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Contact Resonance Atomic Force Microscopy (CR-AFM)


Contact Resonance AFM (CR-AFM) is one of the most reliable and accurate AFM methods for nanoscale elastic/viscoelastic property measurements. In terms of elastic modulus measurement CR-AFM 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.



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. 

Schematic of CR-AFM measurement setup
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 done either by an analytical model or numerical calculations in the absence of an analytical solution. 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
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.


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
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
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. 

STM and CR-AFM images over the same area of a granular Au film
(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. 

CR-AFM maps over a Cu line embedded into a low-k dielectric material
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.



Relevant Publications


Impact and customers

  • Develop instrumentation, measurement protocols, and calibration procedures for various AFM-based nanomechanical property measurements. Promote CR-AFM methodology for readily integration into existing AFM platforms.
  • Perform state-of-the-art quantitative nanoscale mechanical property measurements on samples and devices from various academic institutions, government laboratories, and industries.
  • Collaborations with and knowledge dissemination to AFM developers on nanoscale mechanical property measurements and analysis.


Created May 3, 2023, Updated May 5, 2023