Analytical models of threshold voltage and breakdown voltage of short-channel MOSFETs derived from two-dimensional analysis

An approximate analytical solution for the surface potential is used to derive the threshold voltage. 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 MOSFETs is discussed. The simple models of threshold and breakdown voltage of short-channel MOSFETs are helpful both for circuit-oriented analysis and process diagnosis where statistical use of the model is often needed.