Peak Force Torsional Resonance Microscopy for Accurate Nanoscale Characterization of In-Plane and Out-of-Plane Mechanical Properties

Abstract

Accurately measuring both in-plane and out-of-plane mechanical properties is essential for understanding material behavior at the nanoscale. Conventional atomic force microscopy (AFM) techniques often struggle with the coupling between vertical and lateral forces, which can distort lateral mechanical property measurements. To address this limitation, we propose a novel Peak Force Torsional Resonance (PFTR) method that combines Peak Force Tapping for precise height control with torsional resonance for in-plane property extraction. This approach effectively decouples vertical and lateral forces, significantly reducing the influence of topography and vertical interactions on lateral measurements. Additionally, we introduce a mathematical model to accurately quantify lateral properties, such as shear modulus and lateral viscosity, independent of height variations. Experimental results confirm that the PFTR method achieves high-resolution imaging of both in-plane and out-of-plane mechanical properties, offering a more accurate and reliable solution for nanoscale mechanical characterization compared to conventional AFM-based methods. Note to Practitioners—This work addresses a common challenge in nanoscale mechanical property measurement: the interference from surface topography that affects accurate imaging of in-plane (lateral) properties. Traditional AFM methods struggle with this coupling effect, making it difficult to reliably measure both in-plane and out-of-plane mechanical characteristics—measurements that are vital in fields such as semiconductor manufacturing and materials development. This paper introduces PFTR Microscopy, a new AFM-based approach designed to decouple these forces and accurately resolve nanoscale mechanical properties. PFTR combines PFT for height control with torsional resonance to extract in-plane mechanical data without distortions from surface topography. By providing clear imaging of lateral properties and reducing topographical artifacts, PFTR enables more reliable assessments of materials such as semiconductor coatings, thin films, and composite compounds used in high-precision industries. PFTR is validated through experimental comparisons with conventional AFM methods, demonstrating that it achieves higher resolution and accuracy in in-plane measurements. While this approach provides robust data for characterizing homogeneous materials, further research is needed to adapt it for complex, heterogeneous surfaces and to simplify calibration for broader industrial application. The ability to distinguish mechanical properties at the nanoscale also suggests potential for applications in MEMS design, failure analysis, and the characterization of soft or biological materials.