Scanning capacitance microscopy (SCM) is a doping profile extraction using a nanometric probe as a gate of a metal-oxide-semiconductor (MOS) structure and measuring the differential capacitance. Thanks to the complete MOS equations, the authors propose in this article a description of the differential capacitance calculation. This analytic presentation is based on the solution of the Poisson-Boltzmann equation in the unidimensional mode in silicon and a decomposition of the probe in elementary rings giving capacitance from the surface probe and silicon. As [dC(V-g)/dV(g)]alpha(d Psi(s)/dV(g)), this presentation yields to the importance of the surface band bending Psi(s) at the oxide-semiconductor interface. The dC(V-g)/dV(g) calculation shows that the contact of the probe with the sample has its main contribution over a few nanometers. Results are. discussed to obtain a calibration of a SCM probe available in a large range of doping and voltage and to assess the dC(V-g)/dV(g) signal after erosion of the probe by successive scans. (c) 2007 American Vacuum Society.