Analytical models of threshold voltage and breakdown voltage of short-channel MOSFET´s derived from two-dimensional analysis

Analytical models of threshold voltage and breakdown voltage of short-channel MOSFET´s are derived from the combination of analytical consideration and two-dimensional numerical analysis. An approximate analytical solution for the surface potential is used to derive the threshold voltage, in contrast with the charge conservation approach which has been usually taken. It is shown that the surface potential depends exponentially on the distance from the drain, and this causes the threshold voltage to decrease exponentially with decreasing channel length. The analytical dependence of threshold voltage on device dimensions, doping, and operating conditions is verified by accurate two-dimensional calculations, and the accuracy of the model is attained by slight modification. The breakdown voltage of a short-channel n-MOSFET is lowered by a positive feedback effect of excess substrate current. From two-dimensional analysis of this mechanism, a simple expression of the breakdown voltage is derived. Using this model, the scaling down of MOSFET´s is discussed. The simple models of threshold and breakdown voltage of short-channel MOSFET´s are helpful both for circuit-oriented analysis and process diagnosis where statistical use of the model is often needed.