On the analysis of random doping induced fluctuations in ultra small semiconductor devices by linearization

The basic assumptions used in the analysis of random doping induced fluctuations through the linearization of transport equations are carefully considered. It is proved that, in the framework of the density-gradient model, the terminal currents, transconductance, and threshold voltages of MOSFET and SOI devices are more or less linear with respect to the magnitude of variation of the doping fluctuations. This fact supports the hypothesis of the linearization techniques and explains the good agreement existent in the literature between the results of statistical analysis of semiconductor devices by using the linearization technique and the Monte-Carlo simulations