Ž . Applied Surface Science 123r124 1998 249–254 Contrast mechanism in non-contact AFM on reactive surfaces a, ) b ˇ c c Ruben Perez , Michael C. Payne , Ivan Stich , Kiyoyuki Terakura ´ ´ a Departamento de Fısica Teorica de la Materia Condensada, UniÕersidad Autonoma de Madrid, E-28049 Madrid, Spain ´ ´ ´ b Theory of Condensed Matter, CaÕendish Laboratory, UniÕersity of Cambridge, Madingley Road, Cambridge CB3 OHE, UK c Angstrom Technology Partnership and National Institute for AdÕanced Interdisciplinary Research, JRCAT, 1-1-4 Higashi, Tsukuba, Ibaraki 305, Japan Abstract Total-energy pseudopotential calculations are used to study the imaging process in non-contact atomic force microscopy Ž . on Si 111 surfaces. The atomic resolution seen in the experiments is attributed to the onset of covalent bonding between a localised dangling bond on the atom at the apex of the tip and the dangling bonds on the adatoms in the surface. This interaction dominates the force gradients, which drive the frequency changes used to create the experimental images. Force vs. tip displacement curves provide information about the optimum operation range and show the importance of the relaxation of the tip apex and surface atoms in the understanding of the damping images. q 1998 Elsevier Science B.V. PACS: 61.16.Ch; 71.15.Hx Ž . Keywords: AFM; Non-contact; Total-energy pseudopotential calculations; Force gradients; Atomic resolution; Si 111 1. Introduction Ž . wx The atomic force microscope AFM 1 was de- veloped as a tool capable of resolving surface struc- tures of both conductors and insulators by probing the spatial variation of the interatomic forces be- tween a tip and a surface. However, progress to- wards true atomic resolution in atomic force mi- croscopy in ultrahigh vacuum has been slower than Ž . in scanning tunneling microscopy STM . Operation in the contact regime, where tip and sample are in close mechanical contact, is affected by friction and local deformations of the surface which distort the images in an uncontrolled way. On the other hand, the measurement of the weak forces required for ) Corresponding author. atomic resolution in the non-contact attractive regime is a challenging experimental problem. w x wx Giessibl 2,3 and Kitamura and Iwatsuki 4 showed, for the first time, atomic resolution in the w x non-contact UHV regime using a Si tip scanning a Ž . reactive surface, the reconstructed Si 111 7 = 7 sur- face. These experiments used a novel frequency wx modulation detection scheme 5 that sensed the force gradient, instead of the force itself. A quick comparison of the AFM images in Refs. w x 2–4 with the STM images of the same surface showed that we were still far from an equivalent performance. Giessibl’s experiment showed a low- quality image of the surface, similar to Kitamura and Iwatsuki’s result, except for a small area where suddenly, for the width of a unit cell, the characteris- tic protrusions associated with the 12 adatoms on the top layer of the reconstruction could be clearly seen. 0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII S0169-4332 97 00536-9