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Sub-Surface Elastic Depth-Profiling by Intermittent-Contact Resonance Atomic Force Microscopy


The Intermittent Contact Resonance AFM (ICR-AFM) technique aims to add 3D mechanical property mapping to the surface topographies generated during force-controlled intermittent-contact AFM scans. Through hybrid time and frequency domain measurements, ICR-AFM provides contact stiffness and damping characterizations that can be converted into 3D quantitative elastic/viscoelastic nanoscale maps. It extends the traditional AFM-based 2D surface mechanical characterization to the sub-surface quantitative profiling of material heterogeneities, structural changes, and compositions. When paired with computation modeling and other AFM-based property characterization methods, ICR-AFM offers new avenues to examine the structure-property relationship at the nanoscale.


Structure-property characterization is of increasing relevance to nanoscale technologies (e.g., electronic industry, micro- and nano-electromechanical systems, composite materials, coatings etc.) that require precise shaping and ordering of materials into component structures. As this control aims to advance towards the atomic limit, better optimization of the fabrication process is sought not only through dimensional metrology but also by controlling various material properties with the necessary spatial resolution. Scanning probe microscopy-based techniques offer advanced and versatile techniques able to access locally a nanoscale region of interest. In this regard, ICR-AFM operates at the spatial resolution of the AFM and provides a 3D mechanical characterization of the sub-surface region underneath the surface mapped by the AFM.

Schematic ICR-AFM on an elastically inhomogeneous material
Figure 1. ICR-AFM on an elastically inhomogeneous material showing the surface topography (bottom right) and elastic contrast that can be observed in the stiffness maps (top left) obtained from the ICR-AFM signal.

ICR-AFM pairs the concept of CR-AFM with a force-controlled intermittent AFM mode. In CR-AFM, the contact between an AFM probe and a sample is mechanically vibrated to observe how the resonance frequencies of the cantilever are affected by the tip-sample mechanical interaction. By considering the dynamics of the system (cantilever-tip-sample coupling) the measured contact resonance frequencies are converted into the tip-sample contact stiffness, which in turn is used to determine the elastic modulus of the sample based on a contact mechanics model. Nominally, CR-AFM operates in AFM contact mode, which means that CR-AFM measurements are made while the AFM scans the surface at a prescribed load. As such, the CR-AFM is essentially a 2D material property characterization and was used mainly for quantitative measurements of materials that might have in-plane heterogeneity but otherwise are homogeneous in their sub-surface regions. The in-depth response of a sample can be better captured by AFM modes that probe the sample intermittently with the applied force ramped during each contact. ICR-AFM (Figure 1) operates in such a force-controlled intermittent AFM scanning mode and the change in the contact resonance is measured as the tip is brought in and out of contact with the sample at each location in the scan. Once assembled over the scanned area, the depth-dependent ICR-AFM contact stiffness measurements provide a 3D mechanical characterization of the sub-surface region and can resolve possible material inhomogeneities.

Schematic diagram of ICR-AFM mode
Figure 2. Left panel: Schematic diagram of ICR-AFM mode, with the amplitude modulation controlled by a peak-force tapping (blue loop) and frequency modulation controlled by a phase-locked-loop system (red loop). Right panel: the cantilever deflection during one peak-force tap is shown as the superimposed responses to the tip-sample interactions of the two excitations (slow-blue, fast-red).

An implementation of ICR-AFM on PeakForce Tapping (PFT) AFM mode was developed in the Nanomechanical Properties Group at NIST by Gheorghe Stan and Richard Gates (US Patent 9535085, 2017). The PFT amplitude modulation operates at low fixed frequencies (between 0.5 kHz and 2.0 kHz) and prescribed peak-force (maximum applied force on the tip-sample contact). On top of the PFT operation, ICR-AFM adds an independent frequency modulation of small amplitude to the cantilever by means of a frequency-controlled tracking system like a phase-lock-loop (PLL) module. As shown in Figure 2, the two modulations are applied to the tip–sample contact through two separated actuators and at unrelated frequencies for crosstalk reduction: the amplitude modulation is at a non-eigenmode of the cantilever (2 kHz or less) and the frequency modulation is at one of the cantileverʼs eigenmodes (in the hundreds of kHz to few MHz range). The right panel of Figure 2 shows that (going from left to right) as the tip is brought in and out of contact during one PFT oscillation, the resonance frequency of the cantilever shifts from its free value to higher and higher values and goes back to its free value: at position (1), on approach, a high load imposes a high shift in the contact resonance frequency; at position (2), on retract, a lower applied load provides a lower shift in the contact resonance frequency; at position (3), the cantilever is out of contact and the resonance frequency returns to its free oscillation value.

Relevant Publications

  • Gheorghe Stan, Santiago D. Solares, Bede Pittenger, Natalia Erina, and Chanmin Su, Nanoscale mechanics by tomographic contact resonance atomic force microscopy, Nanoscale 6, 962 (2014) (
  • Gheorghe Stan and Richard S. Gates, Intermittent contact resonance atomic force microscopy, Nanotechnology 25, 245702 (2014) (
  • Gheorghe Stan, Ebony Mays, Hui Jae Yoo, and Sean W. King, Nanoscale tomographic reconstruction of the subsurface mechanical properties of low-k high-aspect ratio patterns, Nanotechnology 27, 485706 (2016) ( 
  • Gheorghe Stan, Richard S. Gates, Qichi Hu, Kelvin Kjoller, Craig Prater, Kanwal Jit Singh, Ebony Mays, and Sean W. King, Relationship between chemical structure, mechanical properties and materials processing in nanopatterned organosilicate fins, Beilstein Journal of Nanotechnology 8, 863 (2017) (
  • Gheorghe Stan and Richard S. Gates, Intermittent contact resonance atomic force microscopies and process for intermittent contact resonance atomic force microscopy, US Patent 9535085 (2017) (
  • Gheorghe Stan, Ebony Mays, Hui Jae Yoo, and Sean W. King, The effect of edge compliance on the contact between a spherical indenter and a high-aspect-ratio rectangular fin, Experimental Mechanics 58, 1157 (2018) (
  • Gheorghe Stan, The effect of edge compliance on the adhesive contact between a spherical indenter and a quarter-space, International Journal of Solids and Structures 158, 165 (2019) (

Major Accomplishments

Contact resonance frequency measured by ICR-AFM
Figure 3. Contact resonance frequency measured by ICR-AFM (bottom) during scanning over organosilicate high-aspect ratio fins (top). A change in the contact resonance frequency is observed at each tap only on top of the fins and shows strong dependences on the width and proximity to the edges of the fins.

The distinctive capabilities of ICR-AFM were proved on mapping the depth and width dependencies of the contact stiffness of nanoscale high-aspect ratio organosilicate patterns (refer to Figure 3). As can be seen in Figure 3, at each tap on top of the patterns, as the tip is pushed in and out of contact, the eigenmode frequencies of the cantilever vary in accordance to the induced change in the stiffness of the tip-sample contact. The measured ICR-AFM signal reveals strong variations as a function of size (width of the fins) and position with respect to the edge (edge compliance). By using their space locations (x and y for in-plane positions and z for the applied force), the ICR-AFM measurements can be assembled into a 3D volume of data (left panel in Figure 4), being possible to slice off tomographic sections along various directions. From this ICR-AFM data volume, the construction of the 3D elastic modulus tomography is obtained through an inverse problem, which is to find the elastic profile over the sensed depth in such a way that the calculated stiffness response of the material probed will match the depth dependence of the measured contact stiffness. By considering a layered variance in the elastic modulus of the structures and contribution from the edge compliance to the measured contact stiffness, the ICR-AFM measurements were converted into the 3D elastic modulus map through an iterative fit procedure. The results showed an increased stiffening of the exposed top and sidewall surfaces over a length scale of 10 nm to 20 nm compared with the bulk values of the material (right panel of Figure 4). In the case of very thin patterns, as narrow as 20 nm, the stiffening extends over the entire volume. This enhance in material stiffness is directly related with the structural alterations sustained by the organosilicates during processing (plasma etching, plasma ash, wet cleaning, etc.).     

Surface topography and corresponding CR frequency maps
Figure 4. Left: Surface topography and corresponding CR frequency maps at three applied loads. Right: selective surface topography and reconstructed elastic modulus tomography of the structures. Lateral and vertical variations in the elastic modulus are observed in both front-view (across the patterns) and depth-view (along the patterns); the locations of the patterns are marked by gray traces in the basal plane.

The ICR-AFM measurements can be paired with other nanoscale characterization techniques to detail the structure-property relationship of materials at the nanoscale and how this is affected by processing. We have combined ICR-AFM with atomic-force-microscopy-based infrared spectroscopy (AFM-IR) to investigate the correlations between material properties and chemical structure during the fabrication of 20 nm to 500 nm wide patterns in a nanoporous organosilicate material. We showed that by combining these two techniques (Figure 5, left), one can clearly observe variations of chemical structure and mechanical properties that correlate with the fabrication process and the feature size of the organosilicate fins. Specifically, we have observed an inverse correlation between the concentration of terminal organic groups (Si-CH3) and the stiffness of nanopatterned organosilicate fins (Figure 5, right). The selective removal of the organic component during etching results in a stiffness increase and reinsertion via chemical silylation results in a stiffness decrease. Examination of this effect as a function of fin width indicates that the loss of terminal organic groups and stiffness increase occur primarily at the exposed surfaces of the fins over a length scale of 10 nm to 20 nm.

Combined mechanical (ICR-AFM) and chemical (AFM-IR) measurements
Figure 5. Left: Combined mechanical (ICR-AFM) and chemical (AFM-IR) measurements on high-aspect ratio organosilicate patterns. Right: Si-CH3 absorbance (AFM-IR) and Young’s modulus (ICR-AFM) as functions of the feature size for unpatterned and patterned nanoporous organosilicates.

Future work will be focused on three areas: 1) further development and implementation of ICR-AFM on various AFM platforms (e.g. high-speed force-volume) and with other driving excitations (e.g. photothermal/thermal noise actuation of the cantilever); 2) test ICR-AFM applicability on various inhomogeneous materials and structures; 3) explore/adopt appropriate contact mechanics models (either analytically or by modeling) to convert ICR-AFM measurements into intrinsic material property parameters.

  • This effort is part of the Nanomechanical Properties Group Project structure and falls under the Physical, Chemical, and Mechanical Properties of Materials Program of the Materials Measurement Science Division (MMSD).
Created September 4, 2020