Characterisation of the Material and Mechanical Properties of Atomic Force Microscope Cantilevers with a Plan-View Trapezoidal Geometry

Ashley D Slattery,Adam J Blanch,Cameron J Shearer,Renee V Goreham,Sarah L Harmer,Andrew J Stapleton,Jamie S Quinton,Christopher T Gibson

doi:10.3390/app9132604

Abstract

Cantilever devices have found applications in numerous scientific fields and instruments, including the atomic force microscope (AFM), and as sensors to detect a wide range of chemical and biological species. The mechanical properties, in particular, the spring constant of these devices is crucial when quantifying adhesive forces, material properties of surfaces, and in determining deposited mass for sensing applications. A key component in the spring constant of a cantilever is the plan-view shape. In recent years, the trapezoidal plan-view shape has become available since it offers certain advantages to fast-scanning AFM and can improve sensor performance in fluid environments. Euler beam equations relating cantilever stiffness to the cantilever dimensions and Young’s modulus have been proven useful and are used extensively to model cantilever mechanical behaviour and calibrate the spring constant. In this work, we derive a simple correction factor to the Euler beam equation for a beam-shaped cantilever that is applicable to any cantilever with a trapezoidal plan-view shape. This correction factor is based upon previous analytical work and simplifies the application of the previous researchers formula. A correction factor to the spring constant of an AFM cantilever is also required to calculate the torque produced by the tip when it contacts the sample surface, which is also dependent on the plan-view shape. In this work, we also derive a simple expression for the torque for triangular plan-view shaped cantilevers and show that for the current generation of trapezoidal plan-view shaped AFM cantilevers, this will be a good approximation. We shall apply both these correction factors to determine Young’s modulus for a range of trapezoidal-shaped AFM cantilevers, which are specially designed for fast-scanning. These types of AFM probes are much smaller in size when compared to standard AFM probes. In the process of analysing the mechanical properties of these cantilevers, important insights are also gained into their spring constant calibration and dimensional factors that contribute to the variability in their spring constant.

Highlights

Cantilever devices have been used as the key sensing elements in a number of instruments, including the atomic force microscope (AFM), and mass, fluid, and viscosity sensors
Accurate spring constant calibration of an AFM cantilever is critical to precisely measure adhesive forces between the tip and the surface of a sample [1,2,3,4,5], measure the mechanical properties of sample surfaces [6,7,8,9], and determine the appropriate force to accurately determine the thickness of 2D materials, such as graphene [10]
We demonstrate the applicability of the Sader indirect [16] spring constant calibration method for FastScan A probes which have proven challenging to calibrate using some of the standard methods such as the thermal noise method [43]

Summary

Introduction

Cantilever devices have been used as the key sensing elements in a number of instruments, including the atomic force microscope (AFM), and mass, fluid, and viscosity sensors. Since the development of the AFM, a number of techniques have been developed to determine the spring constant of cantilevers These techniques can be divided into different categories and include methods based on Euler beam equations [13,14,15], the resonant frequency response of the cantilever [16,17,18,19,20,21], thermal noise-based methods [22,23,24,25,26,27], loading the cantilever with a known force [28,29,30,31,32,33], or a combination of these [34]

Methods

Results

Conclusion