Cantilever Dynamics Of AFM Scanning Over Quantum Dots

Atomic resolution is achieved successfully with noncontact atomic force microscopy (nc-AFM) using frequency modulation (FM) technique on cleaved surface of various types of materials, including rutile TiO2. For true atomic resolution on not cleaved surface becomes feasible, the nc-AFM cantilever dynamics scanning over quantum dots in different shapes is studied theoretically.Models of pentahedron, hemisphere, spherical cap quantum dots as well as the combinations of the quantum dots of plane, pentahedron and spherical cap are set up. The interaction force between Si tip-surface of quantum dots in different shapes in radial route, vertical route, superposition route and superposition s1 route is calculated from the Lennard-Jones potential and Hamaker theory. Frequency shift in the different scanning routes is studied by numerical integration of the equation of motion of cantilever. Frequency shift image in nc-AFM is studied by silicon tip scanning over rutile TiO2 (001) surface in vertical route and superposition s1 route with different parameters.With work above-mentioned, interaction force between tip and the surface of quantum dot in different shapes show peak nature abruptly at Ti⁴⁺ and O^2- ions; the quantity, position and periodical nature of the tip-surface interaction force peak are analyzed. Frequency shift versus tip equilibrium position show that the frequency shift increases dramatically or rapidly before the contact point in vertical route and superposition s1 route. Atomic resolution is achieved by frequency shift image for rutile TiO₂ (001) surface of pentahedron quantum dot in vertical route, spherical cap quantum dot in superposition s1 route and combination quantum dot in combination route scanning along [110] direction.