On Mapping Subangstrom Electron Clouds with Force Microscopy

In 2004 Hembacher et al. (Science 2004, 305, 380-383) reported simultaneous higher-harmonics atomic force mocroscopy (AFM)/scanning tunneling microscopy (STM) images acquired while scanning a graphite surface with a tungsten tip. They interpreted the observed subatomic features in the AFM images as the signature of lobes of increased electron density at the tungsten tip apex. Although these intriguing images have stirred controversy, an in-depth theoretical feasibility study has not yet been produced. Here we report on the development of a method for simulating higher harmonics AFM images and its application to the same system. Our calculations suggest that four lobes of increased electron density are expected to be present at a W(001) tip apex atom and that the corresponding higher harmonics AFM images of graphite can exhibit 4-fold symmetry features. Despite these promising results, open questions remain since the calculated amplitudes of the higher harmonics generated by the short-range forces are on the order of hundredths of picometers, leading to very small corrugations in the theoretical images. Additionally, the complex, intermittent nature of the tip-sample interaction, which causes constant readjustment of the tip and sample orbitals as the tip approaches and retracts from the surface, prevents a direct quantitative connection between the electron density and the AFM image features.