Theory of Scattering of Electrons in a Nondegenerate-Semiconductor-Surface Inversion Layer by Surface-Oxide Charges

Abstract

We present a systematic study of the effects of (i) the screening by mobile carriers, (ii) the correlation of the oxide charges, (iii) the distribution of the surface-oxide charges in the oxide, and (iv) the distribution of the electrons in the surface channel on the electron mobility in a nondegenerate-semiconductor-surface inversion layer covered with an insulator or oxide. It is found that the Debye-Huckel screening parameter for a two-dimensional classical electron gas is not valid for most ranges of temperature and electron concentration of practical interest. In these temperature and electron concentration ranges, the formula overestimates the screening effect. The effect of position correlation of the surface-oxide charges on the surface mobility is discussed in detail in the hard-sphere model. Correlation effect is important, especially at low temperatures where the mean electron wavelength is greater than the mean separation among the surface-oxide charges. Both the distribution of the surface-oxide charges in the oxide layer and the distribution of the electrons in the surface channel have similar effects in reducing scattering. Evaluation of experimental surface-conductivity mobility of electrons in a nondegenerate Si-Si${\mathrm{O}}_2$ surface channel due to scattering by surface-oxide charges is made.