Trolling Mode Technique Long Tip Dynamics for the Contact Resonance Theoretical Model

Abstract

The field of Atomic Force Microscopy (AFM) continues to grow in applicationand development due to the vast amount of research performed over the past threedecades. The measurement capabilities and measurement methodologies of AFMcontinue to expand and far surpass the original capabilities of its 1986 inception. Anin-depth exploration of the capabilities of AFM has resulted in the development ofinnovative data acquisition methods accompanied by the use of theoretical modelsin order to accurately interpret results. One of these methods is Contact ResonanceAtomic Force Microscopy (CR AFM) and is characterized by its ability to retrievemechanical properties of materials such as Young's Modulus of Elasticity. CR AFMutilizes a mathematical model designed using the physical and geometrical parametersof the AFM probe. Although the compilation of this novel microscopy researchhas proven to rapidly increase the versatility AFM, the main challenges that characterizethe field of nanotechnology are still present. Since working with sampleswhose dimensions are in the nanoscale presents a challenge for sample interactionand examination, new AFM techniques, such as the Trolling Mode Technique (TMT)have been developed. The use of TMT involves physically modifying the traditionalAFM probe to overcome some of the inherent challenges nanotechnology poses. Inthis document, we present an updated theoretical model for the CR AFM method,specifically tailored for the use of the TMT experimental setup during a CR AFMviscoelastic property retrieval trial. We derive the mathematical model and providecalibration for the parameters required in order to utilize the model. We then, verifythe accuracy of our model by comparing our results to a 3D finite element model.Through this investigation, we create an updated CR AFM model which can be implementedfor TMT that provides a higher degree of accuracy than the traditional model.