Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Nanoscale Mechanics by Contact Resonance Atomic Force Microscopy (CR-AFM)


Through its contact-based accessibility to the nanoscale, the atomic force microscopy (AFM) provides a 3D topographical imaging of various surfaces and structures. Besides this topographical mapping, AFM facilitates many nanoscale property measurements, with mechanical properties being directly rendered by most of the commonly used and a few specially devised AFM modes. One of the most reliable and accurate AFM methods for nanoscale elastic/viscoelastic property measurements is the contact-resonance AFM (CR-AFM), which in terms of elastic modulus measurement has a large range from few GPa to hundreds of GPa. Over the years we have continuously improved the quantitative CR-AFM measurements in terms of instrument developments, elastic modulus calibration, contact mechanics analysis, and applications on a variety of materials and structures, including but not limited to elastic properties of one-dimensional structures (nanowires, nanotubes, fibers), thin film coatings, layered materials, organosilicate patterns, nanocomposites, etc. Paired with the built-in nanoscale positioning of the AFM, the integrative CR-AFM measurements provide a unique mechanical characterization for the next generation of materials and structures used in nanoscale applications and devices.


Contact-resonance AFM (CR-AFM) has been demonstrated to provide accurate, noninvasive, and reliable measurements at the nanoscale.  In CR-AFM the local elasticity of a surface is probed by observing the shift in one of the eigenmode resonance frequencies of an AFM probe brought into contact with the surface.  The resonance frequencies of the AFM cantilever change in accordance to the elastic stiffness of the probe-sample contact. A schematic of an AFM probe mechanically modulated from the base of the cantilever while in elastic contact with a sample is shown on the left part of Figure 1. An example of measured CR frequency spectrum on a Si surface is shown on the right part of Figure 1, with the first two eigenmode resonance frequency peaks of the cantilever shifting from their out-of-contact (blue) to in-contact (red) values.

Schematic of CR-AFM measurement setup
Figure 1. Left: Schematic of CR-AFM measurement setup, with a mechanical modulation from the base of the cantilever. Right: CR-AFM frequency spectrum highlighting the shift in the resonance frequency of the first two eigenmodes from out-of-contact to contact on a Si surface.

Based on the cantilever dynamics, the measured CR frequencies are converted into contact stiffnesses, which further are used to determine the elastic modulus of the sample tested by applying an appropriate contact mechanics description to the tip-sample contact. This poses a few challenges in terms of unavailable geometrical parameters (e.g. tip shape, contact radius), different surface mechanics across materials (e.g. adhesion, viscoelasticity), and lack of analytical contact mechanics models for various sample geometries. The analysis of the contact mechanics is resorted to numerical calculations in the absence of an analytical solution. For example, in Figure 2 is shown an adhesive contact between a spherical rigid indenter and an edge geometry from a numerical calculation of a boundary element method. Also, the accuracy of CR-AFM measurements is greatly enhanced by using reference materials, with successive measurements on the test material and reference materials of known elastic moduli; this procedure can circumvent some parameters that are not available for measurement.

Tip-sample contact geometry
Figure 2. Left: Tip-sample contact geometry nearby to the edge of a quarter-space sample. Right: Surface stress and deformation from an adhesive contact between a rigid indenter and a quarter-space sample.

CR-AFM has the spatial resolution on the order of several nanometers (limited by the contact radius of the probing tip) and a measurement uncertainty of about ± 5 % for elastic moduli in the range of a few GPa to hundreds of GPa. With the AFM versatility of probing substrate-supported nanostructures, CR-AFM can be used for the elastic modulus measurements of various one-dimensional nanostructures (nanowires, nanotubes), two-dimensional systems (atomic layers, thin coatings), as well as three-dimensional architectures (patterns, composites). CR-AFM requires no additional testing device or specimen manipulation and it was implemented in various forms on most of the AFM platforms.

In addition to a specialized AFM-based mode like CR-AFM, we also apply other commonly used modes like Force Volume, PeakForce Tapping, and Amplitude Modulation AFM (Tapping AFM) to study various nanoscale mechanical property measurements (e.g. adhesion, dissipation, phase contrast, etc.). Moreover, the AFM itself can be used in various setups to manipulate and probe specimens in bending, fracture, and other nanoscale mechanical tests.   

Relevant Publications


Major Accomplishments

CR-AFM calibration on multiple reference materials. When some of the geometrical parameters like tip radius or cantilever stiffness are not readily available in CR-AFM measurements, the alternative is to perform CR-AFM tests on some reference materials in addition to that on the test sample. By taking the ratio of the contact stiffnesses measured on test and reference materials, the unknown parameters are eliminated (under the assumption that the contact geometry is preserved during measurements) and the elastic modulus of the test sample is quantitatively determined. The uncertainty of the measurements is greatly reduced when two reference materials with elastic moduli bracketing that of the test material are used for CR-AFM calibration.

Dual reference calibration method schematic
Figure 3: Dual reference calibration method for CR-AFM measurements, with the two reference materials having elastic moduli that bracket that of the test sample.

CR-AFM on one-dimensional nanostructures. CR-AFM was successfully applied to measure the elastic moduli of various nanowires and nanotubes. Detailed modeling, both analytical and numerical, were used either to assess the surface effects on the core-shell composition of some nanowires or just determine the elastic moduli of one-dimensional nanostructures with unconventional geometries. Unlike most of the currently developed nanoscale mechanical tests for one-dimensional nanostructures (e.g. tensile tests observed inside a scanning electron microscope), CR-AFM requires no additional testing device or manipulation but simply substrate-supported specimens.

chematic CR-AFM measurements
Figure 4: Schematic CR-AFM measurements (left) and relative contact stiffness (right) at various points measured on the substrate along either side of a NW and over the NW’s top.

CR-AFM mapping on granular surfaces. By performing CR-AFM measurements during an AFM topographical scanning, a map of the elastic modulus can be retrieved from the measured CR frequencies and be associated to the scanned surface. The conversion from the measured CR frequencies to elastic moduli preserves the CR contrast on flat regions within the scanned surface. However, variations in the contact geometry during scanning must be accounted for on surfaces with significant roughness, granularity, sharp edges, or any other non-flat geometries for correct elastic modulus determination. For example, in Figure 5 is shown an example on an Au granular surface, for which the local topographical configuration of the contact geometry had to be combined with the measured CR frequency in the construction of the elastic modulus map.

STM and CR-AFM images over the same area of a granular Au film
Figure 5: (a) and (b) STM and CR-AFM images over the same area of a granular Au film; (c) CR frequency sweeps along a scan line; (d) A selected triple grain-junction from (a); (e) The interception between the tip and the surface shown in (d) is in the form of a multi-asperity contact. With the contact geometry detailed in (e), the STM and CR-AFM images are self-consistently correlated to construct (f) the contact area and (g) the elastic modulus maps. The scale bars in (a), (b), (f), and (g) are 100 nm.   

Load-dependent CR-AFM on Cu/low-k dielectric circuits. Better description of the tip-sample contact mechanics is obtained in load-dependent CR-AFM measurements, namely when same material is tested under a series of different loads. Such measurements help in narrowing down the contact mechanics model that needs to be used and reduce the uncertainty of the determined elastic moduli. In Figure 6 are shown CR-AFM maps in terms of CR frequency and amplitude over a Cu line embedded into a low-k dielectric material. On one hand, the CR frequency contrast is associated solely to the elastic response of the two materials and, on the other hand, both CR frequency and CR amplitude maps must be combined to assess the damping response of the materials mapped.

CR-AFM maps over a Cu line embedded into a low-k dielectric material
Figure 6: CR-AFM maps over a Cu line embedded into a low-k dielectric material. The maps of topography ((a), (d) and (g)), contact resonance frequency ((b), (e) and (h)) and resonance amplitude ((c), (f) and (i)) were recorded during CR-AFM scans at various loads: 50 nN ((a)–(c)), 110 nN ((d)–(f)) and 215 nN ((g)–(i)). The scan area was 650 nm x 1000 nm. The topography and contact resonance maps are shown in three-dimensional views and the resonance amplitude maps in two-dimensional views.

Additional Nanoscale Property Measurements


Nanoscale bending tests by AFM manipulation. A sequential AFM manipulation-scanning protocol was developed to bend nanowires (NWs) simply held by adhesion on a flat substrate. The adhesion between the NWs and substrate provided strong-enough forces to maintain the NWs in the imposed bending states. In various bending configurations (hook and loop), it was possible to observe large bending stress states of Si NWs as their radius of curvature was progressively reduced (refer to Figure 7). The bending states prior to failure were analyzed in detail to measure the bending dynamics and the ultimate fracture strength of the investigated nanowires. The benefit of the method is that it does not require special grips at the ends of the NW tested and allows a post-observation of the bending states.

 AFM probe as a nanoscale manipulator
Figure 7: By using an AFM probe as a nanoscale manipulator, a Si NW was progressively bent from a straight state (top left) to fracture (right top). The intermediate bending states were imaged in regular AFM scans (counterclockwise from top left to top right) to detail the accommodated stress during bending and capture the maximum bending strength of the nanowire prior to its fracture.

Nanoscale buckling of high-aspect-ratio organosilicate fins during hard-mask patterning. A hybrid characterization method was implemented to analyze quantitatively the buckling of organosilicate fins that are capped with hard masks of TiN in the process of lithographic formation of Cu/low-k dielectric circuits. Based on measurements of mechanical properties and geometric dimensions, the states of fins with various degrees of buckling were accurately described and used to put together a framework for guiding the design of future nanoscale interconnect architectures.

AFM view of the top and sides of buckled fins
Figure 8: Left: AFM view of the top and sides of buckled fins. Top right: AFM maps of the top of the buckled fins in states of various degrees of buckling amplitude and wavelength. Bottom right: TEM image of the cross-section of buckled TiN-capped fins.

Nanoparticle size metrology. Inherently, the synthesized nanoparticles have a large size distribution that can adversely affect their use and performance in various applications in the fields of medicine, biology, and material science. We use AFM to accurately measure the size distribution of various nanoparticles (e.g. Au, silica, Zn, Cu, PEGylated metallic particles etc.) simply supported on flat substrates (e.g. fresh cleaved mica).

AFM images of silica nanoparticle
Figure 9: AFM images of silica nanoparticle separation based on size-dependent aggregation induced by the critical Casimir effect: Before (left) and after (right) separation.


Created September 3, 2020