Sensitivity and resolution in noncontact electrostatic force microscopy in the case of a constant potential

Abstract

The basic dynamic equations of the electrostatic force microscope are derived, in the case of a constant potential applied to a spherical tip above a conducting plane sample. The microscope tip moves in the electrostatic field, providing a force supposed to be inversely proportional to the distance. The linear and nonlinear approximations are treated to obtain the amplitude and phase of the vibration, at a fixed frequency. Optimal experiment conditions, i.e., distance, frequency, and voltage, which give the best sensitivity and lateral resolution, are discussed. The stability of the oscillations during the scans is dependent on the experiment conditions. In addition to the tapping regime, we show that two stable noncontact regimes may exist in some conditions. Only one stable noncontact oscillation occurs at a working frequency equal or superior to the natural frequency of the system. When a distance equal to the free amplitude is selected, the phase shift due to the potential is linear in function of the applied potential (instead of quadratic as observed at larger distances) and a good sensitivity to the potential of the sample is obtained. The theoretical lateral resolution is derived in the linear and nonlinear approximations, and is shown to depend strongly on the mean tip-sample distance. In the examples shown, the best resolution values are reached at a very close distance, with values much lower than the tip apex radius.