Quantitative Subsurface Atomic Structure Fingerprint for 2D Materials and Heterostructures by First-Principles-Calibrated Contact-Resonance Atomic Force Microscopy.

Interfaces and subsurface layers are critical for the performance of devices made of 2D materials and heterostructures. Facile, nondestructive, and quantitative ways to characterize the structure of atomically thin, layered materials are thus essential to ensure control of the resultant properties. Here, we show that contact-resonance atomic force microscopy-which is exquisitely sensitive to stiffness changes that arise from even a single atomic layer of a van der Waals-adhered material-is a powerful experimental tool to address this challenge. A combined density functional theory and continuum modeling approach is introduced that yields sub-surface-sensitive, nanomechanical fingerprints associated with specific, well-defined structure models of individual surface domains. Where such models are known, this information can be correlated with experimentally obtained contact-resonance frequency maps to reveal the (sub)surface structure of different domains on the sample.