Revisiting the theory behind AFM indentation procedures. Exploring the physical significance of fundamental equations

Fundamental contact mechanics models concerning the interaction of an axisymmetric indenter and an elastic half-space are usually employed in atomic force microscopy (AFM) indentation methods. In this paper, a simplified ‘equivalent’ physical system is used to correlate basic magnitudes such as the applied force on an elastic half space, the Young’s modulus, the contact radius and the indentation depth. More specifically, the equations correlating the above magnitudes are derived using fundamental physics instead of the typical rigorous mathematical process with a small error. In addition, the relation between a force-indentation curve and the indenter’s shape is also presented in detail in order to help students and non-specialists in contact mechanics to obtain a strong background to the AFM indentation theory.