Date of Award


Publication Type

Master Thesis

Degree Name



Electrical and Computer Engineering

First Advisor

Sazzadur Chowdhury


Applied sciences




This thesis develops a readily computable closed-form analytical model to determine the pull-in voltage of an Atomic Force Microscope (AFM) probe under electrostatic actuation. The analytical model has been derived based on the Euler-Bernoulli beam theory, Taylor series expansion of the electrostatic energy stored in the AFM probe, and deflection function of the first natural mode of a cantilever beam. The model takes account of the electrostatic energy associated with the fringing field capacitances between the AFM probe cantilever and the substrate to develop a more accurate model of the stored electrostatic energy after the system is biased with a DC voltage. The developed energy model is then used to develop a highly accurate closed-form model for the pull-in voltage of the AFM probe. The developed closed-form model has been verified by comparing the model predicted values with published experimental results with a maximum deviation of 3.36%. The model has also been compared with a published curve model and 3-D electromechanical finite element analysis (FEA) results. The results are found to be in excellent agreement.