Atomic resolution in noncontact AFM by probing cantilever frequency shifts

Rutile TiO₂ (0 0 1) quantum dots (or nano-marks) in different shapes were used to imitate uncleaved material surfaces or materials with rough surfaces. By numerical integration of the equation of motion of cantilever for silicon tip scanning along the [1 1 0] direction over the rutile TiO₂ (0 0 1) quantum dots in ultra high vacuum (UHV), scanning routes were explored to achieve atomic resolution from frequency shift image. The tip–surface interaction forces were calculated from Lennard–Jones (12-6) potential by the Hamaker summation method. The calculated results showed that atomic resolution could be achieved by frequency shift image for TiO₂ (0 0 1) surfaces of rhombohedral quantum dot scanning in a vertical route, and spherical cap quantum dot scanning in a superposition route.