On the Electron Transient Response in a 50 nm MOSFET by Ensemble Monte Carlo Simulation in Presence of the Smoothed Potential Algorithm

The inclusion of a smoothed potential algorithm within the Ensemble Monte Carlo method (EMC) to account for quantization effects in the inversion layer of a silicon n-MOSFET has been discussed by several authors. Most of the data reported deal with steady state terminal current, transconductance, and capacitance. Within this approach, the electric field acting on each particle is computed from the smoothed potential, which introduces a potential barrier underneath the gate region that pushes the carriers away from the interface, thus accounting for space quantization effects. However, in the EMC method, the electric field at the interface is also used to compute the displacement charge/current during the transient regime. In the implementation of the smoothed potential algorithm, care must be taken when computing this component of the total gate charge. We distinguish between two differently computed electric fields, one from the smoothed potential used for the charge transport and the other one computed from the real potential, as obtained from the solution of Poisson's equation, and used for the displacement charge. We propose this procedure in order to properly include space quantization effects, and at the same time avoid the inaccuracy introduced by the smoothed potential in the displacement charge.