Quantitative electrostatic force measurement and characterization based on oscillation amplitude using atomic force microscopy

Measurement of electrostatic force at the micro-/nanoscale has a great scientific value and engineering significance. This paper develops a new determination method of electrostatic forces based on Kelvin probe force mode in atomic force microscopy (AFM). Applying DC voltage and AC voltage simultaneously, we measured the oscillation amplitudes of the probe at two specific frequencies. By the equivalent parallel-plate capacitor model and the vibration theory, we established quantitative relationship between electrostatic force and AFM raw data, and derived a complete and practical formula for calculating electrostatic force. Then, the fundamental characteristics of electrostatic force with time were revealed, and the changes of all components of electrostatic force with tip–sample distance and applied AC peak voltage were discussed in detail. The regulation effects of the distance and the voltage on the total electrostatic force were also compared. Furthermore, we pointed out the main advantages and disadvantages of this method and stated the applicable conditions of the conclusions according to the experimental results and theoretical analysis.