# Analysis of contact stiffness in Ultrasound Atomic Force Microscopy: Three-dimensional time-dependent ultrasound modeling

## TL;DR

This paper introduces a dynamic 3D ultrasound modeling approach for US-AFM that captures time-dependent contact stiffness variations, improving the understanding and optimization of subsurface imaging contrast.

## Contribution

It presents the first time-dependent 3D ultrasound analysis for contact stiffness in US-AFM, moving beyond static simulations to better predict image contrast.

## Key findings

- Time-dependent ultrasound analysis reveals modulation frequency effects.
- Dynamic modeling improves contrast prediction accuracy.
- 3D analysis enhances subsurface nanoimaging techniques.

## Abstract

Ultrasound Atomic Force Microscopy (US-AFM) has been used for subsurface imaging of nanostructures. The contact stiffness variations have been suggested as the origin of the image contrast. Therefore, to analyze the image contrast, the local changes in the contact stiffness due to the presence of subsurface features should be calculated. So far, only static simulations have been conducted to analyze the local changes in the contact stiffness and, consequently, the contrast in US-AFM. Such a static approach does not fully represent the real US-AFM experiment, where an ultrasound wave is launched either into the sample or at the tip, which modulates the contact stiffness. This is a time-dependent nonlinear dynamic problem rather than a static and stationary one. This letter presents dynamic 3D ultrasound analysis of contact stiffness in US-AFM (in contrast to static analysis) to realistically predict the changes in contact stiffness and thus the changes in the subsurface image contrast. The modulation frequency also influences the contact stiffness variations and, thus, the image contrast. The three-dimensional time-dependent ultrasound analysis will greatly aid in the contrast optimization of subsurface nanoimaging with US-AFM.