Skip to content
6CCVD Research

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-05-06
JournalBeilstein Journal of Nanotechnology
AuthorsNicholas Chan, Carrie Lin, Tevis D. B. Jacobs, Robert W. Carpick, Philip Egberts
InstitutionsUniversity of Calgary, University of Pennsylvania
Citations6
AnalysisFull AI Review Included

Quantitative Determination of Interaction Potential Using FM-AFM

Section titled “Quantitative Determination of Interaction Potential Using FM-AFM”

Executive Summary

Section titled “Executive Summary”

This research introduces a robust methodology combining frequency-modulated Atomic Force Microscopy (FM-AFM) and Transmission Electron Microscopy (TEM) to experimentally determine and validate parameters for theoretical surface interaction potentials.

  • Novel Methodology: The technique integrates high-resolution FM-AFM force measurements with precise, experimentally determined 3D tip apex geometry (via TEM) to generate theoretical force curves for comparison.
  • Material System & Results: For the silicon oxide (SiOx) tip interacting with a diamond (100) substrate, the best-fit parameters assuming a 6-12 Lennard-Jones (LJ) potential were determined: Work of Adhesion (Wadh) = 80 ± 20 mJ/m2 and Range of Adhesion (z0) = 0.6 ± 0.2 nm.
  • Validation Tool: The method serves as the first experimental technique capable of verifying material interaction potential parameters across a range of tip-sample separation distances for an arbitrarily shaped tip apex.
  • Model Inadequacy: A critical finding is that the experimentally derived force curves qualitatively deviate from the theoretical 6-12 LJ model, exhibiting weaker attraction at larger separations and weaker repulsion at smaller separations.
  • Engineering Implication: This deviation suggests that the widely used 6-12 LJ potential is not suitable for accurately modeling near-contact interactions in the silicon oxide-carbon material system, necessitating the development of improved potential forms.
  • Experimental Environment: All force spectroscopy measurements were conducted in an Ultrahigh Vacuum (UHV) environment (1 x 10-10 Torr) to minimize environmental contamination and adsorbed layers.

Technical Specifications

Section titled “Technical Specifications”

The following table summarizes the key experimental and derived parameters for the SiOx-Diamond system study.

ParameterValueUnitContext
Work of Adhesion (Wadh)80 ± 20mJ/m2Best-fit 6-12 LJ parameter
Range of Adhesion (z0)0.6 ± 0.2nmBest-fit 6-12 LJ parameter
AFM ModeFrequency Modulation (FM)N/AUsed for force spectroscopy
Operating Pressure1 x 10-10TorrUltrahigh Vacuum (UHV)
Cantilever MaterialSilicon (with native oxide)N/APPP-NCL Nanosensors probe
Substrate MaterialSingle-crystal diamond (100)N/ANominally flat surface
Cantilever Spring Constant (k)30.5N/mDetermined via beam geometry method
Oscillation Amplitude (a)12 ± 1nmSet amplitude during Δf-d acquisition
Diamond RMS Roughness0.78nmMeasured over 500 nm x 500 nm area
Tip Apex CharacterizationTEM (JEOL 2010F)N/AUsed for 3D tip geometry reconstruction

Key Methodologies

Section titled “Key Methodologies”

The quantitative determination of the interaction potential involved a multi-step process integrating advanced microscopy and computational modeling:

  1. Sample Preparation and Cleaning:

    • Single-crystal diamond (100) samples were cleaned ultrasonically (acetone, then ethanol, 20 min each).
    • Samples and AFM probe were baked at 120 °C in the UHV chamber to remove residual moisture and adsorbates.

  2. Pre-Experiment Tip Characterization (TEM):

    • The silicon AFM tip apex was imaged using TEM prior to AFM measurements.
    • The 2D TEM profile was rotated and stitched to account for cantilever tilt and holder angle (22.5° offset).
    • The 2D profile was converted into a 3D axisymmetric tip volume using the method of disks, providing the precise geometry for modeling.

  3. FM-AFM Data Acquisition:

    • The tip-sample contact potential difference was compensated using a DC bias determined by measuring frequency shift versus sample bias voltage.
    • Frequency shift-displacement (Δf-d) curves were acquired on an 8 x 8 grid (500 nm x 500 nm area) on the diamond surface, with 20 curves per grid cell.

  4. Experimental Force Curve Extraction:

    • Experimental Δf-d curves were analytically converted into interaction force-distance (F(z)) curves using the Sader and Jarvis inversion method (Equation 2).
    • Curves exhibiting multiple localized force minima (indicative of noise or artifacts) were disregarded.

  5. Theoretical Force Curve Generation:

    • Theoretical Lennard-Jones F(z) curves were generated by numerically integrating the 6-12 LJ surface-traction equation (Equation 3) across the experimentally determined 3D tip geometry.
    • Wadh and z0 parameters were systematically varied (Wadh: 0.01 to 150 J/m2; z0: 0.1 to 3 nm) to create a library of theoretical F(z) curves.

  6. Parameter Fitting and Validation:

    • A least squares regression analysis was performed to align the experimental F(z) curves (which lack absolute separation distance) with the theoretical LJ F(z) curves.
    • The best-fit Wadh and z0 values were determined by minimizing the squared residual between the experimental and theoretical curves.

Commercial Applications

Section titled “Commercial Applications”

This methodology and its findings are highly relevant to engineering fields requiring precise control and modeling of interfacial forces at the nanoscale, particularly involving hard materials like diamond and silicon.

Industry/FieldRelevance and Application
Nanotribology & AdhesionProvides fundamental, validated parameters (Wadh, z0) necessary for accurate contact mechanics models (e.g., JKR, DMT) and simulations of friction and wear.
Data Storage TechnologyEssential for designing and optimizing interfaces in high-density hard disk storage and other devices where stiction and friction must be minimized at the nanometer scale.
MEMS/NEMS DesignCritical for predicting and mitigating adhesive failure (stiction) in micro- and nano-electromechanical systems, such as DLP micromirrors, which rely on low-adhesion coatings.
Computational Materials ScienceServes as an experimental validation tool for refining and developing new pair potentials (beyond 6-12 LJ) for mismatched material systems (e.g., silicon oxide/carbon), improving the fidelity of Molecular Dynamics (MD) simulations.
Advanced Coatings & InterfacesApplicable to characterizing the interaction potential of novel hard engineering materials and coatings (like diamond-like carbon, DLC) used in extreme environments.
View Original Abstract

The interaction potential between two surfaces determines the adhesive and repulsive forces between them. It also determines interfacial properties, such as adhesion and friction, and is a key input into mechanics models and atomistic simulations of contacts. We have developed a novel methodology to experimentally determine interaction potential parameters, given a particular potential form, using frequency-modulated atomic force microscopy (AFM). Furthermore, this technique can be extended to the experimental verification of potential forms for any given material pair. Specifically, interaction forces are determined between an AFM tip apex and a nominally flat substrate using dynamic force spectroscopy measurements in an ultrahigh vacuum (UHV) environment. The tip geometry, which is initially unknown and potentially irregularly shaped, is determined using transmission electron microscopy (TEM) imaging. It is then used to generate theoretical interaction force-displacement relations, which are then compared to experimental results. The method is demonstrated here using a silicon AFM probe with its native oxide and a diamond sample. Assuming the 6-12 Lennard-Jones potential form, best-fit values for the work of adhesion ( W adh ) and range of adhesion ( z 0 ) parameters were determined to be 80 ± 20 mJ/m 2 and 0.6 ± 0.2 nm, respectively. Furthermore, the shape of the experimentally extracted force curves was shown to deviate from that calculated using the 6-12 Lennard-Jones potential, having weaker attraction at larger tip-sample separation distances and weaker repulsion at smaller tip-sample separation distances. This methodology represents the first experimental technique in which material interaction potential parameters were verified over a range of tip-sample separation distances for a tip apex of arbitrary geometry.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1998 - Annual Proceedings - Reliability Physics (Symposium)

Reads Similar to This

Optical Magnetometry Based on Nanodiamonds with Nitrogen-Vacancy Color Centers RETRACTED - FIB in-situ fabrication of pseudo vertical diamond Schottky diode - H-terminated ohmic contact and O-terminated Schottky barrier THE EFFECTS OF BORON DOPING ON RESIDUAL STRESS OF HFCVD DIAMOND FILM FOR MEMS APPLICATIONS