Numerical Analysis of Sub-Atomic AFM Imaging in Ultra-High Vacuum: Coupling Quantum Mechanics With Continuum Dynamics
Recent reports of sub-atomic resolution AFM images acquired using transition metal tips have sparked debate within the AFM community. However, an in-depth theoretical feasibility study of this work has yet to be produced. We focus on the tungsten/graphite system investigated by Hembacher and coworkers [Science 305, 380–383 (2004)] in which experimental higher-harmonics images revealed four-leaf clover symmetry features within the tungsten atom diameter. The authors interpret these features as the footprint of four bonding lobes of increased charge density at the tip apex atom, thought to be caused by covalent-like bonding in the bulk. Here we present our development of a computational method ranging from density functional theory to continuum dynamics for simulating the imaging process. We find that four lobes of increased electronic density are indeed present for W(001) tips and demonstrate the ability of the chemical forces on the tip apex atom to produce higher harmonics images.