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
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
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
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
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
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.
1. "A practical guide for analysis of nanoindentation data,"
M.L. Oyen and R.F. Cook, J. Mech. Behavior Biomedical Mat., 2 (2009)
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
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)
5. Intermolecular and Surface Forces, 2nd Edition, J.
Israelachvili, Elsevier Academic Press, London (1991).
"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)
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.
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.
Copyright AZoNano.com, Dr. Robert Cook (NIST)
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