Analysis of the narrow gate effect in submicrometer MOSFET´s

The narrow gate effect produces an increasing threshold voltage with decreasing gate width. Our previous approximate formulae, based on shifting the gate-edge position, predicts the variation of the threshold voltage with gate width accurately in the super-micrometer width range, but error begins to increase when the gate width is less than a critical value which is about 1 µm for 200-A gate oxide 7000-A field oxide and cm^-3substrate doping. The physical reason of this error is delineated and combined with two-dimensional numerical analyses to give a new formulae based on shifting the gate-center position as the gate width narrows. The parameters of this new formula may be obtained either from two-dimensional computation or experimental measurements. The error is less than 2 percent at a dc gate bias of 5 V.