# Nanoscale capacitance spectroscopy based on multifrequency electrostatic force microscopy

## TL;DR

A new microscopy method called MFH-EFM allows precise nanoscale capacitance measurements at high frequencies, improving the study of dielectric properties in materials.

## Contribution

MFH-EFM introduces a multifrequency approach for measuring capacitance gradients at arbitrary frequencies with high spatial resolution.

## Key findings

- MFH-EFM reduces signal background from long-range electrostatic interactions, enabling highly localized measurements.
- The method operates up to 5 MHz using standard AFM equipment and an external lock-in amplifier.
- It can be extended to gigahertz frequencies and improves precision in studying dielectric effects.

## Abstract

We present multifrequency heterodyne electrostatic force microscopy (MFH-EFM) as a novel electrostatic force microscopy method for nanoscale capacitance characterization at arbitrary frequencies above the second cantilever resonance. Besides a high spatial resolution, the key advantage of the multifrequency approach of MFH-EFM is that it measures the second-order capacitance gradient at almost arbitrary frequencies, enabling the measurement of the local dielectric function over a wide range of frequencies. We demonstrate the reliable operation of MFH-EFM using standard atomic force microscopy equipment plus an external lock-in amplifier up to a frequency of 5 MHz, which can in principle be extended to gigahertz frequencies and beyond. Our results show a significant reduction of signal background from long-range electrostatic interactions, resulting in highly localized measurements. Combined with refined tip–sample capacitance models, MFH-EFM will enhance the precision of quantitative studies on dielectric effects in nanoscale systems across materials science, biology, and nanotechnology, complementing established methods in the field.