responses of many materials are in the center of the map, exhibiting viscous-elastic-plastic behavior. See Ref. 1 for more details.

At the smallest length scales, AFM probes of ≈ 10 nm radius are used to measure the effects of humidity on the adhesion of ≈ 1 nm radius contacts.⁶ Analyses show that the work of adhesion includes contributions from elastic deformation of the probe and surface, van der Waals interactions between the probe and surface, and the capillary water meniscus surrounding the probe-surface contact.

At the same scale in ultra-high vacuum (UHV), conducting-probe AFM is used to measure the properties of metal-insulator-metal tunnel junctions formed by small molecules⁷ or self-assembled monolayers⁸ on gold surfaces. The mechanical and electrical properties of such junctions are strongly coupled and the electrical tunneling barrier properties are a function of the nanonewton-scale contact forces. These measurements are critical to the design and operation of nanoelectromechanical systems, in which nanometer-scale contacts are used.

At slightly larger scales, using 20 nm to 40 nm AFM probes and 2 nm to 3 nm contacts, contact resonance AFM (CR-AFM) techniques are used to measure and map elastic moduli with better than 10 nm spatial resolution. CR-AFM maps of nano-crystalline gold,⁹ grain size ≈ 70 nm, show significant elastic inhomogeneity with grain boundaries considerably more compliant than the grains, often a factor of two smaller in modulus (see Figure 2).

Figure 2. Map of the elastic modulus of nanocrystalline gold illustrating the compliant grain boundaries. This effect is critical in determining the elastic properties of nanogranular materials, as such materials contain much greater proportions of grain-boundary material relative to their macrogranular counterparts. See Ref. 9 for more details.

Conversely, CR-AFM measurements on ZnO³ and Te⁴ nanowires (NWs) show significant modulus increases, a factor of two greater than bulk values, for NWs with radii less than ≈ 50 nm, indicative of extremely strong surface influences. Such measurements enable predictions of the responses of nanomaterials to stress and open the possibility for tuning nanomaterial properties through size control.

At the largest AFM scale, using 12 µm colloidal probes and 20 nm contacts, adhesion measurements reveal the dominance of the capillary meniscus force at micro-scale contacts, and force invariance with relative humidity.¹⁰ Similar measurements in UHV show significant ductility associated with contact fractures, even for nominally brittle materials such as silicon.¹¹ Measurements such as these reveal mechanical phenomena intrinsic to the nano-scale, and in this case are critical in designing microelectromechanical devices against failure by friction or stiction effects.

At very small length scales, metal plasticity becomes quantized as yield is associated with the nucleation or propagation of individual dislocations. IIT measurements using diamond probes with large included angle are used to measure the onset of yield in single crystals with indentation depths of ≈ 10 nm (≈ 30 nm indentation radius).¹² Combined with AFM measurements of the exact shape of the probe, the ideal-crystal shear yield stress is determined.

IIT measurements with probes of small included angle are used to measure the nano-scale toughness of brittle materials, as such acute probes can generate very small indentation cracks. Acute indentation crack length measurements of nanoporous thin film dielectric materials show that toughness is invariant for cracks as small as 300 nm.¹³ Yield stress and toughness place fundamental limits on the loads materials can withstand, and these measurements are critical for reliability of microelectronic devices, in which metals and dielectrics are used pervasively at the nano-scale.

Non-contact CRM and EBSD techniques are used to map stress distributions in loaded components: CRM maps with ≈ 70 nm pixel size and better than ≈ 10 MPa stress resolution allow direct measurement of stress concentrations at defects in silicon (see Figure 3).^2,14 Selection of different laser excitation wavelengths for the Raman signal allows for probing at different depths from 50 nm to 1.5 µm subsurface.

EBSD maps with ≈ 10 nm spatial resolution provide comparable stress resolution and complementary 30 nm surface-localized probing. Measurements on a model wedge indentation in Si show agreement between the two techniques provided the information depths are comparable.² Nano-scale stress mapping is perhaps the most exciting nanomechanical measurement technique being developed, as it enables direct verification of the connection between material nanomechanical properties and the performance of nanomechanical devices.

Figure 3. Stress map of a 20 µm long wedge indentation in silicon: Red indicates regions of compressive stress, blue tensile stress. Knowledge of the complicated stress field is critical for determining the reliability of microelectromechanical systems devices. See Ref. 2 for more details.

Taken together, the measurements discussed above, along with many others, point to a vibrant and exciting time for nanomechanical applications of materials. New phenomena are being discovered at the nano-scale, leading to advances in physics, chemistry, and mechanical metrology. These advances are in turn enabling the development of new nanomechanical measurement tools.

In concert with advances in computational power, which regularly enables multi-million atom simulations of behavior, such measurement tools now have the precision and spatial resolution to refine the predictive abilities of simulations, further speeding the commercialization of nanotechnology for both consumer and industrial products.

References

1. "A practical guide for analysis of nanoindentation data," M.L. Oyen and R.F. Cook, J. Mech. Behavior Biomedical Mat., 2 (2009) 396-407.
2. "Comparison of Nanoscale Measurements of Strain and Stress using Electron Back Scattered Diffraction and Confocal Raman Microscopy," M.D. Vaudin, Y.B. Gerbig, S.J. Stranick, and R.F. Cook, Appl. Phys. Letters 93 (2008) 193116.
3. "Diameter-dependent Radial and Tangential Elastic Moduli of ZnO Nanowires," G. Stan, C.V. Ciobanu, P.M. Parthangal, and R.F. Cook, Nano Letters 7 (2007) 3691-3697
4. "Effect of surface proximity on the elastic modulus of Te nanowires," G. Stan, S. Krylyuk, A. Davydov, M. Vaudin, and R.F. Cook, Appl. Phys. Letters 92 (2008) 241908.
5. Intermolecular and Surface Forces, 2nd Edition, J. Israelachvili, Elsevier Academic Press, London (1991).
6. "Origin of Adhesion in Humid Air," D.-I. Kim, J. Grobelny, N. Pradeep, and R.F. Cook, Langmuir 24 (2008) 1873-1877.
7. "Mechanical and Electrical Coupling at Metal-Insulator-Metal Nano-Scale Contacts,"D.-I. Kim, N. Pradeep, F. W. DelRio, and R.F. Cook, Appl. Phys. Letters 93 (2008) 203102.
8. "Elastic, adhesive, and charge transport properties of a metal-molecule-metal junction: the role of molecular orientation, order, and coverage," F.W. DelRio, K.L. Steffens, C. Jaye, D.A. Fischer, and R.F. Cook, Langmuir (2009) DOI: 10.1021/la902653n .
9. "Mapping the elastic properties of granular Au films by contact resonance atomic force microscopy," G. Stan and R.F. Cook, Nanotechnology 19 (2008) 235701.
10. "Quantification of the meniscus effect in adhesion force measurements," J. Grobelny, N. Pradeep, D.-I. Kim, and Z.C. Ying, Appl. Phys. Letters 88 (2006) 091906.
11. "Ductility at the nanoscale: Deformation and fracture of adhesive contacts using atomic force microscopy," N. Pradeep, D.-I. Kim, J. Grobelny, T. Hawa, B. Henz, and M.R. Zachariah, Appl. Phys. Letters 91 (2007) 203114.
12. "Finite element analysis and experimental investigation of the Hertzian assumption on the characterization of initial plastic yield," L. Ma, D.J. Morris, S.L. Jennerjohn, D.F. Bahr, and L. Levine, J. Mater. Res. 24 (2009) 1059-1068.
13. "Indentation fracture of low-dielectric constant films, Part I. Experiments and observations," D.J. Morris and R.F. Cook, J. Mater. Res. 23 (2008) 2429-2442; "Part II. Indentation fracture mechanics model," D.J. Morris and R.F. Cook, J. Mater. Res. 23 (2008) 2443-2457.
14. "Effect of crystallographic orientation on phase transformations during indentation of silicon,"Y.B Gerbig, S.J. Stranick, D.J. Morris, M.D. Vaudin, and R.F. Cook, J. Mater. Res., 24 (2009) 1172-1183.

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