Effective mobility in silicon surface channels as measured with the MOS transistor

A detailed study, both theoretical and experimental, was made of the effective mobility in silicon surface channels. Theoretical pursuits included a) ,specialization of the existing effective mobility theory to silicon and to the MOS transistor, and b) extension of the existing effective mobility theory by the removal of various simplifying assumptions. Mobility measurements were confined primarily to inversion p-channel MOS transistors, although some built-in-channel and inversion n-channel results were obtained. A careful examination of effective mobility theory revealed that the Schrieffer constant field approximation introduced a significant error into the mobility predicted for the operational region of an inversion-channel, MOST. Extensive numerical calculations using the exact-field diffuse scattering theory exhibited a strong bulk doping dependence which was open to direct experimental verification. Theoretical extensions of the existing theory were accomplished through the direct integration of the Boltzmann equation. An effective mobility expression, valid for a non-constant 7: and for an arbitrary surface scattering condition was developed employing this technique. Theoretical consideration was also given to the problems of part-spectral scattering and to that of a non-constant electric field parallel to the surface of the semiconductor. Finally, a general solution of the Boltzmann equation was obtained for the many valley band structure which is appropriate for electrons in silicon. It was shown that the mobility is isotropic in the plane parallel to the surface if the field perpendicular to the surface is oriented in a.OOO) direction. Mobility formulas and calculations were presented for this particular orientation. Experimentally, great care was taken to obtain accurate transistor. parameters and thus eliminate the error due to parametric uncertainty. This was accomplished, in part, through the fabrication of an MOS capacitor adjacent to each transistor. The experimental mobility deduced under the constant Qs s assumption, when compared with the exact-field diffuse scattering theory, was still found to be high near the band edge and low near the turn-on of inversion-channel devices. Further, the doping dependence expected near turn-on was not observed. The discrepancies between theory and experiment near turn-on were concluded to be a direct result of a variation in the surface state concentration. The disagreement near the band edge was attributed to the failure of the existing diffuse scattering theory in this region. On the basis of the data presently available, however, it was felt that no definite conclusion could be made concerning the nature of the surface scattering.U of I OnlyThesi