An analytical threshold voltage roll-off equation for MOSFET by using effective-doping model

This paper presents a new analytical threshold voltage roll-off equation for MOSFET by effective-doping model. The short-channel MOSFET is viewed as distributed MOS capacitors with different effective-doping concentration in series. The 2D scale-length approach is adopted to find the potential distribution and the corresponding effective-doping concentration. The source and drain controlled charges are averaged over the channel depletion region to provide more realistic account of the effective-doping concentration. In addition, the lowering of the required band bending and the widening of the channel depletion are considered. As a result, the sub-exponential dependence of the threshold voltage roll-off on channel length is observed. The two governing factors, channel length and drain voltage, can be decoupled in the limit of a mild short-channel effect.