Taylor expansions of band-bending in MOS capacitance: application to scanning capacitance microscopy

The differential capacitance C( V(g)) = dQ(M)/dV(g) in a metal-oxide-semiconductor structure introduces the silicon capacitance C(s)( Psi(S)) = -dQ(S)/d Psi(S) depending on the surface band-bending Psi(S) at the oxide-semiconductor interface. In order to calculate the dependence of C(s) on the gate voltage V(g), we propose in this paper a simple numerical method, based on first-order Taylor expansions, to inverse the explicit equation V(g) = f ( Psi(S)). This method is then applied to calculate the analytic differential capacitance of the scanning capacitance microscope ( SCM) in all conditions relative to physical parameters of SCM such as oxide thickness, doping profiles and probe erosion. It results in a competitive tool for SCM users to evaluate the theoretical values of capacitance and differential capacitance in all configurations.