Study of the variation of the threshold voltage with the doping concentration and channel length

Threshold voltage is an important parameter in case of device modelling. Variation of threshold voltage affects significantly the modelling of a device specially in case of short channel MOSFET. Variation of threshold voltage also affects the analysis of circuits. Threshold voltage depends on different parameters like doping concentration, surface potential, channel length, oxide thickness, temperature etc. Threshold voltage also depends on random dopant fluctuation. In wide planar transistors the threshold voltage is essentially independent of the drain-source voltage and is therefore a well defined characteristic, however it is less clear in modern nanometer-sized MOSFETs due to drain induced barrier lowering. Survey of different literatures on device modelling shows the necessity of the study of the variation of the threshold voltage with the doping concentration, channel length and oxide thickness. Here the variation of the threshold voltage has been studied through empirical formula and graphically.