What is it about?

Advances in nanoscale material design rely at some extent on the ability of measuring the material properties at that scale. This echoes the words of William Thompson (Lord Kelvin): “If you cannot measure it, you cannot improve it”. Atomic Force Microscopy (AFM) is one of the tools that provides access at the nanoscale and, at the same time, measures various interactions to extract local material parameters. For example, the dielectric constant of a thin film can be resolved from the measured electrostatic force interaction between a conductive AFM probe and a dielectric film. To know the dielectric constant value and its variation within nanometer range is a growing need in the fabrication of denser Cu/low-dielectric constant integrated circuits in high-performance semiconductor electronics.

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Why is it important?

Due to convenience and direct interpretation, analytical models and simple numerical modeling are usually preferred to convert AFM measurements into quantitative parameters. However, as is the case of long-range electrostatic interactions, an integral modeling of all the contributions from various parts of the AFM probe to the measured forces might be available only through a detailed numerical analysis. For the first time we used an integral, large-scale, three-dimensional (3D) numerical modeling to calculate in detail the electrostatic interaction between a conductive AFM probe and a dielectric film as part of a dielectric force microscopy setup. This included the local electrostatic interaction over the nanometer-micrometer scale, going from few nanometers (AFM apex) to tens of micrometers (AFM cone) and hundreds of micrometers (AFM cantilever). The obtained measurement sensitivities are relevant in selecting the optimal AFM scanning mode and its operational parameters for given film thicknesses and dielectric constants but also show the critical role of numerical analysis to the correct interpretation of the measurements.


A precise and accurate determination of the dielectric constant from electrostatic force microscopy measurements requires a 3D finite element modeling as described in this work with the probe geometry and dimensions replicating those of the actual probe and the exact probe-sample configuration of the measurement. The dielectric constant then would be determined through an inverse problem by minimizing the difference between the calculated and measured force or frequency response. Also, the 3D modeling of electrostatic force microscopy measurements might be the only solution in the case of materials or structures containing dielectric heterogeneity at the nanoscale. These include - but are not limited to - nanoscale patterns, embedded circuits, and layered structures of various electronic devices.

Gheorghe Stan
National Institute of Standards and Technology

Read the Original

This page is a summary of: Dielectric constant measurement sensitivity in electrostatic force and force gradient microscopy-based modes, Journal of Applied Physics, August 2023, American Institute of Physics,
DOI: 10.1063/5.0160540.
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