Impact of the transmission line properties of a metal-ultrathin silicon dioxide-semiconductor field-effect transistor on the extracted inversion-layer thickness

The effective thickness of the inversion layer, expressed in terms of the inversion charge centroid, is determined by capacitance measurements in the weak, moderate and strong inversion regimes using a new model for the gate-to-channel capacitance which takes into account quantum and transmission line effects in all the regimes. It is shown that the extracted inversion-layer thickness, using the capacitance-voltage method in a typical frequency range of 10–100 kHz, is unambiguous only for short channel metal-silicon dioxide-semiconductor field effect transistors with channel length Lm less than 1 μm. For long channel devices having Lm>(5–10) μm the extraction is very difficult due to the dominant impact of the transmission line effect on the measured capacitance value. The effective inversion-layer thickness is found to follow a 1/Ninvm law where Ninv is the inversion-layer concentration (m≅1/3 in the weak inversion regime, m=1/2–1 in moderate inversion regime and m=1/3 in the strong inversion regime). In the strong inversion regime the effective inversion-layer thickness is exactly equal to the real inversion-layer centroid which can be rather accurately described, as is shown, using the electric quantum limit approximation. In the moderate and weak inversion regimes the dependence can be explained in terms of the real average charge centroid and an effective conducting area under the gate which is smaller than the real area due to fluctuations of the surface potential. The surface potential fluctuation can be attributed to dopant distribution fluctuations.