Modeling and experimental investigation of cantilever dynamics in force detected single electron tunneling

The dynamic response of a voltage biased oscillating cantilever probe is investigated through experimental and theoretical analysis as it approaches a dielectric surface. When the tip reaches the appropriate gap single electron tunneling events are detected between the metallic tip and the surface. The tunneling events cause a decrease of the electrostatic force and force gradient acting between tip and sample. The change in the electrostatic force is detected as an abrupt decrease of the cantilever oscillation amplitude. Additionally, due to the nonlinear interaction between tip and sample, the cantilever oscillation amplitude in very close proximity of the sample can have multiple values. Typically, as the tip-sample gap is reduced, a transition between two stable cantilever oscillation modes is detected as an abrupt increase in the oscillation amplitude. If this transition occurs at a gap larger than the tunneling gap, no tunneling event is detected. A theoretical model that includes both the electrostatic and mechanical effects has been developed to investigate the cantilever response in close proximity of the sample. The model, which includes the effects of the single electron tunneling events, is in good agreement with the measurements.