Determination of electrostatic force and its characteristics based on phase difference by amplitude modulation atomic force microscopy

Electrostatic force measurement at the micro/nano scale is of great significance in science and engineering. In this paper, a reasonable way of applying voltage is put forward by taking an electrostatic chuck in a real integrated circuit manufacturing process as a sample, applying voltage in the probe and the sample electrode, respectively, and comparing the measurement effect of the probe oscillation phase difference by amplitude modulation atomic force microscopy. Based on the phase difference obtained from the experiment, the quantitative dependence of the absolute magnitude of the electrostatic force on the tip-sample distance and applied voltage is established by means of theoretical analysis and numerical simulation. The results show that the varying characteristics of the electrostatic force with the distance and voltage at the micro/nano scale are similar to those at the macroscopic scale. Electrostatic force gradually decays with increasing distance. Electrostatic force is basically proportional to the square of applied voltage. Meanwhile, the applicable conditions of the above laws are discussed. In addition, a comparison of the results in this paper with the results of the energy dissipation method shows the two are consistent in general. The error decreases with increasing distance, and the effect of voltage on the error is small.