A compact model of gate current due to Fowler–Nordheim tunneling is presented, which agrees closely with the self-consistent numerical analyses of the surface inversion region of metal–oxide–semiconductor field-effect transistors (MOSFETs). The model can quantify the measured data with the accuracy practically identical to the time consuming numerical simulation. It is also shown conclusively that image force lowering of the oxide barrier height is negligible for the oxide as thin as 1 nm. The quantum barrier lowering resulting from subband splitting is rigorously incorporated, including the effect of two-dimensional electrons inverted at the higher lying subbands. Finally, it is pointed out that the compact model can be readily generalized to include the direct tunneling in deep submicron MOSFETs.

We report a new quantum effect in metal-oxide-semiconductor field-effect transistor (MOSFET), namely that the twodimensional (2-D) inversion charge falls substantially short of the classically predicted linear increase with gate voltage (V G ) in strong inversion. This effect is to be effectively quantified via the threshold voltage (V TH ) increasing with V G in the classical current-voltage (I-V) model and is called herein the threshold voltage creep (VTH-creep). In 0.18 m MOSFET, for example, VTH-creep amounts to 58% of the V TH at the device turn-on point, when V G is swept from 0.5 to 2 V. Additionally, the VTHcreep significantly affects the extraction of effective mobility ( eff ) from the I-V data. VTH-creep is shown a key to the accurate I-V modeling and constitutes one of the most clearly observed quantum phenomena in MOSFET.

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