An improved high-frequency MOS capacitance formula

Abstract

Minority carriers within the inversion layer of an inverted MOS capacitor can move in response to a high-frequency ac signal even though the total minority-carrier charge is fixed at the value set by the dc bias. In this paper a simple explicit formula for the high-frequency capacitance which includes this ac inversion layer polarization effect is derived. The derivation is based upon the assumption that the distribution of minority carriers within the inversion layer is governed by a constant quasi-Fermi level, independent of position within the inversion layer. Hence, the resulting capacitance formula is restricted to the case where minority-carrier trapping by defects in the inversion layer or at the interface do not significantly hinder the ac response of the minority carriers. Comparison of the new formula with the calculations of Sah, Pierret, and Tole, which have as their main approximation the neglect of the ac minority-carrier movement, shows that the neglect of this effect leads to a 7% error in strong inversion at 1013/cm3. Comparison with the commonly used formulas of Lindner and of Grove, which contain approximations in addition to the neglect of inversion layer polarization, shows that these formulas are in error by 9% and 4%, respectively, in strong inversion at a doping level of 1013/cm3. Although more accurate than these other calculations in strong inversion, the Grove model is less accurate in depletion and weak inversion. Figures illustrating the error involved in all three earlier approaches as a function of bias with doping level as a parameter are presented.