Quantitative atomic force microscopy

Hagen Söngen,Angelika Kühnle,Ralf Bechstein

doi:10.1088/1361-648x/aa6f8b

Abstract

A variety of atomic force microscopy (AFM) modes is employed in the field of surface science. The most prominent AFM modes include the amplitude modulation (AM) and the frequency modulation (FM) mode. Over the years, different ways for analyzing data acquired with different AFM modes have been developed, where each analysis is usually based on mode-specific assumptions and approximations. Checking the validity of the seemingly different approximations employed in the various analysis methods can be a tedious task. Moreover, a straightforward comparison of data analyzed with different methods can, therefore, be challenging. Here, we combine the existing evaluation methods which have been separately developed for the different AFM modes and present a unifying set of three equations. These three AFM equations allow for a straightforward analysis of AFM data within the harmonic approximation, regardless of the AFM mode. The three AFM equations provide the three and only pieces of information about the tip-sample force available within the harmonic approximation. We demonstrate the generality of our approach by quantitatively analyzing three-dimensional AFM data obtained in both the AM and FM mode.

Highlights

Three decades have passed since atomic force microscopy (AFM) has been invented [1]
Different ways for analyzing data acquired with different AFM modes have been developed, where each analysis is usually based on mode-specific assumptions and approximations
We demonstrate the generality of our approach by quantitatively analyzing three-dimensional AFM data obtained in both the amplitude modulation (AM) and frequency modulation (FM) mode

Summary

Introduction

Three decades have passed since atomic force microscopy (AFM) has been invented [1]. During this time a number of experimental strategies for obtaining AFM data have been developed, namely static AFM as well as the dynamic AFM modes using ‘amplitude modulation’ [2] (AM), ‘phase modulation’ [3] (PM) and ‘frequency modulation’ [4] (FM). Numerous theoretical studies have been devoted to a quantitative understanding of the recorded AFM data in the respective modes. Three pieces of information about the tip-sample force can be obtained, namely the average even. We provide the three AFM equations which allow to obtain these three pieces of information. They are valid for analyzing AFM data irrespective of the specific AFM mode. We will derive the three AFM equations: first, we will split the tip-sample force into an even and an odd part. The three AFM equations will be obtained They connect the quantities measured in AFM with the three and only pieces of information about the tip-sample force available in AFM within the harmonic approximation.

Derivation of the three AFM equations

The three pieces of information about the tip sample force

Experimental demonstration