Analytic description of scanning capacitance microscopy

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(Vg)∕dVg]α(dΨs∕dVg), this presentation yields to the importance of the surface band bending Ψs at the oxide-semiconductor interface. The dC(Vg)∕dVg 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(Vg)∕dVg signal after erosion of the probe by successive scans.