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
W_{\min}
which is about 1 µm for 200-A gate oxide 7000-A field oxide and
2 \times 10^{16}
cm
^-3
substrate 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.