Microscopic inhomogeneities of the surface-oxide charge density cause spatial variations of the subband energy levels of electrons in the surface-inversion channel of a metal-oxide-semiconductor (MOS) system. A simple model is presented which relates the root-mean-square fluctuations of the subband levels to the surface-oxide charge distribution. The effects of the induced changes of the electron density in the surface channel are included in the linear-screening theory, using the one-subband approximation. It is found that the expression for the screening parameter is not valid for the practical surface-electron densities attainable for a Si-Si${\mathrm{O}}_2$ system. An alternative classical approach is proposed to take the screening effects into account. Numerical examples are given for a patchwork distribution of surface-oxide charges at the oxide-semiconductor interface. The surface-potential fluctuation at weak inversion and/or for large surface-oxide charge-density fluctuation, where the linear approximation fails, is also estimated. The effects of subband-level fluctuation in relation to experimental studies of electronic properties in semiconductor surface-inversion channels are discussed.

• Received 23 July 1973

DOI:https://doi.org/10.1103/PhysRevB.9.527