Analytical approach of hot electron transport in small size MOSFET's

A one-dimensional analytical description of the current transport in MOS transistors with a channel length of the order of 1 μm is presented. The theory is based on the empirical Scharfetter and Gummel formula expressing the velocity-field relation of the charge carriers in the Si bulk. A new formula is derived taking into account the surface condition. The analysis of the hot electron behavior in Si-inversion layers suggests the formulation of a new criterion for the failure of the usual "gradual channel approximation", replacing the classical "pinch-off" concept by a field relation factor f=Ey/Ex. I-U characteristics for different transistor channel lengths are calculated and compared with experimental data and with two-dimensional analyses. The agreement between both these results and our formulation is quite good and proves the accuracy of the one-dimensional approach.